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Development of an Experiment for Investigating DEVELOPMENT OF AN EXPERIMENT FOR INVESTIGATING THE MAGNETOHYDRODYNAMIC RICHTMYER–MESHKOV INSTABILITY ____________________________________________________________________________________________________________ A Dissertation presented to the Faculty of the Graduate School at the University of Missouri ____________________________________________________________________________________________________________ In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy ____________________________________________________________________________________________________________ by ROY C. ALLEN IV ____________________________________________________________________________________________________________ Dr. Jacob A. McFarland, Dissertation Supervisor JULY 2019 © COPYRIGHT BY ROY C. ALLEN IV 2019 ALL RIGHTS RESERVED The undersigned, appointed by the dean of the Graduate School, have examined the dissertation entitled DEVELOPMENT OF AN EXPERIMENT FOR INVESTIGATING THE MAGNETOHYDRODYNAMIC RICHTMYER–MESHKOV INSTABILITY presented by Roy C. Allen IV, a candidate for the degree of Doctor of Philosophy, and hereby certify that, in their opinion, it is worthy of acceptance. Approved by: Chair of Committee, Dr. Jacob A. McFarland ______________________________ College of Engineering - Department of Mechanical & Aerospace Engineering University of Missouri – Columbia Committee Members, Dr. Gary L. Solbrekken _______________________________ College of Engineering - Department of Mechanical & Aerospace Engineering University of Missouri – Columbia Dr. Robert A. Winholtz _______________________________ College of Engineering - Department of Mechanical & Aerospace Engineering University of Missouri – Columbia Dr. Randy D. Curry __________________________________ College of Engineering - Department of Electrical Engineering & Computer Science University of Missouri – Columbia Dr. Karl D. Hammond ________________________________ College of Engineering - Department of Chemical Engineering University of Missouri - Columbia Date Approved: [MAY 8, 2019] DEDICATION To my late Uncle Cecil W. Dinan who was a surviving combat veteran of the D-Day Landing at Omaha Beach, World War II, and one of the finest people I have ever had the pleasure of knowing. To my second cousin Lynn Exposito who is a surviving “Tunnel Rat” combat veteran of the Vietnam War. I think about your phenomenal courage and heroism daily. To my friend and thesis advisor, the late Steve R. Nagel, former NASA astronaut and Space Shuttle Commander. –“It really is rocket science” To my Uncle Richard L. Wollschlager, for showing me how to design and build anything I set my mind to. I never would have thought race cars, houses, and sailboats would turn into a supersonic shock tube, a 25,000° F plasma torch, and a magnetic field capable of suppressing magnetohydrodynamic instability. Most important, to my wife, Colleen, and my parents, Roy and Gail. Your relentless love and support in every sense has allowed me to achieve all of this, even if you still don’t understand what I am talking about. ACKNOWLEDGMENTS A decade-long academic endeavor is not sustained or successfully completed without significant help and support along the way. I would like to acknowledge and thank as many people as possible for their generosity and support while I completed mine. I honestly feel blessed to have been provided the opportunity to pursue this dissertation and Ph.D. degree and could not have done so without them. First, I thank my advisor, Dr. Jacob A. McFarland, for giving me a chance as a Ph.D. research assistant and believing that I really could build anything; for shaping me into the experimentalist I have become, for having faith and trusting me when things were still not fully understood even the day before crucial deadlines, and for challenging me to the fullest extent to be the best scientist I could be. It is through his guidance and mentoring that I have embarked on the most significant project I have ever had the opportunity and pleasure to work on. I thank Dr. Paul M. Rutherford for encouraging and preparing me as a high school student at Summit Technology Academy to embark on this collegiate engineering journey. I also thank Dr. Kyle Anderson for his tremendous teaching efforts and for putting up with me in as an International Baccalaureate student in high school. My lab mates have played such a vital role in my success at the Missouri Fluid Mixing and Shock Tube Lab (FMSTL) and I could not have done this without them. John Middlebrooks has been such a crucial member of the FMSTL and the extra set of hands necessary to complete the experiments presented in this dissertation. In particular I thank ii Wolfgang Black, my good friend and partner in crime. Wolfgang has always helped me work through not only the problems and perils of this dissertation but through coursework and the emotional stress induced by high-level research. I am truly grateful we got to spend all ten years at Mizzou together. I thank Dr. Randy D. Curry and the research personnel at the Center for Physical and Pulse Power Electronics, who have provided me with what amounts to a blank check through the loaning of their research equipment, lab space, time, ideas, and effort to complete the various tasks required to finish this project. Generating atmospheric plasma on an extremely limited budget, for example, would otherwise have been nearly impossible without their generous contributions. One of the most critical and difficult parts of this project could not have been able to be completed without the help of Dr. Karl Hammond. He has taught me a great deal about statistical thermodynamics and helped me understand the necessary components of the theory developed for the 2D Monochromatic Imaging Method used to characterize the plasma torch for my dissertation. He is one of the smartest and most dedicated professors I know; someone that truly cares about the success of students both inside and outside his lab. I can’t express enough how much I appreciate all the time and assistance Dr. Hammond has provided to me. I also thank Dr. Gary L. Solbrekken, Dr. Robert A. Winholtz, Dr. Craig A. Kluever, and all my professors for teaching me and preparing me, both inside and outside the classroom. Your efforts will culminate in success and are appreciated by me with the utmost gratitude. iii At Mizzou, many staff members helped me with obtaining and manufacturing the materials and parts needed to complete the experiments performed and presented in this dissertation. Marilyn Nevels is such an excellent administrative assistant and the MU College of Engineering wouldn’t run so successfully without her working tirelessly to do anything and everything to help students such as myself. Ghassan Al Bahhash and Matthew Marciniak have helped me machine, construct, and fix nearly every component of the plasma torch. Their efforts are unmatched when it comes to helping not only me but any and all other students in any way they can. They’re always a positive influence and they make machining and fixing anything a blast. I sincerely thank my family for the love and support they have provided to me all my life and for helping me become the person I am today. My Aunt Barb, who has always been like a second mother to me, for providing me with my first engineering job after earning my Bachelor’s Degree, which allowed me to do some pretty amazing things. The opportunity she provided ultimately inspired me to go back to school and learn how to do more. Uncle Richard, who was my first boss when I started working at age 12, for teaching me how to build virtually anything, how to do it right, and to “be in control of my environment.” My sister Katie, who is the most gifted and dedicated elementary school teacher I know and one of the best people I know. I can definitively say that I can perform at the highest levels of research because she is such a phenomenal little sister who inspired me greatly as we were growing up. I owe more to her than she knows. Additionally, I thank my grandparents, Buck & Wilma Allen and Keith & Ginger Goeglein, for all their support of my academic goals and for naming me their favorite (#1) grandchild! iv Of course, the people I owe everything in this world to are my parents. I can’t think of a time when they were unable or unavailable to help me in whatever way was necessary throughout my life. They have provided the financial backing for everything from my undergraduate degree to completing six more years of school without having to stress about whether I could afford a meal or gas to get back to the lab. I have inherited everything from their analytical and managerial skills to their humor and humility. No matter what I am interested in or what the cost, they never waiver or hesitate to support me in any and every way they can. I only hope that now that I am completing this chapter of my life, I can begin to repay them. Finally, I thank my best friend, my biggest fan, and the most important person to me in life, my wonderful wife Colleen. What a phenomenal rollercoaster ride it has been. All the late nights and early mornings of wondering where I was and then remembering you are married to a Ph.D. candidate studying magnetohydrodynamic instabilities were very tough, to say the least. I appreciate so much how Colleen chose to forgo date nights and weekend trips and so much more so that I could continue to work, and she still had a hot meal ready for me when I finally did come home. She has kept me grounded,
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