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Experiments and Simulations on the Incompressible, Rayleigh-Taylor Instability with Small Wavelength Initial Perturbations

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Experiments and Simulations on the Incompressible, Rayleigh-Taylor Instability with Small Wavelength Initial Perturbations Experiments and Simulations on the Incompressible, Rayleigh-Taylor Instability with Small Wavelength Initial Perturbations Item Type text; Electronic Dissertation Authors Roberts, Michael Scott Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 06/10/2021 00:55:18 Link to Item http://hdl.handle.net/10150/265355 EXPERIMENTS AND SIMULATIONS ON THE INCOMPRESSIBLE, RAYLEIGH-TAYLOR INSTABILITY WITH SMALL WAVELENGTH INITIAL PERTURBATIONS by Michael Scott Roberts A Dissertation Submitted to the Faculty of the AEROSPACE AND MECHANICAL ENGINEERING DEPARTMENT In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY WITH A MAJOR IN MECHANICAL ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA 2012 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dis- sertation prepared by Michael Scott Roberts entitled Experiments and simulations on the incompressible, Rayleigh-Taylor insta- bility with small wavelength initial perturbations and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. Date: November 7 2012 Edward Kerschen Date: November 7 2012 Hermann Fasel Date: November 7 2012 Arthur Gmitro Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: November 7 2012 Dissertation Director: Jeffrey Jacobs 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Michael Scott Roberts 4 ACKNOWLEDGEMENTS The road to my PhD has been a long one, but well worth it. I must of course thank my family for always believing in me. Even when I sometimes doubted myself, they did not. With what they lacked in truly understanding what I was going through in my studies, they made up for in unwavering support. Luckily, I usually have good friends that I am able to talk to about my academic woes and for this I am grateful as well. In recent years Kung Fu class helped me grow as a person and gave me the tools to deal with stressful situations. Although times may become stressful, it is important to live in the moment without overwhelming oneself with what might be or might have been. The words of Si Gong taught me to remain calm even when the river around me becomes turbulent. I have learned a lot over the years and using this knowledge in a way that would help others would be a very noble and satisfying vision for myself. My advisor, Dr. Jacobs, always had meaningful input every step of the way along my journey. While other professors often force their students to fend for themselves, he did not and for this he has earned my complete respect. I am also thankful to Bill Cabot, my mentor while I was at LLNL. He always had insight into solving problems that I would often encounter with my simulations and was willing to assist even after I left LLNL and there was no longer any obligation for him to do so. The people I have worked with through the years were an important part of my research. Many problems would not have been solved without their input and for this I am grateful and humbled. Also, the help with editing this massive document is much appreciated and I would not have been able to finish in the time frame desired without key editors. “We must acknowledge that the key is to be patient and make it to the end” “Knowing others is wisdom, knowing yourself is Enlightenment” -Lao Tzu This research was supported by Lawrence Livermore National Laboratory and by DOE NNSA under its Stewardship Science Academic Alliance program. 5 TABLE OF CONTENTS LISTOFFIGURES ................................ 7 LISTOFTABLES ................................. 10 ABSTRACT .................................... 11 CHAPTER1 INTRODUCTION . .. .. 12 1.1 BackgroundandMotivation . 12 1.2 PreviousResearch............................. 23 1.3 ProposedResearch ............................ 36 1.4 Self-Similarity . 38 CHAPTER 2 EXPERIMENTAL APPARATUSES . 41 2.1 WeightandPulleyDropTower . 41 2.1.1 DropTowerandTestSled . 41 2.1.2 ReleaseMechanism ........................ 44 2.1.3 Acceleration Production . 45 2.1.4 Data Acquisition and Timing . 48 2.2 LinearInductionMotorDropTower. 53 2.2.1 DropTowerandTestSled . 53 2.2.2 ReleaseMechanism ........................ 53 2.2.3 Acceleration Production . 54 2.2.4 Data Acquisition and Timing . 56 2.3 FluidTanks ................................ 57 CHAPTER 3 EXPERIMENTAL LIQUIDS AND IMAGING . 61 3.1 RefractiveIndexMismatch. 62 3.1.1 Liquid Combinations . 62 3.1.2 Mixing Layer Imaging . 67 3.1.3 Mixing Layer Imaging Artifacts . 73 3.2 AbsorptionImagingLiquids . 91 3.3 OtherImagingConcepts . .101 CHAPTER 4 INITIAL PERTURBATIONS . 105 4.1 ForcedInitialPerturbations . .105 4.2 Background Noise Induced Initial Perturbations . 113 4.2.1 BackgroundNoise. .114 6 TABLE OF CONTENTS – Continued CHAPTER 5 NUMERICAL SIMULATIONS . 121 CHAPTER 6 RESULTS AND DISCUSSION . 126 6.1 Experimental Qualitative Results . 126 6.2 Experimental Quantitative Results . 139 6.2.1 Mixing Width and Reynolds Number Plots . 143 6.2.2 GrowthParameterPlots . .145 6.3 Numerical Qualitative Results . 156 6.4 NumericalQuantitativeResults . .159 6.4.1 GrowthParameterPlots . .160 6.5 Comparison ................................167 CHAPTER7 CONCLUSION . .. .. .171 APPENDIX A MATHEMATICAL DERIVATIONS . 174 A.1 Viscous Linear Stability Theory . 174 A.2 ViscousEffects ..............................189 A.3 Parametric Excitation with Viscous Damping . 190 A.4 Uncertainty Analysis and Absorption Analysis . 197 A.5 SphericalCapImplementation . .204 APPENDIX B COMPUTER PROGRAMS . 207 B.1 TankLidSphericalCapG-CodeProgram . .207 B.2 MatlabFFTPolarizationProgram . .207 B.3 Matlab Triangular Tank Beer’s Law Uncertainty Program . 208 B.4 Matlab Gradient Refractive Index Model Program . 211 B.5 Matlab Interfacial Tension Calculation Program . 213 B.5.1 myfun.f ..............................214 B.6 DuffandHarlowSolutionFortranProgram. .214 B.7 JavaImageAnalysisProgram . .220 B.7.1 Main.java .............................220 B.7.2 Excel.java .............................243 B.8 JavaStackEnsembleAverageProgram . .259 REFERENCES...................................264 7 LIST OF FIGURES 1.1 Explanation of buoyancy instability for general fluid particle . 13 1.2 Explan of RTI where the deformed intf displaces a fluid particle . 14 1.3 Rayleigh-Taylor explanation . 16 1.4 Depiction of indirect drive ICF . 18 1.5 RTIinICFcapsule ............................ 19 1.6 Evolution of the Rayleigh-Taylor instability. 21 2.1 WPSystem,largerangeaccelerationoutput . 43 2.2 WPreleasemechanismrendering . 44 2.3 WPsystemaccelerationplot. 46 2.4 Renderings of the Weight and pulley system. 47 2.5 WPtestsledrendering .......................... 47 2.6 Imagingsystemdiagram ......................... 50 2.7 Acomputer generated image ofthe LIM drop tower. 54 2.8 AccelerationplotforLIMsystem . 56 2.9 SolidWorksDrawingofWPTank . 58 2.10 WP, 0.5 Atwood num, miscible unforced exp with small balloons . 59 2.11 WP, 0.5 Atwood num, miscible unforced exp with large balloon . 60 2.12 WP, 0.5 Atwood num, miscible unforced exp with external balloon . 60 3.1 Polarization gated unmatched refractive index images . 70 3.2 Povraymixingregionrendering . 71 3.3 Povray 3D view rendering with mismatched RI . 72 3.4 Miscible, 0.5 Atw num WP exp displaying three regions . 73 3.5 Miscible, 0.5 Atw num LIM exp displaying three regions . 74 3.6 Gradientrefractiveindexmodel . 78 3.7 Sim of parallel light rays of refractive mismatched combination . 79 3.8 Sim of 27 degree light rays of refractive mismatched combination . 80 3.9 Sim of ±14 degree light rays of refractive mismatched combination . 81 ± 3.10 Experimental investigation of mirage effect . 84 3.11 Test displaying obvious mirage effect . 85 3.12 responseofmirageeffectfromstirring. 86 3.13 Three-axis accelerometer measurements on WP system . ... 88 3.14 Possible explanation for three regions . 90 3.15 Triangulartankdepiction . 94 3.16 SoldiWorks triangular tank drawing . 95 8 LIST OF FIGURES – Continued 3.17 Beer’s law verification for experiment using anethole . 96 3.18 Beer’s law contrast comparison plot . 101 3.19 LST heavy liquid nD and isopropyl alcohol nD vs. wavelength . 102 4.1 Non-uniformity of amp from horizontal forcing of small wavelength .107 4.2 Rendering of the vertically constrained
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