Jets for Inertial Fusion Applications
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SHOCK ATTENUATION IN TWO-PHASE (GAS-LIQUID) JETS FOR INERTIAL FUSION APPLICATIONS A Thesis Presented to The Academic Faculty by C´elineC. Lascar In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Mechanical Engineering Georgia Institute of Technology December 2007 SHOCK ATTENUATION IN TWO-PHASE (GAS-LIQUID) JETS FOR INERTIAL FUSION APPLICATIONS Approved by: Professor Said I. Abdel-Khalik, Professor Daniel W. Tedder Committee Chair School of Chemical and Biomolecular School of Mechanical Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Cyrus K. Aidun Professor Donald R. Webster School of Mechanical Engineering School of Civil Engineering Georgia Institute of Technology Georgia Institute of Technology Professor S. Mostafa Ghiaasiaan Date Approved: 20 August 2007 School of Mechanical Engineering Georgia Institute of Technology A` mon Ch´eri, qui se reconnaˆıtra. Merci pour ton amour. iii ACKNOWLEDGEMENTS The successful completion of this thesis would not have been possible without the support and the guidance of many individuals. Foremost, I would like to thank my advisor and committee chairman, Dr. Said I. Abdel-Khalik. His invaluable advice and support throughout these past three years are greatly appreciated. I would also like to thank the additional members of my thesis committee, Dr. Cyrus K. Aidun, Dr. S. Mostafa Ghiaasiaan, Dr. Daniel W. Tedder, and Dr. Donald Webster for their recommendations and support. A special thanks is due to Mr. Dennis L. Sadowski for his efforts in this project. I am very grateful for his inexhaustible efforts in the design, construction, and op- eration of the experimental apparatus. I would also like to thank my laboratory colleagues whose support and camaraderie have been indispensable: Tim Koehler, Lorenzo Crosatti, Dr. Sam Durbin, Brandon Weathers, Chad Dillon, Tony Jones, Joseph Hu, Bo Lu and Dr. Vladimir Novak. Most importantly, I wish to express my deepest appreciation to my parents, Catherine and Jean-Luc, my grand-mother, Gigi, and my brother, Guillaume, with- out whom all my achievements would have been impossible. I would especially like to thank Lee for his support, patience, and understanding. iv TABLE OF CONTENTS DEDICATION . iii ACKNOWLEDGEMENTS . iv LIST OF TABLES . viii LIST OF FIGURES . xii NOMENCLATURE . xxiii SUMMARY . .xxviii I INTRODUCTION . 1 1.1 Energy from Fusion . 2 1.1.1 Principles of Inertial Fusion Energy (IFE) . 5 1.1.2 Z-Pinch IFE Chamber . 7 1.2 Objectives . 10 II LITERATURE REVIEW . 13 2.1 Dynamics of Vertical Annular Jet . 13 2.2 Wave Propagation in Two-Phase Media . 17 2.3 Shock Mitigation in Z-Pinch IFE Reactors . 19 2.4 Pressure Wave due to an Exploding Wire . 23 2.5 Two-Phase Flow Models . 24 2.6 Measurements of Void Fraction . 28 III EXPERIMENTAL APPARATUS AND PROCEDURES . 32 3.1 Small-Scale Experimental Loop . 32 3.1.1 Small-Scale Loop Components . 32 3.1.2 Flow Conditioner and Nozzle Design for a Planar Jet . 33 3.1.3 Flow Conditioner and Nozzle Design for a Circular Jet . 38 3.1.4 Flow Conditioner and Nozzle Design for an Annular Jet - Confinement Options and Components . 40 3.2 Large-Scale Experimental Loop . 44 v 3.2.1 Large-Scale Loop Components . 44 3.2.2 Flow Conditioner and Nozzle Design for the Annular Jet - Confinement and Components . 46 3.3 Settings of the Small- and the Large-Scale Experimental Loops . 49 3.3.1 Setting the Superficial Liquid Velocity and Gas Void Fraction 49 3.3.2 Photographs of Two-phase Jets . 53 3.4 Measurements of Void Fraction and Slip Ratio Distribution . 54 3.4.1 Instrumentation for Void Fraction Measurements . 54 3.4.2 Void Fraction and Slip Ratio Measurement Procedures . 57 3.5 Measurements of Shock Attenuation . 60 3.5.1 Instrumentation . 60 3.5.2 Shock Attenuation Test Procedures . 64 IV EXPERIMENTAL RESULTS AND DISCUSSION . 65 4.1 Interfacial Structures . 65 4.1.1 Flow Visualizations . 65 4.1.2 Bubble Size Measurement . 73 4.1.3 Correlations of the Sauter Diameter . 79 4.2 Void Fraction and Slip Ratio Distribution Measurements . 83 4.2.1 Void Fraction . 83 4.2.2 Slip Ratio . 91 4.2.3 Comparison with Empirical Correlations . 94 4.3 Shock Attenuation with Two-Phase Annular Jets . 101 4.3.1 Repeatability between Experiments . 101 4.3.2 Effects of Void Fraction and Pulser Input Energy on Shock Attenuation . 107 4.3.3 Scale Effects . 109 V NUMERICAL MODELING . 112 5.1 Single-Phase Jet Modeling . 112 5.1.1 Problem Description and Meshing . 112 vi 5.1.2 Conclusions on Single-Phase Jet Modeling . 114 5.2 Two-Phase Jet Modeling . 118 5.2.1 Two-Phase Modeling in F LUENT r . 118 5.2.2 Parametric Analysis and Conclusions on Two-Phase Jet Mod- eling . 119 VI CONCLUSIONS AND RECOMMENDATIONS . 122 6.1 Conclusions . 123 6.1.1 Interfacial Structures . 123 6.1.2 Void Fractions and Slip Ratio Distribution Measurements . 125 6.1.3 Shock Attenuation with Two-Phase Annular Jets . 127 6.1.4 Numerical Modeling . 129 6.2 Contributions . 130 6.3 Recommendations . 132 APPENDIX A FLOW VISUALIZATION . 134 APPENDIX B BUBBLE.M MAT LABr PROGRAM LISTING . 140 APPENDIX C BUBBLE DIAMETER DENSITIES AND FITTED NORMAL DISTRIBUTIONS . 142 APPENDIX D EXPERIMENTAL VALUES OF VOID FRACTION AND SLIP RATIO . 154 APPENDIX E PRESSURE HISTORY DATA FOR SHOCK ATTENUATION EXPERIMENTS . 165 APPENDIX F ERROR ANALYSIS . 229 APPENDIX G MODELING IN F LUENT r . 239 REFERENCES . 283 vii LIST OF TABLES 3.1 Detailed list of the small-scale experimental loop components . 34 3.2 Detailed list of flow conditioner and nozzle sections for the planar jet 36 3.3 Detailed list of flow conditioner components for the planar jet . 37 3.4 Detailed list of flow conditioner and nozzle sections for the circular jet 39 3.5 Detailed list of flow conditioner components for the circular jet . 39 3.6 Detailed list of flow conditioner and nozzle sections for the small an- nular jet . 42 3.7 Detailed list of flow conditioner components for the small annular jet 42 3.8 Detailed list of the small-scale experimental loop components . 42 3.9 Detailed list of the large-scale experimental loop components . 48 3.10 Detailed list of flow conditioner and nozzle sections for the small an- nular jet . 50 3.11 Detailed list of flow conditioner components for the small annular jet 50 3.12 Detailed list of the ORTEC radiation instruments . 56 3.13 Settings of the ORTEC radiation instruments . 58 3.14 Detailed list of pressure transducers and their characteristics . 61 4.1 Detailed list of flow visualization experiments for planar, circular, and annular jets . 65 4.2 Detailed list of test conditions for void fraction and slip ratio distribu- tion measurements . 84 4.3 Ratios of αjet(x = 15.9 cm) over αjet(x = 2.9 cm) for 2 m/s ≤ jl,e≤ 4 m/s and 1% ≤ αe ≤ 5% in the case of the planar jet . 91 4.4 Values recommended for C0, a, b, and c in the proposed correlation (Equation 4.48), respectively for the planar and the circular jets . 101 4.5 Detailed list of test conditions for small-scale annular jet experiments 104 4.6 Detailed list of test conditions for large-scale annular jet experiments 110 5.1 Detailed list of the boundary conditions and their parameters . 114 E.1 Table example for data related to small-scale annular jet experiments conducted with unconfined shocks . 166 viii E.2 Detailed list of pressure pulse characteristics for Test #1 of Table 4.5 167 E.3 Detailed list of pressure pulse characteristics for Test #2 of Table 4.5 167 E.4 Detailed list of pressure pulse characteristics for Test #3 of Table 4.5 168 E.5 Detailed list of pressure pulse characteristics for Test #4 of Table 4.5 168 E.6 Detailed list of pressure pulse characteristics for Test #5 of Table 4.5 169 E.7 Detailed list of pressure pulse characteristics for Test #6 of Table 4.5 169 E.8 Table example for data related to small-scale annular jet experiments conducted with radially-confined shocks . 171 E.9 Detailed list of pressure pulse characteristics for Test #7 of Table 4.5 171 E.10 Detailed list of pressure pulse characteristics for Test #8 of Table 4.5 172 E.11 Detailed list of pressure pulse characteristics for Test #9 of Table 4.5 173 E.12 Detailed list of pressure pulse characteristics for Test #10 of Table 4.5 174 E.13 Detailed list of pressure pulse characteristics for Test #11 of Table 4.5 175 E.14 Detailed list of pressure pulse characteristics for Test #12 of Table 4.5 176 E.15 Detailed list of pressure pulse characteristics for Test #13 of Table 4.5 177 E.16 Detailed list of pressure pulse characteristics for Test #14 of Table 4.5 178 E.17 Detailed list of pressure pulse characteristics for Test #15 of Table 4.5 179 E.18 Detailed list of pressure pulse characteristics for Test #16 of Table 4.5 180 E.19 Table example for data related to small-scale annular jet experiments conducted with radially- and axially-confined shocks . 182 E.20 Detailed list of pressure pulse characteristics for Test #19 of Table 4.5 182 E.21 Detailed list of pressure pulse characteristics for Test #21 of Table 4.5 184 E.22 Detailed list of pressure pulse characteristics for Test #22 of Table 4.5 186 E.23 Detailed list of pressure pulse characteristics for Test #23 of Table 4.5 188 E.24 Detailed list of pressure pulse characteristics for Test #24 of Table 4.5 190 E.25 Detailed list of pressure pulse characteristics for Test #25 of Table 4.5 191 E.26 Detailed list of pressure pulse characteristics for Test #26 of Table 4.5 193 E.27 Detailed list of pressure pulse characteristics for Test #27 of Table 4.5 195 E.28 Detailed list of pressure pulse characteristics for Test #28