A COMPUTATIONAL FLUID DYNAMICS STUDY OF THE SMALLEST FLYING INSECTS Shannon Kathleen Jones A dissertation submitted to the faculty at the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Curriculum of Bioinformatics and Computational Biology. Chapel Hill 2016 Approved by: Laura Miller Tyson Hedrick Gregory Forest William Kier Jan Prins ©2016 Shannon Kathleen Jones ALL RIGHTS RESERVED ii ABSTRACT Shannon Kathleen Jones: A Computational Fluid Dynamics Study of the Smallest Flying Insects (Under the direction of Laura Miller and Tyson Hedrick) The flight of insects has fascinated scientists for centuries, and a large body of work has focused on understanding the intricacies of the aerodynamics of these organisms. Most of this work has focused on the flight of insects ranging in size from a fruit fly to a hawkmoth. The smallest flying insects, however, are ten times smaller than a fruit fly, and much less is known about their wing kinematics and aerodynamics. These insects fly at Reynolds numbers on the order of 10, and at this scale relative viscous forces are much greater than they are for larger insects. Consequently, these small insects must overcome significant aerodynamic challenges in order to propel themselves. The main goal of this dissertation is to better understand the challenges of flying at low Reynolds numbers and to investigate possible mechanisms to overcome those challenges. I used the immersed boundary method to solve for the fluid flow around insect wings in both two- and three-dimensions. In Chapter 3, I use a two-dimensional model to explore theoretically whether small insects could “swim” through the air using a drag-based stroke mechanism to generate vertical force. Chapter 4 investigates the aerodynamic role of bristled wings, especially engaged in wing-wing interactions. And finally, Chapter 5 introduces a three-dimensional revolving wing which is used to explore the forces and flow structures generated at low Reynolds numbers. iii Overall, the results suggest that there are drastic differences in the aerodynamics of flight at the scale of the smallest flying insects, which makes their flight more challenging, compared to larger insects. As the Reynolds number decreases, drag increases and the lift-to-drag ratio decreases significantly. Chapter 3 reveals that neither lift- nor drag-based vertical force generation mechanisms are very efficient at the range of the smallest flying insects. Chapter 4 demonstrates that bristled wings could reduce the force required to fling the wings apart during clap and fling while still maintaining lift during translation. And Chapter 5 shows that both the leading edge vortex and trailing edge vortex remain attached to the wing and spanwise flow decreases as the Reynolds number is lowered. iv To my parents. v ACKNOWLEDGEMENTS I am eternally grateful to my family and friends. I would especially like to thank my parents for their continued support and assistance over the years, but especially recently for being such wonderful grandparents. My brother, Christopher, has come to my rescue during more than one inconvenient computer failure. My husband, Chris, has been a constant source of love and support all these years. And my dear little Oliver has helped me maintain perspective and remember what is most important. I’d also like to thank Becky for our long walks and chats. My current and former lab mates have been wonderful friends and colleagues: Austin Baird, Nick Battista, Jeremy Greeter, Christy Hamlet, Alex Hoover, Julia Samson, Arvind Santhanakrishan, Dwight Springthorpe, Christopher Strickland and Lindsay Waldrop. You all have provided much needed support, feedback, and friendship. Alex’s advice for using IBAMR was incredibly valuable for the work presented in this dissertation. I would also like to thank Ryan Laurenza, Carol Knight, Young Yun and Daniel Goldfarb for their assistance on projects in the Miller lab, including some of the work presented here. Thank you to my committee members: Greg Forest, Bill Kier and Jan Prins for positive and constructive conversations about my research and career guidance. I am grateful to have such kind and supportive scientists help me along the way. I would also like to thank Boyce Griffith for making IBAMR freely available. I’d also like to express my gratitude for the financial support I received during my graduate years. My graduate work was partially funded by a UNC Merit Assistantship, a vi National Science Foundation Graduate Research Fellowship (NSF GRFP Grant No. DGE- 1144081), and a graduate fellowship from SAMSI. And last, but not least, I’d like to thank my advisors, Laura Miller and Ty Hedrick. In addition to being a brilliant scientist, Ty is always available to chat and provide his assistance. I was shocked when he asked me to present my research project at a conference just 2 months into my lab rotation with him, but I’m glad he encouraged me to push beyond my comfort zone. I’m also incredibly grateful for his support and advice as I welcomed a little one into my family. And of course, I’d like to express my deepest appreciation and gratitude to Laura for her guidance, patience, and caring. She has been a terrific advisor and friend, and she provided an excellent atmosphere for doing research. I am amazingly fortunate to have found an advisor who cares so much about her students, not just as scientists, but as individuals. I have been inspired by her kindness and selflessness on more occasions than I can count. Without her patience and support over these last few years, I would never have been able to finish my dissertation. vii TABLE OF CONTENTS LIST OF TABLES ......................................................................................................................... xi LIST OF FIGURES ...................................................................................................................... xii CHAPTER 1: INTRODUCTION ....................................................................................................1 1.1 The smallest flying insects. ................................................................................................... 1 1.2 It’s difficult to be small (or life at lower Reynolds numbers). .............................................. 3 1.3 Aerodynamics of the smallest flying insects. ........................................................................ 5 1.3.1 Previous work in small insect flight. .............................................................................. 5 1.3.2 Lift vs. drag..................................................................................................................... 8 1.3.3 Bristled wings. .............................................................................................................. 10 1.4 Computational work in small insects. ................................................................................. 13 1.4.1 Previous computational studies in small insect aerodynamics. .................................... 13 1.4.2 Three-dimensional studies of the smallest flying insects. ............................................ 15 1.5 Concluding remarks. ........................................................................................................... 16 CHAPTER 2: METHODS .............................................................................................................17 2.1 Numerical Method............................................................................................................... 17 2.1.1 Immersed Boundary Method. ....................................................................................... 17 2.1.2 IBFE Method ................................................................................................................ 24 2.2 Software .............................................................................................................................. 25 2.2.1 IBAMR ......................................................................................................................... 25 2.2.2 Mesh generation ........................................................................................................... 28 2.2.3 Fluid visualization ........................................................................................................ 28 viii 2.2.4 Force analysis ............................................................................................................... 28 CHAPTER 3: LIFT VS DRAG BASED MECHANISMS FOR VERTICAL FORCE PRODUCTION IN THE SMALLEST FLYING INSECTS.......................29 3.1 Introduction ......................................................................................................................... 29 3.2 Methods ............................................................................................................................... 30 3.2.1 Prescribed wing kinematics. ......................................................................................... 30 3.2.2 Numerical method. ....................................................................................................... 32 3.2.3 Grid convergence study. ............................................................................................... 34 3.2.4 Comparison to existing numerical data. ....................................................................... 36 3.3 Results ................................................................................................................................