ABSTRACT Title of Thesis: UNSTEADY LOW REYNOLDS NUMBER AERODYNAMICS OF A ROTATING WING Degree Candidate: Siddarth Kolluru Venkata Degree and Year: Master of Science, 2012 Thesis directed by: Assistant Professor Anya R. Jones Department of Aerospace Engineering Micro air vehicles (MAVs) are small, unmanned aircraft useful for reconnais- sance. The small size of MAVs presents unique challenges as they operate at low Reynolds numbers O(104), and they share a ight regime with insects rather than conventional aircraft. The low Reynolds number regime is dominated by poor aero- dynamic characteristics such as low lift-to-drag ratios. To overcome this, birds and insects utilize unsteady high lift mechanisms to generate su cient lift. A leading edge vortex (LEV), one of these unsteady lift mechanism, is thought to be responsi- ble for the high lift generated by these natural iers, but the factors which contribute to the formation, stability, and persistence of LEVs are still unclear. The objectives of this study are to: 1) qualitatively understand the formation of the LEV by evaluating the e ect of wing acceleration pro les, wing root geometry, Reynolds number, and unsteady variations of pitch, 2) quantify whether high lift can be sustained at low Reynolds numbers on a rotary wing in continuous revolution, and 3) determine the e ect of wing exibility on the unsteady lift coe cient. Experiments were performed on a rotating wing setup designed to model the translational phase of the insect wing stroke during hover. Experiments were per- formed in a water tank at Reynolds numbers between 5,000 and 25,000, and the ow was investigated using dye ow visualization, as well as lift and drag force measurements. A rigid wing and a simple one degree-of-freedom exible wing were tested. Dye ow visualization on a rotating wing showed the formation of a coherent LEV near the wing root. The LEV became less coherent further outboard, and eventually burst. As the wing continued to rotate, the location where the LEV burst moved inboard. Dye injection within the burst vortex showed the formation of multiple small scale shedding vortices that traveled downstream and formed a region of recirculating ow (i.e., a burst vortex). Parameter variations in this experiment included velocity pro les, acceleration pro les, and Reynolds numbers. High lift and drag coe cient peaks were measured during the acceleration phase of the wing stroke at Reynolds numbers of 15,000 and 25,000. After the initial peak, the coe cients dropped, increased, and eventually attained a \steady- state" intermediate value after 5 chord-lengths of travel, which they maintained for the remainder of the rst revolution. When the wing began the second revolution, both the lift and drag coe cients decreased, and leveled out at a second interme- diate value. Force measurements on a chordwise exible wing revealed lower lift coe cients. For all of the cases tested, high lift was achieved during the accelera- tion phase and rst revolution of the wing stroke, though values dropped during the second revolution. UNSTEADY LOW REYNOLDS NUMBER AERODYNAMICS OF A ROTATING WING by Siddarth Kolluru Venkata Thesis submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial ful llment of the requirements for the degree of Masters of Science 2012 Advisory Committee: Assistant Professor Anya R. Jones, Chairman/Advisor Associate Professor James D. Baeder Associate Professor J. Sean Humbert c Copyright by Siddarth Kolluru Venkata 2012 Dedication To my past, present, and future family. ii Acknowledgments First, I would like to express my deep appreciation for my advisor and mentor, Dr. Anya R. Jones, for her continual guidance and encouragement to look at things from di erent perspectives. Her enthusiasm towards this work always inspired me to give my best in all respects. I would also like to thank the members of my thesis committee Dr. James D. Baeder and Dr. J. Sean Humbert for their contributions to this thesis. Special thanks to Andrew Lind for all the time he spent editing my drafts and critiquing my presentations. I also would like to thank Kristy Schlueter, Mark Glucksman-Glaser, Mac MacFarlane, and Moble Benedict for allowing me to bounce ideas o them, and for all their support throughout my research. I would like to acknowledge Nate Beals, Gino Perrotta, and Bao Zhang for their meticulous machining skills and all the help they provided throughout the experimentation process. Warm thanks to my friends, Matt Collett, Pratik Bhandari, Hunter Nelson, Levi DeVries, Ganesh Raghunath, Teju Jarugumilli, Camden Mamigonian, Elena Shrestha, Yashwant Ganti, Shivaji Medida, Taran Kalra, Mathieu Amiraux, and Shane Boyer who made grad school a blast. Finally, this acknowledgment will not be complete without the mention of my parents and sisters who have always supported me and inspired me to work harder. iii Table of Contents List of Tables vi List of Figures vii 1 Background 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Comparison of MAV Platforms . . . . . . . . . . . . . . . . . 2 1.2 Low Reynolds Number Flight Regime . . . . . . . . . . . . . . . . . . 4 1.3 Flapping Wing Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.1 Avian Versus Insect Flight . . . . . . . . . . . . . . . . . . . . 6 1.3.2 Insect Wing Kinematics . . . . . . . . . . . . . . . . . . . . . 6 1.4 Unsteady Lift Enhancement Mechanisms . . . . . . . . . . . . . . . . 8 1.4.1 Dynamic Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.2 Leading Edge Vortex . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.3 Rotational Circulation . . . . . . . . . . . . . . . . . . . . . . 13 1.4.4 Wake Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4.5 Wing Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Experimental Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.1 Insect like Flapping . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.2 Revolving Models . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5.3 Computational Studies . . . . . . . . . . . . . . . . . . . . . . 29 1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.7 Objective of Present Work . . . . . . . . . . . . . . . . . . . . . . . . 31 1.8 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2 Methodology 33 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Wing Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3.1 Rotation Only . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.3.2 Pitch and Rotation . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4 Test Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.5 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.5.1 Dye Flow Visualization . . . . . . . . . . . . . . . . . . . . . . 51 2.5.2 Force Measurements . . . . . . . . . . . . . . . . . . . . . . . 52 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3 Flow Visualization Results 59 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2 Baseline Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3 Variation of Reynolds Number . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Variation of Velocity Pro les . . . . . . . . . . . . . . . . . . . . . . . 66 3.5 Variation of Wing Root Geometry . . . . . . . . . . . . . . . . . . . . 70 iv 3.6 Flow Structures Post-LEV-Burst . . . . . . . . . . . . . . . . . . . . 74 3.6.1 Variation of Acceleration Pro les . . . . . . . . . . . . . . . . 75 3.6.2 Variation of Angle of Attack . . . . . . . . . . . . . . . . . . . 80 3.7 Pitching and Rotating Wing . . . . . . . . . . . . . . . . . . . . . . . 83 3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4 Force Measurements Results 88 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.2 Baseline Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2.1 Acceleration Phase . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2.2 Constant Velocity Phase . . . . . . . . . . . . . . . . . . . . . 94 4.3 Variation of Velocity Pro les . . . . . . . . . . . . . . . . . . . . . . . 98 4.4 Variation of Acceleration Pro les . . . . . . . . . . . . . . . . . . . . 103 4.5 Variation of Reynolds Number . . . . . . . . . . . . . . . . . . . . . . 108 4.6 Wing Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5 Concluding Remarks 122 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.2 Conclusions of the Study . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2.1 Flow Visualization on the Rotating Wing . . . . . . . . . . . . 123 5.2.2 Flow Visualization on the Pitching-and-Rotating Wing . . . . 124 5.2.3 Force Measurements on the Rotating Wing . . . . . . . . . . . 125 5.3 Remarks for Future Work . . . . . . . . . . . . . . . . . . . . . . . . 126 v List of Tables 2.1 Parameter variations for qualitative tests. . . . . . . . . . . . . . . . . 50 2.2 Parameter variations for quantitative tests. . . . . . . . . . . . . . . . 50 2.3 RMS error for lift and drag force measurements for the rigid wing. . . 55 2.4 RMS error for lift and drag force measurements for the exible wing. 55 4.1 Maximum angular acceleration at Re = 15,000. . . . . . . . . . . . . 98 4.2 Theoretical added mass peak values at Re = 15,000. . . . . . . . . . . 109 4.3 Steady-state lift coe cient average values. . . . . . . . . . . . . . . . 117 4.4 Steady-state drag coe cient average values. . . . . . . . . . . . . . . 117 4.5 Steady-state lift-to-drag ratio averages. . . . . . . . . . . . . . . . . . 120 vi List of Figures 1.1 Black Widow MAV, from Ref [5]. . . . . . . . . . . . . . . . . . . . . 3 1.2 Minimum drag coe cients of di erent airfoils throughout a range of chord Reynolds numbers, from Ref [11]. . . . . . . . . . . . . . . . . . 5 1.3 Insect wing kinematics, from Ref [17]. . . . . . . . . . . . . . . . . . . 7 1.4 Visualization of a helical LEV indicating a strong axial ow, from Ref [22]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Vortex breakdown over a delta wing, from Ref [25]. . . . . . . . . . . 12 1.6 Dickinson?s Robo y setup, from Ref [16]. . . . . . . . . . . . . . . . . 13 1.7 Experimental and numerical lift coe cients for a fruit y wing at a Reynolds number of 136, showing the two lift peaks at the end of the upstroke and the beginning of the downstroke, from Ref [30]. . . . . . 15 1.8 Model system consisting of two rigid elliptical sections connected by a hinge with torsion spring used by Toomey and Eldredge, from Ref [40]. 17 1.9 Force measurements for various exible wings at a Reynolds number of 20,000, from Ref [44]. . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.10 Flow visualization around a female hawkmoth in a wind tunnel, from Ref [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.11 Birch and Dickinson?s setup: a) Fences on the leading edge, b) Fences on the trailing edge, c) Acrylic tip wall. The column on the right shows the presence of vorticity, from Ref [18]. . . . . . . . . . . . . . 24 1.12 Chordwise ow visualization images by Ramasamy and Leishman: d) Start of translational stroke, e) Accelerating wing, f) Midpoint of translational motion, g) Spilled LEV, h) Formation of new LEV, i) Multiple vortices, from Ref [31]. . . . . . . . . . . . . . . . . . . . . . 26 2.1 The pitching and rotating wing setup. . . . . . . . . . . . . . . . . . 34 2.2 The pitching-and-rotating wing on the U-bracket assembly and wing dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3 L-bracket assembly with exible wing and force balance. . . . . . . . 36 2.4 Flexible wing at rest. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 vii 2.5 Top-down view schematic of the rotating-only wing setup. . . . . . . 39 2.6 Rotating wing kinematics for a wing accelerating linearly in time, over 0.25, 0.50, 0.75 and 1.0 chord-length of travel at a three-quarter span Reynolds number of 5,000. . . . . . . . . . . . . . . . . . . . . . 40 2.7 Commanded linear wing kinematics as a function of time for wing accelerating and decelerating over 0.50 chord-length of travel at a three-quarter span Reynolds number of 15,000. Angular velocity is given by black solid lines and acceleration by red dashed lines. The blue dashed-dot line indicates !max. . . . . . . . . . . . . . . . . . . . 41 2.8 Smoothed kinematics G(t) and scaled kinematics (t). . . . . . . . . 42 2.9 Angle of attack as a function of time for a = 50 (red) and a = 100 (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.10 Characteristic times, as de ned by Eldredge et al. [68]. . . . . . . . . 43 2.11 Angular velocity as a function of time for various values of a. . . . . . 45 2.12 Commanded wing kinematics for wing accelerating over 0.50 chord- lengths to a Reynolds number of 15,000. . . . . . . . . . . . . . . . . 47 2.13 Rotating wing kinematics for a wing accelerating over 0.50 chord- length of travel at a three-quarter span Reynolds number of 5,000 for di erent values of a. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.14 Pitching-and rotating wing kinematics. The stroke angle is indi- cated by the dashed-dot green line and the pitch angle by the solid red line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.15 Fast fourier transforms of the lift force for two power supplies. . . . . 53 2.16 Un ltered lift coe cient data is shown in blue, low-pass ltered data is shown in red, and the moving averaged data is shown in green for a rigid wing at a Re = 15,000. . . . . . . . . . . . . . . . . . . . . . . 54 2.17 The lift and drag coe cients are shown in blue for a rigid wing at Re = 15,000, and the upper and lower bounds of the RMS error are shown in red. The wing is accelerating over 0.50 chord-lengths of travel and the velocity pro le is heavily smoothed (a = 30). . . . . . 57 3.1 Dye injection at wing root. Flow visualization for Re = 5,000 near the beginning of the wing stroke. The velocity pro le is linear in time, accelerating over 0.5 chord-lengths of travel. . . . . . . . . . . . . . . 61 viii 3.2 Dye injection at wing root. Flow visualization for Re = 5,000 for three revolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3 Dye injection at wing root. Flow visualization for Re = 10,000 for three revolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4 Comparison of the linear and heavily smoothed (a = 30) velocity pro les. Wing is accelerating over 0.50 chord-lengths of travel at Re = 5,000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.5 Dye injection at wing root. Flow visualization for Re = 5,000 near the beginning of the wing stroke. The velocity pro le is heavily smoothed (a = 30), accelerating over 0.5 chord-lengths of travel. . . . . . . . . . 68 3.6 Comparison of the linear and smoothed velocity pro les at s=c = 1.9. 69 3.7 Closed wing root con guration. . . . . . . . . . . . . . . . . . . . . . 70 3.8 Closed root con guration. Dye injection at wing root. Flow visual- ization for Re = 5,000 near the beginning of the wing stroke. The velocity pro le is linear, accelerating over 0.5 chord-lengths of travel. 71 3.9 Closed root con guration. Dye injection at wing root. Flow visual- ization for Re = 5,000. . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.10 Dye ow visualization of a rotating wing at a xed angle of attack of 45 deg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.11 S-shaped ow structure observed in all three acceleration cases soon after the end of the wing?s acceleration phase. d1s=c 0:26, d2s=c 0:31, and d3s=c 0:43. . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.12 Comparison of ow structures. . . . . . . . . . . . . . . . . . . . . . . 80 3.13 Dye ow visualization of a rotating wing at a xed angle of attack of 15 deg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.14 Dye ow visualization of a pitching and rotating wing. . . . . . . . . 84 4.1 Lift and drag coe cients for a rotating wing at a xed angle of attack of 45 deg accelerating over 0.50 chord-lengths of travel at a three- quarter span reference Reynolds number of 15,000. . . . . . . . . . . 90 4.2 Heavily smoothed velocity pro le: angular velocity with respect to s=c at a Reynolds number of 15,000. . . . . . . . . . . . . . . . . . . 91 ix 4.3 The acceleration phase for a rotating wing at a xed angle of attack of 45 deg accelerating over 0.50 chord-lengths of travel at a three-quarter span reference Reynolds number of 15,000. . . . . . . . . . . . . . . . 92 4.4 A at plate at a xed angle of attack can be modeled as a cylinder with a diameter d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.5 Constant velocity phase lift and drag coe cients for a rigid rotating wing at a xed angle of attack of 45 deg accelerating over 0.50 chord- lengths of travel at a three-quarter span reference Reynolds number of 15,000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.6 Lift-to-drag ratio versus s/c for the rotating wing at Re = 15,000 accelerated over 0.50 chord-lengths of travel. . . . . . . . . . . . . . . 97 4.7 Comparison of three di erent velocity pro les for a rotating wing at Re = 15,000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.8 Comparison of the acceleration phase for three di erent velocity pro- les for a rotating wing at Re = 15,000. . . . . . . . . . . . . . . . . 101 4.9 Acceleration and jerk with respect to time for the two smoothed pro- les, heavily smoothed (blue) and lightly smoothed (red) for a wing accelerating over 0.50 chord-lengths of travel. . . . . . . . . . . . . . . 102 4.10 Raw and ltered lift coe cients for three di erent velocity pro les for a rotating wing at Re = 15,000. . . . . . . . . . . . . . . . . . . . 104 4.11 Constant velocity phase lift and drag coe cients. Comparison of three di erent sa=c for a rotating wing at Re = 15,000. . . . . . . . . 106 4.12 Comparison of the acceleration phase for three di erent accelerations for a rotating wing at Re = 15,000. The dashed blue, red and green lines indicate the transition from acceleration to constant velocity for the respective sa=c values. . . . . . . . . . . . . . . . . . . . . . . . . 107 4.13 Raw lift coe cients for the acceleration portion of the wing stroke. . 108 4.14 Lift and drag coe cients. Comparison of di erent Reynolds numbers for a rotating wing accelerating over 0.50 chord-lengths of travel. . . . 110 4.15 Steady-state exible wing positions. . . . . . . . . . . . . . . . . . . . 112 4.16 Coe cient of lift and drag for a rigid and half chord exible wing at Re = 15,000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 x 4.17 Comparison of the acceleration phase for the coe cient of lift and drag for a rigid and half chord exible wing at Re = 15,000. . . . . . 114 4.18 Coe cient of lift and drag for a rigid and half chord exible wing at Re = 25,000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.19 Lift-to-drag ratio for the rigid and exible wing. . . . . . . . . . . . . 119 xi NOMENCLATURE Angle of attack, deg Wing stroke angle, deg Kinematic viscosity, m2/s ! Angular velocity, rad/s b Span, m c Wing chord, m CL Lift coe cient CD Drag coe cient D Drag, N k Reduced frequency, !c=Uref L Lift, N L=D Lift-to-drag ratio Re Reynolds number, Urefc= s Distance traveled at 3/4 span, m sa Distance at 3/4 span over which wing accelerates, m t Time, s Uref Reference velocity, m/s CFD Computational Fluid Dynamics LE Leading Edge LEV Leading Edge Vortex MAV Micro Air Vehicle PIV Particle Image Velocimetry TE Trailing Edge xii Chapter 1 Background 1.1 Introduction Over the last decade, advances in micro-technologies such as miniature cam- eras, infrared sensors, and hazardous substance detectors have increased interest in highly portable platforms [1]. One such platform is the micro air vehicle (MAV). Research into MAVs can be traced back to 1997 when the Defense Advanced Re- search Projects Agency (DARPA) started a program to develop and demonstrate a new type of small air vehicle. This program was intended to inspire the invention of small vehicles capable of sustained hover with a maximum dimension of only 15 cm. The goal of this program was to develop and test emerging technologies that could evolve into a mission-capable ight system for military surveillance and reconnaissance applications. A typical MAV has a cruise ight speed near 15 m/s and operates at Reynolds numbers O(100,000) or lower, sharing a ight regime with birds and insects rather than conventional aircraft [2]. While the de nition of a MAV has now grown to encompass a variety of small vehicles, enormous scienti c interest continues to drive the development of bird and insect scale autonomous MAVs. Since MAVs are pri- marily of interest for reconnaissance missions, both endurance and maneuverability are critical. Keenon and Grasmeyer [3, 4] have argued that very small \insect-sized" 1 MAVs could give the modern military signi cant operational advantages, despite the currently lower-than-desirable levels of performance of most hover-capable MAVs. Many scenarios are extremely challenging, requiring the vehicle to operate outdoors in gusty environments as well as within con ned spaces such as buildings or caves. Possible missions suggested for MAVs are squad-level combat, battle damage assessment, air or artillery spotting, sensor dispersal, communications relay, and detection of mines and hazardous substances. MAVs could also be equipped with small jamming systems to confuse radar or communications equipment at very short range. MAVs capable of hovering and vertical ight could be used to scout buildings for urban combat and counter-terrorist operations. A MAV could also be included in an airman?s survival kit, used by a downed pilot to keep track of approaching enemy search parties, or relay communications to search and rescue units. To suc- cessfully execute these missions, MAVs should be capable of e cient hover and also be extremely maneuverable. At large scales, extreme maneuverability is achieved through use of rotary wings, but at MAV-size scales, a bio-inspired apping wing ight may be desirable. To this end, the present work has examined, under con- trolled laboratory conditions, some of the unsteady ow phenomenon responsible for lift generation on a apping wing in hover. 1.1.1 Comparison of MAV Platforms Many xed-wing MAV designs, like the Black Widow MAV (Figure 1.1), have been successfully developed and ight tested. They are e cient and have an en- 2 Fig. 1.1: Black Widow MAV, from Ref [5]. durance close to 30 minutes [5]. However, these xed-wing vehicles lack the ability to hover, and therefore may have di culty operating in highly constrained environ- ments such as inside buildings or urban areas. Rotary-wing MAVs, on the other hand, have the capability to hover, but their e ciency is signi cantly lower com- pared to their xed-wing counterparts [6]. Furthermore rotary-wing MAVs have limited maneuverability and are less e cient when compared to their larger scale counterparts [7]. The square-cube law is a basic geometric sizing rule stating that wing area is proportional to the square of the characteristic dimensions [8]. This law leads to structural weight becoming a dominant design driver as aircraft get larger. This is illustrated by most birds not being able to hover, while hummingbirds and fruit ies have tremendous vertical climb and hover capabilities [4]. This means that geomet- ric scaling of xed wings and helicopters may not be ideally suited for operating in 3 this completely di erent aerodynamic regime. Therefore, it is important to investi- gate alternate solutions by drawing inspiration from nature?s iers. As McMasters and Henderson put it, \humans y commercially or recreationally, but animals y professionally" [9]. However, there are two challenges in utilizing the apping wing concept for MAVs: emulating their wing kinematics, and understanding the result- ing complex aerodynamics. 1.2 Low Reynolds Number Flight Regime MAVs operate in the low Reynolds number regime (103 - 105), which, compared with large, manned ight vehicles, have unfavorable aerodynamics characteristics in steady ow, such as high minimum drag coe cients and low lift-to-drag ratios [10]. Figure 1.2 shows that minimum drag coe cients measured for di erent airfoils are signi cantly higher for lower Reynolds numbers. MAVs? small geometric dimensions, however, do result in some favorable scal- ing characteristics, such as reduced stall speed and better structural survivability. When compared to other rotating-wing MAV systems, it is clear that apping wings have thus far achieved relatively low values of hovering e ciencies. However, bio- inspired apping wings may still be a viable option as a hovering MAV platform because of their maneuverability and agility at this scale [12]. 4 Fig. 1.2: Minimum drag coe cients of di erent airfoils throughout a range of chord Reynolds numbers, from Ref [11]. 1.3 Flapping Wing Flight Birds and insects are able to generate lift at angles of attack for which the wings of conventional aircraft are stalled, thus achieving a higher lift coe cient. Therefore, an understanding of natural ight will not only help improve aerodynamics, but ultimately in uence design and enable new, more e cient and capable MAVs. The nature of apping wing ight introduces several levels of complexity, primarily due to the unsteady wing kinematics. These unsteady kinematics can lead to the generation of a large number of unconventional and unsteady ow phenomena, which contribute signi cantly to the resultant forces and moments on the wing. 5 1.3.1 Avian Versus Insect Flight In order to further understand apping wing aerodynamics, it is important to rst understand the di erence between the two main modes of apping ight in nature: insect and avian (bird) ight. Conventional xed-wing aircraft rely on the forward motion relative to the air to produce lift. Biological iers, on the other hand, not only move their wings forward relative to the air, but also ap up and down, plunge, and sweep. Ellington et al. [13] made the general observation that birds typically operate with attached turbulent ow over their wings and keep the ow attached while insects, on the other hand, have sharp leading edges and separated laminar ow over their wings. The di erence in structure and kinematics of bird and insect wings re ect this di erence in the ow around their wings. Birds y in the Reynolds number range of 103 < Re < 105 while insects y in the Reynolds number range of 101 < Re < 103, thus the Reynolds number of the MAV ight dictates which mechanism is to be adopted. The most signi cant and relevant di erence is the ability to hover. While most insects can hover, this capability is restricted to only a few species of birds, such as hummingbirds. 1.3.2 Insect Wing Kinematics Many insects y using a reciprocating wing motion [12]. The wing kinematics of this reciprocating motion feature two translational motions and two rotational motions. The translational motions are called the downstroke and upstroke, where the wing sweeps through the air at a relatively large xed pitch. The two rotational 6 Fig. 1.3: Insect wing kinematics, from Ref [17]. motions are called pronation and supination, where the wing rapidly changes its pitch to reverse the direction of its sweep. Combined, these wing motions result in an overall stroke trajectory in which the wingtip path forms a closed loop and the wings are at a positive angle of attack during both translational motions [14]. Figure 1.3 shows a schematic of a representative apping cycle, which con- tinuously repeats the process of pronation, downstroke, supination, and upstroke [15]. Insects can also tilt the reference plane of apping (the stroke plane), thereby varying the direction of the net aerodynamic forces. During the downstroke and upstroke high-lift is produced, in part, by the formation of a leading edge vortex on the wing [13]. Signi cant lift is also produced during supination and pronation due to rotational circulation and wake capture, a phenomenon that occurs as the wing passes through its own wake created during the previous half-stroke [16]. 7 1.4 Unsteady Lift Enhancement Mechanisms Natural iers utilize unsteady apping mechanisms to generate lift and thrust. Steady and quasi-steady aerodynamic theory, experiments, computations, and mod- eling have not yet fully explained the ability of apping wing iers to generate the required lift to achieve hover and to y forward at the observed speeds [18]. It is therefore necessary to look at unsteady e ects. The unsteadiness of a ow is characterized by the ratio between forward ve- locity and apping velocity, known as the reduced frequency k = ! c Uref (1.1) where ! is the apping frequency, c is the wing chord, and Uref is the reference linear velocity. The reduced frequency determines whether either unsteady or quasi-steady methods can be used. Flow is unsteady if k > 0, but can generally be considered quasi-steady for a reduced frequency 0 < k < 0:03, where unsteady e ects are not very signi cant [12]. For 0:03 < k < 0:1, ow can be considered moderately unsteady, and beyond k = 0.1 ow is considered fully unsteady. k is typically between 1 and 10 for small insects [12]. The unsteady aerodynamics of insects is characterized by a constant apping motion which enables them to hover. Unsteady lift mechanisms are therefore known to be important, but they are not fully understood. In particular, several unsteady lift mechanisms on apping wings have been recognized in previous research (e.g., Ref [16, 13, 19]) and have been examined further during the course of the present research. 8 1.4.1 Dynamic Stall Dynamic stall has been observed on helicopter blades and is known to cause the formation, shedding, and downstream convection of a strong vortex-like disturbance rising from near the leading edge [11]. The concept of dynamic stall centers on the timescale of vortex growth when ow separates from the leading edge. During this process, the uid mechanics of stall are usually very di erent from those obtained on an airfoil under static conditions [20]. Once the airfoil exceeds the static stall angle, lift continues to increase despite ow reversal in the boundary layer. As the angle of attack increases further, ow separates at the leading edge and a vortex forms. This vortex convects over the surface of the airfoil, causing additional lift and so the lift curve slope increases [21]. Once the vortex reaches the trailing edge, the ow is fully separated and there is a sharp drop in lift. The ow does not reattach until the angle of attack is reduced to below the static stall angle. A similar type of ow has been observed on insect like apping wings, resulting in the formation of the leading edge vortex. 1.4.2 Leading Edge Vortex The formation of a LEV has been noted during many types of apping wing motions. When the angle of attack of a wing is greater than the stall angle, the ow separates and rolls up into a vortex. This vortex is known as the leading edge vortex (LEV), and is a result of dynamic stall [22]. In apping wing ight, the presence of LEVs is thought to be essential to delay stall and to augment aerodynamic force 9 production during translation of apping wings. The LEV forms on the upper surface of the wing and can be responsible for signi cantly increasing lift on the wing. Van Den Berg et al. showed that the LEV can supply up to two-thirds of the required lift during the downstroke [22]. A vortex attached to the leading edge of the wing allows the ow outside of the vortex to reattach to the wing. There are two theories to explain this increase in lift, but these are equivalent. The rst, the pressure approach, suggests that the presence of a LEV lowers the local pressure on the upper surface of the wing, thus resulting in an increase in the overall lift [13]. The second, the circulation approach, suggests that the net circulation about the wing is increased due to the presence of the leading edge vortex; the circulation is a measure of the velocity di erence above and below the wing [13]. One of the rst studies to investigate vorticity in apping wing ight was by Maxworthy [23]. He observed that during a wing stroke, a vortex formed at the leading edge which then connected to larger vortices at the wingtip. The vortices remained attached and stable through the entire downstroke, therefore explaining the increased lift that could not be explained by inviscid models. He also described a helical structure of the LEV where signi cant axial ow near the leading edge transported vorticity from the LEV core to the wingtips. In another study, Van Den Berg and Ellington visualized ow around a me- chanical model of the ying hawkmoth, Manduca sexta, and demonstrated a LEV forming at the base of the wing and spiraling outward to join the tip vortices [22]. Near the base of the wing, the vortex diameter was quite small and grew radially 10 Fig. 1.4: Visualization of a helical LEV indicating a strong axial ow, from Ref [22]. along the leading edge until merging with the tip vortex that swept backward. Smoke visualization indicated a coherent helical vortex starting at the base and stretching more than two thirds of the wing before the structure broke down and connected to larger structures near the wingtips. Figure 1.4 shows an increase in LEV size with distance from the root of the wing. Vortices form as the ow separates over the sharp leading edges, and are stabilized by an axial ow along the leading edge. The e ects observed by the above mentioned models are similar to the thin surfaces of certain delta wing aircraft that use axial ow to maintain a stable LEV for lift production [18, 19]. This ow gives the delta wing a high stall angle of attack, which can be exploited for takeo , landing, and maneuvering [24]. The delta wing owes much of the lift that it is able to generate to the vortex which is initiated at the leading edge of the wing. This vortex contains a substantial axial velocity component. At high angles of attack, the vortex on a delta wing breaks down. Figure 1.5 shows the vortex breakdown of two leading edge vortices at a location about two-thirds along their length over the top of the wing. The vortex at the top of the photograph exhibits spiral breakdown, where the diameter of the core 11 increases and the axial velocity component is no longer unidirectional. The vortex at the bottom of the photograph exhibits a bubble-type of vortex breakdown, where the ow becomes chaotic after vortex bursts. When breakdown occurs, the axial velocity component decreases and the pressure increases, the wing loses lift, and the wing stalls [24]. Fig. 1.5: Vortex breakdown over a delta wing, from Ref [25]. LEVs have also been experimentally identi ed and studied on live insects and birds, as well as mechanical models, e.g., Ref [16, 13, 26, 27, 28]. The phenomenon has been further studied numerically using CFD, e.g., Ref [29, 30]. The detailed characteristics of LEVs, including their formation and shedding processes, have been the focus of much recent research, e.g., Ref [18, 31, 32]. Given its ability to augment the lifting performance of a wing, exploiting the aerodynamic bene ts of 12 LEV generation could be critical in the successful design of MAVs. 1.4.3 Rotational Circulation Fig. 1.6: Dickinson?s Robo y setup, from Ref [16]. While wing translation with leading edge vorticity is thought to be the pri- mary source of unsteady aerodynamic force production, rotation of the wing during supination and pronation can contribute signi cant lift as well. In fact, force analy- sis done on Drosphelia kinematics indicated that 35% of total lift production occurs during wing rotation [33]. Dickinson et al. [16] used their ?Robo y? (a dynami- cally scaled robot that consists of six servo-motors and two coaxial arms, shown in Figure 1.6) along with various rotational patterns, to investigate the relationship 13 between kinematics and lift generation. They identi ed two lift force peaks at the end and beginning of each stroke, during pronation and supination. The rst force peak (shown in Figure 1.7) can be explained by rotational circulation. The wing?s own rotation serves as a source of circulation to generate an upward force [16]. This mechanism, rotational circulation, is akin to the Magnus e ect on a spinning base- ball [34]. The surface of the rotating ball pulls air within its boundary layer as it spins, thus serving as a source of circulation. As the ball moves through the air, this circulation will increase the total ow velocity on one side and decrease it on the other. During the rotational phase of an insect wing stroke, the direction and magnitude of this rotational lift force is dependent on the pitch angle variation dur- ing rotation, the direction of free-stream velocity, and the location of the pitch axis [16,35]. 1.4.4 Wake Capture The wing kinematics employed by insects consists of a reciprocating apping motion, so their wake repeatedly moves through the wake generated by the previous strokes. This interaction, known as wake capture, may augment the lift force [36]. Wake capture can produce lift by transfer of uid momentum associated with large scale vortical ow shed from the previous stroke to the wing at the beginning of each half stroke [37]. The wing meets the wake created during the previous stroke after reversing its direction, thus increasing the e ective ow speed surrounding the airfoil, which generates the second force peak (shown in Figure 1.7) as observed 14 first peak second peak Fig. 1.7: Experimental and numerical lift coe cients for a fruit y wing at a Reynolds number of 136, showing the two lift peaks at the end of the upstroke and the beginning of the downstroke, from Ref [30]. 15 by Dickinson et al [16]. The key di erence between wake capture and rotational circulation is that while rotational circulation manifests as a force transient dur- ing rotation, wake capture always occurs after rotation and is re ected as a force transient in the next half stroke. 1.4.5 Wing Flexibility Although research on exible wing aerodynamics has been far less extensive than on rigid wings, membrane airfoils (similar to those observed in nature), are likely to be used on MAV ight vehicles due to their low weight. Even though exible wings add an additional complexity posed by the aeroelasticity, they have been shown to improve performance at high angles of attack through passive shape adaptation [38]. In particular, the stall angle of attack has been shown to increase as much as 20 deg when using a exible wing versus a rigid wing, while maintaining comparable lift-to-drag ratios throughout the range of angle of attack [12]. At pre- stall conditions, rigid and membrane wings demonstrate similar lift characteristics [39]. Natural insect wings have complex elastic structures with variable sti ness along several axes. Adding some structural exibility (as opposed to a rigid wing) to a apping wing has been shown to be bene cial for performance as it allows for the passive control of wing pitch [40]. A two-panel hinged wing serves as a useful model of the passive deformation of an insect wing. A exible wing can be modeled as a rigid anterior section and a rigid posterior portion separated spanwise by a 16 Fig. 1.8: Model system consisting of two rigid elliptical sections connected by a hinge with torsion spring used by Toomey and Eldredge, from Ref [40]. hinge at the mid-chord [41, 42]. This model of a exible wing (refer to Figure 1.8) as a linkage of rigid panels has previously been used in computational, modeling, and experimental work by Eldredge and Toomey [40, 43, 39]. Their wing model consisted of two rigid sections connected by a hinge with a torsion spring (to model the insect wing?s structural sti ness). Both experimental and numerical techniques were used in conjunction to investigate, among other things, the physics behind lift generation on a exible wing. Toomey et al. [43] found that the power needed to ap the wing was reduced for the exible wing compared to the rigid wing, but that at large heave amplitudes the e ectiveness of the exible wing was reduced due to premature detachment of the LEV, reducing lift on the wing. Hui et al. [44] examined various exible wing structures (latex, nylon, and wood) to evaluate their implications on apping wing aerodynamics. He showed 17 that the exible membrane wings were found to have better overall aerodynamic performance (i.e., lift-to-drag ratio) than the rigid wing at an angle of attack of 10 deg. The rigid wing (wood) was found to have better lift production performance for apping ight in general. The latex wing, which was the most exible among the three tested wings, was found to have the best thrust generation performance for apping ight because the apping motion of the rigid wing would induce ad- ditional drag instead of generating lift. The less exible nylon wing, which had the best overall aerodynamic performance, was found to be the worst for apping ight applications. Figure 1.9 shows the measured lift coe cients, drag coe cients, and the lift-to-drag ratio with respect to the orientation angle for the three tested wings by Hui et al. The orientation angle (OA) is the angle of attack of the tested wings with respect to the incoming ows. All three wings were found to have very comparable aerodynamic performances at small orientation angles (OA<10 deg). The exible membrane wings were found to have slightly larger lift and drag co- e cients compared with the rigid wood wing at relatively high orientation angles (OA>10 deg). Kim et al. [45] developed a biomimetic exible apping wing using micro- ber composite actuators and experimentally investigated the aerodynamic performance of the wing under apping and non- apping motions in a wind tunnel. Results showed that the camber due to wing exibility could produce positive e ects (i.e., stall delay, drag reduction, and stabilization of the LEV) on apping wing aerody- namics in the quasi-steady and unsteady regions. Agrawal and Agrawal [46] investigated the bene ts of insect wing exibility on 18 (a) Lift coe cient (b) Drag coe cient (c) Lift-to-drag ratio Fig. 1.9: Force measurements for various exible wings at a Reynolds number of 20,000, from Ref [44]. 19 apping wing aerodynamics based on experiments and numerical simulations. They compared the performance of two synthetic wings: 1) a exible wing based on a bio-inspired design of the hawkmoth (Manduca Sexta) wing, and 2) a rigid wing of similar geometry. The results demonstrated that more thrust was generated by the bio-inspired exible wing compared to the rigid wing in all wing kinematic patterns considered. This agrees with the results of Hui et al. [44]. They emphasized that coupled uid-structure simulations of exible apping wings are required to gain a fundamental understanding of the physics and to guide optimal apping wing MAV designs. 1.5 Experimental Models 1.5.1 Insect like Flapping Experimental and computational investigations of insect-like apping wing motions have shown that the ow structures in the wake of low aspect ratio wings have complex three-dimensional forms, which can be fundamentally di erent from their two-dimensional counterparts. Ellington et al. [47, 48, 49] provides a detailed analysis of wing geometry, kinematics, a discussion on aerodynamic mechanisms, and information on lift and power requirements of natural iers. Ellington con rmed that most hovering animals ap their wings in a horizontal stroke plane and examined the idea that vorticity generated by separation at the edges of the wing could be a lifting mechanism for hovering ight. He speculated that the LEV may be the primary lift generating vortex, and that the induced spanwise ow from root to tip 20 may prevent the LEV from shedding throughout each half stroke. Technological advances during the 1990?s allowed for more advanced experiments to test these hypotheses. In a later study by Ellington [13], three-dimensional ow visualization was performed on an actual hawkmoth apping in a wind tunnel, shown in Figure 1.10. He demonstrated that the LEV remains attached to the surface of wing longer than if ow were purely two-dimensional. Upon performing ow visualization using a robotic model of a apping hawkmoth, Ellington et al. [13] observed signi cant spanwise ow within the LEV core, which he then attributed to a spanwise pressure gradient due to higher velocities of the wing tip. He hypothesized that this spanwise ow drains some of the vorticity of the LEV outboard to the wing tip. This, he postulated, retards the vorticity accumulation in the LEV, as compared to the two- dimensional case. Further tests by Usherwood and Ellington [19] on a mechanical model of a hawkmoth showed a strong LEV during the downstroke and spanwise ow within the LEV core from the wing root to the tip. Near the wing tip, the LEV joined with the tip vortex. It was noted that LEV formation resembled the process of dynamic stall. They also found that the LEV had a helical structure similar to that of a delta wing, and Usherwood et al. hypothesized that the spanwise ow was responsible for this. These results, coupled with the ow visualization done on their robotic apping model of the hawkmoth, provided new insight into hovering ight. Birch and Dickinson [18] used digital particle image velocimetry (DPIV) to measure the velocity eld around a apping robotic model of a fruit y. They found 21 Fig. 1.10: Flow visualization around a female hawkmoth in a wind tunnel, from Ref [13]. 22 only a very small spanwise velocity in the LEV. Additionally, they observed a large tip vortex attached to the wing, which induced spanwise ow behind the LEV, near the wing?s trailing edge, as well as a strong downward ow around the wing. The ow from the previous wing stroke also contributed to this downward ow. Birch and Dickinson hypothesized that this induced downward ow signi cantly lowers the e ective angle of attack of the wing, thus retarding the growth of the LEV and delaying shedding. To further study the e ect of spanwise ow, Birch and Dickinson [18] applied fences and ba es on the upper surface of the wing (as shown in Figure 1.11) to inhibit spanwise ow. They demonstrated that despite decreased spanwise ow, the LEV still did not detach from the wing. These authors emphasized that their results suggested some dependence upon Reynolds number as it a ects the stabil- ity characteristics of the LEV. This hypothesis is di erent from those reported by Ellington [13]. Therefore, there is disagreement over the mechanisms that keep the LEV attached to a wing. In another study, Birch and Dickinson [50] made force measurements on the apping motion of a dynamically scaled fruit y wing at two di erent chord Reynolds number of 120 and 1,400. They found that the wing showed relatively constant force generation during its wing stroke. They suggested this could be due to the presence of a stable LEV. They also noted a higher lift coe cient occurred at higher chord Reynolds numbers. The maximum lift coe cient at a chord Reynolds number of 120 was 1.7, whereas at a chord Reynolds number of 1,400 they found a maximum lift coe cient of 2.1 [50]. 23 Fig. 1.11: Birch and Dickinson?s setup: a) Fences on the leading edge, b) Fences on the trailing edge, c) Acrylic tip wall. The column on the right shows the presence of vorticity, from Ref [18]. 24 More recently, Srygley and Thomas [27] have observed LEVs on butter y wings in free ight at Re = O(103)1 and examined the LEV development in various modes of ight (climb, maneuver, forward ight). During climb, they found that two LEVs formed on the upper surface of the wings. They postulated that in these particular ight modes, the insect required more lift and modi ed its wing kinematics to exploit lift enhancement from the LEVs. During forward ight, however, the LEVs were not observed on the wings. Their research also demonstrated that the LEV generated by the butter y produced a LEV of approximately constant diameter across the wing span, as opposed to the spiral LEV structure seen on the hawkmoth [27]. Extensive ow visualization studies were performed by Singh and Chopra [15] and Ramasamy and Leishman [31] on a MAV scale apping wings at a Reynolds number of 15,500. Their work showed the formation of unstable (i.e., shedding) LEVs. Figure 1.12 shows the LEV shedding process through the downstroke of the wing motion as taken from Ramasamy and Leishman [31]. Additionally, they showed that the shedding of the LEV occurred despite a signi cant spanwise ow on the upper surface of the wing. They noted that the continuous presence of at least one vortex over the wing might help to explain the sustained lift generation shown by apping wings during stationary hovering ight. Wilkins and Knowles [51] showed that for an LEV to be stable, the creation of vorticity at the leading edge must be matched perfectly by the convection and di usion of vorticity into the wake, thus creating a stable equilibrium. Spanwise 1An estimate calculated from the free stream velocity and the known dimensions of the Vanessa atlanta butter y. 25 Fig. 1.12: Chordwise ow visualization images by Ramasamy and Leishman: d) Start of translational stroke, e) Accelerating wing, f) Midpoint of translational mo- tion, g) Spilled LEV, h) Formation of new LEV, i) Multiple vortices, from Ref [31]. ow therefore provides a mechanism that stabilizes the LEV, generating su cient lift. This agrees with what Ellington and Usherwood determined earlier [52]. Sane et al. [53] concluded that axial ow through the LEV core stabilized the LEV at the laminar Reynolds number of insect ight even at large incidence, inde nitely delay- ing stall. At Reynolds numbers less than 100, the three-dimensional ow around a apping wing was remarkably self-stabilizing. At higher Reynolds numbers, the LEV periodically grew and broke away, limiting the mean value of the lift coe cients. Sane attributed this instability to the absence of axial ow. 1.5.2 Revolving Models The propeller-like rotating wing is a popular model of insect-like apping. It was designed to isolate the translational phase of the wing stroke. To date, 26 propeller experiments typically involve rotating a wing at a constant angle of attack in the absence of a free-stream. Usherwood and Ellington experimentally studied revolving hawkmoth wings at Re O(103). Usherwood et al. showed that the lift coe cient was found to decrease as Reynolds number increased from 10,000 and 50,000. He postulated that a weaker LEV formed at higher Reynolds number [19, 54]. Usherwood and Ellington also examined the lift and drag production on rotating wings for a fairly wide range of parameters, including angle of attack, twist, and camber. At an angle of attack around 41 deg, they showed that wing lift coe cient can reach as high as 1.75 if a stable LEV is produced over the wing. At lower Reynolds numbers O(1,000), DeVoria et al. [55] experimentally in- vestigated the three-dimensional vortex ow of low aspect ratio plates executing rotational motions from rest at xed angles of attack. DeVoria employed ow vi- sualization and DPIV to examine the ow structure on a trapezoidal plate and a rectangular plate. For the trapezoidal plate at angle of attack of 90 deg, the ow was found to be dominated by a strong trailing vortex, while the overall ow structure was a symmetrical ring-like vortex. At high speeds, the ring-like vortex was observed to shed before the wing motion ended. DPIV results indicated that this was due to a strong root-to-tip velocity induced by the tip vortices, and a Kelvin-Helmholtz-like instability in the separated shear layer at the tip. For the rectangular plate at a xed angle of attack of 45 deg, ow visualization revealed the presence of a strong spanwise ow and an attached LEV early in the motion, which then burst over the outboard half of the wing. The LEV observed on the wing was spiral-shaped and attached to the wing early in the wing motion. Kelvin-Helmholtz-like instabilities 27 were observed in the shear layer, and he postulated that this contributed to the breakdown of the LEV structure. In another study, Ozen et al. used PIV to characterize the steady-state ow structure on a low aspect ratio rotating plate at xed angles of attack ranging from 30 to 75 degrees in a water tunnel. He observed a stable LEV for a range of Reynolds numbers between 3,600 and 14,500 [56]. Other experiments on a rotating wing model accelerating to similarly high Reynolds numbers focused on the wing startup and revealed the development of an unstable LEV that forms and sheds early in the wing stroke, resulting in high-lift transients. Jones and Babinsky [57, 58, 59] studied the uid dynamics associated with a three-dimensional 2.5% thick waving at plate. The ow development around a waving wing at Re = O(104) was studied using PIV to capture the unsteady ve- locity eld. Vorticity eld computations and a vortex identi cation scheme revealed the structure of the three-dimensional ow- eld, characterized by strong leading edge vortices. A transient high-lift peak approximately 1.5 times the quasi-steady value occurred in the rst chord-length of travel, caused by the formation of a strong attached leading edge vortex. This vortex then separated from the leading edge, re- sulting in a sharp drop in lift. As weaker leading edge vortices continued to form and shed, lift values recovered to an intermediate value. They also reported that the wing kinematics had only a small e ect on the aerodynamic forces produced by the waving wing if the acceleration is su ciently high. 28 1.5.3 Computational Studies In addition to the experimental studies, numerous studies have been conducted using computational uid dynamics (CFD). Computations on apping wings have speci cally examined the aerodynamic characteristics of hawkmoth and fruit y wing shapes. Liu et al. [60] conducted numerical simulations of the ow around a hawkmoth in order to study the unsteady aerodynamics of hovering ight. The LEV and the spiral axial ow during translation in their results are consistent with those reported by Ellington. Shyy and Liu [29] performed CFD on apping wings for a range of Reynolds numbers, and speci cally examined the hawkmoth and fruit y wing geometries used in previous research. They found a much more pronounced spanwise ow through the core of the LEV on the hawkmoth wing compared to the fruit y, which was consistent with previous ndings by Usherwood and Ellington [19]. In their evaluation of the stability of the LEV, the results showed that the fruit y wing maintained a stable LEV throughout its translational stroke, whereas on the hawkmoth model, the LEV was shed during the downstroke. Bush et al. [61] successfully reproduced LEV behavior at low and moderate Reynolds numbers in terms of LEV stability and spanwise ow as observed by Birch and Dickinson [62], using an immersed boundary solver. The computed drag during translational apping, agreed with the experimental data of Sane and Dickinson [63]. In another study, Blondeaux et al. [64] and Dong et al. [65] characterized the features of vortical structures and their interaction in the near-wakes of an 29 elliptical planform undergoing periodic apping motion. They presented a basis for comparison with selected features of the aforementioned force measurements and visualization studies. Taira and Colonius [66] computed the wake structure from various con gurations of impulsively translating plates and characterized the strong interaction between the tip and trailing edge vortex systems. Brunton et al. [67] used the same computational approach used by Taria to de ne the wake structure of a pitching plate. 1.6 Summary MAVs are likely to bene t by mimicking some features of insect ight kine- matics. Although conventional xed wings can perform well in the laminar ow regime, at very low Reynolds numbers, it is possible to generate higher lift forces using a apping wing con guration by exploiting unsteady aerodynamic mecha- nisms. Various lift enhancement mechanisms that are employed by insects were discussed, including LEVs, rotational circulation, and wake capture. Experimental and computational studies on both real and mechanical insects have identi ed the LEV as an important high lift mechanism that accounts for some of the additional lift produced by apping insect wings when compared to xed or rotary wings. However, there remains considerable uncertainty about the factors that control the stability of the LEV. Therefore, understanding the LEV characteristics, such as the formation, persistence and shedding, may be important for the design of a successful MAV. 30 1.7 Objective of Present Work The objectives of the present work are: 1. To qualitatively understand the formation, stability, persistence, and impor- tance of the leading edge vortex in the generation of lift on insect-like apping wings by evaluating the e ect of: Wing acceleration pro les Wing root geometry Reynolds number 2. To characterize the ow structure on a pitching-and-rotating wing and thereby understand the e ect of unsteady variations of pitch on the three-dimensional ow structures. 3. To determine whether LEVs can provide high lift at low Reynolds numbers on a rotary wing in continuous revolution. 4. To quantify the e ect of wing exibility on the lift and drag coe cients on a rotating wing and determine whether there are advantages over a rigid wing. To this end, the work presented in this thesis employs a new three-dimensional model for the insect-like wing stroke, combining both wing rotation and unsteady pitch changes. This setup combines unsteady wing rotation (including starting/stopping, acceleration pro les, and continuous revolution) and unsteady variations in pitch. Dye ow visualization is used to qualitatively understand the evolution of unsteady 31 ow structures on a rotating wing. Force measurements are used to investigate the lift and drag produced on a rotating wing at a xed angle of attack. Finally the ow structures on a pitching-and-rotating wing were qualitatively characterized. 1.8 Outline of Thesis The present work explores the development of the LEV and the role it plays in generating lift on apping wings. The motivation behind MAV development and the fundamentals of apping wing aerodynamics have been discussed in this chap- ter. A review of past research on unsteady lift mechanisms, especially the LEV, and comparisons between rigid and exible wings has also been presented. Chapter 2 gives a comprehensive description of the experimental techniques that were utilized to characterize the LEVs and to measure the aerodynamic forces, including dye ow visualization and force measurements. The fundamental principles, equipment used, and challenges unique to each experimental technique are explained. Chapters 3 and 4 document the results in terms of qualitative ( ow visualization) and quantitative (force measurements) results for rigid and exible wings at di erent Reynolds num- bers, velocity pro les, and acceleration pro les. Chapter 5 concludes the thesis by discussing the signi cance of the ndings and suggesting future experiments towards a better understanding of apping wings for MAV applications. 32 Chapter 2 Methodology 2.1 Overview Dye ow visualization and force measurement experiments were performed to gain new insight into hovering aerodynamics and help understand the complex ow eld generated by a rotating wing. This chapter provides a description of the experimental setups, the equipment used, and the challenges in performing such experiments. 2.2 Experimental Setup Experiments were performed in a 4 ft 4 ft 4 ft (1.2 m 1.2 m 1.2 m) water tank (shown in Figure 2.1) at the Low Reynolds Number Aerodynamics Labora- tory (LRAL) at the University of Maryland, College Park. The target Reynolds number range for these experiments is 5,000 to 25,000, selected to provide data for comparison with results available at Reynolds numbers between 1,000 and 50,000. Water was used as the working uid so that measurable lift and drag forces could be obtained without the need for high rotation speeds. For example, the Reynolds number is de ned as Re = Uref c (2.1) 33 wing bracket assembly tank wall stepper motor & encoder belt drive axis of rotation 4 ft 4 ft 4 ft Fig. 2.1: The pitching and rotating wing setup. where Uref is the local velocity at the three-quarter span reference plane (shown in Figure 2.2(a)), c is the wing chord, and is the kinematic viscosity of the working uid. Rearranging to solve for Uref , Uref = Re c : (2.2) The kinematic viscosity of water is 1.052 10 5 ft2 s 1 and the kinematic viscosity of air is 1.640 10 4 ft2 s 1. Keeping the chord of the wing constant at 0.25 ft (3 in) and a picking reference Reynolds number of 15,000, for water : Uref = 15; 000 1:052 10 5 3 = 0:63 ft s 1 (2.3) for air : Uref = 15; 000 1:640 10 4 3 = 9:84 ft s 1 (2.4) therefore, operating in water allows for approximately 93% slower rotational speeds than air. It is easier to capture ow structures at slower rotational speeds for dye ow 34 (a) U-bracket assembly (b) Wing dimensions Fig. 2.2: The pitching-and-rotating wing on the U-bracket assembly and wing di- mensions. visualization experiments as there is enough time for the dye to ll the structures completely, making them easier to see. Figure 2.1 shows the pitching-and-rotating wing setup. The wing rotation was driven by a stepper motor above water and pitch by a submerged servo motor. Above the tank, an aluminum structure (80/20) supported the rig and stepper motor. A 0.5 in diameter stainless steel rod extended down into the tank and was inserted into a bearing on the tank oor. The top of this rod was connected to a belt drive system consisting of toothed pulleys (1:5), a rubber toothed belt, a stepper motor with a maximum torque of 265 oz-in, a driver, and an encoder to record position data. The stepper motor was controlled via LabVIEW through a NI USB X-Series 6341 DAQ card. The experimental rig was designed such that, depending on the type of testing 35 0.5c 0.5c Force balance Rounded edges Free to pivot about the mid-chord Fig. 2.3: L-bracket assembly with exible wing and force balance. (rotating-only or pitching-and-rotating), the rig can be modi ed to handle either a submersible servo motor for pitch control (Figure 2.2(a)) or a force transducer (Figure 2.3). The submersible servo motor was used to vary the angle of attack of the wing, and the force transducer was used to measure the forces acting on the rotating-only wing. For the pitching-and-rotating wing setup, a Traxxas waterproof servo motor (max torque 84 oz-in) was mounted near the wing root, on a Delrin U- bracket. The motor can drive 45 deg pitch changes about the leading edge via a tygon shaft as shown in Figure 2.2(a). The Delrin U-bracket was then mounted on the long stainless steel shaft. The distance between the wing root and the axis of rotation was 0.65c. A schematic of the setup with dimensions is shown in Figure 2.2(b). For the rotating-only wing setup, a force transducer (discussed further in Section 2.5.2) was mounted near the wing root on a Delrin L-bracket. A rectangular wing with a chord of 3 in and an aspect ratio 2 was machined from a 4.5% thick berglass at plate. The chord of the wing was sized to allow ve chord-lengths of space between the wing tip and the walls of the tank to avoid wall 36 e ects. Tip vortices are typically about one and a half times the chord of the wing [24], therefore a distance of ve chord-lengths was chosen to aviod interference from the walls of the tank. Natural iers employ exible wings, therefore, a \ exible-wing" free-to-pivot about the half chord was also machined from the 4.5% thick berglass at plate. The aspect ratio 2 exible wing shown in Figure 2.3 was hinged at the half chord by a 6 in nylon rod and dismantled chain links. This design was adopted from Eldredge and Medina [39]. However, unlike the wing developed by Eldredge et al., the exible wing used in this experiment was not given structural sti ness by the use of a spring, and the gap between the panels was not covered or lled in (except by the nylon rod). Since the trailing half chord of the exible wing was free-to-pivot, it hung down vertically (at a 90 deg angle of attack) before the wing motion began, as illustrated in Figure 2.4. The anterior portion of the wing was held at a xed angle of attack of 45 deg. Once the wing began rotating, the trailing half of the wing de ected upwards to a \steady-state" position. 2.3 Wing Kinematics Experiments were performed at a local Reynolds number ranging from 5,000 to 25,000 at the three-quarter span reference plane. The stroke angle, , is de ned as the angle through which the wing rotates from rest to the point of interest. It is given by the encoder, which is mounted to the bottom of the stepper motor that drives wing rotation. Figure 2.5 shows the top-down view of the wing rotation in 37 Fig. 2.4: Flexible wing at rest. the tank. The non-dimensional distance traveled at the three-quarter span reference plane is s=c (Equation 2.5), where s is the arc length traveled by the three-quarter span reference plan normalized by c, the wing chord, and is the stroke angle in radians. s c = 2:15 : (2.5) In Equation 2.5, the 2.15c is the distance from the axis of rotation to the three- quarter span reference plan. 2.3.1 Rotation Only The wing was set at a xed angle of attack and accelerated linearly from rest over distances of 0.25, 0.50, 0.75, and 1.0 chord-lengths of travel at the reference plane as shown in Figure 2.6. The distance over which the wing accelerated is de ned as sa and is normalized by the wing chord c. This ratio is expressed as sa=c. The acceleration phase of the wing stroke was programmed using two di erent velocity 38 Fig. 2.5: Top-down view schematic of the rotating-only wing setup. pro les, linear and smoothed. The linear velocity pro le is given by !(t) = !max t1 t (2.6) where !(t) is the angular velocity, !max is the prescribed steady-state rotational velocity to be reached at a time t1, and t is time. t1 is the time over which the wing accelerates from rest to constant angular velocity. !max was determined based on the required three-quarter span Reynolds number (Re3=4), using Uref = rref !max (2.7) where Uref is the reference velocity at the three-quarter span reference plane and rref is the distance from the axis of rotation to the three-quarter span reference plane, equal to 2.15c. Therefore, U3=4 = 2:15 c !max: (2.8) Substituting Equation 2.8 into Equation 2.1, Re3=4 = 2:15 !max c2 : (2.9) 39 0 0.5 1 1.5 2 2.5 3 3.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 t (sec) ? (rad/s ) s a /c = 0.25 s a /c = 0.50 s a /c = 0.75 s a /c = 1.0 (a) Angular velocity as a function of time 0 0.2 0.4 0.6 0.8 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 ? (rad) ? (rad/s ) s a /c = 0.25 s a /c = 0.50 s a /c = 0.75 s a /c = 1.0 (b) Angular velocity as a function of stroke angle Fig. 2.6: Rotating wing kinematics for a wing accelerating linearly in time, over 0.25, 0.50, 0.75 and 1.0 chord-length of travel at a three-quarter span Reynolds number of 5,000. Figure 2.7 shows !max and t1 for a wing with constant acceleration over 0.50 chord- lengths of travel. The abrupt starting and stopping that occurs during the linear velocity pro le can cause vibrations during testing. To mitigate this, the beginning and end of the wing stroke was smoothed as illustrated in Figure 2.12. Moreover, this more closely resembles the kinematics of a natural ier [12]. A hyperbolic cosine function for smoothing apping wing kinematics was orig- inally developed by Eldredge et al. [68] for a pitch-up, hold, and pitch-down kine- matic study. The function smooths the higher derivatives of the motion to minimize acceleration e ects, and was de ned as G(t) = ln cosh(aU1(t t1)=c) cosh(aU1(t t4)=c) cosh(aU1(t t2)=c) cosh(aU1(t t3)=c) (2.10) (t) = max G(t) max(G(t)) (2.11) 40 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 t (sec) ? (rad/s ) 0 0.5 1 1.5 2 2.5 3 d? /dt (rad/ s2 ) ? max t1 (a) Accelerating wing 15.4 15.6 15.8 16 16.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 t (sec) ? (rad/s ) ?3 ?2.5 ?2 ?1.5 ?1 ?0.5 0 d? /dt (rad/ s2 ) (b) Decelerating wing Fig. 2.7: Commanded linear wing kinematics as a function of time for wing accel- erating and decelerating over 0.50 chord-length of travel at a three-quarter span Reynolds number of 15,000. Angular velocity is given by black solid lines and ac- celeration by red dashed lines. The blue dashed-dot line indicates !max. where G(t) smooths the transition from rest to a constant velocity. In the process of smoothing the function, G(t) also changes the scaling, therefore (t) (Equation 2.11) was used to scale the smoothed function (G(t)) to the required angle of attack, as illustrated in Figure 2.8. In Equations 2.10 and 2.11, c is the wing chord, is the angle of attack for the wing as a function of time, max is the maximum angle of attack, and a is a user-de ned value that controls the sharpness of the function. The value of a must be greater than 1 and is typically less than 200. A low value of a (a = 50) results in a very smooth transition, whereas a large value of a (a = 100) results in a sharp transition. Figure 2.9 shows the angle of attack as a function of time for two a values. The time constants t1 through t4 are characteristic times chosen by the user to 41 0 2 4 6 8 10 0 2 4 6 8 10 12 14 16 18 t (sec) ? (rad ) scaled smoothing function ?(t) smoothing function G(t) Fig. 2.8: Smoothed kinematics G(t) and scaled kinematics (t). 0 2 4 6 8 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 t (sec) ? (rad ) t1 t2 t3 t4 Fig. 2.9: Angle of attack as a function of time for a = 50 (red) and a = 100 (blue). 42 t 1 t 4 t 2 t 3 time ? constant velocity phase deceleration phase acceleration phase Fig. 2.10: Characteristic times, as de ned by Eldredge et al. [68]. t the prescribed motion in Eldredge?s equation. t1 is the beginning of the pitch-up motion, t2 is the time at the end of the pitch-up and the beginning of the hold, t3 is the time at the beginning of the pitch-down and the end of the hold, and t4 is the end of the motion. In Figure 2.9, t1 = 2 s, t2 = 3 s, t3 = 7 s, and t4 = 8 s and these times are shown by the vertical black lines. Figure 2.10 is a schematic showing the characteristic times as de ned by El- dredge et al. [68], as well as the three phases of the wing stroke as they relate to the rotating wing: the acceleration phase, the constant velocity phase, and the deceler- ation phase. The three phases are analogous to the phases de ned by Eldredge et al. The accelerating phase is analogous to his pitch-up phase, the constant velocity phase is analogous to his hold phase, and the decelerating phase is analogous to his pitch-down phase. Adjustments were made to Equation 2.10 to apply it to a xed-pitch rotating 43 wing stroke. Here, the modi ed smoothing function is R(t) given in Equation 2.12. H(t) (Equation 2.13) is a scaling function used to scale R(t) such that R(t)max is equal to !max in a manner similar to Equation 2.11. H(t) is stretched using B (Equa- tion 2.14) such that the function ranges from 0 to !max. Finally, !(t) is the angular velocity where !max is the maximum angular velocity, given by Equation 2.15. In rotating wing experiment the wing starts from rest, i.e., t1 = 0, but the smoothing function is not de ned for t1 = 0 since the natural log of hyperbolic cosine is unde ned at zero. Therefore, t1 was arbitrarily set to 30% of t2 and the value of t2 was unchanged. Thus the value of t1 determines the wing?s acceleration1. Increasing the value of t1 while keeping the value of t2 the same reduces the time over which the wing accelerates, which in turn increases the jerk. The new smoothing pro le is a piecewise function for the three phases of the wing stroke: acceleration, constant velocity, and deceleration. Each phase is now explained in detail: 1. Acceleration Region (t1 t t2) In the acceleration phase of the wing stroke, R(t) = ln cosh(aUref (t t1)=c) cosh(aUref (t t2)=c) (2.12) H(t) = !max R(t) max(R(t)) (2.13) B = !max [!max min(H(t))] (2.14) !(t) = B[H(t) min(H(t))] (2.15) 1By setting t1 = 30% of t2 the wing is forced to accelerate from rest to a constant velocity only over 70% of the original time. This increases the value of the wing?s acceleration and therefore the kinematics are not strictly comparable to the linear velocity pro le. This is discussed in further detail in Section 3.4 and Section 4.3. 44 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 t (sec) ? (rad/s ) a = 10 a = 30 a = 80 a = 200 sharper transitions smoother transitions Fig. 2.11: Angular velocity as a function of time for various values of a. where R(t) smooths the transition from accelerating to constant velocity, and H(t) scales R(t) to achieve the required value of !max. B (Equation 2.14) is a stretching parameter used to stretch the scaled smoothing function (Equa- tion 2.13), and !(t) is the wing?s angular velocity as a function of time. In the above equations, Uref is the linear velocity at three-quarter span reference plane on the wing and !max is the maximum angular velocity. a is a user- de ned value that controls the sharpness of the function and has to be greater than 1. The value of a typically ranges from 1 to 200. Past 200 the function does not change much. (This is similar to the sharpness controller de ned by Eldredge et al.). Lower values of a lead to smoother transitions and higher values of a lead to sharper transitions. Figure 2.11 shows the angular velocity as a function of time during the acceleration phase for di erent a values. The value of a was set to either 30 (heavily smoothed) or 75 (lightly smoothed) 45 for all the results discussed in this thesis. Figure 2.13 shows the velocity pro les for the two values of a used. It should be noted that, for these wing kinematics, since the desired wing angular velocity increases with Reynolds number so does the value of the wing?s acceleration. Therefore, the value of the wing?s acceleration depends both on the Reynolds number and the distance over which the wing accelerates from rest to constant angular velocity. 2. Constant Velocity Region (t2 < t < t3) !(t) = !max (2.16) In this region the angular velocity is constant and equal to !max as the wing is not accelerating. The value of !max is determined based on the required three- quarter span Reynolds number and can be found by rearranging Equation 2.9 such that !max = Re3=4 2:15 c2 (2.17) where is the kinematic viscosity of water and c is the wing chord. 3. Deceleration Region (t3 t t4) In order to have a symmetric velocity pro le, it was required that the wing decelerate in the same manner that it accelerates. Therefore, the velocity pro le for the deceleration phase is the velocity pro le from the acceleration phase mirrored and shifted by a value t3. Equations 2.12 to 2.14 remain unchanged and Equation 2.15 becomes !(t) = B[H(t) min(H(t))] (2.18) 46 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 t (sec) ? (rad/s ) 0 1 2 3 4 5 6 7 8 d? /dt (rad/ s2 ) (a) Velocity and acceleration 0 0.1 0.2 0.3 0.4 0.5 0.6 ?300 ?200 ?100 0 100 200 300 t (sec) jerk (rad/ s3 ) 0 1 2 3 4 5 6 7 8 d? /dt (rad/ s2 ) (b) Acceleration and jerk Fig. 2.12: Commanded wing kinematics for wing accelerating over 0.50 chord-lengths to a Reynolds number of 15,000. Figure 2.12 shows the smoothed wing kinematics for a wing accelerating over 0.50 chord-lengths of travel. The angular velocity (!) is shown by the solid black curve, angular acceleration is shown by the dashed red curve, and jerk is shown by the solid blue curve as a function of time. The velocity pro le was heavily smoothed (a = 30). Figure 2.13 compares the two smoothing pro les used. The heavily smoothed (a = 30) curve is shown in solid red, and lightly smoothed curve (a = 75) is shown in dashed blue. 2.3.2 Pitch and Rotation Previous rotary wing experiments have neglected pitch variations [40, 56], but pitch variations can have a substantial e ect on the ow eld and lift production. The unique pitching and rotating model described here was designed to bridge the gap between two current models: transient and quasi-steady revolving wings, and 47 0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 t (sec) ? (rad/s ) (a) Angular velocity as a function of time 0 0.05 0.1 0.15 0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ? (rad) ? (rad/s ) (b) Angular velocity as a function of stroke angle Fig. 2.13: Rotating wing kinematics for a wing accelerating over 0.50 chord-length of travel at a three-quarter span Reynolds number of 5,000 for di erent values of a. pitching and plunging wings. This is achieved by including both propeller-like wing rotation about the root and pitch variations about the leading edge. The wing was driven in both pitch (via the submergible servo motor) and rotation (via the stepper motor) simultaneously. The angle of attack was varied from 0 deg to 45 deg over 1.3 chord-lengths of travel in wing rotation. The commanded wing kinematics are shown schematically in Figure 2.14. The solid red lines indicate wing pitch and the green dashed-dot line indicates wing rotation. The time t1c represents the time required for the three-quarter span reference location of the wing to travel 1.3 chord-lengths, and the wing?s angle of attack to change from 0 deg to 45 deg. Wing rotation was initiated when the angle of attack was at its minimum, = 0 deg. The wing was then linearly accelerated to its maximum rotational velocity over 0.25 chord-lengths of travel. The reduced frequency (a measure of the unsteadiness of the ow, de ned in Section 1.4) of this motion is k = 0:59. Like the 48 Fig. 2.14: Pitching-and rotating wing kinematics. The stroke angle is indicated by the dashed-dot green line and the pitch angle by the solid red line. rotating-only wing, the wing was accelerated to an angular velocity corresponding to a Reynolds number of 5,000, in this case over 0.25 chord-lengths of travel. 2.4 Test Matrix The test matrix is divided into qualitative and quantitative studies. Parame- ters that were varied for the qualitative rotating wing experiment include angle of attack, angular velocity pro le, Reynolds number, wing root geometry (discussed in Section 3.5), and point of dye injection. The experiments described here used the values of these properties given in Table 2.1. Parameters that were varied for the quantitative rotating wing experiments include angular velocity pro le, Reynolds number, and wing exibility. The experiments described here used the values of these properties given in Table 2.2. The parameters that remained unchanged throughout this thesis are: 49 Table 2.1: Parameter variations for qualitative tests. Angle of attack 15 deg, 45 deg, 0 to 45 deg3 3/4 span Reynolds number 5,000, 10,000 Accelerating over 0.25, 0.50, 0.75, 1.0 Velocity pro le linear, heavily smoothed Wing root geometry open root, closed root Point of dye injection half span, wing root Table 2.2: Parameter variations for quantitative tests. 3/4 span Reynolds Number 10,000, 15,000, 25,000 Accelerating over 0.25c, 0.50c, 1.0c Velocity pro le linear, heavily smoothed, lightly smoothed Wing exibility rigid, half chord exible 1. Planform shape and thickness 2. Aspect ratio 2 3. Distance from the axis of rotation to the wing root 2Except for Section 3.5. 3Pitching-and-rotating wing case. 50 2.5 Experimental Methods Qualitative dye ow visualization and quantitative force measurements were performed on a rotating-only and a pitching-and-rotating wing. Each of the methods are described in this section. 2.5.1 Dye Flow Visualization Dye ow visualization was performed to gain a qualitative understanding of the three-dimensional LEV structures that form on a rotating-only and pitching- and-rotating wing. A mixture of 60% blue food coloring, 20% ethanol, and 20% milk was injected into the ow. When mixed correctly, the dye attains a state of neutral buoyancy and neither sinks nor rises in the quiescent water. A stainless steel hypodermic needle was xed along the chord of the upper surface of the wing at the root and half span (in separate experiments), injecting dye normal to the leading edge. The ow rate was controlled using a NE-300 syringe pump. The still images shown here were taken from videos, recorded using a Nikon D7000 (HD video at 23 fps). Illumination was provided by a pair of 1000 W halogen lamps. The dye ow rate was balanced between providing su cient dye to properly visualize the ow structures and preventing an in uence on the ow. The best ow rate was determined by a trial and error process. There was a 10 minute wait time between each test to allow the water to settle. 51 2.5.2 Force Measurements A submersible ATI Nano17i force transducer capable of measuring three force components up to 25 N with a resolution of at least 1/160 N, and three torque components up to 250 N-mm with a resolution of at least 1/32 N-mm was used for all the force measurements. The force transducer was powered by a low-noise power supply by BK Precision (model number: XLN10014). Force data was acquired using a LabVIEW X-Series 6341 DAQ card at a sampling frequency of 10,000 Hz and exported to MATLAB for analysis. Each test case was repeated ve times and the forces were averaged over all runs. The averaged raw force measurements were ltered using a 4th order Butterworth low-pass lter at 30 Hz. Several experiments were performed in order to reduce/improve the signal-to-noise ratio. One of the factors that played a big role in reducing the noise was the power supply used to operate the stepper motor. Figure 2.15 shows the fast fourier transforms (FFT) of the lift force for the two di erent power supplies tested (noisy and low-noise). Peaks that remained the same regardless of the power supply were at frequencies less than 25 Hz. This indicated that the peaks at higher frequencies were a result of the noise in the power supply. Therefore, a 30 Hz cuto frequency was chosen for the lter. The raw and ltered lift coe cient is shown in Figure 2.16. The force measurements collected were reported as wing lift and drag coe - cients. The measured lift is acting on the entire wing, so was integrated along the span to account for the span-varying wing velocity. The lift force on the wing is 52 0 50 100 150 200 250 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Single?Sided Amplitude Spectrum of y(t) Frequency (Hz) |Y(f) | (a) Power supply 1 0 50 100 150 200 250 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Single?Sided Amplitude Spectrum of y(t) Frequency (Hz) |Y(f) | (b) Power supply 2 Fig. 2.15: Fast fourier transforms of the lift force for two power supplies. given by L = Z rt rr CL U2maxc 2 dr (2.19) where the velocity is Umax = !max r (2.20) and rt and rr are the distances between the axis of rotation and wingtip and axis of rotation and root, respectively. Substituting for Umax, L = Z rt rr CL !2maxr 2c 2 dr (2.21) L = CL c!2max 2 Z rt rr r2 dr (2.22) L = CL c!2max 2 r3 3 rt rr (2.23) L = CL c!2max 6 (r3t r 3 r); (2.24) and rearranging to solve for CL, CL = 6L !2maxc(r 3 t r3r) : (2.25) 53 0 2 4 6 8 10 ?2 ?1 0 1 2 3 4 time (sec) C L Raw cL 30Hz filtered cL w/ 0.03 sec moving average Fig. 2.16: Un ltered lift coe cient data is shown in blue, low-pass ltered data is shown in red, and the moving averaged data is shown in green for a rigid wing at a Re = 15,000. Similarly, the drag coe cient is given by CD = 6D !2maxc(r 3 t r3r) (2.26) where L is the lift, D is the drag, is the density of water, !max is the maximum angular velocity, and rt and rr are the distances between the axis of rotation and wingtip and axis of rotation and root, respectively. After the Butterworth lter was applied to remove the electrical noise, a 0.03 second moving average was applied to the ltered data. A plot of the un ltered, ltered, and moving average data for one case (rigid wing at Re = 15,000) is shown in Figure 2.16 as an example. 54 Table 2.3: RMS error for lift and drag force measurements for the rigid wing. Re sa=c Velocity Pro les CL RMS error CD RMS error 10,000 0.50 heavily smoothed 0.91 0.69 15,000 heavily smoothed 0.28 0.49 0.25 lightly smoothed 0.27 0.33 linear 0.46 0.39 heavily smoothed 0.20 0.32 0.50 lightly smoothed 0.29 0.42 linear 0.23 0.32 heavily smoothed 0.40 0.40 1.0 lightly smoothed 0.25 0.30 linear 0.17 0.41 25,000 0.50 heavily smoothed 0.13 0.14 Table 2.4: RMS error for lift and drag force measurements for the exible wing. Re sa=c Velocity Pro le CL RMS error CD RMS error 15,000 0.50 heavily smoothed 0.17 0.27 25,000 0.50 heavily smoothed 0.08 0.08 55 Noise in the force measurements was attributed to several factors, such as vibrations in the experimental rig and electrical signal interference due to the power supply. The force transducer was very sensitive and even picked up vibrations of doors closing, people walking, as well as other equipment being used in the lab. Therefore, it was crucial to acquire data only when surrounding environment was quiet. Another factor that introduced noise was the movement of water in the tank, therefore it was important to wait for at least fteen minutes for the water to settle between tests. The wait time was determined by examining the water and measuring the time it took for the water to settle down completely. To quantify the error in the force transducer measurements, the RMS error was calculated. RMS error is de ned as the square root of the variance and is de ned as RMS error = rPn i=1(raw1;i ltered1;i) 2 n : (2.27) The RMS error for the various cases tested is summarized in Table 2.3 for the rigid wing and in Table 2.4 for the exible wing. Heavily smoothed refers to a = 30, and lightly smoothed refers to a = 75 in the kinematics Equations 2.12 - 2.15. For the Re = 10,000 case, the signal-to-noise ratio is very low and the RMS is much higher than the other cases, therefore, none of the data for this case is shown in the following chapters. An example that demonstrates the bounds of RMS error for lift and drag coe cients for a rigid wing at Re = 15,000 is shown in Figure 2.17. The red curves are the RMS error and imply that 70% of the raw data lie within them. 56 0 2 4 6 8 10 ?2 ?1 0 1 2 3 C L time (sec) (a) Lift coe cient 0 2 4 6 8 10 ?2 ?1 0 1 2 3 C D time (sec) (b) Drag coe cient Fig. 2.17: The lift and drag coe cients are shown in blue for a rigid wing at Re = 15,000, and the upper and lower bounds of the RMS error are shown in red. The wing is accelerating over 0.50 chord-lengths of travel and the velocity pro le is heavily smoothed (a = 30). 2.6 Summary Two experimental setups are described here, the rotating-only wing model and the pitching-and-rotating wing model. The rotational motion is controlled by a stepper motor mounted above the water tank. The stepper motor is computer controlled and can be programmed to perform various kinematics. The rotating wing experiment was designed to model the translational phase of the insect wing stroke during hover with a simple set of kinematics. The wing is started from rest and rotates about the root in a propeller-like manner. A submersible servo motor is used to control the angle of attack. For the rotating-only wing model the wing is xed at a constant angle of attack, whereas for the pitching-and-rotating wing model, the angle of attack was varied from 0 deg to 45 deg. This rig allows 57 for variation of a wide range of parameters including wing root geometry, angle of attack, Reynolds number, acceleration pro les, velocity pro les, and wing exibility. Qualitative analysis was performed using dye ow visualization at the wing root and half span. Lift and drag forces were measured using a six-component submersible force transducer. Flow visualization results on the rotating wing described here are presented in Chapter 3, and the force measurement results are presented in Chapter 4. 58 Chapter 3 Flow Visualization Results 3.1 Overview Dye ow visualization was used to qualitatively study the evolution of unsteady ow structures on the rotating wing. Several parameters including dye injection location, angle of attack, wing root geometry, velocity pro les, acceleration pro les, Reynolds number, and unsteady variations in pitch were varied to gain insight into their in uence on the development of the ow and the leading edge vortex (LEV). Dye ow visualization is a relatively simple and inexpensive method that can be used to gain a qualitative understanding of three-dimensional ow structures. The experiments discussed here were performed on both a rotating wing at a xed angle of attack and a pitching-and-rotating wing. Dye was injected at two locations on the wing, at the wing root and the half span. Dye injection at the wing root revealed the presence of a coherent LEV along the leading edge that burst at some location along the wing span. In a separate set of experiments to get a better understanding of the ow structures post-LEV-burst, dye was injected at the half span location on the wing. Dye injection at the half span revealed the presence of a recirculating region form post-LEV-burst. 59 3.2 Baseline Case The rotating wing was xed at an angle of attack of 45 deg. Figure 3.1 shows chordwise views of the wing at multiple points in the wing stroke at a three-quarter span Reynolds number of 5,000. In each of these images, the wing is rotating from left to right in a tank of quiescent water such that the leading edge of the wing appears near the top of the image and the trailing edge near the bottom. A leading edge vortex (LEV) is observed to form as soon as the wing motion begins. A LEV forms when the ow around the leading edge begins to ow from the bottom of the wing to the top, and does so by curling up at the leading edge, forming a vortex. The presence of spanwise ow is revealed by the motion of the dye from the injection point at the wing root to the wing tip. Figure 3.1 shows four images from early in the wing stroke, illustrating the formation of the LEV and the existence of spanwise ow. (Some dye blobs are also visible, a result of starting the dye injection before the wing motion). The leading edge vortex begins to form almost immediately when the wing begins to rotate, and is already visible by s=c = 0.64 as in Figure 3.1(a). Slightly later in the wing stroke (Figure 3.1(b)), a distinctive LEV is observed. Spanwise ow becomes visible along the leading edge as the dye moves from the wing root towards the wing tip. As the wing continues to rotate, the dye continues to convect through the LEV core due to spanwise ow. In Figure 3.1(d) at s=c = 2.3, a coherent LEV is observed along the leading edge of the wing near the root. This LEV becomes less well-de ned and \bursts" at the quarter span location on the wing (indicated by the black dotted line). 60 (a) s=c = 0.64 (b) s=c = 0.78 (c) s=c = 1.0 (d) s=c = 2.3 Fig. 3.1: Dye injection at wing root. Flow visualization for Re = 5,000 near the beginning of the wing stroke. The velocity pro le is linear in time, accelerating over 0.5 chord-lengths of travel. 61 (a) s=c = 3.9, b1=c = 0.70 (b) s=c = 18.6, b2=c = 0.47 (c) s=c = 32.3, b3=c = 0.30 Fig. 3.2: Dye injection at wing root. Flow visualization for Re = 5,000 for three revolutions. 62 In order to examine the persistence of this LEV structure, the wing was rotated for three revolutions ( = 1,080 deg and s=c = 40.53). Figure 3.2 shows spanwise views of the wing at a xed angle of attack of 45 deg for three revolutions at a Reynolds number of 5,000. A coherent LEV was observed to persist near the wing root for all revolutions. The dye injected at the wing root enters the core of the LEV as it forms and travels through the vortex core towards the wing tip. At some point along the wing span, the LEV becomes less coherent and the line of dye becomes less well-de ned. When this occurs, the vortex is said to have burst (similar to the formation seen on delta wings, as described in Section 1.4.2). Vortex breakdown occurs when a single LEV is unable to contain all the vorticity present in the ow. The burst point moves inboard as the wing continues to rotate. The distance from the wing root to the point where the LEV burst is de ned as b and is then non-dimensionalized by the chord. This ratio is then referred to as bx=c, where x corresponds to the revolution the wing is in. In Figure 3.2(a), the wing is in the rst revolution, corresponding to a s=c= 3.9. Here the vortex preserves its structure and remains coherent for a b1=c = 0.70. As the wing continues to rotate (see Figure 3.2(b) and 3.2(c)), the location at which the vortex bursts moves towards the wing root. This happens because the vorticity increases as the wing continues to rotate for multiple revolutions, and the coherent portion of the LEV is unable to contain the vorticity within itself. The length of the coherent part of the vortex has reduced by 57% of its original length at s=c = 32.3. After the vortex bursts, the ow becomes chaotic and loses the organization it had, though it does retain some circulation. 63 3.3 Variation of Reynolds Number All of the qualitative results described in the previous section were obtained at Re = 5,000. In an e ort to begin to understand how Reynolds number a ects the leading edge vortex, the Reynolds number was increased from 5,000 to 10,000 and the ow visualization is repeated. Figure 3.3 shows the ow visualization images for three revolutions at a three-quarter span Reynolds number of 10,000. A LEV is still present along the leading edge of the wing, but appears lighter in color as the dye di uses more quickly when the wing velocity is increased. Similar to the previous case, a coherent LEV is formed which then bursts at some location along the span. However, at this higher Reynolds number, the LEV appears to burst slightly closer to the root. To avoid confusion from the previous case (at Re = 5,000), the distance from the root to the point of vortex burst is now indicated by e and, similar to the previous case, it is then non-dimensionalized by the wing chord, c. In this case e1=c = 0.55, e2=c = 0.39, and e3=c = 0.28. The length of the coherent part of the LEV is reduced by 49% of its original length at a s=c = 32.2. This reduction in the length of the orderly portion of the LEV is smaller than the Re = 5,000 case. Since the wing is operating at a higher Reynolds number, the vorticity that forms at the leading edge is higher than the Re = 5,000 case. The LEV is unable to contain all the vorticity in a single vortex and then bursts forming several small scale vortex structures. This agrees with the ndings by Lentink and Dickinson [69]. 64 (a) s=c = 3.2, e1=c = 0.55 (b) s=c = 18.5, e2=c = 0.39 (c) s=c = 32.2, e3=c = 0.28 Fig. 3.3: Dye injection at wing root. Flow visualization for Re = 10,000 for three revolutions. 65 0 0.5 1 1.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 time (s) ? (rad/s ) linear smoothed (a) Angular velocity as a function of time 0 0.5 1 1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time (s) d? /dt (rad/ s2 ) linear smoothed (b) Angular acceleration as a function of time Fig. 3.4: Comparison of the linear and heavily smoothed (a = 30) velocity pro les. Wing is accelerating over 0.50 chord-lengths of travel at Re = 5,000. 3.4 Variation of Velocity Pro les Another parameter that was varied in this series of rotating wing experiments was the velocity pro le. As explained earlier in Section 2.3.1, the smoothed velocity pro le has two advantages over the linear pro le: 1) it reduces vibrations that may be caused due to instantaneously starting and stopping the wing motion, and 2) it more closely resembles the kinematics of an insect?s wing stroke. This set of experiments was performed to determine whether smoothing the velocity pro le in uenced the LEV development in any way. For all the cases presented earlier, the wing?s velocity was increased linearly (i.e., with a constant acceleration) from rest to a constant velocity. Before com- paring the ow structures of the linear pro le to that of the smoothed pro le, it is important to compare the acceleration pro les for each case. The wing was ac- 66 celerated over 0.50 chord-lengths of travel with di erent accelerations1. Figure 3.4 shows the two velocity pro les (linear and heavily smoothed) at Re = 5,000. It can be seen that the slope for the smoothed pro le is much steeper than that of the linear pro le. The di erence in acceleration is a result of setting t1 = 30% of t2 (see Section 2.3.1), thus decreasing the time allowed for the wing to reach its constant velocity, and therefore increasing its acceleration. As a result, the acceleration dur- ing the constant acceleration portion of the wing stroke for the linear and smoothed pro le is 0.58 rad/s2 and 0.86 rad/s2 respectively, which resulted in a di erence of approximately 33% between the two cases. Some of the e ects of increasing accel- eration, i.e., larger vortices and faster shedding vortices (discussed in more detail in Section 3.6.1), are therefore expected. Figure 3.5 shows chordwise views of the rigid wing accelerating over 0.50 chord- lengths of travel. As soon as the wing begins to rotate, a LEV begins to form at the leading edge as seen at s=c = 0.19 in Figure 3.5(a). Soon after, the LEV grows and dye can be seen convecting through the core of the LEV. Similar to the other case described in Section 3.2, spanwise ow is observed from the root to the tip of the wing. Finally, at a later time s=c = 1.9 as seen in Figure 3.5(d), a coherent LEV is observed along the leading edge of the wing. This LEV then bursts near the quarter span location on the wing. The basic structure of the ow is the same as discussed previously and shown in Figure 3.1. The one observable di erence between tests with the linear and 1This is true for the linear case, however, for the heavily smoothed case the distance over which the wing accelerates was reduced by 30% of the original distance. 67 (a) s=c = 0.19 (b) s=c = 0.28 (c) s=c = 0.54 (d) s=c = 1.9 Fig. 3.5: Dye injection at wing root. Flow visualization for Re = 5,000 near the beginning of the wing stroke. The velocity pro le is heavily smoothed (a = 30), accelerating over 0.5 chord-lengths of travel. 68 (a) Linear velocity pro le (b) Heavily smoothed velocity pro le Fig. 3.6: Comparison of the linear and smoothed velocity pro les at s=c = 1.9. smoothed velocity pro les is that the entire LEV formation process begins much earlier in the wing stroke for the smoothed case (s=c = 0.19) when compared to that of the linear case (s=c = 0.64). Since the wing is accelerating much faster for the smoothed case, vorticity begins to form earlier and causes the ow to roll into a vortex sooner in the wing stroke. Figure 3.6 compares the linear velocity pro le to the smoothed velocity pro le at the same point in the wing stroke, s=c = 1.9. For the linear case shown in Figure 3.6(a), only a dye blob is present, whereas for the smoothed case, shown in Figure 3.6(b), the LEV has begun to form. The LEV bursts at the quarter-span location for both cases, at s=c = 1.9 for the heavily smoothed case, and at s=c = 2.3 for the linear case. However, these di erences observed maybe due to the higher acceleration rather than the smoothed velocity pro le. This set of experiments should be repeated after the acceleration of the two cases are matched. 69 Closed root Dye injection at root Original wing root Fig. 3.7: Closed wing root con guration. 3.5 Variation of Wing Root Geometry The goal of this portion of the study was to qualitatively understand the e ect of the wing root geometry on the development and persistence of LEVs in unsteady (early in the wing stroke) and quasi-steady (after multiple revolutions) conditions. The root of the wing was covered in an attempt to study the in uence of the root vortices on the LEV. In order to reduce their e ect, the wing root was \closed" using book laminate. The book laminate was xed onto the root of the wing using electrical tape. This removed the gap between the wing and the shaft, as seen in Figure 3.7. The dimensions of this plastic piece were 3 in 1.8 in. It is important to note that by covering the wing root, the e ective aspect ratio (span/chord) increased from 2 to 2.6. In addition to the change in aspect ratio, the radial location of the wing root also shifts. As a result, dye injection shown here was not performed at the \true" wing root, but in the same location as in previously shown results. The location where the dye is injected will be referred to as the \original" wing root for all the results discussed in this section. 70 (a) s=c = 0.67 (b) s=c = 0.71 (c) s=c = 0.90 (d) s=c = 2.2 Fig. 3.8: Closed root con guration. Dye injection at wing root. Flow visualization for Re = 5,000 near the beginning of the wing stroke. The velocity pro le is linear, accelerating over 0.5 chord-lengths of travel. 71 Figure 3.8 shows chordwise views of the wing at a three-quarter span Reynolds number of 5,000. Images were taken at approximately the same s=c as that of the open root case (see Figure 3.1). The formation of a leading edge vortex is once again observed at s=c = 0.67, similar to Figure 3.1(a). The LEV begins to grow, and draws the initial dye blob that was present on the wing into its core (Figure 3.8(b)). Figure 3.8(c) shows the presence of spanwise ow on the surface of the wing. Dye begins to convect through the core of the vortex and moves towards the tip of the wing. Finally, at a s=c = 2.2, a coherent LEV is observed along the leading edge, which bursts at approximately 1/5 of the original span. Here the burst appears to take place a little earlier than the open root con guration, where the vortex burst at approximately 1/4 span (shown in Figure 3.1(d)). However, if the book laminate was accounted for, the burst location is approximately a third of the new span, so its di cult to draw any conclusions at this time. The next step was to determine how long this LEV persisted and whether or not the location where the vortex bursts moved inward as it did on the open-root con guration. Figure 3.9(a) shows the presence of a coherent LEV along the leading edge. The LEV then loses its orderly nature and bursts at f=c = 0.64 (measurements based on original span). At a later time, s=c = 4.5 (Figure 3.9(b)), the coherent portion of the LEV does not appear to be present. Finally, at a s=c = 5.0 shown in Figure 3.9(c), the dye appears to have dissipated almost completely and a LEV is no longer visible. Unlike the open-root con guration, a coherent LEV did not persist for multiple revolutions. This could be a result of closing the root of the wing. Perhaps the vortices at the wing root played a role in preserving the LEV at 72 (a) s=c = 2.8, f=c = 0.64 (b) s=c = 4.5 (c) s=c = 5.0 Fig. 3.9: Closed root con guration. Dye injection at wing root. Flow visualization for Re = 5,000. 73 the leading edge. This could also be a result of not injecting the dye at the true wing root. Perhaps the burst location has moved inboard prior to the dye injection location. In order to better understand the e ect of wing root geometry on the rotating wing, these experiment should be repeated by physically reducing the length of the tygon shaft (refer to Section 2.2) and therefore moving the actual wing root to the central shaft instead of using book laminate. In this manner, the aspect ratio of the wing would remain the same and a direct comparison could be made. Unfortunately, this test could not be completed with the current model since the steel anged collar prevents mounting the wing close to the shaft at an angle of attack of 45 deg (see Figure 3.7). 3.6 Flow Structures Post-LEV-Burst For this set of experiments, dye was injected at the half span location to discern the ow structures within the burst LEV. All the images shown here focus on the region outboard of the half span and do not capture the coherent vortex at wing root described earlier. The wing was rotated about the root at a three-quarter span Reynolds number of 5,000. It was accelerated from rest to a constant velocity over 0.50, 0.75, and 1.0 chord-lengths of travel (linear velocity pro le) and the ow structures at the three di erent acceleration pro les are compared. 74 3.6.1 Variation of Acceleration Pro les The goal of this study was to determine the e ect of wing acceleration on the ow structures within the burst LEV. Figure 3.10 shows chordwise views of the wing corresponding to approximately equal points in the wing stroke (s=c) for di erent wing accelerations (sa=c). The three columns represent three di erent accelerations, sa=c = 0.5, 0.75, and 1.0, and the rows represent the progression in time, given by the number of chord-lengths traveled at three-quarter span, s=c. It is important to note that when the value of s=c is less than sa=c, the image was captured while the wing was accelerating. When s=c is greater than sa=c, the image was captured while the wing was rotating at a constant velocity. (I.e., Figures 3.10(a-c,e,f) were captured during the acceleration phase, while the rest were captured during the constant velocity phase). In all of the cases shown here, the development of the ow on the rotating wing appears to follow a progression|the formation of a vortex at the leading edge, the pairing of shed vortices, and nally, a region of recirculating separated ow, referred to as the burst vortex in Section 3.2. The rst row in Figure 3.10 shows the formation of the initial vortex for the three wing acceleration cases. This initial vortex forms at s=c 0:3 in all three cases, but the vortices appear to be larger for larger sa=c or lower wing acceleration values. When the wing is accelerating faster (Figure 3.10(a)) the oncoming ow has to negotiate a sharp turn more quickly, whereas for a lower wing acceleration (Figure 3.10(c)) the ow can make a more gradual turn, therefore resulting in larger vortices for lower wing accelerations. The 75 ?? ? = 0.50 ? ? = 0.35 ?? ? = 0.75 ? ? = 0.32 ?? ? = 1.00 ? ? = 0.32 ?? ? = 0.50 ? ? = 0.64 ?? ? = 0.75 ? ? = 0.63 ?? ? = 1.00 ? ? = 0.64 1st vortex 1st vortex 1st vortex 1st & 2nd vortices pair 3rd vortex 3rd vortex 1st & 2nd vortices pair Separate 1st & 2nd vortices 3rd vortex d1c d2c d3c A C B D F E ?? ? = 1.00 ? ? = 1.1 ?? ? = 0.75 ? ? = 1.1 ?? ? = 0.50 ? ? = 1.1 ?? ? = 0.50 ? ? = 1.4 ?? ? = 1.00 ? ? = 1.4 Shed vortices ?? ? = 0.75 ? ? = 1.4 d 0 .50 d 0 .75 d1.0 G I H J L K 76 ?? ? = 0.50 ? ? = 2.2 ?? ? = 0.75 ? ? = 2.1 ?? ? = 1.00 ? ? = 2.1 M O N Fig. 3.10: Dye ow visualization of a rotating wing at a xed angle of attack of 45 deg. diameter of the initial vortex is de ned as d and is then non-dimensionalized by the wing chord. This ratio is then referred to as dxc=c, where x corresponds to the column the wing is in (i.e., the distance over which the wing is accelerated). The physical size of the vortex in the third column, d3c=c 0:21, is greater than that in the rst column, d1c=c 0:16. In the second row of Figure 3.10, the rst vortex has shed and a second vor- tex has also formed and shed. As the third vortex forms, the rst and second shed vortices pair and begin rotating about a common point. The images taken at s=c 0:6 (Figure 3.10(d-f)) illustrate this process, though the ow appears to be at a slightly di erent stage for each acceleration case. In Figures 3.10(d,e) (sa=c = 0.50 and 0.75), the rst and second vortices have paired. In Figure 3.10(f) (sa=c = 1.0), these vortices are about to pair, but have not done so yet. Note that Figure 3.10(d) was captured during the constant velocity phase and Figures 3.10(e,f) were captured while the wing was accelerating. Another interesting feature seen in Figure 3.10(d) is an S-shaped structure. 77 ?? ? = 0.50 ? ? = 0.56 ?? ? = 0.75 ? ? = 0.80 ?? ? = 1.00 ? ? = 1.10 d1s d2s d3s 1st vortex 2nd vortex 3rd vortex Fig. 3.11: S-shaped ow structure observed in all three acceleration cases soon after the end of the wing?s acceleration phase. d1s=c 0:26, d2s=c 0:31, and d3s=c 0:43. This structure appears soon after the wing reaches the constant velocity phase for all three acceleration cases, as shown in Figure 3.11. For the sa=c = 0.50 case, the S-shaped structure consists of the rst and second shed vortices, which will soon pair (see Figure 3.10(d)), and a newly-formed third vortex. The length of the S appears to increase as the wing acceleration decreases. The value of d3s=c 0:43 for sa=c = 1.0, while d1s=c 0:26 for sa=c = 0.50. Just past this point in the wing stroke, the vortices at the bottom of this structure begin to recirculate, causing them to move along the surface of the wing towards the leading edge. Returning to Figure 3.10, rows 3 and 4 (corresponding to s=c 1:1 and 1.4), illustrate the path taken by the shed vortices. The vortices that formed at the leading edge initially traveled downstream over the wing, but eventually reverse direction and move along the upper surface of the wing towards the leading edge, forming a region of recirculating ow over the upstream half-chord. This counter- 78 clockwise motion is indicated by the arrows in row 4. Vortices are shed o the leading edge and travel approximately half-way down the chord, where they contact the wing surface. It can be seen that the precise distance traveled prior to impact depends on the acceleration. For sa=c = 0.50 shown in Figure 3.10(g), the shed vortices impact the wing upstream of mid-chord, but at sa=c = 1.0 shown in Figure 3.10(i) they impact just downstream of mid-chord. When these shed vortices collide with the wing, they deform. Interaction with the solid boundary causes these now-deformed vortices to move along the wing towards the leading edge, thus forming a region of recirculating ow. Figure 3.12(a) shows the ow structures visible when dye is injected at the wing root, and Figure 3.12(b) shows a chordwise view of the ow structure at the half span, indicated by the solid yellow line in Figure 3.12(a). Both images are from di erent s=c but the ow structure does not change signi cantly after the LEV bursts. Figure 3.12(b) indicates that after the vortex bursts at some location along the span, it lost its coherent structure but retained some recirculation, and forms a recirculating separated region. This recirculating region contains vortices that were previously shed, as well as new vortices that continue to shed as the wing rotates. Later in the wing stroke, when s=c 2:1 (row 5 of Figure 3.10), the ow is fully-separated with a large recirculating region. The size of the recirculating region increases with sa=c. When sa=c = 0.50 (Figure 3.10(m)), the recirculating region covers approximately 75% the wing chord and has not quite reached the trailing edge. When sa=c = 0.75 (Figure 3.10(n)), the recirculating ow extends to the trailing edge. For sa=c = 1.0 (Figure 3.10(o)), the recirculating region is past the 79 (a) s=c = 3.9 (b) s=c = 1.4 Fig. 3.12: Comparison of ow structures. trailing edge. This recirulating region, i.e., the burst vortex, covers the outboard portion of the wing as seen in Figure 3.1. 3.6.2 Variation of Angle of Attack The experiment described in Section 3.6.1, was repeated with a xed angle of attack of 15 deg. Figure 3.13 shows the chordwise views of ow visualization images for the di erent wing accelerations (columns) throughout the wing stroke (rows). The rst row in Figure 3.13(a-c) shows the rst shed vortex at the half span, and the second vortex starting to form. Very little dye is entrained in the rst vortex at sa=c = 0.50 (Figure 3.13(a)), but this vortex is more visible in the image taken at sa=c = 0.75 (Figure 3.13(b)). In Figure 3.13(c) a dye blob is visible in addition to the initial vortex. This blob is a result of injection of some dye before the start of the wing motion. Overall, it appears that the vortices formed at = 15 deg are smaller than those that form at = 45 deg, and travel downstream over the surface of the wing rather than lifting o the wing?s surface as they do at = 45 deg. 80 ?? ? = 0.50 ? ? = 1.2 ?? ? = 0.75 ? ? = 1.2 ?? ? = 1.0 ? ? = 1.1 ?? ? = 1.0 ? ? = 1.0 ?? ? = 0.75 ? ? = 0.76 ?? ? = 0.50 ? ? = 0.61 ?? ? = 0.50 ? ? = 1.5 ?? ? = 0.75 ? ? = 1.6 ?? ? = 1.0 ? ? = 1.6 ?? ? = 1.0 ? ? = 2.7 ?? ? = 0.75 ? ? = 2.7 ?? ? = 0.50 ? ? = 2.9 x1c x2c x3c 1st vortex 2nd & 3rd vortices merged 1st vortex 2nd & 3rd vortices 1st vortex 2nd vortex x1c x2c x3c 1st vortex 1st vortex 1 st vortex 1st vortex 1st vortex 1st vortex Initial dye blob Initial dye blob Shed vortices dye blob A B C D E F G H I J K L Fig. 3.13: Dye ow visualization of a rotating wing at a xed angle of attack of 15 deg. In Figures 3.13(d-f)), at s=c 1:2, all three cases show di erent development stages of the ow structures on the wing. In each case, the rst vortex has shed and traveled to a di erent location, xc, downstream over the surface of the wing. At this point in the wing stroke, the shed vortex has moved more than half the chord-length downstream in Figure 3.13(d) at sa=c = 0.50, but only about one-third of a chord-length in Figure 3.13(f). Furthermore, the development of the next few vortices vary amongst the acceleration cases. Figure 3.13(d) (sa=c = 0.50, s=c = 1.2), shows the rst vortex at x1c=c 0:55, while the subsequent vortices have shed and merged with each other. In the second acceleration case, sa=c = 0.75 (Figure 3.13(e)), the initial vortex has traveled to 81 x2c=c 0:49 and the next few vortices have formed, but have not yet merged. In the third case where sa=c = 1.0 shown in Figure 3.13(f), the rst vortex has traveled a distance x3c=c 0:32, and the next vortex has begun to form. The di erences in the development and migration of the vortices observed here suggest that the wing acceleration can a ect the timing of vortex formation and shedding on a rotating wing at a 15 deg angle of attack. Later in the wing stroke, at s=c 1:6 (shown in Figures 3.13(g-i)), the rst vortex has moved further along the wing in each of the three acceleration cases. This shed vortex appears to move downstream faster for slower wing accelerations. The velocities (relative to the wing itself) at which the vortex travels downstream between 1.2 and 1.6 chord-lengths of wing travel are approximately 0.039 m s 1, 0.030 m s 1, and 0.014 m s 1 for acceleration over 0.50, 0.75, and 1.0 chord-lengths of travel, respectively. At s=c 1:6, the locations of the initial vortices are x1c=c 0:77, x2c=c 0:64, and x3c=c 0:43. Unlike the 45 deg angle of attack case, there does not appear to be an obvious recirculating region present. The fourth row of Figure 3.13(j-l) illustrates the ow structure for the three di erent acceleration cases much later in the wing stroke, at s=c 2:7. In all three cases, there is a trail of shed vortices extending along the surface of the wing from the leading edge to the trailing edge without forming a recirculating region. 82 3.7 Pitching and Rotating Wing The rotating wing experiment was extended to include unsteady variations in pitch at a Reynolds number of 5,000. The angle of attack of the wing was varied from 0 deg to 45 deg over 1.3 chord-lengths of travel at the three-quarter reference plane in wing rotation, using the underwater servo motor as described in Section 2.3.2. The dye was injected at the half span location. As seen from the rotating wing experiments, a coherent LEV is present along the leading edge but bursts prior to reaching the half span location on the wing. All the images in this section show the ow structures on the outboard half of the wing. Results of dye ow visualization for the pitching and rotating wing case are given in Figure 3.14. In this gure, the ?+? superscript on denotes that the wing?s angle of attack is increasing. The ?-? superscript denotes a decreasing angle of attack. The angle of attack given here was calculated by correlating the known pitch kinematics with the stoke angle obtained from the encoder. Figure 3.14(a) shows the wing pitching up near the beginning of the wing stroke. The wing executed one pitch stroke (0 to 45 to 0 deg) before wing rotation began, resulting in excess dye present in the background and a dye blob on the wing. At this point in time, the ow looks much like it did near the start of the = 15 deg rotating-only wing stroke, as shown in Figure 3.13(d-f). Flow is largely along the surface of the wing, and contains vortices that move downstream towards the trailing edge. In Figure 3.14(b), the wing stroke has progressed to 18 deg, s=c = 0.34. 83 ?+ ???????? s/c = 0.15 ?+ ???8 deg s/c = 0.34 ?+ ??27 deg s/c = 0.53 ?- ??10 deg s/c = 2.0 ?- ??27 deg s/c = 1.4 ?+ ??37 deg s/c = 0.75 ?- ??37 deg s/c = 1.1 ?+ ??42 deg s/c = 0.87 ?+ ??35 deg s/c = 14.0 Shed vortices Dye Blob dSF dSF dSF New vortex A B C D E F G H I Fig. 3.14: Dye ow visualization of a pitching and rotating wing. Flow has continued along the surface of the wing and curves towards the wing root on the downstream half of the chord. The surface of the wing has a white line from leading to trailing edge at half span. This physical mark is highlighted by the dashed white line in Figure 3.14(a-c) to illustrate the extent of spanwise ow. Near the leading edge, vortices have formed, and a region of recirculating ow begins to form around them. Later in the wing stroke, at s=c = 0.53, this recirculating region has grown larger and ow along the trailing half of the wing has continued towards the trailing edge and root. 84 In Figure 3.14(d), the recirculating region has grown further and is now more well de ned. In this view, the white line on the wing is more obvious, and it is clear that dye has moved toward the wing tip at the leading edge and towards the wing root at the trailing edge. As the wing stroke progresses, dye near the leading edge continues to move towards the tip. The distance of the dye along the leading edge from the half span location is de ned as dSF . In Figure 3.14(e), the distance dSF has increased, and continues to do so in Figure 3.14(f). It also becomes clear that the dye at the trailing edge is now moving towards the wing tip. Figure 3.14(e) shows the ow at 42 deg, near the maximum angle of attack. It was previously noted that on a rotating-only wing at = 45 deg, the ow is fully separated from the wing and recirculates in a burst vortex. In the pitching and rotating setup, the recirculating region near the leading edge is on the surface of the wing and the ow along the back half of the wing remains intact. For the pitching and rotating wing, however, does not remain constant, but decreases immediately upon reaching max = 45 deg. When the wing begins to pitch down, the structure of the ow begins to break up, and the recirculating region is less de ned as shown in Figure 3.14(f). The images in Figure 3.14(f-h) were taken as the wing pitched down. As decreased, the trailing edge of the wing rose, and the region of recirculating ow near the leading edge was ejected from the wing?s surface. In Figure 3.14(g), any organization that the recirculating region might have previously had has largely vanished, and by Figure 3.14(h) only a cloud of dye remains well above the wing. It is interesting to note that this cloud of dye has moved vertically o of the wing 85 rather than downstream towards the trailing edge. Additionally, the newly injected dye has also risen o of the wing?s surface. Finally, Figure 3.14(i) shows the ow much later in the wing stroke and at 35 deg. There is less dye in the ow and thus the large-scale structures are not visible. At this point, a new vortex has formed and ow has reattached to wing?s surface downstream of this new vortex. 3.8 Summary This chapter presented results for dye ow visualization experiments performed on a rotating-only wing and a pitching-and-rotating wing, with a focus on the three- dimensional ow structures that formed on a xed-pitch rotating wing. When dye was injected at the wing root, a coherent LEV was observed along the leading edge which then burst at the quarter span location along the wing, very similar to the LEV seen on delta wings. As the wing continues to rotate, the location where this LEV becomes less well-de ned and the burst point moves inboard. When the LEV burst, the ow became chaotic and recirculating ow covered the remaining outboard portion of the wing. The small scale ow structures in burst vortex were not clearly visible when dye was injected at the wing root. In order to get a better understanding of the ow structures within the burst LEV, dye was then injected at the half span location. Dye ow visualization on the rotating-only wing at half span was performed at two xed angles of attack of 45 deg and 15 deg. The distance over which the 86 wing was accelerated was varied and the ow structures were compared for three di erent acceleration values. At a xed angle of attack of 45 deg, the value of the wing?s acceleration a ected vortex size. Lower acceleration values resulted in larger vortices. Vortices shed and formed a recirculating region, which provided new insight into the ow structures post-LEV-bust. At a xed angle of attack of 15 deg, the acceleration a ected the speed of which vortices were shed rather than vortex size and a recirculation region was absent. Unsteady variations of pitch were introduced to the rotating-only wing. Dye ow visualization was performed at the half span location on the wing. At low angles of attack, the ow structures were similar to those observed on the rotating-only wing at an angle of attack of 15 deg. At high angles of attack, however, a large recirculation region near the leading edge was observed, with attached ow behind it. 87 Chapter 4 Force Measurements Results 4.1 Overview This chapter presents quantitative results from investigating the lift and drag produced on a rotating-only wing at a xed angle of attack of 45 deg. Force measure- ments were used to quantify the aerodynamic forces produced by the ow structures discussed in the previous chapter. Unsteady force measurements were acquired for a 720 degree wing stroke. As previously described, the six-axis force transducer has a capacity of 25 N in the x, y and z directions with a rated resolution of 1/160 N, as well as a torque capacity of 250 N-mm with a rated resolution of 1/32 N-mm. The measured forces were normalized using CL = 6L !2maxc(r 3 t r3r) (4.1) CD = 6D !2maxc(r 3 t r3r) (4.2) as described in Section 2.5.2, where !max is the maximum angular velocity, and rt and rr are the distances between the axis of rotation and wingtip and axis of rotation and root, respectively. As described in Section 2.5.2, the lift and drag signals were ltered and a 0.03 second moving average was applied. Several parameters including velocity pro les, acceleration pro les, Reynolds number, and wing exibility were varied. 88 4.2 Baseline Case To better understand the force history of the rotating wing, a baseline case is rst discussed in detail. Figure 4.1 shows the coe cients of lift and drag with respect to the stroke-to-chord ratio (s=c) for a wing accelerating over 0.50 chord-lengths of travel at a three-quarter span Reynolds number of 15,0001. The velocity pro le was heavily smoothed (a = 30), and is shown in Figure 4.2. In both Figures 4.1 and 4.2 the rst vertical black line corresponds to the transition to constant velocity, the second vertical line marks the end of the rst rotation, and the third line represents the beginning of deceleration. The coe cients of lift and drag initially overshoot, then undershoot, increase again, and eventually level o to an intermediate value for the remainder of the rst revolution. After the wing enters the second revolution, the coe cients begin to decrease again before leveling out to a second value until the wing begins to decelerate. The acceleration region and the constant velocity region are explained in further detail to better understand the behavior of the force coe cients. 4.2.1 Acceleration Phase Figure 4.3 shows the lift and drag coe cients early in the wing stroke, i.e., the acceleration phase of Figure 4.1. The vertical black line indicates the end of the acceleration phase and the beginning of the constant velocity phase. During this 1The Reynolds number for the baseline case described here is much higher than the baseline case described in the previous chapter. This is because at low Reynolds numbers, the signal-to-noise ratio of the force transducer was very low. 89 0 5 10 15 20 25 ?2 ?1 0 1 2 3 C L s/c end of acceleration start of deceleration first revolution second revolution (a) Lift coe cient 0 5 10 15 20 25 ?2 ?1 0 1 2 3 C D s/c (b) Drag coe cient Fig. 4.1: Lift and drag coe cients for a rotating wing at a xed angle of attack of 45 deg accelerating over 0.50 chord-lengths of travel at a three-quarter span reference Reynolds number of 15,000. 90 0 5 10 15 20 25 0 0.2 0.4 0.6 0.8 1 1.2 s/c ? (rad/s ) first revolution second revolution end of acceleration start of deceleration Fig. 4.2: Heavily smoothed velocity pro le: angular velocity with respect to s=c at a Reynolds number of 15,000. acceleration region, the value of CL peaks at approximately 3.04 and CD peaks at a value near 2.92. The initial peak observed in Figure 4.3 is a result of a combination of the inertial force and added mass. The wing was rotated in air to measure the inertial forces, the forces measured were very small and were within the noise of the force transducer. Since the inertial forces on the wing were small it can be concluded that a majority of the initial peak is a result of added mass. Added mass is the enhanced and/or altered inertia of an object that is caused by motion of a uid around the object [70]. When a apping wing accelerates through a uid, it forces some uid to accelerate with it and the inertial resistance of this uid creates a reaction force on the wing [71]. Knowledge of added mass is very crucial to understand the performance of objects (in this case, a at plate) 91 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 C L s/c acceleration phase constant velocity phase (a) Lift coe cient 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 C D s/c (b) Drag coe cient Fig. 4.3: The acceleration phase for a rotating wing at a xed angle of attack of 45 deg accelerating over 0.50 chord-lengths of travel at a three-quarter span reference Reynolds number of 15,000. 92 underwater. The drag added mass of a at plate at a xed angle of attack can be theoretically modeled as a cylinder with a diameter d as shown in Figure 4.4, where the diameter is de ned as d = c sin( ) (4.3) where c is the wing chord and is the angle of attack. For a cylinder accelerating in a stationary uid, Jones et al. [71] found the pressure force in the x-direction per unit length of a cylinder to be F 0 p = 1 4 d2 du dt (4.4) where is the density of the uid, d is the diameter of the cylinder, and du/dt is the linear acceleration. In this case, the pressure force is acting in the same direction as the drag and can therefore account for the added mass phenomenon in the drag force. The total drag force acting on the cylinder is therefore Fd = Z rt rr 1 4 d2 du dt dr (4.5) where rt and rr are the distances between the axis of rotation and wingtip and axis of rotation and root, respectively. The linear acceleration can be converted to the angular acceleration using: u = r! (4.6) du dt = r d! dt (4.7) where r is the radius. Substituting Equation 4.7 into 4.5 Fd = Z rt rr 1 4 d2 r d! dt dr: (4.8) 93 Integrating Equation 4.8, Fd = 1 8 d2 d! dt r2t r 2 r : (4.9) Substituting Equation 4.3 into 4.9, Fd = 1 8 c2 sin2( ) d! dt r2t r 2 r : (4.10) Substituting Equation 4.10 into 4.2, CDaddedmass = (3=4) c sin2( )(d!=dt)(r2t r 2 r) !2max(r 3 t r3r) : (4.11) The maximum value of added mass of a rotating wing is thus CDpeak = max (3=4) c sin2( )(d!=dt)(r2t r 2 r) !2max(r 3 t r3r) (4.12) where is the angle of attack, c is the wing chord, d!/dt is the angular acceleration of the wing, !max is the maximum angular velocity, and rt and rr are the distances between the axis of rotation and wingtip and axis of rotation and root, respectively. It should be noted that the added mass is proportional to the angular acceleration of the wing, therefore, increasing the acceleration should result in a larger added mass peak. The theoretical drag coe cient added mass peak at s=c 0:02 (calculated using Equation 4.12) was found to be 2.28, suggesting that the peak observed in the experimental data (shown in Figure 4.3) is indeed due to added mass. 4.2.2 Constant Velocity Phase Figure 4.5(a) focuses on the constant velocity region of Figure 4.1(a), and the axes have been adjusted to provide clarity. After the wing enters the constant 94 d ? c Fig. 4.4: A at plate at a xed angle of attack can be modeled as a cylinder with a diameter d. velocity phase, the lift and drag coe cients level out to an intermediate value for the remainder of the rst revolution. This \steady-state" is achieved after about 1.4 s (5 chord-lengths of travel and approximately 133 deg stroke angle). The value of CL and CD appear to be essentially constant for about 2.8 s ( 8.5 chord-lengths and approximately 227 deg stroke angle). The \steady-state" mean for this region of the rst revolution was found to be 1.85 for the coe cient of lift and 1.55 for the coe cient of drag. After the wing enters the second revolution, the coe cients begin to decrease before leveling out to a second intermediate value. The coe cient of lift and drag averaged over 8.5 chord-lengths of travel (to remain consistent with the previous revolution results) during the second revolution are 1.44 and 1.21, respectively. A 22% reduction of CL and CD was observed from the rst revolution. It is postulated that this is a result of the wing interacting with the wake from its previous stroke. The aerodynamic e ciency, quanti ed by L=D, is shown in Figure 4.6. Similar 95 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 C L s/c first revolution second revolution ?CL = 0.41 1.85 1.44 8.5 chord?lengths 8.5 chord?lengths (a) Lift coe cient 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 C D s/c 8.5 chord?lengths first revolution second revolution ?CD = 0.34 1.55 1.21 8.5 chord?lengths (b) Drag coe cient Fig. 4.5: Constant velocity phase lift and drag coe cients for a rigid rotating wing at a xed angle of attack of 45 deg accelerating over 0.50 chord-lengths of travel at a three-quarter span reference Reynolds number of 15,000. 96 0 5 10 15 20 25 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 L/ D s/c first revolution second revolution Fig. 4.6: Lift-to-drag ratio versus s/c for the rotating wing at Re = 15,000 acceler- ated over 0.50 chord-lengths of travel. to previous gures, the black vertical line (s=c = 13.5) marks the end of the rst revolution and the beginning of the second revolution. The lift-to-drag ratio ap- pears to remain roughly constant through out the two revolutions. This is because reduction of CL for the second revolution is proportional to the reduction in CD (ap- proximately 22%). This leads to an averaged (over each revolution) lift-to-drag ratio of 1.19 for the rst revolution and 1.17 for the second revolution. The di erence is so small that it is within experimental error. 97 Table 4.1: Maximum angular acceleration at Re = 15,000. Accelerating over Velocity pro le Maximum angular acceleration (rad/s2)2 0.25c smoothed (both) 15.5 linear 6.2 0.50c smoothed (both) 7.8 linear 3.1 1.0c smoothed (both) 3.9 linear 1.6 4.3 Variation of Velocity Pro les As described in Chapter 2, the wing stroke was programmed using three di er- ent velocity pro les: linear in time, heavily smoothed (a = 30), and lightly smoothed (a = 75). The wing was accelerated such that it reached its maximum angular veloc- ity after 0.25, 0.50, or 1.0 chord-lengths of travel at the three-quarter span reference plane (plots shown in Section 2.3). For each case, the wing stroke was symmetric such that the wing acceleration and deceleration phases were equal and opposite. The wing reached a maximum stroke angle ( ) of 720 deg, corresponding to s=c = 27. The maximum angular acceleration for all the tested velocity pro les is given in Ta- ble 4.1. The goal of this set of experiments was to determine the e ect of the velocity 2The maximum angular acceleration is the same for both of the smoothed cases, however, the instantaneous acceleration values during transition are higher for the lightly smoothed case. 98 pro le on the lift force generated by the wing. In order to compare the di erence be- tween the smoothed and the linear velocity pro les, it was important that the value of the accelerations were same. However, during the acceleration and deceleration phase of the wing stroke mentioned in Section 3.4, the acceleration of the smoothed and the linear cases were di erent. This di erence in the acceleration values was a result of setting t1 = 30% of t2 as explained in Section 2.3.1. As a result, the accelerations for the smoothed cases were 60% (see Table 4.1) greater than that of the linear case. Therefore, the transients observed during the acceleration and deceleration phase for the smoothed and unsmoothed velocity pro les cannot be di- rectly compared. A slightly better comparison can be made with the linear velocity pro le accelerating over 0.25 chord-lengths of travel, though the acceleration still di eres by approximately 20%. Figure 4.7 shows the coe cients of lift and drag with respect to the stroke-to- chord ratio for the three di erent velocity pro les at Re = 15,000. The coe cient curves for the smoothed cases correspond to sa=c = 0.50 and the coe cient curves for the linear case correspond to sa=c = 0.25. The three lines, blue, red and green correspond to the linear, heavily smoothed, and lightly smoothed velocity pro les, respectively. The three vertical lines indicate the end of acceleration phase, the end of the rst and beginning of second revolution, and the beginning of the deceleration phase. Regardless of the velocity pro le, an initial transient peak is observed. The coe cients then undershoot, overshoot again, and eventually achieve a relatively constant value after 5 chord-lengths of travel. As previously seen in Section 4.2, the coe cients decrease when the wing enters the second revolution. Another transient 99 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 s/c C L linear heavily smoothed lightly smoothed first revolution second revolution end of acceleration start of deceleration (a) Lift coe cient for entire wing stroke max = 720 deg 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 s/c C D linear heavily smoothed lightly smoothed (b) Drag coe cient for entire wing stroke max = 720 deg Fig. 4.7: Comparison of three di erent velocity pro les for a rotating wing at Re = 15,000. 100 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 s/c C L linear heavily smoothed lightly smoothed constant velocity phase acceleration phase (a) Lift coe cient for early wing stroke 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 s/c C D linear heavily smoothed lightly smoothed (b) Drag coe cient for early wing stroke Fig. 4.8: Comparison of the acceleration phase for three di erent velocity pro les for a rotating wing at Re = 15,000. 101 0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 4 5 6 7 8 time (sec) d? /dt (rad/ s2 ) heavily smoothed lightly smoothed (a) Acceleration vs. time 0 0.1 0.2 0.3 0.4 0.5 ?600 ?400 ?200 0 200 400 600 time (sec) jerk (rad/ s3 ) heavily smoothed lightly smoothed 60% increase (b) Jerk vs. time Fig. 4.9: Acceleration and jerk with respect to time for the two smoothed pro les, heavily smoothed (blue) and lightly smoothed (red) for a wing accelerating over 0.50 chord-lengths of travel. trough is observed when the wing decelerates. This is in agreement with the results seen in Figure 4.7. Only the shape of the transients during the acceleration and deceleration phase are a ected by smoothing the velocity pro le (see Figure 4.8). Even though the maximum angular acceleration of the two smoothed cases are the same, the heavily smoothed case has a much lower jerk when compared to the lightly smoothed case. Figure 4.9 compares the acceleration and jerk for a wing accelerating over 0.50 chord-lengths of travel at a Reynolds number of 15,000. The higher jerk in Figure 4.9(b) for the lightly smoothed case compared to the heavily smoothed case is a result of sharper transitions during acceleration. Therefore a higher jerk implies a higher instantaneous value of acceleration which results in a larger added mass. If the added mass is higher, the peak in the force coe cients will be higher as well. This agrees with the coe cients in Figure 4.8. 102 Figure 4.8 focuses on the early wing stroke to highlight the transients of CL and CD that occur during the wing?s acceleration. The lightly smoothed case has a greater transient peak than the heavily smoothed case. A phase shift between the two cases is also observed. Figure 4.10(a) shows the raw and ltered data for the linear velocity pro le early in the wing stroke. In this a phase shift is observed, which is a result of ltering. However, Figure 4.10(b) shows the raw data for all three pro les to show that the phase shift observed between the two smoothed cases is not a result of ltering. Both velocity pro les result in the same overall shape regardless of the value of the transient or the phase shift. Once the wing completes the acceleration phase, the coe cients converge to similar values and trends. The transient peak for the linear case is very sharp and abrupt, unlike the two smoothed cases. This sharp and abrupt nature of the linear pro le coe cients is a result of the jump in the acceleration of the wing as shown in Figure 2.7. The value of the linear pro le peak is lower than the two smoothed cases. This is likely because the acceleration for the linear pro le is 20% lower than that of the smoothed cases. This was veri ed using Equation 4.12. The theoretical added mass for both the smoothed cases is 2.28, whereas the added mass for the linear case is 1.82, which is 20% less than 2.28. This agrees with the experimental results. 4.4 Variation of Acceleration Pro les For this set of experiments, the heavily smoothed velocity pro le and three- quarter span reference Reynolds number of 15,000 were used, and the distance over 103 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 s/c C L Raw cL 30Hz filtered cL (a) Lift coe cient for linear velocity pro le 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 C L s/c lightly smoothed heavily smoothed linear (b) Lift coe cient for all three cases Fig. 4.10: Raw and ltered lift coe cients for three di erent velocity pro les for a rotating wing at Re = 15,000. 104 which the wing accelerated (and thus the value of the wing?s acceleration) was varied. The wing was accelerated from rest to constant velocity over 0.25, 0.50 and 1.0 chord-lengths of travel at the three-quarter span reference span. The distance over which the wing accelerated is denoted as sa and is non-dimensionalized using the wing?s chord. This ratio is expressed as sa=c. Table 4.1 shows the value of the wing?s acceleration for each of the three cases. Figure 4.11 shows the lift and drag coe cient curves for di erent values of sa=c. As in previous gures, the vertical black line indicates the end of the rst revolution and the beginning of the second. The vertical line indicating the end of the acceleration phase is not shown as it varies for the three cases. As in the baseline case described in Section 4.2.1, a transient peak is observed as soon as the wing beings to accelerate. The maximum angular acceleration determines the magnitude of the peak (refer to Equation 4.12). For all values of sa=c, the \steady-state" lift and drag coe cients (past 1 chord-length of travel since the largest distance over which the wing accelerates is 1 chord-length) are the same for all acceleration pro les. Figure 4.12 shows the acceleration phase of the wing stroke for each of the three cases. The dashed blue, red, and green vertical lines mark the end of acceleration for the sa=c = 0.25, 0.50 and 1.0 cases, respectively. Since sa=c = 0.25 has the greatest acceleration, it was expected to have the greatest peak as shown in Table 4.2. The added mass values were calculated using Equation 4.12. At sa=c = 0.25, a high peak is observed in both the lift and drag coe cients with a max CL 4.5 and max CD 4.0. The max coe cients of lift and drag were both approximately 3.0 for sa=c = 0.50 and the coe cients were both approximately 1.75 for sa=c = 1.0. In all 105 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 s/c C L s a /c = 0.25 s a /c = 0.50 s a /c = 1.0 first revolution second revolution (a) Lift Coe cient 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 s/c C D s a /c = 0.25 s a /c = 0.50 s a /c = 1.0 (b) Drag Coe cient Fig. 4.11: Constant velocity phase lift and drag coe cients. Comparison of three di erent sa=c for a rotating wing at Re = 15,000. 106 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 s/c C L s a /c = 0.25 s a /c = 0.50 s a /c = 1.0 (a) Lift Coe cient 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 s/c C D s a /c = 0.25 s a /c = 0.50 s a /c = 1.0 (b) Drag Coe cient Fig. 4.12: Comparison of the acceleration phase for three di erent accelerations for a rotating wing at Re = 15,000. The dashed blue, red and green lines indicate the transition from acceleration to constant velocity for the respective sa=c values. 107 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 s/c C L s a /c = 0.25 s a /c = 0.50 s a /c = 1.0 Fig. 4.13: Raw lift coe cients for the acceleration portion of the wing stroke. three cases, a high added mass peak is observed for the lift and drag coe cients, the peaks then undershoot, rise again, and eventually level out after 5 chord-lengths of travel. The raw lift coe cients for this portion of the wing stroke are shown in Figure 4.13. 4.5 Variation of Reynolds Number All the quantitative results presented thus far have been at a Reynolds number of 15,000. To investigate the e ect of Reynolds number on the rotating wing, di er- ent Reynolds numbers were achieved by rotating the same wing at di erent angular velocities. The other Reynolds numbers tested were 10,000 and 25,000. This range of Reynolds numbers were chosen due to the limitations of the force transducer. Unfortunately the data collected at a Reynolds number of 10,000 is not shown as 108 Table 4.2: Theoretical added mass peak values at Re = 15,000. Accelerating over Maximum angular acceleration (rad/s2) Theoretical added mass max(CD) Measured max(CD) 0.25c 15.5 4.54 3.98 0.50c 7.8 2.28 2.92 1.0c 3.9 1.14 1.74 the signal to noise ratio was very poor and this resulted in very high RMS error values, as shown previously in Table 2.3. Figure 4.14 compares the lift and drag coe cients for two Reynolds numbers of 15,000 and 25,000. The wing travels faster for the higher Reynolds number, but by plotting the force coe cients with respect to s=c (instead of time) the forces can be compared as the stroke angle varies. An initial added mass peak is seen for both cases. After the initial peak, the coe cients fall, rise again, and eventually settle into a \steady-state" value. After the wing nishes the rst revolution, there is a drop in both the lift and the drag coe cient curves regardless of the Reynolds number. These are the same trends which have were discussed in earlier sections. Increasing the Reynolds number from 15,000 to 25,000 does not appear to a ect the force coe cients. In Figure 4.14(a), the curves lay near each other, and both curves follow the same trends previously described. For 1 s=c 5, there 109 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 s/c C L Re = 15,000 Re = 25,000 end of acceleration start of deceleration first revolution second revolution (a) Lift Coe cient 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 s/c C D Re = 15,000 Re = 25,000 (b) Drag Coe cient Fig. 4.14: Lift and drag coe cients. Comparison of di erent Reynolds numbers for a rotating wing accelerating over 0.50 chord-lengths of travel. 110 is a small di erence in how the two curves increase, but the di erence is within experimental error (error bars shown in Figure 4.14(a)). Figure 4.14(b) shows the drag coe cient curves for the two Reynolds numbers. Unlike the lift curves, there is a small noticeable di erence in the values. The drag coe cient is consistently slightly higher for Re = 25,000 when compared to Re = 15,000 case. However, the di erence is very small and is within experimental error so a de nitive conclusion cannot be drawn. Overall, lift and drag coe cients do not appear to change signi cantly in the Reynolds number range tested. 4.6 Wing Flexibility All the experiments described to this point used a rigid wing. Since natural iers employ exible wings, further experiments were performed to investigate and compare a \ exible wing" to its rigid counterpart. The exible wing was modeled with two segments con gured to allow passive deformation about the half chord as described by Eldredge [40, 43, 39] and in Section 1.4.5. The anterior section of the wing was xed at a constant angle of attack of 45 deg, and the posterior section was allowed to passively deform. Since the trailing half-chord of the exible wing was free-to-pivot, it hung down vertically (at a 90 deg angle of attack) before the wing motion began. Figure 4.16(a) shows the coe cient of lift for the two wings at a Reynolds number of 15,000. The schematic of the exible wing in Figure 4.15(a), shows the wing?s steady-state position at a Reynolds number of 15,000. The passively 111 Re = 15,000 Re = 25,000 450 350 ?eff ? 50 0 450 660 ?eff ? 35 0 (a) Re = 15,000 Re = 15, 0 Re = 25,000 450 350 ?eff ? 50 0 450 660 ?eff ? 35 0 (b) Re = 25,000 Fig. 4.15: Steady-state exible wing positions. deforming trailing half of the exible wing de ects by an angle of 35 deg during steady-state, resulting in an e ective angle of attack of 50 deg. The e ective angle of attack of 50 deg is close to the angle of attack of the rigid wing (45 deg). Since the e ective angle of attack of the exible wing is very similar to the angle of attack of the rigid wing, the forces generated by both wings should be about equal. Figure 4.16(a) shows that the two wings do generate similar amounts of lift. Like the rigid wing, the lift coe cient decreases from the rst to the second revolution. It is also important to note that during the acceleration and deceleration phases, the peak lift coe cient of the rigid wing is much greater than the corre- sponding peak for the exible wing (shown in Figure 4.17). It is postulated that the force the uid exerted on the exible wing was less than the force exerted on the rigid wing, since the passive half of the exible wing was free to deform during the acceleration and deceleration phases. Figure 4.16(b) shows the drag coe cient for the two wings at Reynolds number 112 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 s/c C L rigid wing flexible wing first revolution second revolution end of acceleration start of deceleration (a) Lift Coe cient 0 5 10 15 20 25 ?2 ?1.5 ?1 ?0.5 0 0.5 1 1.5 2 2.5 3 s/c C D rigid wing flexible wing (b) Drag Coe cient Fig. 4.16: Coe cient of lift and drag for a rigid and half chord exible wing at Re = 15,000. 113 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 s/c C L rigid wing flexible wing acceleration phase constant velocity phase (a) Lift Coe cient 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 s/c C D rigid wing flexible wing (b) Drag Coe cient Fig. 4.17: Comparison of the acceleration phase for the coe cient of lift and drag for a rigid and half chord exible wing at Re = 15,000. 114 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 s/c C L rigid wing flexible wing second revolutionfirst revolution end of acceleration start of deceleration (a) Lift Coe cient 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 s/c C D rigid wing flexible wing (b) Drag Coe cient Fig. 4.18: Coe cient of lift and drag for a rigid and half chord exible wing at Re = 25,000. 115 of 15,000. One prominent feature of the plot is the relatively large peak coe cient of drag for the half chord exible wing as compared to the peak coe cient of drag for the rigid wing (see Figure 4.17(b)). The passive portion of the exible wing hangs vertically when the wing is at rest. When the wing begins to accelerate, the forces pushing this portion of the wing to its steady-state position (see Figure 4.15(a)) oppose the wing motion. Initially, the passive portion of the wing acts like a wall to the oncoming ow, and therefore most of the forces on the section are drag forces. As the ow continues to push the wing to its steady-state position, the drag decreases since the ow encountered a smaller frontal area. Once in \steady-state", the rigid wing and exible wing had similar values of drag coe cient. During the second revolution, however, the drag of the rigid wing decreased considerably as compared to the exible wing. This might have been due to the exible wing de ecting in a way that kept the drag coe cient at a high value when the wing moved through its wake from the rst rotation. Figure 4.16 shows that the lift and drag coe cients in the constant velocity region for both wings were very similar. The experiment was repeated for Re = 25,000 to study the e ect of Reynolds number on performance. The unsteady lift peaks during the acceleration and decel- eration portions of the wing motion can again be seen in Figure 4.18. \Steady-state" is achieved after 1.4 s (5 chord-lengths of travel) for the rigid wing, but after only about 0.7 s (2 chord-lengths of travel) for the exible wing. This could be a result of the exible wing?s ability to deform, which causes variations of the e ective angle of attack. This may allow the overall exible wing circulation to achieve a stable value in a shorter time. 116 Table 4.3: Steady-state lift coe cient average values. Steady State Region Re = 15,000 Re = 25,000 First Rotation CLflex = 1.79 CLflex = 1.37 CLrigid = 1.86 CLrigid = 1.90 Second Rotation CLflex = 1.41 CLflex = 1.20 CLrigid = 1.44 CLrigid = 1.46 Table 4.4: Steady-state drag coe cient average values. Steady State Region Re = 15,000 Re = 25,000 First Rotation CDflex = 1.57 CDflex = 1.04 CDrigid = 1.55 CDrigid = 1.64 Second Rotation CDflex = 1.39 CDflex = 1.01 CDrigid = 1.21 CDrigid = 1.30 117 The \steady-state" mean of the lift coe cient over 8.5 chord-lengths of travel, for the rigid wing and exible wing are given in Table 4.3. The rst rotation average on the rigid wing at Re = 15,000 was CL = 1.86 and the second rotation average was CL = 1.44. These averages are similar to the corresponding exible wing values for Re = 15,000. However, at a Re = 15,000, the exible wing lift coe cients are higher than the corresponding exible wing values at Re = 25,000. This is because an increase of Reynolds number to 25,000 caused the de ection angle of the passive half of the exible wing to increase to approximately 66 deg, which was greater than the 45 deg angle of attack of the anterior section of the wing (refer to Figure 4.15(b)). This resulted in an e ective angle of attack of approximately 35 deg for the exible wing, reduced from 50 deg at Re = 15,000. This decreased e ective angle of attack accounts for the lower lift coe cients measured for the exible wing at Re = 25,000. The aerodynamic e ciency, quanti ed by L=D, of both wings is shown for Reynolds numbers 15,000 and 25,000 in Figure 4.19(a) and 4.19(b). Comparing the performance of the two di erent wings reveals that the e ciency of the rigid wing was higher throughout both rotations at a Reynolds number of 15,000. At Re = 25,000, the e ciency of the exible wing was higher than the rigid wing during the rst rotation. However, e ciency of the exible wing approached the e ciency of the rigid wing during the second rotation. The \steady-state" L=D values for both Reynolds numbers can be found in Table 4.5. It can be seen that the performance of the exible wing at Re = 25,000 was generally better than at Re = 15,000. This improved performance persisted though the second revolution as well. It is postulated that the angle by which the posterior section exible wing 118 0 5 10 15 20 25 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 s/c L/ D rigid wing flexible wing second revolutionfirst revolution (a) Re = 15,000 0 5 10 15 20 25 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 s/c L/ D rigid wing flexible wing first revolution second revolution (b) Re = 25,000 Fig. 4.19: Lift-to-drag ratio for the rigid and exible wing. 119 Table 4.5: Steady-state lift-to-drag ratio averages. Steady State Region Re = 15,000 Re = 25,000 First Rotation L=Dflex = 1.11 L=Dflex = 1.30 L=Drigid = 1.19 L=Drigid = 1.16 Second Rotation L=Dflex = 1.02 L=Dflex = 1.18 L=Drigid = 1.17 L=Drigid = 1.12 de ects changes during the second revolution, resulting in a lower e ective angle of attack. Further experimentation is required to con rm this hypothesis. 4.7 Summary This chapter presented and discussed force measurements for a rigid and chord- wise exible rotating wing at a xed angle of attack of 45 deg. As the wing accel- erated, a peak is observed in the lift and drag coe cients. This peak is largely due to added mass. The added mass was theoretically calculated for the drag force and agreed with the peaks observed from the experimentation. After the initial peak, the coe cients undershoot, increase again and eventually attain a \steady-state" after 5 chord-lengths of travel (approximately 133 deg of rotation). The coe cients remain at this intermediate value for the remainder of the rst revolution. When the wing begins the second revolution, both the lift and drag coe cients begin to decrease again and level out at a second intermediate value until the wing begins to decelerate. The lift and drag coe cients values decrease by approximately 22% 120 from the rst to the second revolution. Other parameters that were varied include velocity pro les, acceleration pro- les, Reynolds number and wing exibility. Varying the velocity and acceleration pro les only a ected the acceleration phase of the lift and drag coe cients. Higher accelerations resulted in a higher added mass and peak value of the coe cients. Increasing the Reynolds number from 15,000 to 25,000 did not have an e ect on the rigid wing, but signi cant di erence was observed on the exible wing. This di erence in the coe cients observed on the exible wing is a result of the ability of wing?s ability to passively deform. At a Re = 15,000, the the angle of attack (chord line from leading edge to trailing edge) was 50 deg, and at Re = 25,000 the angle of attack was 35 deg. For all cases tested, a high lift was achieved during the acceleration phase and in the rst revolution, though values dropped o in the second revolution. 121 Chapter 5 Concluding Remarks 5.1 Overview The work presented in this thesis examined the ow and forces acting on a model of a hovering insect wing stroke. The wing stroke was modeled as a xed angle of attack rectangular at plate of aspect ratio 2 rotating about the root. Dye ow visualization was performed at Reynolds numbers of 5,000 and 10,000 to identify the ow features that formed on the wing. A force balance was used to quantify the aerodynamic forces produced by these ow structures. Due to the limitations of the submersible force transducer used, the force acting on the wing were measured at higher Reynolds numbers of 15,000 and 25,000. Several parameters were varied in each set of experiments. Additionally, a new model that introduced unsteady pitch variation on the rotating wing was developed. Preliminary dye ow visualization was performed on the pitching-and-rotating wing to begin to characterize the e ect of unsteady pitch variations on the structure of the ow. 122 5.2 Conclusions of the Study 5.2.1 Flow Visualization on the Rotating Wing 1. Dye injection at the wing root at a Reynolds number of 5,000 indicated the formation of a coherent leading edge vortex (LEV) near the wing root, as shown in Figure 3.1. Further outboard, the leading edge vortex became less coherent and eventually burst. As the wing continued to rotate for multiple revolutions, the spanwise location where the leading edge vortex burst moved inboard towards the wing root (Figure 3.2). 2. The ow structures at a Reynolds number of 10,000 were similar to those observed on the Re = 5,000 case. The location along the wing span where the leading edge vortex burst moved inboard towards the wing root at the higher Reynolds number. The length of the coherent portion of the leading edge vortex appeared to be smaller than for the Re = 5,000 case. It is hypothesized that increasing the Reynolds number induces vortex bursting earlier. This is in agreement with previous ndings by Lentink and Dickinson [69]. 3. Closing the gap between the wing root and the axis of rotation caused the leading edge vortex to burst nearer to the wing root, and no coherent leading edge vortex was observed for multiple revolutions (see Figures 3.8 and 3.9). However, in this setup the dye was not injected at the true wing root, so it is possible that a coherent leading edge vortex exists inboard the dye injection location. 123 4. Dye injection performed in the burst vortex revealed several small scale vor- tices forming and shedding at the leading edge. Shed vortices traveled down- stream over the wing and began recirculating about a point. As time pro- gressed, this recirculation region grew and a large scale recirculating region (i.e., the burst leading edge vortex) was observed, extending from the leading edge to the trailing edge. 5. Regardless of the wing?s acceleration, a recirculation region formed when the wing?s angle of attack was 45 deg. At lower acceleration rates, larger vortices formed on the rotating wing. At higher acceleration rates the vortices shed with at a higher frequency. 6. At a xed angle of attack of 15 deg, unlike the 45 deg case, no recirculation region was present (see Figure 3.13), suggesting that there is no attached leading edge vortex present on the wing at this incidence. 5.2.2 Flow Visualization on the Pitching-and-Rotating Wing 1. A new pitching-and-rotating wing model was designed and constructed to introduce unsteady pitch variations on the rotating wing. Wing rotation was driven by a stepper motor above the water line and unsteady pitch variations by a submergible servo motor. 2. At low angles of attack, the ow structures on the pitching-and-rotating wing were similar to the ow structures observed on the rotating-only wing at an angle of attack of 15 deg. 124 3. At high angles of attack, a large recirculating region formed near the leading edge with attached ow behind it. As the wing pitched down, the recirculating region was ejected o the wing vertically instead of shedding downstream as in the xed angle of attack case. These ow structures appeared to reestablish for the subsequent pitch cycles. 5.2.3 Force Measurements on the Rotating Wing 1. During the acceleration phase of the rotating wing stroke, a high peak in the lift and drag coe cients was observed. This peak is attributed to the added mass of the wing due to the unsteady motion. The added mass was calculated analytically for the drag force and agreed with the peaks observed experimentally. 2. During the constant velocity phase of the wing stroke, the force coe cients decreased. They brie y undershot but eventually increased, and after 5 chord- lengths of travel leveled out at an intermediate value for the remainder of the rst revolution. See Figure 4.5(a) for an example. 3. During the second revolution of the constant velocity phase of the wing stroke, both the lift and drag coe cients decreased again and leveled out at a second, lower, intermediate value until the wing begins to decelerate. The residual velocity present in water from the previous wing stoke, induced a downwash on the wing. This downwash reduced the e ective angle of attack of the wing resulted in lower coe cients. 125 4. Varying the distance over which the wing accelerated, and thus the wing ac- celeration, only a ected the force coe cients during the acceleration phase of the wing stroke (see Figure 4.12). 5. The shape of the lift curve for the exible wing was similar to that of the rigid wing. The initial peak observed on the exible wing was much smaller than that observed on the rigid wing. 6. At a Reynolds number of 15,000, the rigid and exible wings had approxi- mately the same force coe cients, likely because the steady-state de ection angle of the exible wing resulted in an e ective angle of attack near that of the rigid wing. At Re = 25,000, the trailing half of the wing de ected upwards, resulting in a angle of attack that was much lower than the angle of attack of the rigid wing, and lower lift and drag coe cients. 5.3 Remarks for Future Work The current work revealed a coherent leading edge vortex near the root of a rotating wing and began investigating a wide variety of possible parameter vari- ations. This experimental setup developed here could be used as-is to provide a more complete understanding of the many factors that may a ect the stability of the leading edge vortex. Some suggestions for near-term future work are as follows: 1. Dye ow visualization on the rotating wing at a xed angle of attack showed the LEV burst at the quarter span location on the wing. However, when the 126 wing was further rotated, the length of the coherent portion of the LEV grew and burst further outboard. Similarly, when the forces were measured, after the initial peak the coe cients undershot, overshot and eventually settled at an intermediate value for the remainder of the rst revolution. It is unclear as to what causes this initially burst LEV to grow or why the force coe cients uctuate. This region of the wing stroke should be studied more closely to understand the behavior of the LEV within 5 chord-lengths of travel. 2. To fully understand the e ect of smoothing the wing?s velocity pro le, the acceleration of the linear and smoothed cases should be matched and force measurements and dye ow visualization repeated for these cases. This will help understand if there is any merit in smoothing the velocity pro le, and what the e ect of doing so is on the ow on the wing and the forces produced. 3. To better understand the e ect of the wing root geometry, the gap between the wing root and the axis of rotation should be eliminated by reducing the length of the tygon shaft rather than lling it in as was done in the current work. This would maintain the aspect ratio of the wing (though it would alter the radius of gyration). Dye ow visualization should then be performed at the true wing root. This will help determine whether a coherent leading edge vortex is present for multiple revolutions very near the wing root. 4. For the exible wing, a spring could be incorporated in an attempt to increase lift and/or L=D while keeping the bene ts of a hinged wing?s ability to deform. Additional force measurements could also be performed on both the exible 127 wing used in this experiment, and also another con guration of an aspect ratio 2 wing that is free to rotate about the leading edge. This test case would isolate the passively deforming portion of the wing and would help to better understand the aerodynamic forces that act on passively deforming wings. Flow visualization could be done on all of the wings described above. Finally, high speed videos could be taken of the accelerating portion of the wing stroke. This data, combined with force measurements, will help to illuminate the mechanisms that occur during the accelerating phase of the rotation. 5. The pitching-and-rotating wing model developed in this work is a new and unique model. This uniqueness should be exploited in an attempt to under- stand the bene ts of introducing unsteady variations in pitch on the rotating- only wing model. Flow visualization should be performed by injecting dye at the wing root. This will help determine the e ect of pitch on the coher- ent leading edge vortex near the wing root. After qualitatively understanding the behavior of the ow structures, particle image velocimetry should be per- formed on the pitching-and-rotating wing. A crucial parameter that was not varied in this work is the reduced frequency (k). The reduced frequency can be easily varied by increasing or decreasing the rate of change of pitch by programing the servo motor appropriately. An understanding of the e ects of the reduced frequency could prove to be very crucial to be able to successfully exploit unsteady mechanism which will help design a apping wing micro air vehicle. 128 The research presented in this thesis has provided a well-rounded qualitative understanding of the ow structures near the leading edge of a rotating wing. How- ever, several quantitative properties such as the vorticity, circulation, and strength of the leading edge vortex are still unknown. A quantitative method such as parti- cle image velocimetry is required to measure these properties of the ow structures. 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