CFD Analysis and Design Optimization of Flapping Wing Flows Martin Alexander Jones North Carolina A&T State University A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department: Mechanical Engineering Major: Mechanical Engineering Co-Advisor: Dr. Kunigal Shivakumar Co-Advisor: Dr. Nail Yamaleev Greensboro, North Carolina 2013 i School of Graduate Studies North Carolina Agricultural and Technical State University This is to certify that the Doctoral Dissertation of Martin Alexander Jones has met the dissertation requirements of North Carolina Agricultural and Technical State University Greensboro, North Carolina 2013 Approved by: Kunigal Shivakumar Nail Yamaleev Co-Advisor Co-Advisor Sanjiv Sarin D ean, The Graduate School Eric Nielsen Arturo Fernandez Committee Member Committee Member Samuel Owusu-Ofori Julius Harp Department Chair Graduate School Representative Sanjiv Sarin Dean, The Graduate School ii © Copyright by Martin Alexander Jones 2013 iii Biographical Sketch Martin Jones received his B.S. in Physics with a minor in Mathematics and a M.S. in Nuclear Physics from North Carolina A&T State University in the summer of 2007 and 2009, respectively. This work concludes efforts towards a Ph.D. degree in Mechanical Engineering at NC A&T State University on Computational Fluid Dynamics (CFD) analysis and Design Optimization of flapping-wing flows that occur at low Reynolds numbers using CFD. He has performed CFD analysis and design optimization of unsteady turbulent flows using Fully Unstructured Navier – Stokes 3D (FUN3D) solver developed by NASA Langley Research Center. To highlight some of his research, in 2006, he was awarded a summer fellowship from the Leadership Alliance to work with Professors Callan and Bialek at Princeton University. There he learned about techniques in Computational Biology and Biophysics to discover binding sites of proteins in what was thought to be the “junk DNA” regions of the genome of several yeast species in the Saccharomyces genus. During his tenure as a masters graduate student, he did much of his work at Thomas Jefferson National Laboratory where he helped build, install, and do analysis on one detector in a complex of electronic and particle detection equipment for the SANE (Spin Asymmetries on the Nucleon Experiment) experiment in Hall – C at JLab. In the summer of 2011, he did a sojourn at NASA Langley Research Center in Hampton, VA. There he did CFD analysis on a UAV (Unmanned Aerial Vehicle) called KAHU as a part of the Configuration Aerodynamics Branch under the tutelage of Sally Viken. He was invited by his current advisor, Dr. Nail Yamaleev, to study CFD in 2009. This experience has added to his understanding of numerical methods greatly. iv Dedication To my Father, Counselor, and Comforter + To my parents + To my mentors _________________________________ = v Acknowledgements This is for all the teachers in my life. To my Mother, Father, and Sister: So many lessons I’ve learned, you taught me to seek greatness, and to love God. I attribute almost everything I am to you guys, thanks. Never to forget my extended family: my Grandparents, of who I remember teaching me being Grandma Jones and Mommybee: thanks to you! For the teachers in my later years: A few of you have stood out from public school, especially my violin teacher, Ms. Barbee. I’m sad you couldn’t teach us just a few more years until I graduated from high school. And the man that showed us a Physics video that changed my life forever, also my swim coach!: Coach Griffin. And to the teachers in my undergraduate years: All the experiences I had in all that I went through, thanks to Dr. Bililign, for broadening my horizons, Dr. Danagoulian and his wife, you have both touched my heart, Dr. Sandin (Maybe one day my family will have a Jones Para- docs!), Dr. James, just for you and your wonderful style, Dr. Gasparian, for your seriousness regarding dedication to physics, Dr. Kebede, thanks for the talks, Doc Lock, thanks for the camaraderie, my thesis advisor, Dr. Ahmidouch, for your kindness, and Dr. Levy, for heartwarming dedication to my well-being. And to my graduate teachers: My Doctoral Committee, Dr. Shivakumar, Dr. Yamaleev, Dr. Nielsen, and Dr. Fernandez, thank you for all your guidance and presence on the committee. To my other doctoral teachers: Dr. Sundaresan, Dr. Kabadi, Dr. Kizito, Dr. Antonio, Dr. Ferguson, for your support and experience during my stay. To my formal mentors: Dr. Shivakumar and Dr. Yamaleev, both of your guidance and understanding have known no bounds, and it has been my pleasure working with you in the vi student/mentor capacity to transfer confidence, respect, and friendship. I look forward to future collaboration in the future. And to my informal mentors: It was my dream to be like the famous physicists of old and live a life of discovery like them. I have that now. (Or it’s a process.) I spent a lot of time learning physics and math from you, Bob. My time spent with you was precious. You saw me wake up into enlightenment, and you taught me how to listen, like you said, a major problem with our culture today. I knew you like a Grandpa, one that I never had as an adult. You are famous in your own right and are a true American scholar. And to my mentor: Dr. Levy (And Dr. Michelle!). I was so enthusiastic about taking your Physics class that first time around and somehow that grew into a lasting relationship because I guess we both love solving problems so much, even if we sometimes want to solve problems like the minimum number of times it takes to weigh 50 doughnuts with a scale balance when one weighs less than the others! I haven’t figured that one out yet. You have helped me when I was at my worst, going far beyond the duties of just an ordinary teacher. You let me work with you on a problem for my very first paper. I have received more than I could ever have imagined from you and Academia and I look forward to the future. I also don’t want to forget the NASA CAS and CCMR staff and student colleagues for all your encouragement and help. I love all of you and wish the best on you all. Thanks. Martin A. Jones vii Table of Contents List of Figures .............................................................................................................................x List of Tables .......................................................................................................................... xiii Key to Symbols or Abbreviations .............................................................................................xiv Abstract ......................................................................................................................................2 CHAPTER 1 Introduction ...........................................................................................................3 1.1 Unsteady Physics Mechanisms Involved in Insect Flight ....................................................4 1.1.1 Insect flight kinematics. .................................................................................................5 1.1.2 Unsteady Mechanisms. ...................................................................................................7 1.2 Model Selection. ................................................................................................................9 1.3 Objectives of the Research ............................................................................................... 10 1.4 Scope of the Dissertation ................................................................................................. 10 1.5 Philosophy Used in this Dissertation ................................................................................ 11 CHAPTER 2 Governing Navier-Stokes Equations and Numerical Scheme................................ 14 2.1 Introduction and Theory................................................................................................... 14 2.2 Second-Order Node-Centered Finite Volume Scheme ...................................................... 16 2.3 Moving Grids .................................................................................................................. 17 2.4 Geometric Conservation Law (GCL). .............................................................................. 18 2.5 Second-order Backward Difference (BDF2) Scheme ....................................................... 19 2.6 Spalart-Allmaras Turbulence Model ................................................................................ 20 2.7 Low-Mach Preconditioner ............................................................................................... 21 viii CHAPTER 3 CFD Analysis of Flapping-Wing Flows ............................................................... 23 3.1 Introduction ..................................................................................................................... 23 3.1.1 Literature survey. ......................................................................................................... 23 3.1.2 Validation of FUN3D code........................................................................................... 26 3.2 Three-Dimensional Simulations ....................................................................................... 29 3.2.1 Wing kinematics. ......................................................................................................... 29 3.2.2 Computational grid....................................................................................................... 30 3.2.3 Grid refinement study. .................................................................................................. 31 3.2.4 Reynolds number sensitivity......................................................................................... 32 3.2.5 Simulation of gust pulse. .............................................................................................. 33 3.3 Results ............................................................................................................................. 34 3.3.1 Frontal gust. ................................................................................................................. 34 3.3.2 Downward gust. ........................................................................................................... 38 3.3.3 Side gust. ..................................................................................................................... 41 3.4 Discussion ....................................................................................................................... 46 CHAPTER 4 Adjoint-based Optimization of Flapping–Wing Flows ......................................... 50 4.1 Introduction ..................................................................................................................... 50 4.2 Governing Equations and Numerical Method ................................................................... 52 4.3 Wing Kinematics and Associated Design Variables ......................................................... 53 4.4 Shape Parameterization .................................................................................................... 54 ix 4.5 Time-Dependent Adjoint-Based Optimization Methodology ............................................ 57 4.6 Numerical Results ............................................................................................................ 59 4.7 Shape, Kinematics, and Shape/Kinematics Cases ............................................................. 62 4.7.1 Shape optimization. ...................................................................................................... 62 4.7.2 Kinematics optimization. .............................................................................................. 66 4.7.3 Combined Kinematics and Shape Optimization. ........................................................... 70 4.8 Validation of optimization results .................................................................................... 75 4.9 Discussion ....................................................................................................................... 76 CHAPTER 5 Concluding Remarks and Future Research ........................................................... 79 5.1 Concluding Remarks ........................................................................................................ 79 5.1.1 Wind gust analysis. ...................................................................................................... 79 5.1.2 Adjoint-based optimization. ......................................................................................... 80 5.2 Future Research ............................................................................................................... 81 References ................................................................................................................................ 84