Fuel Performance Modeling of High Burnup Mixed Oxide Fuel for Hard Spectrum Lwrs

Fuel Performance Modeling of High Burnup Mixed Oxide Fuel for Hard Spectrum LWRs

by Yanin Sukjai

M.S., Nuclear Science and Engineering (2014) Massachusetts Institute of Technology

B.Eng., Mechanical Engineering (2001) King Mongkut’s University of Technology North Bangkok

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

February 2018

Signature of Author: ______Yanin Sukjai Department of Nuclear Science and Engineering September 28, 2017

Certified by: ______Koroush Shirvan, Ph.D. Assistant Professor of Nuclear Science and Engineering Thesis Supervisor

Certified by: ______Ronald G. Ballinger, Ph.D. Professor of Nuclear Science and Engineering Professor of Materials Science and Engineering Thesis Reader

Accepted by: ______Ju Li, Ph.D. Battelle Energy Alliance Professor of Nuclear Science and Engineering Professor of Materials Science and Engineering Chair, Department Committee on Graduate Students

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Fuel Performance Modeling of High Burnup Mixed Oxide Fuel for Hard Spectrum LWRs

Yanin Sukjai

Submitted to the Department of Nuclear Science and Engineering on September 28, 2017 in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Nuclear Science and Engineering

ABSTRACT

According to the future of the nuclear fuel cycle study at MIT, a reactor with a conversion ratio around one can achieve desired objectives in the long-term sustainability of uranium and reduction of transuranic wastes. This finding relaxes the need for sodium fast reactors (SFR) in a closed-loop nuclear fuel cycle and enables high-conversion light water reactors (HC-LWR) to be used as an alternative. HC-LWRs have two major advantages over SFRs. First, apart from the reactor core, the remaining reactor system can be based on existing LWR technology. Second, extensive operating experience and a proven record of high reliability of LWRs would ease licensing and commercialization processes. Therefore, operating HC-LWRs instead of SFRs may be more economically and technically viable with lower capital and development cost for the near term. This type of reactor is being developed by Hitachi Ltd. under the name of resource- renewable boiling water reactor (RBWR).

This study focuses on RBWR-TB2, transuranic burning version of RBWR. To demonstrate that the RBWR-TB2 can operate safely within design constraints and regulatory limits, the thermo- mechanical behavior of this reactor has been analyzed through fuel performance modeling.

Due to its unique design characteristics, several physical phenomena at high temperature and high burnup typically ignored in most LWR fuel performance codes can potentially become active under RBWR’s operating conditions. These phenomena involve migration of fuel constituents and fission products, the evolution of O/M ratio with burnup, high burnup structure (HBS) formation, accelerated corrosion, hot pressing, gaseous fuel swelling, hydride precipitation and hydrogen migration in the cladding. Semi-empirical models describing porosity and cesium migration behaviors have been replaced with mechanistic models. All of these phenomena have been successfully implemented in a modified version of FRAPCON-3.5 known as FRAPCON-3.5 EP where EP stands for enhanced performance.

The fuel performance comparison between RBWR-TB2 and ABWR fuel rods suggest that because of high axial peaking factors and relatively flat power history, fuel temperature is

3 significantly higher in fissile zones of the RBWR-TB2 leading to various undesirable effects such as excessive fission gas release and cladding deformation. Local fuel burnup in fissile zones of RBWR-TB2 is multiple times higher than that of ABWR leading to excessive fuel swelling, accelerated cladding oxidation, and PCMI at fissile-blanket interfaces. Even if the RBWR-TB2 has to operate under such demanding conditions with a small margin to fuel melting, a steady- state fuel performance analysis still shows that this reactor can operate safely with an acceptable thermo-mechanical performance.

In the future optimization of RBWR-TB2 performance, several fuel design strategies are recommended based on a series of sensitivity studies. The sensitivity study on key design parameters indicates that using annular fuel geometry and more hypostoichiometric fuel (lower O/M ratio) could reduce fuel temperature at high burnup. For better resistance to cladding corrosion and PCMI, it is recommended to increase cladding thickness and decrease fuel density.

Thesis Supervisor: Koroush Shirvan Title: Assistant Professor, Department of Nuclear Science and Engineering

Thesis Reader: Ronald G. Ballinger Title: Professor, Department of Nuclear Science and Engineering and Department of Materials Science and Engineering

Acknowledgement

I would like to express my most profound gratitude to my former and late thesis advisor, Professor Mujid S. Kazimi, for his continuous guidance, support, and encouragement during the course of my academic journey. Without his patience and understanding during my time at MIT, this thesis would not be possible. Not only did he serve as my former thesis advisor, but he was also my role model professionally. His ability to analyze complicated technical issues and clearly convey the essential information for the audiences is one of the most important characteristics of a successful researcher. I feel honored to have the opportunity to work with him. May your soul rest in peace; you will always be remembered, Professor Kazimi.

I owe a great debt to my current thesis supervisor, Professor Koroush Shirvan, for his continuous support and help throughout my thesis. This thesis would have been greatly delayed had he not immediately taken me into his supervision and research group. I was deeply impressed and influenced by his diligence, positive attitude, attention to detail, and unending desire for learning. He assisted me in every step of my research: literature review, model simplification, code diagnostics, data analysis, and troubleshooting. More than an advisor, he is a real friend who helped and encouraged me at difficult moments.

I am equally grateful to Professor Ronald Ballinger, my thesis reader, for taking me in as his student immediately after the passing of Professor Kazimi. The discussions we had during group meetings have always been of great value, along with his comments, and suggestions on the thesis. I also would like to thank Professor Ju Li for having accepted my request and served as a thesis committee member. As a world-renowned expert in materials science and engineering, he has broadened my vision and provided insights from a different point of view in this work.

My thanks are also extended to Dr. Aydin Karahan who had previously developed FRAPCON- EP to the point at which this work had started.

I wish to thank NSE colleagues and Thai friends at MIT for their hospitality, friendship, and advice throughout my study. My special thanks go to my fellow classmate and Thai friend, Mr. Ittinop Dumnernchanvanit, who has always support me socially and academically since the first

5 day I landed at the Logan airport.

I would like to thank my parents, Mr. Ekkachai Sukjai and Mrs. Nichapa Sukjai, my brother, Mr. Thanakorn Sukjai, my wife, Ms. Lalita Urasuk, my son, Ratchanin Sukjai, and my daughters, Pimonnart Sukjai and Natacha Sukjai, for their unconditional love and support. Thanks for taking care of me and being a source of knowledge, morale, and inspiration throughout my entire life.

Finally, I would like to express my deep appreciation to the Royal Thai Government, the King Mongkut's University of Technology Thonburi (KMUTT), Hitachi Limited of Japan, and the Center for Advanced Nuclear Energy Systems (CANES) at MIT for their financial support for my graduate study.

Table of Contents Abstract ...... 3 Acknowledgement ...... 5 Table of Contents ...... 7 List of Figures ...... 10 List of Tables ...... 21 Nomenclature ...... 22 Chapter 1 ...... 23 1.1 Thesis objective ...... 23 1.2 Motivation ...... 23 1.2.1 Transuranic waste incineration in high-conversion LWRs ...... 23 1.3 Scope of work...... 30 1.4 Nuclear fuel performance modeling ...... 32 1.4.1 FRAPCON-3 fuel performance code ...... 34 1.4.2 FRAPCON-EP ...... 37 1.5 Thesis organization ...... 39 Chapter 2 ...... 41 2.1 History of HC-LWR development ...... 41 2.2 General description and design characteristics of RBWR-TB2 ...... 54 2.3 Material challenges associated with RBWR-TB2 ...... 60 Chapter 3 ...... 64 3.1 Parameters affecting thermal conductivity ...... 65 3.2 Thermal conductivity correlations for mixed oxide fuels ...... 68 3.3 Comparison of thermal conductivity correlations ...... 86 3.4 Benchmarking with experimental data ...... 96

3.5 Effect of PuO2 content on MOX thermal conductivity ...... 106 Chapter 4 ...... 117 4.1 Porosity migration and central void formation ...... 118 4.2 Plutonium migration ...... 125 4.3 Oxygen-to-metal ratio variation with burnup ...... 133 4.4 Oxygen-to-metal ratio variation with temperature ...... 144

4.5 Cesium migration and formation of Joint Oxyde-Gaine (JOG) ...... 151 4.6 High-burnup structure and RIM porosity ...... 171 4.7 Hot-pressing ...... 175 4.8 Fuel swelling from gaseous fission products ...... 177 4.8.1 Intragranular gas swelling ...... 179 4.8.2 Intergranular gas swelling ...... 181 4.9 Accelerated corrosion at high burnup ...... 187 4.10 Hydrogen migration and hydride precipitation in cladding ...... 195 Chapter 5 ...... 203 5.1 Modification of FRAPCON-3.5 EP for fast reactor conditions ...... 203 5.2 Validation of plutonium and porosity migration models ...... 205 5.3 Validation of cesium migration model in-pile reactor experiments ...... 216 5.4 Validation of cesium migration model with out-of-pile experiments ...... 236 5.5 Sensitivity study of cesium migration model on cesium fuel swelling rate ...... 248 5.6 Validation of hydrogen migration model ...... 262 Chapter 6 ...... 269 6.1 Reactor condition and fuel rod geometry ...... 269 6.2 Radial power profile and fast neutron flux ...... 270 6.3 Power history and axial peak factor ...... 276 6.4 Results of fuel performance simulation ...... 279 6.4.1 Rod-average and local fuel burnup ...... 279 6.4.2 Average fuel temperature ...... 281 6.4.3 Fuel centerline temperature ...... 282 6.4.4 Plenum pressure and fission gas release ...... 287 6.4.5 Cladding corrosion ...... 290 6.4.6 Structural radial gap and interfacial pressure ...... 292 6.4.7 Cladding hoop stress and strain ...... 294 6.4.8 Porosity migration and central void formation ...... 296 6.4.9 Plutonium redistribution ...... 298 6.4.10 Oxygen-to-metal ratio radial redistribution ...... 300 6.4.11 Cesium migration and JOG formation ...... 302

6.4.12 Hydrogen redistribution and precipitation ...... 306 6.5 Parametric study on important fuel design parameters ...... 309 6.5.1 Initial fuel-clad gap thickness ...... 310 6.5.2 Fuel density ...... 317 6.5.3 Oxygen-to-metal ratio ...... 326 6.5.4 Helium pressure ...... 333 6.5.5 Central void diameter ...... 340 6.5.6 Cladding thickness ...... 351 6.6 Code-to-code comparison between FRAPCON-3.5 and FRAPCON-3.5 EP ...... 361 6.6.1 RBWR-TB2 design ...... 362 6.6.2 ABWR design ...... 376 Chapter 7 ...... 390 7.1 Summary ...... 390 7.1.1 Evaluation of thermal conductivity correlation for mixed oxide fuel ...... 390 7.1.2 Development of physical phenomena at high temperature and high burnup ...... 391 7.1.3 Validation of FRAPCON-3.5 EP with experimental data ...... 394 7.1.4 Fuel performance modeling of RBWR-TB2 ...... 396 7.2 Conclusions ...... 399 7.3 Recommendations for Future Work ...... 401 7.3.1 Full-core fuel performance analysis for RBWR-TB2 ...... 401 7.3.2 Fuel performance modeling of RBWR-TB2 in transient conditions ...... 403 7.3.3 Out-of-pile experiments for fuel constituent migration under temperature gradient… ...... 403 7.3.4 Experimental evaluation of MOX thermal conductivity at high burnup ...... 404 7.3.5 In-pile experiment for accelerated corrosion at high neutron fluence ...... 405 7.3.6 Theoretical and experimental study of O/M ratio evolution with burnup ...... 406 References ...... 408 Appendix A: Material properties of HT-9 and SS-304 Stainless Steel ...... 432 Appendix B: Sample input files ...... 458

List of Figures Figure 1: Once-through fuel cycle [3]...... 25 Figure 2: Closed-loop fuel cycle [3]...... 26 Figure 3: Natural uranium requirement over the course of simulation [5]...... 28 Figure 4: Total amount of TRU in the system [5]...... 28 Figure 5: High level waste in geological repository [5]...... 29 Figure 6: Levelized cot of electricity [5]...... 30 Figure 7: Complexity of nuclear fuel performance modeling [6]...... 34 Figure 8: Simplified FRAPCON-3 flowchart [7]...... 36 Figure 9: Classification of high-conversion LWR [11]...... 42 Figure 10: Moderator-to-fuel ratio and breeding ratio comparison [36]...... 50 Figure 11: Rate of formation and consumption of TRUs [37]...... 53 Figure 12: (a) Reactor pressure vessel of RBWR (b) Horizontal cross-section of RBWR reactor core [42]...... 55 Figure 13: Axial and hexagonal configuration of RBWR-TB2 fuel bundle [42]...... 56 Figure 14: Horizontal configuration of RBWR-TB2 [42]...... 56 Figure 15: Axial LHGR of the RBWR-TB2 as a function of core height [39]...... 57 Figure 16: Local fuel burnup of the RBWR-TB2 as a function of axial node and time step...... 58 Figure 17: Axial void fraction of RBWR-TB2 as a function of relative core height [42]...... 59 Figure 18: Comparison of normalized neutron spectra for the RBWR-AC, RBWR-Th, SFR and ABWR [43]...... 60 Figure 19: Axial peaking factor vs. core height of ABWR and RBWR-TB2...... 61 Figure 20: Effect of fuel swelling and thermal stress [44]...... 62 Figure 21: Consequence of pellet-cladding interaction (PCI) [44]...... 62 Figure 22: Parameters affecting thermal conductivity [56]...... 66

Figure 23: Electron density of state of UO2 (a), ThO2 (b), and PuO2 (c). Cross-hatched bands indicate occupied level [59]...... 68 Figure 24: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 2.0...... 90 Figure 25: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 2.0...... 90 Figure 26: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 1.95...... 91 Figure 27: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 1.95...... 92 Figure 28: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 2.0...... 93 Figure 29: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 2.0...... 94 Figure 30: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 1.95...... 95 Figure 31: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 1.95...... 96

Figure 32: Measured vs. calculated thermal conductivity of MOX and UO2 using Duriez- modified NFI and Duriez-Lucuta correlations...... 99

Figure 33: Measured vs. calculated thermal conductivity of MOX and UO2 using Inoue-modified NFI and Inoue-Lucuta correlations...... 100

Figure 34: Measured vs. calculated thermal conductivity of MOX and UO2 using Baron, Halden, and Amaya correlations...... 101

Figure 35: Measured vs. calculated thermal conductivity of MOX and UO2 using Duriez- modified NFI and Duriez-Lucuta correlations...... 103

Figure 36: Measured vs. calculated thermal conductivity of MOX and UO2 using Inoue-modified NFI and Inoue-Lucuta correlations...... 104

Figure 37: Measured vs. calculated thermal conductivity of MOX and UO2 using Baron, Halden, and Amaya correlations...... 105

Figure 38: Thermal conductivity of fresh MOX as a function of PuO2 content [78]...... 107 Figure 39: Thermal conductivity correlation recommended by Nichenko and comparison with experimental result (100% TD) [65]...... 110

Figure 40: Effect of PuO2 on thermal conductivity by Matsumoto et al. [69]...... 110 Figure 41: The variation of thermal conductivity of MOX as a function of uranium composition [70]...... 111

Figure 42: Thermal conductivity as a function of temperature at varying PuO2 weight fraction [78]...... 113 Figure 43: Comparison of Duriez-modified NFI correlation with measured thermal conductivity

of MOX at 5 and 30 wt% PuO2 from Gibby [78]...... 113 Figure 44: Calculated thermal conductivity of MOX as a function of PuO2 weight fraction from empirical correlation proposed by Gibby [78]...... 114

Figure 45: Multiplying factor to the Duriez-modified NFI correlation with reference PuO2 weight fraction at 30 wt%...... 115 Figure 46: Cross section of mixed oxide fuel rod irradiated at 56 kW/m to 25 MWd/kgHM [126]...... 119 Figure 47: Schematic of restructured regions [126]...... 120 Figure 48: Comparison of fuel temperature calculated from three-region model and measured porosity [127]...... 122 Figure 49: Electron probe microanalysis (EPMA) false color X-ray maps showing radial distribution of U, Pu, and Am. The concentration increases in the following order: green, yellow and red [140]...... 127 Figure 50: Fuel restructuring and radial distribution of Pu and Am after 10 minutes and 24 hours irradiation at high LHGR conditions [140]...... 128

Figure 51: The oxygen potential at four different radial positions at high burnup UO2 fuel [141]...... 135 Figure 52: Burnup dependence of the oxygen potential at 750 oC for different irradiated oxide fuel [144]...... 136 Figure 53: Oxygen potential measurement of irradiated Phoenix fuel of initial composition of

(U0.8Pu0.2)U1.98 [146]...... 136 Figure 54: A unit volume of fresh and irradiated mixed oxide fuel as a constant mass system [126]...... 137

Figure 55: partial molar enthalpy and entropy of oxygen in mixed oxide fuel [126]...... 142 Figure 56: Axial 137Cs activity profiles in fuel rod C-10 and C-19 [159]...... 152 Figure 57: The axial distribution of Cs and I under simulated temperature gradients [173]...... 153 Figure 58: 137Cs and 134Cs radial distribution profile at 22.9 and 48.26 MWd/kgHM [170]. .... 154 Figure 59: 137Cs and 134Cs radial distribution profile at higher fuel temperature [170]...... 155 Figure 60: Localized cladding strain as a result of cesium migration [161]...... 155 Figure 61: X-ray mapping of the JOG compounds at peak power node at high burnup. The gap region is filled with chemical compounds of mainly Cs, Mo and O [163]...... 156 Figure 62: Gamma scan of 137Cs of solid and annular pellets [164]...... 157 Figure 63: EPMA mapping images of JOG showing complex compounds of Cs and Mo [172]...... 159 Figure 64: Axial distribution of 137Cs intensity along the fission column [164]...... 160 Figures 65: Ceramographs of transverse section from bottom to top of fuel column [164]...... 160 Figure 66: EPMA mapping of the gap region of position B [164]...... 162 Figure 67: EPMA mapping of the gap region of position C [164]...... 162 Figure 68: As-fabricated grain (left) vs. high burnup structure (right) [49]...... 173 Figure 69: Porosity evolution as a function of local burnup in HBS region...... 175

Figure 70: (a) Ceramograph of gas bubbles in irradiated UO2 [196] and (b) schematic representation of intra-granular and inter-granular gas bubbles [197]...... 179 Figure 71: A schematic representation of a TKD grain of equal side [199]...... 182 Figure 72: Schematic illustration of connected tunnel of grain edge bubbles [200]...... 183 Figure 73: Two-stage oxidation process of zirconium alloys [201]...... 188

Figure 74: Possible phases of zirconium oxide (ZrO2) in LWR conditions [202]...... 188 Figure 75: Schematic of zirconium oxide formation showing barrier and porous layers [201]. 189 Figure 76: Schematic of 3-stage oxidation model proposed by Zhou et al. [203]...... 191 Figure 77: Oxide thickness, hydrogen content and rod growth as a function of fast fluence [205]...... 192 Figure 78: Acceleration in oxide layer thickness at high burnup in Zircaloy-2 [208]...... 193 Figure 79: Acceleration in HPUF at high burnup in Zircaloy-2 [203]...... 193 Figure 80: Hydrogen concentration as predicted by a default correlation in FRAPCON-3.5. ... 195 Figure 81: Non-uniform distribution of zirconium hydride in a typical LWR cladding [212]. .. 196 Figure 82: Radial distribution of hydride in Zircaloy cladding [213] [214]...... 196 Figure 83: Azimuthal distribution of hydride in Zircaloy cladding [213]...... 197 Figure 84: Hydride distribution at the inter-pellet gap cladding compared to mid-pellet cladding [215]...... 198 Figure 85: Power history of B11 experiment [227]...... 207 Figure 86: Axial peaking factor of B11 experiment...... 207 Figure 87: Central void diameter as a function of axial height for Am-1-1-1 rod...... 208 Figure 88: Central void diameter as a function of axial height for Am-1-2-1 rod...... 209 Figure 89: Central void diameter as a function of axial height for Am-1-2-2 rod...... 209

Figure 90: Plutonium concentration as a function of fuel radius for Am-1-1-1 rod...... 210 Figure 91: Plutonium concentration as a function of fuel radius for Am-1-2-1 rod...... 210 Figure 92: Plutonium concentration as a function of fuel radius for Am-1-2-2 rod...... 211 Figure 93: Power history of B14 experiment [227]...... 212 Figure 94: Axial peaking factor of B14 experiment [124]...... 213 Figure 95: Central void diameter as a function of axial height for PTM0001 rod...... 214 Figure 96: Central void diameter as a function of axial height for PTM0002 rod...... 214 Figure 97: Central void diameter as a function of axial height for PTM0003 rod...... 215 Figure 98: Central void diameter as a function of axial height for PTM0010 rod...... 215 Figure 99: Plutonium concentration as a function of fuel radius for PTM0001 rod...... 216 Figure 100: Plutonium concentration as a function of fuel radius for PTM0010 rod...... 216 Figure 101: Power history of ACO-1 fuel rod...... 219 Figure 102: Axial peaking factor of ACO-1 fuel rod...... 219 Figure 103: Relative 137Cs concentration as a function of axial height of ACO-1 fuel rod...... 220 Figure 104: Cladding strain at EOL as a function of axial height of ACO-1 fuel rod...... 221 Figure 105: Power history of fuel rods in ACO-3 experiment [166]...... 222 Figure 106: Peak cladding midwall temperature of fuel rods in ACO-3 experiment [166]...... 223 Figure 107: Axial peaking factor of ACO-3 experiment [166]...... 223 Figure 108: Relative 137Cs concentration as a function of axial height of 150073 fuel rod...... 225 Figure 109: Relative 137Cs concentration as a function of axial height of 150080 fuel rod...... 225 Figure 110: Relative 137Cs concentration as a function of axial height of 150088 fuel rod...... 225 Figure 111: Relative 137Cs concentration as a function of axial height of 150094 fuel rod...... 226 Figure 112: Cladding strain at EOL as a function of axial height of 150073 fuel rod...... 227 Figure 113: Cladding strain at EOL as a function of axial height of 150080 fuel rod...... 227 Figure 114: Cladding strain at EOL as a function of axial height of 150088 fuel rod...... 228 Figure 115: Cladding strain at EOL as a function of axial height of 150094 fuel rod...... 228 Figure 116: Histories of maximum LHGR and maximum cladding temperature of fuel rods in C3M experiment [165]...... 230 Figure 117: Axial profiles of fast neutron fluence and life-averaged cladding midwall temperature of C3M experiment [165]...... 231 Figure 118: Relative 137Cs concentration as a function of axial height of G305 fuel rod...... 232 Figure 119: Relative 137Cs concentration as a function of axial height of G339 fuel rod...... 232 Figure 120: Relative 137Cs concentration as a function of axial height of G357 fuel rod...... 233 Figure 121: Cladding strain at EOL as a function of axial height of G305 fuel rod...... 234 Figure 122: Cladding strain at EOL as a function of axial height of G339 fuel rod...... 235 Figure 123: Cladding strain at EOL as a function of axial height of G357 fuel rod...... 235 Figure 124: Schematic representation of experimental device for Experiment #1 [170]...... 237 Figure 125: Schematic representation of experimental device for Experiment #2 [170]...... 238 Figure 126: Schematic representation of stainless steel test capsule showing the location where the additives (Cs, I, Te, and Mo) were introduced at hot end...... 239

o Figure 127: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1000 C...... 242 o Figure 128: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1200 C...... 242 o Figure 129: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1320 C...... 243 o Figure 130: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1400 C...... 243 Figure 131: Location of Cs-137 peaks as function of time of Peehs’s Experiment #2...... 245 Figure 132: Axial distribution of Cs-137 activity before and after thermal treatment ...... 246 Figure 133: Comparison of cesium diffusion coefficients used during simulation with correlations from literature ...... 248 Figure 134: Relative 137Cs concentration as a function of axial height of 150073 fuel rod...... 251 Figure 135: Relative 137Cs concentration as a function of axial height of 150080 fuel rod...... 251 Figure 136: Relative 137Cs concentration as a function of axial height of 150088 fuel rod...... 252 Figure 137: Relative 137Cs concentration as a function of axial height of 150094 fuel rod...... 252 Figure 138: Average fuel temperature of high and low swelling models as a function of time. 254 Figure 139: Average fuel temperature at EOL of high and low swelling models as a function of axial node...... 254 Figure 140: Centerline fuel temperature of high and low swelling models as a function of time...... 255 Figure 141: Centerline fuel temperature at EOL of high and low swelling models as a function of axial node...... 255 Figure 142: Plenum pressure of high and low swelling models as a function of time...... 256 Figure 143: Fission gas release of high and low swelling models as a function of time...... 257 Figure 144: Minimum structural radial gap of high and low swelling models as a function of time...... 258 Figure 145: Structural radial gap at EOL of high and low swelling models as a function of axial node...... 258 Figure 146: Interfacial pressure of high and low swelling models as a function of time...... 259 Figure 147: Cladding hoop stress of high and low swelling models as a function of time...... 260 Figure 148: Cladding hoop stress at EOL of high and low swelling as a function of axial node...... 260 Figure 149: Cladding hoop strain of high and low swelling models as a function of time...... 261 Figure 150: Cladding hoop strain at EOL of high and low swelling models as a function of axial node...... 262 Figure 151: Axial distribution of hydrogen concentration in Sawatzky’s experiment #1...... 264 Figure 152: Axial distribution of hydrogen concentration in Sawatzky’s experiment #2...... 265 Figure 153: Power history of fuel rod 1079 of Gravelines nuclear power station [242]...... 267 Figure 154: Axial peaking factor used in Lacroix [244] and this study...... 267 Figure 155: Total hydrogen concentration as a function of clad radius...... 268 Figure 156: Normalized radial peaking factors for RBWR-TB2 and ABWR...... 272 Figure 157: Cross-section view of RBWR-TB2 assemblies in SERPENT...... 273 Figure 158: Fast neutron flux of RBWR-TB2 at 0, 40, and 80 MWd/kgHM...... 274

Figure 159: Specific power of RBWR-TB2 at 0, 40, and 80 MWd/kgHM...... 275 Figure 160: Specific fast flux of RBWR-TB2 at 0, 40, and 80 MWd/kgHM...... 276 Figure 161: Power history of RBWR-TB2 and ABWR...... 278 Figure 162: Axial peaking factor of RBWR-TB2 and ABWR...... 278 Figure 163: Rod-average fuel burnup of RBWR-TB2 and ABWR as a function of time...... 280 Figure 164: Local fuel burnup of RBWR-TB2 and ABWR at EOL...... 280 Figure 165: Average fuel temperature of RBWR-TB2 and ABWR as a function of time...... 281 Figure 166: Average fuel temperature of RBWR-TB2 and ABWR as a function of relative axial length...... 282 Figure 167: Centerline fuel temperature of RBWR-TB2 and ABWR as a function of time...... 283 Figure 168: Centerline fuel temperature of RBWR-TB2 and ABWR as a function of relative axial length...... 284 Figure 169: Axial variation of fuel centerline and fuel melting temperature at EOL of RBWR- TB2...... 285 Figure 170: Axial variation of fuel melting temperature and plutonium content at EOL of RBWR-TB2...... 286 Figure 171: Reduction of fuel melting temperature of RBWR-TB2 with plutonium content at BOL and EOL...... 287 Figure 172: Plenum pressure of RBWR-TB2 and ABWR as a function of time...... 288 Figure 173: Fission gas release of RBWR-TB2 and ABWR as a function of time...... 290 Figure 174: Oxide layer thickness of RBWR-TB2 and ABWR as a function of time...... 291 Figure 175: Average hydrogen concentration of RBWR-TB2 and ABWR as a function of time...... 292 Figure 176: Structural radial gap of RBWR-TB2 and ABWR as a function of time...... 293 Figure 177: Interfacial pressure of RBWR-TB2 and ABWR as a function of time...... 294 Figure 178: Cladding hoop stress of RBWR-TB2 and ABWR at peak axial node as a function of time...... 295 Figure 179: Cladding hoop strain of RBWR-TB2 and ABWR at peak axial node as a function of time...... 296 Figure 180: Central void diameter of RBWR-TB2 along axial nodes...... 297 Figure 181: Central void diameter of ABWR along axial nodes...... 298 Figure 182: Radial distribution of plutonium of RBWR-TB2 at peak axial node...... 299 Figure 183: Radial distribution of plutonium of ABWR at peak axial node...... 300 Figure 184: Radial distribution of O/M ratio of RBWR-TB2 at peak axial node...... 301 Figure 185: Radial distribution of O/M ratio of ABWR at peak axial node...... 302 Figure 186: Axial distribution of cesium of RBWR-TB2...... 303 Figure 187: Axial distribution of cesium of ABWR...... 304 Figure 188: Radial distribution of cesium of RBWR-TB2...... 305 Figure 189: Radial distribution of cesium of ABWR...... 305

Figure 190: Axial distribution of hydride precipitation of RBWR-TB2 at cladding outer surface...... 307 Figure 191: Axial distribution of hydride precipitation of ABWR at cladding outer surface. ... 307 Figure 192: Radial distribution of hydrogen solute of RBWR-TB2...... 308 Figure 193: Radial distribution of hydrogen solute in ABWR...... 309 Figure 194: Average fuel temperature of RBWR-TB2 at 55 and 110 μm as a function of time. 311 Figure 195: Centerline fuel temperature of RBWR-TB2 at 55 and 110 μm as a function of time...... 311 Figure 196: Average fuel temperature of RBWR-TB2 at 55 and 100 μm at EOL as a function of axial node...... 312 Figure 197: Centerline fuel temperature of RBWR-TB2 at 55 and 100 μm at EOL as a function of axial node...... 313 Figure 198: Fission gas release of RBWR-TB2 at 55 and 110 μm as a function of time...... 314 Figure 199: Plenum pressure of RBWR-TB2 at 55 and 110 μm as a function of time...... 314 Figure 200: Interfacial pressure of RBWR-TB2 at 55 and 110 μm at peak axial node as a function of time...... 315 Figure 201: Cladding hoop stress of RBWR-TB2 at 55 and 110 μm at peak axial node as a function of time...... 316 Figure 202: Cladding hoop strain of RBWR-TB2 at 55 and 110 μm at peak axial node as a function of time...... 317 Figure 203: Rod average burnup of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 318 Figure 204: Local burnup of RBWR-TB2 at fuel density of 80-95 %TD as a function of axial node...... 319 Figure 205: Average fuel temperature of RBWR-TB2 at fuel density of 80- 95 %TD as a function of time...... 320 Figure 206: Centerline fuel temperature of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 321 Figure 207: FGR of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 322 Figure 208: Plenum pressure of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 322 Figure 209: Total void volume of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 323 Figure 210: Interfacial pressure of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 324 Figure 211: Cladding hoop stress of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 325 Figure 212: Cladding hoop strain of RBWR-TB2 at fuel density of 80-95 %TD as a function of time...... 326

Figure 213: Average fuel temperature of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time...... 327 Figure 214: Centerline fuel temperature of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time...... 328 Figure 215: Fission gas release of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time...... 329 Figure 216: Plenum pressure of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time. 330 Figure 217: Interfacial pressure of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time...... 331 Figure 218: Cladding hoop stress of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time...... 332 Figure 219: Cladding hoop strain of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time...... 332 Figure 220: Average fuel temperature of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time...... 334 Figure 221: Centerline fuel temperature of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time...... 335 Figure 222: Fission gas release of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time...... 336 Figure 223: Plenum pressure of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time...... 337 Figure 224: Interfacial pressure of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time...... 338 Figure 225: Cladding hoop stress of RBWR-TB2 at helium pressure of 1.90-2.00 as a function of time...... 339 Figure 226: Cladding hoop strain of RBWR-TB2 at helium pressure of 1.90-2.00 as a function of time...... 340 Figure 227: Rod average burnup of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 341 Figure 228: Local burnup of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of axial node...... 342 Figure 229: Average fuel temperature of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 343 Figure 230: Average fuel temperature at EOL of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of axial node...... 344 Figure 231: Centerline fuel temperature of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 345 Figure 232: Fission gas release of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 346

Figure 233: Plenum pressure of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 347 Figure 234: Void volume of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 348 Figure 235: Interfacial pressure of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 349 Figure 236: Cladding hoop stress of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 350 Figure 237: Cladding hoops strain of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time...... 351 Figure 238: Average fuel temperature of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 353 Figure 239: Centerline fuel temperature of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 354 Figure 240: Fission gas release of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 355 Figure 241: Plenum pressure of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 356 Figure 242: Oxide layer thickness of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 357 Figure 243: Clad-average hydrogen concentration of RBWR-TB2 at cladding thickness of 0.6- 0.9 mm as a function of time...... 358 Figure 244: Interfacial pressure of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 359 Figure 245: Cladding hoop stress of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 360 Figure 246: Cladding hoop strain of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time...... 361 Figure 247: Average fuel temperature of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 364 Figure 248: Average fuel temperature of RBWR-TB2 at EOL as calculated by FRAPCON-3.5 and 3.5 EP as a function of axial node...... 365 Figure 249: Centerline fuel temperature of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 366 Figure 250: Centerline fuel temperature of RBWR-TB2 at EOL as calculated by FRAPCON-3.5 and 3.5 EP as a function of axial node...... 367 Figure 251: Fission gas release of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 368 Figure 252: Plenum pressure of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 369

Figure 253: Oxide layer thickness of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 370 Figure 254: Hydrogen concentration of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 371 Figure 255: Structural radial gap of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 372 Figure 256: Interfacial pressure of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 374 Figure 257: Cladding hoop stress of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 375 Figure 258: Cladding hoop strain of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 376 Figure 259: Power history of an average fuel rod in ABWR...... 377 Figure 260: Average fuel temperature of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 378 Figure 261: Centerline fuel temperature of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 380 Figure 262: Fission gas release of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 381 Figure 263: Plenum pressure of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 382 Figure 264: Total void volume of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 382 Figure 265: Fuel axial extension of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 383 Figure 266: Oxide layer thickness of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 384 Figure 267: Hydrogen concentration of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 384 Figure 268: Structural radial gap of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 385 Figure 269: Gap conductance of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 386 Figure 270: Interfacial pressure of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 387 Figure 271: Cladding hoop stress of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 388 Figure 272: Cladding hoop strain of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time...... 389

Figure 273: Sample core map of RedTail predictions for maximum plenum pressure for (a) Zirconium-based cladding and (b) SiC-based cladding [54]...... 402 Figure A.1: Poisson’s ratio as a function of temperature Zircaloy-2, SS-304 and HT-9...... 433 Figure A.2: Specific heat as a function of temperature Zircaloy-2, SS-304 and HT-9...... 435 Figure A.3: Thermal conductivity as a function of temperature Zircaloy-2, SS-304 and HT-9. 436 Figure A.4: Thermal expansion as a function of temperature Zircaloy-2, SS-304 and HT-9. ... 438 Figure A.5: Void swelling as a function of neutron fluence for SS-304...... 440 Figure A.6: Void swelling as a function of neutron fluence for HT-9...... 440 Figure A.7: Irradiation growth as a function of neutron fluence for Zircaloy-2, SS-304 and HT-9...... 441 Figure A.8: Cladding hardness as a function of temperature for Zircaloy-2, SS-304 and HT-9. 442 Figure A.9: Emissivity as a function of temperature for Zircaloy-2, SS-304 and HT-9...... 443 Figure A.10: Elastic modulus as a function of temperature for Zircaloy-2, SS-304 and HT-9. . 446 Figure A.11: Shear modulus as a function of temperature for Zircaloy-2, SS-304 and HT-9. ... 446 Figure A.12: Oxide growth rate constant as a function of temperature for SS-304...... 451 Figure A.13: Oxide thickness as a function of time for HT-9...... 451 Figure A.14: Oxide thermal conductivity as a function of temperature for Zircaloy-2, SS-304 and HT-9...... 452 Figure A.15: Yield and ultimate strength as a function of temperature for SS-304...... 454 Figure A.16: Yield and ultimate strength as a function of temperature for HT-9...... 455 Figure A.17: Multiplying factor to account for irradiation hardening effect of stainless steel. . 455

List of Tables Table 1: Spent fuel inventories in spent fuel pools and dry-cask storage as of the end of 2007 [1]...... 24 Table 2: Plant specification and core design [42]...... 54 Table 3: Experimental data of MOX thermal conductivity...... 97

Table 4: Experimental data of UO2 thermal conductivity at high burnup...... 98 Table 5: Root mean square and standard deviation of kcalculated-kmeasured of thermal conductivity correlations...... 102

Table 6: Root mean square and standard deviation of kcalculated-kmeasured of thermal conductivity correlations after exclusion of unirradiated data...... 105 Table 7: Probable chemical and physical states of fission products in near-stoichiometric mixed oxide fuel [126]...... 134 Table 8: Elemental fission product yield in a fast neutron spectrum [126]...... 139 Table 9: Fuel rod characteristics of JOYO B11 experiments [227]...... 206 Table 10: Fuel rod characteristics of JOYO B14 experiments [227]...... 211 Table 11: Design parameters for ACO-1 and ACO-3 experiments [228]...... 217 Table 12: Irradiation condition of fuel rods in ACO-3 experiments [166]...... 221 Table 13: Design parameter of C3M fuel rods [165]...... 229 Table 14: Diffusion coefficient and heat of transport of cesium used in simulation ...... 246 Table 15: Description of Sawatzky’s experiments [241]...... 263 Table 16: Fuel rod design and geometry of fuel rod 1079 of Gravelines nuclear power station [244]...... 266 Table 17: Fuel rod design and geometry of RBWR-TB2 and ABWR...... 270 Table 18: Key design parameters of RBWR-TB2 fuel rods...... 309 Table 19: Comparison of fuel geometry at different cladding thickness...... 352 Table 20: A summary of key design parameters, their effects on fuel performance, and recommended values for further revisions...... 399 Table 21: A comparison of fuel design characteristics of current and future RBWR-TB2...... 401 Table A.1: Density, melting point and heat of fusion of Zircaloy, SS-304, and HT-9...... 432

Nomenclature

ABWR advanced boiling water reactor MPa megapascal(s)

BOL beginning-of-life MWd megawatt-day(s)

EOL end-of-life MWth megawatt(s)-thermal

EPRI Electric Power Research Institute NRC Nuclear Regulatory Commission

FBR fast breeder reactor O/M oxygen-to-metal ratio

FGR fission gas release PCMI pellet cladding mechanical interaction FFTF fast flux testing facility PNNL Pacific Northwest National HBS high burnup structure Laboratory HC-LWR high-conversion light water PuO reactor 2 plutonium dioxide

HPUF hydrogen pickup fraction PWR pressurized water reactor

JAEA Japan Atomic Energy Agency RBWR resource-renewable boiling water reactor JOG Joint Oxyde-Gaine RIA reactivity insertion accident kgU kilogram(s) of uranium RPV reactor pressure vessel kgHM kilogram(s) of heavy metals SBA station blackout accident LHGR linear heat generation rate SFR sodium fast reactor LOCA loss of coolant accident T.D. theoretical density LWR light water reactor TRU transuranic elements MOL middle-of-life U-235 uranium-235 MOX mixed oxide U.S. United States of America MIT Massachusetts Institute of uranium dioxide Technology UO2

Chapter 1

Introduction

1.1 Thesis objective

The objective of this thesis is to propose and analyze advanced fuel designs for the applications of plutonium and transuranic (TRU) waste incineration in light water reactors (LWR). With TRU burning and multi-recycling capability, this advanced water-cooled reactor is designed for use in a closed-loop nuclear fuel cycle to alleviate the accumulation of spent nuclear fuel from the current fleet of LWRs. This thesis addresses key design challenges of fuel element associated with TRU burning through fuel performance modeling. Thermal, chemical and mechanical behaviors of fuel rods are investigated to ensure an acceptable performance and reliability throughout reactor operation.

1.2 Motivation

1.2.1 Transuranic waste incineration in high-conversion LWRs

Although nuclear power is an extensive and reliable source of carbon-free energy, it is associated with various challenges that it needs to overcome. One of the most critical challenges for nuclear power sustainability is long-term radioactive waste management from depleted reactor fuels. Currently, global production of spent fuel from light water reactors (LWR) is approximately 10,500 metric tons of heavy metal per year, with roughly 8,500 tons of heavy metal going into long-term storage and about 2,000 tons of heavy metal being reprocessed. By the end of 2009, the global inventories of spent fuel were about 240,000 metric tons, mostly stored on-site [1]. Based on this figure in 2009 and the current global production rate of LWR spent fuel, the projected global inventories of spent fuel will have likely increased to about 313,500 metric tons by the end of 2016. For a typical LWR spent fuel with an average burnup of 50 MWd/kgHM, the composition is made of about 93.4% uranium (~0.8% U-235), 5.2% fission products, 1.2% plutonium and 0.2% minor actinides (neptunium, americium, and curium) [1]. During the first hundred years, the decay heat and radioactivity are dominated by fission products. After that, the

source of total radioactivity primarily comes from transuranic elements which will last for several hundred thousands of years until the ingestion toxicity of spent fuel become less than that of natural uranium [1]. With current waste disposal method, the time span of the nuclear waste toxicity can persist far beyond the lifespan of human civilization. The top 10 countries holding spent fuel are shown in Table 1. The United States so far has been the largest holder and producer of spent fuel. By the end of 2010, the total U.S. amount of spent fuel was 64,500 tons including 15,350 tons in dry casks [1]. This number has been increased to nearly 70,000 metric tons according to data published by the U.S. Energy Information Administration (EIA) in 2015 [2].

Table 1: Spent fuel inventories in spent fuel pools and dry-cask storage as of the end of 2007 [1]. Country Spent fuel inventory Spent fuel policy (tons of heavy metal) USA 61,000 Direct disposal Canada 38,400 Direct disposal Japan 19,000 Reprocessing France 13,500 Reprocessing Russia 13,000 Direct disposal and reprocessing South Korea 10,900 Storage, disposal undecided Germany 5,850 Direct disposal United Kingdom 5,850 Reprocessing but future unclear Sweden 5,400 Direct disposal Finland 1,600 Direct disposal

Direct disposal is a final step in a once-through open fuel cycle (OTC) where spent nuclear fuel is discarded as waste in geological repositories without extracting any fissile materials left in the spent fuel. Figure 1 illustrates the concept of the once-through fuel cycle. Although not very effective in term of resource utilization, the once-through fuel cycle offers the most convenient way to handle spent nuclear fuel. To date, this is the most economic fuel cycle to operate nuclear power plants because the fuel cost represents only a small fraction of total cost of electricity generation. Most of the world’s reactors operate based on this cycle [3].

Figure 1: Once-through fuel cycle [3].

Nevertheless, the once-through fuel cycle has some disadvantages in terms of fuel sustainability and waste disposal. The current knowledge of uranium resources indicates that there are some 3.5 million tons of uranium exploitable at below $80 per kg [4]. The current estimate of all expected uranium resources is four times more. At the current consumption rate of fresh uranium ore of about 67,000 tons per year, this figure will continue to increase as nuclear power expands [4] . It is expected that by the end of 2035 the consumption will be in the range of 98,000 and 136,000 tons of uranium per year [4]. Although the uranium resource is plentiful at least for the first half of the 21th century, long-term uranium scarcity in the next 200 years is inevitable. Assuming no additional discovery of large uranium resources, the 14 million tons of uranium ore would be depleted by 2226 at the current consumption rate of 67,000 tons per year. However, if the consumption rate continues to increase, the year of uranium depletion should occur earlier: 2159 and 2119 for the consumption rate of 98,000 and 136,000 tons, respectively. Another issue for the once-through fuel cycle is the disposal of spent nuclear fuel. In this case, the capacity of long-term repositories may not be sufficient. In fact, suitable sites for geological repository may not be available in certain countries.

It is understandable that the land area and geological characteristics of each country highly influence the decision on disposal policy of spent nuclear fuel. It can be seen that, for countries with large area like the United States, Russia and Canada or having low population density like Sweden and Finland, direct disposal of spent fuel is more favorable. However, for countries with limited land area and high population density, reprocessing seems to be unavoidable.

Reprocessing refers to a partially closed-looped nuclear fuel cycle where spent nuclear fuel from LWRs is reprocessed to extract the remaining fissile materials for further use. In this cycle, plutonium, transuranic elements (TRUs), and long-live fission products are separated by various

25 chemical processes. The recovered fissile contents are then mixed with depleted uranium, a leftover from uranium enrichment process, passed through fuel fabrication and returned to LWRs for power production. Figure 2 illustrates the closed-loop fuel cycle. Ideally, it is possible to sustain reactor operation without external supply of fissile material because, in fast breeder reactors, they can breed more fuel than they consume. However, a fully closed fuel cycle is not currently achievable because of technology and economic constraints [3].

Figure 2: Closed-loop fuel cycle [3].

Since the economics of nuclear power is dictated by the capital cost of nuclear reactors and their associated infrastructure, the type of nuclear reactor plays a major role in the fuel cycle option [3]. As of now, reprocessing is not a viable option mainly because the capital cost of fast breeder reactors (FBRs) is high and uncertain. Furthermore, to resolve technical and reliability issues of FBR technology, significant investment in research and development is necessary. However, if the capital cost of FBRs could be reduced with a less expensive reactor type and if limited operational experience of FBRs could be replaced with more mature technology then the technical and economic challenges associated with fully closed fuel cycle could be overcome. It will then make the closed fuel cycle more appealing and economically competitive for deployment.

When referring to an FBR, a sodium-cooled fast breeder reactor (SFR) is typically chosen as a representative of this technology due to historical reasons, and past experience of building and operating several experimental FBRs. According to a fuel cycle study at MIT, it is suggested that a reactor with conversion ratio (the ratio of fissile material at discharge to fissile material at loading) near unity may be more desirable because it relaxes the technical limitations of using SFR in a closed-loop fuel cycle while maintaining similar objectives in term of long-term sustainability of uranium and reduction in spent fuel mass and repository needs [3].

Technical limitations that hinder the widespread adoption of SFR technology include the fact that metallic sodium as reactor coolant reacts violently with water/steam which is used as working fluid in a power conversion cycle of SFRs. Additionally, sodium coolant can become activated from neutron irradiation during operation. In addition, liquid sodium is opaque, making visual maintenance somewhat difficult and complicated. Several engineering workarounds are required to overcome these issues such as the inclusion of a secondary sodium loop, advanced sealing technology, and high-precision measurement and handling.

Studies also indicate that LWRs can be designed to be self-sustaining with conversion ratio slightly above 1.0; no external fissile material is needed at equilibrium cycle [3] [5]. High- conversion LWRs, LWRs with conversion ratio near unity, have several advantages as an alternative to SFRs. First, apart from the reactor core, the remaining reactor system can be based on existing LWR technology. Second, extensive operating experience and proven record of high reliability of LWRs would ease the licensing and commercialization processes. From that, it can be inferred that the capital and operating costs would be similar to existing LWRs. Consequently, operating high-conversion LWRs instead of SFRs in a close-looped fuel cycle may be more economically and technically viable with higher reliability but lower capital and development cost [3].

To compare the performance of high-conversion LWRs and FBRs in a closed-loop fuel cycle, a fuel cycle simulation has been performed using CAFCA (Code for Advanced Fuel Cycle Analysis) [5] and the results have shown relatively comparable performance in terms of natural uranium requirement, total TRU inventory, repository storage capacity as shown in Figures 3, 4, and 5, respectively. In this study, a reduced-moderation boiling water reactor (RBWR) was used

27 as a representative of high-conversion LWRs with conversion ratio around one while a sodium fast reactor was used as a representative of fast breeder reactor with a similar conversion ratio. It can be clearly seen that fuel recycling and reprocessing in a closed-loop fuel cycle can conserve natural uranium resource and significantly reduce TRU inventory and repository capacity.

6.E+06 OTC Reference Scenario 5.E+06 RBWR Reference Scenario 4.E+06 FBR Reference Scenario 3.E+06

2.E+06

1.E+06

Natural Uranium Requirement [MT] Natural Uranium Requirement 0.E+00 2010 2030 2050 2070 2090 2110 Time [year] Figure 3: Natural uranium requirement over the course of simulation [5].

14000 OTC Reference Scenario 12000 RBWR Reference Scenario 10000

8000 FBR Reference Scenario 6000

4000

TRU in the System [MTHM] TRU 2000

0 2010 2030 2050 2070 2090 2110 Time [year] Figure 4: Total amount of TRU in the system [5].

450000 OTC Reference Scenario 400000 RBWR Reference Scenario 350000 FBR Reference Scenario 300000 250000 200000 [MTHM] 150000 100000 50000 HLW in Repository -HLW equivalent YM 0 2010 2030 2050 2070 2090 2110 Time [year] Figure 5: High level waste in geological repository [5].

However, any process that involves fuel recycling and reprocessing will increase the overall cost of electricity. As previously mentioned, the once-throughout fuel cycle currently is the most economically favorable fuel cycle. With a lower capital cost of higher-conversion LWRs, the negative impact on levelized cost of electricity can be mitigated. As shown in Figure 6, the increase in electricity cost of an RBWR was around 5% higher than OTC while that of FBR could be twice as much as RBWR cost increase.

94 OTC Reference Scenario 92 RBWR Reference Scenario FBR Reference Scenario 90

86 LCoE [$/MWhr] 84

80 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110 Time [year] Figure 6: Levelized cot of electricity [5].

Although the RBWR was designed based on the proven technology of the advanced boiling water reactor (ABWR), the unique characteristics of RBWR necessitate further research. From a fuel performance prospective, the technical challenges associated with RBWR are: (1) higher axial peaking factor, (2) higher local burnup, (3) harder neutron spectrum and (4) higher temperature gradient at the seed-blanket interfaces. Additional information on RBWR designs and challenges are described in Chapter 2.

1.3 Scope of work

This thesis focuses on the application of high-conversion LWRs for TRU incineration specifically a transuranic burning version of the reduced-moderation boiling water reactor (RBWR-TB2)1. To demonstrate its performance and safety during operation, thermal, chemical and mechanical behaviors of RBWR-TB2 fuel rods are analyzed through fuel performance modeling. The ultimate goal is to ensure that the fuel rod can survive throughout operation without fuel melting or cladding failure.

1 TB2 stands for transuranic burner 2.

RBWR-TB2 fuel is designed to operate at higher linear heat generation rate (LHGR) and higher local burnup beyond typical operating conditions of LWRs; therefore, several physical phenomena generally experienced in fast reactors which operate at high temperature and fuel burnup are expected to occur in RBWR-TB2 fuel rods.

A steady-state fuel performance modeling code, FRAPCON, is used as a primary tool in this study. However, FRAPCON was originally designed to include only physical phenomena relevant to LWRs. Thus, physical models at high temperature and high burnup are not included in the code. In this work, the code required modifications to better represent them in RBWR- TB2 conditions. Furthermore, important physical models such as fuel restructuring, plutonium redistribution, and cesium migration have been validated with experimental data from sodium fast reactors.

For model validation purposes, the code needed to be modified to better reflect experimental conditions in sodium fast reactors. By default, zirconium-based alloys are the only cladding options available in FRAPCON. Since fast reactors use stainless steel as cladding; therefore, the material properties of stainless steels needed to be added. This work includes two types of stainless steels: HT-9 and SS-304 as representative of ferritic/martensitic steels and austenitic steels, respectively. In addition, the coolant properties needed to be changed from water to sodium.

To illustrate the differences in thermo-mechanical behavior of RBWR-TB2 and a typical BWR, fuel performance comparison between RBWR-TB2 and ABWR are performed. Key performance indicators necessary for licensing such as maximum fuel temperature, oxide layer thickness, and cladding stress and strain are compared and discussed. The results from the simulation can also provide critical feedback to the neutronic design team. This work also includes sensitivity analysis on key design parameters so that the results can be used as guidance for fuel design changes.

1.4 Nuclear fuel performance modeling

The reactor design process typically involves various calculations: neutronic, thermal hydraulic, fuel performance, and transient/accident analyses. It is an iterative and circular operation as it can start at any process in the cycle but eventually all design constraints have to be met.

Neutronic simulation predicts the behavior of neutrons, fission reactions, and heat generation rate. The scale of calculation can range from a single fuel rod to an entire reactor core. Then, thermal hydraulic simulation describes the behavior of cooling water during operation. It can cover only a single flow channel around a fuel rod or multiple channel of a core. In LWRs, water serves as both coolant and neutron moderator; therefore, the changes in cooling water condition will have direct impact on the neutronic behavior of a reactor core. Perturbations from steady- state conditions such as startup, shutdown, or power fluctuation are covered in transient analysis. Accident analysis addresses the behavior of the reactor and its auxiliary system during accidents such as reactivity insertion accident (RIA), loss of coolant accident (LOCA), or station blackout accident (SBA).

Fuel performance simulation looks into the physical characteristics of the fuel operation; it predicts thermal, mechanical and chemical behavior of a fuel rod under extreme conditions in a reactor core and estimates whether the fuel rod is going to survive throughout operation without fuel melting or cladding failure. It is a multi-disciplinary field as it involves several aspects of sciences: nuclear physics, material science, chemistry, and mechanical engineering. The scale of problem can range from the atomistic scale involving the dynamics of material properties under irradiation up to engineering scales such as the effect of pressure, temperature, and stress on fuel behavior. One of the most fundamental assumptions in fuel performance modeling is that each fuel rod does not directly interact with other rods. Therefore, fuel performance is modeled and analyzed separately for each fuel rod. Typically, fuel performance modeling looks at the peak rod condition i.e. the fuel rod that is exposed to highest burnup or higher LHGR throughout the fuel cycle. If the peak rod can survive; it is assumed that the remaining rods can also survive.

In addition, nuclear regulators usually establish several constraints based on predictions from fuel performance modeling. For example, fuel temperature has to be below melting point.

Zircaloy cladding temperature must not exceed 1473 K (1200 oC) to prevent autocatalytic reaction between zirconium and water. Maximum fuel burnup may not exceed 62 MWd/kgHM to prevent cladding failure during transient conditions. End-of-life cladding strain may not exceed 1% to allow coolable geometry of a fuel rod. Therefore, fuel performance modeling is an important part of the reactor licensing process.

The behavior of fuel rods depends on various parameters, and some of them are highly interrelated. Thermal parameters such as the temperature distribution within the fuel rod are not only a function of thermal conductivity and heat transfer coefficient across material boundaries, they also depend on mechanical and chemical effects such as the size of fuel-cladding gap and thickness of cladding oxide layer. Likewise, mechanical parameters such as the stress and strain depend on thermal and chemical effects such as thermal expansion and material property change. Chemical parameters such as fission gas release and oxidation rate varies according to mechanical and thermal states of the materials. All of these inter-correlations in nuclear fuel performance modeling are illustrated in Figure 7. Parameters in red boxes are designated as input while ones in blue boxes are boundary conditions. Cladding and fuel parameters are placed in purple and green boxes, respectively.

Figure 7: Complexity of nuclear fuel performance modeling [6].

1.4.1 FRAPCON-3 fuel performance code

FRAPCON is a computer code that calculates the steady-state behavior of light-water reactor fuel rods as a function of burnup. The code was originally developed by the Pacific Northwest National Laboratory (PNNL) for use by the U.S. Nuclear Regulatory Commission (NRC) to calculate thermal, mechanical and material evolution of the fuel and the cladding of a single fuel rod as a function of time and burnup based on initial core conditions and power history up to maximum rod-average burnup of 62 MWd/kgHM [7].

The phenomena modeled in the code include (1) heat conduction through the fuel and cladding to the coolant; (2) cladding elastic and plastic deformations; (3) fuel-cladding mechanical interactions; (4) fission gas release from the fuel and rod internal pressure; and (5) cladding oxidation [7]. The code is designed to simulate the behavior of a single fuel rod under the slowly

changing conditions during in-core performance (typically called steady state, although the power derived from the rod can vary during its residence in the core). By definition, steady-state conditions imply that power and boundary conditions changes must be sufficiently slow for a quasi “steady-state” to exist during a portion of the irradiation. . This includes situations such as long periods at constant power and slow power ramps that are typical of normal power reactor operation.

FRAPCON uses a single-channel coolant enthalpy rise model to calculate the axial distribution of the bulk coolant temperature. It uses a finite difference heat conduction model to calculate the temperature distribution within a fuel pellet. Variable mesh spacing is also implemented to accommodate the power peaking at the pellet edge that occurs in high-burnup fuel. The code can calculate the variation with time of all significant fuel rod parameters, including fuel and cladding temperatures, cladding hoop strain, cladding oxidation, fuel irradiation swelling, fuel densification, fission gas release, and rod internal gas pressure. The code calls for material properties from the MATPRO material properties subroutines [7].

FRAPCON can be used to simulate light water and heavy water reactor fuels. Available materials for the fuel pellet, gas gap and cladding include uranium dioxide (UO2) and mixed

oxide pellet ceramic, integrated burnable absorber fuel, zirconium diborate coated UO2, pellet material mixed with gadolinium, zirconium-based alloys cladding which comprises: Zircaloy-2, Zircaloy-4, ZIRLO and M5 [7].

FRAPCON solves the equations iteratively by calculating the interrelated effects of fuel and cladding temperature, rod internal gas pressure, fuel and cladding deformation, release of fission product gases, fuel swelling and densification, cladding thermal expansion and irradiation- induced growth, and cladding corrosion as functions of time and linear power. The calculation procedure of FRAPCON is illustrated in a simplified flowchart as shown in Figure 8. The calculation begins by processing input data. Then, the initial fuel rod state is determined through a self-initialization calculation. Time is advanced according to the input-specified time-step size, a steady-state solution is performed, and the new fuel rod state is determined. The new fuel rod state provides the initial state conditions for the next time step. The calculations are cycled in this manner for the number of time steps as specified by users. The response at each time step is

determined by repeated cycling through two nested loops of iterative calculations until the fuel- cladding gap temperature difference and internal gas pressure converge [7].

Figure 8: Simplified FRAPCON-3 flowchart [7].

FRAPCON was chosen as a primary tool for this work because its source code is publicly available so that it is possible to modify the code with additional physical models or material properties. Given its creditability as an independent audit tool in NRC’s reviews of industry fuel performance codes in the United States, FRAPCON should provide reasonably accurate results within the limitations of the code.

Given the fact that FRAPCON was originally developed for conventional LWR fuel designs, several physical phenomena at high burnup and high temperature regime are not modeled in the code. For example, given a regulatory burnup limit of 62 MWd/kgHM, a high burnup structure (HBS) phenomena that usually occurs beyond this burnup limit are not included. Fuel constituent transport models under temperature gradient are not covered. This is understandable because in typical LWR fuel rods where fuel temperatures are well below its melting point, these phenomena are negligible. Nevertheless, FRAPCON was determined to serve as a reliable platform for advanced fuel design in this work because the code has been extensively benchmarked and validated with experimental data [7]. After additional models that represent physical phenomena at high temperature and high burnup are included, it can credibly be used to accurately analyze the behavior of RBWR fuel rods.

1.4.2 FRAPCON-EP

FRAPCON-EP is a modified version of FRAPCON-3.3 where EP stands for enhanced performance [8] [9] [10]. It was developed to improve prediction capability of FRAPCON-3.3 beyond a regulatory burnup limit of 62 MWd/kgHM and to address physical phenomena that become important only at high temperature and high burnup. Similar to other versions, FRAPCON-3.3 was originally developed to simulate fuel rod behaviors in typical LWR conditions which operate at relatively low temperature i.e. fuel temperature is less than half of melting point. Because of this limitation, the code did not explicitly model migration behavior of fuel constituents such as uranium, plutonium, oxygen, porosity, and fission products which normally occur at high temperature under steep temperature gradients. In addition, fuel swelling from gaseous fission products was assumed negligible in FRAPCON-3.3 which may be the case under typical LWR operating conditions. Given a burnup limit of 62 MWd/HM, high burnup structure (HBS) formation which usually occurs beyond this burnup limit are not covered.

FRAPCON-EP introduces several physical models that represent time-dependent behavior of fuel constituents under steep temperature gradient and high temperature. From a uniform radial distribution of plutonium, oxygen and fission products, FRAPCN-EP employs mechanistic models based on Fick’s law of diffusion and thermal migration (Soret’s effect) to describe the evolution of these species under the effect of temperature. A change in radial distribution of

plutonium will directly impact the radial power profile of a fuel pellet and fuel thermal conductivity. Oxygen migration affects the oxygen-to-metal ratio (O/M) and fuel thermal conductivity locally. As a representative of volatile fission products, cesium migration was modeled in FRAPCON-EP because of its high mobility and tendency to cause localized fuel swelling. Fuel porosity migration was also modeled in FRAPCON-EP. Under high temperature gradient, as-fabricated porosity migrates to higher temperature region, concentrates at fuel center and eventually forms a central void. The formation of central void changes fuel geometry from solid pellet to an annular pellet which affects temperature distribution in the fuel.

For physical phenomena at high burnup, FRAPCON-EP includes HBS formation, O/M variation with burnup and acceleration in corrosion and hydriding. High burnup structure is a change in fuel microstructure from a dense crystal structure with grain size of around 10 microns to a porous structure with a significantly smaller grain size (0.01-0.1 microns). Usually occurs at fuel periphery where temperature is below 1273 K (1000 oC), the occurrence of HBS increase fuel porosity and degrade fuel thermal conductivity at high burnup. As a result of fission reaction which releases two oxygen atoms in oxide fuel and contamination of fission products in fuel matrix, O/M ratio increases with burnup. This phenomenon had been captured in FRAPCON-EP.

In zirconium alloy cladding, oxidation resistance comes from the existence of secondary phase particles (SPP) which are intermetallic precipitate of zirconium and alloying elements. However, these particles will become amorphous or completely dissolved in the fuel cladding matrix as free metallic particles at high burnup. Once a complete dissolution of SPP takes place, acceleration in corrosion and hydriding of cladding can occur. FRAPCON-EP uses neutron flux and irradiation time to estimate threshold neutron fluence in which SPPs are completely dissolved. After that, a higher oxidation rate is assumed which will result in higher concentration of hydrogen in the cladding.

Although, various physical phenomena at high temperature and high burnup have been modeled and described in FRAPCON-EP, there was still significant room for improvement. For example, several physical models such as porosity migration and cesium migration were based on empirical models. Fundamentally, the overall behaviors of these models are heavily depends on arbitrary empirical constants and their applicability is often limited to a specific set of empirical

data on which they were developed. To improve the generality of these models, a more mechanistic and general approach was used to describe these phenomena. Furthermore, a base version of FRAPCON-EP needed to be upgraded to a more recent version of FRAPCON so that the code can gain benefits from enhanced capability, updated material property correlations, and improved fuel behavior models.

1.5 Thesis organization

This thesis consists of seven chapters and two appendices covering background information, material property development, physical model implementation, experimental validation and sensitivity analysis on key design parameters.

Chapter 1 describes the main objectives and motivation of using advanced LWR for plutonium and transuranic waste incineration. A brief description of a fuel performance code FRAPCON and its variants are also given.

Chapter 2 describes a brief history of high-conversion LWR designs as plutonium breeder and transuranic waste burner including Hitachi RBWR designs. With emphasis on transuranic waste incineration, specific design of RBWR-TB2 is described in details about its characteristics and material challenges in term of fuel performance.

Chapter 3 presents a literature review of various thermal conductivity correlations for MOX fuels developed over the years. A benchmarking of these correlations is performed to highlight the effects of dependent variables on thermal conductivity values. Comparison between correlations and experimental data are performed in order to identify the most appropriate one for RBWR-TB2 analyses.

Chapter 4 presents physical phenomena relevant to RBWR-TB2 conditions which operate at high temperature and high burnup. Physical phenomena at high temperature such as fuel constituent migration and gaseous fuel swelling are covered. Degradation of material properties at high burnup including corrosion, high burnup structure formation are also discussed in this chapter.

Chapter 5 presents the validation effort of some of the physical models implemented in FRAPCON-3.5 EP. To compare the code with experimental data from fast reactors, additional code modification to better reflect fast reactor conditions such as sodium coolant and stainless steel cladding is discussed.

Chapter 6 includes results of fuel performance modeling of RBWR-TB2. Several key performance indicators in fuel modeling such as fuel temperature, oxide layer thickness, cladding stresses and strains are presented and discussed. Sensitivity study of fuel rod behavior relative to key design parameters including a different type of cladding material are included in this chapter.

Chapter 7 summarizes the observations and conclusions drawn from the work performed for the thesis. Further improvements and opportunities for future research are also discussed.

Chapter 2

High-conversion Light Water Reactors

2.1 History of HC-LWR development

The High-Conversion LWR (HC-LWR) is a collective term used to describe a type of advanced LWR design with a conversion ratio higher than currently operating LWRs. From a fuel cycle prospective, LWR serves in three different roles: fuel consumer, power producer, and waste producer. On the other hand, the HC-LWR was designed to produce power at the same level as an LWR but consume less fuel and generate less waste with multi-recycling or Transuranic Waste (TRU) burning capability. Being able to recycle its spent nuclear fuel indefinitely translates to a significant reduction in natural uranium ore and amount of waste to be stored in geological repositories, thereby, increasing fuel resource sustainability and at the same time reducing environmental burden from nuclear waste.

The HC-LWR can be categorized based on its fuel composition: U-Pu or U-Th cycles. Then, it can be further categorized by its coolant characteristics: pressurized water or boiling water. In addition, it is also possible to use heavy water (D2O) instead of light water (H2O) as coolant to attain high conversion ratio and multi-recycle capability. However, since it does not exactly fall under the definition of the HC-LWR design, heavy water cooled reactors are not included in this review. A chronological list of some of HC-LWR designs is shown in Figure 9 [11].

High-Conversion Light Water Reactor

Fuel composition Uranium-Plutonium Uranium-Thorium

Boiling Pressurized Boiling Pressurized Coolant Water Water Water Water

RMWR (Takeda 1995) B&W PWR HCBWR LWBR (Edlund 1975) (Downar 2001) (Connors 1979)

BARS (Toshiba 2001) KWU APWR RMPWR Seed Blanket (Lindley 2014) (Broeders 1985) (Nunez-Carrera 2008) FLWR (JAEA 2009) HGLWBR (Radkowsky 1988) RBWR-Th (Ganda, 2012) RBWR (Hitachi 2009) RCVS (Framatome 1988)

Big Mac (Ronen 1998)

RMR-PWR (JAERI 2003)

Figure 9: Classification of high-conversion LWR [11].

The development of the HC-LWR began roughly a decade after fast breeder reactors during the 1970s. At that time, nuclear power was rapidly expanding and there was an ongoing concern over scarcity of natural uranium resource. By the 1980s, advances in geological exploration and uranium mining technology proved that uranium resource was not going to be a problem at least until the end of 21st century although the long-term issue of spent nuclear fuel from LWRs still persist [12]. Fast breeder reactors—nuclear reactors that can produce more fuel than they consume—were specifically designed as a countermeasure to this problem [13]. These reactors need to be cooled by a non-moderating coolant such as sodium, helium, or lead. With limited experience with such designs and successful deployment of light water as coolant in the nuclear navy program [14], there were some interests to pursue a light water reactor design with higher

conversion ratio as an alternative development route [15]. HC-LWR achieves multi-recycling or TRU burning capability by reducing neutron moderation in the core; thereby, shifting the neutron spectrum toward higher energy. Even though various HC-LWR designs have been proposed over the years, most of them share this characteristic to some extent. Depending on the nature of coolant, different design strategies are used to harden the neutron spectrum.

High-Conversion Pressurized Water Reactor

In pressurized water systems, reduction in neutron moderation is generally achieved by displacing water volume with fuel volume. Edlund was the first to propose the idea of retrofitting an existing PWR with new fuel assembly design capable of achieving higher conversion ratio [16]. In this design, the fuel assemblies are arranged in hexagonal lattice so that they can pack more fuel per unit area than a standard square lattice. Fuel rod pitch and assembly pitch are reduced; thus displacing water volume even further. As a result, the conversion ratio is increased from 0.5 to 0.9. A Babcock and Wilcox PWR was used as a template for this reactor concept.

This reactor is designed to use uranium-plutonium mixed oxide (UO2-PuO2 or MOX) as fuel. A negative void reactivity coefficient was achieved based on neutronic calculations [17].

Broeders and Donne proposed a high conversion advanced PWR (APWR) based on a German Kraftwerk Union (KWU) PWR using MOX fuel in a hexagonal tight lattice geometry. In a homogeneous core design, fuel rod geometry is identical; only fissile plutonium content changes in the radial direction to smoothen the radial power distribution. In a heterogeneous core design, the reactor core is divided into two radial zones: seed and blanket. Seed area is defined by an

inner core area with MOX fuel whereas the blanket area is an outer core area with depleted UO2 [18]. With radial seed-blanket designs, the conversion ratio of KWU APWR increased from 0.90 in a homogeneous core design to 0.96 in the heterogeneous core design and maintained a negative void reactivity coefficient from increased neutron leakage from seed to blanket zones.

However, PWR designs with a tight lattice and simple heterogeneous core can only achieve conversion ratio slightly below 1.0 at best. This is because the presence of single-phase liquid water in PWRs makes it difficult to increase conversion ratios greater than 1.0 unless some

advanced features such as a spectral shift mechanism, multi-stage operation with rapid reprocessing or complex core heterogeneity are used.

Radkowsky and Shayer achieved a higher conversion ratio of 1.08 in their High Gain Light Water Breeder Reactor (HGLWBR) design [19]. HGLWBR uses multi-stage and multi-core operation with rapid fuel reprocessing to achieve the high conversion ratio under the condition of PWR. HGLWBR operates in two stages of operation using two reactor cores: pre-breeder and breeder. In the pre-breeding stage, spent fuel from an LWR is fed to pre-breeder to maximize Pu- 241 production. Pu-241 is needed to achieve breeding capability in HGLWBR because the η value (number of neutrons emitted per neutron absorbed) is higher for Pu-241 than Pu-239 for neutron energies below 0.1 MeV. Given short half-life of 14.4 years for Pu-241, the fuel reprocessing and fabrication time has to be reduced to 3 months between discharging from pre- breeders cores and loading into breeder cores. To further increase breeding potential, high- density metallic Pu-Zr fuel is used in seed region whereas depleted UO2 is used in blanket region.

Spectral shift mechanism was used in RCVS reactor to promote fuel breeding where RCVS stands for Réacteur Convertible à Variation de Spectre [20]. The core was designed with an inner seed region using either enriched UO2 or MOX fuel, surrounded by an axial and radial blanket

region of depleted UO2 and stainless steel reflector. Fuel assemblies were arranged in a hexagonal lattice with capability of changing neutron spectrum with burnup. Essentially, they are fuel assemblies with water holes and removable fuel rods inside. Initially, they are filled with

depleted UO2 to make use of excess reactivity for plutonium breeding during the beginning of cycle (BOC). As excess reactivity decreases with burnup, these removable fuel rods are gradually pulled out of the core for further reprocessing. The remaining water holes are then filled with water thus allowing moderator-to-fuel ratio to increase and neutron spectrum to shift toward thermal spectrum for better fissioning of fissile materials. This design achieved a conversion ratio of 0.95 with negative void reactivity coefficient.

An example of micro-heterogeneity configuration was proposed in the so-called “Big Mac” design which is a high conversion PWR that stacks alternating layers between MOX (seed) and

natural UO2 (blanket) within a fuel rod [21]. The core dimension is similar to typical PWRs – 3.6

m height and 3.37 m diameter. Each layer is 3 cm thick. Because of neutron leakage from seed to blanket, this arrangement promotes plutonium breeding in blanket layer and increases conversion ratio up to 0.92 with negative void reactivity coefficient.

The RMWR-PWR is a Japanese design of a high-conversion PWR as a variant in the RMWR series which mostly focuses on high-conversion BWRs [22]. This design achieves conversion ratio around 1.0 and negative void reactivity coefficient with the use of zirconium hydride

(ZrH1.7) rods to soften the neutron spectrum in the blanket zone [23]. The RMWR-PWR employs both micro-heterogeneity at both fuel rod and assembly level to promote fuel breeding. A fuel rod is stacked with axially alternating layers between MOX and depleted UO2. The fuel

assembly comprises of inner seed fuel rods (MOX) and outer blanket fuel rods (depleted UO2). The fuel assemblies are arranged in a hexagonal tight lattice to reduce neutron moderation. Stainless steel was used instead of zirconium because of the high linear heat rate and the allowance of a reduction in cladding thickness. Subsequent design iterations of the RMWR-PWR eliminated zirconium hydride rods in blanket zone through optimization of various parameters including the length of seed and blanket in a fuel rod and number of rings in seed and blanket in an assembly [24]. Cladding material was also changed from stainless steel to Zircaloy to improve neutron economy in the core.

The RMWR-PWR was recently examined by Andrews et al. [25] for further improvement of the conversion ratio. The goal of this study was to increase the conversion ratio beyond 1.0, thus, achieving fuel breeding capability in a pressurized water environment. A fuel assembly of RMWR-PWR as proposed by Shelley et al. [24] was used as a reference design. With the use of higher density fuel form such as uranium-plutonium mononitride, (U,Pu)N, and a replacement of water rods with voided rods, it was possible to further reduce the moderator-to-fuel ratio of the assembly and increase the conversion ratio from 1.0 to around 1.03 at a single batch discharge burnup of 35 MWd/kgHM. This work also investigated some safety parameters including thermal hydraulics and reactivity coefficients. Although, the moderator density coefficients in cases of nitride fuels were found to be positive, the coupled power coefficients were more negative and should ensure the safety of the reactor in off-normal conditions. The author also pointed out that the radially reflective boundary conditions which are typically used in assembly-

45 level neutronic calculations might produce somewhat more conservative results than a full-core analysis which considered neutron leakage in radial directions.

It is worth to mention the Shippingport Light Water Breeder Reactor (LWBR) as a proven demonstration of breeding capability in a pressurized light water environment [15]. It is a high- conversion PWR design based on uranium-plutonium cycle in the first and second cores and uranium-thorium fuel cycle in the third and final core. Closely-packed hexagonal lattice and seed-blanket assembly design again were used to increase the conversion ratio. In the first two cores, fuel composition was made of highly enriched uranium oxide (93% U-235) as fissile material in the seed zone and natural uranium oxide as fertile material in the blanket zone. The last core was made of fissile uranium oxide (U-233) as seed and natural thorium oxide as blanket. It was the only high-conversion LWR that progressed through conceptual design, construction, operation and decommission – a full life cycle. Fuel breeding capability was proven in the final core of the LWBR with UO2-ThO2 fuel; approximately 1.4% more fissile materials were found in the core after it had been operating for 5 years during the last stage of its operation from 1977 to 1982 [26].

Achieving a conversion ratio greater than 1.0 is less difficult in uranium-thorium fuel than uranium plutonium, because of the neutronic characteristic of U-233 as a fissile nuclide. Naturally, the η value of U-233 is greater than 2 in a wider energy range than that of other fissile nuclides, making it possible for fuel breeding even in a thermal spectrum.

A more recent design of high-conversion PWR featuring thorium fuel was proposed by Lindley and Parks under the name of reduced-moderation PWR (RMPWR) [27] [28]. RMPWR was designed for TRU incineration instead of fuel breeding or fuel self-sustainability through multi- recycling of Th-TRU fuel in a pressurized water environment. One unique feature of this design is the range of fuel isotopic composition which is considerably more complex than U-TRU or U- Pu fuel. In oxide form, the fuel composition of RMPWR comprises Th-TRU fuel where TRUs come from LWR spent fuel and Th-U fuel where various isotopes of uranium (U-233, U-234, and U-236) are generated through neutron absorption in thorium. RMPWR was designed to be compatible with current generation of PWR such as EPR or AP1000 [28]; therefore, the fuel assembly is arranged in square lattice with similar fuel rod pitch as typical PWR. Neutron

moderation is reduced by increasing fuel rod diameter so that the moderator-to-fuel ratio was reduced from 1.98 in a reference PWR design to 1.09 in the RMPWR. Negative void reactivity coefficient is achieved through multiple zoning of fuel composition. In heterogeneous fuel assembly design, Th-U fuel rods are placed in the central region and Th-TRU fuel rods in the assembly periphery. In heterogeneous core design, fuel assemblies of entirely Th-U and Th-TRU rods are arranged in a perfect checkerboard lattice. Depending on fuel design, the TRU incineration rate of RMPWR ranges from approximately 170-190 kg per year per 1 GWth reactor. Axial heterogeneity is not incorporated in the RMPWR. Unlike breeder or break-even reactors where the use of thorium fuel increases the fuel breeding potential because of the η

value of U-233, for TRU burning application, ThO2-based fuel offers little advantage over UO2- based fuel because of complexity in fuel composition [29].

High-Conversion Boiling Water Reactor

In terms of fuel breeding, the boiling water reactor (BWR) has some advantages over pressurized water reactors (PWR) because it operates with the presence of boiling and two-phase coolant. Naturally, a two-phase mixture of liquid water and steam has lower density than single-phase liquid water. Therefore, the neutron moderation somewhat diminishes toward the top of reactor core. In traditional BWRs, it is necessary to include water rods – empty fuel rods without end caps – to serve as water flow channels and allow more liquid water to reach through the top without boiling and improve neutron moderation around the vicinity. In-core boiling and lower neutron moderation makes it relatively easier to increase conversion ratio in a BWR. Unlike a PWR which relies only on water volume reduction, in BWRs, both water volume and water density can be manipulated to achieve the objectives of hardened neutron spectrum and increasing conversion ratio. The concept of a high-conversion BWR received particular attention in Japan because it is more suitable to the country’s situation where BWRs are a majority of its reactor fleet.

This review includes three high-conversion BWR designs from Toshiba, Japan Atomic Energy Agency (JAEA) and Hitachi. Although, they share many similarities in designs features such as a shorter core, closely-packed fuel lattice, and high void fraction in the core, some differences in

fuel composition, geometry, and functionality do exist. Most of these designs are based on uranium-plutonium cycle thus the fuel composition is made of either enriched uranium or MOX.

Toshiba proposed a high-conversion BWR and named it BWR with Advanced Recycle System (BARS) [30]. The design was based on an existing design of advanced boiling water reactor (ABWR) – the latest generation of currently operating BWR – to reduce capital and development cost. Unlike any other high-conversion LWR, BARS uses a tightly-packed triangular fuel lattice arranged in a square fuel assembly. Core height was reduced from a full-length at 3.7 m in the ABWR design to 1.6 m in a normal fuel assembly and 0.8 m in a partial fuel assembly. BARS features a seed-blanket design with full-length and half-length fuel assemblies. The partial-length fuel assembly serves as a neutron-streaming channel in the upper half of the core to increase neutron leakage thus achieving a negative void reactivity coefficient through the cycle. The average void fraction of BARS is about 0.6 leading to a conversion ratio of 1.04. Another technique to improve the conversion ratio is to reduce cladding thickness so that fuel volume is increased but sufficient cooling is preserved. However, it comes with some penalty in term of neutron economy because stainless steel cladding is required given reduced strength because of reduction in thickness. To flatten power peaking, the fuel assembly of BARS contained different zones of plutonium weight fraction: 11% in low enrichment zone and 14-17% in high enrichment zone. The latest design effort has included thermal hydraulic analyses [31] [32] [33].

JAEA applied the concept of multi-role reactors in their high-conversion BWR design called Flexible Light Water Reactor (FLWR). It is also designed based on the ABWR with tight hexagonal lattice and seed-and-blanket MOX fuel design and increased average void fraction in the core. FLWR cores can be configured into different roles in a fuel cycle: TRU burner or plutonium breeder. The TRU burning version of FLWR is called high-conversion FLWR (HC- FLWR) and plutonium breeder version is called Reduced-Moderation Water Reactor (RMWR). In HC-FLWR, the conversion ratio is 0.84 with capability to use processed fuel that contains minor actinides [34]. HC-LWR fuel rods are segregated into three zones: lower blanket zone at the bottom, seed zone at the middle and another blanket zone at the top.

RMWR is a fuel breeder version of FLWR with a conversion ratio of 1.04. In the RMWR, the moderator-to-fuel ratio is reduced even further than the HC-FLWR by reducing fuel rod gap and

increasing fuel rod diameter. In addition, RMWR fuel rods have five zones. From the bottom to the top, there are lower blanket, lower seed, middle blanket, upper seed and upper blanket zones. These two reactor cores share some similarities in size and shape of fuel assembly so they can be converted into one another. This feature allows some flexibility in the fuel cycle if future needs arise. To maintain necessary neutron leakage and negative void reactivity coefficient, the core height of these reactors are significantly shorter than original length of ABWR: 0.95 m in HC- FLWR and 1.255 m in RMWR.

Hitachi also designed a series of high-conversion BWRs under the development name of Resource-Renewable Boiling Water Reactor (RBWR). This reactor concept was first proposed by Takeda et al. in 1995 [35] and is still under active development to date [36]. Similar to previous high-conversion BWRs described above, the reactor core of the ABWR was used as a design template and then several techniques were incorporated to reduce moderator-to-fuel ratio and harden the neutron spectrum. Hitachi also conceptualized RBWRs as multi-role reactors in a multi-stage fuel cycle; therefore, several design variants of RBWR were proposed. Classified by their roles in the fuel cycle, there are 5 different variants of RBWR to date: RBWR-T3, RBWR- AC, RBWR-Th, RBWR-TB, and RBWR-TB2. Each core design has different geometry, composition and purposes but they share the similar goal of being a better alternative to Sodium Fast Reactor (SFR), whether in the role of initiator, breeder reactor or TRU burner. As an initiator, RBWR-T3 uses enriched UO2 to operate and is designed to maximize plutonium production left in the spent fuel. The RBWR-AC is designed to be a self-sustaining reactor, where it breeds fuel as much as it consumes during its lifetime. The fuel of RBWR-AC is composed of TRUs extracted from spent nuclear fuels in depleted uranium matrix. At equilibrium, the fuel composition at the end of cycle will be approximately the same as at the beginning of cycle. On the other hand, RBWR-TB uses a slightly different geometry and composition to maximize the fission of TRUs [11].

Regardless of the design purposes, all RBWRs share the same technical challenge in that H/HM ratio (the ratio between moderator and fuel) has to be decreased to reduce the moderation in the reactor core so that they can breed fuels or incinerate TRU wastes via high-energy neutrons. Several design techniques have been used to harden the neutron spectrum and promote fuel breeding: (1) reducing water density by increased boiling, (2) reducing water volume with tight

49 lattice in a hexagonal geometry, and (3) increasing neutron absorption in a blanket region with axial heterogeneity by alternating blanket and seed regions in the fuel rod [11]. Figure 10 compares moderator-to-fuel ratio and breeding ratio of conventional BWR, RBWR-AC, RBWR- TB and RBWR-TB2 [36]. It can be seen that as the moderator-to-fuel ratio decreases; breeding ratio increases accordingly. With breeding ratio close to 1.0, RBWR-AC and RBWR-TB can sustain a continuous cycle without the need for external fissile material. Having lower breeding ratio by design, RBWR-TB2 requires external fissile TRUs from LWR spent fuels.

Figure 10: Moderator-to-fuel ratio and breeding ratio comparison [36].

The RBWR-T3 serves as an initiator in a closed-loop nuclear fuel cycle with the purpose of maximizing plutonium production from natural uranium without multi-recycling capability [11]. The spent fuel of the RBWR-T3 can be fed to RBWR-AC where multi-recycling of its own fuel is possible. Given its objective of once-through plutonium breeding, the neutron spectrum of RBWR-T3 is more thermalized than any other versions of the RBWR. The fuel composition of the RBWR-T3 is enriched UO2 in a hexagonal lattice. To allow more neutron moderation, the fuel rod pitch and inter-assembly pitch are wider than in other RBWR designs. The average void

fraction is similar to current ABWRs. In addition, water rods are included in the center of RBWR-T3 fuel assembly to increase neutron moderation in the upper region of the core.

The RBWR-AC is a self-sustaining version of the RBWR [36]. In other words, the RBWR-AC can perpetually operate with its own spent fuel except for the first fuel loading which requires an external source of fissile materials. The first batch of RBWR-AC fuel can be loaded with TRUs extracted from spent fuel from a LWR or RBWR-T3 to initiate an indefinite fuel recycling. Several design techniques are used to the harden neutron spectrum in the RBWR-AC in order to achieve self-sustainability or conversion ratio slightly above 1.0 and, at the same time, maintain a negative void reactivity coefficient. The RBWR-AC fuel assembly is arranged in a tightly- packed hexagonal lattice with small pitch-to-diameter ratio and narrow inter-assembly gap. Core flow rate is reduced by a factor of 2.5 when compared to that of the original ABWR; this makes core-averaged void fraction increase because of additional boiling. RBWR-AC fuel rods have 5 axial zones. From the bottom to the top, there are lower blanket, lower fissile, middle blanket, upper fissile and upper blanket zones. Seed-and-blanket design in conjunction with a much short core in RBWR-AC results in higher neutron leakage from the fissile zone which helps mitigate reactivity insertion upon core voiding. Fuel compositions in the blanket zone are made of

depleted uranium in the form of oxide (UO2) whereas in fissile zones they are made of mixed oxides of uranium, plutonium and minor actinides. Multiple plutonium enrichment zones reduce radial power peaking within a fuel assembly.

The RBWR-Th is a companion design of RBWR-AC with different fuel composition and axial seed-blanket zoning [28] [37] [38] [39]. As the name suggests, the RBWR-Th uses ThO2 instead of depleted UO2 in both fissile and blanket zones. It was designed to be a fuel-self-sustaining reactor which operates on the U-Th fuel cycle with U-233 as fissile material. Common design characteristics for high-conversion BWRs are also found in RBWR-Th: tight hexagonal lattice, high void fraction and high exit steam quality. However, the core height of RBWR-Th is not as short as any other designs. In fact, the length of the fuel rod is similar to the original ABWR at around 3.8 m whereas it is around 1.4 m in RBWR-AC design. In the RBWR-Th, there are 3 axial zonings: lower blanket, middle fissile zone and upper blanket. Middle blanket zone was eliminated; the upper and lower fissile zones were combined and elongated into a middle fissile zone. The RBWR-Th also achieves fuel sustainability with conversion ratio slightly above 1.0,

meaning that only externally supplied natural ThO2 is needed to feed the reactor. Reactivity coefficients for fuel temperature, coolant void, and power are all negative in this design.

The RBWR-TB is a TRU burning version of the RBWR [36]. The primary goal of this reactor is to completely eliminate the total amount of TRU through multi-recycling. Initiation of the RBWR-TB cycle can be made by loading TRU materials from an RBWR-AC. After that, it can consume its own spent fuel. Unlike the RBWR-AC which was designed to operate indefinitely, RBWR-TB was designed to operate for a limited amount of time until TRUs are completely incinerated. Performance of the RBWR-TB is defined by fission efficiency instead of a conversion ratio where fission efficiency is defined as the net decrease in TRUs divided by the total amount of actinides at the end of cycle. Currently, the RBWR-TB is able to attain fission efficiency of 51% meaning that at discharge it can burn half of TRUs loaded at the beginning of cycle. Therefore, the amount of TRUs can be reduced from 100% down to less than 1% after 8 cycles of operation in the RBWR-TB. Given that the total fuel residence time in the RBWR is approximately 4 years; it would take less than 40 years to completely incinerate the TRUs left from the fuel cycle. This may be viewed as a counter-productive measure if we are to sustain nuclear power generation; however, in the case of a nuclear phase-out scenario, RBWR-TB would significantly reduce the future burden of safeguarding TRU materials which would remain radioactive for hundreds of thousands of years. The core design of the RBWR-TB differs from the RBWR-AC in that it has a shorter core height, smaller fuel rod diameter, smaller rod pitch, and larger inter-assembly gap. The height of the fissile and blanket zones are also different from RBWR-AC. The lower blanket zone is eliminated. All of these adjustments are required to enable the RBWR-TB to recycle of TRUs multiple times under a different in neutron spectrum.

The RBWR-TB2 is a modified version of RBWR-TB proposed by the Electric Power Research Institute (EPRI) [40]. Unlike RBWR-TB which was specifically designed for a nuclear phase-out scenario, the purpose of RBWR-TB2 is to reduce of the amount of TRUs from spent fuel of existing LWRs and to sustain nuclear power generation. The design of the RBWR-TB2 is somewhat similar to that of RBWR-TB except that it requires additional fissile plutonium enrichment to compensate for the reactivity penalty of LWR spent fuels. Fission efficiency of RBWR-TB2 is currently rated at 45% whereas TRU production efficiency is 22% in ABWRs. Fission efficiency is defined as a net decrease in TRUs divided by total amount of fissioned

actinides through the total fuel residence time in the core. The TRU production efficiency is an inverse quantity of the fission efficiency; it is a net increase in TRU divided by total amount of fissioned actinide at the end of cycle. Essentially, these two values indicate that the amount of TRUs produced from two units of ABWR would be suppressed by one unit RBWR-TB2.

Figure 11 compares the formation rate of TRUs (both fissile and non-fissile isotopes) in metric tons per year per reactor of conventional BWRs with that of RBWR-TB and RBWR-TB2. For conventional BWRs, these values are positive. For RBWR-TB and RBWR-TB2, negative values in both fissile and non-fissile TRU isotopes means there is a net decrease in their quantity, every operation cycle [41].

Figure 11: Rate of formation and consumption of TRUs [41].

For the application of TRU incineration in advanced LWRs, this thesis specifically focuses on RBWR-TB2 design which recently received more attention than any other variants of RBWR [42] [43] [44] [45] [46]. More details about its design, characteristics and challenges in term of fuel performance will be discussed in the next section.

2.2 General description and design characteristics of RBWR-TB2

To reduce capital and development cost, the RBWR was designed with a commonality concept in that, except the reactor core, all other components in the power plant such as steam separator, steam dryer, steam turbine, condenser, feedwater pumps are the same as currently operating ABWRs. Even the reactor core of the RBWR was designed to fit within reactor pressure vessels of existing ABWRs. The common plant specifications of RBWR and ABWR are listed in Table 2 [42]. At the plant scale, both reactors are designed to deliver the same amount of power in the same reactor pressure vessel (RPV) at the same operating pressure.

Table 2: Plant specification and core design [42]. Reactor RBWR ABWR Thermal Power (MW) 3,926 3,926 Electrical Power (MW) 1,356 1,356 RPV Diameter 7.1 7.1 Core pressure 7.2 7.2 Number of fuel bundles 720 872 Fuel lattice type Hexagonal Square Lattice pitch (mm) 199 155 Number of control rods 223 205 Control rod type Y-type Cross-shape

Figure 12(a) shows the reactor pressure vessel of the RBWR [42]. A core configuration in horizontal cross-section view is shown in Figure 12(b) [42]. It can be seen that the RBWR reactor core is composed of 720 fuel bundles, and 223 control rods which is common to all design variants of RBWR.

(a) (b) Figure 12: (a) Reactor pressure vessel of RBWR (b) Horizontal cross-section of RBWR reactor core [42].

RBWR core is designed as a parfait core concept as the axial configuration of RBWR fuel assembly employs axial segregation between seed and blanket regions to enhance fuel breeding and/or promote transmutation reactions of TRUs. As an example of this concept, an RBWR-TB2 fuel bundle is shown in Figure 13 [42]. In this design, an internal blanket of depleted uranium is placed between lower and upper fissile zones. Then the upper and lower blankets are attached the upper and lower fissile zones, respectively. This parfait design is necessary to keep the void reactivity coefficient negative when the axial power changes due to the change of void fraction during transients. Furthermore, neutron absorber zones are attached above and below the fuel zones to increase negativity of void reactivity coefficient. The upper neutron absorber rod is a

sealed tube filled with B4C pellets while the lower neutron absorber zone is filled with B4C pellets at the bottom of the fuel rod. So, in each fuel rod, there are six zones: (1) lower neutron absorber, (2) lower fissile, (3) internal blanket, (4) upper fissile, (5) upper blanket, and (6) plenum.

Figure 13: Axial and hexagonal configuration of RBWR-TB2 fuel bundle [42].

Figure 14 shows a horizontal cross-section view of the fissile zones of the RBWR-TB2 fuel bundle [42]. For this specific design, the bundle-average plutonium content as expressed in term of plutonium weight fraction is approximately 80% and 70% in the lower and upper fissile zones, respectively.

Figure 14: Horizontal configuration of RBWR-TB2 [42].

Because of its unique pattern of axial segregation between seed and blanket regions, considerable variation in linear heat generation rate (LHGR) between each zone exists. The axial power distribution in the RBWR-TB2 exhibits multiple peak spots and a very steep gradient at the fissile-blanket interfaces as shown in Figure 15 [47]. It can be seen that the LHGR in the upper fissile zone could be as high as 35 kW/m at the middle-of-life and stay above 25 kW/m throughout the cycle. This is quite a significant departure from typical operating condition of LWRs which is around 15-25 kW/m [48].

35 BOL MOL 30 EOL

15 Local LHGR (kW/m) Local LHGR 10

0 0 20406080100120 Axial Length (cm) Figure 15: Axial LHGR of the RBWR-TB2 as a function of core height [47].

Because of these peaking regions, local burnup in fissile zones are extremely high. It can be seen from Figure 16 that local fuel burnup at end-of-life are on the order of 120 and 160 MWd/kgHM in the lower and upper fissile zones, respectively. This ultra-high level of burnup has never been achieved before in LWRs [49] [50] and could pose significant challenges in term of material property degradation. Double peaking axial power distribution profiles and ultra-high local fuel burnup are one of the most important design departures of RBWRs from BWRs.

180 BOL 160 MOL EOL 140

120

100

60 Local Burnup (MWd/kgHM) 40

0 0 20 40 60 80 100 120 Time (Days) Figure 16: Local fuel burnup of the RBWR-TB2 as a function of axial node and time step.

As result of water volume reduction due to the tight hexagonal fuel lattice and increased boiling by reduction of coolant mass flow rate, core-averaged void fraction of the RBWR-TB2 is 56% whereas that of an ABWR is 36%. Relatively speaking, this is a 55% increase from current operating condition of an ABWR as shown in Figure 17 [51]. The void fraction gradient in RBWR-TB2 also differs from that of the ABWR due to axial heterogeneity configuration. It can be noticed that the void fraction rises significantly faster in the lower fissile zone of RBWR-TB2. Then it tends to decrease in the internal blanket zone. Upon reaching the upper fissile zone, the void fraction rises again to reach 80% void fraction at core exit. On the other hand, the void fraction in the ABWR steadily increases from core inlet to exit. Although the core flow rate of RBWR-TB2 is reduced by a factor of 2.5 when compared to ABWR, with significantly higher core exit quality and void fraction, steam flow rate to turbine can be maintained at a similar level of an ABWR.

Figure 17: Axial void fraction of RBWR-TB2 as a function of relative core height [51].

A comparison of the neutron spectra of the RBWR-AC, RBWR-Th, ABWR as a representative of LWR and an SFR as a representative of fast breeder reactor is given in Figure 18 [52]. The neutron spectra of the RBWR-TB and RBWR-TB2 are not included here because they are not publically available yet. However, they are expected to be quite similar to that of RBWR-AC and RBWR-Th. As can be seen from the figure, the ABWR shows a typical neutron spectrum for a water-cooled reactor—double peaks in neutron flux at thermal (~0.1 eV) and fast (~1 MeV) energy regions. The neutron spectrum of the SFR also exhibits a usual behavior of fast reactors—a mountain-like spectrum with a single peak at around 0.5-1 MeV with higher neutron flux intensity than LWRs. With several design techniques to reduce moderation, it can be clearly seen that neutron thermalization and thermal flux peaks no longer exist in RBWRs. In fact, their neutron spectra look a lot like that of fast reactors. Furthermore, both types of RBWRs have a significantly higher portion of neutron at energy above 1 MeV and in epithermal energy than the SFR making it possible to breed sufficient fissile materials to achieve a conversion ratio of 1.0 and can perpetually recycle plutonium and minor actinides. With this hardened neutron spectrum, it is also possible to burn TRU wastes in RBWR-TB2 design.

Figure 18: Comparison of normalized neutron spectra for the RBWR-AC, RBWR-Th, SFR and ABWR [52].

2.3 Material challenges associated with RBWR-TB2

Although the RBWR-TB2 was designed based on the proven technology of the ABWR, its unique characteristics necessitate further considerations especially in terms of thermo- mechanical behaviors throughout fuel cycle. As can be clearly seen from Figure 19, the axial peaking factor of RBWR-TB2 is extremely high and discontinuous especially at fuel-blanket interfaces in order to keep core thermal output the same as with the ABWR with much shorter fuel length (around 1 m in RBWR-TB2 and 3.7 m in ABWR). In fact, the active fuel zone of RBWR-TB2 is even shorter than 1 m because it has to accommodate the blanket region which roughly takes approximately half of the total fuel length. As a result, the axial peaking factor of the RBWR-TB2 peaks at around 2.5-2.6 in the upper fissile zone at the beginning-of-life (BOL) and middle-of-life (MOL). These peaks tend to decrease as burnup increases and the blanket zone takes part in power generation toward the end-of-life (EOL). On the contrary, the axial peaking factor of the ABWR is considerably smoother with lower-magnitude peaks at around 1.5-1.6—a typical values of LWRs. Significant LHGR variation at the fuel-blanket interfaces would directly result in a very steep temperature gradient and it would likely cause additional thermal stress in the cladding due to differential thermal expansion.

4 ABWR BOL 3.5 ABWR MOL ABWR EOL RBWR-TB2 BOL 3 RBWR-TB2 MOL RBWR-TB2 EOL 2.5

1.5

0.5

0 0 0.5 1 1.5 2 2.5 3 Axial peaking factor Figure 19: Axial peaking factor vs. core height of ABWR and RBWR-TB2.

When compared to the ABWR, RBWR-TB2 fuel was designed to operate at higher peak burnup, higher linear heat generation rate (LHGR), and higher fast neutron fluence. Operating at higher LHGR may result in significant increase in fuel temperature and create several undesirable effects such as increased fuel swelling, fuel thermal expansion and fission gas release. High local burnup in the fissile zones could impact the degradation of material properties such as fuel density, fuel thermal conductivity which is heavily affected by fission product contamination, oxygen-to-metal (O/M) ratio, porosity, and microstructural changes. Therefore, several physical phenomena at high temperature and high burnup regime such as fuel restructuring, fuel constituent redistribution, and fission product migration are expected to occur in RBWR-TB2.

Figure 20 schematically shows the effect of excessive fuel swelling and thermal stresses on fuel and cladding deformation. From a uniform cylindrical shape, thermal stress causes a fuel pellet to crack and form an hourglass shape. During operation, fuel swelling will cause the fuel and cladding to be in direct contact when the gap between fuel and cladding closes at high burnup. At

61 this stage, the cladding will deform into a shape reflecting that of the fuel pellet making the cladding to look like a bamboo stalk. Direct contact between fuel and cladding adversely affects cladding integrity because it increases mechanical load and the risk of cladding failures from chemical interactions with corrosive fission products such as iodine and cadmium which will eventually lead to stress-corrosion cracking [53]. The failure from hard contact between fuel and cladding is termed pellet-cladding interaction (PCI). An example of cladding failure from stress corrosion cracking from hard contact and missing pellet fragment is shown in Figure 21.

Figure 20: Effect of fuel swelling and thermal stress [53].

Figure 21: Consequence of pellet-cladding interaction (PCI) [53].

In addition, the fast neutron flux of RBWR-TB2 is higher than a conventional BWR because of harder neutron spectrum; therefore, at the same burnup, irradiation damage in structural

components such as fuel cladding, control rods, channel box from fast neutrons is expected to be higher. Particularly for fuel cladding, higher fast neutron fluence may lead to acceleration of corrosion and hydriding in zirconium alloy cladding after a complete dissolution of secondary phase particles (SPPs) after neutron fluence threshold is exceeded [8] [9] [54]. The presence of zirconium hydride severely degrades mechanical strength of metallic zirconium cladding and results in a loss of ductility. As water flow through the core and is exposed to neutron and gamma irradiation, a wide variety of radiolysis products are generated. The most commons

species are H2 and H2O2. H2O2 can then decompose to O2 and H2O and remain dissolved in the

water. The presence of oxidants like H2O2 and dissolved O2 in the water increases the corrosion potential of the cladding. Naturally, free hydrogen radicals produced from radiolysis can recombine with the dissolved oxygen, become water molecules, and buffer the corrosion potential. However, this dissolved hydrogen can easily be lost once the water turns into steam

near top of the core as the H2 concentration in the water drops dramatically after boiling occurs. With increased boiling, the water chemistry of RBWR-TB2 is expected to be somewhat different

than that of the ABWR. In this case, the concentration of dissolved H2 in the core of RBWR-TB2 should be lower from higher core exit quality and core-averaged void fraction. In addition, the

effect of radiolysis, the concentration of dissolved O2, and the corrosion potential of water in the core of RBWR-TB2 are expected to be higher than in ABWR because of an increase in fast neutron flux.

Therefore, to accurately model the behavior of fuel rods under the conditions of RBWR-TB2, these design characteristics and physical phenomena at high temperature and high burnup have to be taken in account when performing thermomechanical analysis of fuel behavior. All of these phenomena relevant to RBWR-TB2 are modeled and discussed in Chapter 4.

Chapter 3

Evaluation of Thermal Conductivity Correlation for Mixed Oxide Fuels

Thermal conductivity is one of the most important material properties for fuel performance modeling because it dictates the fuel temperature distribution within fuel pellets. Fuel temperature relates directly or indirectly to all life-limiting parameters such as fission gas release, fuel melting, fuel swelling, and pellet-cladding interactions (PCI). Therefore, accurate prediction of thermal conductivity is a key element to achieve reliable simulation results for the thermo-mechanical behavior of fuel rods.

The objective of this work is to find an appropriate correlation for MOX fuel for use in the RBWR-TB2 which likely deviates from the applicability of default correlations in FRAPCON- 3.5 in terms of fuel burnup and plutonium weight fraction effects.

FRAPCON-3.5 currently has three options for thermal conductivity correlations: (1) Modified

NFI for UO2 and (U,Gd)O2, (2) Duriez-Modified NFI for MOX and (3) Halden for UO2,

(U,Gd)O2 and MOX. The Halden correlation is provided as an option while the other two are default models. These correlations are recommended up to a rod-average burnup of 62 MWd/kgHM which corresponds to a peak local burnup of around 150 MWd/kgHM at the pellet edge in LWRs. However, RBWR-TB2 fuel rods are designed to reach a higher rod-average burnup of roughly 70 MWd/kgHM with a peak local burnup of around 160 MWd/kgHM in fissile zones. Therefore, the applicability of these correlations needs to be re-evaluated using more recent experimental data.

For the MOX fuel option in FRAPCON-3.5, the Duriez-Modified NFI correlation is applicable for plutonium content from 3 to 15% weight fraction. According to Duriez [55], the effect of plutonium content on thermal conductivity in this range is negligible. In other words, thermal

conductivities of MOX at 3 to 15 wt% PuO2 are the same in Duriez-Modified NFI correlation.

However, the RBWR-TB2 was designed to use (U-TRU)O2 mixed oxide fuel which comprises

20% depleted UO2, 70% PuO2, and 10% Minor Actinides (NpO2, AmO2, CmO2, etc.) by weight. The effect of higher weight fraction of plutonium with addition of minor actinides should thus be carefully examined.

In this section, the brief history of MOX thermal conductivity correlations during the last three decades is presented. Emphasis is given on the selection and evaluation of default correlations from earlier to recent versions of FRAPCON. Then, we will compare a default correlation for MOX in FRAPCON-3.5, Duriez-Modified NFI, with other alternatives from the open literature.

Generally, development of thermal conductivity correlations can be categorized by type of samples: fresh and irradiated fuels and by type of measurements: in-pile fuel temperature and out-of-pile thermal diffusivity. Irradiated fuels can be measured both in-pile and out-of-pile but fresh fuels have to be measured out-of-pile to avoid irradiation effects. Direct out-of-pile measurement tends to be more reliable because important parameters can be controlled individually whereas reproducibility for in-pile measurement cannot be fully ensured. From out- of-pile measurement, thermal conductivity is derived from thermal diffusivity, density and heat capacity which are well-defined in the laboratory environment. The evaluation of thermal conductivity from in-pile temperature measurement is less accurate because of its integral nature in the reactor environment. To calculate thermal conductivity from in-reactor centerline temperature measurement, one has to solve a radial heat transfer equation from fuel pellet center to cladding outer surface which involves some uncertainties from estimation of fuel-cladding gap conductance.

3.1 Parameters affecting thermal conductivity

Fuel thermal conductivity depends on various parameters acting at different length scales. Most of them dynamically change during in-pile irradiation. At the macroscopic scale, temperature and burnup are two dominant factors because they generally represent the state of the fuel. High temperature represents the state of disorder in the crystal lattice and triggers another heat transfer mechanism through electron conduction. Fuel burnup represents the state of impurities and microstructural damage of the fuel. It can be viewed as a collective term which implicitly includes various effects from irradiation such as fission product contamination and

65 microstructural damage. Microscopic parameters such as stoichiometry (oxygen-to-metal ratio), and additive content (Pu, Gd, Cr) also play a critical role in determining thermal conductivity.

For non-conducting ceramics such as UO2 and MOX, heat is primarily transferred though atomic vibration. In this case, any microscopic perturbation to perfect crystal lattice would contribute to thermal conductivity degradation. Figure 22 illustrates parameters affecting thermal conductivity at microscopic scales where it can be further subdivided into mesoscopic and atomic level contributions.

Figure 22: Parameters affecting thermal conductivity [56].

Mesoscopic-level parameters involve imperfections in the microstructure of the oxides such as porosity, fission product precipitates, and intra-granular and inter-granular bubbles of fission gases. For fission products that are insoluble in the fuel matrix, they exist in the form of oxide precipitates, metallic inclusions, and inert gas atoms. Their impacts on thermal conductivity can be estimated by composite material correlations such as the Maxwell-Eucken or Loeb formulae [57] [58].

Atomic-level parameters are point defects including vacancies, interstitials, and substitutions of impurity atoms in the lattice such as Pu, Gd and fission products. Both point defects and substitutional atoms induce static displacements of host atoms from their equilibrium lattice sites. They serve as phonon scattering centers due to the differences in inter-atomic bonding

66 potential, ionic radii, and atomic mass, thereby limiting the phonon mean free path and lowering the rate of heat transport. Their effects are usually modeled in a form of k = 1/(A+BT) where k is thermal conductivity, A is a collective term representing thermal resistance due to phonon scattering by point defects and substitutional atoms and BT represents intrinsic lattice thermal resistance from phonon-phonon scattering. Stoichiometry or oxygen-to-metal ratio (O/M) has a major impact on overall thermal conductivity because it represents the state of oxygen vacancies in hypo-stoichiometric fuel (O/M < 2.0) or oxygen interstitials in hyper-stoichiometric fuel where (O/M > 2.0.).

During operation, fuel chemical composition, lattice structure and microstructure change markedly under intense neutron irradiation and high temperature. Because of their complexity and inter-correlation, it is difficult to isolate and model their effects individually. In practice, a number of parameters in thermal conductivity correlations are often reduced by retaining only the most influential parameters in the correlations while the effect of other parameters are implicitly taken into account by adjusting the models to experimental results.

In general, thermal conductivity of oxide fuels can be expressed as

1 k= +Ce (1) A+BT where the first term 1/(A+BT) represents lattice conduction by phonons and the second term CeDT represents high-temperature conduction through electron pair mobility. At temperatures below 1600 K, electron conduction is negligible. However, it becomes an important mode of heat transfer above 2000 K. Electronic contribution to thermal conductivity at high temperature is an important feature of UO2 because it does not exist in ThO2 and PuO2. This is because the presence of 5f valence electron at -2.3 eV in UO2 helps narrowing the gap between valence and conduction bands [59]. As shown in Figure 23, both ThO2 and PuO2 have larger valence- conduction band gaps at -6 eV [59]. This large energy barrier makes it very difficult for valence electrons in ThO2 and PuO2 to jump over the band gaps to the conduction bands and transfer the heat even at high temperature. From this information, ThO2 and PuO2 are classified as pure electronic insulators while UO2 can be viewed as semi-conductor at high temperature.

Figure 23: Electron density of state of UO2 (a), ThO2 (b), and PuO2 (c) [59].

Fuel burnup introduces several atomic perturbations such as soluble fission products, non- stoichiometry, interstitials, vacancies, and substitutions of foreign atoms. In general, thermal conductivity decreases with increasing burnup. To take into account the effect of burnup into the phonon conductivity term 1/(A+BT), there are two approaches: (1) modifying the empirical constants A and BT and (2) formulating multiplying factors based on fuel burnup. In the first approach, linear or quadratic equations may be used to capture burnup dependency in the phonon-defect (A) and phonon-phonon (BT) terms. For example, from constant values of fresh fuel, they may be changed to a burnup-dependent equation as A0+A1*bu and (B0+B1*bu)T where bu is fuel burnup, T is fuel temperature and A0, A1, B0, and B1 are new empirical constants derived from irradiated data. In the second approach, multiplying factors are formulated based on irradiated data without modifying original empirical constants derived from unirradiated data.

3.2 Thermal conductivity correlations for mixed oxide fuels

Due to complexity and inter-correlation of various parameters, especially burnup and material defects, thermal conductivity correlations for nuclear fuels are often derived from experiments by which certain mathematical functions are formulated with some empirical parameters to

68 match experimental data. Although there have been some efforts to evaluate thermal conductivity from computational atomistic simulation, these simulation results are only applicable to fresh fuel [60] [61] [62] [63] [64] [65] [68] [67] [70] [69] [70] [71]. They did not extend their evaluation beyond zero burnup potentially because of the complexity and uncertainty in representing atomic models of nuclear fuels at high burnup.

For oxide fuels, a number of thermal conductivity measurements have been carried out since the 1960s and since then a number of empirical correlations based on original measurements or literature review have been proposed [55] [72] [73] [74] [75] [76] [77]. In this section, the focus is given to experimental programs and thermal conductivity correlations developed for MOX fuel. Direct experimental programs for MOX thermal conductivity are somewhat underrepresented when compared with UO2 [56]. Before describing thermal conductivity correlations, it is worth to mention experimental results published over the years on thermal diffusivities for both fresh and irradiated samples. Experiments related to fresh samples will be covered first followed by irradiated ones. It is also beneficial to mention the difference between

MOX for light water reactors (LWR) and fast reactors (FBR). For LWR MOX, the PuO2 weight fraction is typically below 15% whereas it will be greater than 20% for FBR MOX. This is because of differences in fission cross sections in thermal and fast spectrum.

For unirradiated samples, Gibby evaluated thermal conductivity of fresh samples of UO2, PuO2 and MOX from 5 to 30 wt% PuO2 from laser-flash thermal diffusivity measurements [78]. The study observed a systematic reduction in thermal conductivity as a result of plutonium addition into the UO2 matrix. Using a simplified theory of lattice defect thermal resistance in dielectric solids, the model predicts that the thermal conductivity of MOX is lowest at 70 wt% PuO2.

Fukushima et al. [79] studied the effect of fission product addition (Nd and Eu) to MOX thermal conductivity. In this work, thermal diffusivities of near-stoichiometric MOX at 20 wt% of PuO2 with small additions of Nd and Eu up to 10 mol% were measured. It was found that the addition Nd and Eu gradually decreased MOX thermal conductivity. Thermal resistivity derived from lattice defect models agreed well with measurements. It was also found that the effect of lattice strain is more important than the effect of mass difference.

However, Schmidt et al. [80] [81] and Beauyy [82] [83] published contradicting results to that of

Gibby. They observed that the inclusion of Pu into UO2 matrix reduces overall thermal conductivity but not in a continuous way. In the range of 0 to 22 wt% PuO2, Beauyy noticed two local maximum at around 3 and 15 wt% PuO2 while Schmidt et al. found a local maximum at 15 wt% PuO2.

Bonnerot [84] conducted thermal diffusivity measurement of 18 values of PuO2 weight fraction from 0 to 100 wt%. It was found that the addition of PuO2 has moderate effect of MOX thermal conductivity. For stoichiometric MOX at 20 wt% of PuO2, the thermal conductivity was found to be 6% lower than stoichiometric UO2.

Duriez et al. [55] carried out a number of measurements on fresh MOX samples with Pu concentration from 3 to 15% and found that MOX thermal conductivity was significantly lower than that of UO2. It was also observed that the effect of PuO2 in the range of 3 to 15 %wt was negligible. Thermal diffusivity measurement of higher PuO2 concentration at 21.4 wt% was also conducted and the results were found to be significantly lower than samples in the range of 3-15 wt% PuO2. The study concluded that there was a significant difference in thermal conductivity for FBR and LWR MOX due to PuO2 concentration and microstructure caused by the addition of PuO2 into UO2 matrix.

Morimoto et al. [85] [86]measured thermal conductivity of (U,Pu,Am)O2 at 30 wt% of PuO2 and

0.7-3 wt% of AmO2 from 900 to 1773 K. The studied found that the presence of Am slightly decreased the thermal conductivity of the mixtures. The experimental results fitted well with a classical phonon transport model of 1/(A+BT) up to about 1500K. It was observed that the coefficient A increased linearly with Am content but small variation for the coefficient B.

Sengupta et al. [87] investigated the thermal conductivity of stoichiometric MOX at 44 wt%

PuO2—the highest PuO2 concentration in open literature. As expected, thermal conductivity of

MOX at 44 wt% PuO2 was found to be noticeably lower than MOX at 30 wt% PuO2. o Reportedly, at 1273 K (1000 C), thermal conductivity of MOX containing 44 wt% PuO2 was found to be 1.803 W/m/K while that of 30% PuO2 was 2.326 W/m/K. Similar to Gibby [78] and

Martin [88], this study confirmed the effect of PuO2 content on thermal conductivity reduction of MOX.

Morimoto [89] performed thermal diffusivity measurement of hypo-stoichiometric and stoichiometric MOX fuels at temperature from 990 to 2190 K using the laser flash method. This study intended to correlate the effect of high temperature to oxygen-to-metal ratio of the samples. They observed a reduction in O/M for stoichiometric samples above 1800 K while they found no significant changes in O/M for samples with O/M less than 1.95.

Staicu [90] investigated the effect of heterogeneity in fresh MOX fuel by comparing samples manufactured differently with different microstructures. For homogenous MOX fuel, samples came from SBR (Short Binderless Route) route with 4.8, 5.6 and 11.1 wt% PuO2 and a sol-gel

MOX with 7.8 wt% PuO2. The heterogeneous fuels were MIMAS (Micronized Master Blend)

MOX with 7.0 and 9.0 wt% PuO2. It was observed that the thermal conductivity of homogenous

MOX fuel was close to that of UO2 and the weight fraction of PuO2 does not have significant impacts on thermal conductivity. However, thermal conductivity of heterogeneous MOX fuel was found to be significantly lower than homogenous MOX and UO2. Given a similar PuO2 content of both homogenous and heterogeneous samples, it was pointed out that the main cause of thermal conductivity difference was due to the stoichiometry effects and this difference tends to disappear at high burnup.

Prieru et al. [91] measured various thermal properties including thermal conductivities of fresh samples of Np-MOX and Am-MOX which are mixed oxides of uranium and plutonium with small additional neptunium and americium. The uranium and plutonium weight fraction were 74% and 22%, respectively. The addition of Np was in the range of 0.5-2wt% and 0.35-2 wt% for Am. It was found that Np-MOX has a slightly higher thermal conductivity than Am-MOX.

However, both samples had lower thermal conductivity than UO2 but comparable, within 10% measurement uncertainty, to thermal conductivity of LWR MOX and FBR MOX from literature sources.

For irradiated samples, Yamamoto et al. [92] measured thermal conductivities of FBR MOX with 28.8 wt% at 0.5 MWd/kgHM and 17.7 wt% Pu at 8, 10 and 35 MWd/kgHM but surprisingly did not clearly observe thermal conductivity degradation due to burnup.

A series of experiments have been carried out at the Halden reactor to investigate the effect of burnup on thermal properties of both UO2 and MOX [93] [94] [95]. High burnup was achieved by retrieving fuel rods from commercial BWRs, refabricating them into instrumented fuel rods equipped with centerline thermocouples, pressure gauge, cladding elongation detector, and finally re-irradiating these test rods in the Halden boiling water reactor (HBWR). Reported burnup of these samples for MOX and UO2 test rods were 84 and 72 MWd/kgHM, respectively [96]. Fresh MOX fuel rods were also tested at the Halden reactor [97]. With on-line instrumentation capability, it was possible to continuously monitor the evolution of fuel centerline temperature and internal rod pressure since the beginning of irradiation which corresponds to fuel burnup from 0-32 MWd/kgHM. However, due to the nature of in-pile reactor experiments, fuel thermal conductivities were not directly measured. Instead, the researchers had to rely on various in-situ measurements such as centerline temperature, internal rod pressure, fuel dimension to formulate thermal conductivity correlations which introduced many uncertainties in both measurements and theoretical models. Alternatively, these experimental results were used to benchmark other correlations developed from direct out-of-pile thermal diffusivity measurements [96] [97] [98].

Cuzzo et al. [99] reported thermal diffusivity of irradiated UO2 and MOX samples with fuel burnup in the range of 31-36 MWd/kgHM. Thermal conductivity was inferred from laser-flash diffusivity measurement. It was found that, at similar burnup, the thermal conductivity of UO2 and MOX was in the same range. One thing to note about this finding was that the PuO2 content in MOX samples before irradiation was relatively small (3.7 wt%). So, the effect of plutonium depletion in MOX and plutonium buildup in UO2 may contribute to this behavior.

Staicu et al. [100] measured thermal diffusivity of LWR MOX at 23, 42, 44 and 47 MWd/kgHM from MOX samples fabricated from different methods i.e. SBR, MIMAS, and OCOM. SBR (Short Binderless Route) yields a homogenous distribution of plutonium in the matrix whereas MIMAS (Micronized Master Blend) and OCOM (Optimized Co-milling Method) provide

72 heterogeneous microstructure of the MOX samples. The results suggested that there thermal conductivities were not significantly different between homogeneous and heterogeneous MOX.

Nakae et al. reported another experiment at the Halden reactor on high burnup fuel rods up to 74

MW/kgHM [101]. Fuel samples were LWR MOX (8.4 wt% PuO2), and UO2 (8% enrichment).

Both heterogeneous (MIMAS) and homogenous (SBR) MOX and UO2 fuel rods were taken from commercial PWRs, re-fabricated and re-instrumented into instrumented fuel assemblies (IFA). Thermal conductivities were indirectly inferred from plots of centerline temperatures vs. linear heat generation rates (LHGR). In this case, higher thermal conductivity corresponded with to lower fuel temperature given the same amount of LHGR increase. It was unexpectedly found that the thermal conductivity of UO2 was less than that of MOX at 80 MWd/kgHM. Various speculations were given to explain this experimental finding such as non-stoichiometry, cracking, porosity and microstructure. However, no definitive causes of these counter-intuitive findings were confirmed and more direct thermal conductivity or diffusivity measurements were needed to confirm these results.

There are a sizable number of correlations for fresh MOX that have been proposed over the years [102] [55] [72] [75]; most of them were developed from out-of-pile thermal diffusivity measurements or literature reviews of published experimental data. In this thesis, the work of Philipponneau et al., Duriez et al., Inoue et al. and Baron et al. are presented.

Philipponneau [102]proposed a correlation based on a literature review of thermal diffusivity measurements of FBR MOX at approximately 20 wt% PuO2. Both stoichiometric and nonstoichiometric fuels were included in the formulation. In this work, the fuel composition was written in short form as U0.8Pu0.2U2-x where x represents a deviation from stoichiometry. In this case, when x is equal to zero, it means that the fuel is at stoichiometric composition and the subscripted numbers represent mole fraction of each constituent. For fresh MOX, the correlation takes into account the effect of temperature, non-stoichiometry, and porosity. However, Philipponneau suggested that the effect of plutonium content in the range of 15-30 wt% in MOX fuels should be ignored. The Philipponneau’s correlation is given by:

1 = + 76.38 × 10 (2) 1.528√ + 0.00931 − 0.1055 + 2.885 × 10

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

T = temperature in range of 500 K < T < 3000 K

x = deviation from stoichiometry = |2.0 – O/M|

α = porosity adjustment term = × .

p = fractional porosity (% TD)

Duriez [55] performed comprehensive thermal diffusivity measurements of hypo-stoichiometric

LWR MOX where the PuO2 weight fraction was in the range of 3 to 15%. The range of oxygen- to-metal ratio examined was between 2.00 to ~1.95. Temperature ranges from 700 to 2300 K.

The study found that thermal conductivity of MOX is significantly lower than that of UO2 although Duriez et al. did not recommend this correlation for MOX with PuO2 weight fraction less than 3%. Likewise, this correlation was not recommended for MOX with plutonium content greater than 15%. To substantiate this recommendation, another set of measurements were

performed with FBR MOX at 21.4 wt% PuO2 and LWR MOX at 15 wt% PuO2 and the results confirmed that MOX at 21.4 wt% PuO2 has significantly lower thermal conductivity than LWR

MOX at 15 wt% PuO2. However, in this work, the plutonium content in the range of 3-15 wt% had a negligible impact to thermal conductivity of the mixtures; therefore, this parameter was not included into the correlation. The Duriez’s correlation for fresh MOX thermal conductivity is given below:

1 1.689 × 10 13520 = + − (3) 2.85 + 0.035 + (2.86 − 7.15) ×10

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

T = temperature in range of 700 K < T < 2600 K

x = deviation from stoichiometry = |2.0 – O/M|

α = porosity adjustment term =

p = fractional porosity (% TD)

Inoue [72] re-examined Philipponneau’s correlations and found that it tends to underestimate the thermal conductivity when compared with short-term irradiation experiments in JOYO—an experimental fast reactor in Japan. A new correlation was proposed based on extensive experimental data for unirradiated samples. The source of data included those that were used to develop Philipponneau’s correlations plus some additional data points from literature. To convert thermal diffusivity data to thermal conductivity, the specific heat correlation from Fink [103] and the fuel density and porosity correction formula from Loeb [57] were incorporated into the correlation. Inoue used a general formula as proposed by Harding and Martin [104]and fitted empirical constants to match the data points. For the high temperature electronic conductivity

part, Inoue used a correlation developed for UO2 by Harding and Martin [104] and cited the work

of Ronchi [105] which found that, above 2400 K, thermal conductivity of MOX and UO2 are similar [72]. Similar to Philipponneau’s correlations, this correlation also does not separately treat the effect of plutonium content and is applicable for MOX with PuO2 in the range of 15-30 wt%. This new correlation gave a better prediction of centerline fuel temperature than Philipponneau’s correlations and it was recommended for FBR MOX fuel. The Inoue’s correlation for fresh MOX is given by:

1 4.715 × 10 16361 = + − (4) 0.06059 + 0.2754√ + 2.011 × 10

where k100 = thermal conductivity of MOX at 100% TD (W/m/K)

T = temperature in range of 700 K < T < 2600 K

x = deviation from stoichiometry = |2.0 – O/M|

Note that Inoue proposed the correlation at 100% TD and did not incorporate a porosity correction factor and left it as a user’s defined adjustment.

Baron and Couty reviewed thermal diffusivity measurements of UO2 and UO2-Gd2O3 conducted in the framework of NFIR program [75] and proposed a unified correlation applicable for UO2,

UO2-Gd2O3 and LWR MOX when PuO2 weight fraction is less than 10%. The ranges of applicability are: temperature from 250 to 1800 K, Gd2O3 content from 0 to 12 wt%, oxygen-to- metal ratio from 1.995 to 2.045. Loeb and Roess’s correlation was chosen as the porosity correction term. Similar to previously mentioned correlations, this correlation disregards the effect of plutonium content in MOX when PuO2 is less than 10 wt%. The Baron and Couty’s correlation is given by:

1 = + α() (5) +++ + ( ++ )

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

A0 = 0.0524 A1 = 4.0 A2 = 0.3079 A3 = 12.2031

-4 -4 B0 = 2.553x10 B1 = 8.606 x10 B2 = -0.0154

T = temperature in oC

x = deviation from stoichiometry = |2.0 – O/M|

×() α(T) = temperature-dependent porosity adjustment term = .()

β (T) = 2.7384-0.58x10-3T if T < 1273.15 oC or β (T) = 2 if T >= 1273.15 oC

p = fractional porosity (% TD)

The above correlations are developed as stand-alone correlations for fresh MOX fuel. To take into account the effect of burnup, they may be combined with burnup dependent terms which take into account the effects of fission product, radiation damage and thermal annealing. These burnup correction terms can be formulated as separate multiplying factors or adjustments to phonon-defect (parameter A) and phonon-phonon (parameter B) in the standard 1/(A+BT) lattice

conduction model. Some correlations may cover both fresh and irradiated fuel. In this case, the effect of burnup is already included in the correlations. However, due to the small number of experimental samples and difficulties in isolating the effect of individual parameters, burnup dependent terms in MOX thermal conductivity correlations are often derived from measurement of irradiated UO2 samples at high burnup.

Ohira and Itakagi [73] proposed a NFI (Nuclear Fuel Industries) correlation based on their experimental data for UO2 up to 61 MWd/kgHM as shown in Equation 6. From the original phonon transport equation of 1/(A+BT), they proposed that the effect of fission products can be modeled by modifying the phonon-defect parameter A as a linear function with burnup and, f(bu) the effect of radiation damage slightly evolves with burnup, g(bu). A temperature annealing term, h(T), is used to reduce the effect of radiation damage at high temperature.

1 = + +D (6) () + ()+() +()ℎ()

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

T = temperature in range of 300 K < T < 3000 K

x = deviation from stoichiometry = |2.0 – O/M|

A = 2.85x+0.035 m-K/W

B = (2.86-7.15x)*10-4 m/W

C = -5.47*10-9 W-K/m

D = 13520 K

f(bu) = effect of soluble fission products in the matrix = 0.00187*bu

g(bu) = effects of irradiation defects = 0.038*bu0.28

h(T) = temperature annealing of irradiation defects =

This correlation was chosen by PNNL [98] to be used in FRAPCON-3.3 with some modifications of the electron thermal conductivity term. Instead of using 3rd and 4th order polynomials with temperature, Lanning modified the electronic conduction term with an Arrhenius form C/T2*exp(-D/T) using experimental data from Caroll et al. [106] and Ronchi et al. [107]. Later, the effect of gadolinium oxide was incorporated into the correlations. This new correlation was termed modified NFI for high burnup UO2 fuel.

For MOX fuel, Lanning applied the fresh MOX thermal conductivity proposed from Duriez. This correlation was developed from out-of-pile thermal diffusivity measurements of fresh MOX

samples with 3-15 wt% PuO2. The effect of non-stoichiometry was taken into account by modifying the phonon-defect parameter A(x) and phonon-phonon interaction terms as B(x) where x is a deviation from stoichiometry (x = |O/M-2|). Lanning chose burnup dependent terms (f(bu),g(bu) and h(T)) from the NFI correlation to describe the degradation mechanism of MOX thermal conductivity at high burnup. PNNL also added a multiplying term to g(bu)h(T) to reduce the effect of annealing at low burnup (< 20 GWd/kgHM) and brings it back to nominal value at higher burnup. The pre-exponential constant for electronic conductivity terms was slightly reduced from the Duriez correlation and this new correlation is termed Duriez-Modified NFI as shown in Equation 7. It is the default and recommended thermal conductivity correlation for LWR MOX in FRAPCON-3.3 or newer.

1 = + (7) () +×+()+() +1−0.9(−0.04)()ℎ()

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

T = temperature in range of 300 K < T < 3000 K

x = deviation from stoichiometry = |2.0 – O/M|

a = 1.1599, gad = weight fraction of gadolinia (Gd2O3)

A = 2.85x+0.035 m-K/W

B = (2.86-7.15x)*10-4 m/W

9 Cmod = 1.5*10 W-K/m

D = 13520 K

f(bu) = effect of soluble fission products in the matrix = 0.00187*bu

g(bu) = effects of irradiation defects = 0.038*bu0.28

h(T) = temperature annealing of irradiation defects =

Another approach to evaluate the thermal conductivity of irradiated fuel is to manufacture oxide fuel with fission products artificially added into the matrix. This way, the condition of nuclear fuel at high burnup can be simulated. Fresh fuels with fission product additives are collectively termed as SIMFUEL. For MOX fuels, there were two prominent experimental works on SIMFUEL measurement. Hartlib [108] evaluated the degradation of thermal conductivity of SIMFUEL MOX from artificial fission products mixed in the matrix and then Philipponneau developed a thermal conductivity correlations based on this experimental data for FBR MOX. The most comprehensive work of SIMFUEL evaluation was presented by Lucuta et al. [74] who proposed that the effect of burnup on fuel thermal conductivity can be separated into 4 different multiplying factors as shown in the Equations 8-13:

= (8)

1.09 0.0643 1 = + √ (9) . 1.09 0.0643 √ + √ . √

0.019 × 1 =1+ (10) − 1200 3 − 0.019 × 1+− 100

1− = (11) 1+(−1)

= 1.0 (12) 0.2 =1− (13) − 900 1+− 80

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

T = temperature (K)

bu = burnup in atom% (1 atom% = 9.383 MWd/kgHM)

s = shape factor (= 1.5 for spherical pores)

p = porosity fraction

In this formula, k0 is the unirradiated thermal conductivity of UO2 or MOX at 100% TD. The

effects of plutonium content and non-stoichiometry can be optionally included into the k0 term.

F1 represents the effect of soluble fission products contamination in the lattice. F2 characterizes

the effect of non-soluble fission products as metallic inclusions and oxide precipitates. F3 accounts for the effect of porosity and bubble contribution using the Maxwell-Eucken formula

for composite materials. F4 refers to the effect of non-stoichiometry by which Lucuta et al. assumed this factor to be 1.0 as the fuel is assumed to be stoichiometric. F5 describes the effect of radiation damage which can be recovered when fuel temperature is in the range of 600-1200 K.

The Lucuta correlations have been widely adopted in many fuel performance codes [109] [110] because of its modular structure where they can be applied to any unirradiated thermal conductivity correlations. Previously in FRAPCON-3.2, an outdated version of FRAPCON developed since 1997, a correlation proposed by Fink was adopted for thermal conductivity of

UO2. Various burnup dependent terms as suggested by Lucuta were later incorporated to account for the effect of burnup [98]. The Lucuta model was compared with both in-pile and out-of-pile experiments of Ohira and Itagaki [73] and Lanning [98] and the results suggested that it overestimated thermal conductivity at high burnup although the model gave reasonable predictions of experimental results reported by Minato et al. [111].

From the NFIR framework, Baron [112] also developed a new set of correlations developed from

experimental data for irradiated UO2 up to 80 MWd/kgHM. Note that this correlation has different empirical parameters as shown in Boron’s correlation for unirradiated fuel. The effect

of burnup, non-stoichiometry, PuO2 and Gd2O3 are included as modification of parameters A and B. As shown in Equation 14, the effect of non-stoichiometry is modeled as a linear dependence term to the A as A1x. The effect of plutonium is modeled as a linear dependence term to the

parameter B as B1q. Finally, the effect of Gd2O3 is modeled as quadratic expansion terms to both 2 2 parameters A and B as A2g+A3g and B2g+B3g . The effect of burnup was taken as a modification to lattice parameters of the oxides which can be expressed as quadratic functions

with burnup as shown in parameters A0 and B0 of the Equation 14. Note that electronic conductivity term is not affected by burnup. The Baron’s correlation of irradiated fuels is given by:

1 + = + − (14) +++ + ((1+) ++ )

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

-2 -3 -5 2 A0 = 4.645x10 +7.792 x10 bu-3.422 x10 bu

A1 = 4.0 A2 = 0.611 A3 = 11.081

-4 -6 -8 2 B0 = 2.123x10 -2.292 x10 bu+1.328x10 bu

-4 -2 B1 = 0.8 B2 = 9.603x10 B3 = -1.768x10

C = 5.516x109 D = -4.302x1010 W-K/m W = 1.41-1.6x10-19 J

k = Boltzmann’s constant = 1.38x10-23 J/K

T = temperature in K

bu = burnup in MWd/tHM

x = deviation from stoichiometry = |2.0 – O/M|

g = gadolinium oxide weight fraction

q = plutonium oxide weight fraction

Based on extensive in-reactor data for fuel temperature and LHGRs of various test rods at the Halden reactor, Wiesenack and Tverberg developed self-contained thermal conductivity

correlations for UO2, UO2-Gd2O3 and MOX known as the Halden correlations [76]. Without reliance on an external source of burnup dependent terms, these correlations are applicable for both fresh and irradiated fuels. The original correlation did not include dependence on stoichiometry but when cited by Lanning [98] it was modified with a stoichiometry term. Similar

empirical constants are applied for both UO2 and MOX in this correlation. However, a factor of

0.92 was used to multiply the phonon conduction to convert the correlation from UO2 to MOX. Similar to other correlations, fuel burnup only effects the phonon conduction term. The ranges of applicability are temperature from 300 to 3000 K, plutonium content from 0 to 7 wt%, rod- average burnup from 0 to 62 MWd/kgHM. The Halden correlation for MOX is expressed as:

0.92 = +() (15) (, , ) + (, )

where k95 = thermal conductivity of MOX at 95% TD (W/m/K)

A(gad,x,bu) = 0.1148+1.1599*g+1.1599*x+0.004*bu

B(bu,T) = 2.475x10-4(1-3.3x10-3bu)ϑ

C = 0.0132 D = 0.00188

T = temperature in oC

ϑ = minimum of 1650 oC or current temperature in Celsius

bu = burnup in MWd/kgHM

x = deviation from stoichiometry = |2.0 – O/M|

g = gadolinium oxide weight fraction

A more recent MOX thermal conductivity correlation was proposed by Amaya [77]. This correlation was based on the Klemens’ theory and a literature review of thermal diffusivity

measurement of unirradiated MOX and irradiated UO2. Unlike other correlations where the effect of plutonium is often neglected or they are applicable to only certain ranges of plutonium content, the Amaya correlation specifically addresses a wider range of PuO2 weight fraction from

0 to 30% of PuO2. Theoretically, this correlation could be extended to 100% weight fraction

(pure PuO2) but it has not been validated yet. From Klemens’ theory, it is proposed that the

plutonium exists as an impurity and will cause the lattice of UO2 to shrink due to the difference in ionic radii and masses between U and Pu. This lattice strain serves as phonon scatter centers

and their effects were assumed to be proportional to weight fraction of PuO2. The effects of plutonium content and burnup in the Amaya correlations were formulated as multipliers to the phonon term of unirradiated thermal conductivity of pure UO2, therefore, it will not follow a standard 1/(A+BT) formula. Note that the high-temperature electronic conduction is expressed by a cubic term. In addition, the effects of non-stoichiometry and gadolinia were not proposed in

the original correlation, although they can be later incorporated into the k0 term.

= + (16)

= (17)

=, exp, (18)

where kPu = thermal conductivity of unirradiated MOX at 100% TD (W/m/K)

k0 = thermal conductivity of unirradiated UO2 = 1/(0.0308 + 0.0002294T) from Gibby [78]

T = temperature in K

yPu = PuO2 weight fraction

-3 D0,Pu = 0.209 m-K/W D1,Pu = 1.09x10 1/K

C = 5.95x10-11 1/K

To take into account the effect of burnup, Amaya proposed somewhat complicated correlations as shown below. Essentially, they are a multiplier to the un-irradiated thermal conductivity of

UO2.

1 1 = − + (19)

1 = (20) 1−4 Θ

1 1 +Θ + −Θ 2 2 = (21) √2Θ

1 1 +Θ − −Θ 2 2 = (22) √2Θ

3 = (23)

Θ= ××1+− + (24)

where kPu = thermal conductivity of unirradiated MOX at 100% TD (W/m/K)

k0 = thermal conductivity of unirradiated UO2 = 1/(0.0308 + 0.0002294T) from Gibby [78]

T = temperature in K

t = temperature in oC

o o tr = temperature of recovering stage in C = 650 C from Amaya and Hirai [113]

n = coefficient = 5 from Amaya and Hirai [113]

bu = fuel burnup in MWd/kgHM

yPu = PuO2 weight fraction

2 α0 = thermal diffusivity of pure UO2 = 1/(0.46586+0.087386T) in cm /s from Amaya and Hirai [113]

5 u = group velocity of phonon in UO2 crystal = 3.09x10 cm/s from Amaya and Hirai [113]

19.1 -2.6 2 L = phonon mean free path in UO2 = 1/(10 (2R) πR ) cm from Amaya and Hirai [113]

R = radius of microbubbles in nanometers, assumed 1 nm from Amaya and Hirai [113]

-3 -4 DFP = 6.69x10 exp(-3.28x10 T) from Amaya and Hirai [113]

A = coefficient representing the effect of phonon scattering effects from point defects. A equals to 1 when assuming no radiation damage recovery and 0 when full recovery is expected.

-3 DPu = 0.209exp(1.09x10 T) from Amaya et al. [77]

C = 5.95x10-11 1/K

To validate this correlation, Amaya et al. used MOX test fuel rods irradiated in a commercial BWR which were then re-fabricated and re-irradiated in Halden reactor. The achievable burnups at the Halden reactor were in the range of 77-79 MWd/kgHM. The correlation was then used

calculate fuel centerline temperature using the thermal conductivity integral method. The results from the experiments seemed to favor the coefficient A to be around zero which indicated some recovery of irradiated-induced point defects at high burnup. It was also observed that the effect

of Pu addition faded out at high burnup i.e. thermal conductivity of MOX and UO2 are similar at high burnup. The comparison between measured fuel temperature and calculated fuel temperature using this correlation seemed to agree well. In addition, Amaya correlation is evaluated at 100% TD so it needs to be adjusted to correct for porosity before benchmarking if other correlations which are typically evaluated at 95% TD.

3.3 Comparison of thermal conductivity correlations

To compare thermal conductivity correlations for irradiated fuels, burnup-dependent terms need to be included into the thermal conductivity correlations that were originally developed for fresh fuels. This approach has been done for the Duriez-Modified NFI correlation which will be used as reference model in this work. Another way to include burnup effects into the Duriez correlation is to multiply by burnup degradation factors proposed by Lucuta. This correlation will be referred to as Duriez-Lucuta correlation. Since Baron et al. had proposed a separate correlation for irradiated fuel, the fresh fuel correlation will be neglected. Given that Philipponneau and Inoue’s correlations were formulated from somewhat similar experimental databases for FBR MOX and Inoue seemed to give a better prediction for fuel centerline temperature measurements, the Inoue’s correlation is chosen for further consideration. Similar to the Duriez’s correlations, it will be modified by burnup dependent terms by Lanning (modified NFI) and Lucuta as Inoue-modified NFI and Inoue-Lucuta, respectively. The remaining correlations i.e. Baron, Halden and Amaya were originally developed with burnup dependence so they are already suitable for comparison.

After the inclusion of burnup dependent terms from Lanning, the Inoue-modified NFI can be expressed as

1 = + (25) () +×++() + 1 − 0.9(−0.04)()ℎ()

where k100 = thermal conductivity of MOX at 100% TD (W/m/K)

T = temperature in range of 300 K < T < 3000 K

x = deviation from stoichiometry = |2.0 – O/M|

a = 1.1599, gad = weight fraction of gadolinia (Gd2O3)

A(x) = 0.06059 + 0.2754√ m-K/W

B = (2.011)*10-4 m/W

9 Cmod = 1.5*10 W-K/m

D = 13520 K

f(bu) = effect of soluble fission products in the matrix = 0.00187*bu

g(bu) = effects of irradiation defects = 0.038*bu0.28

h(T) = temperature annealing of irradiation defects =

Essentially, the parameters A and B are taken from Inoue’s correlation while the remaining parameters are the same as the Duriez-modified NFI’s correlation.

In total, there are 7 thermal conductivity correlations for MOX to be compared in this work: (1) Duriez-Modified NFI (default model of FRAPCON 3.5), (2) Duriez-Lucuta, (3) Inoue- modified NFI, (4) Inoue-Lucuta, (5) Baron, (6) Halden, and (6) Amaya. For Amaya’s correlation, although it is possible to use other correlations to represent the variable k0 for unirradiated UO2, for the sake of originality, the correlation as appeared in the paper will be used for this comparison. This may create significant errors because it does not take the effect of non-stoichiometry into account.

Another important aspect for this comparison is the use of porosity correction factors to adjust the correlations to the same porosity. Traditionally, each thermal conduction correlation tends to

choose different formulae to best fit their experimental data. Historically, there have been four widely used formulae: modified Loeb, Maxwell-Eucken, Biancharia-modified Maxwell-Eucken and Schultz as shown below.

=1− modified Loeb (26)

= Maxwell-Eucken (27)

= Biancheria’s modified Maxwell-Eucken (28) ()

=(1−) Schultz (29)

where F = effective porosity correction factor

P = porosity fraction from 0.0 to 1.0

α1 = a coefficient between 2.5±1.5 for 0 < P < 0.1

β = a coefficient = 2

α2 = a coefficient = 1.5 for spherical pores

γ = a coefficient between 1.5-3.0

It can be seen that there are a wide range of formulae and coefficients available and they can significantly impact the value of thermal conductivity. Different porosity factors could change the thermal conductivity values by 7 to 10%. Therefore, porosity correction factor needs to be the same to avoid biases when benchmarking thermal conductivity correlations. In this work, the modified Maxwell-Eucken with porosity shape factor of 1.5 was chosen. In fact, this formula was chosen as one of the four Lucuta burnup degradation factors.

To describe general trends of thermal conductivity values at different temperatures, burnup and stoichiometric states, these correlations are compared with each other with the following ranges of parameters:

 Temperature = 300-3000 K  Fuel burnup = 0 and 100 MWd/kgHM  Oxygen-to-metal ratio (O/M) = 2.0 and 1.95  Porosity fraction = 0.05

 PuO2 weight fraction = 0.3

Figure 24 shows thermal conductivity of MOX at 0 MWd/kgHM and O/M = 2.0 as predicted by the Duriez-modified NFI, Duriez-Lucuta, Inoue-modified NFI, and Inoue-Lucuta correlations. These correlations are grouped together because they share similar foundations; they are modified from original correlation for fresh fuels by some burnup degradation factors. As expected, the modified-NFI and Lucuta models at 0 MWd/kgHM have no effect here i.e. Duriez- modified NFI and Duriez-Lucuta are almost identical except at very high temperature. Similar behaviors can also be observed between Inoue-modified NFI and Inoue-Lucuta; they are nearly identical until 2500 K. This is because the parameters C and D in the electronic conductivity terms were slightly reduced in the modified NFI model as proposed by Lanning [98].

The effect of burnup is illustrated in Figure 25 where these correlations are compared at 100 MWd/kgHM. In this case, it can be seen that the thermal conductivities at very high temperature (> 2500 K) are not affected by burnup because point defects and other imperfections in the lattice caused by burnup do not significantly impact electronic conductivity. Another observation is that the Lucuta model tends to be less conservative as it predicts higher thermal conductivities than the modified NFI model.

0 MWd/kgHM O/M = 2.0 9 Duriez-modified NFI Duriez-Lucuta 8 Inoue-modified NFI Inoue-Lucuta 7

2 0 500 1000 1500 2000 2500 3000

Figure 24: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 2.0.

100 MWd/kgHM O/M = 2.0 3 Duriez-modified NFI Duriez-Lucuta Inoue-modified NFI Inoue-Lucuta

2.5

1.5 0 500 1000 1500 2000 2500 3000

Figure 25: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 2.0.

The effect of non-stoichiometry at 0 and 100 MWd/kgHM is shown in Figures 26 and 27, respectively which clearly demonstrates the strong influence of stoichiometry on thermal conductivity. At both 0 and 100 MWd/kgHM, the thermal conductivities of MOX greatly decrease when O/M changes from 2.0 to 1.95. Any deviation from stoichiometry can be generally viewed as imperfections in crystal lattices of the oxides. In the case of hypo- stoichiometry (O/M < 2.0), these defects exist in the form of oxygen vacancies. For hyper- stoichiometry (O/M > 2.0), excess oxygen atoms in the form of interstitials serve as phonon scattering centers and reduce mean free paths of phonons. However, the deviation from stoichiometry does not affect electronic conductivity. At 0 MWd/kgHM, it can also be observed that the effect of non-stoichiometry is more pronounced in the Duriez correlations because it predicts lower values than the Inoue correlation. At 100 MWd/kgHM, Duriez-Lucuta predicts the lowest thermal conductivity at low temperature because radiation damage term has strong impact in this temperature but it tends to fade away above 1200 K because of thermal annealing.

0 MWd/kgHM O/M = 1.95 5 Duriez-modified NFI Duriez-Lucuta 4.5 Inoue-modified NFI Inoue-Lucuta 4

3.5

2.5

1.5 0 500 1000 1500 2000 2500 3000

Figure 26: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 1.95.

100 MWd/kgHM O/M = 1.95 2.8 Duriez-modified NFI 2.6 Duriez-Lucuta Inoue-modified NFI Inoue-Lucuta 2.4

2.2

1.8

1.6

1.4

1.2 0 500 1000 1500 2000 2500 3000

Figure 27: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 1.95.

Next, a set of thermal conductivity correlations originally developed with burnup dependent terms are compared using the same ranges of parameters shown earlier. Figure 28 compares the thermal conductivity of MOX at 0 MWd/kgHM and O/M = 2.0 as predicted by the Baron, Halden, and Amaya correlations. Note than the Duriez-modified NFI is included in the figure as reference. These correlations produce remarkably similar values for phonon conductivity when temperature is below 2000 K. Different empirical constants in electron conductivity term seem to show their impact at high temperature. For Duriez-modified NFI, Baron, and Halden, the electron conductivity is modeled by an Arrhenius form while Amaya uses a 3rd order polynomial of temperature. In this case, the Amaya correlation predicts lower values than the Duriez- modified NFI. On the other hand, the Baron and Halden predict significantly higher values than the reference model. It is worth mentioning that even though the Baron and Amaya correlations

include the PuO2 content into their correlations; its impact of overall conductivity is not clearly visible when compared to the Duriez-modified NFI and the Halden correlations.

0 MWd/kgHM O/M = 2.0 9 Duriez-modified NFI Baron 8 Halden Amaya 7

2 0 500 1000 1500 2000 2500 3000

Figure 28: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 2.0.

At 100 MWd/kgHM, the Baron, Halden and Amaya correlations produce somewhat comparable values whereas the Duriez-modified NFI predicts higher thermal conductivity at low temperature as shown in Figure 29. The Halden correlation seems to yield the most conservative value in the phonon conductivity regime when temperature is below 2000 K. In contrast, the Baron and Halden correlations predict higher thermal conductivities at high temperature. Once again, the effect of burnup does not influence electron conductivities in these correlations.

100 MWd/kgHM O/M = 2.0 4 Duriez-modified NFI Baron 3.5 Halden Amaya

2.5

1.5

1 0 500 1000 1500 2000 2500 3000

Figure 29: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 2.0.

Figure 30 compares non-stoichiometric effects on these four correlations which clearly show the varying degrees of reduction in thermal conductivity values at the same O/M ratio. Since the original Amaya correlation does not include non-stoichiometry into its correlation, it gives the highest values. The Baron correlation seems to penalize non-stoichiometry the most while the Duriez-modified NFI and the Halden are situated in the middle of these two extremes. The trend is reversed again at high temperature since the Amaya correlation does not give much credit for electron conductivity whereas the Baron and the Halden predicts significant contribution from electron conductivity at high temperature.

0 MWd/kgHM O/M = 1.95 9 Duriez-modified NFI 8 Baron Halden Amaya 7

1 0 500 1000 1500 2000 2500 3000

Figure 30: Thermal conductivity of MOX at 0 MWd/kgHM and O/M = 1.95.

After the inclusion of fuel burnup and non-stoichiometry as shown in Figure 31, the Baron correlation seems to give the most conservative values for phonon conductivity while the Amaya correlation predicts the highest values because non-stoichiometry is not included. The Duriez- modified NFI and the Halden correlations produce somewhat similar values until electron conductivity dominates at high temperature. At 100 MWd/kgHM, the Amaya correlation predicts the highest values in the phonon conductivity regime but the lowest values in the electron conductivity regime. At high temperature, the Baron and the Halden correlations reverse the trends and predict the highest values of thermal conductivities.

100 MWd/kgHM O/M = 1.95 4 Duriez-modified NFI Baron 3.5 Halden Amaya

2.5

1.5

1 0 500 1000 1500 2000 2500 3000

Figure 31: Thermal conductivity of MOX at 100 MWd/kgHM and O/M = 1.95.

3.4 Benchmarking with experimental data

In the previous section, it was observed that the Lucuta burnup factors are less conservative than the modified NFI model and the Duriez correlation places a higher penalty on non-stoichiometry than the Inoue correlation. The Baron and the Halden correlations are more conservative than the Duriez-modified NFI when temperature is below 2000 K but they become less conservative in higher temperature range.

Since the prediction of these correlations varies significantly depending on temperature, burnup, and stoichiometry, it is necessary to benchmark them with available experimental data so that its appropriateness for use in RBWR-TB2 conditions can be evaluated. First, experimental data from the open literature on thermal conductivities evaluated from laser-flash thermal diffusivity measurements are compiled from both original and review papers [55] [72] [78] [79] [85] [87] [92] [99] [100] [102] [114]. Using correlations presented earlier, calculated thermal

96 conductivities will then be compared with measured ones. Differences between measured and calculated values are statistically evaluated to find the best-fit correlation.

Table 3 provides chronological list of thermal conductivity measurement carried out over the years. Note that the numbers of data points are roughly estimated from graphical measurements; therefore, some overestimation may occur when the experimental results were presented as lines instead of exact data points. However, this should not impact the calculation of thermal conductivity because these correlations are supposed to provide continuous values of thermal conductivity at any given temperature, burnup and porosity.

Table 3: Experimental data of MOX thermal conductivity.

Source Burnup Temperature Porosity O/M PuO2 # of data (MWd/kgHM) (K) (%) Weight points Fraction (%) Hetzler 1967 0.0 1070-2200 0.0 1.98-2.0 20 43 Elbel "DUEL-II" 1968 0.0 1080-1700 0.0 1.96 21 15 Van Craeynest and 0.0 780-2100 0.05 1.98-2.00 20 38 Weilbacher 1968 Van Craeynest 1968 0.0 370-2300 0.0-0.05 1.96-2.00 20 77 Gibby 1969 0.0 770-1840 0.05 1.96-2.00 20 77 Laskiewicz 1971 0.0 1200-2550 0 2.0 20 13 Gibby 1971 0.0 370-1930 0.02- 2.0 0-100 253 0.04 Schmidt 1971 0.0 904-2000 0.05 1.93-2.00 20 25 Weilbacher 1972 0.0 770-2700 0.05 1.93-2.00 20 30 Weilbacher 1974 0.0 970-2370 0.05 1.94-2.00 20 24 Fukushima 1983 0.0 700-1800 0.0-0.05 2.0 20 47 Elbel 0.0 1050-1900 0.0 1.97 23 23 "Phenix1/SaphirM1" 1985 Elbel "SNR- 0.0 1070-1870 0.0 1.98 20 15 Phenix1/SaphirM2/S49" 1988 Bonnerot 1988 0.0 1030-2370 0.05 1.98-1.99 24-30 115 Yamamoto 1993 0.0-35 860-1900 0.065 1.97 17.7 17 Topliss 1995 0.0 670-1280 0.0 2.0 10 8 Kosaka 1997 0.0 570-1880 0.0 2.0 10 13 Duriez 2000 0.0 660-2370 0.037- 1.95-2.00 3-21.4 818 0.05

Rao 2006 0.0 673-1473 0.04 2.0 21-40 25 Morimoto 2008 0.0 860-1780 0.06-0.1 1.915- 30 84 1.999 Sengupta 2009 0.0 870-1800 0.05 1.98 44 11 Cuzzo 2010 30-35 500-1500 0.05 2.0 3.7 65 Staicu 2011 0.0-44.5 525-1450 0.05 2.0 3.5-5.5 205

It can be seen that there are a plenty of thermal diffusivity measurements of fresh MOX (Burnup = 0 MWd/kgHM) whereas that for irradiated MOX (Burnup > 0 MWd/kgHM) are relatively sparse. Because of limited information, it was decided to include the thermal conductivity

measurements of high burnup UO2 for a better comparison of these correlations [115] [116] [73] [111] [117] [118] [119] [120] [121]. These data points may not be viewed as good

representatives of MOX for RBWR-TB2 because the plutonium content in high burnup UO2 remains relatively small (< 5 wt%). It should be noted that that plutonium content in irradiated MOX as reported by Staicu et al. [100] and Cuzzo’s et al. [99] were also small at 5.5 wt% and

3.5 wt%, respectively. Although Yamamoto et al. [92] investigated MOX at higher PuO2 fraction of at around 18 wt%, it is still lower than fuel composition of RBWR-TB2 at 70% of PuO2. This

concentration is expected to be higher due to thermal migration of PuO2 toward the fuel center. However, since the purpose of this comparison is to observe how each correlation would behave at high burnup, it should be reasonable to include thermal conductivity measurements at high

burnup for both UO2 and MOX. Table 4 summarizes a chronological list of experimental results

of high burnup UO2 included in this benchmarking.

Table 4: Experimental data of UO2 thermal conductivity at high burnup.

Source Burnup Temperature Porosity (%) O/M # of data (MWd/kgHM) (K) points Lucuta 1992 0-72.5 300-1773 0.05 2 27 Lucuta 1995 0-75 296-1773 0.05 2.0-2.084 154 Ohira and Itagaki 1997 22-61 333-1673 0.05 2 14 Minato 2001 0-38.5 370-1770 0.03-0.04 1.983-2.001 82 Amaya 2002 39-60 450-1500 0.036-0.045 2 26 Ronchi 2004 34-92 500-1450 0.05 2 60 Walker 2006 102 560-1100 0.05 2.005 21 Amaya 2010 60-126 284-1415 0.06 2 13

Staicu 2014 0-76 300-1500 0.04-0.11 2 255

A scatter plot between measured and calculated thermal conductivity using Duriez-modified NFI and Duriez-Lucuta is shown in Figure 32. Although, most of these data points overlaps each other, calculated values from Duriez-modified NFI are slightly lower than those from Duriez- Lucuta. A diagonal line in the figure represents a perfect agreement between measured and calculated values. The points below and above this line indicate underestimations and overestimations, respectively.

9 Duriez-modified NFI 8 Duriez-Lucuta

2 Calculated Thermal Conductivity (W/m/K) Calculated Thermal Conductivity

1 123456789 Measured Thermal Conductivity (W/m/K)

Figure 32: Measured vs. calculated thermal conductivity of MOX and UO2 using Duriez- modified NFI and Duriez-Lucuta correlations.

As shown in Figure 33, calculated thermal conductivities using the Inoue-modified NFI and Inoue-Lucuta also exhibit similar trend; they are mostly comparable except for certain data points that the Inoue-modified NFI predicts slightly lower values than the Inoue-Lucuta.

Inoue-modified NFI 8 Inoue-Lucuta

2 Calculated Thermal Conductivity (W/m/K)

1 123456789 Measured Thermal Conductivity (W/m/K)

Figure 33: Measured vs. calculated thermal conductivity of MOX and UO2 using Inoue-modified NFI and Inoue-Lucuta correlations.

A comparison of the Baron, Halden and Amaya correlations with experimental data is shown in Figure 34. It can be seen that the Amaya correlation tends to overestimate thermal conductivities. This is primarily because of the lack of treatment on non-stoichiometry. The Baron correlation produces a wider spread around the diagonal line when compared to the Halden correlation. In this case, it appears that the Halden correlation is more accurate than the other two.

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10 Baron 9 Halden Amaya 8

Calculated Thermal Conductivity (W/m/K) 2

1 12345678910 Measured Thermal Conductivity (W/m/K)

Figure 34: Measured vs. calculated thermal conductivity of MOX and UO2 using Baron, Halden, and Amaya correlations.

However, due to a large number of data points plotted in these figures, it is quite difficult to visually quantify the accuracy of their predictions. Therefore, statistical indicators such as root mean square (RMS) and standard deviation (SD) can be used to represent a central tendency and spread of data. In this case, the differences between calculated and measured thermal conductivities can be used to evaluate the predictive capability of correlations. In the case of perfect agreements between experiments and calculations, these values are zero. The formulae for RMS and SD are given by Equations 30, 31 and 32.

1 ( − ) = ( − ) (30)

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1 ( − ) = (( − ) −) (31)

1 ( − ) = ( − ) (32) where N = number of data

kcalculated = calculated thermal conductivity by correlations (W/m/K)

kmeasured = measured thermal conductivity (W/m/K)

μ = arithmetic mean of the samples

The RMS and SD of the differences between calculated and measured thermal conductivities of 7 correlations considered in this work are shown in Table 5. Except for Baron and Amaya, the remaining correlations are relatively similar in term of RMS and SD of the deviation from experiments. However, the Duriez-modified NFI seems to be slightly more accurate than the others.

Table 5: Root mean square and standard deviation of kcalculated-kmeasured of thermal conductivity correlations.

Correlation RMS(kcalculated-kmeasured) SD(kcalculated-kmeasured) Duriez-modified NFI 0.2022 0.1866 Duriez-Lucuta 0.2055 0.1953 Inoue-modified NFI 0.2262 0.2259 Inoue-Lucuta 0.2130 0.2109 Baron 0.3211 0.3209 Halden 0.2186 0.2134 Amaya 0.4158 0.3593

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Since the majority of data points used in this benchmarking are thermal conductivities evaluated at zero burnup; the accuracy at zero burnup will heavily influence the root mean square of the errors. To eliminate this influence, thermal conductivity measurements at 0 MWd/kgHM should be excluded. After the exclusion of zero burnup data, the plot of measured vs. calculated thermal conductivities using Duriez-modified NFI and Duriez-Lucuta is shown in Figure 35. This time, the overlapping of data points is less than before and the Duriez-modified NFI still produces a more conservative result than the Duriez-Lucuta correlation.

6 Duriez-modified NFI 5.5 Duriez-Lucuta

4.5

3.5

2.5

Calculated Thermal Conductivity (W/m/K) 1.5

1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Measured Thermal Conductivity (W/m/K)

Figure 35: Measured vs. calculated thermal conductivity of MOX and UO2 using Duriez- modified NFI and Duriez-Lucuta correlations.

Similarly for the Inoue-modified NFI and Inoue-Lucuta correlations, the differences between these two correlations are more visible after filtering zero burnup data as illustrated in Figure 36. Once again, it is observed that the modified NFI model for burnup effect predicted slightly lower values than the Lucuta model.

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6 Inoue-modified NFI 5.5 Inoue-Lucuta

4.5

3.5

2.5

Calculated Thermal Conductivity (W/m/K) 1.5

1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Measured Thermal Conductivity (W/m/K)

Figure 36: Measured vs. calculated thermal conductivity of MOX and UO2 using Inoue-modified NFI and Inoue-Lucuta correlations.

Finally, the Baron, Halden, and Amaya correlations are compared with measured thermal conductivity at high burnup in Figure 37. This time, the overestimation observed previously for Amaya correlation seems to be smaller with less data points above the diagonal line. The Baron and Halden give a reasonably conservative prediction as most of the data point stay below the diagonal line; however, the Halden correlation appears to be more accurate as the data points stay closer to the diagonal line.

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6 Baron 5.5 Halden Amaya 5

4.5

3.5

2.5

Calculated Thermal Conductivity (W/m/K) 1.5

1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Measured Thermal Conductivity (W/m/K)

Figure 37: Measured vs. calculated thermal conductivity of MOX and UO2 using Baron, Halden, and Amaya correlations.

A similar statistical analysis has been carried out after the exclusion of zero burnup data. The remaining data points are thermal conductivity values of irradiated samples only. Then the RMS and SD of kcalculated-kmeasured are calculated and summarized in Table 6. This time, all correlations are quite comparable in term of RMS and SD of the errors. The Amaya correlation exhibits the lowest RMS followed by the Duriez-modified NFI and Duriez-Lucuta, respectively.

Table 6: Root mean square and standard deviation of kcalculated-kmeasured of thermal conductivity correlations after exclusion of unirradiated data.

Correlation RMS(kcalculated-kmeasured) SD(kcalculated-kmeasured) Duriez-modified NFI 0.2710 0.2108 Duriez-Lucuta 0.2847 0.2464 Inoue-modified NFI 0.3119 0.2508 Inoue-Lucuta 0.2785 0.2730 Baron 0.3733 0.2784

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Halden 0.2940 0.2102 Amaya 0.2584 0.2340

From the comparison of root mean square and standard deviation of kcalculated-kmeasured, it appears that the default correlation in FRAPCON-3.5 provides a reasonable prediction of MOX at low burnup and it seems to give a conservative prediction of thermal conductivity at high burnup. Therefore, the Duriez-modified NFI was chosen for use in fuel performance modeling of RBWR-TB2.

3.5 Effect of PuO2 content on MOX thermal conductivity

A majority of the correlations discussed previously do not explicitly include PuO2 weight fraction into their formulations. For example, Duriez et al. [55] claimed that its effect is small in the range of 0-15% weight fraction; therefore, the plutonium content was disregarded. Inoue et al. [72] proposed a single correlation covering the whole range of plutonium content from 15-30 wt%.

However, the fuel composition of MOX for RBWR-TB2 contains around 60-70 wt% PuO2 plus some minor actinides. This concentration is likely to be higher in the center of fuel rods due to thermal migration of fuel constituents. Previous experimental investigations [122] [123] [124] have shown that, from a uniform weight fraction at the beginning of life, plutonium tends to migrate up the temperature gradients and form plutonium-enriched zones in the center. The plutonium content in this region could be 30-40% higher than the initial plutonium concentration. Therefore, the effect of PuO2 content on thermal conductivity of MOX fuels should be taken into account when analyzing RBWR-TB2 fuel rods. Since the Duriez-modified NFI does not include plutonium content into the correlation, it is proposed that the effect of plutonium content on thermal conductivity of MOX can be represented by multiplication factors. Fundamentally, this is similar to burnup factors developed by Lucuta et al. [74]. At any given temperature and plutonium weight fraction, the multiplication factors can be computed and multiply by the Duriez-modified NFI correlation to adjust thermal conductivity according to its plutonium content.

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In formulation of these factors, one approach is to use experimental data from Gibby [78] which conducted a comprehensive evaluation of the effect of plutonium content on thermal conductivity of fresh MOX. Gibby et al. measured thermal diffusivities of pure UO2, pure PuO2, MOX at 5, 12, 20, 25, 30 wt% from 373 K (100 oC) to 1473 K (1200 oC). It was observed that an

increase in PuO2 content resulted in a minor but consistent decrease in thermal conductivities of MOX. This is an expected behavior because of similarities in atomic radii and masses between

uranium and plutonium ions. The effect of PuO2 content on thermal conductivity of MOX is summarily shown in Figure 38.

Figure 38: Thermal conductivity of fresh MOX as a function of PuO2 content [78].

A systematic decrease in thermal conductivity with PuO2 content can be observed at any temperature interval. However, the impact tends to diminish as temperature increases. At a o temperature of 1473 K (1200 C), the thermal conductivity of UO2, PuO2 and MOX are

relatively comparable. It should also be noted that the samples with 30% and 100% PuO2 had different microstructure and lower density than other samples. The density of these two samples was reportedly around 92% TD while other samples had 97% TD on average. Therefore, the

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density of 30% and 100% PuO2 sample was corrected using Biancheria’s modified Maxwell-

Eucken formula. The microstructure of samples at 0-25% PuO2 appeared to be similar in terms of grain size, pore size and distribution while the sample at 30% PuO2 showed some localized

concentration regions of large pores. The sample at 100% PuO2 was manufactured differently as it was prepared by pneumatic impaction instead of sintering. In addition to plutonium content, the differences in microstructure and porosity fraction could also be contributing factors to a sharp drop in thermal conductivity at 30% PuO2. To address this deficiency and to extend the

range of plutonium content to cover the whole range from 0 to 100 wt% PuO2, Gibby [78] applied theoretical models based on thermal resistance of a dielectric solid. The model comprises contributions from phonon-defect and phonon-phonon interactions. This empirically derived correlation is a function of temperature, plutonium weight fraction, and the atomic masses and

radii, lattice constants, melting points of UO2 and PuO2. The calculation results at different temperatures are shown in Figure 38 as solid lines. According to the correlation, it is indicated

that the thermal conductivity of (U,Pu)O2 mixtures will have a minimum at around 70 wt% PuO2 which corresponds to roughly 16% decrease in thermal conductivity from UO2.

Alternatively, the effect of plutonium content on thermal conductivity of MOX has been also investigated using molecular dynamics (MD) simulations and some thermal conductivity correlations derived from MD results were also proposed to cover the whole range from

concentration of pure UO2 to pure PuO2. In this case, these correlations can be converted into multiplying factors by normalizing them to a reference concentration.

The MD simulation can also be further categorized based on thermal equilibrium conditions as equilibrium (EMD) and non-equilibrium molecular dynamics (NEMD) simulations. In an EMD simulation, the system is assumed to be in thermal equilibrium; there is no temperature difference in an ensemble. The thermal conductivities are then calculated as the time integral of the heat flux autocorrelation function which is a function of atomic mass, atomic radii, particle velocity, ionic charge, and the potential energy and inter-atomic forces between a pair of atoms [64].

In NEMD simulation, where temperature gradient is allowed in the ensemble, thermal conductivities can be directly evaluated using Fourier’s law. In this case, a simulated system is

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divided into several thin slabs and temperature gradient is introduced by assigning higher temperature (more kinetic energy) to the other end. As the simulation progresses, particles will elastically collide to exchange momentum and energy. By tracking particle trajectories and velocities, local heat flux and temperature of each zone in the ensemble can be estimated and the ratio of heat flux and temperature gradient can be used to evaluate thermal conductivities [63].

Arima et al. [61]computed thermal conductivity of hypostoichiometric MOX using EMD simulation between 300 to 2000 K. Oxygen-to-metal ratio and plutonium content were in the ranged of 1.94-2.00 and 0 to 30 wt%, respectively. Simulation results showed that the thermal

conductivity remained almost constant from 0 to 30 wt% PuO2. The study found that the effect of non-stoichiometry is more important than the plutonium content.

Nichenko and Staicu [65] expanded the range of EMD simulation to cover the whole range of plutonium concentration from 0 to 100 wt% in the temperature range from 400 to 1600 K. The simulation results showed a systematic decrease in thermal conductivity of MOX as plutonium

increase and found a minimum concentration at 45 wt% PuO2 with roughly 14% reduction from

pure UO2 value as depicted in Figure 39. It was also observed at pure PuO2 has lower thermal conductivity than pure UO2. Nichenko and Staicu also proposed a plutonium correction factor

that can be used to adjust the thermal conductivity of pure UO2 to MOX given plutonium weight fraction.

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Figure 39: Thermal conductivity correlation recommended by Nichenko and comparison with experimental result (100% TD) [65].

Matsumoto et al. [69] used NEMD to investigate the thermal conductivities of UO2, PuO2 and

(U0.8Pu0.2)O2 from 300 to 2000 K. It was found that the thermal conductivity of (U0.8Pu0.2)O2 is

comparable to UO2 and slightly lower than PuO2 as shown in Figure 40.

Figure 40: Effect of PuO2 on thermal conductivity by Matsumoto et al. [69].

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Ma et al. [67] investigated several physical properties of hypostoichiometric MOX at 25 wt%

PuO2 with varying O/M ratio from 1.975-2.0 and stoichiometric MOX with varying plutonium

content from 15-30 wt% PuO2. This study confirmed that the effect of non-stoichiometry is more pronounced when compared with that of plutonium addition. Also, the EMD results showed small deviation in thermal conductivity in MOX with plutonium weight fraction from 15-30 %. Consequently, it was suggested that with the presence of oxygen vacancies in hypostoichiometric fuel, the effect of plutonium content up to 30 wt% is negligible.

Cooper et al. [70] used NEMD to investigate the thermal conductivity of MOX over the whole range of plutonium concentration. The results showed a minor reduction in thermal conductivity even at low temperature because the effect of plutonium as substitutional defects in the lattice is

small although non-negligible. The study also suggested that PuO2 has a higher thermal

conductivity than UO2 so that the lowest thermal conductivity occurred at 25% PuO2 as higher thermal conductivity of PuO2 outweighs the substitutional defects of plutonium ions. Figure 41 shows how thermal conductivity changes with different uranium composition and temperature. Derived from NEMD results, Cooper also proposed analytical expressions for thermal conductivity of MOX as a function of temperature and uranium composition.

Figure 41: The variation of thermal conductivity of MOX as a function of uranium composition [70].

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In summary, these computational studies produced a wide variety of results and conclusions.

Some studies [60] [61] [62] [63] [70] claimed that the effect of PuO2 is negligible in the range of

their studies while others [65] [70] argued that although the impact of PuO2 content to thermal conductivity is small, it should not be neglected. These contradictions essentially originated from differences in thermal conductivity estimation by EMD or NEMD methods and in interatomic potential functions used in their calculations. The accuracy of these functions changes over a wide range of temperature from 300 to 3000 K. Reportedly, it is still a challenge to define a universal interatomic potential function that accurately reproduces several physical properties of

UO2 and PuO2 over this range. Furthermore, some MD investigations showed contradictions to experimental data. For example, Cooper et al. predicted that the lowest thermal conductivity of

MOX is at 30 wt% PuO2 but recent experimental findings by Rao et al. [114] and Sengputa et al.

[87] have shown that the thermal conductivity of MOX at 40 and 44 wt% PuO2 is lower than that

of MOX at 30 wt% PuO2. Given the uncertainties of the results of MD simulation, it is more preferable to rely on empirical correlations developed from experimental results instead of correlations developed from computational results. In this case, the work of Gibby was chosen as a framework for developing plutonium multiplying factors so that the Duriez-modified NFI correlation can adjust its value according to the plutonium content.

First of all, the data points published by Gibby [78] needed to be graphically extracted for further analysis. A reconstruction of selected experimental values is shown in Figure 42 which clearly shows a systematic reduction in thermal conductivity as plutonium content increases from 0 to 30 wt%. In addition, since the Duriez-modified NFI does not have plutonium content in the correlation, it is important to find a reference concentration in Gibby’s data that matches the calculated values. As shown in Figure 43, thermal conductivity as calculated by the Duriez- modified NFI correlation appears to fit quite well with measured thermal conductivity at 30 wt%

PuO2. Therefore, the thermal conductivity of MOX at 30 wt% PuO2 is chosen as a reference point and it will be used to formulate plutonium multiplying factors. However, it should also be noted that this reference point is only valid for the Duriez-modified NFI correlation. To apply these factors to other correlations, a new reference concentration would need to be evaluated from Gibby’s data.

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8 0% PuO 2 5% PuO 7 2 20% PuO 2 30% PuO 2 6

4 Thermal Conductivity (W/m/k) Conductivity Thermal 3

2 200 400 600 800 1000 1200 1400 1600 Temperature (K)

Figure 42: Thermal conductivity as a function of temperature at varying PuO2 weight fraction [78].

8 5% PuO 2 30% PuO 7 2 Duriez-modified NFI

4 Thermal Conductivity (W/m/k) Thermal Conductivity 3

2 200 400 600 800 1000 1200 1400 1600 Temperature (K) Figure 43: Comparison of Duriez-modified NFI correlation with measured thermal conductivity

of MOX at 5 and 30 wt% PuO2 from Gibby [78].

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The plutonium multiplying factors are formulated based on an empirical correlation proposed by Gibby [78] as shown in the solid lines of Figure 38. This correlation provides a continuous prediction of thermal conductivity over the continuous range of plutonium content from 0 to 100 wt%. Since the original correlation was given in a rather complex form, it was more convenient for implementation in a computer code to use a graphical method to extract the information as point-wise data sets and then use a 2-D interpolation method to evaluate these factors on-the-fly given the plutonium weight fraction and temperature. First, the solid lines in Figures 38 were

extracted as data points. A reconstruction of thermal conductivity of MOX as a function of PuO2 weight fraction at different temperatures is shown in Figure 44.

373.15 K 8 473.15 K 673.15 K 873.15 K 7 1073.15 K 1473.15 K 6

3 Thermal conductivity (W/m/K)

1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PuO weight fraction 2

Figure 44: Calculated thermal conductivity of MOX as a function of PuO2 weight fraction from empirical correlation proposed by Gibby [78].

Then, the multiplying factors can be evaluated by normalizing the whole data sets with thermal

conductivity at 30 wt% PuO2. As shown earlier in Figure 43, the Duriez-modified NFI correlation matches relatively well at this weight fraction. Therefore, any deviation in plutonium

114 weight fraction from 30 wt% would result in a change in thermal conductivity as depicted in Figure 45. However, since the temperature range considered in Gibby’s work was from around 400-1500 K, it is further assumed that the multiplying factors can be linearly extrapolated beyond the original temperature limits. In other words, the relationship between plutonium weight fraction, fuel temperature and MOX thermal conductivity outside this original temperature range remains linear so that a linear extrapolation method can be used to describe its behavior.

1.25 373.15 K 1.2 473.15 K 673.15 K 873.15 K 1.15 1073.15 K 1473.15 K 1.1

1.05

1 Multiplying factor Multiplying

0.95

0.9

0.85 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PuO weight fraction 2

Figure 45: Multiplying factor to the Duriez-modified NFI correlation with reference PuO2 weight fraction at 30 wt%.

These multiplying factors have been successfully implemented into FRAPCON 3.5 EP so that the Duriez-modified NFI correlation can be changed by plutonium weight fraction. To evaluate a multiplying factor at any given weight fraction and temperature, bilinear interpolation scheme was used as a table lookup method as defined by the following equations:

− − (, ) = (,) + (,) (33) − −

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− − (, ) = (,) + (,) (34) − −

− − (, ) = (, ) + (, ) (35) − − where x = given plutonium concentration (wt %)

y = given temperature (K)

f(x, y) = a multiplying factor evaluated at given plutonium concentration and temperature

x1 = plutonium concentration at lower interval

x2 = plutonium concentration at upper interval

y1 = temperature at lower interval

y2 = temperature at upper interval

f(x1, y1) = a multiplying factor at x1 and y1

f(x2,y1) = a multiplying factor at x2 and y1

f(x1,y2) = a multiplying factor at x1 and y2

f(x2, y2) = a multiplying factor at x2 and y2

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Chapter 4

Physical Phenomena Relevant to RBWR-TB2

Because of thermal-hydraulic and neutronic constraints, the fuel rod height of the RBWR-TB2 is reduced from around 3.7 m in the ABWR to around 1.2 m. In fact, the active fuel length (high power-producing zone) is even shorter because of axial heterogeneity in the design—axially alternating zones between fissile and blanket. In this case, a significant fraction of fuel length has to be allocated for the blanket zones (low power-producing zone). While the active fuel length of the ABWR could be as long as 3.6-3.7 m, that of the RBWR-TB2 is limited to around 0.5-0.6 m. Therefore, in order to keep the core thermal output the same as the ABWR with much shorter fuel length, the LHGR in fissile zones of RBWR-TB2 has to be very high. Higher fuel rating and smaller fuel volume results in a significant increase in fuel temperature and burnup. With the reduced moderation design, the harder neutron spectrum in the core also increases neutron irradiation damage to structural components such as cladding, reactor vessel, control rods, etc. When compared to conventional LWRs, RBWR-TB2 was designed to operate at much higher fuel temperature, local burnup and fast neutron fluence to the point where it resembles operating conditions of fast reactors especially in the fissile zones. In fact, many design characteristics of RBWR-TB2 are closely similar to fast reactors except the use of water as moderator and coolant. In normal LWR operating conditions, where fuel temperature is below half of melting point, fuel restructuring, central void formation, and fuel constituent redistribution were hardly observed so that these phenomena are often neglected in LWR fuel performance codes. However, they become relevant at high temperature and high burnup conditions.

Normally experienced in fast reactor conditions i.e. LHGR and local fuel burnup exceed 30 kW/m and 100 MWd/kgHM, respectively, the following physical phenomena are expected to occur in RBWR-TB2: (1) fuel restructuring which leads to fuel porosity migration and subsequent central void formation, (2) redistribution of fuel constituents e.g. plutonium, oxygen, and cesium under high temperature and steep thermal gradient, (3) Increase in fuel swelling from gaseous fission products, (4) less plutonium accumulation at the periphery region and a flatter radial power profile, (5) high burnup structure (HBS) formation in the periphery region, and (6)

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accelerated corrosion and hydriding after a complete dissolution of secondary phase particles (SPPs) in cladding.

All of these phenomena had been previously modeled and implemented in FRAPCON 3.3 [10] [98]. This heavily modified version of FRACPON 3.3 was later termed FRAPCON-EP where EP stands for Enhanced Performance [8] [9]. However, FRAPCON 3.3 is an outdated code as it has been released for more than 10 years [10] [98] and it had been officially superseded by newer versions. To gain the benefits of more recent material property correlations and fuel behavior models, it was decided to upgrade FRAPCON-EP from a base version of FRAPCON-3.3 to FRAPCON-3.5 [7]. Released in 2014, FRAPCON 3.5 is based on the same standard and code structure of FRAPCON-3.3 thus making the migration of physical models previously implemented in FRAPCON-EP more efficient. The upgraded code will be referred to as FRAPCON-3.5 EP.

Although most of the physical models are adopted from the earlier version of FRAPCON-EP [8] [9], some models were revised and upgraded to a more mechanistic approach. These models are described in the following subsections.

4.1 Porosity migration and central void formation

When compared to other types of nuclear fuel, oxides have one of the lowest thermal conductivities [125]. This natural characteristic limits the rate of heat transport within the fuel pellets, increases temperature gradient and makes the fuel temperature during power operation higher than other types of fuels. In the RBWR-TB2, fuel rods in fissile zones operate at much higher LHGR than typical LWRs. High temperature and large temperature gradients in highly rated fuel rods results in significant changes in fuel microstructure and porosity distribution which become effective when fuel temperature exceeds the original sintering temperature of the pellets which ranges from 1800-2000 K. Consequently, the microstructure of the fuel tends to change from a homogenous structure across the pellet to three different zones depending on local fuel temperature. After restructuring, the fuel is divided into columnar-grain, equiaxed-grain and as-fabricated grain regions. The as-fabricated porosity also rearranges under steep temperature gradient and it tends to migrate toward to centerline to form a central void. Figure 46 shows an

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example of restructured fuel of mixed oxide irradiated at a very high LHGR of 56 kW/m to a burnup of 25 MWd/kgHM [126].

Figure 46: Cross section of mixed oxide fuel rod irradiated at 56 kW/m to 25 MWd/kgHM [126].

It can be seen that, from an original solid pellet with uniform porosity distribution, this fuel pellet had been transformed in to an annular pellet with a central void created by an accumulation of as-fabricated porosity at the center. The size of this central void is roughly 30% of the fuel diameter. Next to the central void is a solid region characterized by large columnar grains and lenticular pores which respectively orient themselves parallel and perpendicular to the thermal gradient. The fuel in this region is highly densified because of porosity migration toward the center. These pores migrated up the temperature gradient and are responsible for the formation of the central void. A significant fraction of as-fabricated porosity existed in this sample because the fuel was quite porous with a density of around 84% TD, allowing the movement of pores at high temperature. Ideally, if the fuel is fully dense with zero porosity, fuel restructuring and

119 porosity migration may not occur. The next layer after the columnar grain region is called equiaxed grain region. This region is characterized by significant grain growth from as- fabricated conditions. Grain growth in ceramic materials is not unique to nuclear applications and does not require irradiation to occur. In this region, fuel temperature is a major driving factor for the formation of equiaxed grains. As-fabricated porosity is slightly densified in this region and migrated toward the columnar grain region. The outermost layer of restructured fuel is called as-fabricated region. It is the region where temperature is too low to cause any change to the original microstructure. Therefore, the as-fabricated porosity remains unchanged in this region. A schematic of fuel restructuring regions are illustrated in Figure 47.

Figure 47: Schematic of restructured regions [126].

To quantitatively describe fuel restructuring and porosity migration behavior, a simplified three- region model has been widely used [126] [127]. In this model, the fuel is subdivided into 3

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regions according to its local fuel temperature. The porosity in each restructured regions are then assumed constant where the columnar-grain region has the highest density, followed by equiaxed-grain and as-fabricated regions. For example, the columnar-grain region with a density of 97% TD may form whenever fuel temperature exceeds 2000 K, while the equiaxed-grain region with a density of 92% TD exists when temperature is between 1700 and 2000 K and no restructuring (no change in fuel density) when fuel temperature is below 1700 K. Finally, the size of the central void can be calculated using conservation of mass. This method has an advantage of less computational cost but it cannot fully describe the dynamics of temperature and porosity distribution during restructuring. In addition, the assumption of constant porosity in restructured regions could potentially lead to an underestimation of fuel centerline temperature because, in reality, fuel porosity in each restructured zone continuously changes with local temperature and fuel radius. Lackey et al. [127] has demonstrated the inability of the three-region model to capture the variation of porosity in restructured regions that eventually led to the underestimation of centerline temperature. As shown in Figure 48, fuel porosity in restructured regions was higher than initially believed. According to the three-region model, the fuel density in the columnar-grain region was assumed constant at 3% whereas it ranged from 3 to 8% from measurements. Similarly, in the equiaxed zone, fuel porosity was actually in the range of 8 to 18% not a constant value at 8% as assumed in the three-region model. Although, it is possible to assign different porosity values into each restructured zone, the use of step function with only 3 intervals inherently compromises the accuracy of capturing the behavior of continuous function. This three-region model has been implemented in a previous version of FRAPCON-EP [8] [9]. In this thesis, a more mechanistic model has been implemented in FRAPCON-3.5 EP to better describe fuel restructuring and porosity migration phenomena. This model takes into account the continuous evolution of the porosity distribution based on pore velocity and the following assumptions.

1. As-fabricated porosity consists of closed pores and these pores only migrate up the temperature gradient in the radial direction 2. All pores are of the same size and volume regardless of radial position and time. No formation of larger pores due to collisions and coalescences.

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Figure 48: Comparison of fuel temperature calculated from three-region model and measured porosity [127].

Based on these assumptions, the governing equation for pore redistribution kinetic is given by:

P 1   rv P (36) t r r p where P = Fuel porosity as a function of time and radial position (%)

v p = Pore velocity (m/s) subject to the following initial and boundary conditions:

P(r,t  0)  P0 (37)

P(r  R fo ,t)  P0 (38)

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where P0 = Initial fuel porosity (%)

R fo = Fuel outer radius (m)

In this work, the pore velocity correlation was taken from Karahan [128] which expressed the pore velocity as a function of temperature and temperature gradient as

66490 T v  0.3376exp( ) (39) p T r

where T = Fuel temperature (K)

T = Temperature gradient in radial direction (K/m) r

To implement a set of differential equations into computer codes and then to solve them using numerical methods, they need to be transformed from continuous to discrete forms. In this case, time-dependent variables are discretized according to the explicit forward Euler method whereas spatial dependent variables are discretized using the finite difference method. The discretized form of the governing equation is given below:

i1 t i t t t1 ri1v p Pi1  ri v p Pi Pi  Pi  2t 2 2 (40) rri1  rri

t where Pi = Fuel porosity at radial node i of current time step t (%)

t1 Pi = Fuel porosity at radial node i of previous time step t-1 (%)

t = Time step (sec)

i1 v p = Pore velocity at node i+1 (m/s)

i v p = Pore velocity at node i (m/s)

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ri1 = Fuel radius at node i+1 (m)

ri = Fuel radius at node i (m)

rri1 = Outer boundary of radial node i (m)

rri = Inner boundary of radial node i (m)

For the calculation of pore velocity, radial temperature gradient is approximated by

 T  T  T    i1 i1 (41)  r i ri1  ri1

 T  where   = Temperature gradient at radial node i (K/m)  r i

Ti1 = Fuel temperature at radial node i+1 (K)

Ti1 = Fuel temperature at radial node i-1 (K)

ri1 = Fuel radius at node i+1 (m)

ri1 = Fuel radius at node i-1 (m)

As a result of porosity migration, central void formation can be calculated from conservation of mass equation given below.

R foR fo R 2  P 2rdr  P(r)2rdr 0 0 R  R01R (42) 1 

where R0 = Fuel inner radius before restructuring (m)

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R1 = Fuel inner radius after restructuring (m)

To calculate the size of a central void, trapezoidal numerical integration with variable spacing was used to approximate the integrand of porosity and fuel radius before and after restructuring. Although the fuel temperature keeps changing until the end of life, fuel restructuring tends to reach equilibrium in a few days or months of operation. In this work, the fuel restructuring period is conservatively set to reach saturation after 10 MWd/kgHM. This burnup limit was established according to the fuel densification model currently implemented in FRAPCON-3.5 which assumed no additional densification beyond this burnup limit [7].

4.2 Plutonium migration

When oxide fuel is under a steep temperature gradient and sufficiently high temperature, major fuel constituents such as plutonium, uranium, oxygen and certain fission products will become mobile and redistribute to hotter or colder regions depending on heat of transport values. For species with positive heat of transport, they tend to migrate to down the temperature gradient to lower temperature regions toward the fuel surface. Those with negative heat of transport such as plutonium and minor actinides will migrate in the opposite direction to higher temperature regions toward the fuel center.

Plutonium migration is one of the most important phenomena in fast reactors which clearly differentiates fuel behavior of fast reactors from thermal reactors. Generally, thermal diffusion is considered a primary mechanism for plutonium redistribution. This behavior becomes more effective when fuel temperature is above 70% of its melting point. For the case of mixed oxide, this is around 2,200 K. In thermal reactors, although the temperature gradient may be large enough to cause migration, the fuel temperature itself is not high enough to provide sufficient activation energy for plutonium atoms to overcome the thermal migration barrier. As a result, plutonium migration is hardly observed for MOX in LWRs; instead, plutonium buildup from neutron capture of U-238 near the fuel periphery is one of the most common mechanisms at high burnup [129]. In RBWR-TB2 which operates at similar operating conditions to fast reactors, plutonium migration is expected to occur. The redistribution of plutonium content can greatly impact fuel performance because it will affect the radial power profile, fuel thermal conductivity,

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melting temperature, and oxide valence state across the fuel pellet. To accurately predict the centerline temperature, the effect of plutonium accumulation toward the center needs to be properly addressed in fuel performance codes.

Several investigations have been performed during the 1970s to describe plutonium migration from both out-of-pile experiments and post irradiation examinations [127] [130] [131] [132] [133] [134] [135]. These studies found that the migration of plutonium is driven by three primary mechanisms: (1) solid state thermal diffusion, (2) vapor transport by migrating pores and (3) vapor transport via cracks. Solid state thermal diffusion (the Soret effect) is believed to be the dominant mechanism because it is a long-lasting process that is continuously developing throughout the cycles [131] [133]. In contrast, the transport of plutonium by migrating pores seems to have a limited contribution only at the beginning of irradiation until the formation of a central void is complete [135] [134]. Similarly, vapor transport via cracks has a negligible contribution for long-term operation because cracks can heal relatively fast at high temperature [131] [132].

Recent experimental evidence from short-term experiments [122] [123] [124] [136] [137] have confirmed the existence of fuel restructuring and plutonium migration under high temperature and steep temperature gradient. In this work, the samples were MOX fuels with plutonium content of 29 wt% and axially varying americium content between 3 and 5 wt%. The fuel samples were fabricated and sintered to achieve a density of 93% TD One sample was irradiated at a LHGR of 43 kW/m for 10 minutes and the other two samples were irradiated at 45 kW/m for 24 hours in the experimental fast reactor JOYO in Japan. Figure 49 shows qualitative characteristic X-ray maps for U, Pu, and Am around a central void after 24 hours of irradiation at 45 kW/m. In the figure, X/L values of 0.05, 0.45 and 0.98 represent the bottom, middle and top of fuel sample, respectively. Because of plutonium migration, it can be clearly seen that the concentration of Pu and Am increased whereas that of U decreased in the vicinity of the central void.

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Figure 49: Electron probe microanalysis (EPMA) false color X-ray maps showing radial distribution of U, Pu, and Am. The concentration increases in the following order: green, yellow and red [140].

Figure 50 simultaneously shows the evolution of a central void and radial distributions of Am and Pu after 10 minutes and 24 hours of irradiation. The two figures on the left show a rapid transformation in fuel microstructure as the existing pores migrated up the temperature gradient to form a central void only after 10 minutes and the process is complete after 24 hours of irradiation. The two figures on the right show the radial concentration of Am and Pu. It can be noticed that from a uniform concentration of 29 wt% for Pu and 5% for Am, these two species migrated to the inner regions of the fuel near the central void and increased the concentration to around 35% for Pu and around 6% for Am. In this experiment, the corresponding centerline

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temperature when LHGR ranged from 43-45 kW/m was estimated to be around 2600 K. At this high temperature, it was sufficient to cause thermal migration of fuel constituents.

Figure 50: Fuel restructuring and radial distribution of Pu and Am after 10 minutes and 24 hours irradiation at high LHGR conditions [137].

The redistribution of fissile material will contribute to the change of the radial power profile as more power will be generated from the inner regions. In addition, fuel thermal properties such as thermal conductivity, melting temperature, will likely be affected by the accumulation of these species. If this behavior was not included in fuel performance codes, the centerline temperature would be underestimated by assuming uniform plutonium distribution within the pellets.

To model plutonium migration by a solid state diffusion mechanism, Fick’s first law of diffusion and thermal diffusion (the Soret effect) can be used to describe the diffusion currents of

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plutonium under the influence of concentration gradient in the first term and temperature gradient in the second term of Equation 43 as shown below:

(1− ) =− ∇ + ∇ (43)

By assuming that plutonium can only migrate in the radial direction similar to heat transport, the plutonium current becomes.

(1− ) =− + (44)

where QPu= heat of transport = -146.5 kJ/mol

R = universal gas constant = 8.314 J/mol/K

CPu = Plutonium concentration (wt%)

2 DPu = U-Pu interdiffusion coefficient (m /s)

Time-dependent behavior of plutonium migration in radial direction can be modeled using Fick’s second law of diffusion (the continuity equation) as follows:

= −. (45)

1 =− ( ) (46)

Similar to porosity migration, forward Euler and finite difference methods are used to discretize time-dependent and spatial-dependent variables, respectively. The discretized form of the continuity equation is given below:

× − × + × − × , =, +2Δ (47) −

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,= Plutonium concentration at node i of current time step (wt%)

, = Plutonium concentration at node i of previous time step (wt%)

= fuel radius at node i

= fuel radius at node i-1 to the left of node i

= fuel radius at node i+1 to the right of node i

= Outer boundary of radial node i (m)

= Inner boundary of radial node i (m)

= Positive plutonium current emerging from node i-1 towards the outer part of the fuel (atom/m2/s)

= Positive plutonium current emerging from node i towards the outer part of the fuel (atom/m2/s)

= Negative plutonium current emerging from node i towards the inner part of the fuel (atom/m2/s)

= Negative plutonium current emerging from node i+1 towards the inner part of the fuel (atom/m2/s)

From the continuity equation, it can be seen that the positive and negative currents of plutonium are required. In this case, the positive current is defined as plutonium atoms moving from inner to outer regions in radial geometry whereas the negative currents move in the opposite direction. Since plutonium current has two contributing terms from concentration and temperature gradients, we need to distinguish the signs of each term. Given that the heat of transport of ( ) plutonium and temperature gradient are always negative, the term − is always negative. In contrast, because of the accumulation of plutonium in the center, the plutonium concentration in the inner regions will always higher than that in the outer region,

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thus, making the term − always positive. As a result, the positive and negative plutonium fluxes are defined as follows:

=− (48)

(1− ) =− (49)

The discretized forms of positive and negative plutonium currents are given by:

, −, () =−() (50) −

,1 − , − () =−() (51) −

where C Pu,i = Plutonium concentration at radial node i (wt%)

CPu,i1 = Plutonium concentration at radial node i+1 (wt%)

CPu,i1 = Plutonium concentration at radial node i-1 (wt%)

Ti = Fuel temperature at radial node i (K)

Ti1 = Fuel temperature at radial node i+1 (K)

Ti1 = Fuel temperature at radial node i-1 (K)

ri1 = Fuel radius at node i+1 (m)

ri1 = Fuel radius at node i-1 (m)

U-Pu interdiffusion coefficient is given as follows:

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55351 =3.4×10 ×− (52)

where T = fuel temperature (K)

Assuming that plutonium atoms do not migrate outside of the fuel pellet surfaces and that a uniform concentration of plutonium exists at the beginning of life, the initial and boundary conditions can be defined as follows:

(, = 0) = (53)

(=,) = 0 (54)

= , = 0 (55)

where CPu0 = initial plutonium concentration (wt%)

2 (=,) = Negative plutonium current at inner fuel radius (atom/m /s)

2 = ,= Positive plutonium current at outer fuel radius (atom/m /s)

By solving the set of equations described above, the time-dependent behavior of plutonium concentration in each radial node can be determined. Subsequently, the plutonium concentration profile will be used to update fuel thermal properties such as thermal conductivity, melting point, and oxide valence state at every time step. To update the radial power profile, it is assumed that the fission rate density is directly proportional to local plutonium concentration as follows:

(, ) () = (56)

where P(r) = Radial power profile at radial node i

P0 = Initial radial power profile

CPu(r,t) = Plutonium concentration at radial i and time step t (wt%)

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CPu0 = Initial plutonium concentration (wt%)

4.3 Oxygen-to-metal ratio variation with burnup

It is commonly known that not only does the fission reaction split uranium or plutonium atoms into two lighter elements known as fission products, but it also breaks chemical bonding between fissile isotopes and its molecular constituents such as oxygen, nitrogen, carbon, or zirconium unless the fuel is in pure elemental form. Specifically for oxide fuels, there are two oxygen atoms being released from uranium or plutonium oxide molecules for every fission event. Table 7 summarizes the most probable chemical and physical states of major fission products in near- stoichiometric mixed oxide fuel [126]. Some of the fission products may have the same valence as uranium and plutonium and are able to recombine with the released oxygen atoms, form oxide compounds and maintain the oxidation state of the fuel. However, not all of the fission products can take all of released oxygen atoms from fission. Some of them do not react with oxygen and stay in elemental forms as inert gases or metallic precipitates. Those that do may form oxides of a lower oxygen-to-metal ratio than the uranium and plutonium. These fission products in general cannot effectively consume all oxygen atoms released from fission. As a result, the remaining oxygen dissolves in fuel matrix, increases oxygen potential and eventually increases oxygen-to- metal (O/M) ratio of the fuel. In the case of oxide fuels, the fission reaction can alternatively be viewed as an oxidizing process. In a closed system where conservation of oxygen atoms within the fuel volume is assumed or in the case that oxygen migration out of the fuel surfaces is negligible, the oxygen potential and oxygen-to-metal ratio should essentially increase with burnup.

Although the relationship between the oxygen potential and O/M ratio of unirradiated fuel is well defined [138], the translation from oxygen potential to O/M ratio for irradiated fuel involves large uncertainties. This is because many assumptions and allowances have to be made to take into account the effect of actinide production/depletion and dissolved fission products in the lattice. However, it is generally accepted that the oxygen potential and O/M ratio are directly proportional; the higher the oxygen potential, the more hyperstoichiometric is the state of the fuel.

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Table 7: Probable chemical and physical states of fission products in near-stoichiometric mixed oxide fuel [126]. Chemical group Physical state Probable valence Zr and Nb Oxide in fuel matrix; some Zr 4+ in alkaline earth oxide phase Y and rare earths Oxide in fuel matrix 3+ Ba and Sr Alkaline earth oxide phase 2+ Mo Oxide in fuel matrix or 4+ or 0 element in metallic inclusion Ru, Tc, Rh, and Pd Element in metallic inclusion 0 Cs and Rb Elemental vapor or separate 1+ or 0 oxide phase in cool regions of fuel I and Te Elemental vapor; I may be 0 or 1- combined with Cs as CsI Xe and Kr Elemental gas 0

Several oxygen potential measurements of irradiated samples have been performed in the past [138] [139] [140] [141] [142]. Included herein are some relevant examples of how the oxygen potential evolves as a function of burnup.

Walker et al. [138] have performed oxygen potential measurements on irradiated UO2 samples from a commercial PWR with an average burnup of 102 MWd/kgHM using a solid electrolyte galvanic cell. Figure 51 shows the oxygen potential of irradiated samples at 4 different radial positions where r/r0 represents the distance from the pellet center. It can be seen that the oxygen potentials of all irradiated samples are higher than (become less negative) the unirradiated stoichiometric UO2. In addition, the values of oxygen potential noticeably increase with fuel radius corresponding to the local burnup profile of LWR at high burnup where plutonium is accumulated at the fuel periphery.

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Figure 51: The oxygen potential at four different radial positions at high burnup UO2 fuel [138].

The work of Matzke [141] emphasized the oxygen potential in the rim region of high burnup

UO2 fuel. However, it also included some experimental results for oxygen potential of irradiated

samples of UO2, (U0.98Gd0.02)O2 and (U0.8Pu0.2)O2-x from other literature i.e. Matzke et al. [143], Adamson and Carney [139], and Une et al. [140]. Figure 52 shows the burnup dependence of the oxygen potential at 1023 K (750 oC) for various oxide fuels. It can be noticed that all of fuel samples exhibit a similar trend as oxygen potentials increase with burnup in a non-linear fashion.

Another example of oxygen potential increase as a result of burnup is presented from another work of Matzke et al. [143] as shown in Figure 53. In this work, the oxygen potentials of fresh and irradiated samples of hypostoichiometric mixed oxide were measured using a solid state galvanic cell. The irradiated samples were irradiated at 3.8, 7.0, and 11.2 at% in the Phoenix fast reactor. The results clearly show a monotonic increase in oxygen potential as a function of burnup as the oxygen potential become less negative than the fresh samples. Differences in

135 oxygen potential at the edge and center of the fuel can also be noticed even though the magnitudes of potential difference are not as high as those observed in LWRs.

Figure 52: Burnup dependence of the oxygen potential at 1023 K (750 oC) for different irradiated oxide fuel [141].

Figure 53: Oxygen potential measurement of irradiated Phoenix fuel of initial composition of

(U0.8Pu0.2)U1.98 [143].

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For fuel designs with ultra-high burnup targets as would exist in RBWR-TB2, the evolution of oxygen-to-metal ratio (O/M) with burnup is critically important for fuel performance evaluation because the oxidation state of oxide fuel strongly affects several material properties. First and foremost, thermal conductivity is heavily dependent on stoichiometric state of the fuel such that a change in O/M with burnup will significantly alter the temperature distribution. For hypostoichiometric fuel (O/M < 2.0), the effect of burnup will likely be beneficial because it helps in increasing the O/M ratio toward stoichiometry. On the other hand, it will be detrimental for stoichiometric (O/M = 2.0) and hyperstoichiometric fuels (O/M > 2.0) because it drives the fuel away from the optimal condition at stoichiometry. In addition, the O/M ratio is highly correlated with the oxygen potential of the fuel. An increase in oxygen potential with burnup will promote internal corrosion of the cladding. Mechanical performance at high burnup can also be affected because the creep properties of the fuel depend on the O/M ratio. Finally, the O/M ratio may have some influence on the diffusion coefficients of various species of fission products in the oxide fuel; which in turns will indirectly impact the behavior of fission gas release and fuel swelling at high burnup. Therefore, in order to describe the evolution of O/M ratio with burnup, a simplified approach proposed by Olander [126] was used. In this model, the fuel volume is modeled as a control mass system where all of the fuel constituents are not allowed to move out of the fuel. Figure 54 depicts a unit volume of fuel in both fresh and irradiated conditions.

Figure 54: A unit volume of fresh and irradiated mixed oxide fuel as a constant mass system [126].

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In this case, the number of oxygen atoms in the fresh fuel is

= ( + ) (57) where O/M = oxygen-to-metal ratio at beginning of life

3 = Initial number of uranium atoms (atom/m )

3 = Initial number of plutonium atoms (atom/m )

The initial atomic fraction of plutonium is defined as

= (58) +

Initially, the fuel mainly comprises of three elements: uranium, plutonium and oxygen. As a result of fission, fuel constituents change into a mixture of various substances as shown in Figure 54. The fraction of the initial heavy-metal atoms after burnup, β, is given by

+ = 1 − (59) +

and the ratio of plutonium to total heavy-metal atoms is

= (60) +

The number of uranium and plutonium atoms remaining after burnup is then:

= (1−)(1−)( +) (61)

=(1−)( +) (62)

The value of q depends on the conversion ratio and its variation with burnup. For fast spectrum reactors including RBWR-TB2, assuming no net change in plutonium content during irradiation or a constant conversion ratio of unity, the value of q can be simplified to

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= (63) 1−

For fission products, they can be classified into groups according to their chemical states as defined in Table 7. Within a particular group, these elements exhibit similar chemical and physical behavior in the irradiated fuel. The elemental yield of each fission product group is given in Table 8. The concentration of fission product in a particular group remaining after burnup is then

=( +) (64)

where Yi = the sum of the elemental yields of all fission products in group i

3 Ni = number of atoms of all fission products in group I (atom/m )

Table 8: Elemental fission product yield in a fast neutron spectrum [126]. Elemental yield Chemical group 235U 239Pu 15% 239Pu 85%238U Zr+Nb 0.298 0.204 0.219 Y+rare earths 0.534 0.471 0.493 Ba+Sr 0.149 0.096 0.109 Mo 0.240 0.203 0.206 Ru+Tc+Rh+Pd 0.263 0.516 0.456 Cs+Rb 0.226 0.189 0.209 I+Te 0.012 0.070 Xe+Kr 0.251 0.248

Of all fission product groups, molybdenum is one of the most important elements in determining oxygen potential after burnup because of its duality in valence state. From Table 7, probable valence of molybdenum in fuel matrix can be either 4+ if it remains in the metallic state or 0 if it

reacts with oxygen and forms an oxide. This is because the free energy of formation of MoO2 is comparable to the oxygen potential of nearly stoichiometric mixed oxide fuel. Therefore, the chemical state of molybdenum cannot be definitely assigned to a single chemical state.

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Olander [126] described the chemical states of molybdenum in irradiated mixed oxide fuel based on the following chemical reaction

+ → (65)

At thermodynamic equilibrium, this condition must be satisfied

( ) Δ =Δ − 66

where Δ = the free energy of formation of MoO2 = −574 + 164 (kJ/mole)

Δ= the oxygen potential (kJ/mole)

= atom fraction of molybdenum as oxide in fuel matrix

= atom fraction of molybdenum as element in metallic inclusion

T = fuel temperature in K

R = universal gas constant = 8.314 J/mole/K

The partitioning of molybdenum as oxide (MoO2) in the fuel matrix and as element (Mo) in the metallic inclusions can be described by the quantity fMo, which is defined as the fraction of the

total molybdenum oxidized to MoO2. In terms of fMo and the concentrations of the other species, the atom fraction of molybdenum as oxide in the fuel matrix can be defined as

f = (67) + + + + −

3 where = the concentrations of uranium (atom/m )

3 = the concentrations of plutonium (atom/m )

3 = the sum of the concentrations of yttrium and the rare earths (atom/m )

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= the total concentration of molybdenum in both oxide and metallic inclusion (atom/m3)

= the concentration of zirconium and niobium dissolved in the fuel matrix (atom/m3)

3 = the concentration of the alkaline earth oxide in the fuel matrix (atoms/m )

Similarly, the atom fraction of molybdenum in the metallic inclusion is

(1−f) = (68) + (1−)

where = the sum of the concentration of the noble metals ruthenium, technetium, rhodium, and palladium.

By substituting Equations 61-64, 67 and 68 into Equation 66 and some mathematical

simplification, the thermodynamic equilibrium between Mo and MoO2 can be described as a function of burnup and concentrations of uranium, plutonium and fission products.

f + (1− ) Δ = Δ − × (69) 2 1− 1−f + + + −

The oxygen potential of the fuel in Equation 69 can be written as

Δ =Δ −Δ (70)

where Δ = partial molar enthalpy of oxygen in mixed oxide fuel (kJ/mole)

Δ = partial molar entropy of oxygen in mixed oxide fuel (kJ/mole)

The partial molar enthalpy and entropy of oxygen as functions of plutonium or uranium valence are illustrated in Figure 55 [126]. Now the thermodynamic state of the irradiated fuel depends on

two unknowns: (1) the fraction of oxidized molybdenum (fMo) and (2) the valence of one of the

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actinides (VPu or VU). Because the values of VPu and VU depend on each other; they cannot be both unknowns at the same time.

To solve for these two unknowns, another equation is required to complete the system of equations: oxygen balance. It is necessary to assume that there are no net changes in oxygen concentration and electrical charge as a result of irradiation so that the electrical neutrality of the control mass system in Figure 54 can be preserved.

Figure 55: partial molar enthalpy and entropy of oxygen in mixed oxide fuel [126].

If the final state of the fuel matrix is such that VU = 4 and VPu < 4 (hypostoichiometric state), the charge balance on the fuel oxide phase is

2 =4 + +4( −) +3 +4 (71)

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The analogous charge balance for the case of VU > 4, VPu = 4 (hyperstoichiometric state) is

2 = +4 +4( −) +3 +4 (72)

3 where = the concentrations of oxygen in fuel matrix after burnup (atom/m )

All of the fission product concentration terms can be expressed in terms of burnup, elemental yield, and the uranium and plutonium concentrations so that the oxygen balance equation becomes

For hypostoichiometric fuel (UqPu1-qO2-x), VU = 4, VPu = 4+2x/q

2 =4(1−)(1−) + (1−) + (2 +4 +3 +4 ) (73)

For hyperstoichiometric fuel (UqPu1-qO2+x), VU = 4+2x/1-q, VPu = 4

2 = (1−)(1−) +4(1−) + (2 +4 +3 +4 ) (74) where x = deviation from stoichiometry = |/ − 2|

At every burnup step, the value of β and q are known. The elemental yields of each fission product groups are constant with burnup and can be found from Table 2. The free energy of formation of MoO2 (Δ) is already given as a function of temperature. Depending on the stoichiometric state of the fuel, it is possible to simultaneously solve a system of 2 equations 2 unknowns of molybdenum thermodynamic equilibrium (Equation 69) and oxygen balance

(Equation 73 or 74) for a fraction of molybdenum in oxide state () and valence states of

either plutonium or uranium ( or ). Finally we can solve for a variable x which is a deviation from stoichiometry and then convert it to the oxygen-to-metal ratio, respectively, at that time step.

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4.4 Oxygen-to-metal ratio variation with temperature

Not only does the oxygen-to-metal ratio evolve with burnup, but it also changes considerably under the influence of temperature gradient within a fuel pellet. The temperature-dependent behavior of the oxygen-to-metal ratio is primarily caused by the redistribution of oxygen atoms by thermal diffusion and changes in local oxygen potential and chemical states of all fission products. As discussed in the previous section, the oxygen-to-metal ratio influences several material properties. Fuel thermal conductivity is highly dependent on the stoichiometric state of the fuel such that a variation of O/M ratio with local fuel temperature and temperature gradient will significantly alter the temperature distribution. Such inter-correlation between fuel temperature and O/M ratio could create positive and negative feedback loops on both variables so the evolution of O/M ratio with temperature need to be addressed when analyzing fuel rods with high LHGR rating such as RBWR-TB2 designs.

The problem of oxygen migration has been investigated by many researchers during the 1970s [144] [145] [146] [147] [148] [149]. Similar to plutonium migration, two migration mechanisms were proposed: (1) solid state thermal diffusion and (2) vapor phase transport through cracks and

pores via oxygen carrying species such as CO-CO2, H2O-H2, UO3, and PuO. However, Bober and Schumacher [148] have found that oxygen redistribution still occurred even in fully dense samples where no gas pathways and transport of oxygen carriers were available. They concluded that solid state thermal diffusion is a dominant mechanism of oxygen transport. Then, Sari and Schumacher [149]performed a series of experiments and confirmed that solid state transport was the predominant mechanism because oxygen is highly mobile even in the solid phase of the fuel and contribution from gas transport via connected pores was limited because volume fraction of the connected cracks and pores were small when compared to the solid phase volume. They capitalized on this proposition and proposed a solid state theory of oxygen migration through thermal diffusion and measured oxygen heat of transport for both hypostoichimetric and hyperstoichimetric fuels. Based on Sari and Schumachers’ model, Lassmann [150] developed the OXIRED (oxygen redistribution) model for the redistribution of oxygen in nonstoichiometric mixed oxide fuels and implemented it into the TRANSURANUS fuel performance code. The OXIRED model can calculate the time evolution of the O/M ratio as a function of burnup and radial temperature profile. However, the burnup-dependent behavior of O/M ratio in OXIRED

144 model is based on a simple empirical correlation where O/M ratio was assumed to linearly increase with burnup at a certain rate. Since then, the OXIRED model has been widely used to describe the behavior of oxygen redistribution of non-stoichiometric UO2 and MOX fuels. Several OXIRED-based models were proposed and implemented into other fuel performance codes such as FEAST-OXIDE [128], FRAPCON-EP [8] [9] and SFPR [151] or separately implemented in a commercial finite element code, COMSOL, to study the effect of oxygen redistribution in coupled heat and oxygen transport problems [152] [153] [154].

In this work, the OXIRED model covering oxygen redistribution under temperature gradient was implemented into FRAPCON-3.5 EP but the burnup dependent portion was discarded because it was superseded with a more mechanistic model from Olander [126]. The OXIRED model describes diffusing species as oxygen vacancies and interstitials in hypostoichiometric and hyperstoichiometric fuels, respectively. The fluxes of oxygen vacancies and interstitials can be described by the following equations:

(1−) =− ∇ + ∇ (75) 1+/

=− ∇ + ∇ (76) 1+/ where D = diffusion coefficient of oxygen vacancies, v, or interstitial, i (m2/sec)

Cv, Ci = atomic fraction of oxygen vacancies and interstitials, respectively

γ = activity coefficient

Qv, Qi = molar effective heat of transport of oxygen vacancies and interstitials, respectively (J/mol)

R = universal gas constant = 8.314 J/mol/K

T = absolute temperature (K)

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The atomic fraction of oxygen vacancies (Cv) and interstitials (Ci) can be correlated to the deviation from stoichiometry in the following manner:

= (77) 2

= (78)

= −2= − 2 (79) +

According to Sari and Schumacher [149], in the case of dilute solutions of oxygen vacancies and

interstitials, the terms(1−), / and / become unity and the flux of oxygen vacancies and interstitials can be simplified into one equation and the subscript i and v can be replaced with subscript O which represents oxygen atoms.

=− ∇ + ∇ (80)

The time-dependent behavior of oxygen migration in radial direction can be modeled using Fick’s second law of diffusion (the continuity equation) as follows:

=−. (81)

If axial symmetry is assumed and axial gradients are neglected, the continuity equation becomes

1 =− ( ) (82)

Similar to plutonium migration, forward Euler and finite difference methods are used to discretize time-dependent and spatial-dependent variables, respectively. The discretized form of the continuity equation is given below:

× − × + × − × , =, +2Δ (83) −

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where ,= Oxygen concentration at node i of current time step

, = Oxygen concentration at node i of previous time step

= fuel radius at node i

= fuel radius at node i-1 to the left of node i

= fuel radius at node i+1 to the right of node i

= Outer boundary of radial node i (m)

= Inner boundary of radial node i (m)

= Positive oxygen current emerging from node i-1 towards the outer part of the fuel (atom/m2/s)

= Positive oxygen current emerging from node i towards the outer part of the fuel (atom/m2/s)

= Negative oxygen current emerging from node i towards the inner part of the fuel (atom/m2/s)

= Negative oxygen current emerging from node i+1 towards the inner part of the fuel (atom/m2/s)

Since oxygen current has two contributing terms from concentration and temperature gradients, we need to distinguish the signs of each term. Given that the heat of transport of oxygen vacancies/interstitials and temperature gradient are always negative, the term − is always negative. In contrast, because of the accumulation of oxygen vacancies/interstitials in the center, the oxygen concentration in the inner regions will always higher than that in the outer region, thus, making the term − always positive. As a result, the positive and negative oxygen fluxes are defined as follows:

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=− (84)

=− (85)

The discretized forms of positive and negative oxygen currents are given by:

, −, ( ) =−() (86) −

,1 − , − ( ) =−() (87) −

where CO,i = Oxygen concentration at radial node i

CO,i1 = Oxygen concentration at radial node i+1

CO,i1 = Oxygen concentration at radial node i-1

Ti = Fuel temperature at radial node i (K)

Ti1 = Fuel temperature at radial node i+1 (K)

Ti1 = Fuel temperature at radial node i-1 (K)

ri1 = Fuel radius at node i+1 (m)

ri1 = Fuel radius at node i-1 (m)

If conservation of mass is assumed then oxygen atoms cannot migrate outside of fuel pellet surfaces and the radial distribution of O/M ratio is uniform at the beginning of life, the initial and boundary conditions can be defined as follows:

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(, = 0) = (88) 2

(, = 0) = (89)

(=,) = 0 (90)

= , = 0 (91)

where x0 = initial deviation from stoichiometry = |O/M - 2|

2 (=,) = Negative oxygen current at inner fuel radius (atom/m /s)

2 = ,= Positive oxygen current at outer fuel radius (atom/m /s)

As described in the OXIRED model, the molar effective heat of transport of oxygen vacancies for hypostoichiometric fuel is given by

= −8.12 × 10 (4.85) < 3.3 (92)

= −3.96 × 10 + 2.38 × 10 −3.6×10 3.3 ≤ < 4.0 (93)

For hyperstoichiometric fuel, the molar effective heat of transport of oxygen interstitials is given as

= −3.5 × 10 (−17) ≥ 4.0 (94)

To evaluate the effective heat of transport of both oxygen vacancies and interstitials, the values of the valence of uranium and plutonium oxides as a function of deviation from stoichiometry are required. According to Olander [126], hyperstoichiometric mixed oxide has thermodynamic

properties equivalent to stoichiometric PuO2 and a hyperstoichiometric UO2. Therefore, the

compound (U1-qPuq)O2-x may be represented as a mixture of q mole fraction PuO2 and 1-q mole 4+ 5+ fraction UO2+m where m = x/(1-q). The uranium ions in UO2+x are a mixture of U and U (or possible U4+ and U6+). Since the addition of one O2- ion requires that two U4+ ions are converted to U5+ ions, the fraction of the total uranium in the compound UO2+x which is in the 5+ valence

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state is 2x. The average valance of the uranium ions in hyperstoichiometric material is therefore given by

2 =4+ (95) 1−

This formula also applies to the valence of pure UO2 by setting q to zero. The compound (U1-

qPuq)O2-x can be treated as an ideal solution of 1-q mole fraction UO2 and q mole fraction PuO2-m where m = x/q. Electric neutrality in plutonium oxides is maintained by conversion of some Pu4+ 3+ to Pu . In PuO2-x, the fraction of plutonium in the 3+ valence state is 2x and the average valence of the plutonium ions is therefore

2 =4− (96)

In the OXIRED model, the same correlation for diffusion coefficient of oxygen vacancies and interstitials atoms was suggested and it was later updated in FEAST-OXIDE to match the results reported by Lassmann [150].

−7500 =3.5×10 (97)

Unlike other chemical species, the direction of oxygen migration may appear to be bidirectional. For example, in the hypostoichiometric state (O/M < 2.0), the O/M ratio is lower in the center than in the periphery and oxygen atoms may appear as if they migrated to the lower temperature region. On the other hand, in hyperstoichiometric state (O/M > 2.0), the O/M ratio is higher in the center and it may look as if the direction of migration was reversed to the higher temperature region. This is primarily because of the way oxygen vacancies and interstitials relates to oxygen- to-metal ratio and deviation from stoichiometry. In fact, the movement on oxygen vacancies and interstitials is always unidirectional to higher temperature region. As the oxygen vacancies and interstitials migrate to the center of a fuel pellet, the deviation from stoichiometry, x, also increases in higher temperature and decreases in lower temperature regions accordingly. For hyperstoichiometric fuel, this will straightforwardly result in an increase in O/M ratio in the center. However, when it is converted back to O/M ratio, this variable becomes negative for

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hypostoichiometric fuel and it will result in a reduction of the O/M ratio in the center and an increase in O/M ratio at the fuel periphery. Overall, it may appear as if the oxygen atoms migrated to lower temperature regions in this case.

4.5 Cesium migration and formation of Joint Oxyde-Gaine (JOG)

Cesium is one of the most important fission products created during irradiation of nuclear fuel because of the following characteristics: (1) Cesium is abundant in nuclear fuel because it has a relatively high fission yield (~20%) and long half-lives (~30 years). (2) It has high mobility because of its low melting point (~300 K) and boiling point (~950 K). (3) Cesium is volatile at high temperature and can readily react with fuel, cladding and coolant. (4) It can migrate to the low temperature region and form complex compounds with fuel constituents and causes localized fuel swelling [155].

The migration of cesium and its chemical interactions have been reported by a number of experimental studies. They are mostly observed in fast reactors because these reactors operate at high temperature and high burnup [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166]. However, this phenomenon has also been observed in LWR fuel rods at high burnup and high LHGR during transients [155] [167] [168] [169].

Neimark et al. [156] examined two stainless-steel-clad mixed-oxide fuel rods irradiated in the EBR-II experimental fast reactor in the U.S. to a burnup of 11 at% (approximately 104 MWd/kgHM) and observed a noticeable migration of cesium at the top and bottom of the fuel column in the blanket zones. As shown in Figure 56, greater migration of cesium and higher 137Cs activities are observed in fuel rod C-19 with lower O/M ratio. The initial O/M ratio of fuel rods C-19 and C-10 are 1.94 to 1.97 and 1.99 to 2.00, respectively. This finding suggested that when the oxygen potential and O/M ratio are not high enough, cesium is likely to remain in an unoxidized state as elemental cesium which leads to stronger migration because of its higher mobility. The cesium atoms are thermodynamically driven toward the blanket zones because of

lower temperature and an abundant oxygen supply in UO2 pellets.

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Figure 56: Axial 137Cs activity profiles in fuel rod C-10 and C-19 [156].

Haas et al. [157] reported a similar finding from mixed oxide fuel bundles irradiated in the fast breeder prototype reactor SNR in France. Each bundle consisted of 34 fuel rods irradiated to a peak burnup of 10.6 at% (approximately 99 MWd/kgHM). Gamma ray scanning showed that cesium migrated radially and axially toward the ends of the fuel column. Again, it was observed that the fuel with high O/M ratio exhibited less migration of cesium. It was then suggested that with high O/M ratio, oxygen potential is sufficient for cesium to form stable cesium oxides and becomes stationary.

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An out-of-pile experiment has been conducted by Peehs et al. [170]to study the effect of temperature gradient on the migration of cesium and iodine. In this experiment, fuel pellets were 137 131 prepared from UO2 powder artificially doped with Cs and I to reflect the condition at 25 MWd/kgHM. The O/M ratio was maintained at stoichiometry. They were then loaded into 11 mm long tubular molybdenum heating elements. The temperatures at both ends were kept constant by water cooling. A parabolic temperature distribution similar to that of LWR can be simulated in this arrangement. Figure 57 shows the Cs and I axial distribution when the temperature in the middle was varied from 1273 K (1000 oC) to 1673 K (1400 oC). From a uniform distribution at the beginning, under the influence of high temperature and high temperature gradient, both Cs and I migrated to both ends of the heating elements where temperatures were maintained at 573 K (300 oC) to 593 K (320 oC).

Figure 57: The axial distribution of Cs and I under simulated temperature gradients [170].

Migration of cesium has also been observed in irradiated LWR fuel rods. Manzel et al. [167] examined 3 irradiated fuel rods and 2 irradiated fuel segments from commercial PWRs irradiated at LHGR between 20 and 25 kW/m and burnup ranging from 13 to 48 GWd/kgHM. At the end of its steady state operation, one fuel rod was exposed to a transient LHGR of 40.4 kW/m for 48

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hours. The maximum centerline temperature was reported to be between 1488 K (1215 oC) and 1523 K (1250 oC). Figure 58 shows the radial distribution of 137Cs and 134Cs at 22.9 and 48.26 MWd/kgHM which reflects the radial burnup distribution as a result of plutonium build-up and self-shielding near the periphery. The ratio of cesium activity between pellet rim and center was about 1.44 and 1.51.

Figure 58: 137Cs and 134Cs radial distribution profile at 22.9 and 48.26 MWd/kgHM [167].

The effect of higher fuel temperature on radial migration of cesium is shown in Figure 59 where fuel center temperatures were increased to around 1773 K (1500 oC) and 1973 K (1700 oC). The ratio of cesium activity between pellet rim and center was increased to 5.5 for 137Cs and 8.0 for 134Cs for a fuel rod segment operated at standard PWR power to a burnup of 13.49 MWd/kgHM but the gas gap was filled with argon instead of helium to increase fuel temperature. Another fuel rod was subjected to a fast power ramp with a terminal power at 40.4 kW/m for 48 hours holding time. The cesium activity ratio between pellet rim and center was 3.0 for 137Cs and 14.0 for 134Cs. The results from this experiment suggested that cesium migration is a thermally activated phenomenon.

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Figure 59: 137Cs and 134Cs radial distribution profile at higher fuel temperature [167].

The consequences of cesium migration on fuel and cladding performance have been reported by Asaga et al. [158] and Tsai et al. [159] where a fuel bundle of 37 stainless-steel clad mixed-oxide fuel rods was irradiated in EBR-II. The steady state LHGR of the test rods ranged from 30 to 36 kW/m. The peak burnup was reached at ~9.8 at% (~92 MWd/kgHM).

Figure 60: Localized cladding strain as a result of cesium migration [158].

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Figure 60 shows the axial profiles of cladding strain for different design groups. Major differences in group A, B, and C were pellet density, cladding material, and diametral gap. Significant effects of cesium migration can be observed in SS316 fuel pins as the locations of cladding strain peaks corresponded with those of cesium activity peaked at both the top and bottom of fuel column.

Tourasse et al. [160] examined mixed-oxide fuel pins irradiated up to 14 at% (~130 MWd/kgHM) in the Phoenix experimental fast reactor. Radial migration of fission products at high temperature and high burnup has been reported. The complex compounds of cesium, molybdenum, and oxygen found in the fuel-cladding gap were first termed JOG (Joint Oxyde- Gaine) as shown in Figure 61. The formation of JOG has significant impact on both thermal and mechanical behaviors of fuel rods because it affects the way gap conductance and PCMI evolves during operation.

Figure 61: X-ray mapping of the JOG compounds at peak power node at high burnup. The gap region is filled with chemical compounds of mainly Cs, Mo and O [160].

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Another irradiation experiment in EBR-II on stainless-steel clad mixed-oxide fuel had been reported by Boltax et al. [161]. The fuel pins were irradiated to a burnup of 5 at% (~47 MWd/kgHM) and 7.5 at% (~70 MWd/kgHM) for two cladding alloys: a ferritic-martensitic alloy, PNC-FMS, and an advanced austenitic stainless steel, PNC 1520. Both solid and annular pellets were included in the test. Figure 62 shows gamma scans of 137Cs for both types of fuel. Because of cesium migration, accumulation of cesium at the pellet-pellet gaps and near the top and bottom of fuel column can be clearly observed for both types of fuel. This works also

mentioned that different compounds of cesium such as Cs2UO4 or Cs2MoO4 may be formed in the fuel-cladding gap depending on local fuel temperature and oxygen potential.

Figure 62: Gamma scan of 137Cs of solid and annular pellets [161].

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Supporting evidence for cesium migration even in LWRs was provided by Walker et al. [155] where irradiated samples from commercial LWRs were subjected to transient conditions at which the fuel temperatures were greater than 1473 K (1200 oC). Normalized radial

concentration profiles of xenon and cesium retained in the UO2 samples were found to be similar indicating that cesium and xenon may share the same release pathway at temperatures above 1473 K (1200 oC). The differences in release behavior between xenon and cesium were noted at the pellet periphery where fuel temperatures fell below a threshold of 1473 K (1200 oC). The possible explanations were that, below 1473 K (1200 oC), cesium remains in a compressed liquid state or reacts with other fission products to form stable, solid compounds thus rendering it immobile. This work also reported an accumulation of cesium at pellet-pellet interfaces once the LHGR exceeds 30 kW/m.

Recent examples of radial migration of cesium and the formation of JOG in LWRs were reported by Van den Berghe et al. [168] where EPMA has been performed at the fuel-cladding interfaces

of irradiated UO2 fuel rods that were exposed to an LHGR of 22-32 kW/m to a burnup of 23 MWd/kgHM. It was found that the fuel-cladding gap was closed and filled with an interaction

layer. This bonding layer was composed of various phases, from the cladding inward, Zr, ZrO2,

Zr-Cs-O, U-Cs-O and UO2. Because of cesium migration, a similar bonding layer at high LHGR and high burnup in irradiated LWR fuel rods has also been reported in Kleykamp et al. [171] and Yagnik et al. [172].

Under typical LWR conditions, the behavior of cesium is somewhat inert because of its small concentration and relatively low fuel burnup. In addition, the fuel temperature under steady-state normal operation in LWRs is not high enough to trigger the migration process [155]. However, the behavior of cesium migration may no longer be neglected in the RBWR-TB2 because of its high temperature and high burnup operating conditions.

For sodium-cooled fast reactors, a more recent example of this behavior has been reported by Kurosaki [169]. The fuel rod was made of mixed oxide fuel irradiated in JOYO at high LHGR of 38 kW/m for 1019 effective full power days (EFPD) to reach a peak burnup of 144 MWd/kgHM. Figure 63 shows the formation of JOG and complex compounds of Cs and Mo in the fuel- cladding gap regions by electron probe microanalysis (EPMA).

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Figure 63: EPMA mapping images of JOG showing complex compounds of Cs and Mo [169].

Inoue et al. [162] presented a comprehensive characterization of the evolution of JOG and its effect on thermal performance of fuel rods. The experimental results were compiled from a number of irradiation tests conducted over a period of two decades at JOYO and other fast reactor facilities. The fuel rods were typically fabricated of mixed-oxide fuel in stainless steel cladding with a helium gas gap. Collectively, it was found that the fuel-cladding gap width decreases with burnup up to 50 MWd/kgHM which is consistent with classical understanding of fuel rod behavior. However, beyond 50 MWd/kgHM, some fuel rods showed large residual gap greater than a half of initial gap width. For fuel rods that did not develop JOG, the fuel-cladding gap remained closed. It was proposed that the formation of JOG in the gap depends on local burnup, LHGR, fuel surface temperature, cladding inner surface temperature. Axial migration and accumulation of cesium neat the top and bottom of fuel rods were also reported.

Additional investigation on the evolution of JOG and cesium migration based on irradiation tests at JOYO has been reported by Maeda et al. [163] [164] where a number of stainless-steel clad mixed oxide fuel rods were irradiated up to a maximum burnup of 98 MWd/kgHM in the assembly, 127 MWG/kgHM in the fuel rod, and 130 MWd/kgHM in the specimen. LHGR

159 ranged from 48.4 to 12.9 kW/m during the course of irradiation. Evidence of axial migration of cesium has been demonstrated in Figure 64 where the 137Cs intensity from gamma scanning was compared with the amount of 137Cs generated by the ORIGEN-2 code.

Figure 64: Axial distribution of 137Cs intensity along the fission column [164].

This work also revealed an interesting and complicating behavior of cesium because different compounds of cesium may be formed at different axial locations depending on surface temperatures and oxygen potential. Ceramographs at several axial positions of a fuel pin with averaged burnup 110.6 MWd/kgHM are shown in Figure 65 where dfb stands for distance from core bottom in mm. Positions A and B represents the bottom of the fuel, C and D represent the middle and top of the fuel, respectively.

Figures 65: Ceramographs of transverse section from bottom to top of fuel column [164].

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At the position A, the fuel-cladding gap was closed without a layer of JOG and a porous microstructure known as the RIM structure was formed near the fuel periphery. Above position B where the intensity of 137Cs was peak, the formation of JOG was found. Figure 66 shows EPMA mapping of position B showing that the gap layer was primarily filled with Cs, Mo, U, and O. At the location C where fuel surface temperature was higher, the JOG layer was mainly comprised of Cs, Mo, and O without fuel matrix elements as shown in Figure 67.

In the range of oxygen potential and fuel surface temperature of fast reactors, cesium uranate

(Cs2UO4) and cesium molybdate (Cs2MoO4) are identified as the most probable chemical

compounds to be formed. However, since the Gibbs free energy of formation of Cs2UO4 is lower

than that of Cs2MoO4, it is expected that Cs2UO4 is formed early during irradiation and once the

oxygen potential increases and more Mo is produced as a result of burnup, Cs2MoO4 is then formed at a later stage of irradiation. From the EPMA images, it appears that Cs2MoO4 is more

preferred at higher oxygen potential and fuel surface temperature whereas Cs2UO4 is more likely to form in low temperature and oxygen potential near top and bottom of the fuel columns.

Different chemical compounds of cesium have major implications for fuel rod performance.

Cs2MoO4 is believed to help improved gap conductance and delay the onset of PCMI pressure because of its softness which effectively acts as cushion between the fuel and cladding surfaces.

On the contrary, Cs2UO4 is a mechanically strong material and is thought to be the primary cause of localized fuel swelling and cladding strain at the top and bottom of fuel rods where cesium tends to accumulate.

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Figure 66: EPMA mapping of the gap region of position B [164].

Figure 67: EPMA mapping of the gap region of position C [164].

Uwaba et al. [165] [166] published detailed investigations on irradiation performance of mixed oxide fuel rods at high burnup. The work focused on the effects of cladding void swelling and cesium migration on cladding diametral strain at end-of-life. Fuel rod designs, irradiation conditions, and power histories were given in detail such that it was possible to use as reference for the validation of cesium migration model implemented in this work. Additional details on the work of Uwaba et al. will be discussed in the next chapter.

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There were two major approaches to quantitatively describe cesium migration and its subsequent interactions: (1) two-stage migration process [173] [174] [175] and (2) thermal diffusion based on concentration and temperature gradient [176] [177] [178] [179] [180] [181].

In the two-stage migration process, cesium migration is divided into radial and axial directions. In the radial direction, the cesium is assumed to rapidly migrate within the solid pellet as a result of or in conjunction with oxygen thermal migration and the radial distribution of cesium can be

∗ descried by an Arrhenius-type equation: () = () where N(r) is the cesium concentration at radial position r, A is an empirical constant representing cesium transport within fuel pellets, Q* is the effective heat of transport of cesium, R is a universal gas constant and T(r) is the corresponding temperature at r. In the axial direction, the transport of cesium across pellet- pellet interfaces occurs as a result of evaporation-condensation process, and the total flux of cesium across the surface can be described by another Arrhenius-type equation: =

(ℎ) − () () where is the total flux of cesium, k is an empirical constant

representing the mobility of cesium from evaporation-condensation process, ΔHv is the partial molar heat of vaporization of cesium.

Adamson and Vaidyanathan [173] [174] made an early attempt to capture these phenomena using the two-stage migration process. Their models were also based on out-of-pile experimental results and thermochemistry. It was implemented in their computer code called cesium-fuel reaction swelling (CFRS) and was benchmarked with experimental data from EBR-II and FFTF fuel rods. Furuya et al. [175] later employed this model in a computer code called MINERVA that was specifically developed to describe cesium migration and swelling in irradiated mixed oxide fuel. Predictions from MINERVA were compared with experimental results from JOYO.

The second approach to model cesium migration is by a thermal diffusion mechanism. This method is more common to other chemical species in fuel pellets such as plutonium and oxygen. It is widely adapted by many fuel performance codes for fast reactors such as TRAFIC [178], GERMINAL [179] [180] and CEPTAR [181]. Some considerations of cesium migration by thermal diffusion in LWRs have been studied by Rest [176] and Imoto [177]. This method allows the prediction of the JOG layer as a result of cesium radial migration. The thickness of

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JOG plays a major role in the evaluation of gap conductance which has a strong feedback to fuel temperature. Using the condition of chemical equilibrium and diffusion, the transport of volatile fission products e.g. Cs, I, CsI, Cs2MoO4, Cs2UO4 has been comprehensively described by Rest [176] and implemented in a computer code FASTGRASS. Imoto [177] utilized the thermal migration model based on irreversible thermodynamics and derived the time-dependent radial distribution of cesium concentration. It was found that the Arrhenius-type equation used to describe cesium radial concentration in the two-stage migration process can only be justified in the case of steady-state which is hardly achieved during irradiation.

In the previous version of FRAPCON-EP, cesium migration behavior was described only in the axial direction based on the evaporation and condensation part of the two-stage migration process while the radial migration portion and the formation of JOG were not implemented [8]. Fundamentally, the overall behavior of this model heavily relied on an arbitrary constant known as the mobility of cesium vapor. This constant has to be specifically adjusted to match experimental results of a particular reactor design. Previously, this constant was adjusted to match a series of fast reactor experimental data [128].

Therefore, to broaden the applicability of the model, a more mechanistic and general model based on a thermal migration mechanism should be used. In this work, the previous cesium migration model has been replaced with a thermal diffusion model based on Fick’s first and second laws of diffusion in both radial and axial directions [128] [181]. It is assumed that the flux of cesium will stop moving once it reaches the top and the bottom of fuel rod or fuel temperature is below 950 K (melting point of cesium). The governing equations for cesium migration and the fluxes of cesium under the influence of temperature and concentration gradient are given by:

C Cs  J Y F (98) t Cs Cs

Q J  D C  D C Cs T (99) Cs Cs Cs Cs Cs RT 2

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3 where CCs = Concentration of cesium (atoms/m )

2 JCs = Flux of cesium (atoms/m /sec)

YCs = Fission yield of cesium (~20%)

F = Fission rate density (fission/m3/sec)

2 DCs = Diffusion coefficient of cesium (m /sec)

QCs = Heat of transport of cesium = 60,000 (J/mole)

T = Fuel temperature (K)

R = Universal gas constant = 8.314 J/mole/K

If axial symmetry is assumed and axial gradients are included, the continuity and cesium flux equations become

1 =− − + (100) , ,

=− − (101) ,

=− − (102) ,

Similar to plutonium and oxygen migration, forward Euler and finite difference methods are used to discretize time-dependent and spatial-dependent variables, respectively. The discretized form of the continuity equation is given below:

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− + − , × −, × +, × −, × , , , , , =, +2Δ + Δ − −

+Δ (103)

where ,= Cesium concentration at node i of current time step

, = Cesium concentration at node i of previous time step

Δ = time step (seconds)

= fuel radius at node i

= fuel radius at node i-1 to the left of node i

= fuel radius at node i+1 to the right of node i

= Outer boundary of radial node i (m)

= Inner boundary of radial node i (m)

= fuel axial height at node j

= fuel axial height at node j-1 below of node j

= fuel axial height at node i+1 above node j

,= Positive radial current of cesium emerging from node i-1 towards the outer part of the fuel (atom/m2/s)

,= Positive radial current of cesium emerging from node i towards the outer part of the fuel (atom/m2/s)

,= Negative radial current of cesium emerging from node i towards the inner part of the fuel (atom/m2/s)

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,= Negative radial current of cesium emerging from node i+1 towards the inner part of the fuel (atom/m2/s)

,= Positive axial current of cesium emerging from node j-1 towards the upper part of the fuel (atom/m2/s)

,= Positive axial current of cesium emerging from node j towards the upper part of the fuel (atom/m2/s)

,= Negative axial current of cesium emerging from node j towards the lower part of the fuel (atom/m2/s)

,= Negative axial current of cesium emerging from node j+1 towards the lower part of the fuel (atom/m2/s)

Since cesium current has two contributing terms from concentration and temperature gradients, we need to distinguish the signs of each term. Given that the heat of transport of cesium is positive and the radial temperature gradient is always negative, the term − is always positive. In contrast, because of the accumulation of cesium toward the fuel periphery, the cesium concentration in the outer regions will always higher than that in the inner region, thus, making the term − always negative. As a result, the positive and negative cesium fluxes are defined as follows:

=− (104) ,

=− (105) ,

The discretized forms of positive and negative cesium currents are given by:

− =−( ) , (106) , −

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− =−( ) , , (107) , −

where CCs,i = Cesium concentration at radial node i

CCs,i1 = Cesium concentration at radial node i+1

CCs,i1 = Cesium concentration at radial node i-1

Ti = Fuel temperature at radial node i (K)

Ti1 = Fuel temperature at radial node i+1 (K)

Ti1 = Fuel temperature at radial node i-1 (K)

ri1 = Fuel radius at node i+1 (m)

ri1 = Fuel radius at node i-1 (m)

Similar treatment can be applied for axial cesium currents and it will not be repeated here, however, it is worth to mention that the axial temperature gradient can be both negative and positive depending on the axial position. Because cesium fluxes from concentration and temperature gradient are always in opposite directions, therefore, the cesium current terms used in the discretized forms have to be switched accordingly.

The above equations are subject to the following initial and boundary conditions.

CCs (r,t  0)  0 (108)

J z,Cs  0 at z = 0 and z = L (109)

J r,Cs  0 at r = Rfi (110)

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J r,Cs  J z,Cs  0 when T < 950 K (111)

where R fi = fuel inner radius (m)

L = fuel rod length (m)

Diffusion coefficient of cesium is given by the following expressions [181]

DCs  D1  D2  D3 (112)

 6.9510 4  10   D1  7.610 exp  (113)  RT 

2 0 D2  S J v cv (114)

40 D3  2 10  F (115)

5.48104 J  1013  exp( ) (116) v RT

2    s S  zv0 4K' cv   1 2 2 1 (117) 2Z  J v ( s S  ZV0 ) 

5.52104 V  exp( ) (118) 0 RT where S = Jump distance of cesium atoms, corresponding to1/ 3 (  4.091029 m3 )

J v = Jump frequency (1/s)

0 cv = Content of vacancy

15 -2  s = Sink intensity = 10 m

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Z = Number of sites surrounding a defect = 2

K’ = Generation rate of defect = 104 (defect/atom/s)

F = Fission rate density (fission/m3/sec)

The thickness of the JOG layer can be computed according to the amount of cesium migrated to the outer region and released out of the fuel pellet. In this work, the method and assumptions as proposed by Ozawa et al. [181] and Melis et al. [179] [180] have been adopted. First, it is assumed that the JOG layer is entirely made of Cs2MoO4 and does not cause additional cladding stress even when PCMI occurs. Then, the pre-requisite for JOG formation are: (1) sufficient oxygen potential must be available to cause the chemical reaction between cesium and molybdenum so the oxygen-to-metal ratio in fuel outer region has to be above 1.985, (2) fuel surface temperature has to be below 1373 K and clad surface temperature has to be below 873 K

so that the fuel-cladding gap temperature is under the dissociation temperature of Cs2MoO4 at 1200 K. The expression below is used to calculate the JOG thickness.

= ,()2∆ + − (119)

where = JOG Thickness (m)

2 ,() = Positive radial current of cesium at fuel pellet surface (atoms/m /sec)

= Fuel outer radius (m)

Δ = time step (seconds)

= Molecular weight of Cs2MoO4 = 426 (g/mole)

23 = Avogrado’s number = 6.022x10 (atoms/mole)

3 = density of Cs2MoO4 = 4 (g/cm )

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The effect of the JOG layer on fuel temperature can be treated as adding another layer of thermal resistance onto the fuel pellet surface in a similar manner as the zirconium oxide layer on the cladding outer surface. However, the formation of the JOG layer will have another effect in

reducing the fuel-cladding gap thickness thus improving the gap conductance. Since ≪

, the temperature drop across the JOG layer can be approximately by the following equation

′′ ∆ = (120)

where ∆ = Temperature drop across the JOG layer

′′ = Heat flux at fuel surface (W/m2)

= Thermal conductivity of Cs2MoO4 (W/m/K)

. = +0.03+3.2×10 × .

As a result of cesium migration, fuel swelling from solid fission product is affected. In this work, it is separated into two components: cesium and non-cesium. From [8] [182], it is suggested that cesium contributes to fuel swelling at a rate of 0.47% per 10 MWd/kgHM while the contribution of other fission products to fuel swelling is given as 0.2% per 10 MWd/kgHM.

By solving the governing equations for cesium migration, the radial and axial distribution of cesium concentration at every time step can be obtained. After normalization, it can then be used to adjust the distribution of cesium fuel swelling portion while preserving the total amount of fuel swelling from solid fission products which is directly proportional to fuel burnup.

4.6 High-burnup structure and RIM porosity

During its life cycle in a reactor, nuclear fuel experiences a few thousand displacements per atom from its initial lattice position. In LWRs, for example, each atom of nuclear fuel receives approximately 1 displacement per atom (DPA) per day. Most displaced atoms can elastically return to its original position; however, some atoms are permanently relocated and cause

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structural defects within the materials. Starting at local burnup of around 60 MWd/kgHM [183] and at irradiation temperature below 1073 K [49], another phase of localized fuel restructuring begins to take place, and the fuel structure completely transformed after 75 MWd/kgHM. This restructuring process results in a new fuel morphology, known as high burnup structure, to relate its occurrence with local burnup. It may also be called the rim structure to reflect the radial location when this phenomenon usually occurs.

High burnup structure (HBS) is a microstructural transformation of fuel material in response to an accumulation of point and extended defects. It is a natural self-reorganizing process in order to minimize the local internal energy of its structures. Although the exact mechanisms for HBS formation are not yet known, its characteristics are quite well-known by grain subdivision and accumulation of intergranular closed pores. From a typical grain size of around 10 μm, it is divided by a factor of 100 into submicron grains with a size of about 0.1-0.3 μm. These new submicron grains appear to be free of fission gas bubbles and extended defects. Fission gas bubbles are removed from the fuel matrix and are accumulated in micron-sized pores. HBS is typically found in a thin region of the fuel pellet near periphery where fuel temperature is below a threshold temperature of around 1073 K. Above the threshold temperature; HBS does not form because fuel temperature is high enough to heal structural defects through thermal annealing.

The formation of HBS can be observed in both thermal and fast reactors types of fuels: UO2 and MOX fuel in LWRs [184] [185], and fast reactor U-Pu oxide, carbide, and nitride fuels [164] [185] [186].

Figure 68 shows scanning electron microscopy (SEM) images of unirradiated UO2 fuel and fuel with local burnup of 75 MWd/kgHM. It can be seen that from a large grain size with distributed pores in the original structure, the fuel transformed into cauliflower-like one with numerous submicron grains and large pores accumulated outside of these small grains.

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Figure 68: As-fabricated grain (left) vs. high burnup structure (right) [49].

The formation of HBS and its effect on porosity evolution becomes relevant in the case of RBWR-TB2 because this reactor is designed to operate at a high local burnup exceeding 100 MWd/kgHM in both upper and lower fissile zones. The high concentration of porosity and fission gases formed in the HBS region is a primary concern over the occurrence of HBS. In terms of fuel performance, it could lead to sudden fission gas release during transients e.g. reactivity initiated accidents. Increased porosity in the HBS region degrades fuel thermal conductivity and may cause additional fuel swelling which could promote PCMI and cladding deformation.

In this work, a simple empirical model is used to describe the porosity evolution as a result of HBS formation. This model was originally proposed by Spino et al. [183]and the rates of porosity increase were later adjusted to match the experimental data published thereafter [184] [185] [187] [188]. The model has been adopted in some fuel performance codes [8] [189] [190]. In this model, fuel porosity in the HBS region is assumed to linearly increase as a function of local burnup when fuel temperature is below threshold temperature of 1073 K and local burnup exceeds 60 MWd/kgHM. The porosity evolution as a result of HBS formation is given as below.

0 < 60 =0.275 60 < < 100 (121) 0.063 > 100

where PHBS = Fuel porosity fraction (%)

BU = Local burnup (MWd/kgHM)

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To reflect the ability of the HBS region in the retention of fission gases, once the HBS is formed in a given radial node, additional fuel swelling from HBS porosity is added to the fuel matrix while contributions from intra-granular and inter-granular gas swelling are proportionally reduced with local fuel burnup when it exceeds 60 MWd/kgHM. Once the local burnup exceeds 100 MWd/kgHM, it is assumed that the formation of HBS is complete and fission gases can no longer accumulate inside the grains and at the grain boundaries. Instead, all gaseous species have to remain in the form of large pores outside of newly subdivided grains in the HBS region. As a consequence, the intra-granular and inter-granular gas swelling disappears from the fuel matrix and only HBS porosity remains as a contribution to fuel swelling at the corresponding radial locations.

= ( +) + < 60 (122)

( − 60) = ( + ) ×1− + + 60 < < 100 (123) 40

= + > 100 (124)

where Stotal = Total fuel swelling (%)

Sinter = Fuel swelling from inter-granular gas bubbles (%)

Sintra = Fuel swelling from intra-granular gas bubbles (%)

Ssolid = Fuel swelling from solid fission products (%)

PHBS = Fuel porosity fraction (%)

Comparison of the empirical model with available experimental data from the open literature is shown in Figure 69 [184] [185] [187] [188]. It can be noticed the rate of porosity increase chosen in this model conservatively covers the upper limits for most of the experimental data points.

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Model Une et al. (2001) 20 Spino et al. (2005) Noirot et al. (2006) Noirot et al. (2008)

10 Fuel Porosity (%)

0 0 50 100 150 200 250 Local Burnup (MWd/kgHM) Figure 69: Porosity evolution as a function of local burnup in HBS region.

4.7 Hot-pressing

Hot pressing is a deformation process of a fuel pellet which allows the fuel radius to become smaller when under compressive stress from PCMI contact. The underlying principle of this physical phenomenon is the irradiation-induced sintering of as-fabricated porosity due to external pressure. In this case, the external pressure is defined as a difference between PCMI contact pressure and pore pressure, which is assumed to be the same as the plenum gas pressure. In other words, hot pressing can be viewed as a long-term and continuous densification process if necessary conditions such as irradiation, temperature and external stress are met. This physical phenomenon becomes effective when the fuel temperature is at elevated temperature approximately above half of fuel melting point (~1500 K).

The impact of the hot pressing mechanism is an additional reduction to cladding stress and strain from PCMI because in the current structural mechanics model, FRACAS-I, uses rigid-pellet

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assumption where the fuel radius can continuously expand outward due to thermal expansion, relocation, and irradiation swelling whereas negative contributions to fuel radius are limited at densification and relocation recovery. Since the densification process is assumed to reach equilibrium after 10 MWd/kgHM and relocation recovery can claim up to half of the initial gap thickness, their contributions to the reduction of pellet radius is not as strong as other pellet expansion phenomena. However, since the hot pressing is a function of PCMI contact pressure, the higher the pressure, the smaller fuel pellets will become. This negative feedback mechanism could help regulating the cladding stress and strain at high burnup and high temperature conditions. In normal operating conditions of LWRs, hot pressing is typically ignored because fuel temperature is not high enough for this process to become relevant. However, in the RBWR- TB2 design, various radial locations of fuel pellets are expected to operate well above half of fuel melting point. Therefore, hot pressing is expected to become effective and should be included in fuel performance analysis.

In this work, the hot pressing model based on lattice diffusion creep is adopted. The model was already included in MATPRO [191] [192] but it was not activated in a default version of FRAPCON-3.5. The hot pressing model is given as follows:

1 1− . 54126 =1.8×10 × − (124)

where ρ = Fuel density fraction (%)

T = Fuel temperature (K)

PPore = Effective hydrostatic stress on as-fabricated pores (Pa) = PPCMI-PPlenum

PPCMI = Interfacial pressure from PCMI (Pa)

PPlenum = Plenum gas pressure (Pa)

G = Grain size (μm) = 10 μm

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Essentially, this model represents thermal creep behavior of the fuel above ~1500 K; however, below this threshold temperature, irradiation creep dominates over thermal creep and its effect on hot pressing should be accounted for. This can be accomplished by establishing a lower temperature limit that can effectively represent irradiation creep. Therefore, the diffusional thermal creep correlation given by Routbort et al. [193] and irradiation induced creep correlation given by Combette et al. [194] are equated to find the effective temperature for hot pressing in the case that fuel temperature is below half of fuel melting point. This temperature serves as a minimum threshold temperature which represents the effect of irradiation creep. The hot pressing correlation uses the higher values between the fuel temperature and the effective temperature.

3.23 × 10 92500 = − (125)

=1.78×10 (126)

−92500 46552.5 = = (127) 1.78 × 10 76.58 − () × 3.23 × 10

where Teff = Effective temperature for hot pressing (K)

σ = External stress (MPa)

G = Grain size = 10 μm

φ = Fission rate density (fission/m3/s)

R = Universal gas constant = 1.987 cal/mol/K

4.8 Fuel swelling from gaseous fission products

In earlier versions of FRAPCON, fuel swelling has only one contribution from solid fission product accumulation which is modeled as a linear dependence with local fuel burnup whereas the contributions from gaseous fission products were ignored [10] [195]. A gaseous swelling model has been introduced in FRAPCON-3.5 to reflect past ramp test results where gaseous fuel

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swelling may influence permanent cladding hoop strain of high burnup fuel rods [7]. However, the implemented model is purely empirical and independent of the fission gas release mechanism. It is modeled as a linear strain component in the fuel thermal expansion subroutine and as a function of temperature over a range of local fuel temperatures from 1233 K to 2105 K. The model gradually takes effect between 40 and 50 MWd/kgHM by applying a factor that varies from 0 to 1 at 40 and 50 MWd/kgHM, respectively. In order words, the gaseous swelling is assumed to be zero if the local fuel burnup is below 40 MWd/kgHM or the local fuel temperature is below 1233 K or above 2105 K. Although empirical models are computationally efficient to represent any physical phenomena, they are often limited to a specific set of empirical data on which it was developed. In this work, the generality of the gaseous swelling model is extended such that it can cover a wider range of reactor operation conditions. This improvement can be accomplished by implementing a physics-based model which coupled the processes of fission gas release to gaseous fuel swelling in FRAPCON-3.5 EP. In this case, the default fission gas release model by Forsberg-Massih [7] serves as source terms and/or boundary conditions for intra-granular and inter-granular gas swelling models.

With the physics-based model, it is possible to differentiate between contributions from gas bubbles within grains and those that accumulate at grain boundaries so that microscopic parameters such as grain size, dissolution rate, and diffusion coefficient play a significant role in gaseous swelling behavior while the previous empirical model does not have this capability. Fuel swelling from gas bubbles within the grains and at grain boundaries are termed intra-granular and inter-granular gas swelling, respectively.

Figure 70(a) shows an accumulation of gas bubbles inside the grains as small pores and along the grain boundaries as large elongated pores of irradiated UO2. A schematic representation of these bubble formation and distributions are shown in Figure 70(b). This is a more accurate representation of gaseous fission products in irradiated nuclear fuels. In this case, the intra- granular and inter-granular gas bubbles and their impacts to fuel swelling are then treated separately.

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(a) (b)

Figure 70: (a) Ceramograph of gas bubbles in irradiated UO2 [198] and (b) schematic representation of intra-granular and inter-granular gas bubbles [197].

4.8.1 Intragranular gas swelling

Intra-granular gas swelling implemented in this work is based on a rate theory model proposed by Wood and Matthew [182] which was named Simple Operational Gas Swelling and Release I (OGRES-I) for intra-granular gases. In this model, behavior of intra-granular gas bubbles depend on 4 processes: (1) nucleation of bubbles on vacancy clusters in fission tracks, (2) dissolution of bubbles by fission spikes, (3) migration of fission gas atom from interior of the fuel grain to grain boundaries, and (4) bubble movement toward grain boundary under temperature gradient (effective only above 1873 K). OGRES-I model describes intra-granular gas behaviors according to a system of equations given below:

=− + − − + (128)

= + − (129)

= − (130)

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= + (131)

= (132)

=4 (133)

=2 (134)

3ℎ = (135) 4

3 where Cgf = Concentration of fission gas atoms in fuel matrix (atoms/m )

3 Cgb = Concentration of fission gas atoms in intra-granular bubbles (atoms/m )

3 Cb = Concentration of intra-granular bubbles (bubbles/m )

3 Ct = Total fission gas concentration inside the grain (atom/m )

= Rate of change of fission gas deposited into grain boundaries (atoms/m3/s)

Yg = Fission gas yield = 0.31 atoms/fission

= Fission rate density (fission/m3/s)

2 Dg = Fission gas diffusion coefficient (m /s)

= Sink strength of bubbles

B = Bubble resolution constant (1/s)

K = Bubble nucleation constant (1/s) = 0.027B

Nb = Fission gas atom per intra-granular bubble

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Rb = Intra-granular gas bubble radius (m)

R = Radius of fission spike = 6 nm

L = Length of fission spike = 6 μm

hs = fitting parameter = 0.6 [184]

-29 3 bv = Van der Waals constant for xenon = 8.5x10 m [184]

The system of equations described above is solved simultaneously using finite difference and forward Euler methods. Contribution to fuel swelling from intra-granular gas bubbles is a sum of dissolved gas atoms in fuel matrix and gas bubbles in the grains which can be approximated by:

4 =4.1×10 + (136) 3

Although, the magnitude of intra-granular gas swelling is generally small under normal operating conditions of LWRs, its contribution may no longer be negligible at higher temperature regime.

4.8.2 Intergranular gas swelling

The inter-granular gas swelling model as proposed by Matthew and Wood [198]or Simple Operational Gas Swelling and Release II (OGRES-II) is used in conjunction with existing fission gas release model by Forsberg-Massih [7] to describe the behavior of intra-granular gas bubbles and its influence to fuel swelling. The Forsberg-Massih model provides the production and release rates of fission gases to grain boundaries as well as grain boundary saturation—the inventory limit of fission gas accumulation at grain boundaries.

In the OGRES-II model, grain structures of UO2 or MOX fuel are represented by a three- dimensional array of tetrakaidecahedral (TKD) cells as shown in Figure 71. This geometrical arrangement is one of the most efficient ways for packing equal-sized objects together to fill space with minimal surface area. It comprises 8 hexagons, 6 squares, 14 faces, 24 corners and 36 edges. As exists in nature, the TKD geometry offers a more realistic microstructural representation of a grain and a network of grain boundaries than a spherical grain assumption.

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However, to simplify the calculations of grain boundaries swelling, a volume of TKD grain is approximated as a sphere with a diameter equals to a grain size.

Figure 71: A schematic representation of a TKD grain of equal side [199].

This model assumes that, through diffusion from the grain interior, once fission gases arrive at grain boundaries, they can either accumulate at the faces or edges of the grain. However, since the atomic bonding force is weaker at grain edges, it is more convenient for fission gas bubbles to grow, coalesce, and form a tunnel network of elongated pores as shown in Figure 72. Eventually, these interconnected channels along grain edges serve as an escape route of fission gases to fuel pellet surface.

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Figure 72: Schematic illustration of connected tunnel of grain edge bubbles [200].

This tunnel can be modeled as a tube that follows the path of grain edges. From the TKD grain shape and assuming the semi-dihedral angel of tunnel radius as 50o for a grain edge bubble, the grain boundary area occupied by tunnels and fractional grain edge swelling are defined by the following expressions:

∆ =1.29 − 0.6041 (137)

∆ = 0.5104 − 0.1613 (138) where ∆ = Surface fraction of grain edge bubble to TKD grain volume

∆ = Volume fraction of grain edge bubble to TKD grain volume

rt = Tunnel radius of grain edge bubbles (m)

a = effective grain radius = 5 μm

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The formation of grain edge tunnels can be characterized by two parameters: pinch off time and coalescence time. The pinch off time indicates the amount of time for a connected tunnel to collapse into bubbles while the coalescence time describes the time it takes for the bubbles to inflate into a tunnel. The evolution of tunnel radius is defined by the following equations.

= 1.12 −1 (139) +

= (140) Ω

() 1.30403 = 0.11452 + (141)

2.876 × 10 =1.38×10 − (142)

where rt0 = initial tunnel radius (~0.01 microns)

t0 = Pinch off time of a tunnel (s)

tc = Coalescence time of the new created string of bubbles (s)

= Arrival rate of fission gas atoms per meter of the grain edge (atom/s)

k = Boltzmann constant = 1.38x10-23 J/K

T = Temperature (K)

2 De = Surface diffusion coefficients (m /s)

γ = Surface free energy = 0.6 J/m2

-29 3 Ω = Atomic volume of UO2 = 4.09x10 m

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Pext = External pressure (Pa) = PPCMI-Pplenum

a1 = Empirical constant = 0.003

a2 = Empirical constant = 2.2

In addition, the model treats the behavior of gas bubbles at grain boundaries differently if the concentration of fission gases is below or above a threshold value known as grain boundary saturation. Before grain boundary saturation, the arrival rate of fission gas atoms to grain edges is proportional to the effective grain radius, surface fraction of grain edge bubble, and the rate of fission gas arriving at grain boundaries as calculated by the Forsberg-Massih model.

∆ = 0.834 (143)

where = Rate of fission gas accumulation at grain boundaries (atom/m2/s)

After grain boundary saturation the model assumes that all fission gases arriving at grain boundaries are to be deposited at grain edges and causes an increase in grain edge swelling. However, OGRES-II recommended a limit of grain edge swelling to 6% [198].

However, before grain saturation, a certain fraction of fission gases that do not reach the grain edges is assumed to be deposited at grain faces. The rate of fission gas accumulation at grain faces is defined by

∆ = 1− (144)

where = the arrival rate of fission gases to grain faces before grain boundary saturation (atom/m2/s)

The gaseous swelling from grain face bubbles can be calculated from the following equations

3 = (145)

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3 Where Vgf = Volume of grain face bubble (m )

3 Cgf = Concentration of grain face bubble (bubble/m )

a = Effective grain radius (5 μm)

The concentration of fission gas bubbles at grain faces is given as a function of temperature by

3.312 × 10 = 1928 (146)

The maximum allowable concentration of grain face bubble is 1014 atoms/m2.

The volume of grain face bubble can be determined from the following equations

4 = () (147) 3

3 3 () =1− () + () (148) 2 2

where rf = Radius of grain face bubble (m)

θ = Semi-dihedral angel of grain face bubble = 50o

From the number of fission gas atoms arriving at grain faces, the radius of grain face bubbles can be found from the following mechanical equilibrium condition:

2 = (149) −

After grain boundary saturation, grain faces can no longer accommodate fission gases and the arrival and release rate of fission gases at grain faces equalize, thus the contribution to gaseous swelling from grain face reaches equilibrium after grain boundary saturation.

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However, the gaseous swelling cannot increase indefinitely because there must a natural limit to which gaseous fission products can accumulate within the fuel pellet either within grains or around grain boundaries. From White and Tucker’s model [200], the limit on gaseous swelling depends on local fuel temperature of each radial node and is given by the following equation.

0.2 < 1950 ℃ Δ 4.1−2×10 × 1950 ℃ < ≥ 2000 ℃ = (150) 0.46 − 1.8 × 10 × 2000 ℃ < ≥ 2500 ℃ 1.0 > 2500 ℃

where = Total fractional gaseous swelling

o = Fuel temperature ( C)

4.9 Accelerated corrosion at high burnup

It is conventionally recognized that waterside oxidation of zirconium alloy cladding occurs in two stages. In the first stage, commonly termed pre-transition stage, a protective layer of zirconium oxide is formed and its growth can be described as a cubic growth law up to an oxide thickness of approximately 2 microns. Beyond the first 2 microns, the subsequent oxide layer is consecutively built upon a cycle of formation and breakdown of this protective oxide layer. The duration of each cycle decreases with time and is shorter than the pre-transition stage. The second state is typically known as post-transitions stage and can be well represented by a linear grow rate that encompasses the underlying cubic cycles. A schematic representation of two-stage oxidation of zirconium alloy is shown in Figure 73.

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Figure 73: Two-stage oxidation process of zirconium alloys [201].

Although, the exact mechanisms behind the transition from sublinear to linear growth rate of zirconium alloy oxidation are not yet identified and remains an ongoing research subject, a shift in microstructure of zirconium oxide is thought to be one of the most influential factors for this phenomenon. Under the condition of LWRs, zirconium oxide can exist in 3 possible phases: cubic, tetragonal, and monoclinic [202] as shown in Figure 74. In the range of low pressure, low temperature up to ~1473 K (~1200 oC), the monoclinic phase is the ground state phase of zirconia; however, other phases can also coexists under stress, certain grain size, and doping elements.

Figure 74: Possible phases of zirconium oxide (ZZrO2) in LWR conditions [202].

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It is widely accepted that, during the pre-transition stage, the microstructure of ZrO2 in this layer is predominantly tetragonal. Both tetragonal and cubic phases can be stabilized at this interface because of large compressive stress due to lattice mismatch between the metal and the oxide. The pre-transition oxide layer is dense, protective, and often termed a barrier layer. However, as the stress on the oxide decreases toward the oxide/water interface, the monoclinic phase becomes dominant. The microstructural transition to monoclinic due to stress relaxation is believed to be the cause of the formation of post-transition oxide layer deposited on top of the barrier layer. This post-transition layer is porous, contains a large number of cracks and pores and is known as breakaway layer which results in linear kinetics of oxide layer growth rate. The illustration of barrier and breakaway layers of ZrO2 is shown in Figure 75 where SPP stands for secondary phase particles of alloying elements [201].

Figure 75: Schematic of zirconium oxide formation showing barrier and porous layers [201].

Formation of porosity in zirconium oxide layer during oxidation also plays a contributing role to the transition from cubic to linear oxide growth rate. Point and line defects are formed as the oxide layer grows. As the oxide departs away from metal/oxide interface, stress relaxation, time and temperature cause the defects to migrate, accumulate and lead to the formation of pores which reduces the protectiveness of the post-transition oxide layer.

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Over the years, the two-stage oxidation mechanism has become a standard model to represent the behavior of zirconium oxide growth in LWRs and it has been widely implemented in various fuel performance codes including FRAPCON-3.5. Through rigorous experimental validation and numerous adjustments of empirical parameters, this empirical model has been able to provide an accurate prediction of oxide layer thickness and hydrogen concentration in cladding up to the burnup limit of 62 MWd/kgHM—the upper limit for which FRAPCON was designed.

However, recent experimental findings have observed that there may be a second transition in corrosion rate and hydrogen pickup at high burnup beyond 62 MWd/kgHM [203] [204] [205] [206] [207] [208]. In addition to high burnup condition, the transition in corrosion rate has also been associated with an accumulation of fast neutron fluence beyond 1x1026 n/m2 (>1 MeV) in the cladding. This phenomenon at high neutron fluence is known as accelerated corrosion and hydrogen pickup.

Zhou et al. [203] has proposed a 3-stage cladding corrosion model based on the hypothesis that oxidation kinetics consist of a cubic root law growth in the beginning of the oxidation stage, a linear growth kinetics and a second transition stage. It is based on the assumption that after the amorphization and dissolution of SPPs, acceleration in oxidation and hydrogen pickup fraction will occur. Oxidation will increase at higher linear rate and cladding hydrogen content will increase exponentially as illustrated in Figure 76.

In Zircaloy-2 and Zircaloy-4 claddings, Sn, Fe, Cr, and Ni are used as alloying elements. Because the solubility of Fe, Cr, and Ni is very low at LWR operating temperature, these alloying elements exist in Zr matrix in the form of intermetallic precipitates. In Zircaloy-2, two principal families of SPPs are present: Zr(FeCr)2 and Zr2(NiFe). Because of its relatively higher solubility, Sn remains in solid solution state and does not participate in SPP formation.

Despite its small amount of alloying elements in the Zr matrix cumulatively less than 3 wt%, they provide a significant improvement in term of corrosion resistance and hydrogen pickup to pure Zr, especially alloying elements in SPPs (Fe, Cr, and Ni) which exist only in trace amounts. The exact role of SPPs in the oxidation process is unclear. One postulation is that the SPPs create lattice strain which helps structurally stabilize the formation of protective tetragonal ZrO2 [209]

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or their existence interferes with the rate of electron transports through the oxide layer which potentially delays the oxidation process. Regardless of the underlying mechanism, the effect of SPPs on corrosion resistance is widely recognized; even the same alloys with different sizes and distribution of SPPs can have a tangible effect in corrosion performance [210] [211].

Figure 76: Schematic of 3-stage oxidation model proposed by Zhou et al. [203].

Upon long-term exposure to fast neutron fluence, it has been reported that small SPPs dissolve completely whereas large SPPs reduced in size at high burnup. As a result, SPP elements (Fe, Cr, and Ni) redistribute from the SPPs into the bulk Zr matrix and remains in solid solution well above their solubility limits. An increase in solubility of these elements is potentially due to the presence of irradiation-induced vacancies in the bulk Zr matrix that allow more foreign atoms to exist in its lattice. The presence of dissolved alloying elements as solid solution would also lead to easier hydrogen diffusion across the oxide layer [54].

Valizadeh et al. [205] published the results of TEM and EDX studies of Zircaloy-2 samples that have been irradiated for 3, 5, 6, 7 and 9 years in a Swiss BWR nuclear power plant. The 9 year sample was selected from the two-life rods that had been irradiated up to ultra-high rod average burnups of 78 MWd/kgU. This work confirmed the dissolution and depletion of the alloying elements, such as Fe, Ni, and Cr from intermetallic precipitates at high neutron fluence. It was

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also confirmed that neutron irradiation changes the microstructure of Zr(Fe,Cr)2 and they

become amorphous and progressively dissolve into the Zircaloy-2 matrix, while Zr2(Fe,Ni) size decreases due to Fe dissolution but no amorphization is observed. It was observed that the average size of SPPs increases as the small SPPs are dissolved during irradiation and SPP density decreases as neutron fluence increases. Dissolution of SPPs rapidly increases when neutron fluence exceeds 1x1026 n/m2. Correlations between accelerated corrosion and dissolution of SPPs have been demonstrated by Figure 77 which shows a rapid increase in oxide thickness and hydrogen content for 6 year sample which corresponds to fast fluence of 9.5x1025 n/m2 (> 1 MeV).

Figure 77: Oxide thickness, hydrogen content and rod growth as a function of fast fluence [205].

A similar finding has been reported by Garzarolli et al. [208] and Zhou et al. [203] which observed an accelerated corrosion rate and hydrogen pickup fraction (HPUF) at high burnup in Figures 78 and 79, respectively.

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Figure 78: Acceleration in oxide layer thickness at high burnup in Zircaloy-2 [208].

Figure 79: Acceleration in HPUF at high burnup in Zircaloy-2 [203].

From these experimental observations and the 3-stage cladding corrosion model proposed by Zhou et al. [203], it can be inferred that the acceleration in the oxide growth and hydrogen content after the dissolution of SPPs in the second transition regime can be represented by an increase in oxidation rate applied to linear growth behavior. Therefore, these phenomena can be modeled by applying a simple multiplying factor of 2.2 to the oxide growth rate calculated by a default correlation in FRAPCON-3.5 once neutron fluence exceeds a threshold value of 1x1026 n/m2 (>1 MeV). This multiplying factor was chosen based on an empirical fit to available data

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[9] [54]. Since the original oxide growth model in FRAPCON-3.5 does not have any dependency on neutron fluence, increasing oxidation rate after a certain fluence threshold provides a simple yet effective way to take the effect of neutron fluence and its subsequent phenomena into account.

In earlier versions of FRAPCON, a constant hydrogen pickup fraction assumption was used to evaluate the concentration of hydrogen in cladding. For Zircaloy-4, it was assumed constant at 15% of hydrogen atoms produced from oxidation reactions. For Zircaloy-2, the constant hydrogen pickup fraction at 30% had been used in older versions [10] until it was replaced by an empirical correlation in FRAPCON-3.4 [195] and later versions given by the following equations.

= 22.8 + 0.117( − 20) (151)

where Htotal = Hydrogen concentration in cladding (ppm)

BU = Local fuel burnup (MWd/kgHM)

This burnup-dependent correlation was used to directly calculate the hydrogen content in Zircaloy-2 as opposed to applying a hydrogen pickup fraction to the amount of hydrogen produced converted from oxide layer thickness. However, it seems to breakdown when fuel burnup is beyond the upper design limit of 62 MWd/kgHM as its exponential term rapidly increases which eventually lead to unrealistic results as shown in Figure 80.

To mitigate this issue, the default correlation is used only when fuel burnup is less than 62 MWd/kgHM. Above this burnup threshold, a constant hydrogen pickup fraction at 30% was applied for Zircaloy-2 as implemented in earlier versions of FRAPCON [10]. Since the hydrogen pickup fraction and concentration are coupled with the oxide layer thickness, acceleration in oxidation will correspondingly increase the hydrogen content in the cladding so that the effect of neutron fluence on accelerated corrosion is taken into account.

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106 4.5

3.5

2.5

1.5

Hydrogen concentration (ppm) Hydrogen 1

0.5

0 0 50 100 150 Fuel burnup (MWd/kgHM) Figure 80: Hydrogen concentration as predicted by a default correlation in FRAPCON-3.5.

4.10 Hydrogen migration and hydride precipitation in cladding

During operation of LWRs, corrosion reactions between zirconium alloy cladding and cooling water produces hydrogen as a product of the reaction. These hydrogen molecules can either dissolve into cooling water or enter the cladding and remain in a solid solution state or form hydride precipitates [212]. Under temperature gradients, hydrogen tends to migrate to colder regions in the cladding where solid solubility is low. Localized formation of zirconium hydride can severely degrades cladding ductility. Figure 81 illustrates a non-uniform distribution of zirconium hydride of a typical LWR fuel rod. In the radial direction, high concentrations of hydride precipitates can be observed near the outer cladding surface, forming a region known as the hydride rim. Concentration of hydride precipitates also increases axially as shown in Figure 81 because as coolant temperature rises along the axial direction, so do the corrosion rate and hydrogen concentration in the cladding. Even small cold spots between inter-pellet gaps could serve as localized hydride precipitation spots [212].

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Figure 81: Non-uniform distribution of zirconium hydride in a typical LWR cladding [212].

Experimental evidence of radial distribution of hydride precipitates and development of a hydride rim region near metal-oxide interface can be seen in Figure 82 showing cross-sectional metallography of high burnup cladding samples from PWR reactors [213]. From the work of Bossis et al., the hydrogen concentration in the hydride rim region can go up to 1300 wt. ppm whereas the average hydrogen concentration in the cladding is only 430 wt. ppm. [214]

Figure 82: Radial distribution of hydride in Zircaloy cladding [213] [214].

Since the corrosion and hydride precipitation is highly sensitive to local temperature, even slight variations in cladding temperature could result in non-uniformity of hydride concentration. Therefore, azimuthal temperature variation due to guide tubes, corners, and sides of the

196

assemblies could affect the hydrogen distribution and hydride formation. Azimuthal distribution of hydride has been observed experimentally by Billone et al. [213]where differences in hydrogen concentration between azimuthal zones are greater than 150 wt. ppm as shown in Figure 83.

Figure 83: Azimuthal distribution of hydride in Zircaloy cladding [213].

Localized accumulation of hydride in inter-pellet gaps has been demonstrated by Smith et al. [215] in Figure 84 showing a variation in hydride concentration at different distances from an inter-pellet gap. These three micrographs were taken from different axial elevations of a fuel pellet length. It can be seen that the concentration of hydride is lowest when it is far from inter- pellet gap in Figure 84(a). Concentration of hydride increases significantly in cold spots near inter-pellet gap as shown in Figures 84(b) and 84(c).

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Figure 84: Hydride distribution at the inter-pellet gap cladding compared to mid-pellet cladding [215].

Hydrogen migration and hydride precipitation are particularly important for RBWRs because they are designed to operate at higher cladding temperature, which will result in a higher oxidation rate and higher hydrogen concentration in the cladding. With a hardened neutron spectrum and higher local fuel burnup, accelerated corrosion and hydriding phenomena are likely to occur after neutron fluence exceeds a threshold limit and causes a complete dissolution of secondary phase precipitates (SPPs) of alloying elements in zirconium alloy cladding [9] [54]. Furthermore, cold spots at interfaces between fissile and blanket zones can be viewed as highly vulnerable regions for hydride precipitation and subsequent hydrogen embrittlement.

As cladding ductility depends on hydrogen concentration, it is necessary to accurately predict the behavior of hydrogen migration and hydride precipitation. Essentially, the transport of hydrogen occurs in response to two major driving forces: (1) concentration gradient (Fick’s law) and (2) temperature gradient (Soret effect). According to Puls et al. [216], the effect of stress gradient in the cladding on hydrogen transport is negligible. However, these transport mechanisms are only applicable to hydrogen in solid solution since hydrogen in the hydride phase (zirconium hydride) is not mobile. In this work, a mechanistic model for hydrogen migration and hydride precipitation in radial and axial directions was developed and implemented in FRAPCON-3.5 EP. Note that azimuthal variation cannot be modeled because of axisymmetric assumption of the code. The governing equations for hydrogen transport and hydride precipitation kinetics are given below:

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C H  J  R  R (152) t H precipitation dissolution

C ZrH  R  R (153) t precipitation dissolution

Q J  D C  D C H T (154) H H H H H RT 2

2 R precipitation   (CH  TSSP) (155)

2 Rdissolution   (TSSD  CH ) (156)

3 where CH = Concentration of hydrogen (atoms/m )

2 J H = Flux of hydrogen (atoms/m /sec)

R precipitation = Precipitation rate of hydrogen from solid solution to hydride precipitate (atoms/m2/sec)

Rdissolution = Dissolution rate of hydrogen from hydride precipitate to solid solution (atoms/m2/sec)

2 DH = Diffusion coefficient of hydrogen (m /sec)

QH = Heat of transport of hydrogen = 25100 J/mole

 2 = kinetic parameter for hydride precipitation (1/sec)

 2 = kinetic parameter for hydride dissolution (1/sec)

TSSD = Terminal solid solubility for dissolution (wt. ppm)

TSSP = Terminal solid solubility for precipitation (wt. ppm)

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T = Clad temperature (K)

R = Universal gas constant = 8.314 J/mole/K

From Courty et al. [212], the diffusion coefficient of hydrogen in zirconium is a function of temperature and given by

4.49104 D  7.9107 exp( ) (157) H RT

where T = Clad temperature (K) and R = Universal gas constant = 8.314 J/mol/K

From Courty et al. [212], the precipitation (α) and dissolution (β) kinetic parameters of zirconium hydride are assumed to be equal and can be described by the following expression:

Q   A exp(  ) (158)  RT

where A  62.3 and Q  4.12E4(J/mole)

From Courty et al. [212], TSSD and TSSP are a function of temperature and given by

4328.67 TSSD  106446.7 exp( ) (159) T

4145.72 TSSP  137846.0exp( ) (160) T

The following expression is used to convert TSSP and TSSD from wt. ppm to atom/m3

atom TSSDwt.ppm 1 TSSD   (161)  3  6  m  10  Zr

-29 3 where  Zr = atomic volume of zirconium = 2.3x10 m

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Because of temperature hysteresis in hydride precipitation and dissolution, the governing equations described above can be classified into 4 cases: (1) CH ≥ TSSP, (2) CH ≤ TSSD and

CZrH > 0, (3) CH < TSSD, and (4) TSSD ≤ CH < TSSP.

Case 1 occurs when concentration of hydrogen in solid solution exceeds TSSP, so there will be a net production in hydride from precipitation and transport of hydrogen. The governing equations become

C H  J   2 (C  TSSP) (162) t H H

C ZrH   2 (C  TSSP) (163) t H

Case 2 is when concentration of hydrogen in solid solution is below TSSD and concentration of hydride is greater than zero then there will be a reduction in hydride concentration. The governing equations become

C H  J   2 (TSSD  C ) (164) t H H

C ZrH   2 (TSSD  C ) (165) t H

In cases 3 and 4, the concentration of hydrogen is either below TSSD or in between TSSD and TSSP so that there will be no production or loss of hydride in these two cases, and the governing equation will have only hydrogen transport term.

C H  J (166) t H

C ZrH  0 (167) t

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Given the heat of transport of hydrogen is positive, discretization sand solution methods for hydrogen migration and hydride precipitation are similar to those of cesium migration; therefore, it will not be repeated here.

All of the above equations are subject to the following initial and boundary conditions.

CH (r, z,t  0)  H 0 (168)

J H  0 at z = 0 and z = L (169)

J H  0 at r = Rci (170)

J H  J 0 at r = Rco (171)

3 where H 0 = initial hydrogen concentration in cladding (atoms/m )

2 J 0 = incoming flux of hydrogen (atoms/m /sec)

Rci = cladding inner radius (m).

Rco = cladding outer radius (m).

According to Courty et al. [212], the maximum concentration of hydride per unit volume is 18,200 wt. ppm which is a theoretical limit of hydrogen in stoichiometric zirconium hydride

(ZrH1.66).

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Chapter 5

Validation of FRAPCON-3.5 EP with Experimental Data

Since most of the physical models implemented in FRAPCON-3.5 EP have already been validated in previous work of FEAST-OXIDE [128] and FRAPCON-EP [8] [9], they will not be included in this thesis. Instead, this chapter will focus on the validation of new physical models discussed in previous chapters, namely, fuel restructuring, cesium migration and hydrogen migration phenomena. Even though the plutonium migration model has already been validated in previous work [128], it is included as a supplement because the information is readily available for comparison.

5.1 Modification of FRAPCON-3.5 EP for fast reactor conditions

It is also worth noting that, except for hydrogen migration, most of these experiments have been carried out in a sodium-cooled fast reactor environment. Thus, it is necessary to further modify the code to reflect the experimental conditions in sodium fast reactors. In this case, the cladding properties of HT-9 and SS-304 stainless steel have been added into the code [128] [217] [218] [219] [220] [221] [222] [223] [224] [225]. Material properties include density, melting point, heat of fusion, thermal conductivity, thermal expansion, irradiation swelling, thermal and irradiation creep, elastic and shear modulus, yield strength, Poisson’s ratio, emissivity, surface hardness, and oxidation rate. Detailed descriptions of HT-9 material property correlations can be found in the Appendix A. Coolant properties have also been changed from water to sodium [226]. Since the code uses a single-channel coolant enthalpy rise model to calculate the axial distribution of bulk coolant temperature, the following sodium properties have been included: melting point, boiling point, density, heat capacity, and thermal conductivity. The properties of sodium are given in the following correlations [226]:

= 1014 − 0.235 × (172)

, = −3.001 × 10 × + 1658 − 0.8479 × + 4.454 × 10 × (173)

= 104 + 0.047 × (174)

203 where T = Temperature (K)

3 ρsodium = density of sodium (kg/m )

Cp,sodium = Heat capacity of sedum (J/kg/K)

ksodium = Thermal conductivity of sodium (W/m/K)

From Sobolev [226], the melting and boiling points of sodium are 371 K and 1155 K, respectively. Because the coolant outlet temperature of sodium fast reactors is still below the boiling point of sodium, a single-phase convection heat transfer model can be used to calculate the heat transfer coefficients in the flow channel and the temperature drop across the sodium film layer by the code. From Todreas and Kazimi [125], heat transfer coefficients in a rod bundle geometry can be evaluated from the following heat transfer correlations for liquid metal coolant:

, =× × (175)

. . . = 4.0 + 0.33 × × +0.16× (176) 100

× ℎ = (177) where Pesodium = Peclet number

Nusodium = Nusselt number

2 hsodium = heat transfer coefficient (W/m /K)

G = mass flux (kg/m2/s)

De = hydraulic diameter (m)

P = fuel rod pitch (m)

Dco = outer cladding diameter (m)

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Coolant channel geometry has been modified from a square lattice typically used in LWRs to a hexagonal lattice in sodium fast reactors. The hydraulic diameter of these two lattices can be calculated by the following expressions.

4× − × 4 , = (178) ×

√3 4× × − × 2 4 , = (179) ×

In addition, the existing corrosion and hydrogen pickup models for water had been disabled in order to avoid interruptions and run-time errors due to excessive cladding corrosion. Since the water corrosion model was designed for the operating temperature of LWRs (550-600 K), running the code at higher coolant temperature in the range of sodium fast reactors (600-850 K) would result in an exponential growth of oxide layer thickness. Such occurrence is prohibited so that the code will stop running and error message is reported once excessive oxide layer growth occurs. By disabling corrosion and hydrogen pickup models, the corrosion rate and other chemical interactions between sodium and stainless steel cladding are assumed to be negligible in this work. This assumption is based on the fact that HT-9 and SS-304 stainless steels have high corrosion resistance [227]and that the corrosion rate of austenitic and ferritic steels in sodium is very slight (a few micron per year) [228].

5.2 Validation of plutonium and porosity migration models

Under steep temperature gradient and sufficient thermal energy (fuel temperature above sintering temperature), porosity and plutonium become mobile and migrate to higher temperature regions and this effectively creates a high concentration zone toward the fuel center. The size of the central void, determined from post-irradiation examination, can generally be used to infer the porosity migration behavior. For plutonium concentration as a function of fuel radius, it can be directly measured using electron probe microanalysis (EPMA). In this work, the experimental data from the B11 and B14 experiments in a 140 MWth sodium-cooled fast reactor, JOYO MK- III, in Japan published by Maeda et al. [122] [123] [124], Tanaka et al. [136] [137], and Di

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Marcello et al. [229] have been used for model validation. Table 9 lists fuel rod characteristics of the B11 experiments.

Table 9: Fuel rod characteristics of JOYO B11 experiments [229]. Pin Number Am-1-1-1 Am-1-2-1 Am-1-2-2 Clad inner diameter (mm) 5.56 5.56 5.56 Clad outer diameter (mm) 6.5 6.5 6.5 Pellet diameter (mm) 5.42 5.42 5.42 Fuel height (mm) 200 200 200 Fuel density (% TD) 93 93 93 Filling gas mixture 91% He-9% Kr 91% He-9% Kr 91% He-9% Kr Oxygen-to-metal (O/M) ratio 1.98 1.98 1.95 Fuel composition Am-Np-MOX Am-Np-MOX Am-Np-MOX U Content (wt%) 67 67 67 Pu Content (wt%) 29 29 29 Am (Content (wt%) 2 2 2 Np Content (wt%) 2 2 2

The B11 experiment consists of 3 fuel rod types (Am-1-1-1, Am-1-2-1 and Am-1-2-2). In term of fuel rod design, they are almost identical except for Am-1-2-2, which has a lower O/M ratio (1.95). The power history of the experiment is given in Figure 85. As can be seen from the figure, all fuel rods were subjected to a similar power ramp during the first 24 hours of irradiation. Then, Am-1-1-1 was tested for a very short irradiation time at an LHGR of 43 kW/m for 10 minutes followed by a SCRAM (rapid shutdown) whereas the remaining two rods were exposed to longer irradiation times at this LHGR for 24 hours followed by a normal shutdown. The axial peaking factor for each fuel rod is also shown in Figure 86 [123]. Different locations of each fuel rod in the reactor core resulted in minor differences in axial peaking factors.

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Figure 85: Power history of B11 experiment [229].

It should also be noted that for all figures in this chapter, FRAPCON-3.5 EP will be shortly referred to as FRAPCON whereas the experimental results from published literature will be referred to as Experiment.

1.08 1.06 1.04 1.02 factor 1 0.98 AM‐1‐1‐1 peaking 0.96 AM‐1‐2‐1 0.94 Axial AM‐1‐2‐2 0.92 0.9 0.88 0 0.2 0.4 0.6 0.8 1 Normalized axial position

Figure 86: Axial peaking factor of B11 experiment.

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Figure 87 shows the central void diameter as a function of normalized axial height from FRAPCON-3.5 EP prediction and experiment. It can be noted that the FRAPCON-3.5 EP prediction significantly overestimated the experimental results. This discrepancy clearly illustrates the limitation of the current pore velocity correlation in capturing the behavior of pores in short transient situations. Another possibility is that the correlation was mainly developed to match pore migration behavior at a longer time scale.

AM‐1‐1‐1 0.8 0.7 (mm)

0.6 0.5 0.4 diameter FRAPCON 0.3 void Experiment 0.2

Central 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 Normalized axial position

Figure 87: Central void diameter as a function of axial height for Am-1-1-1 rod.

A comparison of FRAPCON-3.5 EP prediction with experiment of central void diameter for Am- 1-2-1 and Am-1-2-2 fuel rods is given in Figures 88 and 89. When the holding time at high power has been extended from 10 minutes to 24 hours, better agreement in central void diameter is observed.

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AM‐1‐2‐1 1.2

1 (mm)

0.8

0.6 diameter FRAPCON void 0.4 Experiment

0.2 Central

0 0 0.2 0.4 0.6 0.8 1 1.2 Normalized axial position

Figure 88: Central void diameter as a function of axial height for Am-1-2-1 rod.

AM‐1‐2‐2 1.2

1 (mm)

0.8

0.6 diameter FRAPCON void 0.4 Experiment

Central 0.2

0 0 0.2 0.4 0.6 0.8 1 1.2 Normalized axial position

Figure 89: Central void diameter as a function of axial height for Am-1-2-2 rod.

Relative PuO2 concentration as a function of normalized fuel radius for the Am-1-1-1 fuel rod is shown in Figure 90. Plutonium migration behavior is modeled using thermal diffusion (the Soret effect) equations with zero flux boundary conditions at both inner and outer fuel surfaces. It can be seen that the thermal migration model in FRAPCON-3.5 EP predicts a slight increase in plutonium content near the center. However, the magnitude of increase seems to be within ±15% of experimental uncertainties.

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AM‐1‐1‐1 1.3 1.25 1.2 1.15 1.1

concentration 1.05 2 FRAPCON 1 PuO 0.95 Experiment 0.9

Relative 0.85 0.8 0 0.2 0.4 0.6 0.8 1 1.2 Normalized fuel radius

Figure 90: Plutonium concentration as a function of fuel radius for Am-1-1-1 rod.

The radial distribution of plutonium concentration of the Am-1-2-1 and Am-1-2-2 fuel rods is shown in Figures 91 and 92. Similar to porosity migration, the plutonium migration model shows better agreement with experimental data when the duration of experiment is longer. Both fuel rods have shown that plutonium has migrated to the fuel center and increased the concentration by 20-25% from the initial values.

AM‐1‐2‐1 1.3 1.25 1.2 1.15 1.1 concentration 2 1.05 Experiment PuO

1 0.95 FRAPCON 0.9 0.85 Normalized 0.8 0 0.2 0.4 0.6 0.8 1 1.2 Normalized fuel radius

Figure 91: Plutonium concentration as a function of fuel radius for Am-1-2-1 rod.

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AM‐1‐2‐2 1.3 1.25 1.2 1.15 1.1 concentration 1.05 Experiment 1 PuO2 0.95 FRAPCON 0.9

Relative 0.85 0.8 0 0.2 0.4 0.6 0.8 1 1.2 Normalized fuel radius

Figure 92: Plutonium concentration as a function of fuel radius for Am-1-2-2 rod.

The B14 experiment consists of 4 fuel rods with different designs characterized by a combination of O/M ratio and gap thickness: PTM0001 and PTM0003 have smaller gap thickness of 160 μm whereas PTM0002 and PTM0010 have larger gap thickness of 210 μm. Other important design parameters are shown in Table 10.

Table 10: Fuel rod characteristics of JOYO B14 experiments [229]. Pin Number PTM0001 PTM0002 PTM0003 PTM0010 Clad inner diameter (mm) 5.56 5.56 5.56 5.56 Clad outer diameter (mm) 6.5 6.5 6.5 6.5 Pellet diameter (mm) 5.4 5.35 5.4 5.35 Pellet height (mm) 8 8 8 8 Fuel height (mm) 400 400 400 400 Fuel density (% TD) 85 85 85 85 Filling gas mixture 91% He-9% Kr 91% He-9% Kr 91% He-9% Kr 91% He-9% Kr Oxygen-to-metal ratio 1.98 1.98 1.96 2.00 Fuel composition Am-MOX Am-MOX Am-MOX Am-MOX U Content (wt%) 66 66 66 66 Pu Content (wt%) 31 31 31 31

211

Am Content (wt%) 2.4 2.4 2.4 2.4

Figure 93 shows the power history of the B14 experiment which consists of power ramping, a holding period at constant power followed by a transient condition. First, the LHGR was increased to 34.7 kW/m in the first 24 hours and then the power was held for 24 hours before it was increased to 38.6 kW/m followed by a holding period of 24 hours. To simulate transient conditions, the power was rapidly increased to 47 kW/m for 10 minutes in the final stage before a rapid shutdown by manual scram. Rapid shut down helps preserve fuel microstructure and prevent further fuel restructuring during cooling down period.

Figure 93: Power history of B14 experiment [229].

The axial peaking factor for the B14 experiment is shown in Figure 94 [124] which appears to be a symmetric chopped cosine shape. However, since only one axial peaking factor is available in the literature, it is assumed that all fuel rods experienced the same profile.

212

1.08 1.06 1.04 1.02 factor 1 0.98

peaking PTM0001 0.96 0.94 PTM0002 Axial PTM0003 0.92 PTM0010 0.9 0.88 0 0.2 0.4 0.6 0.8 1 1.2 Normalized axial position Figure 94: Axial peaking factor of B14 experiment [124].

Figures 95, 96, 97, and 98 compare central void diameter as a function of axial height from the FRAPCON-3.5 EP calculation with experiment. It can be seen that, with similar power history and axial peaking factor, the predicted results are relatively close to each other. Overall, they are in good agreement with experimental data. The effect of larger gap size results in more fuel restructuring and a larger central void diameter. Given the same gap thickness, fuel rods with higher deviation from stoichiometry exhibit a larger central void diameter, primarily due to the impact of non-stoichiometry on fuel thermal conductivity.

213

PTM0001 1.6 1.4 (mm) 1.2 1 0.8 diameter Experiment 0.6 void FRAPCON 0.4 0.2 Central 0 0 100 200 300 400 500 Axial height (mm)

Figure 95: Central void diameter as a function of axial height for PTM0001 rod.

PTM0002 1.6 1.4 (mm) 1.2 1 0.8 diameter Experiment 0.6 void FRAPCON 0.4 0.2 Central 0 0 100 200 300 400 500 Axial height (mm)

Figure 96: Central void diameter as a function of axial height for PTM0002 rod.

214

PTM0003 1.6 1.4 (mm) 1.2 1 0.8 diameter Experiment 0.6 void FRAPCON 0.4 0.2 Central 0 0 100 200 300 400 500 Axial height (mm)

Figure 97: Central void diameter as a function of axial height for PTM0003 rod.

PTM0010 1.6 1.4 (mm) 1.2 1 0.8 diameter Experiment 0.6 void FRAPCON 0.4 0.2 Central 0 0 100 200 300 400 500 Axial height (mm)

Figure 98: Central void diameter as a function of axial height for PTM0010 rod.

Figures 99 and 100 show the radial distribution of plutonium for the PTM0001 and PTM0010 fuel rods as calculated by FRAPCON-3.5 EP and from the literature. The calculated results match relatively well within experimental fluctuation of ±20%. It can also be noted that PTM0001 has less plutonium concentration in the center than that of PTM0010. This is primarily because of different gap thickness and O/M ratio. PTM0010 has larger gap thickness resulting in higher fuel temperature and more migration potential. Higher oxygen potential for PTM0010 may also affect plutonium thermal diffusion mechanism.

215

PTM0001 1.3 Experiment

1.2 FRAPCON

1.1

Concentration 1 2 PuO 0.9

Relative 0.8

0.7 0 0.2 0.4 0.6 0.8 1 1.2 Normalized fuel radius

Figure 99: Plutonium concentration as a function of fuel radius for PTM0001 rod.

PTM0010

1.6 Experiment 1.5 FRAPCON 1.4 1.3 1.2 concentration 2 1.1 PuO 1 0.9

Relative 0.8 0.7 0 0.2 0.4 0.6 0.8 1 1.2 Normalized fuel radius

Figure 100: Plutonium concentration as a function of fuel radius for PTM0010 rod.

5.3 Validation of cesium migration model in-pile reactor experiments

Not only do actinide elements migrate under the influence of a temperature gradient, volatile fission products such as cesium also become mobile when the fuel temperature is above its migration threshold and in the presence of a large temperature gradient. The migration behavior

216

of cesium can be examined by 137Cs gamma scanning. Gamma ray activities measured from gamma scanning can be used to infer the relative concentration of cesium along the axial direction of fuel rods. In this thesis, the following experimental data were used to validate the cesium thermal migration model as implemented in FRAPCON-3.5 EP: (1) FFTF ACO-1 (2) FFTF ACO-3 and (3) JOYO C3M.

FFTF stands for Fast Flux Test Facility. It is a 400 MWth sodium-cooled fast reactor located in the United States. ACO-1 and ACO-3 are code names of test assemblies as part of the Core Demonstration Experiment (CDE). Experimental data from the ACO-1 experiment was published by Bridges et al. [230] whereas that of ACO-3 was published by Uwaba et al. [166]. In a separate publication, Uwaba et al. [165] also published experimental data from the C3M experiment which was a series of tests conducted in the JOYO experimental fast reactor aimed to assess the integrity of stainless steel cladding at high burnup in fast reactor conditions.

The key design parameters for ACO-1 and ACO-3 can be found in Table 11. According to the table, the irradiation time for ACO-1 is shorter than ACO-3. The ACO-1 fuel pellet is solid type while ACO-3 is made of annular pellet with a fabricated central void.

Table 11: Design parameters for ACO-1 and ACO-3 experiments [230].

Design Parameters ACO-1 ACO-3 Cladding Material HT-9 HT-9 Outer diameter (mm) 6.858 6.858 Wall thickness (mm) 0.533 0.559 Plenum volume (cm3) 23.6 23.6 Wire wrap Material HT-9 HT-9 Diameter (mm) 1.359 1.361 Pitch (mm) 15.24 15.24 Pellet Material MOX MOX

217

Outer diameter (mm) Solid Annular Inner diameter (mm) 0.0 1.473 Smeared density (% TD) 84.3 84.0 Pellet density (% TD) 90.5 92.0 Oxygen-to-metal ratio 1.96 1.95 Fuel composition 24.6 29.0

[Pu/(Pu+U)] (wt%) Duct material HT-9 HT-9 Irradiation Time (EFPD) 645.4 1106.7 Peak nominal cladding 925 922 temperature (K) Peak LHGR (kW/m) 44.49 39.6 Peak burnup (MWd/kgHM) 122.7 181.0 Coolant outlet temperature (K) Start 814 850 End 816 784 Peak fast fluence (1026 n/m2) 19.3 27.4

The power history (Peak LHGR vs time) is given in Figures 101. A straight line power history was inferred from published fuel and cladding temperature in the literature [230]. Since the information on axial peaking factor for ACO-1 fuel rod was not directly available in the literature, it was assumed that that of the ACO-3 fuel rod published by Uwaba et al. [166] is also applicable to ACO-1 fuel rod. Axial peaking factor as used in the simulation is given in Figure 102.

218

50 45 40 35

(kW/m) 30

25 LHGR

20 15 Peak 10 5 0 0 200 400 600 800 Time (Days)

Figure 101: Power history of ACO-1 fuel rod.

1.4

1.2

1 Factor

0.8

0.6 Peaking

0.4 Axial 0.2

0 0 0.2 0.4 0.6 0.8 1 Axial Height (m)

Figure 102: Axial peaking factor of ACO-1 fuel rod.

Figures 103 and 104 show the relative 137Cs concentration and EOL cladding strain as a function of axial height for the ACO-1 fuel rods from the FRAPCON-3.5 EP calculation and experiments. It can be seen that the current cesium migration model by thermal diffusion can generally capture the trend of cesium migration toward lower fuel temperature regions in the top and bottom of fuel rod. Clad straining near top of fuel rod indicates the effect of localized fuel swelling from cesium accumulation as well as the effect of thermal creep at coolant exit temperature. To reflect

219 the actual measurement at room temperature, the cladding strain from thermal expansion has been subtracted from calculated values. However, this model shows its limitations in capturing the discontinuous behavior and exponential increase in the inferred cesium concentration and cladding strain at the top of fuel rod (whether physical or not). Note that the overestimation of cladding strain may have come from the uncertainties in material properties and deformation models for the HT-9 cladding such as irradiation swelling, plasticity, thermal and irradiation creep. In addition, the production of cesium through radioactive decay of fission products such as xenon and iodine during cool-down storage may have contributed to an increase in cesium inventory at top of fuel rod.

5 Experiment 4.5 FRAPCON 4 3.5 3

concentation 2.5

Cs 2 1.5 Relative 1 0.5 0 0 0.2 0.4 0.6 0.8 1 Axial height (m) Figure 103: Relative 137Cs concentration as a function of axial height of ACO-1 fuel rod.

220

1.2 Experiment

1 FRAPCON (%) 0.8 EOL

0.6 strain

0.4 Cladding 0.2

0 0 0.2 0.4 0.6 0.8 1 Axial height (m) Figure 104: Cladding strain at EOL as a function of axial height of ACO-1 fuel rod.

Experimental data for 4 fuel rods are available from the ACO-3 experiments. These fuel rods are identified as 150073, 150080, 150088, and 150094. Additional information regarding their irradiation conditions are given in Table 12. These parameters are used to separately adjust input files to match their conditions at the end of life.

Table 12: Irradiation condition of fuel rods in ACO-3 experiments [166]. Fuel rod ID Pellet peak Peak fast neutron Life-averaged cladding burnup fluence (x1026 n/m2, midwall maximum (MWd/kgHM) E > 0.1 MeV temperatures (K) 150073 223.0 37.5 853 150080 212.3 35.6 810 150088 223.5 37.6 854 150094 231.5 38.9 794

Histories of LHGR, peak cladding midwall temperature, and axial peaking factor are given from the work Uwaba et al. [166] and are shown in Figures 105-107. The LHGR and cladding temperature track each other as they linearly decrease with time. Fluctuation in LHGRs

221 corresponds to repositioning of these fuel rods in the core. Note that the given axial peaking factor shown in Figure 106 has to be normalized so that the averaage value is equal to 1. After normalization, the peak at the middle of fuel rod is 1.2.

Figure 105: Power history of fuel rods in ACO-3 experiment [166].

222

Figure 106: Peak cladding midwall temperature of fuel rods in ACO-3 experiment [166].

Figure 107: Axial peaking factor of ACO-3 experiment [166].

223

Figures 108-111 shows the relative 137Cs concentration as a function of axial height for the 150073, 150080, 150088, and 150094 rods, respectively. Again, the calculated results from FRAPCON-3.5 EP predict a general trend of cesium migration toward colder region of the fuel rod. Experimental results have shown that the 137Cs concentration level in rods 150073 and 150088 are more pronounced than in rods 150080 and 150094 because they were irradiated at higher temperature in the central region of the fuel assembly. In general, good agreement in trends between the model and experimental results of fuel rods 150080 and 150094 is observed. However, the model underestimates the 137Cs concentration near the top of rods 150073 and 150088. Accumulation of cesium near the bottom of fuel rods 150088 and 150094 was well predicted by the model; however, such accumulation did not occur in rods 150073 and 150080. Given a symmetric axial peaking factor and similar power history, accumulation of cesium should occur at both ends of fuel rods according to the thermal migration model. This clearly indicates that there is likely another mechanism that prevents cesium migration. One possible mechanism is the formation of Joint Oxyde-Gaine (JOG) which is a stationary complex compound between cesium, oxygen and other fission products deposited on the fuel outer surface. In this case, the surface temperature has to be sufficiently low enough for such a compound to form and stabilize.

3 Experiment FRAPCON 2.5 137 ‐ Cs

of 2

1.5 Concentration 1

Relative 0.5

0 0 0.2 0.4 0.6 0.8 1 Axial height (m)

224

Figure 108: Relative 137Cs concentration as a function of axial height of 150073 fuel rod.

2.5 Experiment FRAPCON 137

‐ 2 Cs

1.5

1 Concentration

0.5 Relative

0 0 0.2 0.4 0.6 0.8 1 Axial height (m)

Figure 109: Relative 137Cs concentration as a function of axial height of 150080 fuel rod.

3 Experiment FRAPCON 2.5 137 ‐ Cs 2 of

1.5

Concentration 1

Relative 0.5

0 0 0.2 0.4 0.6 0.8 1 Axial height (m)

Figure 110: Relative 137Cs concentration as a function of axial height of 150088 fuel rod.

225

2.5 Experiment

2 FRAPCON 137 ‐ Cs

of 1.5

1 Concentration

0.5 Relative

0 0 0.2 0.4 0.6 0.8 1

Axial height (m)

Figure 111: Relative 137Cs concentration as a function of axial height of 150094 fuel rod.

Figures 112-115 show EOL cladding hoop strain as a function of axial height for rods 150073, 150080, 150088, and 150094, respectively. Generally, FRAPCON-3.5 EP predicts localized cladding straining near the top and bottom of the fuel rods where cesium accumulates. However, it overestimates the magnitude of cladding strains across the axial length even after the cladding strain from thermal expansion was subtracted from the calculated values.

Furthermore, the code does not model a peak in cladding strain at an axial elevation of around 0.3 m. The discrepancy between calculated and experimental results clearly emphasizes the importance of material properties and deformation models in fuel performance modeling. However, it may be acceptable for the scope of this benchmarking since the calculated results tend to be on a conservative side.

226

3.5 Experiment

3 FRAPCON (%)

2.5 EOL

at 2 strain

1.5

Cladding 1

0.5

0 0 0.2 0.4 0.6 0.8 1 Axial height (m)

Figure 112: Cladding strain at EOL as a function of axial height of 150073 fuel rod.

2.5 Experiment

FRAPCON 2 (%)

EOL

at 1.5 strain

1 Cladding 0.5

0 0 0.2 0.4 0.6 0.8 1 Axial height (m)

Figure 113: Cladding strain at EOL as a function of axial height of 150080 fuel rod.

227

3.5 Experiment

3 FRAPCON (%)

2.5 EOL

at 2 strain

1.5

Cladding 1

0.5

0 0 0.2 0.4 0.6 0.8 1 Axial height (m)

Figure 114: Cladding strain at EOL as a function of axial height of 150088 fuel rod.

3.5 Experiment

3 FRAPCON (%)

2.5 EOL

at 2 strain

1.5

Cladding 1

0.5

0 0 0.2 0.4 0.6 0.8 1 Axial height (m)

Figure 115: Cladding strain at EOL as a function of axial height of 150094 fuel rod.

228

The C3M irradiation test in the JOYO MK-III reactor provides experimental data for 3 fuel rods identified as G305, G339 and G357. Specific design parameters of fuel rods in the C3M experiment are listed in Table 13. Generally, they are of similar design but different in irradiation conditions so that they were exposed to different histories of LHGR, burnup, and cladding temperature.

Table 13: Design parameter of C3M fuel rods [165]. Fuel Rod ID G305 G339 G357 Cladding Outer diameter (mm) 6.5 6.5 6.5 Wall thickness (mm) 0.47 0.47 0.47 Wire wrap Outer diameter (mm) 1.34 1.34 1.34 Pitch (mm) 307 307 307 Fuel pellet (solid) Composition [Pu/(Pu+U)] (wt %) 30 30 30 Outer diameter (mm) 5.4 5.4 5.4 Oxygen-to-metal ratio 1.95 1.95 1.95 Pellet density (% TD) 85 85 85 Smeared density (% TD) 80 80 80 Fuel column length (mm) 550 550 550 Blanket pellet (solid) Uranium enrichment 235U/U (wt %) 0.2 0.2 0.2 Outer diameter (mm) 5.1 5.1 5.1 Oxygen-to-metal ratio 2.01 2.01 2.01 Pellet density (% TD) 94 94 94 Smeared density (% TD) 89 89 89 Peak burnup (MWD/kgHM) 113.8 123.2 127.6 Peak LHGR (kW/m) 29.54 32.3 33.81 Peak fast neutron fluence (x 1026 n/m2) 16.0 17.5 18.2 Cladding midwall temperature 801.3 887.6 839.2

229

Histories of the maximum LHGR and maximum cladding temperature for fuel rods in the C3M experiment are given in Figure 116. To convert a history of maximum LHGR into a power history, it has to be divided by a maximum peaking factor first. The axial peaking factor of the fuel rods G305, G339 and G357 can be inferred from the axial profile of fast neutron fluence shown in Figure 117. The history of the cladding midwall temperature given on the second y- axis of the figure can be used for validation of input conditions.

Figure 116: Histories of maximum LHGR and maximum cladding temperature of fuel rods in C3M experiment [165].

230

Figure 117: Axial profiles of fast neutron fluence and life-averaged cladding midwall temperature of C3M experiiment [165].

Figures 118-120 show simulation results from FRAPCON-3.5 EP in comparison with experimental data foro relative 137Cs axial distribution. Similar to experimental results of ACO-1 and ACO-3, the current thermal migration model can predict a higher cesium concentration toward lower temperature regions but it still underestimates the magnitude of 137Cs concentration near the top of the fuel rods.

Nevertheless, it should also be noted that given a symmetric axial peaking factor and lower fuel temperature at the bottom, the axial temperature gradients toward the bottom of fuel rods are higher than those toward to top. However, cesium diffusion coefficients are higher toward the top of fuel rods because of higher fuel temperature. Since the thermal migration model is driven by both temperature gradient and diffusion coefficients, these two effects seem to compensate each othere and results in a symmetric migration of cesium to both ends of fuel rods.

231

2.5 Experiment FRAPCON 2 137 ‐ Cs

1.5

1 Concentration

0.5 Relative

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Axial height (m)

Figure 118: Relative 137Cs concentration as a function of axial height of G305 fuel rod.

4.5 Experiment 4 FRAPCON 137

‐ 3.5 Cs

2.5

2 Concentration 1.5

1 Relative 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Axial height (m)

Figure 119: Relative 137Cs concentration as a function of axial height of G339 fuel rod.

232

2.5 Experiment FRAPCON 137

‐ 2 Cs

1.5

1 Concentration

Relative 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Axial height (m) Figure 120: Relative 137Cs concentration as a function of axial height of G357 fuel rod.

Figures 121-123 show the EOL cladding hoop strain as a function of axial height for rods G305, G339 and G357, respectively. For the C3M experiment, the accumulation of cesium at both ends of the fuel rod only leads to localized cladding strain at the bottom. It can be noticed that the code overestimates cladding strain of G305 across the axial length but it underestimates cladding strain from the middle toward the top of G-339 and G-357.

Although the behavior of cesium migration can be adequately described by the current cesium migration model, it does not translate well to cladding strain as the simulation results cannot capture the peak strain in the middle of fuel rod and the experimental results do not show localized clad straining at the point where cesium accumulates. One of the possible reasons of this discrepancy is that the cladding material used in the C3M experiment was a special grade of SS-316 austenitic stainless steel with the following composition Fe-16Cr-14Ni-0.05C-2.5Mo- 0.7Si-0.025P-0.004B-0.1Ti-0.1Nb. However, in this benchmarking, the material properties and irradiation behavior models of SS-304 austenitic stainless steel were used because the material property information for this special alloy was not readily available. In addition, since the focus of this experimental validation is to assess the ability of the mechanistic cesium thermal migration model, inaccuracies in cladding strain prediction can still be acceptable given that the

233 prediction in general tends to be on the conservative side except certain few spots where FRAPCON-3.5EP underestimates cladding strain. Furthermore, these simulation errors are even less relevant to RBWR-TB2 because the cladding materials will be based on a zirconium alloy. Therefore, the uncertainties in material properties and deformation models as observed in HT-9 stainless steel cladding will not get carried over to analyses of RBWR-TB2 fuel rods.

0.6 Experiment

0.5 FRAPCON (%)

EOL

0.4 at

0.3 strain

0.2 Cladding

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Axial height (m)

Figure 121: Cladding strain at EOL as a function of axial height of G305 fuel rod.

234

0.7

0.6 (%)

0.5 EOL

at 0.4 strain

0.3

Experiment

Cladding 0.2 FRAPCON 0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Axial height (m)

Figure 122: Cladding strain at EOL as a function of axial height of G339 fuel rod.

0.7

0.6 (%)

0.5 EOL

at 0.4 strain

0.3

Experiment

Cladding 0.2 FRAPCON 0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Axial height (m)

Figure 123: Cladding strain at EOL as a function of axial height of G357 fuel rod.

235

5.4 Validation of cesium migration model with out-of-pile experiments

Given some discrepancies between in-pile experiments in fast reactors and simulation results from FRAPCON-3.5 EP, it is beneficial to further validate the cesium migration model with out- of-pile experiments because the in-pile behavior may involve several inter-correlated phenomena which, therefore, come with greater uncertainties.

As cesium belongs to Group I elements of the periodic table, it is considered one of the most chemically reactive elements. Cesium spontaneously ignites in air and violently reacts with water. With constant presence of fission reactions and released oxygen atoms, the behavior of cesium is unavoidably affected in reactor environment whereas such conditions do not exist in out-of-pile experiments. In addition, the presence of other fission products such as iodine, molybdenum, and tellurium in nuclear reactors can further complicate its migration behavior because cesium can react with them and form immobile compounds.

In out-of-pile experiments, the migration behavior of cesium is only affected by the change in temperature and temperature gradient such that thermal migration mechanism may be able to effectively describe such behavior. Although it is possible that cesium may react with fuel constituents such as uranium and plutonium and form stable compounds, such reactions may be inhibited or delayed. Without fission reactions which break chemical bonds between uranium and oxygen, the rise in oxygen potential should be limited in out-of-pile experiments thus limiting chemical interactions of cesium with its surrounding. Therefore, this section aims to use out-of-pile experiments to validate the cesium migration mode currently implemented in FRAPCON-3.5 EP as a supplement to validation work using in-pile experiments in fast reactors.

In this work, experimental results reported by Peehs et al. [170] and Aitken et al. [231] were used as reference for validation. These experiments have been conducted during 1970s and 1980s to observe the effect of temperature and temperature gradient on migration behaviors of cesium.

Peehs et al. [170] carried out two types of out-of-pile experiments to investigate the migration

behavior of Cs and I in UO2: one with parabolic temperature profile and the other with hot and cold ends which will be referred to as Experiment #1 and #2, respectively. Schematic representations of these experimental devices are shown in Figures 124 and 125.

236

Figure 124: Schematic representation of experimental device for Experiment #1 [170].

In the Experiment #1, UO2 pellets were inserted into a molybdenum tube which served as a

heating element and a container. The pellets were artificially mixed with Cs and I into UO2 powder at concentration replicating the condition at 25 MWd/kgHM. Radioactive isotope of cesium and iodine (Cs-137 and I-131) were also included as tracer so that the distribution of cesium and iodine before and after excitements can be detected by gamma scanning. The oxygen-to-metal ratio of the pellets were reported at stoichiometry (O/M = 2.0). A parabolic temperature profile comparable to fuel rod conditions was created through Joule heating of the molybdenum tube and water cooling on both ends. Temperature at the middle the rod ranged from 1273-1673 K (1000-1400 oC) whereas temperatures at both ends were held constant at 473 K (200 oC). The length of sample was 11 mm. The test duration was 5 minutes. The initial concentration of Cs and I was uniform.

237

Figure 125: Schematic representation of experimental device for Experiment #2 [170].

In the Experiment #2, a molybdenum tube was again used as container of UO2 pellets and heating element. However, Cs and I were not homogeneously mixed into the powder instead they were filled into the heated end of the molybdenum tube prior to experiments. The heating method was changed from Joule heating to induction heating. The temperatures at hot and cold ends were held at 1473 K (1200 oC) and 473 K (200 oC), respectively. Water cooling was used to maintain temperature at cold end. The length of sample and duration of test were reportedly 100 mm and 600 minutes, respectively.

Aitken et al. [231] conducted a comprehensive investigation of the transport and reaction of Cs,

Te, I and Mo in (U,Pu)O2 fuel and stainless steel cladding. A series of out-of-pile experiments

have been performed by placing a stainless steel test capsules containing (U,Pu)O2 pellets under constant temperature gradient between 823 K (550 oC) and 1423 K (1150 oC). Fuel composition

was reportedly (U,Pu)O2 at 25 wt% PuO2 and 90-95 % TD. Cladding material was made of SS- 316 austenitic stainless steel. The thermal gradient along the 6-inch length of test capsule was

238

established by inserting hot end into a furnace. The capsules were maintained in the constant temperature gradient for 100 hours. A variety of additives i.e. Cs, I, Te, and Mo can be added into the hot end of the capsules. Oxygen-to-metal ratio of the pellets was varied in the range of 1.94-2.00 to investigate the effect of oxygen potential on chemical interactions between fuel constituents and these additives. However, in this validation work, only the test capsule that contained only cesium is focused. The source of cesium was Cs2O with Cs-137 as a tracer isotope. To minimize chemical interactions and its interference on migration behavior of cesium, the test capsule containing fuel with an O/M ratio of 1.94 (Capsule 4A) was used as reference for model validation. Schematic representation of the test capsule is shown in Figure 126.

Figure 126: Schematic representation of stainless steel test capsule showing the location where the additives (Cs, I, Te, and Mo) were introduced at hot end [231].

To quantitatively model the migration behavior of cesium, stand-alone MATLAB scripts were developed to represent the experimental conditions as described in Peehs et al. [170] and Aitken et al. [231]. Thermal migration mechanism in 1-D based on Soret’s effect and Fick’s law of diffusion was used to predict this phenomenon from the out-of-pile experiments. Time- dependent and spatial dependent variables were discretized and solved according to finite difference and forward Euler methods. Critical parameters such as diffusion coefficient and heat of transport of cesium are already given in Section 4.5.

For Peehs’s experiments, it appeared that the original diffusion coefficient of cesium as used in FRAPCON-3.5 EP (Turnbull’s correlation) was too slow to cause any visible migration at temperature and test duration as described in the paper. Several other correlations for solid state diffusion coefficient of cesium in UO2 have been reviewed and compared; however, none of them could match the experimental results shown in Peehs’s and Aitken’s experiments [155] [177] [176] [181] [191] [192] [232] [233] [234] [235] [236] [237] [238] [239] [240]. To resolve

239

this issue, this work also explored the possibility that cesium could migrate as gaseous species; thus, the solid state diffusion coefficient may be too slow to represent its behavior. To estimate diffusion coefficient of migrating gases, Chapman-Enskog theory of gaseous migration can be used [241]. It was developed based on kinetic theory of molecular motion in dilute gas; this theory is universal for all gases. The expression for gaseous diffusion coefficient is given by:

1 1 1.86 − 3 × × + = (180) ()

where

2 D12 = diffusion coefficient in cm /s

T = absolute temperature in K

p = pressure in atm

M1 and M2 = molecular weight

= collision diameter in angstrom =

= collision integral (unitless)

The interaction is mostly described in Lennard-Jones 12-6 potential. The parameter determines the depth of the potential well and the parameter is proportional to the distance between molecules at which the potential energy reaches a minimum. To determine the collision integral, the parameter / which represents the energy of interaction is given by the following expression:

= × (181)

240

Assuming cesium gas migrating in helium gas, the following parameters are based on the work

of Arefev et al. [242]: (cesium) = 4.55 Angstrom, /= 1108 K and (helium) = 2.58

Angstrom, /= 10.22 K. Then the values of collision integral can be found in Table 5.1-3 of Cussler [241] which will not be included here.

Anyway, after replacing solid state diffusion coefficients using Chapman-Enskog theory, the thermal migration model was still unable to match the experimental results. In fact, gaseous diffusion coefficient was so high that the finite difference scheme sometimes breaks down, thus very small time step was required.

Finally, a manual adjustment to diffusion coefficient and heat of transport of cesium was required. Using the existing parameters described in Section 4.5 as a starting point, the goal was to match the experimental results as closely as possible while using the same thermal migration mechanism as implemented in FRAPCON-3.5 EP.

Figures 127-130 show a comparison between simulation results and experimental data from Peehs’s Experiment 1 when maximum temperature in the middle of the rod was fixed at 1273 K (1000 oC), 1473 K (1200 oC), 1593 K (1320 oC) and 1673 K (1400 oC), respectively. Note that the experimental data and simulation results are normalized such that the area under the curve is equal to 1.0. In general, it can be seen that the model can capture the migration behavior of

cesium to colder temperature regions relatively well especially when Tmax was held at 1273 K (1000 oC) and 1593 K (1320 oC). However, some underestimation can still be observed when o o Tmax was set at 1473 K (1200 C) and 1673 K (1400 C). The source of these discrepancies may

have come from the fact that the diffusion coefficient (DCs) and heat of transport (QCs) used in the simulation were the same for all cases. Although it is possible to individually adjust DCs and

QCs to match the experimental results of each case, doing so would bring further complications without meaningful insight for the validation effort.

241

2.5

Model 1000 C 2

1.5

Relative cesium concentration (-) cesium concentration Relative 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative axial length o Figure 127: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1273 K (1000 C).

4.5

4 Model 1200 C

3.5

2.5

1.5

1 Relative cesium concentration (-) Relative cesium concentration

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative axial length o Figure 128: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1473 K (1200 C).

242

3.5

Model 3 1320 C

2.5

1.5

1 Relative cesium concentration (-) 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative axial length o Figure 129: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1593 K (1320 C).

4.5 Model 1400 C 4

3.5

2.5

1.5

Relative cesium concentration (-) cesium concentration Relative 1

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative axial length o Figure 130: Axial cesium distribution of Peehs’s Experiment #1, Tmax = 1673 K (1400 C).

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Therefore, it would be more preferable to use identical simulation parameters to validate the same set of experiment. Another possible source of error may have originated from normalization scheme because the experimental data was originally reported as a ratio of local

concentration divided by maximum concentration (C/Cmax) and these data points are not normalized. Upon examining the range of these data points, it can be seen that for the case of o o Tmax = 1593 K (1320 C) and 1673 K (1400 C), the measurement did not cover the entire length of the test rod. Instead, the data points only cover from the x/L = 0.2 to 1.0. With the current normalization scheme that equalizes the area under the curve, the axial profiles that have shorter range (smaller area) would have higher values that the one with full range (larger area) after normalization.

Peehs et al. [170] did not include the axial concentration profile of cesium in the Experiment #2; instead the paper reported the change in the peak location of Cs-137 activity. In addition, a variation of cesium migration behavior with O/M ratio has been reported. The general

observation was that the higher O/M, the slower cesium migrates. Using UO2.02, cesium quickly migrates to temperature regions of 1273 K (1000 oC). By increasing heating period, cesium peaks migrate relatively slowly down to temperature of 973 K (700 oC). By increasing O/M to 2.1, the migration behavior changes drastically; cesium is stabilized in a temperature region of about 1000 oC. Reportedly, the axial position of peak Cs activity has shifted around 10 mm in O/M ratio of 2.1 and around 16 mm in O/M ratio of 2.02. Currently, the thermal migration model does not have the capability to mechanistically model the effect of O/M ratio to diffusion

coefficient and heat of transport of cesium and intent to leave it as future work. Hence, the DCs and QCs were manually adjusted to match the experimental results for the case of O/M = 2.02. The simulation result seems to agree reasonably well with experimental data as shown in Figure 131. The discrete behavior of peak locations was a result of discretization of axial length and only the axial node where Cs-137 activity reached its maximum was reported. If a migration distance does not exceed an axial mesh size, the same axial node would be reported at that time step.

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Model 16 O/M 2.02

4 Location of Cs-137 peaks (mm) Location of Cs-137

0 0 100 200 300 400 500 600 Time(minutes) Figure 131: Location of Cs-137 peaks as function of time of Peehs’s Experiment #2.

For Aitken’s experiment, the axial distribution of Cs-137 activity as expressed by the unit of count per minute (cps) was reported. Figure 132 compares the simulation results with experimental data from the Capsule 4A at the beginning (0 hours) and the end of experiment (100 hours). The model took the axial distribution profile at 0 hours from experiment as initial condition and proceeded to further time step and redistribute the local Cs-137 activity according to temperature and temperature gradient at that axial location. In the Capsule 4A, the complete migration of cesium was observed as it has moved almost entirely from its initial position at the hot end to the cold end. The simulation result appears to match relatively well with experimental data as it closely predicted the location of Cs-137 peak near the cold end of the test capsule. However, the model still over-predicted a leftover of Cs-137 activity along its migration path. Essentially, it was a result of concentration gradient (Fick’s law) which counteracts the effect of thermal diffusion. Although it was possible to increase the heat of transport (QCs) to strengthen the thermal diffusion effect, for the sake of consistency, it was decided to keep this parameter the same as in Peehs’s experiments.

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4000 Model 0 hrs 3500 Model 100 hrs Experiment 0 hrs Experiment 100 hrs 3000

2500

2000

1500

Cs-137 activity (counts/min) Cs-137 activity 1000

500

0 0 20 40 60 80 100 120 140 160 z(mm) Figure 132: Axial distribution of Cs-137 activity before and after thermal treatment

In conclusions, this work has demonstrated that the migration behavior of cesium from out-of- pile experiments can be adequately described using a mechanistic thermal diffusion model as implemented in FRAPCON-3.5 EP and some adjustment to key migration parameters. In order to match the experimental data, the diffusion coefficient of cesium were manually adjusted from Turnbull’s correlation until the model produced satisfactory results whereas the value of cesium’s heat of transport from Ozawa et al. [181] was used throughout the simulation. Table 14 summarizes the correlations for DCs after adjustment and the value of QCs used in each out-of- pile experiment.

Table 14: Diffusion coefficient and heat of transport of cesium used in simulation Experiment Simulation parameters Peehs Experiment #1 Q = 6.95E4 J/mol Cs 2 D = 5.3087E-4*exp(-1.389E4/T) m /s Cs

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Peehs Experiment #2 Q = 6.95x104 J/mol Cs 2 D = 1.0622E-4*exp(-1.379E4/T) m /s Cs Aitken Capsule 4A Q = 6.95E4 J/mol Cs 2 D = 9.26E-5*exp(-1.389E4/T) m /s Cs

According to the table, it can be seen that only the pre-exponential factors of the Arrhenius equation are different while the activation energy term and heat of transport term are quite consistent throughout the simulated cases considered in this work.

In addition, it is also beneficial to compare the adjusted correlations with original ones from literature. As shown in Figure 133, the diffusion coefficients of cesium from Turnbull et al. [232], BISON fuel performance code [240], and Chapman-Enskog theory [241] are compared with the adjusted correlations for Peehs’s and Aitken’s experiments. Given that the Turnbull and

BISON correlations are developed for solid state diffusion of cesium in UO2 and Chapman- Enskog theory is intended for gaseous diffusion of cesium vapor in helium gas, they are approximately 10 to 20 orders of magnitude different. Naturally, gaseous diffusion occurs tremendously faster than solid state diffusion. In this case, it appears that the modified correlations are situated in the middle range between solid and gaseous diffusion and they are quite consistent with each other even though they were individually adjusted to match different experiments.

In this validation work, the mode of cesium transport may not be entirely through gaseous diffusion otherwise the diffusion coefficients from Chapman-Enskog theory would have been able to match the experiments. On the other hand, the correlations developed from in-pile reactor experiments were too slow and may not be appropriate for use in out-of-pile experiments. With constant supply of free oxygen atoms from fission reactions, it is understandable that they would interfere with migration mechanism of cesium during irradiation whereas in out-of-pile experiments, there is no net production of oxygen atoms and cesium may be able to migrate faster when such interference is minimized.

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100

10-5

/s) -10 2 10

10-15

10-20

Chapman-Enskog Theory Turnbull 10-25

Diffusion Coefficient (m BISON Peehs Experiment 1 10-30 Peehs Experiment 2 Aitken Capsule 4A

10-35 400 600 800 1000 1200 1400 1600 1800 Temperature (K)

Figure 133: Comparison of cesium diffusion coefficients used during simulation with correlations from literature

5.5 Sensitivity study of cesium migration model on cesium fuel swelling rate

In an effort to reduce the gap between model’s prediction and experimental data, the current cesium migration model could be modified in two ways: (1) adjusting the migration parameters i.e. diffusion coefficients and heat of transport and (2) adjusting the dependent variables i.e. fuel temperature, temperature gradient and local burnup.

Although it is possible to improve the accuracy of the model by arbitrarily adjusting diffusion coefficients and heat of transport of cesium until the model’s predictions match the experimental results, doing so would create contradictions with several correlations proposed in the literature. As shown in the previous section, there are a number of correlations for diffusion coefficients of cesium in irradiated UO2; most of them were developed from post-irradiation examinations or in- pile reactor experiments. Unlike out-of-pile experiments where manual adjustment of migration

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parameters may be justified because experimental conditions are vastly different from the in-pile ones; therefore, the first method is not desirable as it would further reduce the generality of the model. In this case, it is more preferable to rely on experimentally-derived correlations and find a way to adjust other dependent variables in the simulation. As the migration behavior heavily depends on the evolution of fuel temperature, temperature gradient, and local burnup, it is possible to alter these variables by adjusting a fuel swelling rate caused by cesium. Changing fuel swelling rate directly impacts the size of fuel-cladding gap which is subsequently used to determine gap conductance and fuel temperature. Thus, it is expected that by adjusting this parameter, the cesium migration behavior should be affected. Local burnup as a source term of cesium should remain unchanged because there should be no alteration in fissile number density as a result of cesium migration.

Therefore, in this sensitivity study, the existing migration parameters are kept as-is whereas the cesium fuel swelling rate is adjusted according to another reference. In the existing model, the rate of fuel swelling from cesium is set at 0.47% per 10 MWd/kgHM while other solid fission products contributes to fuel swelling at a rate of 0.19% per 10 MWd/kgHM. These figures were based on a model proposed by Matthew and Woods [198]; however, Olander [126] suggested a significantly lower swelling rate at 0.18% per 10 MWd/kgHM. To conserve total fuel swelling rate from solid fission products of the current model, it is implied that fuel swelling rate from other solid fission products should be increased to 0.48% per 10 MWd/kgHM.

To study its effect on cesium behavior, this new fuel swelling rate is then applied to the fuel swelling model of FRAPCON-3.5 EP. Then, the code is used to generate fuel temperature and local burnup necessary for the cesium migration model implemented as stand-alone MATLAB scripts. Experimental results from FFTF ACO-3 experiments are chosen as the representative samples for this study. Information about fuel rod geometry and reactor operating conditions are already described in Section 5.3. It is also noted that, in a following discussion of simulation results, the existing and the new fuel swelling rates will be briefly referred to as high swelling and low swelling models, respectively.

Figures 134-137 show a relative 137Cs concentration as a function of axial height for the 150073, 150080, 150088, and 150094 rods, respectively. In these figures, simulation results from

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MATLAB scripts using the high and low fuel swelling models are compared against experimental data. As shown in Figure 134, the axial distribution of cesium changes drastically as a result of a reduction in cesium fuel swelling rate. The high swelling model predicts that cesium would be concentrated at both ends of fuel rod whereas the experimental finding shows only cesium accumulation at the top of fuel rod. After adjustment of cesium fuel swelling, a better agreement between the model and the experiments can be observed. In the low swelling model, the bottom accumulation disappears while showing a stronger accumulation at the top which is in-line with the experiments. In Figure 135, a similar trend can still be noticed as the experimental results agree relatively well with the low swelling model. In Figure 136, the low swelling model seems to overestimate the magnitude of cesium concentration at the top and bottom of fuel rod; however, the predictions from both models are consistent with each other and the experimental data in term of its distribution profiles. Unlike rods 150073 and 150080, the accumulation cesium at the bottom of fuel rod is observed in rods 150088 and 150094 which make the axial cesium distribution of these rods looks like a U-shape. Anyway, in Figure 137, the low swelling model performs worse than the high swelling model as it overestimates in the amount of cesium at both ends whereas the high swelling model shows a better agreement with the experiment results.

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Experiment High swelling 2.5 Low swelling

1.5

1 Relative Cs Concentration

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Axial Height (m) Figure 134: Relative 137Cs concentration as a function of axial height of 150073 fuel rod.

2.2

Experiment 2 High swelling Low swelling 1.8

1.6

1.4

1.2

1 Relative Cs Concentration Relative 0.8

0.6

0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Axial Height (m) Figure 135: Relative 137Cs concentration as a function of axial height of 150080 fuel rod.

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3.5

Experiment 3 High swelling Low swelling

2.5

1.5

1 Relative Cs Concentration

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Axial Height (m) Figure 136: Relative 137Cs concentration as a function of axial height of 150088 fuel rod.

3.5

Experiment 3 High swelling Low swelling

2.5

1.5

1 Relative Cs Concentration

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Axial Height (m) Figure 137: Relative 137Cs concentration as a function of axial height of 150094 fuel rod.

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In summary, the low swelling model improves the simulation results for the 150073 and 150080 fuel rods as they match relatively well with experiments especially at the top. It also shows a higher concentration of cesium in the middle of the rods. This kind of behavior cannot be predicted by the high swelling model. Previously, the cesium concentration at the bottom is always higher than the middle in all cases. However, there are still some deficiencies in its predictions; it shows less accurate but still consistent results with the high swelling model for 150088 and 150094 fuel rods. After all, this sensitivity study has clearly demonstrated that fuel temperature and temperature gradient play a critical role in cesium migration behavior. Different temperature profiles could lead to a totally different behavior, thus, it is necessary to ensure that fuel temperature used in cesium migration model adequately represents the system being studied.

Since the reduction in cesium fuel swelling rate could offer some improvements from the previous model for a set of experiments conducted in the FFTF reactor; it is interesting to further examine its effects in RBWR-TB2 conditions. However, since the experimental data on cesium distribution of the reactor does not exist, the emphasis is then shifted to the thermomechanical behavior of a fuel rod. Thus, a similar calculation using FRAPCON-3.5 EP has been performed for RBWR-TB2 design. Key performance indicators such as fuel temperature, fission gas release, interfacial pressure, and cladding stress/strain are compared and discussed.

Figure 138 shows the average fuel temperature of high and low swelling models as a function of time. It can be seen that it matches relatively well during an open-gap regime, however, a gradual departure can be observed once the high swelling model reaches a closed-gap regime earlier than the low swelling model. To further examine this variable, a plot of axial distribution of average fuel temperature at EOL is shown in Figure 139. In this case, it can be noticed that the source of temperature difference comes from the internal blanket zone whereas the fuel temperature in the fissile zones is relatively close in both options.

Figures 140 and 141 show the centerline fuel temperature of high and low swelling model as a function of time and axial node at the last time step, respectively. The centerline fuel temperature shows less deviation between the high and low swelling models. Similar to the average temperature, the low swelling model predicts higher fuel temperature in the blanket zone.

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1200

High swelling 1150 Low swelling

1100

1050

1000

950 Average Fuel Temperature (K) Average

900

850 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 138: Average fuel temperature of high and low swelling models as a function of time.

2000

High swelling Low swelling 1800

1600

1400

1200

1000 Average (K) Fuel Temperature

800

600 0 20406080100120 Axial node Figure 139: Average fuel temperature at EOL of high and low swelling models as a function of axial node.

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3000

High swelling Low swelling

2500

2000 Centerline fuel temperature (K)

1500 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 140: Centerline fuel temperature of high and low swelling models as a function of time.

2800

High swelling 2600 Low swelling 2400

2200

2000

1800

1600

1400

Centerline fuel temperature (K) 1200

1000

800 0 20406080100120 Axial node Figure 141: Centerline fuel temperature at EOL of high and low swelling models as a function of axial node.

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Even though different fuel swelling rates may have some effects in fuel temperature, they are not large enough to cause major impacts to plenum pressure and fission gas release as shown in Figures 142 and 143. It can be seen that they are nearly identical to each other.

High swelling Low swelling 7

4 Plenum Pressure (MPa)

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 142: Plenum pressure of high and low swelling models as a function of time.

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High swelling 60 Low swelling

20 Fission Gas Release (%)

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 143: Fission gas release of high and low swelling models as a function of time.

Figure 144 shows the evolution of structural radial gap of high and low swelling models as a function of time. It is noted that this variable is varied across the axial length and only minimum values are shown. In this case, an identical behavior of radial gap is observed primarily because the location where structural radial gap reaches its minimum always occurs in the fissile zones. As fuel temperatures of these two models are almost identical in the fissile zones, it is understandable that the evolution of gap size should be the same. However, the plot of axial distribution of structural radial gap at EOL shows different gap thicknesses between fissile and blanket zones as shown in Figure 145. It can be seen that the fuel-cladding gap in the blanket remains open even in the last time step and the low swelling model predicts larger gap sizes. The difference in gap size is possibly the source of temperature difference between the high and low fuel swelling models.

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60 High swelling Low swelling 50

20 Structural radial gap (microns) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 144: Minimum structural radial gap of high and low swelling models as a function of time.

35 High swelling Low swelling 30

10 Structural radial gap (microns) Structural radial

0 0 20406080100120 Axial node Figure 145: Structural radial gap at EOL of high and low swelling models as a function of axial node.

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With differences in gap thickness, it is also expected that the interfacial pressure should evolve differently between these two models. This speculation has been confirmed in Figure 146 as the low swelling model shows a significant delay in hard contact and the onset of interfacial pressure is prolonged up to 1,100 days whereas, in the high swelling model, such occurrence takes place around 500 days. This effect will have a major implication to cladding stress and strain.

High swelling 35 Low swelling

Interfacial pressure (MPa) Interfacial pressure 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 146: Interfacial pressure of high and low swelling models as a function of time.

Figures 147 and 148 show the cladding hoop stress of high and low swelling models as a function of time and axial node at EOL, respectively. With lower interfacial pressure and identical plenum pressure, the low swelling model predicts a much lower cladding stress when compared to the high swelling model. The axial plot of cladding hoop stress shows that the axial nodes where hard contact occurs are concentrated at the interfaces between the fissile and blanket regions where cesium tends to accumulate. With lower contribution of cesium fuel swelling, the effect of such accumulation to PCMI and cladding stress is reduced accordingly.

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200

High swelling Low swelling

150

100

50 Cladding hoop stress (MPa) Cladding hoop 0

-50 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 147: Cladding hoop stress of high and low swelling models as a function of time.

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High swelling 140 Low swelling

120

100

Cladding hoop stress (MPa) 20

-20 0 20 40 60 80 100 120 Axial node Figure 148: Cladding hoop stress at EOL of high and low swelling as a function of axial node.

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Following a reduction in cladding stress, the cladding strain also shows a significant reduction as shown in Figure 149. The axial variation of cladding hoop strain at EOL is shown in Figure 150. It can be seen that the axial location where the cladding strain peaks is different between the two models. In the high swelling model, the peak occurs at the lower fissile zone interface while it occurs in the upper fissile zone in the low swelling model.

0.8

High swelling 0.7 Low swelling

0.6

0.5

0.4

0.3

Cladding hoop strain (%) 0.2

0.1

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 149: Cladding hoop strain of high and low swelling models as a function of time.

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0.8 High swelling Low swelling 0.6

0.4

0.2

0 Cladding hoop strain (MPa)

-0.2

-0.4 0 20 40 60 80 100 120 Axial node Figure 150: Cladding hoop strain at EOL of high and low swelling models as a function of axial node.

In conclusion, this sensitivity study has demonstrated that not only does a reduction in cesium fuel swelling has a strong impact to cesium migration behavior in fast reactor environment, its effects also propagated to other thermomechanical behaviors of RBWR-TB2. Although the general trends of the predicted results are consistent, the magnitude differences are large enough to cause different conclusions in fuel designs. Therefore, since the high fuel swelling model seems to give more conservative predictions, it is still preferable to use it in further analyses in Chapter 6.

5.6 Validation of hydrogen migration model

In this work, experimental data from Sawatsky's experiment [243]and from post-irradiation examination of high burnup cladding samples from the Gravelines nuclear power station [244] were used to validate the hydrogen migration model. In Sawatzky’s experiment, a cylinder of Zircaloy-2, 1.2 cm in diameter and 2.5 cm in length with initially uniform hydrogen

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concentration was placed under constant temperature gradient for a long period of time. The conditions of the experiments are summarized in Table 15.

Table 15: Description of Sawatzky’s experiments [243]. Experiment #1 Experiment #2 Material Zircaloy-2 Zircaloy-2 Geometry Cylinder Cylinder Diameter (cm) 1.2 1.2 Length (cm) 2.5 2.5 Hot temperature (K) 750 727 Cold temperature (K) 403 430 Initial H concentration (ppm) 130 64 Test duration (days) 34 41

Figure 151 compares simulation results with experimental data from Sawatzky [243]. In addition, a simulation result from BISON is also plotted as reference [245]. Temperature was held at 403 K at x = 0.0 cm and 750 K at x = 2.5 cm. From a uniform concentration at 130 ppm, hydrogen migrates to the cold side on the left and it begins to precipitate when temperature at x = 1. 3 cm and peaks at 0.8 cm when temperatures at these two locations were below 585 K and 520 K, respectively. It appears that the hydrogen migration model matches relatively well with experimental results and the BISON prediction.

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600 H in solid solution H in hydride 500 Total H Sawatsky 1960 BISON

400

300

200

100 In solid solution hydrogen concentration (wt ppm) hydrogen concentration In solid solution 0 00.511.522.5 x(cm) Figure 151: Axial distribution of hydrogen concentration in Sawatzky’s experiment #1.

A comparison of Sawatzky’s experiment #2 with the hydrogen migration model is shown in Figure 152. In this experiment, temperature was held at 430 K at x = 0.0 cm and 727 K at x = 2.5 cm. The initial hydrogen concentration was given at 64 ppm. The results shows that hydrogen begins to precipitate at x = 0.92 cm and peaks at 0.52 cm where temperature fell below 539 K and 492 K, respectively in these two locations. Again, the prediction is in good agreement with experimental results.

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In solid solution hydrogen concentration (wt ppm)

Figure 152: Axial distribution of hydrogen concentration in Sawatzky’s experiment #2.

Although the migration behavior of hydrogen in Zircaloy cladding was clearly demonstrated in Sawatsky’s experiment, it is more beneficial to benchmark the hydrogen migration model with irradiated cladding from actual LWRs. In this case, previous work by J. H. Zhang [244] is particularly useful because a detailed characterization of the hydrogen distribution at high burnup condition was made available. In that work, cladding samples were irradiated up to 4 cycles in the Gravelines nuclear power station. Operating since 1980, it is the 6th largest nuclear power station in the world, produces around 8% of electricity in France, and consists of 6 units of 900 MW Framatome PWRs. Several post-irradiation examinations including image analysis and hot vacuum extraction were used to estimate the overall hydrogen content in the samples. Table 16 summarizes the fuel rod design and geometry of fuel rod 1079 of Gravelines nuclear power station. Power history and axial peaking factor are given in Figures 153 and 154. It should be noted that the axial peaking factor was not originally available from Zhang’s thesis. Therefore, a certain profile has to be assumed. In this work, it was assumed as a straight line of a constant value at 1.0. This profile was used in order to match the input condition of a study by Lacroix [246] which implemented a similar hydrogen migration model in BISON fuel performance code.

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Table 16: Fuel rod design and geometry of fuel rod 1079 of Gravelines nuclear power station [246]. Reactor type Framatome PWR Plenum length (cm) 17.5

Fuel UO2, 4.5% Core active height (m) 3.217 enriched Clad Zircaloy-4 Operating pressure (MPa) 15.5

2 Gap Helium Coolant mass flux (kg/m /s) 3140

Fuel rod diameter (mm) 9.49 Coolant inlet temperature (K) 559

Fuel rod pitch (mm) 12.6 Coolant outlet temperature (K) 596

Fuel pellet diameter 8.2 Rod-averaged burnup 58.23 (mm) (MWd/kgU) Clad thickness (mm) 0.565 Irradiation Time (Days) 1615

Fuel-clad gap thickness 80 (μm)

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20 (kW/m) 15 Power 10 Linear 5

0 0 500 1000 1500 2000 Time (Days) Figure 153: Power history of fuel rod 1079 of Gravelines nuclear power station [244].

1.2

0.8 BOL MOL 0.6 EOL

0.4 Axial peaking factor

0.2

0 00.511.522.533.5 Axial height (m)

Figure 154: Axial peaking factor used in Lacroix [246] and this study.

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Figure 155 shows the total hydrogen concentration as a function of clad radius for fuel rod 1079. Both hydrogen content in the form of solid solution and hydride precipitates are taken into account. The cladding samples were taken near the top of fuel rod at an axial height of 3.097- 3.217 m. From the figure, it can be seen that the hydrogen concentration near the cladding periphery is extremely high (6,000 ppm). It was reported that this hydride rim region is very thin (9 microns). It also appears that simulation results from FRAPCON-3.5 EP and BISON accurately predict the hydrogen concentration in the hydride rim region but underestimate the hydrogen content in inner regions of the cladding.

7000 FRAPCON Experiment 6000 (ppm) BISON

5000

4000 Concentration

3000 Hydrgoen 2000 Total 1000

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Clad radius (mm)

Figure 155: Total hydrogen concentration as a function of clad radius.

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Chapter 6

Performance assessment of RBWR-TB2 fuel rods

This chapter presents simulation results for RBWR-TB2 fuel rods using FRAPCON-3.5 EP. A similar calculation has been performed for ABWR fuel rods using the same code in order to highlight major differences in thermo-mechanical behaviors between these two reactor designs. Sensitivity analysis on key design parameters such as gap thickness, fuel density, oxygen-to- metal ratio, central void diameter, helium pressure, and cladding thickness have been performed to assist future design optimizations. In addition, a comparison of simulation results between FRAPCON-3.5 and FRAPCON-3.5 EP are presented to illustrate the effects of several physical phenomena that become dominant at high temperature and high burnup.

6.1 Reactor condition and fuel rod geometry

The fuel rod design and geometry of the RBWR-TB2 and ABWR are given in Table 17. RBWR-

TB2 uses (U,Pu)O2 or mixed oxide at 70-80% weight fraction of PuO2 while the fuel enrichment of ABWR is at 4.5%. Both reactors use Zircaloy-2 as the cladding and helium as the fill gas. It can be seen from the table that the fuel rod diameter and pitch of RBWR-TB2 are significantly smaller than that of ABWR in order to harden neutron spectrum and reduce moderator-to-fuel ratio. Since the RBWR-TB2 is designed to reach higher fuel burnup, some design parameters are adjusted to alleviate undesirable effects at such conditions. For example, the plenum length of the RBWR-TB2 fuel is increased whereas the initial fuel density is reduced from a typical value of 95 %TD to 89.9 %TD in order to accommodate additional fission gas release and swelling at high burnup. Also, the initial oxygen-to-metal ratio is hypostoichiometric in order to reduce the oxygen potential and fuel cladding chemical interactions (FCCI) at high burnup. In addition, the RBWR-TB2 fuel rods are arranged in a hexagonal lattice whereas the ABWR uses a square lattice; therefore, an expression for hydraulic diameter of a hexagonal lattice has been added to FRAPCON-3.5 EP.

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Table 17: Fuel rod design and geometry of RBWR-TB2 and ABWR. Reactor ABWR RBWR-TB2

Fuel UO2 (U,Pu)O2 Clad Zircaloy-2 Zircaloy-2 Gap Helium Helium Fuel rod diameter (mm) 11.17 7.61 Fuel rod pitch (mm) 14.27 9.58 Fuel pellet diameter (mm) 9.55 6.19 Clad thickness (mm) 0.711 0.6 Fuel composition U content (wt %) 100 20.9 Pu+MA content (wt %) 0 79.1 Fuel-clad gap thickness (μm) 101.6 110 Plenum length (cm) 28.55 50.62 Fuel density (% TD) 95.0 89.9 Oxygen-to-metal ratio 2.0 1.98 Core active height (m) 3.71 1.04 Initial helium pressure (MPa) 0.4 1.0 Irradiation time (Days) 1,500 1,372

6.2 Radial power profile and fast neutron flux

The radial power profile of LWRs changes considerably with burnup. At BOL, the radial power distribution is relatively flat; the local value does not significantly deviate from average value. However, as burnup progresses, the radial power profile continues to develop large peaking near periphery. At EOL, the difference between peak-to-average power can be a factor of 2 or higher depending on irradiation history. This physical phenomenon is quite well known for thermal reactors with enriched uranium fuel and is caused by the effect of transmutation of fertile uranium to fissile plutonium isotopes; its occurrence is highly localized near the edge of the fuel pellet [129]. As a result, the local burnup in this region can be multiple times greater than the

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pellet average value. The formation of the high burnup structure (HBS) and subsequent porosity buildup are developed from excessive irradiation damage and accumulation of gaseous fission products in this region. In terms of material properties, these two phenomena can be viewed as detrimental to thermal performance because they reduce the thermal conductivity of the fuel. However, in terms of heat transfer, the shift in radial power profile from the center to the edge may be as beneficial because it helps reduce the power density in the center where heat transport is limited. Otherwise, the fuel centerline temperature would have been higher at high burnup if the radial power profile had not shifted toward to the periphery. FRAPCON-3.5 is already equipped with a subroutine named TUBRNP which calculates and dynamically updates the radial power profile of LWRs as a function of burnup [7].

However, such conditions are no longer applicable for the RBWR-TB2 because this reactor is designed to operate with much higher plutonium content (>70 wt%) and a harder neutron spectrum. Consequently, the buildup of plutonium and non-uniform distribution of local burnup are not expected to occur in the RBWR-TB2. In fact, the neutronic evaluation of the RBWR-TB2 showed that its radial power profile does not significantly changes with burnup [46] [51]; the power peaking near pellet edge ranges from 1.1 to 1.2 throughout the cycle similar to that in sodium fast reactors. To reflect this situation in fuel performance modeling, the existing algorithm that calculates and updates the radial power profile in FRAPCON-3.5 EP has been deactivated. It is superseded by the radial power profile given in Figure 156. This profile was adopted from Karahan et al. [9] and it is assumed to be constant throughout the cycle. The radial power profiles of an ABWR at BOL and EOL are also included for comparison. Note that if

MOX fuel is used instead of enriched UO2, the magnitude of power peaking at periphery will be lower.

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2.8

ABWR BOL 2.6 ABWR EOL RBWR-TB2 2.4

2.2

1.8

1.6

Radial Power Profile 1.4

1.2

0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized Radial Position Figure 156: Normalized radial peaking factors for RBWR-TB2 and ABWR.

Fast neutron flux indirectly impacts fuel performance modeling as it is central to several cladding deformation models such as irradiation swelling/growth, irradiation creep and irradiation hardening in the plastic deformation regime. In addition, life-limiting properties of cladding such as yield strength, ultimate strength, ductility are also a function of fast neutron flux. In FRAPCON-3.5 EP, fast neutron flux and fluence also have a significant impact on cladding oxidation rate because the criterion for accelerated corrosion phenomena is primarily based on fast neutron fluence.

To estimate the fast neutron flux to the cladding (E > 1 MeV) in RBWR-TB2 conditions, an assembly-level neutronic study was performed using SERPENT [247] with burnup dependent calculations. The model described in SERPENT is a three-dimensional geometry of RBWR-TB2 fuel assemblies including the following axial zones: lower reflector, lower fissile, internal blanket, upper fissile, upper blanket, and upper reflector. Each axial zone is further divided into sub-regions according to axial nodalization. In total, there are 27 axial nodes with variable mesh sizes. However, the active fuel regions consist of 24 axial nodes of burnable materials. Coolant

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density is also axially divided into 24 zones according to its void fraction distribution. Figure 157 depicts a cross section view of RBWR-TB2 fuel assemblies comprising fuel rods, coolant, channel boxes, and a control blade. Flux tally cards2 were specified in SERPENT to keep track of fast neutron flux streaming in and out of cladding regions. Burnup calculation was performed from 0-80 MWd/kgHM at EOL.

Figure 157: Cross-section view of RBWR-TB2 assemblies in SERPENT.

Figure 158 shows fast neutron flux as a function of axial height at different burnup levels. It can be seen that the fast flux decreases with burnup in the upper fissile zone whereas it increases in the lower fissile zone and internal blanket zone representing the effect of fuel depletion in the upper fissile zone and transmutation of fertile uranium to fissile plutonium isotopes in the internal blanket.

2 Tally cards are a set of input commands in SERPENT for obtaining parameters of interest e.g. current, flux, and reaction rates.

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1018 6

0.0 MWd/kgHM 40.0 MWd/kgHM 5 80.0 MWd/kgHM

4 /s) 2

Fast Flux (n/m 2

0 0 0.2 0.4 0.6 0.8 1 1.2 Axial Height (m) Figure 158: Fast neutron flux of RBWR-TB2 at 0, 40, and 80 MWd/kgHM.

In FRAPCON-3.5 EP, instead of using direct values of fast neutron flux, the input variable for fast neutron flux is specified as a ratio of fast neutron flux to specific power. The unit of this quantity is expressed as neutron/m2/s per W/g. For simplicity, it will be referred to as specific fast flux. Therefore, reaction rate tally cards were put in-place to keep track of the axial power distribution. This quantity is then normalized by reactor power and converted to specific power as shown in Figure 159. Generally, the specific power is higher in the upper fissile zone but a similar balancing effect with burnup as with the fast neutron flux can be observed. At EOL, internal blanket zone also provides a noticeable contribution to the specific power.

274

250

0.0 MWd/kgHM 40.0 MWd/kgHM 80.0 MWd/kgHM 200

150

100 Specific Power (W/g)

0 0 0.2 0.4 0.6 0.8 1 1.2 Axial Height (m) Figure 159: Specific power of RBWR-TB2 at 0, 40, and 80 MWd/kgHM.

Dividing the fast neutron flux by the specific power yields a specific fast flux as shown in Figure 160. A default value of 2.21x1016 n/m2/s per W/g in FRAPCON-3.5 EP is also plotted as reference. As burnup progresses, the variation of fast flux and specific power tend to cancel each other out and ultimately result in a relatively constant specific fast flux. From the figure, the specific fast flux of both lower and upper fissile zones is well represented by the default while a lower specific power in the internal blanket zone leads to a higher specific fast flux. Nevertheless, in fuel performance modeling, the emphasis is placed in the high power-producing regions where life-limiting phenomena such as fuel melting, PCMI, cladding deformation occur. These axial regions are often called peak nodes. Since the peak nodes are always located in either the lower or upper fissile zones, a default constant value of 2.21x1016 n/m2/s per W/g for specific fast flux is still applicable for use throughout the simulation. Therefore, the specific fast flux is left as-default in analyses of RBWR-TB2 fuel rods.3

3 However, when the actual profile of specific fast flux was used; FRAPCON-3.5 EP prematurely terminated its calculation as it encountered some run-time errors which resulted in NaN in cladding stress and strain. The diagnostics and migration of these errors were left as future work.

275

1019 0.0 MWd/kgHM 40.0 MWd/kgHM 80.0 MWd/kgHM FRAPCON Default Value

1018 /s per W/g) 2

1017 Specific Fast Flux (n/m

1016 0 0.2 0.4 0.6 0.8 1 1.2 Axial Height (m) Figure 160: Specific fast flux of RBWR-TB2 at 0, 40, and 80 MWd/kgHM.

6.3 Power history and axial peak factor

Thermo-mechanical behaviors of fuel rods are highly sensitive to power history and axial power factor. Several life-limiting parameters can vary significantly when different power histories and axial power profiles are applied, which may lead to different interpretation of the viability of specific reactor designs. Therefore, it is very important that the power history and axial power factor are as accurate as possible to avoid biases and fault rejection based on overly conservative assumptions. In this case, the power history is defined as the variation of linear heat generation rate (LHGR) taken as rod-average values as a function of time whereas the axial peaking factor is the deviation of local LHGR at different axial nodes as a function of time.

Recognized as an independent audit tool for reactor core analysis by the U.S. Nuclear Regulatory Commission (NRC), PARCS (Purdue Advanced Reactor Core Simulator) is a three-dimensional, neutronic simulation code capable of calculating power history and axial peaking factor of all fuel rods in a reactor core as a function of burnup. The code has been extensively benchmarked

276

and validated with experimental data and has been widely adopted as a scientific tool for reactor core analysis in research institutions and universities worldwide. Analytical benchmark with other neutronic codes which employ different computational techniques such as Monte Carlo or Method of Characteristics (MOC) also show as good agreement within the code’s limitation on material properties and cross section databases [248] [249] [250] [251] [252].

In this work, the power history and axial peaking factor of the RBWR-TB2 were calculated by PARCS. Since the code can evaluate all fuel rods in the core, a method to identify a peak rod condition needed to be established. The criterion for the peak rod was developed by taking all fuel rods in the core of RBWR-TB2, roughly 288,000 rods, at EOL condition into consideration. Then, the fuel rod that is exposed to the highest burnup in the last cycle was identified as the peak rod. Then, its power history and axial peaking factor are traced back to the previous cycles at BOL so that the power history and axial peaking factor can be formatted as input parameters for FRAPCON simulation. This approach reflects an actual operating condition that the rod would likely experience if the RBWR-TB2 design is to be built. Note that the peak rod in this assumption is physically the same throughout the cycle.

For the power history of an ABWR, it is a common yet conservative practice to model a peak fuel rod by assuming that the peak rod remains in the core for all cycles. During the first cycle, it is assumed that the LHGR of the peak rod remains constant. After that, the LHGR decreases linearly in subsequent cycles until it reaches 50% of its initial values at the end of cycle. The axial peaking factor of an ABWR was adopted from a reference training material from GE- Hitachi [253].

Power history and axial peaking of the RBWR-TB2 and ABWR are shown in Figures 161 and 162. It can be seen that although the average LHGR of the RBWR-TB2 is lower than that of the ABWR, the local axial LHGR of RBWR-TB2 is much higher especially in the upper fissile zone. This is because in order to keep core thermal power output the same with a much shorter fuel length in case of the RBWR-TB2 (~1.0 m in RBWR-TB2 and ~3.7 m in ABWR), the LHGR of fissile zones has to be very high to compensate power suppression in the blanket zones.

277

30 RBWR-TB2 ABWR 25

15 LHGR (kW/m) 10

0 0 500 1000 1500 Time (Days) Figure 161: Power history of RBWR-TB2 and ABWR.

2.5

RBWR-TB2 BOL RBWR-TB2 EOL ABWR BOL 2 ABWR EOL

1.5

1 Axial Peaking Factor

0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative Axial Length (x/L) Figure 162: Axial peaking factor of RBWR-TB2 and ABWR.

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6.4 Results of fuel performance simulation 6.4.1 Rod-average and local fuel burnup

Fuel burnup is a measure of energy released per unit mass. It is derived from fission rate density, energy released per fission, fuel density, and elapsed time. In general, fuel burnup is used as a fundamental parameter representing the level of irradiation damage and material evolution within the fuel. Higher fuel burnup means higher material damage accumulated and more degradation of thermophysical properties. Fuel burnup is one of the most important performance indicators in fuel performance as it relates to other life-limiting parameters of fuel rods. Many material properties and empirical correlations use fuel burnup as a major dependent variable. In order to highlight major differences between these two reactor designs, it is beneficial to compare the fuel burnup between the RBWR-TB2 and ABWR. Fuel burnup varies both axially and radially as a result of variations in neutron flux and fission reaction rates. Fuel burnups are normally reported as a volume-averaged parameter. However, there are some instances where rod-averaged burnup is not a complete representation of fuel burnup level because of its integrative nature. For example, in axially heterogeneous fuel designs such as with the RBWR- TB2, fuel burnup in fissile and blanket zones can be vastly different. In this case, local fuel burnup can reveal more insights about the actual fuel burnup level in each axial zone. Figure 163 shows rod-average fuel burnup for the RBWR-TB2 and ABWR as a function of time. It can be seen that the average burnup for the RBWR-TB2 is roughly twice of that of the ABWR. Although it may seem like each ABWR fuel rod produces significantly less energy than that of the RBWR-TB2, the thermal power output of these two reactors are equivalent because of a longer active fuel length, and larger fuel pellets of in the ABWR cores. In Figure 164, a large degree of variation in fuel burnup between axial zones at EOL can be observed in the RBWR- TB2 whereas such variation is relatively smooth in the ABWR mainly because of its axially homogeneous fuel design. The local burnup shown in Figure 164 was taken from the fuel pellet center at EOL condition. The peak values in the lower and upper fissile zones of the RBWR-TB2 are approximately 120 and 160 MWd/kgHM, respectively.

279

RBWR-TB2 70 ABWR

20 Rod Average Burnup (MWd/kgHM) 10

0 0 500 1000 1500 Time (Days) Figure 163: Rod-average fuel burnup of RBWR-TB2 and ABWR as a function of time.

180

RBWR-TB2 160 ABWR

140

120

100

Local Burnup (MWd/kgHM) 40

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative Axial Length (x/L) Figure 164: Local fuel burnup of RBWR-TB2 and ABWR at EOL.

280

6.4.2 Average fuel temperature

The average temperature of the fuel is one of the most important parameters in fuel performance modeling. It is evaluated as a volume-average temperature of the entire fuel stack in the rod. Thus, the average fuel temperature takes into account the temperature variation in both axial and radial directions. This parameter is then used in calculating thermal expansion, fission gas release and other important feedback mechanisms. The average fuel temperature as a function of time for the RBWR-TB2 and ABWR is shown in Figures 165, respectively. From the previous section, higher fuel burnup in fissile zones of the RBWR-TB2 could severely degrade fuel properties. At MOL and EOL, the fuel thermal conductivity of the RBWR-TB2 is expected to be much lower than that of the ABWR. This will result in a large increase in fuel temperature for RBWR-TB2 when compared to ABWR.

1200 RBWR-TB2 ABWR 1100

1000

900

800 Average Fuel Temperature (K) Fuel Temperature Average 700

600 0 500 1000 1500 Time (Days) Figure 165: Average fuel temperature of RBWR-TB2 and ABWR as a function of time.

Furthermore, due to the nature of the power history of the RBWR-TB2 which remains relatively constant throughout the cycles and the degradation of fuel thermal conductivity at high burnup,

281

the average fuel temperature will continue to increases with time. In the ABWR, fuel temperature continues to decrease because of the loss of reactivity from fuel depletion. It is also of interest for heterogeneous fuel designs to compare the axial variation of fuel temperature by using radially-averaged values. Figure 166 shows the axial distribution of radially-averaged fuel temperature for the RBWR-TB2 and ABWR at BOL and EOL conditions. As can be seen from the figure, the fuel temperature of RBWR-TB2 varies considerably in each axial zone. Fuel temperature is about 2-3 times higher in fissile zones than in the middle blanket zone which remains relatively low throughout the cycle. In the internal blanket zone, fuel temperature is comparable with the ABWR at EOL.

1800

RBWR-TB2 BOL RBWR-TB2 EOL 1600 ABWR BOL ABWR EOL

1400

1200

1000 Average Fuel Temperature (K) Average Fuel 800

600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative Axial Length (x/L) Figure 166: Average fuel temperature of RBWR-TB2 and ABWR as a function of relative axial length.

6.4.3 Fuel centerline temperature

The centerline fuel temperature is a regulatory limit parameter, which must be lower than the melting point of the fuel at all times. The evolution of centerline fuel temperature with time for

282

the RBWR-TB2 and ABWR is shown in Figure 167. It can be seen that the centerline fuel temperature for the RBWR-TB2 is significantly higher than that of the ABWR. This is because of higher axial peaking factors in fissile zones and a relatively flat power history for the RBWR- TB2. Thermal conductivity degradation at high burnup also plays a major role in the calculated fuel temperature increase. Similar contributing factors that affect the average fuel temperature are also applied to the centerline fuel temperature. The centerline fuel temperature of the RBWR-

TB2 could be as high as 2660 K (melting point of PuO2) toward EOL while that of ABWR

remains well below a melting points of (U,Pu)O2 of around 2900-2950 K at plutonium composition of 30 wt%. Such small margin to fuel melting for RBWR-TB2 even in steady-state fuel performance simulation may require further investigations into fuel behaviors during transient or accident conditions.

3000

RBWR-TB2 ABWR 2500

2000

1500

Centerline Fuel Temperature (K) 1000

500 0 500 1000 1500 Time (Days) Figure 167: Centerline fuel temperature of RBWR-TB2 and ABWR as a function of time.

All of the disadvantages in fuel temperature originated from the shorter core design (~1.0 m in RBWR-TB2 and ~3.7 m in ABWR). With axially heterogeneity, the presence of an internal blanket zone further reduces the active (power-producing) fuel length roughly by half. The

283

consequence of reducing the fuel length while keeping the power output the same is an increase in LHGR and plutonium composition in fissile zones. This creates undesirable effects as observed for fuel burnup and predicted temperatures.

Figure 168 compares the centerline fuel temperature as a function of relative axial length for the RBWR-TB2 and ABWR at BOL and EOL. It can be seen that the fissile zones of the RBWR- TB2 operates around the vicinity or above fuel sintering temperature of 1800 K. At this high temperature, several fuel constituents such as plutonium and oxygen will become mobile. Plutonium migrates up to higher temperature regions whereas oxygen could migrate up or down the temperature gradients depending on current fuel stoichiometry.

3000

RBWR-TB2 BOL RBWR-TB2 EOL ABWR BOL 2500 ABWR EOL

2000 Temperature (K)

1500

Centerline Fuel 1000

500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative Axial Length (x/L) Figure 168: Centerline fuel temperature of RBWR-TB2 and ABWR as a function of relative axial length.

Not only does plutonium migration affect the radial power profile, which represents fission rate density within a fuel pellet, it also causes various changes in fuel material properties. One of the most important properties is fuel melting temperature as it changes with fuel burnup and

284 plutonium weight fraction. The melting temperature of (U,Pu)O2 varies with plutonium content, from 2660 K for pure PuO2 to 3113 K for pure UO2 at zero burnup. It also decreases with fuel burnup at a rate of 0.5 K per MWd/kgHM. Although no fuel melting was calculated by FRAPCON-3.5 EP, it is very important to compare the centerline fuel temperature with the melting temperature because it approaches the melting temperature of PuO2 near EOL. Such comparison is shown in Figure 169 and it shows that the centerline fuel temperature of the

RBWR-TB2 at EOL is close to the melting temperature of a (U,Pu)O2 mixture in the lower fissile zone. In the parametric study sections to be presented later in this chapter, some key design parameters are investigated in an attempt to lower the centerline fuel temperature.

3500

3000

Fuel Melting Temperature 2500 Fuel Centerline Temperature

2000

1500 Fuel Temperature (K) Fuel Temperature

1000

500 0 20406080100120 Axial Node Figure 169: Axial variation of fuel centerline and fuel melting temperature at EOL of RBWR- TB2.

Given that the RBWR-TB2 operates very close to fuel melting, it is also beneficial to examine the axial variation of fuel melting temperature as a function of different plutonium weight fraction in the fissile and blanket zones as shown in Figure 170. It can be seen that due to high plutonium content and high burnup in both fissile zones, the differences in fuel melting

285 temperature between fissile and blanket zone can be as large as 450 K. The minimum fuel melting temperature at EOL was calculated as 2,655 K in the lower fissile zone with plutonium content of around 80 wt% and some reductions from fuel burnup.

3150 90

3100 80

3050 70 Fuel Melting Temperature 3000 Plutonium Content (wt%) 60 2950 50 2900 40 2850 30 2800 Plutonium Content (wt%)

Fuel Melting Temperature (K) 20 2750

2700 10

2650 0 0 20 40 60 80 100 120 Axial Node Figure 170: Axial variation of fuel melting temperature and plutonium content at EOL of RBWR-TB2.

It is noted that, for melting temperature, a rule of mixture of two constituents’ parameters by weight fraction (Vegard's law) can be generally applied. Figure 171 shows a relatively linear correlation between fuel melting temperature at BOL and EOL as a function of plutonium content from 0 wt% up to around 80 wt% of PuO2 and fuel burnup in the range of 0-165 MWd/kgHM. Depending on local burnup in each axial zone, a degradation in fuel melting temperature from burnup ranges from 40-60 K in the lower fissile zone and 70-80 K in the upper fissile zone whereas the reduction in the internal blanket is considerably smaller, roughly 10-25 K.

286

3150 BOL 3100 EOL

3050

3000

2950

2900

2850

2800 Fuel Melting Temperature (K) 2750

2700

2650 0 102030405060708090 Plutonium Content (wt%) Figure 171: Reduction of fuel melting temperature of RBWR-TB2 with plutonium content at BOL and EOL.

6.4.4 Plenum pressure and fission gas release

The plenum pressure is a primary driving force that creates stress and cause deformation to the cladding when the fuel and the cladding are in free-standing mode of operation i.e. no contact pressure from PCMI. Even after the fuel and the cladding are in hard contact; the plenum pressure could make a significant contribution to cladding stress and strain. The plenum pressure is also an indication of how much fission gas is contained in the free plenum volume. Plenum pressure as a function of time for the RBWR-TB2 and ABWR are shown in Figure 172. It can be noticed that the plenum pressure in the RBWR-TB2 increases considerably from 2 MPa at BOL to 7 MPa at EOL. The ABWR also shows a similar trend in plenum pressure increase but to a lesser extent from 0.4 MPa to 6 MPa. Given the coolant pressure in the RBWR-TB2 and ABWR are the same at 7 MPa, it is implied that the cladding of the ABWR is still under compression whereas that of the RBWR-TB2 is initially under compression from external coolant pressure until such condition gradually vanishes when the internal rod pressure increases from

287 accumulated fission gases to the point where it becomes greater than or equal to the external coolant pressure.

RBWR-TB2 7 ABWR

3 Plenum Pressure (MPa) Plenum Pressure 2

0 0 500 1000 1500 Time (Days) Figure 172: Plenum pressure of RBWR-TB2 and ABWR as a function of time.

During the course of operation, approximately 30% of the fission products are in the gaseous state. The compositions of these gases are mainly radioactive isotopes of inert gases (Xe and Kr). As inert gases, they do not react with other materials or dissolve in the fuel. Instead, they exist as bubbles in the fuel matrix. Once generated from fission reactions, these micro-bubbles will migrate to grain boundaries and will accumulate to form larger bubbles. When these bubbles become large enough, they will form inter-boundary connections from fuel matrix to fuel surface. After the formation of inter-connected channels, the fuel will no longer be able to hold fission gases within its matrix and the fission gases will be released to the free plenum volume. In addition, the amount of gas accumulated at grain boundaries also contributes to fuel swelling.

The release of fission gases generates several unfavorable feedback mechanisms that effect fuel performance. First, they will mix into the fuel-cladding gap that is initially filled with helium. The contamination of these gases will reduce gap conductance because the thermal conductivity

288

of fission gases are significantly lower than that of helium. As a result, the temperature drop across the gap will be higher due to fission gas release. Increasing thermal resistance in the gap layer will eventually lead to fuel temperature increase which will further promote the release of fission gases. In addition, the presence of additional gas content into a limited volume will lead to an increase in plenum pressure. The formation and release of gas bubbles inside the fuel matrix creates internal void and porosity within the materials that will also lower thermal conductivity.

Figure 173 shows the fission gas release as a function of time for the RBWR-TB2 and ABWR. It can be seen that the fission gas release of RBWR-TB2 is tremendously higher at around 60% whereas that of ABWR is relatively small as it remains under 15%. Higher fuel temperature plays a critical role in this behavior because operation at higher fuel temperature strongly contributes to early release of fission gases. Fission gas release models are formulated as exponential functions and they are highly sensitive to fuel temperature; small changes in these parameters could result in a large difference in fission gas release. In the current fission gas release model in FRAPCON-3.5 EP, they are divided into three temperature ranges: low, medium and high which corresponds to different release rates. The difference in diffusion coefficients in the fission gas release model can be several orders of magnitude depending on fuel temperature. In general, every 100 K increase in fuel temperature will result in an increase in diffusion coefficient by a factor of 2.16. The impact of large fission gas release can be noticed by the rise of plenum pressure and subsequently cladding stress and strain.

289

70 RBWR-TB2 ABWR 60

20 Fission Gas Release (%)

0 0 500 1000 1500 Time (Days) Figure 173: Fission gas release of RBWR-TB2 and ABWR as a function of time.

6.4.5 Cladding corrosion

The cladding oxidation model in FRAPCON-3.5 EP takes heat flux as one of contributing factors to a growth rate of oxide layer. Given the higher LHGR and smaller outer cladding outer diameter in the RBWR-TB2, it is expected that the cladding corrosion in the RBWR-TB2 would be higher than that of the ABWR. This condition exacerbates further with design constraints of the RBWR-TB2 requiring higher inlet temperature, and lower coolant mass flux. Because of these conditions, a higher oxide layer growth rate is expected even before accelerated corrosion. This speculation has been confirmed in a comparison of oxide layer thickness for the RBWR- TB2 and ABWR as a function of time as shown in Figure 174 showing a higher rate of corrosion in the RBWR-TB2 since the beginning of cycle. Accelerated corrosion would take place after a complete dissolution of SPPs in the zirconium alloy cladding when it has been exposed to neutron fluence beyond 1x1026 neutron/m2 and this will result in an even greater oxide growth rate. Because of the accelerated corrosion effect, higher heat flux, and higher cladding temperature, oxide layer thickness at EOL for the RBWR-TB2 reaches a thickness of 93

290 microns. This oxide layer accounts for 15.5% of total cladding thickness of 0.6 mm. The oxide layer thickness for the ABWR is relatively small when compared to the RBWR-TB2 as it reaches a maximum thickness of around 20 microns at EOL. The average hydrogen concentration in the cladding is directly correlated to the oxide layer thickness. For every chemical interaction between metallic zirconium with water, there will be a certain amount of hydrogen that diffuses into the cladding. Thus, it is expected that the hydrogen concentration in the RBWR-TB2 cladding will be significantly higher than that of the ABWR. As shown in Figure 175, the corresponding average hydrogen concentration is calculated as 1351 ppm in the RBWR-TB2 and 60 ppm in the ABWR. These hydrogen atoms can dissolve in zirconium matrix up to certain concentrations depending on temperature. The hydrogen atoms in excess of solubility will contribute to hydride precipitation in the periphery region of the cladding.

100

90 RBWR-TB2 ABWR 80

Oxide Layer Thickness (microns) Oxide Layer 20

0 0 500 1000 1500 Time (Days) Figure 174: Oxide layer thickness of RBWR-TB2 and ABWR as a function of time.

291

1400

RBWR-TB2 1200 ABWR

1000

800

600

400 Hydrogen Concentration (ppm)

200

0 0 500 1000 1500 Time (Days) Figure 175: Average hydrogen concentration of RBWR-TB2 and ABWR as a function of time.

6.4.6 Structural radial gap and interfacial pressure

The dynamic of fuel-cladding gap thickness can reveal significant underlying phenomena about fuel and cladding interactions. At the initial stage of operation, the fuel radius becomes smaller due to fuel densification, but later in life the fuel radius will increase as a result of fuel relocation, irradiation swelling, and porosity from fission gases. Likewise, the cladding radius is reduced due cladding creep down from the compressive stress due to the high pressure coolant. Along the course of operation, however, the cladding radius will expand because of irradiation swelling, thermal expansion and buildup of internal gas pressure. Depending on power history and initial gap thickness, the closure of fuel-cladding gap can occur in less than 100 days of operation as shown in Figure 176 for the RBWR-TB2 while it is even shorter for the ABWR. Although gap closure can improve gap conductance, direct contact between fuel and cladding imposes additional stress on cladding or Pellet Cladding Mechanical Interactions (PCMI). Besides, chemical reactions between fuel and cladding are not desirable because zirconium is

292 particularly vulnerable to certain fission products such as iodine and tellurium which could lead to stress-corrosion-cracking.

90 RBWR-TB2 80 ABWR

20 Structural Radial Gap (microns)

0 0 500 1000 1500 Time (Days) Figure 176: Structural radial gap of RBWR-TB2 and ABWR as a function of time.

Gap interfacial pressure is an indicator used to distinguish between hard-contact and soft-contact events. Fuel cladding contact is defined as the event when the fuel outer radius and cladding inner radius come within a predetermined distance of one another. Soft contact occurs when the gap size is at its minimum, but gap interface pressure remains zero. As the fuel experiences thermal stress and swelling, cracking and relocation strain occur, creating empty spaces within the fuel. These empty spaces can be recovered by the fuel motion into the gap upon initial contact with the cladding which results in a reduction of fuel outer radius without stress at the surface of both components. Once the recovery of relocation strain reaches its limit, the onset of hard contact will occur as can be seen by a sharp increase in gap interfacial pressure. After hard contact between the fuel and cladding occurs, the gap size will asymptotically reach a minimum value depending on the surface roughness of both surfaces. Additional stress load is acting onto the cladding only when hard contact occurs. Figure 177 shows the behavior of interfacial

293

pressure over the course of operation of the RBWR-TB2 and ABWR. For the RBWR-TB2, after the first inception of gap closure, it takes another 400-500 days before gap interfacial pressure begins to rise and will continue to rise until the end of cycle. It is noted that the thin liner made of mostly pure zirconium and its mitigating effect on PCMI behavior that is present in typical BWR fuel designs are not analyzed in this work.

RBWR-TB2 35 ABWR

Interfacial Pressure (MPa) 10

0 0 500 1000 1500 Time (Days) Figure 177: Interfacial pressure of RBWR-TB2 and ABWR as a function of time.

6.4.7 Cladding hoop stress and strain

Figures 178 and 179 respectively show the evolution of cladding hoop stress and strain at the peak axial node of the RBWR-TB2 and ABWR. Essentially, there are two primary sources of loads: plenum pressure and interfacial pressure from PCMI. For the case of the RBWR-TB2, it appears that the interfacial pressure becomes the dominant source of stress loads acting on the cladding. As it can be seen from Figure 179, the cladding hoop stress behaves according to the change of interfacial pressure. Because of excessive fuel swelling due to higher fuel temperature and the onset of hard contact, a significant increase in cladding stress and strain toward end-of-

294 life can be observed in the RBWR-TB2 when compared to the ABWR. However, the cladding hoop strain in the RBWR-TB2 remains within a regulatory limit of 1%. However, the rapid increase of strain toward EOL requires future attention to this parameter.

200

RBWR-TB2 ABWR 150

100

0 Cladding Hoop Stress (MPa)

-50

-100 0 500 1000 1500 Time (Days) Figure 178: Cladding hoop stress of RBWR-TB2 and ABWR at peak axial node as a function of time.

295

0.9

RBWR-TB2 0.8 ABWR

0.7

0.6

0.5

0.4

0.3 Cladding Hoop Strain (%) 0.2

0.1

0 0 500 1000 1500 Time (Days) Figure 179: Cladding hoop strain of RBWR-TB2 and ABWR at peak axial node as a function of time.

6.4.8 Porosity migration and central void formation

In sections 6.4.8 to 6.4.12, the simulation results of physical phenomena that are expected to occur at high temperature and high burnup will be presented. Although they are specifically developed for RBWR-TB2 conditions, the simulation results using ABWR conditions will be included in order to demonstrate the sensitivity of these models to fuel temperature and burnup. First, the results of the porosity migration and central void formation model are given in Figures 180 and 181 for the RBWR-TB2 and ABWR, respectively. Although, the effect of pore migration and central void formation in the RBWR-TB2 is small, it is non-negligible. It can be seen at 10 MWd/kgHM where pore migration reaches equilibrium, the size of central void is on the order of 0.8 mm in the upper fissile zones whereas the central void in the lower fissile zones is less than 0.1 mm. On the other hand, the central void diameter in the ABWR even after 10 MWd/kgHM is negligibly small (on the order of 45 microns or less). This clearly indicates that radial migration of fuel porosity has not occurred in the ABWR and the fuel porosity remains

296 relatively uniform at initial values because the fuel temperature is too low to accelerate pore velocity and to overcome activation energy for thermal migration.

0.9

0 MWd/kgU 0.8 5 MWd/kgU 10 MWd/kgU 0.7

0.6

0.5

0.4

0.3

Central Void Diameter (mm) 0.2

0.1

0 0 20 40 60 80 100 120 Axial Node Figure 180: Central void diameter of RBWR-TB2 along axial nodes.

297

0.05 0 MWd/kgU 0.045 5 MWd/kgU 10 MWd/kgU 0.04

0.035

0.03

0.025

0.02

0.015 Central Void Diameter (mm) 0.01

0.005

0 0 20 40 60 80 100 120 Axial Node Figure 181: Central void diameter of ABWR along axial nodes.

6.4.9 Plutonium redistribution

Figure 182 shows the radial distribution of plutonium weight fraction for the RBWR-TB2 at the peak axial node located in the upper fissile zone from EOL to BOL. From a uniform plutonium concentration of 69 wt% at BOL, plutonium migrates up temperature gradient to reach a maximum concentration of approximately 77 wt% at EOL. As a result of plutonium migration, the plutonium concentration at the center increases by 8 wt% from its initial value. In the lower fissile zone with initial plutonium of 79 wt%, a similar behavior can be observed but to a lesser degree of increase. In this case, the plutonium concentration at the center of the lower fissile zone increases by 5 wt% from 79 wt% to 83 wt%. The radial distribution of plutonium content in the lower fissile zone will not be shown here for the sake of brevity. The feedback of this phenomenon is a shift in the radial power profile toward the center where fissile material concentration is higher and changes in fuel material properties occur as discussed in the previous sections.

298

78 BOL MOL 76 EOL

68 Plutonium weight fraction (%) Plutonium weight fraction

64 0 5 10 15 20 25 30 35 40 45 Radial node Figure 182: Radial distribution of plutonium of RBWR-TB2 at peak axial node.

Figure 183 shows a radial distribution of plutonium weight fraction for the ABWR at the peak axial node from BOL to EOL. No observable plutonium redistribution occurs in the ABWR and the plutonium concentration remains at the initial values of 0 wt%. This is because the initial fuel

composition comprises only UO2 and currently the thermal migration model does not have a production term for plutonium. In addition, the fuel temperature of ABWR would be too low to cause any noticeable migration.

299

Figure 183: Radial distribution of plutonium of ABWR at peak axial node.

6.4.10 Oxygen-to-metal ratio radial redistribution

Not only does the oxygen-to-metal ratio (O/M) vary with temperature, fuel burnup also results in an overall increase of O/M across the fuel pellet. The direction of oxygen transport depends on fuel stoichiometry. In hypostoichiometric fuel (O/M < 2.0), oxygen will migrate to the lower temperature region. On the other hand, if the fuel is hyperstoichiometric (O/M > 2.0), oxygen will move up to the hotter regions. Figure 184 clearly shows the contradicting behavior of oxygen migration at middle-of-life (MOL) and end-of-life (EOL) for the RBWR-TB2 at the peak axial node. From an initial uniform O/M ratio of 1.98, oxygen migrates to the colder region so that the O/M ratio in the outer regions becomes more stoichiometric. However, once the fuel becomes fully hyperstoichiometric at high burnup, the direction of oxygen migration is reversed. From this point onward, oxygen will migrate to high temperature region in the center.

Figure 185 shows the radial distribution and burnup evolution of O/M ratio from EOL to BOL for the ABWR. Unlike the RBWR-TB2 fuel which begins as hypostoichiometric, the ABWR

300 uses stoichiometric fuel (O/M = 2.0) and this will result in different migration behavior of oxygen. For the ABWR, oxygen will migrate up the temperature gradient. This effect is further pronounced as O/M increases with burnup. The redistribution of oxygen directly impacts the value of O/M and deviation from stoichiometry which is defined as x = |O/M-2|. The deviation from stoichiometry is one of the most important parameters in determining thermal conductivity of both UO2 and MOX fuels. In terms of fuel thermal conductivity, it has a far greater impact than plutonium content or fuel burnup in certain situations. Therefore, the evolution of the O/M ratio with burnup and its radial migration through the fuel pellet have both positive and negative impacts to fuel temperature. For initially hypostoichiometric fuel, the increase in O/M with burnup and migration to fuel periphery may help in improving thermal conductivity in the outer regions of fuel pellet by reducing the deviation from stoichiometry. However, this may come at a price of losing thermal conductivity in the center where it is more important because of higher temperature and heat generation rate in this region. Once the fuel becomes fully hyperstoichiometic at high burnup, oxygen migration toward the center will reduce thermal conductivity even further as this will increase the value of x.

2.03 BOL 2.02 MOL EOL 2.01

1.99

1.98 O/M

1.97

1.96

1.95

1.94

1.93 0 5 10 15 20 25 30 35 40 45 Radial Node Figure 184: Radial distribution of O/M ratio of RBWR-TB2 at peak axial node.

301

2.045 BOL 2.04 MOL EOL 2.035

2.03

2.025

O/M 2.02

2.015

2.01

2.005

2 0 5 10 15 20 25 30 35 40 45 Radial Node Figure 185: Radial distribution of O/M ratio of ABWR at peak axial node.

6.4.11 Cesium migration and JOG formation

Figure 186 illustrates the axial distribution of cesium along the axial nodes of the RBWR-TB2. Since the source term of cesium is derived from fission rate density, without thermo-migration, the axial distribution of cesium concentration would likely follow that of the axial peaking factor. However, because cesium migration is quite effective in the RBWR-TB2, given its high temperature and high burnup conditions, the axial distribution of cesium is expected to change significantly from its initial distribution and the results shown in Figure 186 clearly demonstrates this behavior. It can be seen that cesium migrates down the temperature gradients and forms localized high concentration spots near the fissile-blanket interface zones. Fuel swelling in these interface nodes will be increased as a result of cesium migration and condensation.

302

1026 3.5

BOL 3 MOL EOL ) 3

2.5

1.5

1 Cs Number Density (atoms/m Cs Density Number

0.5

0 0 20 40 60 80 100 120 Axial Node Figure 186: Axial distribution of cesium of RBWR-TB2.

Figure 187 shows the axial distribution of cesium along the axial nodes of the ABWR. Given lower fuel burnup, relatively uniform fuel enrichment, lower LHGR, and longer fuel length of the ABWR design, the cesium migration is not expected to be relevant because of lower fuel temperature and lower temperature gradient. This speculation has been confirmed from the results shown in Figure 187 the cesium is marginally migrated through the axial zones. Except for a small accumulation of cesium at the bottom of the fuel rod, the axial distribution of cesium for the ABWR seems to follow the burnup profile and the axial peaking factor. In the ABWR, the location where fuel swelling reaches its maximum values is relatively close to the peak power-producing node whereas in the RBWR-TB2 it is shifted to locations near fissile-blanket interface zones.

303

1026 2.5 BOL MOL EOL

) 2 3

1.5

Cs Number Density (atoms/m 0.5

0 0 20 40 60 80 100 120 Axial Node Figure 187: Axial distribution of cesium of ABWR.

A similar behavior can also be observed in the radial direction where cesium migrates from the high temperature region in the center to the lower temperature region at the periphery as shown in Figure 188. The assumption is that the migration of cesium will cease once fuel temperature drops below cesium’s melting point at 950 K. Furthermore, as shown in the previous section, the O/M ratio near the periphery readily becomes stoichiometric and hyperstoichiometric at medium and high burnup, respectively. Therefore, the oxygen potential in those regions also increases accordingly. With sufficient oxygen potential, it is expected that the cesium would react with uranium, oxygen and other fission products and then form stable solid compounds and become immobile. From the examination of the surface fuel temperature of the RBWR-TB2, the only instances where fuel surface temperature exceeded 950 K is some few time steps near EOL meaning that, most of the time, cesium could not reach to fuel surface and would stop migration near fuel periphery. Therefore, without cesium flux moving out of fuel surface, JOG cannot be formed in the fuel-cladding gap under RBWR-TB2 conditions. A similar situation also applies to ABWR where cesium would remain within the fuel matrix as shown in Figure 189.

304

1027 7

BOL 6 MOL EOL ) 3

2 Cs Number Density (atoms/m

0 0 5 10 15 20 25 30 35 40 45 Radial Node Figure 188: Radial distribution of cesium of RBWR-TB2.

1026 5

4.5 BOL MOL EOL ) 4 3

3.5

2.5

1.5

Cs Number Density (atoms/m 1

0.5

0 0 5 10 15 20 25 30 35 40 45 Radial Node Figure 189: Radial distribution of cesium of ABWR.

305

6.4.12 Hydrogen redistribution and precipitation

At operating conditions of LWRs, hydrogen atoms that get absorbed into the cladding could either remain dissolved in the zirconium matrix as solute or react with zirconium and precipitate as zirconium hydride (ZrH1.6), depending on cladding temperature and hydrogen concentration. Hydrogen as solute could pose no serious threat to cladding integrity whereas hydride precipitation can severely degrade the ductility and fracture toughness of the zirconium cladding. Under the influence of temperature and concentration gradient, hydrogen exhibits a similar migration behavior as cesium in that it relocates to colder regions of the cladding such as the cladding outer surface, the top and bottom of fuel rods. In case of an axially heterogeneous fuel design such as with the RBWR-TB2, fissile-blanket interfaces could serve as localized cold spots for hydrogen accumulation. Figure 190 shows the axial distribution of hydride precipitation of RBWR-TB2 at the cladding outer surface which is also known as the hydride rim region. It can be observed that hydride concentration in certain axial nodes near the fissile-blanket interfaces have reached a maximum concentration limit of 18,200 wt. ppm (1.82 wt%) at EOL. The excessive hydrogen content in the hydride rim of RBWR-TB2 could be of great concern in a once-through fuel cycle. In this case, the cladding will have to last for an extended period of time in spent fuel pools and geological repositories. The application of the RBWR-TB2 is for multi- recycling of TRU-containing fuels in a close-looped fuel cycle. Therefore, the concerns over hydrogen embrittlement during long-term storage are of secondary importance because the fuel cladding will have to be replaced during reprocessing and fuel re-fabrication. However, there may still be a significant challenge during transients and accident conditions, as the hydride precipitates will reduce the margins to failure of the cladding. As shown in Figure 191, hydride precipitation under ABWR conditions also exhibits a similar behavior of hydrogen migration as with the RBWR-TB2. However, since there are no fissile or blanket zones in the ABWR, the cold spots where hydrogen could accumulate are located at the top and bottom of the fuel rod. In addition, the magnitude of hydrogen concentration with the ABWR is significantly smaller than that of the RBWR-TB2, mainly because of lower oxidation and hydrogen content in the cladding. Lower fuel burnup under ABWR conditions also prevents the onset of accelerated corrosion.

306

104 2 BOL 1.8 MOL EOL 1.6

1.4

1.2

0.8

0.6

0.4

Hydride Precipitate Concentration (wt ppm) 0.2

0 0 20 40 60 80 100 120 Axial Node Figure 190: Axial distribution of hydride precipitation of RBWR-TB2 at cladding outer surface.

1800 BOL 1600 MOL EOL 1400

1200

1000

800

600

400

200 Hydride Precipitate Concentration (wt ppm) Hydride

0 0 20406080100120 Axial Node Figure 191: Axial distribution of hydride precipitation of ABWR at cladding outer surface.

307

The radial distribution of soluble hydrogen for the RBWR-TB2 and ABWR are shown in Figures 192 and 193, respectively. It can be seen that the concentration of soluble hydrogen is significantly smaller when compared to that of hydrogen precipitate. This is because the solubility of hydrogen in zirconium is naturally limited as it cannot exceed the terminal solid solubility for precipitation (TSSP). In this case, the soluble hydrogen concentration will continue to increase until it reaches maximum value of TSSP. Beyond this point, any hydrogen atoms further produced from oxidation will have to stay as hydride precipitate. In fact, soluble hydrogen is the only migrating species because the hydride precipitate is immobile. The source term of soluble hydrogen is calculated by a default correlation in FRAPCON-3.5 EP which converts oxide layer thickness into a radially-averaged concentration of hydrogen. At every time step, the local concentration of soluble hydrogen will be incrementally increasing by this value. Then, the thermal migration mechanism will redistribute a local concentration of soluble hydrogen of each radial node. Since the hydrogen atoms migrate relatively fast, it tends to accumulate in the coldest spots toward to cladding outer surface and cause accumulation of hydride precipitate at the cladding outer surface.

160

140 BOL MOL 120 EOL

100

Hydrogen Solute Concentration (wt ppm) Solute Hydrogen 20

0 12345678910 Radial Node Figure 192: Radial distribution of hydrogen solute of RBWR-TB2.

308

120

100

80 BOL MOL EOL

20 Hydrogen Solute Concentration (wt ppm)

0 12345678910 Radial Node Figure 193: Radial distribution of hydrogen solute in ABWR.

6.5 Parametric study on important fuel design parameters

This section presents a parametric study on important design parameters and their impact on overall fuel performance. In this thesis, a comparison of fuel performance between the following design parameters is presented: (1) fuel-clad gap thickness, (2) fuel density (3) oxygen-to-metal ratio, (4) helium pressure, (5) central void diameter, and (6) cladding thickness. Table 18 shows the range of parameters explored in this section. The reference design parameters are 110 μm for gap thickness, 90 %TD for fuel density, 1.98 for O/M ratio of, 1 MPa for helium pressure, 0.0 mm for central void diameter of, and 0.6 mm for clad thickness.

Table 18: Key design parameters of RBWR-TB2 fuel rods.

Design parameters Range of parameters

Fuel-clad gap thickness (μm) 55 110

309

Fuel density (% TD) 80 85 90 95

Fuel O/M ratio 1.90 1.95 1.98 2.00

Helium pressure (MPa) 1 2 3 4

Central void diameter (mm) 0.0 1.0 1.5 2.0

Clad thickness (mm) 0.6 0.7 0.8 0.9

6.5.1 Initial fuel-clad gap thickness

As discussed earlier in Section 6.4, the structural radial gap and interfacial pressure are particularly important for fuel performance behavior and strongly influence several life-limiting parameters such as fuel temperature and EOL cladding stress and strain. A larger gap can prolong the onset of hard contact and reduce PCMI pressure. However, it will unavoidably increase the temperature drop across the gap which will eventually result in higher fuel temperature. Previously, the gap thickness of the RBWR-TB2 was specified as 55 μm before it was revised to 110 μm. This parametric study aims demonstrate how the fuel performance would have changed if the gap size was reduced to its previous value.

Figures 194 and 195 compare the average and centerline fuel temperature between an initial gap thickness of 55 and 110 μm. It can be seen that, by reducing a gap thickness by a factor of 2, a sizable reduction in average fuel temperature can be achieved. However, it does not seem to have a large impact on centerline fuel temperature after gap closure. This is because of the integral nature of average temperature which includes the blanket zones into the calculation. It appears that the gap remains opens in these regions and large gap would results in higher temperature in the blanket regions. Eventually, this leads to a higher average temperature in 110 μm case. Fluctuation in centerline temperature near EOL at the peak node for the 55 μm case is caused by operating near the melting points where the fuel properties such as heat capacity and thermal expansion are affected.

310

1150 110 microns 55 microns 1100

1050

1000

950

900 Average Fuel Temperature (K)

850

800 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 194: Average fuel temperature of RBWR-TB2 at 55 and 110 μm as a function of time.

3000

110 microns 55 microns 2800

2600

2400

2200

2000 Centerline Fuel Temperature (K) 1800

1600 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 195: Centerline fuel temperature of RBWR-TB2 at 55 and 110 μm as a function of time.

311

In addition, upon examining the axial variation of radially-average fuel temperature and fuel centerline temperature at EOL in the upper and lower fissile zones where fission gases are released the most, as shown in Figures 196 and 197, it can be seen that the fuel temperatures in fissile zones at EOL are quite comparable. The reason for this behavior is because in the fissile zones gap closure occurs approximately 100 days after operation. When the fuel-cladding gap thickness reaches a minimum value of the mean surface roughness between fuel and cladding, thermal contact will take place which considerably improves gap conductance. This effectively equalizes the temperature drop across the gap for both cases and eventually leads to small differences in fuel temperature.

2000

110 microns 1800 55 microns

1600

1400

1200

1000 Average Fuel Temperature (K) Fuel Average

800

600 0 20 40 60 80 100 120 Axial Node Figure 196: Average fuel temperature of RBWR-TB2 at 55 and 100 μm at EOL as a function of axial node.

312

3000

110 microns 55 microns

2500

2000

1500

Centerline Fuel Temperature (K) 1000

500 0 20 40 60 80 100 120 Axial Node Figure 197: Centerline fuel temperature of RBWR-TB2 at 55 and 100 μm at EOL as a function of axial node.

From the trend of fuel temperature, it can be inferred that fission gas release (FGR) and plenum pressure of these two cases should be similar. This speculation has been confirmed by Figures 198 and 199 showing that the differences in FGR and plenum pressure of RBWR-TB2 at the gap thickness of 55 and 110 μm are relatively small.

313

110 microns 55 microns 60

20 Fission Gas Release (%)

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 198: Fission gas release of RBWR-TB2 at 55 and 110 μm as a function of time.

110 microns 55 microns 7

4 Plenum PressurePlenum (MPa)

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 199: Plenum pressure of RBWR-TB2 at 55 and 110 μm as a function of time.

314

Although gap closure occurs roughly at the same time for both gap thicknesses, larger gap size means more allowance for fuel relocation recovery where fuel pellets can recover some of its relocation strain from cracking upon gap closure and the fuel pellet diameter is reduced accordingly. With this phenomenon, there exists a period of gap closure without interfacial pressure increase known as the soft contact period. After the relocation strain has been completely reclaimed, the interfacial pressure will begin to rise and this period is known as hard contact. With larger gap thickness, the duration of soft contact can be extended. As a result of gap thickness reduction, the early onset of hard contact can be observed in the 55 μm initial gap thickness case. In this case, it can be seen from Figure 200 that the interfacial pressure rises as early as by the first 100 days of operation and continues to rise until the end of cycle. However, in the case of 110 μm gap thickness, hard contact is delayed up to 800 days. This is favorable in terms of cladding stress because, without interfacial pressure, the only source of cladding stress is plenum pressure. In this case, it does not appear to be a great concern for the RBWR-TB2.

45 110 microns 40 55 microns

15 Interfacial Pressure (MPa) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 200: Interfacial pressure of RBWR-TB2 at 55 and 110 μm at peak axial node as a function of time.

315

Figures 201 and 202 show cladding hoop stress and strain for the RBWR-TB2 at an initial gap thickness of 55 and 110 μm, respectively. Higher cladding stress can be observed in the 55 μm case mainly due to the early onset of hard contact. In general, the cladding stress corresponds to the behavior of interfacial pressure. Another clear benefit of having a larger gap can be seen in the effect on cladding hoop strain in Figure 47. In this case, the cladding hoop strain for the 55 μm gap thickness exceeds a regulatory limit of 1% at end-of-life whereas it remains under 1% in 110 μm case.

200 110 microns 55 microns

150

100

50 Cladding Hoop Stress (MPa) 0

-50 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 201: Cladding hoop stress of RBWR-TB2 at 55 and 110 μm at peak axial node as a function of time.

316

1.8

110 microns 1.6 55 microns

1.4

1.2

0.8

0.6 Cladding Hoop Strain (%) 0.4

0.2

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 202: Cladding hoop strain of RBWR-TB2 at 55 and 110 μm at peak axial node as a function of time.

6.5.2 Fuel density

Fuel density has a profound impact on a number of phenomena in nuclear reactor analyses including neutronic and thermo-mechanical behaviors because it directly relates to fuel reactivity and fuel burnup. Lowering fuel density may help in delaying the onset of hard contact such that the PCMI pressure at EOL can be reduced. However, it may negatively impact the overall fuel performance due to an increase in fuel burnup. This section examines the positive and negative impacts by increasing and decreasing fuel density from its reference value of 90 %TD.

Figure 203 shows the rod-average fuel burnup for the RBWR-TB2 at fuel densities of 80, 85, 90 and 95 %TD as a function of time. It can be seen that the average burnup is inversely proportional to fuel density; lower fuel density would translate to higher fuel burnup at EOL. In this case, by reducing fuel density to 80 and 85 %TD, the rod-averaged fuel burnup increased to 83 and 78 MWd/kgHM, respectively, from a reference value of 74 MWd/kgHM at 90 %TD. On

317 the other hand, if the fuel density is increased to 95 %TD, the rod-averaged fuel burnup is then reduced accordingly to 70 MWd/kgHM.

In Figure 204, a varying degree of impacts in local fuel burnup from fuel density change can be noticed between fissile and blanket zones as the local burnup in the blanket is slightly affected by fuel density whereas the change in local burnup in the fissile zones is more visible. At 80 and 85 %TD, the EOL local burnup in the lower fissile zone increased to approximately 140 and 130 MWd/kgHM from a reference value of 120 MWd/kgHM at 90 %TD. In the upper fissile zone, the EOL local burnup increased from a reference value of 160 MWd/kgHM at 90 %TD to approximately 180 and 170 at 80 and 85 %TD respectively. At 95 %TD, these values decreased to 110 and 150 MWd/kgHM in the lower and upper fissile zone, respectively.

80 %TD 80 85 %TD 90 %TD 70 95 %TD

20 Rod Average Burnup (MWd/kgHM) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 203: Rod average burnup of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

318

200

80 %TD 180 85 %TD 90 %TD 160 95 %TD

140

120

100

80 Local Burnup (MWd/kgHM) 60

20 0 20 40 60 80 100 120 Axial Node Figure 204: Local burnup of RBWR-TB2 at fuel density of 80-95 %TD as a function of axial node.

The first undesirable side effect of reducing fuel density can be seen with the fuel temperature because a change in fuel density directly affects two important parameters for fuel thermal conductivity: porosity and burnup. As fuel density is inversely proportional to porosity, if fuel density is decreased then the porosity is increased. This will result in a reduction in the effective thermal conductivity and higher fuel temperature. Furthermore, the thermal conductivity of oxide fuels systematically decreases with burnup due to microstructural defects, irradiation damage and fuel lattice contamination by fission products. As a result, an increase in fuel burnup also negatively affects the thermal conductivity. Figure 205 and 206 compare the average and centerline fuel temperature for the RBWR-TB2 at fuel densities of 80- 95 %TD as a function of time. The effect of fuel density on fuel temperature is clear: lower density fuel would lead to higher fuel temperature. Likewise, a significant reduction in fuel temperature can be noticed when a higher density fuel is used. For the case of 80 %TD, temperature fluctuation toward EOL is caused by operating near melting points by which fuel properties such as heat capacity and thermal expansion are affected.

319

1250

80 %TD 1200 85 %TD 90 %TD 95 %TD 1150

1100

1050

1000

950 Average Fuel Temperature (K)

900

850 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 205: Average fuel temperature of RBWR-TB2 at fuel density of 80- 95 %TD as a function of time.

320

3000 80 %TD 85 %TD 2800 90 %TD 95 %TD

2600

2400

2200 Centerline Fuel Temperature (K) 2000

1800 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 206: Centerline fuel temperature of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

As diffusion coefficients of fission gases are strongly dependent by fuel temperature, an increase in fuel temperature would consequentially lead to higher fission gas release (FGR). This behavior is illustrated in Figure 207 where lower density fuel results in a higher percentage of FGR throughout the cycle. A direct consequence of higher FGR is a lower gap conductance due to contamination by fission gases. Higher moles of gases released into the free volume would generally mean higher plenum pressure at EOL. However, this is not the case for the plenum pressure of the RBWR-TB2 at fuel densities of 80-95 %TD as shown in Figure 208 because the trend is reverse; the densest fuel yields highest plenum pressure at EOL although it was lowest from EOL through MOL. Since the plenum pressure is not only dependent on the amount of gases in the plenum, but it also depends on the total void volume within the fuel rod. Therefore, it would be of interest to examine this parameter to confirm the validity of the code calculation.

321

80 80 %TD 70 85 %TD 90 %TD 95 %TD 60

Fission Gas Release (%) Fission 20

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 207: FGR of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

8 80 %TD 85 %TD 7 90 %TD 95 %TD

4 Plenum Pressure (MPa)

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 208: Plenum pressure of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

322

Figure 209 shows the total void volume of the RBWR-TB2 at fuel densities of 80-95 %TD as a function of time. It can be seen that a reduction in plenum pressure for the 80 and 85 %TD cases originated from a higher void volume from increased porosity. With higher void volume, even if the fuel temperature and fission gas release for the 80 and 85 %TD cases are higher, the plenum pressures at EOL of those cases can still be lower than the reference value at 90% TD.

32 ) 3 30

28 80 %TD 85 %TD 26 90 %TD 95 %TD 24

22 Total Void Volume (cm

16 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 209: Total void volume of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

Besides void volume increase, another positive effect of reducing fuel density can be noticed from the interfacial pressure during pellet-cladding mechanical interaction (PCMI). As shown in Figure 210, lower density fuel helps delay the onset of PCMI as it prolongs the period of soft- contact between the fuel and the cladding. With higher porosity which makes the fuel softer, the PCMI pressure is effectively reduced. The delay in gap closure also has an effect on total void volume because the contribution from fuel-cladding gap volume is sizable. With a reduction in interfacial and plenum pressure which are the source of the primary mechanical loads in cladding deformation mechanism, a significant reduction in cladding stress and strain for low density fuel

323 is highly expected. On the other hand, increasing fuel density to 95 %TD causes the early onset of hard contact and PCMI pressure; therefore, cladding stress and strain are expected to increase as a result.

45 80 %TD 40 85 %TD 90 %TD 35 95 %TD

15 Interfacial Pressure (MPa) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 210: Interfacial pressure of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

Although fuel temperature and burnup are higher which cause the fuel to expand and swell more with lower density fuel, lower plenum pressure and interfacial pressure would counter-balance the negative effects on cladding stress and strain. Figure 211 shows cladding hoop stress for the RBWR-TB2 at fuel densities of 80-95 %TD as a function of time. It can be seen that a reduction in interfacial pressure generally corresponds to a reduction in cladding stress as shown in the 80 and 85 %TD cases. Similarly, higher cladding stress is observed in 95 %TD due to higher PCMI pressure.

324

200

80 %TD 85 %TD 90 %TD 150 95 %TD

100

50 Cladding Hoop Stress (MPa) 0

-50 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 211: Cladding hoop stress of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

Figure 212 shows cladding hoop strain for the RBWR-TB2 at fuel densities of 80-95 %TD as a function of time. In this case, another clear benefit of using lower density can be seen with the cladding hoop strain as it shows a considerable reduction in cladding strain for 80 and 85 %TD whereas the cladding hoop strain for 95 %TD exceeds far beyond a regulatory limit of 1% at EOL.

325

80 %TD 1.8 85 %TD 90 %TD 1.6 95 %TD

1.4

1.2

0.8

0.6 Cladding Hoop Strain (%) 0.4

0.2

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 212: Cladding hoop strain of RBWR-TB2 at fuel density of 80-95 %TD as a function of time.

In conclusion, increasing fuel density to 95% TD is not recommended because it would cause significant deformation of the cladding. Although, reducing fuel density to 80 or 85 %TD would have some positive impacts in terms of cladding stress and strain as they are originated from a reduction in PCMI and plenum pressure. However, the negative impacts from fuel burnup increases, lower TRU loading and thermal conductivity reduction cannot be ignored. Therefore, further design optimization on fuel density in the range of 85-90 %TD is recommended.

6.5.3 Oxygen-to-metal ratio

Oxygen-to-metal ratio (O/M) significantly affects fuel thermal conductivity. Since it constantly evolves with burnup, it is important to estimate the impact of initial value of O/M on fuel performance throughout the cycles. Initially hypostoichiometric fuel (O/M < 2.0) would be disadvantageous because of lower fuel thermal conductivity. However, the deviation from stoichiometry (x = |O/M-2|) would become smaller as the O/M increases with burnup. On the

326

other hand, initially stoichiometric fuel (O/M = 2.0) would have higher thermal conductivity at first but this condition may not last long because deviation from stoichiometry will keep increasing with burnup. This would result in a lower thermal conductivity at high burnup. In this section, a comparison of fuel burnup is not necessary because there is no change in fuel volume making the fuel burnup identical for all O/M ratios.

Figure 213 and 214 show the average and centerline fuel temperature for the RBWR-TB2 at O/M ratios of 1.90, 1.95, 1.98 and 2.00 as a function of time. It can be clearly seen that hypostoichiometric fuel exhibits a higher temperature at BOL and the trend is revere from MOL until EOL. On the other hand, the stoichiometric fuel begins with lower fuel temperature up to 200 days. After that the fuel chemical potential becomes oxidizing and deviation from stoichiometry keeps getting larger. As a result, fuel thermal conductivity for an O/M ratio at 2.00 turns out to be the lowest. Lower thermal conductivity results in higher fuel temperature in both radially-averaged value and at the centerline.

1200

O/M = 1.90 1150 O/M = 1.95 O/M = 1.98 O/M = 2.00 1100

1050

1000

950 Average Fuel Temperature (K) Average

900

850 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 213: Average fuel temperature of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time.

327

3000 O/M = 1.90 O/M = 1.95 2800 O/M = 1.98 O/M = 2.00

2600

2400

2200 Centerline Fuel Temperature (K) 2000

1800 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 214: Centerline fuel temperature of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time.

Comparing among hypostoichiometric fuel, it appears that reducing O/M ratios to 1.95 would balance its positive and negative effects on thermal conductivity at both low and high burnup. As thermal conductivity of mixed oxide fuel heavily depends on the deviation from stoichiometry, any configuration that would lead to the smallest departure from stoichiometric condition i.e. O/M = 2.00 would yield the most benefits in term of thermal conductivity. In this case, the O/M ratio of 1.95 would result in a lower average and centerline fuel temperature than the reference O/M ratio of 1.98. Besides, some deviation at BOL up to 200 days for O/M ratios of 1.90 and 1.95, the temperature profiles of these two cases are quite comparable.

Subsequent parameters to be examined are fission gas release and plenum pressure as they are strongly correlated with fuel temperature. Figure 215 shows the fission gas release for the RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time. For initially stoichiometric fuel, its behavior follows closely to that of fuel temperature: lowest FGR at low burnup and highest FGR at high burnup. In this case, the impact of operating at higher temperatures can be clearly seen as

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the hotter fuel releases more fission gases. For all other cases at lower O/M ratios, the FGR seems to converge because of similarity in average fuel temperature.

70 O/M = 1.90 O/M = 1.95 60 O/M = 1.98 O/M = 2.00 50

20 Fission Gas Release (%)

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 215: Fission gas release of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time.

Figure 216 shows the plenum pressure of the RBWR-TB2 at varying O/M ratios. Given no variation in total void volume, the plenum pressure depends solely on the amount of fission gas release to the plenum. Due to its similarity in average fuel temperature, the plenum pressure for O/M ratios = 1.90, 1.95 and 1.98 are quite comparable. For the case of O/M = 2.00, higher temperature fuel then leads to higher plenum pressure although it is less noticeable than the FGR.

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O/M = 1.90 O/M = 1.95 7 O/M = 1.98 O/M = 2.00

4 Plenum Pressure (MPa)

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 216: Plenum pressure of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time.

As a primary source of cladding deformation from PCMI, the interfacial pressure is also affected by O/M ratios of the fuel. The interfacial pressure of the RBWR-TB2 at varying O/M is given in Figure 217. It can be seen that increase in fuel temperature for initially stoichiometric fuel would result in more thermal expansion strain and eventually lead to higher interfacial pressure. On the contrary, for initially hypostochiometric fuel with lower O/M ratios, the magnitude of the interfacial pressure is progressively reduced. The lowest interfacial pressure can be seen when initial O/M is reduced to 1.90. These results also suggest that the cladding hoop stress and strain for the case of O/M = 1.90 would be lowest given that the plenum pressures of all other cases are quite comparable.

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O/M = 1.90 35 O/M = 1.95 O/M = 1.98 O/M = 2.00 30

Interfacial Pressure (MPa) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 217: Interfacial pressure of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time.

Figures 218 and 219 show the cladding hoop stress and strain for the RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time. As expected, the option with lowest cladding hoop stress and strain is when the O/M ratio is reduced to 1.90, although the cladding hoop stress may seem to converge at the O/M ratios of 1.95, 1.98 and 2.00. A clear distinction between different O/M ratios can be seen in the cladding hoop strain. In this case, it can be noticed that when the O/M is increased to 2.00, the cladding hoop strain increased rapidly in the last cycle while reducing O/M from 1.98 to 1.95 and 1.90 would result in noticeable decrease in the cladding hoop strain.

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200

O/M = 1.90 O/M = 1.95 O/M = 1.98 150 O/M = 2.00

100

50 Cladding Cladding Hoop Stress (MPa) 0

-50 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 218: Cladding hoop stress of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time.

0.9

O/M = 1.90 0.8 O/M = 1.95 O/M = 1.98 0.7 O/M = 2.00

0.6

0.5

0.4

0.3 Cladding Hoop Strain (%) 0.2

0.1

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 219: Cladding hoop strain of RBWR-TB2 at O/M ratios of 1.90-2.00 as a function of time.

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Because of several negative effects in fuel temperature, PCMI and cladding strain, it is not recommended to use stoichiometric fuel (O/M = 2.00) in RBWR-TB2. Although the current hypostoichiometric fuel at O/M ratio of 1.98 produces acceptable results, in order to limit the oxygen potential and deviation from stoichiometry at high burnup, consideration for using hypostoichiometric fuel with lower O/M ratios should be given.

However, there are still some uncertainties about the behavior of certain fission products such as Mo, Zr, and Rb that could act as oxygen buffers and may help in stabilizing the oxygen potential at high burnup. In this case, the rate of O/M increase with burnup may be interfered by this buffering effect. Therefore, reducing O/M ratios to 1.95 would balance its positive and negative effects on thermal conductivity both low and high burnup while leaving some margins for oxygen buffering phenomenon.

6.5.4 Helium pressure

Increasing helium pressure improves its thermal conductivity thus reducing temperature drop across the gap at the beginning. However, as fission gases are being generated and released into the free volume, having higher helium pressure at BOL will result in higher plenum pressure at EOL, thus increasing mechanical load on the cladding. This section explores the effects of initial helium pressure on overall fuel performance. Similar to the O/M ratio where there is no alteration to fuel volume, a comparison of fuel burnup is not necessary.

Figures 220 and 221 compare the average and centerline fuel temperature of the RBWR-TB2 at helium pressures of 1, 2, 3, and 4 MPa as a function of time. It can be seen that higher helium pressure results in lower average fuel temperature even though its effect seems to converge at 3 and 4 MPa from BOL through MOL. However, these two cases show a departing trend at around 1100 days and the average fuel temperature at initial helium pressure of 4 MPa turns out to be the highest at EOL. However, the initial helium pressure does not seem to have a major impact to the centerline fuel temperature as they are relatively similar for all cases. From visual examination, the lowest centerline temperature option is when the initial helium pressure is 1 MPa.

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1 MPa 2 MPa 1100 3 MPa 4 MPa

1050

1000

950 Average Fuel Temperature (K) Fuel Average 900

850 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 220: Average fuel temperature of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time.

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2800 1 MPa 2700 2 MPa 3 MPa 2600 4 MPa

2500

2400

2300

2200

2100

Centerline Fuel Temperature (K) 2000

1900

1800 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 221: Centerline fuel temperature of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time.

Figure 222 shows fission gas release for the RBWR-TB2 at helium pressures from 1.0 to 4.0 MPa as a function of time. It can be seen that lower fuel temperature from higher helium pressure would lead to a lower FGR even though its effect seems to be less visible especially near EOL. In this case, the initial helium pressure at 4 MPa has the lowest FGR at BOL and MOL whereas the FGR of all cases are similar at EOL.

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1 MPa 60 2 MPa 3 MPa 4 MPa 50

20 Fission Gas Release (%)

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 222: Fission gas release of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time.

Figure 223 shows the plenum pressure for the RBWR-TB2 at helium pressures from 1.0 to 4.0 MPa as a function of time. Unlike fuel temperature or FGR, the plenum pressure is highly sensitive to the initial helium pressure. Furthermore, the simulation results indicate that increasing the helium pressure by 1 MPa will correspond to an increase in the plenum pressure of around 2 MPa. As a result, the EOL plenum pressures of all cases except 1 MPa end up exceeding the external coolant pressure of 7 MPa. From the figure, it can be noticed that the plenum pressure could reach 14 MPa if the initial helium pressure is set at 4 MPa. As discussed previously, the plenum pressure is one of the two contributors leading to cladding deformation; having too much plenum pressure will adversely impact mechanical integrity of the cladding.

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1 MPa 2 MPa 12 3 MPa 4 MPa

6 Plenum Pressure (MPa)

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 223: Plenum pressure of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time.

Given a considerable increase in plenum pressure, the interfacial pressure from PCMI is also affected by this variation. As shown in Figure 224, the interfacial pressure decreases when the plenum pressure increases. As the plenum pressure represents the level of internal pressurization within a fuel rod, having higher pressure is equal to having a stronger force pushing the cladding further away from the fuel pellet thus increasing fuel-pellet gap thickness. Although this effect could potentially increases fuel temperature and thermal expansion, the results still show a net reduction in the interfacial pressure from high plenum pressure.

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1 MPa 35 2 MPa 3 MPa 4 MPa 30

Interfacial Pressure (MPa) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 224: Interfacial pressure of RBWR-TB2 at helium pressure of 1.0-4.0 MPa as a function of time.

As the modification of initial helium pressure causes an increase in plenum pressure and a decrease in interfacial pressure, it is quite interesting to examine their impacts on cladding stress and strain which are considered as life-limiting parameters in fuel rod operation. Figures 225 and 226 show the cladding hoop stress and strain, respectively, for the RBWR-TB2 at helium pressures from 1.0-4.0 MPa as a function of time. For cladding stress, it can be seen that, cladding stress is lowest when the initial helium pressure is lowest from BOL to MOL. However, when PCMI eventually occurs, the trend is reverse in that highest helium pressure has lowest cladding stress at EOL. On the other hand, such behavior is not observed for cladding hoop strain, as it appears that higher helium pressure always results in higher cladding strain. For the case of an initial helium pressure of 4 MPa, the EOL cladding hoop strain ends up higher than a regulatory limit of 1%.

338

200

1 MPa 2 MPa 150 3 MPa 4 MPa

100

50 Cladding Hoop Stress (MPa) Cladding Hoop 0

-50 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 225: Cladding hoop stress of RBWR-TB2 at helium pressure of 1.90-2.00 as a function of time.

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1.2

1 MPa 2 MPa 1 3 MPa 4 MPa

0.8

0.6

0.4 Cladding Hoop Strain (%)

0.2

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 226: Cladding hoop strain of RBWR-TB2 at helium pressure of 1.90-2.00 as a function of time.

From the comparison of plenum pressure, cladding hoop stress and strain, it appears that increasing the initial helium pressure does not effectively improve fuel performance. Besides some small reductions in average fuel temperature and interfacial pressure, it leads to higher plenum pressure and cladding strain which are more important to cladding integrity at high burnup. Therefore, it is not recommended to increase the helium pressure beyond 1.0 MPa. Conversely, reducing helium pressure below 1.0 MPa could lower gap conductance and increase fuel temperature. All in all, it is recommended to set the initial helium pressure at 1 MPa.

6.5.5 Central void diameter

A central void can significantly lower fuel temperature at the centerline because it eliminates the central region in a fuel rod where the heat source is farthest from the heat sink (coolant). However, displacing a fuel volume with an empty space will increase fuel burnup and negatively

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affect fuel performance. This section aims to explore the appropriate balance between centerline temperature reduction and fuel burnup increase.

Figure 227 shows the rod-average fuel burnup for the RBWR-TB2 at central void diameters of 0.0, 1.0, 1.5, and 2.0 mm as a function of time. As expected, the average burnup increases with a central void diameter. In this case, with a central diameter of 1.0, 1.5, and 2.0 mm, the rod- averaged fuel burnup increased to 76, 78, and 82 MWd/kgHM, respectively, from a reference value of 74 MWd/kgHM without a central void.

80 0.0 mm 1.0 mm 1.5 mm 70 2.0 mm

20 Rod Average Burnup (MWd/kgHM) Rod Average 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 227: Rod average burnup of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

In Figure 228, a central void exhibits a varying degree of impacts as it slightly affects the local burnup in the blanket zones whereas it is more visible in the fissile zones. With a central void diameter of 1.0, 1.5, and 2.0 mm, the EOL local burnup in the lower fissile zone increased to approximately 123, 127, and 133 MWd/kgHM from a reference value of 120 MWd/kgHM without a central void. In the upper fissile zone, the EOL local burnup increased from a reference

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value of 160 MWd/kgHM to approximately 165, 170, and 180 with a central void diameter of 1.0, 1.5, and 2.0 mm respectively.

200

0.0 mm 180 1.0 mm 1.5 mm 160 2.0 mm

140

120

100

80 Local Burnup (MWd/kgHM) 60

20 0 20 40 60 80 100 120 Axial Node Figure 228: Local burnup of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of axial node.

Figure 229 shows the average fuel temperature for the RBWR-TB2 at central void diameters from 0.0-2.0 mm as a function of time. As a result of centerline temperature reduction, the rod- average temperature is also reduced accordingly. It can be seen that the average fuel temperature decreases as central void size increases. However, the feedback of burnup increase tends to balance out the benefit of having a central void. Eventually, with lower fuel thermal conductivity at high burnup, the average fuel temperature of the reference case (initially solid pellet without a central void) turns out to be the lowest fuel temperature option.

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1150

0.0 mm 1.0 mm 1100 1.5 mm 2.0 mm

1050

1000

950 Average Fuel Temperature (K) Average 900

850 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 229: Average fuel temperature of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

A plot of radially-averaged fuel temperature in the fissile and blanket zones may reveal some useful information about the axial distribution of fuel temperature. Figure 230 shows the radially-averaged fuel temperature as a function of axial node for the last time step. It can be seen that the radially-averaged fuel temperatures for annular pellet options are still lower than a solid pellet option in both upper and lower fissile zones. From this plot, it can be inferred that the convergence in rod-average temperature at EOL essentially comes from the blanket zone where annular pellet options have higher fuel temperature than the solid pellet option. It can also be noticed that there is a huge peak in fuel temperature at the axial nodes near interfaces between the upper fissile and the blanket zone of the solid pellet option. Upon examining the local LHGR and gap thickness at that location, this sudden temperature increase was a result of gap reopening, up to 10 microns, due to a gradual LHGR decrease toward EOL. This kind of behavior was also observed in certain time steps throughout of simulation whenever gap reopening events occurred.

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1800

0.0 mm 1.0 mm 1600 1.5 mm 2.0 mm

1400

1200

1000 Average Fuel Temperature (K) Fuel Average 800

600 0 20 40 60 80 100 120 Axial Node Figure 230: Average fuel temperature at EOL of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of axial node.

Figure 231 shows the centerline fuel temperature of the RBWR-TB2 at central void diameters of 0.0-2.0 mm as a function of time. With the annular pellet geometry, considerable reduction in centerline temperature can be obtained. The magnitude of temperature reduction increases with the diameter of the central void and it can be as high as 100, 200, and 300 K with a central void diameter of 1.0, 1.5, and 2.0 mm, respectively. The reduction in fuel temperature in both fissile zones looks very promising because it will eventually lead to a performance improvement in terms of cladding stress and strain.

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2800

0.0 mm 1.0 mm 2600 1.5 mm 2.0 mm

2400

2200

2000 Centerline Fuel Temperature (K) Centerline Fuel 1800

1600 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 231: Centerline fuel temperature of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

As shown in Figure 232, the fission gas release for solid and annular pellets also follows the trends of average fuel temperature in that a larger central void has lower FGR at low burnup in the 1st and 2nd cycles. At higher burnup in the 3rd and 4th cycles, the FGR of annular pellet cases becomes equal to that of solid pellet case as a result of thermal conductivity degradation. At EOL, FGR of all cases seems to converge regardless of temperature.

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0.0 mm 60 1.0 mm 1.5 mm 2.0 mm 50

20 Fission Gas Release (%) Fission

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 232: Fission gas release of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

A comparison of plenum pressure between solid (central void diameter = 0.0 mm) and annular pellets (central void diameter > 0.0 mm) is shown in Figure 233. It can be seen that the plenum pressure also exhibits a similar behavior to FGR in that different void diameter has minor impact on the plenum pressure. This result is quite unexpected because the plenum pressure of annular fuel should be lower than solid pellet given a similar FGR primarily due additional free volume provided by the central void. Therefore, it is of interest to further examine the total void volume of both solid and annular pellets.

346

0.0 mm 1.0 mm 7 1.5 mm 2.0 mm

4 Plenum Pressure (MPa) Plenum Pressure

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 233: Plenum pressure of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

The void volumes of the RBWR-TB2 at central void diameters of 0.0-2.0 mm are shown in Figure 234. The results show that the central void does not significantly increase the total void volume. It can be noted that by adding a central void of 1, 1.5, 2 mm, the total void volume only increases by approximately 1.0, 2.0, and 3.5 cm3 when compared to a solid pellet case. The small increase in void volume then corresponds to a small reduction in the plenum pressure.

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23 0.0 mm 1.0 mm 22 1.5 mm 2.0 mm ) 3 21

19 Total Void Volume (cm

17 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 234: Void volume of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

Comparison of interfacial pressure at different central void sizes should reveal other benefits of adding a central void besides fuel temperature reduction. In this case, Figure 235 shows the interfacial pressure for the RBWR-TB2 at central void diameters of 0.0-2.0 mm as a function of time. The results clearly demonstrate that a sizable reduction in interfacial pressure can be achieved by an annular pellet geometry. Furthermore, it can be noted that the interfacial pressure decreases with larger central void diameters. With lower interfacial pressure, cladding deformation as a result of PCMI is expected to be reduced.

348

0.0 mm 35 1.0 mm 1.5 mm 30 2.0 mm

Interfacial Pressure (MPa) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 235: Interfacial pressure of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

Figure 236 shows cladding hoop stress for the RBWR-TB2 at central void diameters of 0.0-2.0 mm as a function of time. It can be seen that with significant reduction in interfacial pressure, the cladding hoop stress essentially follows the behavior of interfacial pressure given that the plenum pressure of all central void cases are quite similar. The results also suggest that the cladding hoop stress can be lower with larger central void diameter. In particular, the lowest cladding hoop stress is seen when a central void diameter is 2.0 mm.

349

160

140 0.0 mm 1.0 mm 120 1.5 mm 2.0 mm 100

20 Cladding Hoop Stress (MPa) 0

-20

-40 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 236: Cladding hoop stress of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

Since the peak in cladding strain typically occurs near fissile-blanket interfaces in the fissile zones, a reduction in fuel temperature from an annular pellet geometry should also be beneficial in terms of cladding strain reduction. This speculation is confirmed by the results shown in Figure 237 as it is observed that cladding hoop strain can be reduced with the addition of a central void. The results indicate that the cladding hoop strain decreases as the central void diameter increases. Similar to cladding hoop stress, the cladding hoop strain is lowest when a central void diameter is 2.0 mm.

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0.9

0.0 mm 0.8 1.0 mm 1.5 mm 0.7 2.0 mm

0.6

0.5

0.4

0.3 Cladding Hoop Strain (%) 0.2

0.1

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 237: Cladding hoops strain of RBWR-TB2 at central void diameter of 0.0-2.0 mm as a function of time.

Annular pellet geometry changes show a promising result in terms of fuel temperature reduction which directly influences further reductions in other important parameters such as PCMI pressure, cladding stress and cladding strain. Although fuel burnup has to be increased by the addition of a central void, the benefits of lower fuel temperature seems to outweigh its negative impact. Therefore, it is recommended to consider using annular fuel pellets for RBWR-TB2. The sizes of central void diameter can be in the range of 1.0-2.0 mm so that the increase in fuel burnup can be limited. It is noted that the concerns regarding circumferential cracking in the inner region of annular fuel, which may cause fuel fragmentation needs to still be addressed in the fuel qualification testing phase.

6.5.6 Cladding thickness

Having thicker cladding means higher mechanical strength and more tolerance to cladding oxidation. However, increasing cladding thickness will either impact the fuel burnup or thermal

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hydraulic conditions of the flow channel because additional volume for increased thickness will

have to be taken from either the fuel or the coolant. In this study, fuel pellet diameter Dfo is kept constant and outer cladding diameter Dco is increased. By this geometry arrangement, there are no net increases in fuel burnup. Thicker cladding will then displace coolant volume; the effect of this perturbation to the coolant channel has been taken into account by an increase in coolant mass flux and reduction in hydraulic diameters. Table 19 summarizes the fuel geometry at different cladding thicknesses that were evaluated. From a reference cladding thickness of 0.6 mm, the effect of thicker cladding on fuel behavior will be examined in this section. Since there is no alteration to fuel volume, a comparison of fuel burnup is not necessary.

Table 19: Comparison of fuel geometry at different cladding thickness.

Fuel pellet Outer cladding Cladding Gap thickness diameter, D diameter D thickness (mm) fo (μm) co (mm) (mm)

0.6 6.19 110 7.61

0.7 6.19 110 7.81

0.8 6.19 110 8.01

0.9 6.19 110 8.21

A comparison of average and centerline temperature of the RBWR-TB2 at cladding thicknesses of 0.6-0.9 mm are shown in Figure 238 and 239, respectively. The effect of thicker cladding can be clearly seen by an increase in average fuel temperature. This is because as cladding thickness increases, additional thermal resistance in the cladding layer is then increased accordingly. The increased resistance causes a higher temperature drop across the cladding and effectively results in fuel temperature increase. Nevertheless, its effect does not feed back to the centerline temperature as it shows small sensitivity to cladding thickness. Both centerline and average temperature tend to converge at high burnup. In this case, the lowest fuel temperature option is seen when cladding thickness is 0.6 mm.

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0.6 mm 0.7 mm 1100 0.8 mm 0.9 mm

1050

1000

950 Average Fuel Temperature (K) 900

850 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 238: Average fuel temperature of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

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2800

0.6 mm 2700 0.7 mm 0.8 mm 2600 0.9 mm

2500

2400

2300

2200

2100

Centerline Fuel Temperature (K) 2000

1900

1800 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 239: Centerline fuel temperature of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

Figures 240 and 241 show fission gas release and plenum pressure for the RBWR-TB2 at cladding thicknesses of 0.6-0.9 mm as a function of time. It can be seen that these two parameters are barely affected by the change in cladding thicknesses. The reason behind this occurrence is possibly because the change in fuel temperature as induced by thicker cladding may not be sufficient to cause significant change in FGR and plenum pressure.

354

0.6 mm 60 0.7 mm 0.8 mm 0.9 mm 50

20 Fission Gas Release (%) Fission

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 240: Fission gas release of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

355

0.6 mm 0.7 mm 7 0.8 mm 0.9 mm

4 Plenum Pressure (MPa) Pressure Plenum

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 241: Plenum pressure of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

With a larger cladding outer diameter, the wetted surface area of a fuel rod is also increased accordingly. This change will proportionally reduce the surface heat flux in the coolant channel. Reduction in surface heat flux has implications to the growth rate of the oxide layer because the empirical correlations for oxide layer thickness have dependency on surface heat flux. Consequently, the hydrogen concentration in the cladding is also affected by the change in oxide layer thickness as these two parameters are directly proportional to each other. Figures 242 and 243 show reductions in oxide layer thickness and hydrogen concentration as a result of cladding thickness increase. Another advantage of having thicker cladding is that it provides more margins for cladding oxidation. As regulatory guidelines recommend a limit of cladding oxide layer not to exceed 17% of original cladding thickness during a LOCA, thicker cladding would allow more oxide layer to be formed. For comparison, with cladding thickness of 0.6 mm, the maximum allowable oxide layer is around 100 µm whereas it can be increased to 150 µm if the cladding thickness is 0.9 mm.

356

100

90 0.6 mm 0.7 mm 80 0.8 mm 0.9 mm 70

Oxide Layer Thickness (microns) 20

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 242: Oxide layer thickness of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

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1400

0.6 mm 1200 0.7 mm 0.8 mm 0.9 mm 1000

800

600

400 Hydrogen Concentration (ppm)

200

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 243: Clad-average hydrogen concentration of RBWR-TB2 at cladding thickness of 0.6- 0.9 mm as a function of time.

Figure 244 shows the interfacial pressure for the RBWR-TB2 at cladding thicknesses of 0.6-0.9 mm as a function of time. Because of similarities in fuel temperature and burnup, the behavior of interfacial pressure is quite comparable for all cladding thicknesses.

358

45 0.6 mm 0.7 mm 40 0.8 mm 0.9 mm 35

15 Interfacial Pressure (MPa) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 244: Interfacial pressure of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

Although driving forces for cladding deformation i.e. internal pressurization and PCMI are relatively similar in all cases compared, a thicker cladding would have more mechanical strength and results in lower cladding stress and strain. The results in Figures 245 and 246 show the cladding hoop stress and strain, respectively, for the RBWR-TB2 at cladding thicknesses of 0.6- 0.9 mm as a function of time. It can be seen that both cladding stress and strain decrease as the cladding gets thicker. In this case, the option with lowest cladding stress and strain is when the cladding thickness is 0.9 mm.

359

200

0.6 mm 0.7 mm 150 0.8 mm 0.9 mm

100

50 Cladding Hoop Stress (MPa) 0

-50 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 245: Cladding hoop stress of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

360

0.8

0.6 mm 0.7 0.7 mm 0.8 mm 0.6 0.9 mm

0.5

0.4

0.3

Cladding Hoop Strain (%) 0.2

0.1

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 246: Cladding hoop strain of RBWR-TB2 at cladding thickness of 0.6-0.9 mm as a function of time.

In conclusion, it would be beneficial in term of cladding integrity to increase cladding thickness to the same level as in ABWR design i.e. 0.7-0.8 mm. In the case of accelerated corrosion at high burnup, thicker cladding would help retaining cladding strength while allowing more zirconium oxide layer to be formed on its surface without exceeding the maximum allowable oxide layer thickness as recommended by regulatory guidelines.

6.6 Code-to-code comparison between FRAPCON-3.5 and FRAPCON-3.5 EP

In this thesis, the original version of FRAPCON-3.5 has been modified to include several physical phenomena which are expected to become relevant at high temperature and high burnup. The modified version is then called FRAPCON-3.5 EP by which the results shown in all previous sections were calculated. However, it is still of interest to examine the sensitivity of fuel behaviors especially life-limiting parameters to those modifications. In this section, a code-to- code comparison between FRAPCON-3.5 and FRAPCON-3.5 EP are presented. The aim is to

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illustrate the effects of several physical phenomena implemented in FRAPCON-3.5 EP that become dominant at high temperature and high burnup and how they affect key performance indicators such as fuel temperature, fission gas release, and cladding stress and strain. These newly added phenomena are usually detrimental to fuel performance. However, there are some instances of counteracting phenomena that can help alleviate such conditions. To demonstrate such effects on fuel performance, the ABWR is selected as a representative of a lower temperature and lower burnup fuel design and the RBWR-TB2 as a representative of high temperature and high burnup one.

6.6.1 RBWR-TB2 design

In this section, the fuel rod geometry, and operating conditions including power history and axial peaking factor are identical to what was described in Section 6.1 to 6.3 for the RBWR-TB2. The first parameter to be examined is the volume-averaged fuel temperature which could reveal many fundamental differences between these two codes. Figure 247 compares the average fuel temperature for the RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP. It may look as though FRAPCON-3.5 EP predicts a lower fuel temperature than FRAPCON-3.5. However, this is essentially because of the biases introduced to model the RBWR-TB2 fuel rod. In FRAPCON- 3.5, the axial variation of fuel enrichment and plutonium content is not possible. They have to be axially uniform throughout the fuel rod due to code’s limitation. Therefore, in this calculation, it

was assumed that all axial nodes are made of (U,Pu)O2 with plutonium content of approximately 80 wt% as specified in the lower fissile zone. This assumption clearly will exaggerate fuel temperature in the blanket zone that are made of UO2 which has higher thermal conductivity than

(U,Pu)O2. In addition to thermal conductivity, there are also other fuel properties that are

supposed to be those of UO2 but had to be taken as (U,Pu)O2 because of code’s limitation.

Although FRAPCON-3.5 may predict higher fuel temperature in the blanket, this may not be the case in the fissile zones because it lacks several physical phenomena that would become relevant at high temperature and high burnup. First of all, fuel constituent migration was not modelled. Therefore, there is no radial migration of oxygen with temperature gradient. Plutonium composition is assumed to be radially uniform throughout the cycles and does not migrate with temperature gradient. The evolution of O/M ratio with burnup was not captured and it is assumed

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that the O/M ratio does not change with burnup. There is no temperature dependence of fuel swelling because cesium migration was not implemented. Since there was no porosity migration model implemented in FRAPCON-3.5, fuel porosity is assumed to be radially uniform and a central void cannot be formed under this assumption. Although formation of a central void may help in reducing fuel temperature, other interrelated phenomena would eventually result in fuel temperature increase. For example, the effect of plutonium redistribution will cause the shift in radial power profile to the center as more fissile material is concentrated in these regions. Likewise, oxygen migration will cause the accumulation of oxygen interstitials and vacancies in the center and this will effectively increase the deviation from stoichiometry (|O/M-2|) and subsequently reduce fuel thermal conductivity in these regions. The evolution of O/M ratio with burnup will also change fuel thermal conductivity throughout the cycles. With the high burnup structure (HBS) model which allows fuel porosity to increase as a function of burnup, the fuel thermal conductivity near the periphery is reduced even further. Since the HBS can only be form when fuel temperature is below 1073 K, its area of effect is expected to be relatively thin (< 300 microns) when compared to entire fuel radius. Except for porosity and central void formation, all of these phenomena are detrimental to fuel thermal conductivity. Therefore, FRAPCON-3.5 EP should predict higher fuel temperatures in fissile zones. The axial plot of radially-averaged fuel temperature would reveal such variation in fuel temperature between the fissile and the blanket zones.

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1150

FRAPCON 3.5 FRAPCON 3.5 EP 1100

1050

1000

950 Average Fuel Temperature (K) 900

850 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 247: Average fuel temperature of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

As shown in Figure 248, the axial variation of radially-averaged fuel temperature for the RBWR- TB2 at EOL as calculated by FRAPCON-3.5 and 3.5 EP has confirmed the speculation given above. It can been seen that FRAPCON-3.5 predicts higher fuel temperature in the blanket zone where it treats this region as (U,Pu)O2. However, the trend is reversed in the upper and lower fissile zones where FRAPCON-3.5 EP predicts higher fuel temperature. Higher temperatures in fissile zones are results of an accumulation of various effects from physical phenomena implemented into FRAPCON-3.5 EP.

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1800

FRAPCON 3.5 FRAPCON 3.5 EP 1600

1400

1200

1000 Average Fuel Temperature (K) Fuel Average 800

600 0 20 40 60 80 100 120 Axial Node Figure 248: Average fuel temperature of RBWR-TB2 at EOL as calculated by FRAPCON-3.5 and 3.5 EP as a function of axial node.

With mechanistic models for porosity migration and central void formation, it was initially believed that FRAPCON-3.5 EP would predict lower centerline fuel temperature than FRAPCON-3.5 because if a central void of around 1.0-1.5 mm was formed, it could lower centerline temperature by 100-200 K depending on LHGR and burnup. However, this may not be the case as it appears that the diameter of the central void formed during densification period (< 10 MWd/kgHM) was relatively small (< 0.1 mm) in the lower fissile zone because fuel temperature in this region at BOL was not high enough to effectively migrate as-fabricated porosity to the center and form a central void whose size has meaningful effect in centerline temperature reduction. This situation turns out to have a considerable impact on the history of centerline temperature as the axial peaking factor tends to shift from the upper fissile zone at BOL to the lower fissile zone at EOL. From a plot of fuel temperature as a function of axial node, it can be noticed that the upper fissile zone of the RBWR-TB2 exhibits a higher temperature at BOL. As burnup proceeds, the fuel temperature in the lower fissile zone will keep increasing and eventually exceed that of the upper fissile zone at EOL.

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Given that porosity migration and central void formation are not an effective mechanism for centerline temperature reduction, it can be inferred that FRAPCON-3.5 EP would predict a higher centerline temperature than FRAPCON-3.5 because it has incorporated several phenomena that are detrimental to centerline fuel temperature namely plutonium migration, oxygen migration and O/M ratio increase with burnup. The centerline fuel temperature of the RBWR-TB2 as a function time as calculated by FRAPCON-3.5 and 3.5 EP are shown in Figure 249. It can be seen that FRAPCON-3.5 EP predicts a significantly higher centerline temperature than FRAPCON-3.5, roughly 200 K throughout the cycles.

3000

FRAPCON 3.5 FRAPCON 3.5 EP

2500

2000 Centerline Fuel Temperature (K)

1500 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 249: Centerline fuel temperature of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

The axial variation of centerline fuel temperature at EOL of the RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP is shown in Figure 250. The trend is markedly similar to the average fuel temperature besides magnitude difference in that FRAPCON-3.5 predicts higher centerline

temperature in the blanket as it mistakenly treats this regions as (U,Pu)O2 fuel. In the upper and

366

lower fissile zones, FRAPCON-3.5 EP predicts higher temperature because of the phenomena discussed above.

2800

2600 FRAPCON 3.5 FRAPCON 3.5 EP 2400

2200

2000

1800

1600

1400

Centerline Fuel (K) Temperature 1200

1000

800 0 20 40 60 80 100 120 Axial Node Figure 250: Centerline fuel temperature of RBWR-TB2 at EOL as calculated by FRAPCON-3.5 and 3.5 EP as a function of axial node.

As fuel temperature is a primary driver for many intercorrelated phenomena in fuel performance, differences in temperature predictions will lead to further divergence in other parameters. Fission gas release (FGR) is one of the most important parameters that are strongly dependent on fuel temperature. The calculated results for fission gas release as a function of time by FRAPCON- 3.5 and 3.5 EP are given in Figure 251. It appears that FRAPCON-3.5 EP predicts a higher percentage of FGR than FRAPCON-3.5 because of higher temperature in the fissile zones. Although, FRAPCON-3.5 may predict a higher fuel temperature in the blanket zone, this region does not significantly contribute to the overall FGR of the fuel rod because the temperature in the blanket is too low for fission gases to effectively accumulate at grain boundaries and release to the plenum.

367

FRAPCON 3.5 60 FRAPCON 3.5 EP

20 Fission Gas Release (%)

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 251: Fission gas release of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

As a result of higher FGR, the plenum pressure in the RBWR-TB2 as calculated by FRAPCON- 3.5 EP is also expected to be higher than what FRAPCON-3.5 predicts. As expected, the results shown in Figure 252 indicate that the plenum pressure as calculated by FRAPCON-3.5 EP appears to be higher than that calculated by FRAPCON-3.5.

368

FRAPCON 3.5 FRAPCON 3.5 EP 7

4 Plenum Pressure (MPa)

2 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 252: Plenum pressure of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

In FRAPCON-3.5 EP, a phenomenon known as accelerated corrosion after a complete dissolution of the SPPs in the cladding has been proposed and implemented. Essentially, the mechanics of this model is to introduce dependency on neutron fluence to the oxide growth rate. In this work, the neutron fluence limit of 1x1026 n/m2 has been proposed as the upper limit before SPPs are completely dissolved into the zirconium matrix. From this point onward, the zirconium alloy is assumed to lose its oxidation resistance and begins to corrode at a higher corrosion rate enhanced by a multiplying factor of 2.2 from its original value. The occurrence of accelerated corrosion in the RBWR-TB2 is illustrated in Figure 253 when FRAPCON-3.5 EP predicts a departure in oxide layer thickness after 500 days of operation where the peak axial node has accumulated sufficient neutron fluence. Since there is no accelerated corrosion phenomenon implemented in FRAPCON-3.5, after the post-transition stage, the oxide layer growth rate would grow at a constant rate resulting in a linear behavior with time.

369

100

90 FRAPCON 3.5 FRAPCON 3.5 EP 80

Oxide Layer Thickness (microns) Oxide 20

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 253: Oxide layer thickness of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Since hydrogen concentration in the cladding is directly proportional to the oxide layer thickness, the growth rate of hydrogen concentration is also accelerated whenever accelerated corrosion takes place. Figure 254 clearly demonstrates a strong correlation between oxide layer thickness and hydrogen concentration. It can be seen that the point of departure in hydrogen concentration is approximately the same as in oxide layer thickness at about 500 days. A degree of increase in oxide layer thickness and hydrogen concentration is about the same as a multiplying factor of 2.2 introduced into the model.

370

1400

FRAPCON 3.5 1200 FRAPCON 3.5 EP

1000

800

600

400 Hydrogen Concentration (ppm) Hydrogen

200

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 254: Hydrogen concentration of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Up to now, only parameters related to thermal behaviors are presented. However, the mechanical behaviors in response to the physical phenomena implemented in FRAPCON-3.5 EP are just as important to the safety of the fuel design. These mechanical parameters include: radial gap thickness, interfacial pressure, and cladding stress and strain. Figure 255 shows the structural radial gap of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time. It can be see that FRAPCON-3.5 EP predicts that the event of gap closure occurs much early than FRAPCON-3.5. This is primarily due to the effects of several models implemented in FRAPCON-3.5 EP. For example, the inclusion of gaseous fuel swelling which is temperature dependent. Therefore, the fuel will swell more at elevated temperature. Even if FRAPCON-3.5 introduced some elements of fuel swelling from gaseous fission products, its effect is limited only at a certain burnup range beyond that the code assumes that the fission gases will be released out of the fuel entirely and causes no further swelling. Such assumption does not exist in FRAPCON-3.5 EP. Because the existing gaseous fuels swelling model in FRAPCON-3.5 has been replaced with a mechanistic one in FRAPCON-3.5 EP which divides contributions from

371

gaseous swelling into intragranular and intergranular fuel swelling. The rate of fission gas transport to grain boundaries is linked to the Forsberg-Massih fission gas release model. In this case, gaseous fuel swelling will increase with fuel temperature and burnup until it reaches limits imposed by the model. In addition to gaseous fuel swelling, cesium migration allows a major portion of the solid fuel swelling to redistribute according to temperature gradient and causes localized fuel swelling spots along axial nodes. Furthermore, since FRAPCON-3.5 EP predicts a higher fuel temperature throughout the cycles, the effect of fuel thermal expansion to gap size must be also taken into account. Since the structural radial gap shown here is a minimum value out of the entire length a fuel rod, the minimum radial gap as predicted by FRAPCON-3.5 EP is expected to be lower than what predicted by FRAPCON-3.5.

0.07 FRAPCON 3.5 FRAPCON 3.5 EP 0.06

0.05

0.04

0.03

0.02 Structural Radial Gap (microns) 0.01

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 255: Structural radial gap of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

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Intuitively, FRAPCON-3.5 EP should predict a considerably higher interfacial pressure than FRAPCON-3.5 given that it has higher fuel swelling rate, and localized swelling at fissile- blanket interfaces plus the occurrence of early gap closure; however, this is not the case as shown in Figure 256. According to the results shown in the figure, FRAPCON-3.5 EP predicted a prolonged period of soft contact (gap closure without PCMI) whereas the interfacial pressure as calculated by FRAPCON-3.5 rises as soon as the period of relocation recovery is complete. The reason for the delay in PCMI is potentially because of the hot pressing model implemented in FRAPCON-3.5 EP. Essentially, the model allows the fuel pellet to be compressed i.e. becomes smaller in diameter upon hard contact with the cladding. The basic mechanism of this process is that it allows fuel density to increase as a function of interfacial pressure and fuel temperature. With increase in fuel density, the fuel diameter has to be reduced from a conservation of mass. The fundamental idea of hot pressing is that at high temperature, the fuel pellet should become soft enough to be compressible. The hot pressing mechanism effectively serves as an inhibitor of PCMI because as the interfacial pressure increases, the fuel diameter decreases thus suppressing the PCMI. However, there is a limit to which the fuel density can be increased. Once such the limit has been reached, the interfacial pressure will begin to rise. This behavior is illustrated in Figure 256 as FRAPCON-3.5 EP predicts that the period of soft contact would last for 500 days after gap closure. After that, the interfacial pressure will keep increasing and, at EOL, FRAPCON-3.5 EP predicts higher interfacial pressure than FRAPCON-3.5. Since the plenum pressures as calculated by these two codes are relatively similar, the marked differences in interfacial pressure will be directly propagating to cladding hoop stress and strain.

373

FRAPCON 3.5 35 FRAPCON 3.5 EP

Interfacial Pressure (MPa) 10

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 256: Interfacial pressure of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Figure 257 shows the cladding hoop stress for the RBWR-TB2 as calculated by FRAPCON-3.5 and FRAPCON-3.5 EP as function of time. It can be noticed that the behavior of the cladding hoop stress follows the trend of the interfacial pressure. A sudden increase in cladding hoop stress corresponds to a rise in interfacial pressure and this situation applies to both FRAPCON- 3.5 and 3.5 EP. Because of high fuel swelling and concentrated swelling near fissile-blanket interfaces, FRAPCON-3.5 EP predicts higher cladding hoop stress for RBWR-TB2.

374

200

FRAPCON 3.5 FRAPCON 3.5 EP 150

100

50 Cladding Hoop Stress (MPa) 0

-50 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 257: Cladding hoop stress of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

A hard limit on fuel swelling is given in the original FRAPCON-3.5 so the fuel cannot expand more than a specified value. This swelling limit is one of the required inputs with a default value of 5%. When converting from volumetric swelling to geometric expansion, it can be translated to a maximum straining of 1.66% in radial, tangential and axial directions. However, this limitation has been removed from FRAPCON-3.5 EP. Cladding hoop strain for the RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP is shown in Figure 258. It can be seen that the cladding hoop strain increases much earlier in FRAPCON-3.5 soon after gap closure and the relocation recovery period is complete. However, the cladding strain seems to reach a plateau from 600- 1,000 days. With a mild increase at 1,100 days, a second plateau is observed until the end of cycle. On the other hand, due to the effect of hot pressing, FRAPCON-3.5 EP predicts a totally different behavior as the cladding hoop strain remains relatively small during the soft contact period. After the onset of interfacial pressure, the cladding hoop strain begins to rise steadily until it reaches the same cladding hoop strain at EOL. If the cycle is extended, it is highly expected that FRAPCON-3.5 EP would end up predicting higher cladding hoop strain because

375 the maximum limit on fuel swelling has been deactivated. Although there may be some differences in the behavior of cladding hoop strain, both the results from FRAPCON-3.5 and 3.5 EP show that this parameter is still under a regulatory limit of 1%.

0.9

0.8 FRAPCON 3.5 FRAPCON 3.5 EP

0.7

0.6

0.5

0.4

0.3 Cladding Hoop Strain (%) 0.2

0.1

0 0 200 400 600 800 1000 1200 1400 Time (Days) Figure 258: Cladding hoop strain of RBWR-TB2 as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

6.6.2 ABWR design

In this section, the fuel rod geometry, and operating conditions including axial peaking factor are identical to those presented in Section 6.1 to 6.3 for the ABWR. However, this comparison uses a new power history with reduced LHGR to reflect a condition of an average fuel rod in the core. In this case, the LHGR is reduced from 28 kW/m to 20.81 kW/m for the first 500 days and then linearly decreased to 10.405 kW/m at 1500 days. This new power history is shown in Figure 259.

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22 FRAPCON-3.5 20 FRAPCON-3.5 EP

10 LHGR (kW/m)

2 0 500 1000 1500 Time (Days) Figure 259: Power history of an average fuel rod in ABWR.

Following the same set of parameters as discussed in the RBWR-TB2 design, the first one to compare is the average fuel temperature. Figure 260 shows the average fuel temperature of the ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time. For the ABWR which was characteristically designed to operate at lower burnup and lower temperature than the RBWR-TB2, it can be seen that FRAPCON-3.5 EP predicts lower fuel temperatures than FRAPCON-3.5 during the 1st-3rd cycles of operation. Even if they tend to converge at EOL in the 4th cycle, a considerable mismatch of these two codes can be easily observed.

Although most of the physical phenomena implemented in FRAPCON-3.5 EP such as porosity, plutonium and cesium migration are expected to remain dormant, some of which including oxygen migration, oxygen potential evolution with burnup and gaseous swelling should remain active. For average fuel temperature, higher fuel swelling plays a major role in this parameter because a larger fuel pellet means smaller gap thickness and higher gap conductance. With early gap closure, the gap conductance is enhanced even further by mechanical contact between two solid surfaces. With higher gap conductance, the temperature drop across the gap is reduced

377

resulting in temperature reduction across the fuel pellet. Such behavior can be observed during until the 3rd cycle.

However, the situation changes in the 4th cycle. With the oxygen potential evolution model, the O/M ratio increases with burnup. Provided that the ABWR fuel is initially stoichiometric (O/M = 2.0); consequently, it will eventually become hyperstoichiometric (O/M > 2.0) at high burnup. Under this assumption, it effectively means that the deviation from stoichiometry will keep increasing and the fuel thermal conductivity calculated by FRAPCON-3.5 EP will be lower than FRAPCON-3.5 at EOL. Its effect is illustrated in Figure 260 as the average fuel temperature predicted by FRAPCO-3.5 EP converges with FRAPCON-3.5’s result in the last cycle and may even exceed FRAPCON-3.5’s prediction if the cycle length was extended to higher burnup.

1000 FRAPCON-3.5 950 FRAPCON-3.5 EP

900

850

800

750

700 Average Fuel Temperature (K) Average

650

600 0 500 1000 1500 Time (Days) Figure 260: Average fuel temperature of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

An examination of centerline fuel temperature can reveal many interesting interdependent phenomena that still remain active in ABWR conditions. From the results presented in Section

378

6.4.8-6.4.12, it is observed that as-fabricated porosity barely migrates under ABWR conditions and it remains radially uniform at its initial value. Therefore, the size of the central void created from this mechanism is negligible (< 0.05 mm). Plutonium migration is not applicable because

the ABWR fuel is only consisted of UO2. The distribution of cesium also remains unaffected by fuel temperature and temperature gradient. Its distribution essentially follows the shape of local burnup. During the first cycle, FRAPCON-3.5 EP predicts a lower centerline fuel temperature which basically follows the trend of the average fuel temperature as shown in Figure 261. After that, the trend is reverse and the centerline fuel temperature calculated by FRAPCON-3.5 EP is higher than FRAPCON-3.5 except for a short period during a transition between 3rd and 4th cycle. This occurrence can be explained by the effect of oxygen migration and O/M ratio evolution with burnup. Since the ABWR fuel begins in an exact stoichiometric state, any further increase in O/M would result in migration of oxygen interstitials toward the center. Therefore, the fuel thermal conductivity at the center will keep decreasing as it accumulates deviation from stoichiometry from oxygen migration mechanism. The sharp drop from centerline fuel temperature in the FRAPCON-3.5 EP result is likely a result of a sudden change in axial peaking factor during cycle transition as the peaking location shifted from the top toward the bottom at EOL.

379

1600 FRAPCON-3.5 1500 FRAPCON-3.5 EP

1400

1300

1200

1100

1000

900

Centerline Fuel Temperature (K) 800

700

600 0 500 1000 1500 Time (Days) Figure 261: Centerline fuel temperature of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Figure 262 shows the fission gas release for the ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time. It can be seen that both codes predict a similar trend in FGR. The absolute value of FGR at EOL remains relatively small at 2.5% which is an expected behavior for low temperature and low burnup fuel design such as with an ABWR. The effect of average fuel temperature clearly shows its impact here for FGR. In this case, it is observed that FRAPCON-3.5 EP predicts lower FGR in the 1st and 2nd cycles because of lower average fuel temperature. At EOL, both codes predict the same average temperature but FRAPCON-3.5 EP predicts a higher value of centerline fuel temperature. As a result, the FGR turns out to be slightly higher for FRAPCON-3.5 EP because of this difference.

380

FRAPCON-3.5 FRAPCON-3.5 EP 2.5

1.5

1 Fission Gas Release (%)

0.5

0 0 500 1000 1500 Time (Days) Figure 262: Fission gas release of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

The value of plenum pressure should essentially follow the trend of FGR. However, this parameter also depends on the total void volume. As shown in Figure 263, the plenum pressure as calculated by FRAPCON-3.5 EP turns out to be noticeably higher than what FRAPCON-3.5 predicts despite a minor difference in FGR. In Figure 264, it can be seen that FRAPCON-3.5 EP also predicts a lower total void volume (18 cm3 in FRAPCON-3.5 EP vs 22 cm3 in FRAPCON- 3.5). With reduced void volume and similar FGR, the plenum pressure has to unavoidably higher. The reason for such behavior is that FRAPCON-3.5 EP predicts a higher fuel swelling rate and this effect translates into a longer fuel axial extension. Upon examining the fuel axial extension in Figure 265, it can be seen that FRAPCON-3.5 EP predicts a much longer fuel length at EOL (45 mm in FRAPCON-3.5 EP vs 25 mm in FRAPCON-3.5). The longer fuel length effectively reduces total void volume and results in higher plenum pressure.

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1.8

FRAPCON-3.5 FRAPCON-3.5 EP 1.6

1.4

1.2

1 Plenum Pressure (MPa) Plenum

0.8

0.6 0 500 1000 1500 Time (Days) Figure 263: Plenum pressure of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

30 FRAPCON-3.5 FRAPCON-3.5 EP 28 ) 3 26

22 Total Void Volume (in Total Void Volume

18 0 500 1000 1500 Time (Days) Figure 264: Total void volume of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

382

FRAPCON-3.5 45 FRAPCON-3.5 EP

20 Fuel Axial Extension (mm) Extension Fuel Axial 15

5 0 500 1000 1500 Time (Days) Figure 265: Fuel axial extension of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Figures 266 and 267 show the oxide layer thickness and hydrogen concentration as calculated by FRAPCON-3.5 and FRAPCON-3.5 EP. Identical predictions of both oxide layer thickness and hydrogen concentration can be observed. Therefore, it can be inferred that the neutron fluence accumulated in the ABWR design is still below a threshold limit for complete dissolution of SPPs that will trigger accelerated corrosion phenomenon. Without the accelerated corrosion, the values of oxide later thickness and clad-average hydrogen concentration should be identical because the original empirical models as implemented in FRAPCON-3.5 were retained in FRAPCON-3.5 EP.

383

FRAPCON-3.5 FRAPCON-3.5 EP 20

Oxide Layer Thickness (microns) 5

0 0 500 1000 1500 Time (Days) Figure 266: Oxide layer thickness of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

FRAPCON-3.5 60 FRAPCON-3.5 EP

40 Hydrogen Concentration (ppm)

30 0 500 1000 1500 Time (Days) Figure 267: Hydrogen concentration of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

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The time evolution of the structural radial gap for the ABWR as calculated by FRAPCON-3.5 and FRAPCON-3.5 EP is shown in Figure 268. The effect of higher fuel swelling is clearly demonstrated in this parameter because FRAPCON-3.5 EP predicts a much earlier gap closure time at roughly 250 days instead of 500 days of operation as predicted by FRAPCON-3.5. The effect of gap closure is then transferred to gap conductance as depicted in Figure 269. It can be seen that gap conductance exponentially increases shortly after the onset of gap closure and a period of relocation recovery period. This behavior continues until the end of cycles and its impact has already been demonstrated in the reduction in average fuel temperature.

90 FRAPCON-3.5 80 FRAPCON-3.5 EP

20 Structural Radial Gap (microns) Structural Radial

0 0 500 1000 1500 Time (Days) Figure 268: Structural radial gap of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

385

104 4 FRAPCON-3.5 3.5 FRAPCON-3.5 EP

3 /K) 2

2.5

1.5

Gap Conductance (W/m Conductance Gap 1

0.5

0 0 500 1000 1500 Time (Days) Figure 269: Gap conductance of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Figure 270 shows the interfacial pressure for the ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time. It can be noticed that even with the hot pressing mechanism activated, FRAPCON-3.5 EP still predicts higher interfacial pressure and early occurrence of PCMI. This is potentially because of the high density fuel in the ABWR. In this calculation, the fuel density is initially set at 95 %TD. Thus, there is small room available for the fuel pellet to be compressed because the fuel density cannot be compressed beyond its theoretical density. Furthermore, under ABWR operating conditions, the fuel temperature remains well below half of its melting point i.e. < 1500 K. In this temperature regime, hot pressing is not an effective mechanism in reducing fuel pellet diameter. With higher fuel swelling and the early occurrence of gap closure, cumulatively it will result in hard contact and a sharp increase in interfacial pressure. From Figures 267 and 269, the period of soft contact (gap closure without PCMI) during relocation recovery and hot pressing is relatively short when compared to simulation results of RBWR- TB2.

386

FRAPCON-3.5 18 FRAPCON-3.5 EP 16

6 Interfacial Pressure (MPa) 4

0 0 500 1000 1500 Time (Days) Figure 270: Interfacial pressure of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Cladding hoop stress, as calculated by FRAPCON-3.5 and 3.5 EP as a function of time, is shown in Figure 271. With higher interfacial pressure and plenum pressure, cladding hoop stress as calculated by FRAPCON-3.5 EP appears to be significantly higher after gap closure. However, both codes produce an identical result in cladding hoop stress prior to such occurrence. With relatively similar predictions in plenum pressure from both codes, the behavior of interfacial pressure is what caused differentiation in this parameter. It can be seen that the shape of cladding hoop stress follows closely with that of interfacial pressure. This behavior seems to be applicable for both FRAPCON-3.5 and 3.5 EP predictions.

387

80 FRAPCON-3.5 FRAPCON-3.5 EP 60

-20 Cladding (MPa) Hoop Stress Cladding

-40

-60 0 500 1000 1500 Time (Days) Figure 271: Cladding hoop stress of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

Figure 272 shows the cladding hoop strain for the ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time. A good agreement between FRAPCON-3.5 and 3.5 EP is observed in cladding hoop strain up to the 2nd cycle even if the departure in interfacial and cladding hoop stress occur much earlier at the end of the 1st cycle. After that FRAPCON-3.5 EP predicts higher cladding hoop strain. At EOL, the cladding hoop strain calculated by FRAPCON-3.5 remains negative while it is slightly positive when computed by FRAPCON-3.5 EP. Regardless of code versions, the cladding hoop strain in ABWR conditions is still far below a regulatory limit of 1% and more or less consistent.

388

0.14 FRAPCON-3.5 0.12 FRAPCON-3.5 EP

0.1

0.08

0.06

0.04

0.02 Cladding Hoop Strain (%) 0

-0.02

-0.04 0 500 1000 1500 Time (Days) Figure 272: Cladding hoop strain of ABWR as calculated by FRAPCON-3.5 and 3.5 EP as a function of time.

389

Chapter 7

Summary, Conclusions and Recommendations

This chapter summarizes all original contributions that have been made as a result of this thesis. The conclusions drawn from fuel performance analyses and sensitivity studies of various fuel rod designs are presented. Opportunities for future research are also proposed.

7.1 Summary

7.1.1 Evaluation of thermal conductivity correlation for mixed oxide fuel

In this work, relevant parameters affecting the thermal conductivity of oxide fuels were reviewed and discussed. In addition, a brief history of thermal conductivity measurements of MOX fuels carried out during the last 3 decades has been reviewed. Several correlations for MOX thermal conductivity developed from original measurements or literature review of published experimental data were also evaluated. Then the default correlation for MOX in FRAPCON-3.5, the Duriez-Modified NFI, was compared with other alternatives from the open literature. In total, there were 7 correlations analyzed in this work: (1) Duriez-modified NFI, (2) Duriez-Lucuta, (3) Inoue-modified NFI, (4) Inoue-Lucuta, (5) Baron, (6) Halden, and (7) Amaya. The results indicated that the Lucuta model tended to be less conservative as it predicted higher thermal conductivities than the modified NFI. It was observed that the effect of non-stoichiometry was more pronounced in the Duriez correlations because they predicted lower values than the Inoue correlation. At 100 MWd/kgHM, the Baron, Halden and Amaya correlations produced comparable values whereas the Duriez-modified NFI predicted higher thermal conductivity at low temperature. The Halden correlation yielded the most conservative value in the phonon conductivity regime when temperature was below 2000 K. In contrast, the Baron and Halden correlations predicted higher thermal conductivities at high temperature. Since the original Amaya correlation did not include non-stoichiometry in its correlation, it gave the highest values. The Baron correlation penalized non-stoichiometry the most while the Duriez-modified NFI and the Halden were situated in the middle of these two extremes. After the inclusion of fuel burnup and non-stoichiometry, the Baron correlation yielded the most conservative values for phonon

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conductivity while the Amaya correlation predicted the highest values because non- stoichiometry was not included.

Finally, all of the correlations were benchmarked against recent experimental data for both irradiated and unirradiated MOX fuels to evaluate their appropriateness for use in RBWR-TB2 conditions. Root mean square (RMS) and standard deviation (SD) of the difference between calculated and measured thermal conductivities were used as statistical indicators in evaluating the predictive capability of the correlations. The results suggested that the Duriez-modified NFI was more accurate than other correlations even after the exclusion of zero burnup data points. This default correlation in FRAPCON-3.5 gave a reasonable prediction at low burnup and conservative values at high burnup. Therefore, it was chosen for use in fuel performance modeling of the RBWR-TB2.

This work also featured the development of multiplying factors for plutonium content in MOX fuels. Given that the fuel composition of MOX for RBWR-TB2 contained approximately 70-80

wt% of PuO2, it was necessary to include the effect of PuO2 content when evaluating thermal conductivity of MOX fuels. Since the Duriez-modified NFI correlation did not include

plutonium content into the correlation, it was proposed that the effect of PuO2 could be represented by multiplying factors. Given many uncertainties and contradictions around the results of molecular dynamic simulation in the literature, it was more preferable to rely on empirical correlations instead of correlations developed from computational results. In this case, the work of Gibby [78] was chosen as a framework for developing the plutonium multiplying factor. These multiplying factors have been successfully implemented into FRAPCON-3.5 EP so that the Duriez-modified NFI correlation could be changed according to plutonium weight fraction.

7.1.2 Development of physical phenomena at high temperature and high burnup

Except for the use of water as coolant and moderator, the operating conditions and design characteristics of the RBWR-TB2 were similar to fast reactors. Therefore, several physical phenomena that are typically experienced in fast reactor conditions were also expected to occur in RBWR-TB2.

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The first phenomenon included in this work was porosity migration and central void formation as a part of fuel restructuring process. Under the influence of high temperature and large temperature gradient, as-fabricated porosity has a tendency to migrate toward the center and form a central void region. In this thesis, a simplified three-region model was replaced with a more mechanistic model based on pore redistribution kinetics which took into account time and spatial dependent behavior of as-fabricated porosity. Pore velocity was expressed as a function of temperature and temperature gradient. Finally, the size of a central void was evaluated from a conservation of mass.

Major fuel constituents such as plutonium, uranium, oxygen and certain fission products also become mobile under fast reactor conditions and redistribute to hotter and colder regions according to their heat of transport values. Among them, plutonium migration was considered one of the most important phenomena because the change in plutonium composition would affect radial power profile, fuel thermal conductivity, melting point, and oxide valence state across the fuel pellet. A solid state diffusion mechanism derived from Fick’s laws of diffusion and thermal diffusion (the Soret effect) was used to model plutonium migration. Forward Euler and finite difference methods were then used to numerically solve the partial differential equations describing this behavior.

Another equally important constituent is oxygen because the stoichiometric state of oxide fuels as expressed by oxygen-to-metal (O/M) ratio strongly affected several material properties especially fuel thermal conductivity. To capture the evolution of O/M ratio with burnup, a simplified approach proposed by Olander [126] has been adopted in this work. For oxygen migration, a solid state diffusion model known as OXIRED was used to describe temperature- dependent redistribution behavior of O/M ratio.

Because of its abundance, mobility and chemical interactions with fuel, cladding, and coolant, cesium was regarded as one of the most important fission products after xenon and krypton. In this work, cesium received particular attention due to its migration behavior and its contribution to fuel swelling. To quantitatively describe cesium migration and its subsequent interactions, this work replaced an empirical model known as the two-stage migration process with a more

392 mechanistic model based on a thermal migration mechanism. The cesium distribution in both axial and radial directions was used to adjust a portion of solid fuel swelling caused by cesium.

The formation of the high-burnup structure (HBS) and its effect on porosity evolution were also considered in this work because they should become relevant for RBWR-TB2 conditions which were designed to reach high local burnup exceeding 100 MWd/kgHM in fissile zones. A simple empirical model proposed by Spino et al. [183] was used to describe the porosity increase as a result of HBS formation. To reflect the ability of HBS in fission gas retention, an additional mechanism that included fuel swelling from HBS porosity but proportionally reduced the effect of gaseous fuel swelling was implemented.

Another physical phenomenon included for the RBWR-TB2, which became dominant at high temperature (above half of fuel melting point), was hot pressing. The model had already been included as part of a MATPRO subroutine but it was not activated in the default version of FRAPCON-3.5.

The gaseous swelling model in the default version of FRAPCON-3.5 was purely empirical and independent of fission gas release mechanism. This work improved the generality of the gaseous swelling by implementing a physics-based model which coupled the process of fission gas release to gaseous fuel swelling. Originally developed by Wood and Mathews [182], intra- granular and inter-granular gas swelling were quantitative described according to the OGRES-I and OGRES-II models, respectively while the default fission gas release model by Forsberg- Massih served as a source term and/or boundary conditions.

To describe the anticipated acceleration in Zircaloy cladding corrosion after complete dissolution of secondary phase particles (SPP) at high burnup, a conventional two-stage oxidation model for zirconium alloys has been modified with a second transition after a neutron fluence threshold was exceeded. Accelerated corrosion at high neutron fluence could be represented by an increase in oxidation rate applied to the linear growth behavior. In this work, this phenomenon was modeled by applying a multiplying factor of 2.2 to the oxide growth rate calculated by a default correlation in FRAPCON-3.5 once the neutron fluence exceeded 1x1026 n/m2 (> 1 MeV). For hydrogen concentration in Zircaloy-2 cladding, the default correlation in FRAPCON-3.5 tended

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to breakdown when high burnup as its exponential term produced unrealistically high value of hydrogen concentration (> 1x106 ppm). This issue had been mitigated by substituting a default correlation with a constant hydrogen pickup fraction of 30% for Zircaloy-2 once the local burnup threshold of 62 MWd/kgHM was exceeded.

Hydrogen migration and hydride precipitation were particularly important for the RBWR-TB2 which operated at higher cladding temperature and, hence, a higher oxidation rate from accelerated corrosion and hydriding phenomena. In this work, hydrogen transport was modeled according to a thermal diffusion mechanism which described the effects of concentration and temperature gradients to the flux of moving species. Hydride precipitation and dissolution kinetics were modeled according to terminal solid solubility for precipitation and dissolution (TSSP and TSSD, respectively). This coupled system of equations treated the concentration of hydrogen in solid solution as a source term for hydride precipitation when hydrogen concentration exceeded TSSP. Likewise, hydride precipitation served as a source term whenever the hydrogen concentration was below TSSD.

7.1.3 Validation of FRAPCON-3.5 EP with experimental data

In order to validate the new physical models, the calculated results from FRAPCON-3.5 EP have been compared with experimental data. A series of experiments conducted in sodium fast reactors have been used to validate the migration behavior of the following species: (1) porosity, (2) plutonium, and (3) cesium. Results from out-of-pile experiments were also used for validation of the cesium and hydrogen migration models. In addition, the experimental results from irradiated samples in LWRs were also used to validate the hydrogen migration and hydride precipitation kinetics.

To reflect the experimental conditions in sodium fast reactors, the cladding properties of HT-9 and SS-304 stainless steel have been added to the code. The properties of coolant including heat transfer coefficient have been changed from water to sodium. The coolant channel geometry has been changed to hexagonal lattice. Finally, the existing cladding corrosion and hydrogen pickup models have been disable to avoid run-time errors.

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Physical models for porosity migration, central void formation, and plutonium migration have been validated with the experimental data from the B11 and B14 experiments conducted in the JOYO MK-III experimental fast reactor in Japan. In general, the calculation results from FRAPCON-3.5 EP were in good agreement with experimental data except for one experiment (Am-1-1-1) where the testing period was very short (10 minutes). This discrepancy identified a limitation of the model for short transient situation.

Migration behavior of cesium was examined by 137Cs gamma scanning of irradiated fuel rods. The effect of cesium accumulation could also be noticed by localized cladding strain near top and bottom of fuel rods. In this thesis, the gamma activity measurement from experimental fast reactors FFTF and JOYO were compared with calculated results from FRAPCON-3.5 EP. In general, the implemented cesium migration model could capture the trend of cesium migration toward lower temperature regions. Accumulation of cesium near the top and bottom of fuel rods has been well predicted by the model in certain fuel rods. However, there were still some instances where the current model seemed to underestimate the magnitude of cesium concentration near the top of fuel rod and overestimated its concentration near the bottom. The source of the discrepancy may have originated from chemical interactions between cesium and its surrounding substances e.g. uranium, oxygen, and molybdenum since they form a stable chemical compound and stop migration. For cladding strain, although the code was able to capture the localized straining toward the top and bottom of fuel rods, it tended to exaggerate the magnitude of cladding strain by a significant margin especially in ACO-3 experiments. For the C3M experiment, as discussed in Section 5.3, the localized cladding straining in the middle of fuel rod could not be predicted by FRAPCON-3.5 EP. The source of this discrepancy may have come from the fact that the cladding material used in this experiment was a special grade of SS- 316 austenitic stainless steel while the code used the properties of SS-304 austenitic stainless steel during the simulation. However, the inaccuracies in cladding strain prediction could still be acceptable because these simulation errors were less relevant to the RBWR-TB2 design because the cladding materials would be based on zirconium alloy.

To further validate the cesium migration model, out-of-pile cesium migration experiments as reported by Peehs et al. [170] and Aitken et al. [231] were used. Conditions of experiments were replicated in a simplified 1-D cesium migration model separately implemented in MATLAB. It

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was found that the existing correlations for the cesium diffusion coefficient from the open literature were too small to initiate movement of cesium. After some adjustments to the cesium diffusion coefficients with a multiplying factor, the model seemed to adequately predict the behavior of cesium migration.

Experimental results from Sawatsky [241] and J. H. Zhang [242] were used for validation of the hydrogen migration and hydride precipitation model. Sawatsky’s experiments involved placing zirconium tubes with uniform hydrogen concentration under constant temperature gradient for an extended period of time whereas Zhang reported a post-irradiation examination of hydrogen concentration in irradiated cladding samples from the Gravelines nuclear power station in France. Sawatsky’s experiments were separately modeled in MATLAB whereas FRAPCON-3.5 EP was used to calculate the hydrogen concentration of cladding samples from the Gravelines nuclear power station. The calculated results from both MATLAB and FRAPCON-3.5 EP matched relatively well with the experimental results.

7.1.4 Fuel performance modeling of RBWR-TB2

After the development and validation of FRAPCON-3.5 EP were complete, the code has been used to simulate the thermo-mechanical performance of RBWR-TB2 fuel rods. A similar calculation was also performed for an ABWR using the same code to highlight major differences in fuel behaviors between these two designs. When compared to the ABWR, RBWR-TB2 featured smaller fuel rod diameter, tight hexagonal lattice, reduced core flow rate, and shorter fuel length. All of these design features were employed to reduce the moderator-to-fuel ratio and maintain negative void reactivity coefficients. The radial power profile of the ABWR was automatically calculated from an existing subroutine in the code whereas that for the RBWR- TB2 was taken from a previous work and was assumed constant throughout the cycles. For fast neutron flux, a Monte Carlo neutronic code, SERPENT, was used to estimate the axial distribution and burnup dependence of fast flux in RBWR-TB2. The calculation results suggested that the default value of specific fast flux was still applicable for analyses of the RBWR-TB2. For power history and axial peaking factor of the RBWR-TB2, they were extracted from a core-wide neutronic calculation using the PARCS code whereas the power history for the

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ABWR was assumed from a common yet conservative power history for LWRs. The axial peaking factor of the ABWR was taken from the open literature.

Results of fuel performance simulation indicated that the average fuel burnup in the RBWR-TB2 was twice as much as that of the ABWR. Local burnup in the RBWR-TB2 was even higher primarily because of the seed-blanket design. In this case, the peak local burnup in the upper and lower fissile zone of the RBWR-TB2 were approximately 120 and 160 MWd/kgHM, respectively.

With higher fuel burnup and higher LHGR, fuel temperatures in the RBWR-TB2 both volume- averaged and at the centerline were unavoidable higher than in the ABWR by significant margins. Although, fuel melting was not reported by the code, the centerline fuel temperature in the lower fissile zone of RBWR-TB2 operated dangerously close to the melting point of mixed oxide fuels. Such small margin to fuel melting even in steady-state fuel performance simulation may require further investigations into fuel behaviors during transient or accident conditions.

A large increase in fuel temperature and burnup directly affected other life-limiting parameters such as fission gas release and plenum pressure. The simulation results showed that the fission gas release and plenum pressure of the RBWR-TB2 at EOL were significantly higher than those of the ABWR.

Originally, the cladding corrosion rate in the RBWR-TB2 was higher than that in the ABWR by design because of higher heat flux from a smaller cladding diameter and higher coolant inlet temperature. The situation was amplified when taking the effect of accelerated corrosion at high neutron fluence into account. Eventually, the oxide layer thickness as well as cladding hydrogen concentration of RBWR-TB2 as predicted by FRAPCON-3.5 EP ended up as multiple times higher than that of ABWR.

As a result of higher plenum pressure and interfacial pressure from PCMI, the cladding stress and strain in the RBWR-TB2 were noticeably higher than those of the ABWR. However, the cladding hoop strain was still under a regulatory limit of 1%.

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Upon examining various physical models representing fuel behaviors at high temperature and high burnup, simulation results clearly demonstrated that these models became active only when the fuel temperature was high enough to overcome its migration barrier. For porosity migration and central void formation, its effect on the RBWR-TB2 might be small yet it was not negligible. However, such occurrence was virtually non-existent in the ABWR. Similarly for plutonium migration, while this phenomenon had a noticeable impact in RBWR-TB2, there was no observable plutonium redistribution in the ABWR. Oxygen-to-metal (O/M) ratio was the only exception to this generalization as it showed its evolution and migration behavior toward lower temperature regions in hypostoichiometric states and toward higher temperature regions in hyperstoichiometric states. This behavior could also be found in both designs. Cesium migration was quite important in the RBWR-TB2 as it showed localized high concentration spots near fuel- blanket interfaces whereas this phenomenon hardly occurred in the ABWR as the cesium axial distribution of ABWR closely followed the shape of local burnup profile. For hydrogen migration and hydride precipitation, the results suggested that hydride concentration near fuel- blanket interfaces could reach a maximum thermodynamic limit of 1.82 wt% in the hydride rim regions. Although it might not pose a great concern given that the cladding of RBWR-TB2 was designed for reprocessing and refabrication not for long term storage. Similar behavior of hydrogen migration was also observed in the ABWR; however, the magnitude of hydride accumulation at cold spots was significantly smaller. This was because cladding oxidation as a source of hydrogen in ABWR occurred much slower than in RBWR-TB2.

To assist in furthering the design optimization process, a sensitivity study on key design parameters of the RBWR-TB2 has been performed. The following parameters have been examined: (1) gap thickness, (2) fuel density, (3) oxygen-to-metal (O/M) ratio, (4) helium pressure, (6) central void diameter, and (7) cladding thickness. Table 20 summarizes the effects of these parameters to fuel performance and recommended changes for future design revision of RBWR-TB2.

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Table 20: A summary of key design parameters, their effects on fuel performance, and recommended values for further revisions. Design parameters Recommended values Affected fuel performance parameters Gap thickness Use current value at 110 μm Fuel temperature, interfacial pressure, cladding hoop stress and strain Fuel density Decrease to 85-90 % TD Fuel burnup, interfacial pressure, cladding hoop stress and strain O/M ratio Decrease to 1.95-1.98 Fuel thermal conductivity, fuel temperature, FGR Helium pressure Use current value at 1 MPa Plenum pressure, cladding stress and strain Central void diameter Increase to 1.0-2.0 mm Fuel burnup, fuel centerline temperature, plenum pressure Cladding thickness Increase to 0.7-0.8 mm Oxide layer thickness, cladding stress and strain Plutonium content Decrease to less than 30 wt% Fuel thermal conductivity, fuel melting point Cladding protection Use sponge zirconium liner or PCMI, FCCI, interfacial against PCMI other soft materials to protect pressure, cladding hoop cladding’s inner surface stress and strain

7.2 Conclusions

In an effort to demonstrate that the RBWR-TB2—an advanced LWR for plutonium and transuranic waste incineration— can operate safely within design constraints and regulatory limits, thermo-mechanical behaviors of this reactor have been analyzed through fuel performance modeling.

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Assessment of various correlations for MOX thermal conductivity has been performed. The results suggest that the Duriez-modified NFI—a default correlation in FRAPCON-3.5—is more accurate than other correlations and it was chosen for use in fuel performance modeling of the

RBWR-TB2. The effect of PuO2 content has been taken into account through multiplying factors derived from experiments.

Due to its unique design characteristics, several physical phenomena at high temperature and high burnup typically ignored in most LWR fuel performance codes potentially become active under its operating conditions. These phenomena involve migration of fuel constituents and fission products, evolution of O/M ratio with burnup, HBS formation, accelerated corrosion, hot pressing, gaseous fuel swelling, hydride precipitation and hydrogen migration in cladding. Semi- empirical models describing porosity and cesium migration behaviors have been replaced with mechanistic models. All of these phenomena have been successfully implemented in a modified version of FRAPCON-3.5 known as FRAPCON-3.5 EP.

A fuel performance comparison between the RBWR-TB2 and the ABWR fuel rods has been performed. The results suggest that because of high axial peaking factors and relatively flat power history, fuel temperature is significantly higher in fissile zones of the RBWR-TB2 leading to various undesirable effects such excessive fission gas release and cladding deformation. Local burnup in fissile zones of the RBWR-TB2 are multiple times higher than in the ABWR leading to excessive fuel swelling, accelerated cladding oxidation, and PCMI at fissile-blanket interfaces.

Given that the fuel composition of RBWR-TB2 contains around 70-80 wt% of PuO2, the effect

of PuO2 content on a reduction of melting temperature should be rigorously investigated. Although there was no fuel melting calculated by the code, it should be aware that the calculated fuel centerline temperature was dangerously close to its melting temperature. Even if the RBWR- TB2 has to operate under such demanding conditions with small margin to fuel melting, a steady-state fuel performance analysis still shows that this reactor can operate safety with an acceptable thermo-mechanical performance.

However, there is still an opportunity for performance improvement in terms of fuel temperature reduction and better resistance to cladding corrosion and PCMI. In further optimization of the RBWR-TB2 design, several design strategies from sodium fast reactor designs can be leveraged.

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Some of these design recommendations have been discussed in Section 6.5. A summary of design recommendations for future revision of RBWR-TB2 is given in Table 21.

Table 21: A comparison of fuel design characteristics of current and future RBWR-TB2. Design parameters Current RBWR-TB2 Future RBWR-TB2 Plutonium content (wt%) 70-80 < 30 Fuel density (%TD) 90 85-90 O/M Ratio 1.98 1.95-1.98 Central void diameter (mm) 0.0 1.0-2.0 Cladding thickness (mm) 0.6 0.7-0.8 Cladding protection against None Sponge zirconium liner PCMI or other soft materials

7.3 Recommendations for Future Work

7.3.1 Full-core fuel performance analysis for RBWR-TB2

To avoid the assumptions of peak rod condition, coupling of the neutronic and fuel performance analyses should be performed in order to eliminate unrealistic assumptions about power distribution and history for a fuel rod by individually analyzing the LHGR profile and axial peaking factor of each fuel rod and directly inserting these into a fuel performance code. The core map of parameters of interest such as plenum pressure, average fuel temperature, and fission gas release could provide deeper insights to the thermal and mechanical performance of the core without making overly conservative or aggressive assumptions when developing LHGR profiles for fuel performance simulation. However, this task is computationally intensive and cannot be done easily, as we have roughly 288,000 fuel rods in a RBWR-TB2 core. Due to a limited manpower resource, manually preparing input files and running them 288,000 times is very difficult, if not impossible, to accomplish. To perform this task, a special code is required to automate the process of taking output files from neutronic codes, writing input files for fuel modeling codes and displaying the results. The capability of performing full-core fuel performance analysis has been demonstrated in the work of Mieloszyk [54] where full-core neutron codes i.e. CASMO and SIMULATE were used to calculate the axial power distribution and power history of every fuel rod of a PWR core. Then, a script written in Python was used to

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extract the necessary information from these two codes and reformatted it into input files for RedTail — a fuel performance code for LWRs developed at MIT — to analyze the thermo- mechanical behaviors of each individual rod during irradiation. However, due to a limited computing resource, this work assumed that the reactor core was rotationally symmetric and a half of a quadrant (1/8th core symmetry) could represent the neutronic behaviors of the entire core. Figure 273 shows an example of a reactor core map of maximum plenum pressure as calculated by CASMO, SIMULATE and RedTail. Because of its rotational symmetry, only a south-east corner of a PWR core is shown. Furthermore, the sensitivity analyses on key design parameters assumed that the neutronic and thermal hydraulic behaviors of the RBWR-TB2 were not significantly affected by these changes. This assumption needs to be verified through neutronic and thermal hydraulic calculations to make sure that they will not generate any unacceptable results. To optimize fuel design parameters, a multiple loop of calculations in term of reactor physics, thermal hydraulics and fuel performance are usually required.

Figure 273: Sample core map of RedTail predictions for maximum plenum pressure for (a) Zirconium-based cladding and (b) SiC-based cladding [54].

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7.3.2 Fuel performance modeling of RBWR-TB2 in transient conditions

So far, the thermo-mechanical behavior of the RBWR-TB2 in steady-state condition has been analyzed in detail. However, there is still one key missing piece of information which remains largely unexplored: fuel performance modeling during transient and accident conditions. Although it is beyond the scope of this thesis, the entire reactor design could be invalidated if it was found out that the fuel would melt or the cladding would be destroyed from excessive PCMI or oxidation during design basis accidents such as loss of coolant, loss of flow, or rapid reactivity insertion. From steady-state fuel performance modeling, the results showed that even though RBWR-TB2 fuel rods can operate safely within design constraints, its margin to fuel melting is very small at the center. Therefore, to avoid further complications if RBWR-TB2 were to proceed to detailed engineering phase, transient fuel performance should be performed so that any critical issues in its performance could be identified and properly mitigated.

7.3.3 Out-of-pile experiments for fuel constituent migration under temperature gradient

Out-of-pile experiments have some unique advantages over in-pile experiments because many critical parameters can be controlled and isolated. An experimental apparatus can be optimally designed to fit within constrains on budget and resource. The cost of doing out-of-pile experiments is expected to be significantly lower with less difficulties and radiological hazard risks.

According to the thermal migration mechanism, diffusion coefficients and heat of transport are some of the most critical parameters dictating how each species would behave under the influence of temperature gradients. The diffusion coefficients determine the speed of species migration at a given temperature while the heat of transport represents the activation energy required to overcome thermal migration barrier. In this work, several correlations for diffusion coefficients and heat of transport were adopted from literature conducted during 1970s and 1980s. Even if some correlations were extracted from a more recent fuel performance code, they are still based on correlations developed during those periods.

In order to confirm and validate previous experimental results, out-of-pile experiments for fuel constituent migration under temperature gradients should be performed. In this case, similar

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arrangements as carried out in Peehs’s [170] and Aitken’s [231] experiments can be used as a design reference. In this case, the migration species can be any elements of interests such as plutonium, oxygen, cesium, or even porosity. The final outcome of this study is to propose correlations for diffusion coefficient and heat of transport from in-house experiments. The experimental results can be used to predict the distribution of these species as a function of time in a simplified 1D thermal migration model. For porosity, a correlation for pore velocity can be developed if time-dependent behavior of porosity distribution under temperature gradient is known.

Especially for cesium, it would make a significant contribution to knowledge gap if these experiments can verify the dependency between cesium transport and oxygen potential i.e. oxygen-to-metal ratio. As reported by Aitken et al. [231]and Adamson et al. [173], the oxygen- to-metal ratio seemed to have a profound impact on the migration behavior of cesium. So far, the diffusion coefficient for cesium is formulated only as a function of temperature and heat of transport of cesium as a constant value. Thus, the effect of oxygen potential and O/M ratio on the migration behavior of cesium should be investigated. Once a dependency between cesium migration and oxygen-to-metal ratio is confirmed through experiments, the existing correlations for diffusion coefficient and heat of transport of cesium should be revised with the O/M ratio as a dependent variable.

7.3.4 Experimental evaluation of MOX thermal conductivity at high burnup

Even if MOX fuel represents a significant portion of nuclear fuels in commercial reactors, the experimental evaluation of its thermal conductivity at high burnup is considered lacking in both the number of data points and achievable burnup. In this study, a literature survey for thermal conductivity of MOX has been conducted and it showed that the achievable burnup for MOX samples was relatively low, reportedly 44 MWd/kgHM, whereas it could reach as high as 120

MWd/kgHM in UO2 samples. Besides, the plutonium content studied in those experiments are relatively small (< 10 wt%). Therefore, the evolution of thermal conductivity of MOX when plutonium weight fraction is greater than 50 wt% and burnup greater than 100 MWd/kgHM remains experimentally unexplored. To take into account the effect of burnup on thermal conductivity degradation of high burnup MOX, what is currently available now is an

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extrapolation of empirical correlations developed based on data from high burnup UO2 samples. Given that MOX fuel is specifically designed for use in a closed-loop fuel cycle which inherently requires high burnup operation, a direct knowledge of MOX thermal conductivity at high burnup and higher plutonium content would be especially important for both licensing and design optimization of advanced reactors such as the RBWR or SFR. Thus, it is recommended that out- of-pile thermal diffusivity measurements as conducted by Cuzzo et al. [99] or Staicu et al. [100] should performed on MOX samples irradiated to high burnup exceeding 100 MWd/kgHM. The plutonium content in MOX fuel should be greater than 50 wt% to differentiate from past experiments. In-pile centerline temperature measurement of MOX samples in an instrumented fuel rod could also provide valuable information. High burnup can be achieved by the use of spent fuel from commercial reactors, refabrication and multiple irradiations in a research reactor. Because of the integral nature of in-pile measurement and uncertainties in gap conductance evaluation, direct thermal diffusivity measurements of irradiated samples are more preferred. However, obtaining such samples requires a dedicated irradiation campaign in a research reactor, which is admittedly difficult and expensive. Therefore, another possibility to measure thermal conductivities at high burnup is to fabricate artificial fuel replicating the fuel composition at high burnup. Known as SIMFUEL, this method has been done for UO2 samples; therefore, it should also be applicable for MOX [102] [108] [115] [116].

7.3.5 In-pile experiment for accelerated corrosion at high neutron fluence

Based on a limited number of experimental studies on cladding corrosion at high burnup, a second transition in cladding corrosion rate was observed after an accumulation of sufficient irradiation damage from fast neutron fluence. A simplified approach was adopted to address the effect of fast neutron fluence on cladding corrosion rate. It was proposed that after the complete dissolution of SPPs beyond a fast neutron fluence limit of 1x1026 n/m2, oxide growth rate would accelerate by a factor 2.2. However, no effort has been addressed to mechanistically model the precipitation and dissolution of SPPs in Zircaloy cladding. Although many explanations have been hypothesized, currently, the relationships between corrosion resistance and the presence of SPPs are still unclear. With a limited understanding of the mechanism why the presence of SPPs improves corrosion resistance in Zircaloy and the lack of data describing the behavior of SPPs during irradiation, it is currently not possible to develop physical models describing the effect of

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fast neutron to the dissolution process of SPPs. Therefore, it would considerably helpful if an irradiation campaign in a research reactor can be conducted with the aim to specifically investigate the behavior of SPPs under irradiation and how they affect the corrosion performance of Zircaloy cladding. The desired measurements would include: a complete pre- and post- irradiation characterization of particle sizes of SPPs, the concentration of alloying component in the bulk materials, and the oxide layer thickness and hydrogen concentration in the cladding at each measurement point. These types of experiments could be used to confirm and estimate the impact of neutron fluence on corrosion rate and hydrogen pickup fraction. In addition, they can be used to confirm the validity of the current neutron fluence threshold for accelerated corrosion and to evaluate the magnitude of impact in corrosion rate. The ultimate goal is to develop a semi- empirical correlation or a mechanistic model for corrosion rate of Zircaloy by taking neutron fluence and/or neutron flux as dependent variables.

7.3.6 Theoretical and experimental study of O/M ratio evolution with burnup

Not only do nuclear fission reactions split uranium and/or plutonium atoms into two smaller fission products, they also annihilate molecular structures of fuel form e.g. oxide, carbine, nitride, or metallic alloy by breaking chemical bonding between fuel constituents. In the case of oxide fuels, two oxygen atoms are constantly released as a result of one fission event. Under the assumption of mass conservation, the oxygen potential and O/M ratio should progressively increase with burnup. However, some complications exist because these free oxygen atoms can recombine with certain fission products such as cesium, molybdenum, tellurium, or zirconium and form stable oxides. They can essentially serve as oxygen buffer and thereby stabilize the oxygen potential and O/M ratio at stoichiometry. It has been reported that even at high burnup (up to 100 MWd/kgHM) the O/M ratio was still at stoichiometry because of this oxygen buffering effect [138]. In this work, the buffering mechanism of molybdenum has been included by using thermodynamic equilibrium and conservation of charge so that the fraction of molybdenum that gets oxidized and acts as oxygen buffer can be evaluated. However, the migration and chemical interactions of molybdenum and other fission products are not explicitly treated as they are beyond the scope of this study. If the oxygen and other fission products are allowed to migrate outside of the fuel and form complex compounds in the gap, it could significantly compromise the assessment of the oxygen potential and O/M ratio under mass

406 conservation assumption. This knowledge gap requires both experimental and theoretical work to assess the behavior of oxygen and other key oxygen buffering elements. First, neutronic calculation is required to evaluate the inventory of these fission products and then computational thermodynamics is needed to study its chemical states and its chemical interactions with other fuel constituents at high burnup. Finally, thermal diffusion mechanism or atomistic simulation can be used to study the migration behavior of these elements so that the validity of mass conservation assumption can be verified. The other direct yet costly method is to perform in-pile experiments of nuclear fuels and perform oxygen potential measurement of irradiated samples at various stages of burnup. This way, the evolution of O/M ratio with burnup can be verified. Furthermore, the buffering effect of fission products can be confirmed and quantified. The key questions to be addressed are: (1) To what extent these fission products can recombine with the released oxygen?, (2) Does the buffering effect of fission products occurs indefinitely or does it have a burnup limit?, (3) Do operating conditions such as fuel temperature, neutron fluxes and spectrum, has influences on buffering behavior of these fission products?

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Appendix A: Material properties of HT-9 and SS-304 Stainless Steel

The purpose of this section is to summarize the key material properties of HT-9 and SS-304 stainless steel cladding relevant to fuel performance modeling which include: (1) density, (2) melting point, (3) heat of fusion (4) Poisson’s ratio, (5) specific heat (6) thermal conductivity, (7) thermal expansion, (8) irradiation swelling, (9) Meyer hardness, (10) emissivity, (11) elastic modulus and shear modulus, (12) creep, (13) oxidation and hydrogen pickup, (14) oxide layer thermal conductivity and (15) yield and ultimate tensile strength. Two major sources of material properties in this work are: (1) FEMAXI-6 for SS-304 [A1] and FEAST-METAL [A2] for HT-9. Similar to FRAPCON-3.5, FEMAXI-6 is an LWR fuel performance computer code developed by Japan Atomic Energy Agency (JAEA) for use in regulatory applications in Japan. FEAST- METAL is a fuel performance code for sodium-cooled fast reaction applications with extensive material properties database on ferrictic/martensitic steels.

General properties

Density, melting point, and heat of fusion of stainless steel are treated as constant in this study. For SS-304, these properties are based on stainless steel data sheet from AK Steel [A3]. For HT- 9, its properties came from MatWeb online material property database [A4]. Material properties for Zircaloy-2 are extracted directly from FRAPCON-3.5 source code [A5]. Stainless steel is 20- 22% heavier than zircaloy; additional structural loads must be taken into account when designing fuel assemblies made of stainless steel tubes. Melting point of stainless steel is considerably less than that of Zircaloy-2. This might imply that stainless steel might have lower operating margin of safety than zirconium alloys. However, cladding melting point is not a constraint in LWR applications; instead, oxidation reaction and hydrogen embrittlement are the true limiting factor. For zirconium-based alloys, the temperature limit is set well below its melting point at around 1,473 K. Values of these properties are given in Table A.1.

Table A.1: Density, melting point and heat of fusion of Zircaloy, SS-304, and HT-9.

Properties Zircaloy-2 SS-304 HT-9 Density (kg/m3) 6,550 8,030 7,810 Melting point (K) 2,098 1,673 1,743

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Heat of fusion (J/kg) 22.5x104 26x104 26x104

Poisson’s ratio

The correlations for Poisson’s ratio of Zircaloy-2 and SS-304 are adopted from [A1] as given by Equations (A.1) and (A.2). Correlation of HT-9 is extracted from [A2] as shown in Equation (A.3). The plots of Poisson’s ratio as a function of temperature at the range of normal cladding temperature (300-700 K) are given in Figure A.1.

( − 2) = 0.333 + 8.375 ∗ 10 ∗ ( − 273.15) (. 1)

( − 304) = 0.265 + 7.875 ∗ 10 ∗ ( − 273.15) (. 2)

2.137 ∗ 10 − 102.74 ∗ ( − 273.15) ( − 9) = − 1 (. 3) 2 ∗ (8.964 ∗ 10 − 53.78 ∗ ( − 273.15))

where

ν = Poisson’s Ratio (unitless)

T = Temperature (K)

0.45 0.4 0.35 0.3 0.25 Zircaloy-2 0.2 SS-304 0.15 Poisson Ratio HT-9 0.1 0.05 0 300 400 500 600 700 Temperature (K)

Figure A.1: Poisson’s ratio as a function of temperature Zircaloy-2, SS-304 and HT-9.

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Specific heat

For Zircaloy-2, the specific heat information is stored in FRAPCON-3.5 as data points of specific heat and temperature. Linear interpolation method will be used to calculate the specific heat at given temperature. The correlations for SS-304 and HT-9 are adopted from [A1] and [A2] as shown in Equations (A.4) through (A.7), respectively. The plots of specific heat as a function of temperature are given in Figure A.2.

( − 304) = 326 + 0.298 ∗ − 9.5 ∗ 10 ∗ 300 ≤ ≤ 1558 (. 4)

( − 304) = 558.228 ≥ 1558 (. 5)

1 ( − 9) = ( + 273.15 − 227) + 500 < 800 (. 6) 6

3 ( − 9) = ( + 273.15 − 227) + 550 > 800 (. 7) 5

where

Cp = Specific Heat (J/kg/K)

T = Temperature (K)

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1200

1000

800

600 Zircaloy-2 SS-304 400 HT-9 Specific Heat (J/kg/K) Specific Heat

200

0 0 500 1000 1500 2000 Temperature (K)

Figure A.2: Specific heat as a function of temperature Zircaloy-2, SS-304 and HT-9.

Thermal conductivity

The thermal conductivity of the cladding plays an important role in determining the temperature profile of the fuel rod which dictates the fuel swelling, fission gas release and plenum pressure buildup. Thermal conductivity of Zircaloy-2 is based on a model embedded in the source code [A5] as shown in Equation (A.8). For SS-304 and HT-9, the equations for thermal conductivity are adopted from [A1] and [A2] and given by Equations (A.9) through (A.11), respectively. Note that for metals such as zirconium and steels, radiation will not degrade the thermal conductivity of the materials. Therefore, the correlations for thermal conductivity of these materials are expressed a function of temperature only. At the range of cladding temperature (600-700 K), thermal conductivity of stainless steel is higher than Zircaloy-2. Typically, ferritic/martensitic steels (HT-9) have higher thermal conductivity than austenitic steels (SS-304) because of lower content of nickel and chromium. The plots of thermal conductivity as a function of temperature are given in Figure 3.

( − 2) = 7.51 + 2.09 ∗ 10 ∗−1.45∗10 ∗ + 7.67 ∗ 10 ∗ (. 8)

435

( − 304) = 10.65 + 1.326 ∗ 10 ∗ (. 9)

( − 9) = 17.622 + 2.42 ∗ 10 ∗−1.696∗10 ∗ < 1030 (. 10)

( − 9) = 12.027 + 1.218 ∗ 10 ∗ > 1030 (. 11)

where

k = thermal conductivity (W/m/K)

T = temperature (K)

45 40 35 30 25 Zircaloy-2 20 SS-304 15 HT-9 10 5

Thermal Conductivity (W/m/K) Thermal Conductivity 0 0 500 1000 1500 2000 Temperature (K)

Figure A.3: Thermal conductivity as a function of temperature Zircaloy-2, SS-304 and HT-9.

Thermal expansion

Thermal expansion of the cladding dictates the behavior of fuel-cladding gap during the beginning of life because the effect of irradiation swelling is not significant at this stage. Fuel- cladding gap width affects the heat transfer from the fuel to the cladding and overall temperature

436

profile of the fuel rod. Thermal expansion of Zircaloy-2 is based on equations already embedded in the source code [A5] as shown in Equations (A.12) through (A.17). The equations for thermal expansion of SS-304 and HT-9 are adopted from [A1] and [A2] as shown in Equations (A.18) through (A.19). It can be seen that stainless steel expand similar in both circumferential and axial directions. Generally, stainless steel has 3-4 times higher thermal expansion than Zircaloy-2. The plots of thermal expansion as a function of temperature are given in Figure A.4.

∆⁄ ( − 2) =4.95∗10 ∗−1.485∗10

300 < < 1030 (. 12)

− 1083 ∆⁄ ( − 2) = 2.77763 + 1.09822 ∗ cos ∗∗10 161

1083 ≤ ≤ 1244 (. 13)

∆⁄ ( − 2) =9.7∗10 ∗−1.04∗10

1244 ≤ ≤ 2098 (. 14)

∆⁄ ( − 2) =1.26∗10 ∗−3.78∗10

300 < < 1030 (. 15)

− 1083 ∆⁄ ( − 2) = 2.77763 + 1.09822 ∗ cos ∗∗10 161

1083 ≤ ≤ 1244 (. 16)

∆⁄ ( − 2) =9.76×10 ∗−4.4×10

1244 ≤ ≤ 2098 (. 17)

∆⁄ ( − 304) = 1.629 × 10 + 3.285 × 10 ∗

−2.198 × 10 ∗ + 1.629 × 10 ∗ (. 18)

437

∆⁄ ( − 9) = −0.2191 × 10 + 5.678 × 10 ∗

+8.111 × 10 ∗ − 2.576 × 10 ∗ (. 19)

where

ΔL/L0 = linear strain caused by thermal expansion (unitless)

T = temperature (K)

5 SS-304 4 HT-9 3 Circumferential Thermal Expansion Zircaloy-2 2

Thermal Strain (%) Thermal Strain Axial Thermal Expansion Zircaloy-2 1

0 0 500 1000 1500 2000 2500 Temperature (K)

Figure A.4: Thermal expansion as a function of temperature Zircaloy-2, SS-304 and HT-9.

Irradiation swelling

Interactions with radiation induce structural damage and void formation which leads to swelling. In general, cladding swelling occurs simultaneously with fuel swelling and thermal expansion effects in both the fuel and the cladding. But the characteristics of thermal expansion and irradiation swelling are different: thermal expansion is a reversible process whereas the irradiation swelling is not. Furthermore, time scale for irradiation swelling to become significant is longer than thermal expansion. Anyway, all of these effects are important in the evolution of

438

fuel-cladding gap width. At the level of neutron fluence in LWR, generally around 10-20 DPA at EOL, irradiation swelling as well as irradiation growth of stainless steel is pretty low, typically less than 1%. Figures A.5 and A.6 show a void swelling as a function of neutron fluence as well as their associated curve fitting models as given in Equations A.20 and A.21. The models were developed based on information presented in Chapter 2.09 of Comprehensive Nuclear Materials [A6]. Assuming that this stainless steel will expand equally in the plane and through the thickness of the materials, the irradiation growth in axial direction can be determined by dividing the void swelling by 3. The model for irradiation growth of Zircaloy-2 is also given in Equation A.22. A comparison of irradiation growth rate between Zircaloy-2, SS-304 and HT-9 is given in Figure A.7. As can been seen from the figure, irradiation growth of stainless steel at this level of fluence is much lower than that of Zircloy-2. HT-9 void swelling is lower than SS-4 because of lower content of nickel.

( − 304) =2.5∗10 ∗ + 1.984 ∗ + 1.342 ∗ 10 ∗

+3.272 ∗ 10 (. 20)

( − 9) = 0.00588 ∗ + 0.11431 (. 21)

( − 2) =2.18∗10 ∗Φ. (. 22)

where

Sw = swelling rate (%)

Ax = axial growth increment (m/m)

DPA = neutron fluence (displacement per atom (DPA) = 1x1025 n/m2)

T = temperature (K)

Φ = fast neutron fluence (n/cm2) (E > 1.0 MeV)

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18 y = 3E-05x3 + 0.0002x2 + 0.0134x + 0.3273 16 R² = 0.9946

8 SS-304 Poly. (SS-304) 6 Void Swelling (%) 4

0 0 20406080100 Fluence (DPA)

Figure A.5: Void swelling as a function of neutron fluence for SS-304.

1.6 y = 0.00588x + 0.11431 R² = 0.99812 1.4

1.2

0.8 HT-9 0.6 Linear (HT-9) Void Swelling (%) 0.4

0.2

0 0 50 100 150 200 250 Fluence (DPA)

Figure A.6: Void swelling as a function of neutron fluence for HT-9.

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0.9

0.8

0.7

0.6

0.5 Zircaloy-2 0.4 SS-304 0.3 HT-9 Axial Growth (%) 0.2

0.1

0 0 5 10 15 20 25 Fluence (DPA)

Figure A.7: Irradiation growth as a function of neutron fluence for Zircaloy-2, SS-304 and HT-9.

Meyer hardness

Cladding hardness is one of the parameters required for calculating fuel-to-cladding contact conductance and the interfacial pressure when hard contact occurs. Hardness of Zircaloy-2 is extracted directly from FRAPCON-3.5 source code [A5] as shown in Equation (A.23). For SS- 304 and HT-9, cladding hardness as a function of cladding temperature are adopted from [A7] and [A4] as given in Equations (A.24) and (A.25), respectively. The plots of cladding hardness as a function of temperature are given in Figure A.8.

( − 2) =2.6034 ∗ 10 +

∗ −2.6394 ∗ 10 + ∗ 4.3502 ∗ 10 + ∗ (2.5621 ∗ 10) (. 23)

( − 304) = 0.003448 ∗ 1571 ∗ 290 − 0.245 ∗ ( − 273.15 − 25) (. 24)

( − 9) = 0.003448 ∗ (9.807 ∗ 2705.79 ∗ 290 − 0.245 ∗ ( − 273.15 − 25) (. 25)

where

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MH = Meyer hardness (N/m2)

T = temperature (K)

3000

2500

2000

1500 Zircaloy-2 SS-304 1000 HT-9 Mayer Hardness (MPa)

500

0 0 500 1000 1500 2000 Temperature (K)

Figure A.8: Cladding hardness as a function of temperature for Zircaloy-2, SS-304 and HT-9.

Emissivity

Emissivity is a measure of fraction of thermal radiation emitted by the surface relative to a blackbody. The equations for emissivity are given by Equations (26) through (28). The correlations for Zircaloy-2 are from [A5] while SS-304 and HT-9 are from [A8] as shown in Equations (A.26) through (A.28). The plots of emissivity as a function of temperature of Zircaloy-2, SS-304 and HT-9 are given in Figure A.9.

( − 2) = 0.325 + 0.1246 ∗ 10 ∗ (26)

( − 304) = 2.21238 ∗ 10 ∗ − 2.29828 ∗ 10 ∗ + 1.3513 ∗ 10 (27)

( − 9) = 4.39926 ∗ 10 ∗ + 2.65402 ∗ 10 (28)

442

where

Ε = emissivity (unitless)

T = temperature (K)

d = oxide layer thickness (m)

0.9

0.8

0.7 y = 0.0004x + 0.2654 R² = 0.8989 0.6

0.5 Zircaloy-2 2 y = 2E-07x - 0.0002x + 0.1351 SS-304 R² = 0.9991 0.4 HT-9 Emissivity Poly. (SS-304) 0.3 Linear (HT-9) 0.2

0.1

0 0 500 1000 1500 2000 Temperature (K)

Figure A.9: Emissivity as a function of temperature for Zircaloy-2, SS-304 and HT-9.

Elastic and shear modulus

The expressions for elastic and shear modulus for Zircaloy-2 are a function of various parameters: cladding temperature, oxidation, cold work, fast neutron fluence as shown in Equations (A.29) and (A.30) respectively. They are extracted directly from FRAPCON-3.5 manual [A5].

(1.088 × 10 − 5.475 × 10 ×+ ×+ ×) = (. 29)

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where

11 8 10 C1 = (1.16x10 +ctemp*1.037x10 )*5.7015, C2 = 1.0, C3 = -2.6x10

For neutron fluences greater than 1x1022 n/m2

25 25 C2 = 0.88*(1-exp(-fnck/1x10 ))+exp(-fnck/1x10 )

celmod = Young’s moduls (Pa)

ctemp = cladding temperature (K)

deloxy = input average oxygen concentration exlucding oxide layer (kg oxygen/kg Zircaloy) (hardwired to zero in FRAPCON-3.5)

cwkf = input effective cold work (unitess ratio of areas)

fnck = input effective fast fluence (n/m2)

(4.04 × 10 − 2.168 × 10 ×+ ×+ ×) ℎ = (. 30)

where

11 8 10 C1 = (7.01x10 +ctemp*2.315x10 ), C2 = 1.0, C3 = -0.867x10

For neutron fluences greater than 1x1022 n/m2

25 25 C2 = 0.88*(1-exp(-fnck/1x10 ))+exp(-fnck/1x10 )

cshear = shear moduls (Pa)

ctemp = cladding temperature (K)

deloxy = input average oxygen concentration exlucding oxide layer (kg oxygen/kg Zircaloy) (hardwired to zero in FRAPCON-3.5)

cwkf = input effective cold work (unitess ratio of areas)

fnck = input effective fast fluence (n/m2)

For SS-304 and HT-9, the equations for elastic and shear modulus are given by Equations (A.31)-(A.32) from [A1] and Equations (A.33)-(A.34) from [A2], respectively. It can be noticed that neutron fluence does not significantly degrade elastic modulus of metallic materials;

444 therefore, elastic modulus of SS-304 and HT-9 are only expressed a function of temperature only. Note that at the range of cladding temperature, stainless steel has higher elastic and shear modulus by factor of 2. The plots of elastic and shear modulus as a function of temperature of Zircaloy-2, SS-304 and HT-9 are given in Figure A.10 and A.11, respectively.

( − 304) = 21840 − 9.326 ∗ ( − 273.15) ∗ 9.8067 ∗ 10 (. 31)

( − 304) = 104.81 ∗ 10 − 0.0516 ∗ 10 ∗ ( − 273.15) (. 32)

( − 9) = 2.137 ∗ 10 − 102.74 ∗ 10 ∗ ( − 273.15) (. 33)

( − 9) = 8.964 ∗ 10 − 53.78 ∗ 10 ∗ ( − 273.15) (. 34)

where

Ε = elastic modulus (Pa)

G = shear modulus (Pa)

T = temperature (K)

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250

200

150 Zircaloy-2 100 SS-304 HT-9 Young Modulus (GPa) Young Modulus 50

0 0 500 1000 1500 2000 2500 Temperature (K)

Figure A.10: Elastic modulus as a function of temperature for Zircaloy-2, SS-304 and HT-9.

100

50 Zircaloy-2

40 SS-304 HT-9 30 Shear Modulus (GPa)

0 0 500 1000 1500 2000 Temperature (K)

Figure A.11: Shear modulus as a function of temperature for Zircaloy-2, SS-304 and HT-9.

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Creep

Creep is a time-dependent deformation process when materials exposed to stress, temperature and irradiation. Typically, creep rate is divided in two components: thermal creep and irradiation creep. The creep model for Zircaloy-2 is well documented in FRACON-3.5 manual which accounted for both thermal and irradiation creep [A5] and will not be shown in this work. For SS-304, the correlations added to FRAPCON-3.5 EP are adopted from FEMAXI-6 [A1] as shown in Equation (A.35).

Within the range of operating conditions of LWR, the thermal creep of SS-304 can be neglected. Support for this claim can be found in [A9] where the authors claim that, at the extreme operating condition of LWR (200 MPa, 400 C), the resulting strain rate is less than 1x10-10 per hr. For a 3-yr service life, the maximum thermal creep strain is therefore less than 3x10-4% or roughly three orders of magnitude less than irradiation-induced component. The effect of thermal stress is even lower when taking into account the effect of cold work which is expected to lower thermal creep by at least an additional order of magnitude.

= − + (. 35)

where

= irradiation creep strain rate (1/hr)

= neutron energy (MeV)

= fast neutron flux (n/cm2/s)

= equivalent stress (psi)

t = time (hours)

-23 15 -26 C1 = 1.7x10 , C2 = 5.5x10 , C3 = 2.7x10

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For HT-9, the equations for thermal creep and irradiation creep are given in Equations (A.36)- (A.39), respectively. They are adopted from FEAST-METAL [A2]

= +− . (. 36)

where

= irradiation creep strain rate (%/sec)

B0 = 1.83x10-4

A = 2.59x1014

Q = 73000 (Cal/g/mol)

R = 1.987 (Cal/g/mol/K)

T = temperature (K)

= neutron flux (1022 n/cm2/s)

= Equivalent stress (MPa)

= + (. 37)

= exp − + exp − + exp − . exp(− ) (. 38)

=exp − + exp − (. 39)

where

= thermal creep strain rate (%/s)

= primary thermal creep strain rate (%/s)

448

= secondary thermal creep strain rate (%/s)

-3 18 -6 9 9 C1 = 13.4, C2 = 8.43x10 , C3 = 4.08x10 , C4 = 1.6x10 , C5 = 1.17x10 , C6 = 8.33x10

Q1 = 15027 (Cal/g/mol), Q2 = 26451 (Cal/g/mol), Q3 = 89167 (Cal/g/mol),

Q4 = 83142 (Cal/g/mol), Q5 = 108276 (Cal/g/mol)

R = 1.987 (Cal/g/mol/K)

T = temperature (K)

Direct comparison of creep rate for Zircaloy-2, SS-304 and HT-9 is rather complicated expression it involved several external parameters including stress, time, neutron flux and temperature so it will not be shown here. However, from direct observation during simulation, the creep of Zircaloy-2 proceeds much faster than that of SS-304 and HT-9. At BOL, creep rate is controlled by both thermal and irradiation creep, however, as neutron fluence increases, thermal creep diminishes due to strain hardening then irradiation creep will dominate.

Oxidation and hydrogen pickup

A comprehensive corrosion models for zirconium-based alloys are developed in FRAPCON-3.5. The models are developed in two oxide thicknesses: (1) oxide layer thinner than 2 microns and (2) oxide thicker than 2 microns. At the oxide layer thickness less than 2 microns, a cubic rate law for oxide layer thickness is applied while, at thickness greater than 2 microns, flux- dependent linear rate law is applied with rate constant being an Arrhenius function of oxide- metal interface temperature. The expressions for Zircaloy-2 corrosion models are given in FRAPCON-3.5 manual [A5] and will not be shown here.

For SS-304 stainless steel, oxide layer formation is based on a simple parabolic law as proposed by J. Robertson [A10] for SS-304 and by R. L. Klueh and D. R. Harries [A11] for HT-9. The equations for oxide thickness and parabolic rate constants for SS-304 and HT-9 are given by Equation (A.40) through (A.43), respectively. Note that due to limited information and time constraint in this work, growth rate constant of HT-9 is not modeled a function of temperature.

449

However, at normal operating conditions of LWRs, the oxidation rate of stainless steel is expected to be considerably low. The plots of growth rate constant vs. temperature and oxide thickness vs. time of SS-304 and HT-9 are given in Figure A.12 and A.13, respectively.

. ( − 304) =( ∗) (. 40)

( − 304) = 5.84483 ∗ 10 ∗exp(3.55193 ∗ 10 ∗) (. 41)

. ( − 9) =( ∗) (. 42)

( − 9) = 4.41375 ∗ 10 (. 43)

where

x = oxide thickness (m)

2 kp = growth rate constant (m /s)

t = time (s)

T = temperature (K)

Hydrogen pickup fraction is the fraction of hydrogen generated from oxidation reaction between cladding material and water that is absorbed locally by cladding material. Under BWR normal operating conditions, a constant hydrogen pickup fraction has found to be applicable. For Zircaloy-2, a pickup fraction is fixed at 0.30 [A5] and this fraction is assumed to be valid for both SS-304 and HT-9.

450

1.0E+00

1.0E-02

1.0E-04

1.0E-06 Kp (cm^2/s) 1.0E-08 Expon. (Kp (cm^2/s)) 1.0E-10 3.55E-02x 1.0E-12 y = 5.84E-26e Kp (cm^2/s) R² = 9.94E-01 1.0E-14

1.0E-16

1.0E-18

1.0E-20 0 200 400 600 800 1000 Temperature (C)

Figure A.12: Oxide growth rate constant as a function of temperature for SS-304.

9.0E-07 y = 4.41E-10x5.01E-01 R² = 1.00E+00 8.0E-07

7.0E-07

6.0E-07

5.0E-07

4.0E-07 HT-9

3.0E-07 Power (HT- Oxide thickness (m) 9) 2.0E-07

1.0E-07

0.0E+00 0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06 Time (seconds)

Figure A.13: Oxide thickness as a function of time for HT-9.

451

Oxide layer thermal conductivity

Under normal operating conditions of BWR, it is assumed that the only type of oxide layer

formed at the surface of stainless steel is Cr2O3. Another assumption made is that the thermal conductivity of oxide layer remains constant over the temperature range of interest. From a

survey of literature, the thermal conductivity of 10 W/m/K is a lower limit for Cr2O3 materials

[A12]. The plot of oxide layer thermal conductivity of ZrO2 and Cr2O3 are given in Figure A.14.

6 ZrO2 Cr2O3 4

2 OXide Thermal Conductivity (W/m/K)

0 0 500 1000 1500 2000 Temperature (K)

Figure A.14: Oxide thermal conductivity as a function of temperature for Zircaloy-2, SS-304 and HT-9.

Yield and ultimate tensile strength

Yield strength is a transition point where deformation mode changes from elastic (reversible region) to plastic (irreversible region). Ultimate tensile strength is a material capacity limit for withstanding tensile force before breaking. Yield and ultimate strength have two components taken into consideration: temperature and fluence. Each parameter is modeled separately but, at the end, the final values will take both temperature and irradiation hardening effects into account. Yield and ultimate strengths of SS-304 as a function of temperature are adopted from [A7] and

452

[A6]. For HT-9, Yield and ultimate strengths of HT-9 as a function of temperature are adopted from [A13]. The equation for yield and ultimate strength for SS-304 and HT-9 are given by Equation (A.44) through (A.47).

YS(SS-304) = -1.81742x10-6xT3 + 2.52447*10-3*T2 - 1.31709*T + 9.12981*102 (A.44)

UTS(SS-304) = -4.11464x10-6xT3 + 6.86057*10-3*T2 - 3.91129*T + 1.51418*103 (A.45)

YS(HT-9) = -1.03436x10-8xT4 +1.79815x10-5xT3 - 1.10828*10-2*T2

+ 2.61955*T + 4.82376*102 (A.46)

UTS(HT-9) = -4.08317x10-6xT3 + 5.04736*10-3*T2 - 2.18830*T + 1.11478*103 (A.47)

where

YS = yield strength (MPa)

UTS = ultimate tensile strength (MPa)

T = temperature (K)

To account for irradiation hardening effect, the following multiplying factor is developed as a function of neutron fluence. This factor is based on information presented in Chapter 2.09 of Comprehensive Nuclear Material [A6]. First, yield and ultimate strength are evaluated at any given temperature then these values will be multiplied by the multiplying factor calculated based on the level of neutron fluence assuming that neutron fluence is always greater than zero. The expressions for multiplying factor are given by Equations (A.48) and (A.49).

YS Increase = 19.266*ln(Φ) + 70.276 (A.48)

UTS Increase = 7.1278*ln(Φ) + 20.017 (A.49)

where

YS Increase = Increase in yield strength (%)

453

UTS Increase = Increase in ultimate strength (%)

Φ = fast neutron fluence (DPA) (E > 1.0 MeV)

The plots of yield strength, ultimate strength and multiplying factor of SS-304 and HT-9 are shown in Figure A.15 through A.17, respectively.

1000

900 y = -4.11E-06x3 + 6.86E-03x2 - 3.91E+00x + 1.51E+03 800 R² = 9.98E-01

700 Yield Strength 600

500 Ultimate Tensile Strength

400 Poly. (Yield Strength) Strength (MPa) 300 Poly. (Ultimate Tensile 200 y = -1.82E-06x3 + 2.52E-03x2 - 1.32E+00x + 9.13E+02 Strength) 100 R² = 9.97E-01

0 0 200 400 600 800 1000 1200 Temperature K

Figure A.15: Yield and ultimate strength as a function of temperature for SS-304.

454

900 y = -4.08E-06x3 + 5.05E-03x2 - 2.19E+00x + 1.11E+03 800 R² = 1.00E+00

700

600 Ultimate Tensile Strength 500 Yield Strength 400 4 3 2 y = -1.03E-08x + 1.80E-05x - 1.11E-02x + 2.62E+00x Poly. (Ultimate Tensile + 4.82E+02

Strength (MPa) 300 Strength) R² = 1.00E+00 Poly. (Yield Strength) 200

100

0 0 200 400 600 800 1000 Temperature K

Figure A.16: Yield and ultimate strength as a function of temperature for HT-9.

200

180 y = 19.266ln(x) + 70.276 160 R² = 0.8537 140

120 % Increase YS 100 % Increase UTS 80 y = 7.1278ln(x) + 20.017 R² = 0.8403 Log. (% Increase YS) 60 Increase in strength (%) strength Increase in 40

0 0 100 200 300 400 Fluence (DPA)

Figure A.17: Multiplying factor to account for irradiation hardening effect of stainless steel.

455

References

A1. M. Suzuki and H. Saitou, Light Water Reactor Fuel Analysis Code FEMAXI-6 (Ver.1) - Detailed Structure and User’s Manual, JAEA-Data/Code 2005-003. A2. A. Karahan, “Modeling of Thermo-Mechanical and Irradiation Behavior of Metallic and Oxide Fuels for Sodium Fast Reactors”, PhD Thesis, Massachusetts Institute of Technology, 2009. A3. SS304/304L Product Data Sheet, AK Steel, retrieved on May 9, 2013 from http://www.aksteel.com/pdf/markets_products/stainless/austenitic/304_304L_Data_Sheet .pdf. A4. AISI Type 422 Stainless Steel, MATWEB, retrieved on May 9, 2013 from http://www.matweb.com/search/datasheetText.aspx?bassnum=Q422AK A5. K. J. Geelhood, and W. G. Lushcer, “FRAPCON-3.5 : A Computer Code for the Calculation of Steady State, Thermal-Mechanical Behavior of Oxide Fuel Rods for High Burnup, Volume 1,” NUREG/CR-7022, Vol.1, U.S. NRC, 2014. A6. R. J.M. Konings (Editor-in-Chief), Comprehensive Nuclear Materials, 1st Edition, Elsevier Science, 2012. Chapter 2.09 and Chapter 4.02. A7. S. M. Stoller Corporation, An Evaluation of Stainless Steel Cladding for use in Current Design LWRS, NP-2642, EPRI Technical Report, 1982. A8. Thermophysical Properties of Materials for Water Cooled Reactors, IAEA Technical Document, IAEA-TECDOC-949, 1997, retrieved on May 9, 2013 from http://www- pub.iaea.org/MTCD/publications/PDF/te_949_prn.pdf. A9. R. W. Smith and G. S. Was, “FCODE-BETA/SS: A Fuel Performance Code for Stainless Steel Clad Pressurized Water Reactor Fuel”, Nuclear Technology, Vol. 69, 1985. A10. J. Robertson, “The Mechanism of High Temperature Aqueous Corrosion of Stainless Steel”, Corrosion Science, Vol. 32, 1991, 443-465. A11. R. L. Klueh and D. R. Harries, High Chromium Ferritic and Martensitic Steels for Nuclear Applications, ASTM, 2001. A12. J. F. Shackelford and W. Alexander, CRC Materials Science and Engineering Handbook, CRC Press, 2001. A13. F. H. Huang, W. L. Hu, and M. L. Hamilton, “Mechanical Properties of Martensitic Alloy AISI 422”, 16. Annual Symposium of ASTM on effects of radiation on materials,

456

Denver, CO (United States), 21-25 Jun 1992, retrieved on May 9, 2013 from http://www.osti.gov/bridge/servlets/purl/6860470-3SFFIu/6860470.pdf.

457

Appendix B: Sample input files

B.1 FRAPCON-3.5 EP input file for FFTF ACO-1 reference design

***************************************************************************** * frapcon3, steady-state fuel rod analysis code, version 3 * *------* * * * CASE DESCRIPTION: FFTF ACO-1 Fuel Rod * * * *UNIT FILE DESCRIPTION * *------* * Output : * * 6 STANDARD PRINTER OUTPUT * * * * Scratch: * * 5 SCRATCH INPUT FILE FROM ECH01 * * * * Input: FRAPCON3.5 INPUT FILE (UNIT 55) * * * ***************************************************************************** * GOESINS: FILE05='nullfile', STATUS='scratch', FORM='FORMATTED', CARRIAGE CONTROL='LIST' * * GOESOUTS: FILE06='.\ACO-1.out',STATUS='UNKNOWN', CARRIAGE CONTROL='LIST' FILE66='.\ACO-1-plot.out',STATUS='UNKNOWN', CARRIAGE CONTROL='LIST' /*****************************************************************************

$frpcn

im = 155, mechan = 2, nce = 5, ngasr = 45, nr = 17, na = 18,

$end

$frpcon

! Rod size dco = 6.858e-3, thkcld = 0.533e-3, thkgap = 0.102e-3, totl = 91.44e-2, cpl = 91.44e-2,

! Spring dimensions dspg = 5.55e-3, dspgw = 0.860412598e-3, vs = 28,

458

! Pellet shape hplt = 9.8298E-3, rc = 0.0, hdish = 0.0, dishsd = 0.0, chmfrh = 0.0, chmfrw = 0.0,

! Pellet isotropics enrch = 0.711, imox = 1, comp = 24.6, compa = 36*24.6, fotmtl = 1.96, gadoln = 0.0, ifba = 0.0, b10 = 0.0, zrb2thick = 0.0, zrb2den = 90, ppmh2o = 0.0, ppmn2 = 0.0,

! Pellet fabrication den = 90.5, deng = 0.0, roughf = 2E-6, rsntr = 97.2, tsint = 1872.594,

! Cladding fabrication icm = 9, !HT-9 stainless steel zr2vintage = 1, cldwks = 0.2, roughc = 5E-7, catexf = 0.05, chorg = 10.0,

! Rod fill conditions fgpav = 3E5, idxgas = 1, amfair = 0.0, amfarg = 0.0, amffg = 0.0, amfhe = 1.0, amfh2 = 0.0, amfh2o = 0.0, amfkry = 0.0, amfn2 = 0.0, amfxe = 0.0,

! Reactor conditions iplant = -3, nsp = 1, p2 = 155*1.0E5, tw = 155*633.15, go = 7191.169945,7191.169945,7191.169945,7191.169945,7191.169945, 7191.169945,7183.16163,7175.15445,7167.128982,7159.124073, 7152.98481,7144.982038,7136.980399,7128.979894,7122.844506, 7114.846138,7106.829486,7098.833382,7092.701867,7084.707896, 7076.715059,7068.723352,7060.71337,7054.606129,7046.59828, 7038.610969,7030.624787,7024.502004,7016.51795,7008.535026, 7000.533838,6994.43431,6986.454642,6978.456714,6970.479305, 6962.503024,6956.388957,6948.414801,6940.441774,6932.45049, 6926.359659,6918.370501,6910.40185,6902.434328,6894.467931, 6888.362562,6880.398285,6872.415761,6864.453738,6858.352215, 6850.392309,6842.433527,6834.475869,6828.378188,6820.422648, 6812.46823,6804.495579,6796.54341,6790.45056,6782.500505, 6774.551573,6766.603765,6760.514749,6752.569052,6744.605127, 6736.661674,6730.57649,6722.63515,6714.694928,6706.755826, 6698.798504,6692.737477,6684.782269,6676.847516,6668.913883, 6662.83734,6654.905814,6646.975406,6639.026789,6631.098619, 6625.046211,6617.100818,6609.17587,6601.252039,6595.18412, 6587.262392,6579.34178,6571.402966,6565.358175,6557.421467,

459

6549.505189,6541.590026,6533.675978,6527.616663,6519.704714, 6511.774574,6503.864854,6497.809346,6489.901722,6481.995213, 6474.089816,6468.038108,6460.134809,6452.23262,6444.312248, 6436.412284,6430.365357,6422.467488,6414.570728,6406.67508, 6400.631946,6392.738388,6384.826659,6376.935323,6369.045097, 6363.006734,6355.118597,6347.231569,6339.326376,6333.311072, 6325.407969,6317.525246,6309.643632,6303.612838,6295.733309, 6287.854888,6279.958309,6272.082102,6266.075328,6258.181942, 6250.308926,6242.437013,6236.414753,6228.544922,6220.676196, 6212.789325,6206.790086,6198.905297,6191.040862,6183.17753, 6175.315302,6169.301557,6161.441406,6153.563119,6145.705176, 6139.695196,6131.839329,6123.984563,6116.130901,6108.259106, 6102.273093,6094.422604,6086.553987,6078.705704,6072.704215,

pitch = 8.26E-3, icor = 0.0, crdt = 0.0, crdtr = 0.0, crudmult = 0.0, flux = 37*1.68E+17,

! Power history ProblemTime = 1.00E-06,0.2,0.4,0.6,0.8,1.0,4.3,8.7,13,17.3,21.7,26, 30.3,34.7,39,43.3,47.6,52,56.3,60.6,65,69.3,73.6,78,82.3, 86.6,91,95.3,99.6,104,108.3,112.6,117,121.3,125.6,129.9, 134.3,138.6,142.9,147.3,151.6,155.9,160.3,164.6,168.9, 173.3,177.6,181.9,186.3,190.6,194.9,199.3,203.6,207.9, 212.2,216.6,220.9,225.2,229.6,233.9,238.2,242.6,246.9, 251.2,255.6,259.9,264.2,268.6,272.9,277.2,281.6,285.9, 290.2,294.5,298.9,303.2,307.5,311.9,316.2,320.5,324.9, 329.2,333.5,337.9,342.2,346.5,350.9,355.2,359.5,363.8, 368.2,372.5,376.8,381.2,385.5,389.8,394.2,398.5,402.8, 407.2,411.5,415.8,420.2,424.5,428.8,433.2,437.5,441.8, 446.1,450.5,454.8,459.1,463.5,467.8,472.1,476.5,480.8, 485.1,489.5,493.8,498.1,502.5,506.8,511.1,515.5,519.8, 524.1,528.4,532.8,537.1,541.4,545.8,550.1,554.4,558.8, 563.1,567.4,571.8,576.1,580.4,584.8,589.1,593.4,597.8, 602.1,606.4,610.7,615.1,619.4,623.7,628.1,632.4,636.7, 641.1,645.4,

qmpy = 7.455042087,7.455042087,14.90042113,22.35546321, 29.80084225,37.25588434,37.21703083,37.17817732, 37.13922316,37.10036965,37.07117919,37.03232568, 36.99347217,36.95461866,36.9254282,36.8865747, 36.84762053,36.80876702,36.77957656,36.74072305, 36.70186955,36.66301604,36.62406187,36.59497207, 36.5560179,36.5171644,36.47831089,36.44912043, 36.41026692,36.37141341,36.33245925,36.30336944, 36.26451593,36.22556177,36.18670826,36.14785475, 36.11866429,36.07981078,36.04095728,36.00200311, 35.97291331,35.93395914,35.89510563,35.85625213, 35.81739862,35.78820816,35.74935465,35.71040048, 35.67154698,35.64235652,35.60350301,35.5646495, 35.52579599,35.49660553,35.45775202,35.41889851,

460

35.37994435,35.34109084,35.31190038,35.27304687, 35.23419336,35.19533986,35.1661494,35.12729589, 35.08834172,35.04948821,35.02029775,34.98144425, 34.94259074,34.90373723,34.86478306,34.83569326, 34.7967391,34.75788559,34.71903208,34.68984162, 34.65098811,34.6121346,34.57318044,34.53432693, 34.50523713,34.46628296,34.42742945,34.38857594, 34.35938549,34.32053198,34.28167847,34.2427243, 34.2136345,34.17468034,34.13582683,34.09697332, 34.05811981,34.02892935,33.99007584,33.95112168, 33.91226817,33.88307771,33.8442242,33.80537069, 33.76651718,33.73732672,33.69847322,33.65961971, 33.62066554,33.58181203,33.55262157,33.51376807, 33.47491456,33.43606105,33.40687059,33.36801708, 33.32906292,33.29020941,33.2513559,33.22216544, 33.18331193,33.14445842,33.10550426,33.07641445, 33.03746029,32.99860678,32.95975327,32.93056281, 32.8917093,32.8528558,32.81390163,32.77504812, 32.74595832,32.70700415,32.66815065,32.62929714, 32.60010668,32.56125317,32.52239966,32.4834455, 32.45435569,32.41540153,32.37654802,32.33769451, 32.298841,32.26965054,32.23079703,32.19184287, 32.15298936,32.1237989,32.08494539,32.04609188, 32.00723838,31.96828421,31.93919441,31.9003409, 31.86138673,31.82253323,31.79334277,

! Axial power profile iq = 0, x = 0,0.025064529,0.050405084,0.07426181,0.098105708, 0.124955749,0.154786278,0.180114005,0.200990244,0.224834142, 0.253129527,0.279928255,0.306701326,0.336442055,0.375072932, 0.409201007,0.435897107,0.461096549,0.490708993,0.520308609, 0.543985736,0.570604865,0.594256335,0.619378806,0.644488448, 0.669585262,0.693211075,0.718295061,0.743379046,0.768437375, 0.792024702,0.817095859,0.839199358,0.862773857,0.884890184, 0.9144, qf = 0.823110168331523,0.858502603382231,0.890351644521998, 0.922205873684495,0.950511520913323,0.989452537897698, 1.03193176064715,1.06023221997639,1.08854824325067, 1.11685389047950,1.14514397376328,1.16989066325926, 1.18754018888790,1.20517933859422,1.21923877847678, 1.21911945481598,1.21547748921203,1.20829212969713, 1.19044546055932,1.16905020961098,1.15122429244095, 1.12629083560440,1.10136775469016,1.07289090381953, 1.04086547126151,1.00529145664668,0.973271211988249, 0.934148615562890,0.895026019137530,0.848806258967972, 0.806140268754810,0.763469090395783,0.720808288082212, 0.674593715935382,0.635481495432342,0.589246171317736, jn = 1*36,

jst = 155*1, fa = 1.0,

461

! Code operation ngasmod = 2, nunits = 0, crephr = 10, sgapf = 31, slim = 0.05, qend = 0.3, igas = 0, frcoef = 0.015, igascal = 1,

! Code output jdlpr = 0, nopt = 0, nplot = 1, ntape = 0, nread = 0, nrestr = 0,

$end

$frpmox

moxtype = 1, enrpu39 = 34.11330049, enrpu40 = 47.4137931, enrpu41 = 6.773399015, enrpu42 = 11.69950739,

$end

B.2 FRAPCON-3.5 EP input file for ABWR reference design

************************************************************************* * frapcon3, steady-state fuel rod analysis code, version 3 * *------* * * * CASE DESCRIPTION: ABWR Fuel Rod * * * *UNIT FILE DESCRIPTION * *------* * Output : * * 6 STANDARD PRINTER OUTPUT * * * * Scratch: * * 5 SCRATCH INPUT FILE FROM ECH01 * * * * Input: FRAPCON3.5 INPUT FILE (UNIT 55) * * * ************************************************************************* * GOESINS: FILE05='nullfile', STATUS='scratch', FORM='FORMATTED', CARRIAGE CONTROL='LIST' * * GOESOUTS: FILE06='.\abwr_mox.out',STATUS='UNKNOWN', CARRIAGE CONTROL='LIST' FILE66='.\abwr_mox_plot.out',STATUS='UNKNOWN', CARRIAGE CONTROL='LIST' /**************************************************************************** Hitachi ABWR

$frpcn im=113, na=105, nr=45, ngasr=45, mechan=2,

462

$end

$frpcon cpl = 11.24, crdt = 0.0, dco = 0.44, thkcld=0.028, den = 95.5, dishsd = 0.097 dspg = 0.383, thkgap=0.0040, dspgw = 0.04, enrch = 0.71, fgpav = 43.51, hdish = 0.0, hplt = 0.5, icm = 2,pitch = 0.562, icor = 2, idxgas = 1, iplant =-3, iq = 0, jdlpr = 0, fa = 1.0, jn = 25,25,25, imox = 1, comp = 30.0, compa = 105*30, fotmtl = 2.00, totl = 12.17, roughc = 1.97e-5, roughf = 8.3e-5, vs = 100.0, nunits = 1, rsntr = 150.0, nsp=0, nplot = 1, flux = 1.95e16, p2(1) = 1035.0, tw(1) = 533.0, go(1) = 12.269e5, jst = 38*1,38*2,37*3, qf(1) = 0.3961,1.1787,1.4976,1.5942,1.5845,1.5362,1.4879,1.4493,1.4300, 1.4203,1.3816,1.3140,1.2174,1.1208,0.9372,0.8406,0.8019,0.7440,0.6860, 0.6184,0.5507,0.4734,0.3671,0.1546,0.0966, x(1) = 0.0000,0.5071,1.0142,1.5213,2.0283,2.5354,3.0425,3.5496,4.0567, 4.5638,5.0708,5.5779,6.0850,6.5921,7.0992,7.6063,8.1133,8.6204,9.1275, 9.6346,10.1417,10.6488,11.1558,11.6629,12.1700, qf(26) = 0.3575,0.9952,1.2850,1.4010,1.4396,1.4396,1.4010,1.3720,1.3237, 1.2947,1.2464,1.2077,1.1594,1.0918,0.9662,0.9275,0.9179,0.8889,0.8696, 0.8406,0.7923,0.7053,0.5700,0.2512,0.1546, x(26) = 0.0000,0.5071,1.0142,1.5213,2.0283,2.5354,3.0425,3.5496,4.0567, 4.5638,5.0708,5.5779,6.0850,6.5921,7.0992,7.6063,8.1133,8.6204,9.1275, 9.6346,10.1417,10.6488,11.1558,11.6629,12.1700, qf(51) = 0.1884,0.4855,0.5942,0.6522,0.7246,0.8116,0.8986,0.9783,1.0580, 1.1232,1.1884,1.2464,1.2971,1.3406,1.2536,1.2899,1.3768,1.4058,1.4130, 1.3913,1.3333,1.2101,0.9565,0.4420,0.2609, x(51) = 0.0000,0.5071,1.0142,1.5213,2.0283,2.5354,3.0425,3.5496,4.0567, 4.5638,5.0708,5.5779,6.0850,6.5921,7.0992,7.6063,8.1133,8.6204,9.1275, 9.6346,10.1417,10.6488,11.1558,11.6629,12.1700,

ProblemTime=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9, 1,2,5,10,15,30,45,60,75,90,105,120,135,150,165,180, 195,210,225,240,255,270,285,300,315,330,345,360,375,390,405,420, 435,450,465,480,495,510,525,540,555,570,585,600,615,630,645,660, 675,690,705,720,735,750,765,780,795,810,825,840,855,870,885,900, 915,930,945,960,975,990,1005,1020,1035,1050,1065,1080,1095,1110, 1125,1140,1155,1170,1185,1200,1215,1230,1245,1260,1275,1290,1305, 1320,1335,1350,1365,1380,1395,1410,1425,1440,1455,1470,1485,1500,

463 qmpy = 0.6347,1.2693,1.9040,2.5386,3.1733,3.8079,4.4403,5.0749, 5.7096,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443, 6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443, 6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443, 6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.3443,6.2983,6.2523,6.2040, 6.1580,6.1097,6.0637,6.0177,5.9717,5.9235,5.8775,5.8315,5.7855,5.7372, 5.6912,5.6452,5.5969,5.5509,5.5050,5.4590,5.4107,5.3647,5.3187,5.2704, 5.2244,5.1784,5.1324,5.0841,5.0382,4.9922,4.9462,4.8979,4.8519,4.8059, 4.7576,4.7116,4.6656,4.6197,4.5714,4.5254,4.4794,4.4311,4.3851,4.3391, 4.2908,4.2448,4.1988,4.1506,4.1046,4.0586,4.0126,3.9643,3.9183,3.8723, 3.8240,3.7780,3.7321,3.6861,3.6378,3.5918,3.5458,3.4998,3.4515,3.4055, 3.3595,3.3112,3.2653,3.2193,3.1733, slim = .05,

$end

$frpmox enrpu39 = 34.11330049, enrpu40 = 47.4137931, enrpu41 = 6.773399015, enrpu42 = 11.69950739, $end

464