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Investigation of Drag Coefficient and Virtual Mass Coefficient on Rising Ellipsoidal Bubbles

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Investigation of Drag Coefficient and Virtual Mass Coefficient on Rising Ellipsoidal Bubbles AN ABSTRACT OF THE THESIS OF Alexander M. Dueñas for the degree of Master of Science in Nuclear Engineering presented on December 5, 2019. Title: Investigation of Drag Coefficient and Virtual Mass Coefficient on Rising Ellipsoidal Bubbles Abstract approved: _____________________________________________________________________ Qiao Wu Wade R. Marcum Accurately describing drag and virtual mass forces in two-phase flows is crucial for high fidelity modeling of nuclear thermal hydraulic safety systems. This study compares existing drag coefficient, CD, correlations commonly used in computational fluid dynamics (CFD) applications for air bubbles to experimental data collected for ellipsoidal air bubbles of varying diameter. This study also measured the virtual mass coefficient on a cylinder rod using a method that considers viscous and wake effects. This experiment used velocity field measurements obtained with particle image velocimetry (PIV). An experimental flow loop has been built to inject air bubbles of varying diameter into an optically clear acrylic test section and had the capability to use a cylinder rod perpendicular to flow. A rigorous uncertainty analysis is presented for measured values which provided insight for improvements for future experimental studies. These experiments resulted in total, form, and skin drag coefficients to be directly measured with the nominal trend of increasing form drag for increasing bubble diameter experimentally confirmed. The virtual mass coefficient analysis demonstrated a method applicable for steady state conditions. This method was capable of retrieving the potential flow solution when the predicted drag work from the wake was removed and identified experimental setups useful for characterizing the influence of wake dynamics on virtual mass. ©Copyright by Alexander M. Dueñas December 5, 2019 All Rights Reserved Investigation of Drag Coefficient and Virtual Mass Coefficient on Rising Ellipsoidal Bubbles by Alexander M. Dueñas A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Presented December 5, 2019 Commencement June 2020 Master of Science thesis of Alexander M. Dueñas presented on December 5, 2019 APPROVED: Co-Major Professor, representing Nuclear Engineering Co-Major Professor, representing Nuclear Engineering Head of the School of Nuclear Science and Engineering Dean of the Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request. Alexander M. Dueñas, Author ACKNOWLEDGEMENTS I would like to deeply thank my advisors Dr. Qiao Wu and Dr. Wade Marcum for their continual support, challenging myself to be the best that I can, the opportunity to study under them and be a part of their research groups. Acknowledgements must be given to Isaiah Wieland whose collaboration was vital for the construction of our experimental facility. Without his help I could not have collected my data, and debugging issues would have taken so much longer. I also want to thank Musa Moussaoui for his exceptional patience and walking through concepts with me. Chris Nighbert is also recognized and thanked for his efforts to lay the ground work for this project and experimental facility. Additionally, I would like to thank Nick Swango for always willing to help, his invaluable lessons about pipe fitting, and continually reminding me of common sense. I would like to offer special thanks to Dr. Carl Stoots, who is no longer with us, for being a wonderful person and mentor. He is deeply missed. I want to thank my best friend Ari Foley for her always great advice, fantastic humor, and for continually raising the bar on how amazing plots can look. Lastly, I would like to thank my parents David and Joanne Dueñas, my cool older brother Kevin Dueñas, my grandmother Roberta Lowry, and my aunt Beth Berenson for their constant support, encouragement, and love. TABLE OF CONTENTS Section Page 1 Introduction ................................................................................................................. 1 1.1 Motivation ............................................................................................................ 1 1.2 Purpose ................................................................................................................. 2 1.3 Objectives ............................................................................................................. 2 1.4 Document Overview ............................................................................................ 3 2 Survey of Literature .................................................................................................... 4 2.1 Two-Phase Drag ................................................................................................... 4 2.2 Virtual Mass ....................................................................................................... 11 2.3 Two-Phase Experimental Techniques ................................................................ 16 2.4 Summary ............................................................................................................ 21 3 Experimental Facility ................................................................................................ 22 3.1 Facility Description ............................................................................................ 23 3.2 Instrumentation................................................................................................... 23 3.3 Particle Image Velocimetry System ................................................................... 25 3.4 Bubble Injection System .................................................................................... 26 4 Methodology ............................................................................................................. 29 4.1 Drag Coefficient ................................................................................................. 31 4.2 Virtual Mass Coefficient .................................................................................... 35 4.3 Sources of Error ................................................................................................. 39 4.4 Uncertainty Analysis .......................................................................................... 40 5 Results & Discussion ................................................................................................ 43 5.1 Drag Coefficient ................................................................................................. 53 5.2 Virtual Mass Coefficient .................................................................................... 59 6 Conclusions ............................................................................................................... 72 6.1 Significance of Work ......................................................................................... 72 6.2 Assumptions and Limitations ............................................................................. 73 6.3 Observations ....................................................................................................... 74 6.4 Future Work ....................................................................................................... 74 References ......................................................................................................................... 76 Nomenclature .................................................................................................................... 80 Appendix A: Uncertainty Analysis ................................................................................... 82 Drag Coefficient Uncertainty Propagation: .................................................................. 82 Total Drag/Buoyancy Force Uncertainty Propagation: ................................................ 83 Form Drag Uncertainty Propagation: ........................................................................... 83 Skin Drag Uncertainty Propagation: ............................................................................. 86 Area Uncertainty Propagation: ..................................................................................... 87 TABLE OF CONTENTS (CONTINUED) Page Diameter Uncertainty Propagation for V ≥ 0.1 [mL]: .............................................. 87 Tate’s Law Uncertainty Propagation for V < 0.1 [mL]: ........................................... 87 Velocity Uncertainty Propagation: ............................................................................... 88 Pressure Uncertainty Propagation: ................................................................................ 89 Virtual Mass Coefficient Uncertainty Propagation: ..................................................... 93 Reynolds Number Uncertainty Propagation: ................................................................ 95 Appendix B: Potential Flow Kinetic Energy Proof .......................................................... 96 Relative Kinetic Energy ................................................................................................ 96 Relative Velocity .......................................................................................................... 99 LIST OF FIGURES Figure Page Figure 1: Haberman and Morton measured drag coefficients for various liquids [4] .......
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