Effects of Acoustic and Fluid Dynamic Interactions in Resonators: Applications in Thermoacoustic Refrigeration A Thesis Submitted to the Faculty of Drexel University by Dion Savio Antao in partial fulfillment of the requirements for the degree of Doctor of Philosophy June 2013 ii © Copyright 2013 Dion Savio Antao. All Rights Reserved iii If you can trust yourself when all men doubt you, But make allowance for their doubting too; If you can meet with triumph and disaster And treat those two imposters just the same; Or watch the things you gave your life to broken, And stoop and build 'em up with wornout tools; Rudyard Kipling, If, ln. 2, 6 and 8 Omni autem cui multum datum est multum quaeretur ab eo et cui commendaverunt multum plus petent ab eo LVKE 12:48 iv Dedications I would like to first dedicate this dissertation to my role models, my biggest critics and my most fervent supporters, my mum and dad. Next I would like to dedicate this dissertation to my sister; may it motivate her to achieve her own goals and ambitions in life and reach for the stars. Finally, I would like to dedicate this dissertation to the people of India; the taxpayers whose contributions helped provide for my education (from kindergarten to university) and that of so many others. v Acknowledgements At this point, it is important to thank the people and recognise and acknowledge the contributions that made this dissertation possible. First I must thank my dad and mum for their constant love and support and for teaching me (in both words and deeds) that hard work and perseverance are the most important keys to success. I would also like to thank my sister Noelle for her love and support and Vera and Uday Kunte for welcoming me into their family and making their home my home away from home. This dissertation would not be possible without the guidance of my adviser Prof. Bakhtier Farouk. His constant drive to do great research and publish has always inspired (and will always inspire) me to push myself a bit harder and a bit further. I also would like to thank my committee members (Prof. N. Cernansky, Prof. A. Lau, Prof. S. Bose, Prof. A. Clyne, Prof. J. Tangorra and Prof. M. McCarthy) for their useful suggestions that helped improve my dissertation research. I must acknowledge the NSF grant (CBET-0853959) and CFIC (Troy, NY) for supporting the research work reported in this dissertation. I am grateful for the financial support received from the department of Mechanical Engineering and Mechanics (MEM) in the form of teaching assistantships, the Freshman Design Education Fellowship and the Frederic O. Hess Assistantship. I am very grateful to the machinists in the Drexel Machine Shop (Mark Shiber, Paul Velez, Earl Boling and Scott Eichmann) for their guidance which resulted in the two fabricated experimental setups reported in this dissertation. I would like to acknowledge the help and guidance of Dr. Ray Radebaugh (National Institute of Standards and Technology (NIST), Boulder, CO) and Dr. Greg vi Swift (Los Alamos National Laboratory (LANL), Albuquerque, NM), both of whose suggestions guided my initial experiments in cryogenics and thermoacoustics. I would also like to acknowledge Dr. Phil Spoor, Dr. John Corey (both Chart Industries) and Prof. Bart Lipkens (Western New England University) for their help during various stages of this dissertation research. I would also like to thank the undergraduate students in the MEM department who worked with me during my dissertation research, especially Michael Loftus. Finally, I am thankful to the MEM department and Drexel University for providing an excellent graduate education and an invaluable learning experience. I would like to thank my colleagues and friends in the MEM department and the Combustion and Energy group, especially Nusair Hasan, Ersin Sayar and Viral Chhasatia for their camaraderie and always being there to discuss new ideas. vii Table of Contents List of Tables ................................................................................................................... xvi List of Figures ................................................................................................................ xviii Abstract ......................................................................................................................... xxxii Chapter 1 : Introduction ................................................................................................. 1 1.1. Background ........................................................................................................... 1 1.1.1. Acoustics ....................................................................................................... 1 1.1.2. Thermoacoustics ........................................................................................... 6 1.1.3. Cryogenics .................................................................................................... 7 1.2. Dissertation statement ......................................................................................... 10 1.3. Motivation for the dissertation research ............................................................. 11 1.3.1. Development of accurate multi-dimensional PTR models ......................... 11 1.3.2. Investigation of wave-shaping for cryocooler performance enhancement . 14 1.4. Objectives of the dissertation research ............................................................... 16 1.5. Overview of the dissertation ............................................................................... 18 Chapter 2 : Background and Literature Review ........................................................ 21 2.1. Acoustic resonators: consonant and dissonant systems ...................................... 21 2.1.1. Consonant cylindrical resonators ................................................................ 21 2.1.1.1. Limitations of consonant cylindrical resonators ................................ 22 viii 2.1.2. Dissonant wave-shaped resonators ............................................................. 23 2.1.2.1. Experimental and numerical studies of dissonant wave-shaped resonators ........................................................................................................ 24 2.2. Cryogenic refrigeration systems ......................................................................... 27 2.2.1. Dilution refrigeration .................................................................................. 28 2.2.2. Adiabatic demagnetization refrigeration (ADR) ........................................ 29 2.2.3. Sorption refrigeration .................................................................................. 30 2.2.4. Gas cycle refrigeration ................................................................................ 31 2.2.4.1. Recuperative cryocoolers ................................................................... 33 2.2.4.1.1. Joule-Thomson cryocoolers ...................................................... 34 2.2.4.1.2. Brayton cryocoolers .................................................................. 35 2.2.4.2. Regenerative refrigerators .................................................................. 37 2.2.4.2.1. Gifford McMahon and Stirling type cryocoolers...................... 38 2.2.4.2.2. Pulse tube refrigerators/cryocoolers ......................................... 41 2.3. Modeling of PTR systems .................................................................................. 47 2.4. Acoustic streaming and streaming in PTRs ........................................................ 49 2.5. Identification of research areas ........................................................................... 51 Chapter 3 : Numerical Studies of Transport Phenomena in Acoustic Resonators .. 55 3.1. Introduction ......................................................................................................... 55 3.2. Geometry of the consonant and dissonant resonators ......................................... 56 ix 3.3. Numerical model of the acoustic resonator ........................................................ 58 3.3.1. Governing equations ................................................................................... 58 3.3.2. Numerical scheme ....................................................................................... 61 3.4. Numerical model validation with past computational studies ............................ 62 3.4.1. Initial conditions for the numerical model .................................................. 64 3.4.2. Boundary conditions for the numerical model ............................................ 64 3.5. Validation results: Temporal pressure variation ................................................. 65 3.6. Acoustic streaming in a cylinder resonator ........................................................ 69 3.7. Numerical studies of cone shaped resonators: Results and discussion ............... 74 3.7.1. Initial and boundary conditions for the numerical model ........................... 76 3.7.1.1. Initial conditions ................................................................................ 76 3.7.1.2. Boundary conditions .......................................................................... 77 4.7.2. Results: Un-steady processes in the dissonant cone resonator .................. 77 3.7.3. Results: Cycle-steady behavior in the dissonant cone resonator ............... 87 3.8. Non-linear phenomena in dissonant cone resonators ........................................