Modeling of the Thermal Behavior of Irradiated Sphere-Pac Mixed Carbide Fuel
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AN ABSTRACT OF THE THESIS OF Maurice Ades for the degree of Doctor of Philosophy in Nuclear Engineering presented on February 28, 1979 Title: Modeling of the Thermal Behavior of Irradiated Sphere-Pac Mixed Carbide Fuel Redacted for Privacy Abstract Approved: ft f K. L. Peddicord Several fuels are being investigated for fast breeder reactor applications. One promising concept is sphere-pac mixed carbide fuel. As a part of the development of this fuel concept it is necessary to determine the behavior of the irradiatedfuel for safe and reliable operation on a sound economic basis. It is with the thermal aspect of this behavior that the current investigation is concerned. With a view to predicting the overall thermal behavior of the fuel pin during irradiation, theoretical models forvarious phenomena have been developed so that the various interrelated thermal components can be determined. These components include the thermal conductivity of the fuel in its initialconfiguration and during restructuring, the restructuring boundary, thetemperature distribution, the extent of restructuring due tosintering, grain growth and porosity redistribution, fuelswelling and gas release, and the behavior of the fill gas inthe free volume of the fuel pin. A two-dimensional unit cell model is developed toevaluate the effective conductivity of the fuel in itsinitial configuration. By implementing descriptions of sintering mechanisms on this model, the effective conductivity of the fuel during restructuring is evaluated. The restructuring boundary at each axial section is determined based on a thermal conductivity criteria. Under certain conditions the initial fuel configuration in the inner fuel regions is lost and is replaced by a porous pellet-shaped region. In the outer regions, however, fuel restructuring is not completed. The radial temperature distribution is evaluated by finite differences at a discrete number of axial sections. The local heat source has previously been computed foreach section. Allowance is made for axial asymetry as well as power histories. The porosity redistribution in the inner fuel regions which have completed restructuring is evaluated by using a model describing the conser- vation of pores migrating up the thermal gradient. Swelling and gas release are modeled allowing for bubble nucleation, bubble and pore growth and re-solution of gas atoms. Gas release occurs through diffusion of individual gas atomsin the fuel matrix and follows the subsequent buildup ofcontiguous inter- granular bubbles. Allowance is made for changes in the fuel micro- structure due to restructuring andthermally-activated grain growth. Following gas release, the temperature and pressureof the free gas are evaluated. The models describing the various thermalbehavior components were embodied into the computer code SPECKLE-I to predict the thermal response of the irradiated fuel pin. Results computed from SPECKLE -I indicate that the effective fuel conductivity increases with temperature, fill gas pressure and with the extent of sintering occuring between the fuel spheres. As gas release occurs, the effective conductivity is altered by the fission gas and the pressure buildup in the free volume. The fuel temperature, initially high, decreases significantly due to restructuring and is affected by the compensating effects of gas release and pressure buildup. The extent of restructuring and porosity redistribution increases with the fuel power. Fuel swelling and gas release are essentially controlled by the fuel microstructure and porosity. The results indicate that the extent of fuel restructuring affects swelling and gas release. As gas release occurs, the pressure of the fill gas increases significantly, its temperatureremaining almost constant. Results from SPECKLE-I were compared with several fuelirradia- tions. The agreement obtained between predicted and measuredthermal components suggests that SPECKLE-I is a valuable first stepfor evaluating the thermal response of irradiated sphere-pacmixed carbide fuel. The performance of this code, however, can beimproved by further model development and experimentalstudies of phenomena not fully characterized. MODELING OF THE THERMAL BEHAVIOR OF IRRADIATED SPHERE-PAC MIXED CARBIDE FUEL by Maurice Ades A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Commencement June 1979 APPROVED: Redacted for Privacy Professor of Nuclear Engineering In Charge of Major Redacted for Privacy Head of Department of Nuclear Engineering Redacted for Privacy Dean of Graduate School Date thesis is presented February 28, 1979 Typed by Mary Bauman for Maurice Ades ACKNOWLEDGEMENT The present investigation was sponsored by EIR, the Swiss Federal Institute for Reactor Research, Wuerenlingen, Switzerland. Funding for my research by EIR is gratefully acknowledged. I would like to thank my major professor, Dr. K.L. Peddicord for his continued support and guidance during the course of this work. Special thanks are also due to R.W. Stratton, Director of the EIR Fuel Development Program, for his interest and criticism during the realization of the present investigation. I also would like to thank Drs. H. Blank, Hj. Matzke and C. Sari of the Euratom Transuranium Institute, Karlsruhe, Germany, for their appropriate comments on modeling of carbide fuel. Thanks are also due to Dr. J.R. Matthews and Mr. R.D. Bellamy of AERE, Harwell, U.K., for fruitful discussions on modeling. I am also indebted to Dr. A.H. Robinson for his various comments on appropriate numerical methods. At last, but not at least, I am grateful to my spouse, Rebecca, for her encouragement and sacrifice without which this work would not have been possible. TABLE OF CONTENTS Page I. Introduction I.1. General Background 1 1.2. Modeling of the Behavior of Irradiated Pellet Shaped Mixed Oxides 6 1.3. Modeling of the Behavior of Irradiated Pellet Shaped Mixed Carbides 21 1.4. Sphere-Pac Fuel 1.4.1. Description 29 1.4.2. Modeling of Irradiated Sphere-Pac Mixed Carbide Fuels 35 1.5. Research Objectives 37 II. Analytical Description of the Models II.1. Effective Conductivity of Sphere-Pac Fuel 43 II.1.1. Introduction 43 11.1.2. The Model 44 11.1.3. Calculational Procedure 49 11.1.4. Effective Conductivity of the Fine Fraction Unit Cell 49 11.1.5. Effective Conductivity of the Binary Unit Cell 51 11.1.6. Allowance for Fission Gas Release 52 11.2. Effective Conductivity of Sphere-Pac Fuel Undergoing Initial Stage Restructuring 55 11.2.1. Introduction 55 11.2.2. Sintering 56 11.2.2.1. Definition 56 11.2.2.2. Mechanisms 59 11.2.2.3. Effect of Applied Stress - Hot Pressing 65 11.2.2.4. Dominant Sintering Mechanism: Sintering Diagram 66 11.2.3. Evaluation of the Effective Conductivity of Sphere-Pac Fuel Undergoing Sintering . 68 11.2.3.1. The Method 68 11.2.3.2. Restructuring Boundary: The MCB Method 70 11.2.3.3. Effective Conductivity for Finite Time Step Computations 71 11.2.3.4. Allowance for Pressure Buildup and Fission Gas Release 74 11.3. Heat Source 75 11.4. Temperature Distribution 79 11.5. Intermediate Stage Fuel Restructuring 84 Page 11.5.1. Introduction 84 11.5.2. Porosity Redistribution 86 11.5.2.1. Introduction 86 11.5.2.2. The Model 91 11.5.3. Grain Growth 99 11.5.3.1. Introduction 99 11.5.3.2. The Model 101 11.6. Fuel Swelling and Gas Release 105 11.6.1. Introduction 105 11.6.2. Nucleation of Fission Gas Bubbles 106 11.6.3. Re-Solution 111 11.6.4. Allowance for Fuel Porosity 114 11.6.5. The Model 118 11.6.6. Method of Solution 122 11.6.7. Grain Boundary Bubbles 126 11.6.8. Volume Swelling 131 11.6.8.1. Volume Swelling Due to Fission Gas 132 11.6.8.2. Volume Swelling Due to Solid Fission Products 134 11.6.8.3. Total Volume Swelling 137 11.6.9. Gas Release 142 11.6.9.1. Gas Release From a Fuel Grain . 142 11.6.9.2. Total Gas Release 144 11.7. Free Gas Conditions 148 III. Computer Simulation of the Thermal Behavior of Irradiated Sphere-Pac Fuel III.1. Introduction 151 111.2. SPECKLE-I 151 IV. Results and Discussions IV.1. Application of the Models 158 IV.2. Effective Conductivity of Sphere-Pac Fuel 159 IV.3. Effective Conductivity of Sphere-Pac Fuel Undergoing Sintering 165 IV.3.1. Sintering Mechanisms 165 IV.3.2. Effective Conductivity of Sphere-Pac Fuel During Initial Stage Restructuring 175 IV.3.3. Allowance for Gas Pressure and Fission Gas Release 182 187 IV.4. Temperature Distribution and RestructuringBoundary IV.4.1. Computational Results 187 IV.4.2. Effect of Applied Stress 193 IV.4.3. Comparison with Experiments 197 Page IV.5. Porosity Redistribution 198 IV.5.1. Computational Results 198 IV.5.2. Comparison with Experiments 213 IV.6. Fuel Swelling and Gas Release 218 IV.6.1. Preliminary Results 218 IV.6.2. Computational Results 222 IV.7. Free Gas Conditions and Overall Thermal Behavior . 227 IV.8. Limitations of the Models 243 IV.8.1. Effective Conductivity of Sphere-Pac Fuel 244 IV.8.2. Effective Conductivity of Sphere-Pac Fuel Undergoing Sintering 245 IV.8.3. Heat Source 246 IV.8.4. Temperature Distribution 246 IV.8.5. Porosity Redistribution 247 IV.8.6. Grain Growth 249 IV.8.7. Fuel Swelling and Gas Release 250 V. Conclusions and Recommendations V.I. Conclusions 254 V.2. Recommendations for Future Theoretical Studies . 264 V.3. Recommendations for Future Experimental Studies . 267 References 271 Appendix 282 LIST OF ILLUSTRATIONS Figure Page 1. Schematic Representation of Pellet-Shaped and Sphere-Pac Fuel Before and After Irradiation 31 2. Fuel Microstructure and Porosity Distribution in Pelleted (U08Pu02)C Fuel 33 3. Conceptual Flow Chart for a Computer Program to Simulate the Behavior of an Irradiated Sphere-Pac Carbide Fuel Pin 38 4.