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Biomimetics and bio-inspiration for moderate Reynolds number airfoils and aircraft

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Biomimetics and bio-inspiration for moderate Reynolds number airfoils and aircraft

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Content Biomimetics and Bio-inspiration for Moderate Reynolds Number Airfoils and Aircraft by Yohanna G. T. Hanna A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Aerospace Engineering) May 2020 Copyright 2020 Yohanna G. T. Hanna Dedication To my parents, George and Nahed, and my sister, Mariam, for always supporting and encouraging me throughout my life ii Abstract Recently, there has been a push towards smaller unmanned air vehicles (UAVs) due to decreased size and weight of available electronics and actuators. These new vehicles occupy a Reynolds number (Re) regime from 10 4 to 10 5 . At these scales, the aerodynamics of airfoils and nite wings yield nonlinearities in the lift curve and are sensitive to small perturbations in the ow and/or geometry. These sensitivities at once make measurement, prediction and control dicult and at the same time allow for new control strategies. The design space of small wings can readily expand to unusual geometries and mechanisms, and as advanced materials are developed, there is renewed interest in large- and small-amplitude shape changing properties. With the design of wings and aircraft in this moderate Re regime being little understood, this work aimed to predict, quantify, and explain any benets of several planform and airfoil design strategies. First, a MATLAB model based on aerody- namic theory was created to determine the potential ight performance benets of span and chord variations. These included lift to drag ratio optimization for a given ight speed and maneuverability parameters, such as turn radius. It was determined iii that telescoping wings potentially provide greater ight performance benets in com- parison to biomimetic morphing. Absent any special matching shield, the neighboring segments on a telescoping wing introduce stepwise discontinuities in thickness and chord. Direct force balance data and PIV ow measurements of continuous, 3 step, and 7 step wings were made at Re 7:4 10 4 to determine any benecial or adverse eects of such planforms. Fur- thermore, the wings tested had boundary layer trips on the suction surface; therefore, results may also be valid at higher Re. In addition to planform design, airfoil geometry must be carefully selected in this Re regime. While deemed impractical at higher Re, the in uence of porosity at mod- erate Re is less well-known. Here, changes in lift characteristics have been quantied for a porous NACA 0012 airfoil at Re= 510 4 from force balance measurements, and a qualitative examination of the boundary layer has been conducted from dye visual- izations in addition to quantitative particle image velocimetry (PIV) measurements. Because birds and bats occupy the moderate Re regime, they must account for the above mentioned ow sensitivities. These biological systems, however, are not necessarily optimized for ight performance. Therefore, careful consideration was taken not to directly replicate and test biological planforms and airfoils; nonetheless, these animals were used as inspiration for the design principles tested. The results presented here provide insight into the design of moderate Re UAVs. iv Acknowledgments First, I would like to thank my parents, George and Nahed, and my sister, Mariam, for supporting me throughout the years. They have always encouraged my pursuit of higher education, and I would not be where I am today without them. Thank you, Dr. Spedding, for taking me as a graduate student and providing me with invaluable research and career mentorship. I would also like to thank Dr. Uranga and Dr. Luhar for always having an open door and answering my questions. I also thank Dr. Flashner and Dr. Nutt for agreeing to be on my defense committee. Thank you to my lab mates, Joe Tank, Tyler Davis, Saakar Byahut, Michael Kruger, James Croughan, and Bradley McLaughlin. I would like to specially thank Joe and Tyler for always answering my plethora of questions, even after graduating. Thank you, Andrew Chavarin, Vamsikrishna Chinta, Mark Hermes, and Christoph Efstathiou for helping me in the water channel with my experiments. I thank Chelsea Appleget for helping me take prolometer measurements. A warm thank you to Trystan Smith, Chris Ohh, and Shilpa Vijay in the stratied ow lab for always being happy to help and share equipment. v I would really like to thank Rodney Yates for machining parts and helping me x my assemblies, despite not being part of his job description. Thank you to the many undergraduate and high school students that I have mentored during my time at USC. I would like to specically thank Jack Hochschild, Ana Gabrielian, Ethan Strijbosch, Madeline Lazas, Haya Helmy, Patrick Valadez, and Stephen Douglass. They taught me more than I taught them. I would like to thank our collaborators at NextGen Aeronautics, Dr. Jay Kudva and Mark West, and at SRI International, Roy Kornbluh and Gordon Kirkwood, for supporting my research goals and allowing me to take part of such an exciting project. Thank you to everyone in the Aerospace and Mechanical Engineering oce for always being warm and friendly and making the department feel like a family. A special thanks to Silvana Martinez and Chelsea Tobin for always ordering parts for me and processing my reimbursements quickly. vi Table of Contents Dedication ii Abstract iii Acknowledgments v List Of Figures ix List Of Tables xiv List of Symbols xv List of Abbreviations xx Chapter 1: Introduction 1 1.1 Airfoil Studies in Literature . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Eppler 387 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 NACA 0012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Summary of Mechanisms . . . . . . . . . . . . . . . . . . . . . 8 1.2 Avian Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Bio-inspired Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Historical Porous Wing Studies . . . . . . . . . . . . . . . . . . . . . 14 1.5 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 2: Methods and Materials 20 2.1 Wind Tunnel Experiments . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.1 Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.2 Force Balance Calibration and Testing . . . . . . . . . . . . . 21 2.1.3 Stepped Wing Models . . . . . . . . . . . . . . . . . . . . . . 22 2.1.4 Porous Wing Models . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Flow Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.1 Particle Image Velocimetry . . . . . . . . . . . . . . . . . . . . 27 2.2.1.1 Cross-stream Plane PIV on Stepped Wings . . . . . 27 vii 2.2.1.2 PIV on Porous Wings . . . . . . . . . . . . . . . . . 28 2.2.2 Porous Wing Dye Traces . . . . . . . . . . . . . . . . . . . . . 31 Chapter 3: Flight Mechanics 33 3.1 Biomimetic Wing Sweep . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Morphing Aircraft Design Tool . . . . . . . . . . . . . . . . . . . . . 36 3.2.1 Mathematical Method . . . . . . . . . . . . . . . . . . . . . . 36 3.2.2 Telescoping Wing Predictions . . . . . . . . . . . . . . . . . . 39 Chapter 4: Aerodynamic Consequences of Discontinuous Wing Plan- forms 48 4.1 Force Balance Lift and Drag Measurements . . . . . . . . . . . . . . . 48 4.2 Flow Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Chapter 5: Eect of Porosity on Wing Performance at Moderate Re 62 5.1 Permeability and Porosity . . . . . . . . . . . . . . . . . . . . . . . . 63 5.2 Force Balance Lift and Drag Measurements . . . . . . . . . . . . . . . 66 5.3 Dye Traces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.4 Through Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.5 PIV Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.6 Sealed Pore Force Balance Testing . . . . . . . . . . . . . . . . . . . . 82 Chapter 6: Closing Remarks 86 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Reference List 89 Appendix A Surface Roughness Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 99 viii List Of Figures 1.1 Laminar Separation Bubble sectional view. . . . . . . . . . . . . . . . 3 1.2 Drag polars of 2-D E387 airfoils at various Re and facilities. . . . . . 4 1.3 Drag polar and lift curve for an E387 airfoil at various Re. . . . . . . 5 1.4 E387 airfoil with and without internal acoustic forcing. . . . . . . . . 6 1.5 C ` () of NACA 0012 at Re= 5 10 4 with uncertainty bounds. . . . . 7 1.6 Passive a) leading edge ap on an eagle and b) trailing edge ap on a skua . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.7 Sample ight mission with various ight segments. . . . . . . . . . . . 11 1.8 Avian inspired morphing aircraft with a retracting wing. . . . . . . . 12 1.9 Gull wing conguration based on seagull dihedral changes. . . . . . . 13 1.10 A sh bone inspired camber changing airfoil. . . . . . . . . . . . . . . 14 1.11 NACA 0012 with porous strip and cavity below. . . . . . . . . . . . . 16 1.12 Pressure dierence over a parabolic plate. . . . . . . . . . . . . . . . . 16 1.13 Lift versus drag of a porous airfoil. . . . . . . . . . . . . . . . . . . . 17 2.1 Dryden Wind Tunnel experimental setup. . . . . . . . . . . . . . . . . 21 2.2 3D printed wings a without and b with sweep. Mounting rods are not shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 ix 2.3 Wind tunnel test section with force balance and PIV experimental setup. Note, the mirror was not present during force balance experi- ments, and the balance was removed for PIV. . . . . . . . . . . . . . 24 2.4 CAD model of porous wing with zoomed image of the leading edge. . 26 2.5 a) Rear and b) top views of the PIV eld of view. . . . . . . . . . . . 28 2.6 Camera eld of view for porous wing PIV data acquisition. . . . . . . 29 2.7 Sample PIV eld of velocity magnitude of the porous wing at = 0 . The black box in the wake is the region where data is available for both pressure and suction surfaces when splicing elds together. . . . . . . 30 2.8 Water channel experimental setup showing camera and laser sheet placement, as well as positioning hardware. . . . . . . . . . . . . . 32 3.1 Base wing deformed into both Simple Sweep and M Sweep congura- tions with the angles dening each. . . . . . . . . . . . . . . . . . . . 34 3.2 By sweeping the wing, a reduction in D and P req is observed due to a reduction in area. In the top plots, D e , D i , and D are represented by dotted, dashed, and solid lines respectively. . . . . . . . . . . . . . . . 35 3.3 Screenshot of Morphing Aircraft Design Tool displaying default inputs. 39 3.4 NecessaryC L values to maintain steady level ight for varying b andc wing congurations. b and c axes have been rotated for clarity. . . . . 40 3.5 Comparison of L=D for various wing congurations. . . . . . . . . . . 41 3.6 Change of R with U for dierent wing congurations. . . . . . . . . . 41 3.7 Variation of L=D withA and U given a constant b. . . . . . . . . . . 42 3.8 Variation in L=D withA and U given a constant c. . . . . . . . . . . 42 3.9 The minimum turn radius as a function ofU for various wing congu- rations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.10 The maximum turn rate as a function ofU for various wing congura- tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 x 3.11 Surface plot of R min at a constant U with b and c as independent variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.12 Comparison of R min toA and U given a constant c . . . . . . . . . . 45 3.13 P req as a function of U. The orange curve represents the base congu- ration with no additional weight to enable morphing. . . . . . . . . . 46 4.1 Comparisons of C L (left) and C D (right) versus between 3 step and continuous (a and c), 7 step and continuous (b and d), and 7 and 3 step wings (e and f) at Re= 7:4 10 4 . Data are plotted with shaded uncertainty envelopes. . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2 Comparisons ofL=D versus (left) andC L versusC D (right) between 3 step and continuous (a and c), 7 step and continuous (b and d), and 7 and 3 step wings (e and f) at Re= 7:4 10 4 . Data are plotted with shaded uncertainty envelopes. . . . . . . . . . . . . . . . . . . . . . . 51 4.3 Comparisons of C L (left) and C D (right) versus . 3 step (a and d), 7 step (b and e), and continuous (c and f). . . . . . . . . . . . . . . . . 52 4.4 Comparisons of L=D versus (left) and C L versus C D (right). 3 step (a and d), 7 step (b and e), and continuous (c and f). . . . . . . . . . 53 4.5 Starting vortex creation and the generation of circulation about an airfoil according to Kelvin's circulation theorem[72]. . . . . . . . . . . 54 4.6 Horseshoe vortices are superpositioned along a lifting line to create a nonuniform lift distribution[72]. . . . . . . . . . . . . . . . . . . . . . 56 4.7 Prediction of shed vorticity,! z , and circulation, , distribution for the a) continuous and b) 3 step wings. . . . . . . . . . . . . . . . . . . . 57 4.8 Cross-stream plane of streamwise vorticity 0:75c downstream of the a) 3 step, b) 7 step, and c) Continuous wings at = 5 . X mark denotes wing discontinuity locations. . . . . . . . . . . . . . . . . . . . . . . . 58 4.9 Cross-stream plane of streamwise vorticity 0:75c downstream of the a) 3 step, b) 7 step, and c) Continuous wings at = 9 . X mark denotes wing discontinuity locations. . . . . . . . . . . . . . . . . . . . . . . . 59 5.1 Velocity prole of channel ow with a permeable lower wall. . . . . . 64 xi 5.2 DNS results of wall normal vorticity elds. . . . . . . . . . . . . . . . 65 5.3 a)C ` and b)C d with uncertainty envelopes for a quasi-2D NACA 0012 at Re= 5 10 4 for the solid airfoil (red) with comparison to Tank, et al. (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.4 a) L=D versus and b) drag polar for comparison between the solid airfoil (red) and Tank, et al. (blue). . . . . . . . . . . . . . . . . . . . 68 5.5 a)C ` and b)C d versus of a solid (red) and porous (purple) quasi-2D NACA 0012 wing at Re= 5 10 4 . . . . . . . . . . . . . . . . . . . . . 68 5.6 a)L=D versus and b) drag polar for solid (red) and porous (purple) wings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.7 Instantaneous dye images for = [0:0; 0:2; 0:4; 0:5; 0:6; 0:8 ]. Images on the left are of the solid airfoil; those on the right are of the porous airfoil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.8 Three instantaneous ow elds at = 3:0 . Below, is the time- averaged image of 1,300 frames. Solid on left; porous on right. . . . . 71 5.9 Streamwise separation location, estimated from time-averaged dye im- ages for the solid and porous NACA 0012 at Re= 5 10 4 . . . . . . . 72 5.10 Mechanism of pressure driven porous airfoil ow. . . . . . . . . . . . 73 5.11 u ? =U computed using Equation 5.9 and XFOILC p results at Re= 510 4 . 75 5.12 Comparison of boundary layer prole with and without uniform suction. 76 5.13 PIV derived elds of velocity magnitude (left) and spanwise vorticity (right) for = 0 to 1 in 0:2 increments. . . . . . . . . . . . . . . . . 80 5.14 PIV derived elds ofu (left) andw components (right) for = 0 to 1 in 0:2 increments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.15 a) C ` and b) C d versus of a solid (red) and all pores sealed (dark blue) qausi-2D NACA 0012 wings at Re= 5 10 4 . . . . . . . . . . . . 82 5.16 a)L=D versus and b) drag polar of a solid (red) and all pores sealed (dark blue) wings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 xii 5.17 a)C ` and b)C d versus of a solid (red) and ve aft pores open (green) qausi-2D NACA 0012 wings at Re= 5 10 4 . . . . . . . . . . . . . . . 84 5.18 a) L=D versus and b) drag polar of a solid (red) and ve aft pores open (green) wings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.1 a) Chordwise and b) spanwise prolometer traces of machined NACA 0012 wing used in by Tank, et al. . . . . . . . . . . . . . . . . . . . . 99 A.2 a) Chordwise and b) spanwise prolometer traces of the NACA 0012 model printed on the PrintrBot machine. . . . . . . . . . . . . . . . . 100 xiii List Of Tables 4.1 Estimates of circulation for the three wings based on PIV data. for the wingtip, area inboard of the tip, and total area were computed separately, and that was nondimensionalized byUc. Uncertainty for all measurements is estimated to be 0.005. . . . . . . . . . . . . . . . 60 A.1 Roughness measurements of wing samples. All samples had a NACA 0012 prole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 xiv List of Symbols a = speed of sound A = aspect ratio b = span [m] c = chord [m] c = mean aerodynamic chord [m] c r = root chord [m] c t = tip chord [m] C d = sectional drag coecient C D = drag coecient C D0 = zero lift drag coecient C Di = induced drag coecient c f = skin friction coecient C ` = sectional lift coecient C L = lift coecient xv C L;max = maximum lift coecient C ` = lift curve slope of innite wing C L = lift curve slope of nite wing C p = pressure coecient d = sample thickness [m] D = drag force [N] D 0 = zero lift drag force [N] D i = induced drag force [N] D min = minimum drag force [N] e = Oswald eciency factor E = mass specic energy [J/kg] h = average surface height [m] ~ h = local surface height [m] k = Oswald shape term L = lift force [N] L=D = lift to drag ratio (L=D) max = maximum lift to drag ratio Ma = Mach number M max = maximum root bending moment [Nm] xvi n = g-load factor N = maximum g-load factor p = local static pressure [N/m 2 ] p 1 = freestream static pressure [N/m 2 ] P req = power required [W] q = dynamic pressure [N/m 2 ] r = ow resistivity [Pa s/m 2 ] R = range [m] R A = arithmetic mean of Z Re = Reynolds number Re x = Reynolds number as a function of x R min = minimum turning radius R q = root mean square of Z S = planform area [m 2 ] S H = total hole planform area [m 2 ] S wet = total wetted surface area [m 2 ] t = airfoil thickness [m] U = freestrean velocity [m/s] u ? = pore disturbance [m/s] xvii u = time-averaged velocity in x [m/s] v = time-averaged velocity in y [m/s] W = weight [N] w = time-averaged velocity in z [m/s] W bat = battery weight [N] x = streamwise direction [m] x s = top chord normal separation location y = spanwise direction [m] z = cross-stream direction [m] Z = deviation in surface height [m] = angle of attack [ ] stall = angle of attack [ ] = circulation [m 2 /s] = boundary layer thickness [m] = change in a parameter tot = total aircraft eciency = permeability [m 2 ] = sweep angle [ ] in = inboard sweep angle [ ] xviii out = outboard sweep angle [ ] = dynamic viscosity [Pa s] ~ = eective viscosity [Pa s] = kinematic viscosity [m 2 =s] = porosity = density [kg/m 3 ] = porosity coecient ! max = maximum turn rate [rad/s] ! x = streamwise vorticity [1/s] ! y = spanwise vorticity [1/s] xix List of Abbreviations AC = Aerodynamic Center CFD = Computational Fluid Dynamics DNS = Direct Numerical Simulation DWT = Dryden Wind Tunnel E387 = Eppler 387 FDM = Fused Deposition Modeling LSB = Laminar Separation Bubble MS = M Sweep NACA = National Advisory Committee for Aeronautics NASA = National Aeronautics and Space Administration PIV = Partile Image Velocimetry RANS = Reynolds-Averaged Navier-Stokes SS = Simple Sweep UAV = Unmanned Air Vehicle URANS = Unsteady Reynolds-Averaged Navier-Stokes xx xxi Chapter 1 Introduction 1.1 Airfoil Studies in Literature The balance of inertial to viscous terms in the Navier-Stokes equations governing uid motion is expressed by the Reynolds number, Re. A given characteristic ow speed, U, characteristic length scale, l, and kinematic viscosity, , yields Re = Ul : (1.1) Historically, research interests have focused on high Re, on the order of 10 6 and above, due to scales necessary for manned ight. With the increased use of unmanned air vehicles (UAVs) in both military and civilian applications as well as small-scale wind turbines, jet engine fan blades, and high-altitude vehicles [1{3], there has been a growing interest in airfoils at Re between 10 4 and 10 5 , or moderate Re. Applications include surveillance, weapons deployment, search and rescue, and package delivery. 1 Additionally, such UAV's could carry various sensors, including chemical and biolog- ical sensors [4] for scientic research. The performance of a wing or aircraft is characterized by lift, L, and drag, D, which when nondimensionalized by the dynamic pressure, q, and planform area, S, yields the coecient of lift C L = L qS (1.2) and coecient of drag C D = D qS : (1.3) Mueller, et al. [5] discussed how the boundary layer of airfoils at moderate Re are sensitive to free stream uctuations. Additionally, they observed hysteresis in both C L and C D due to varied separation points depending on increasing or decreasing angle of attack, . This is because one branch of the hysteresis loop has a separated laminar boundary layer, while the other branch has attached ow for most of the chord. In the latter case, the laminar free shear layer transitions and reattaches as a turbulent boundary layer [6]. This phenomenon is known as a Laminar Separation Bubble (LSB). Figure 1.1 summarizes the formation of these LSB's. The attached laminar boundary layer encounters an adverse pressure gradient, causing it to separate. The free shear layer develops above the bubble and transitions. 2 Figure 1.1: Laminar Separation Bubble sectional view [7]. Turbulent mixing causes momentum transfer, eliminating the reverse ow bringing about reattachment [8]. LSB's have a signicant impact on the global airfoil oweld and must be understood to eectively design airfoils and wings at moderate Re. Examining classical airfoils such as the Eppler 387 (E387) and the NACA 0012 will provide insight into the unique behavior of airfoils at these Re. 1.1.1 Eppler 387 The E387 is a moderately thick, cambered airfoil designed for sail planes operating at Re> 2 10 5 [9]. At Re below this bound, experimental results on this airfoil show large discrepancies between facilities, as seen in Figure 1.2, due to sensitivities to wind tunnel turbulence levels, model contour accuracy, and model surface roughness [10]. 3 Figure 1.2: Drag polars of 2-D E387 airfoils at various Re and facilities [12]. Replotted by Yang and Spedding [13]. For this reason, the E387 has become a benchmark cross-section used to compare airfoil data between facilities [11]. Selig and McGranahan's [11] experiments examined the lift and drag character- istics of the E387. The atypical shape of the Re=10 5 curve, shown in Figure 1.3, is associated with the formation of a LSB. A common explanation for this phenomenon is as follows. At the bottom corner of the low-drag range, the LSB is short or nonex- istent. As is increased, the adverse pressure gradient becomes greater, causing the bubble to grow, and with it, drag rises to a local maximum. Beyond this point, the bubble begins to shrink, lowering drag, until the top corner of the low drag range is reached. At this point, transition occurs, and no bubble is produced at higher . 4 Measurements made by Spedding and McArthur [14] on the E387 at Re 6 10 4 in the Dryden Wind Tunnel (DWT) at USC showed the breakdown of inviscid ana- lytical theory used to predict induced drag, i.e. drag due to ying with nite wings. Yang and Spedding [13] made measurements in the same tunnel and found that lo- cal spanwise variations in separation location correlated with local changes in C d ; however, this variation does not account for the signicant dierences between facil- ities shown in Figure 1.2. Small holes drilled into the suction surface with embedded chambers caused signicant aerodynamic changes. Acoustic resonance in the cham- bers promoted switching between high and low lift states [9]. With speakers both Figure 1.3: Drag polar (left) and lift curve (right) for an E387 airfoil at various Re [11]. 5 internal and external to the wing, acoustic forcing induced high lift states at par- ticular frequencies, as shown in Figure 1.4, leading to L/D increases by up to 70% [15, 16]. 1.1.2 NACA 0012 Like the E387, the NACA 0012 is a moderately thick airfoil section; however, it is a symmetric section, soC L () andC D () are symmetric about = 0 . The origins of the airfoil are deeply rooted in the infancy of aeronautical design and was originally tested atRe 310 6 [17]. Though the NACA 0012 has become a simple benchmark airfoil at a wide range of Re, McCroskey's [18] comparison of data from more than 40 experiments from various facilities showed even data at high Re are not fully in agreement, and the little data available at moderate Re were in even worse agreement. Figure 1.4: E387 airfoil with and without internal acoustic forcing at Re= 4 10 4 (left) and Re= 6 10 4 (right) [16]. 6 Laitone [19] made measurements at Re= 7 10 4 on a NACA 0012 both facing forward and backwards in addition to a thin wedge and a cambered at plate. Sur- prisingly, the NACA 0012 facing backwards performed better than the same section oriented properly, and the cambered at plate performed the best. By increasing the turbulence levels in the tunnel from 0.02% to 0.10%, lift was increased on a NACA 0012 at a Re= 20; 700 [1]. Huang and Lee [20] observed a shortening of the LSB at Re= 5:5 and 910 4 when turbulence levels were increased from 0.2% to 0.65%. They also saw a nonlinear C L () curve and C L above inviscid theory for small at low turbulence levels. Similar measurements made by Tsuchiya, et al. [21] and Kim, et al. [22] qualitatively agreed with these results. Figure 1.5: C ` () of NACA 0012 at Re= 5 10 4 with uncertainty bounds [23]. Recent experiments show small positive lead to negative lift [23]. The authors associated this with the separation point on the bottom surface being further aft 7 than the separation point on the top surface. This caused a decrease in the down- ward induced velocity. Reynolds-averaged Navier-Stokes (RANS) simulations in the same study was unable to capture this behavior, highlighting the diculty of using computational uid dynamics (CFD) with turbulence models to properly capture the dynamics at these low Re. The presence of a LSB was associated with improved aerodynamic performance. All of this is surprising behavior for a simple symmetric airfoil. 1.1.3 Summary of Mechanisms The boundary layers of airfoils at moderate Re are prone to laminar separation in an adverse pressure gradient. The separated shear layer can then transition to turbulence, and reattachment in the mean, causing LSB's. These LSB's can strongly aect the streamlines outside of the boundary layer, altering the eective shape of the airfoil. The presence of LSB's may cause hysteresis in C L and C D when varying . Acoustic forcing can prevent hysteresis and push the airfoil into a high-lift state. The movement forward and aft of laminar separation points on the top and bottom surfaces can lead to negative lift for small positive . 1.2 Avian Flight Though wind tunnels may have low turbulence levels, a wing in real world ap- plications may only rarely y in such quiet conditions. Coincidently, birds occupy 8 a similar Re regime as the ight vehicles of interest. Birds must provide both lift and thrust to lift themselves up into the air as well as propel themselves forward. Synthetic systems, however, can decouple thrust from the wings by using a motor. Therefore, avian physiology is a solution to moderate Re ight, but may not be ideal for all engineered airframes. Nonetheless, observations of wild birds [24], experiments on trained birds in wind tunnels [25], or measurements of just wings from deceased birds [26] have shown that birds optimize their wing planform for various ight con- ditions. Similar shape changes may be advantageous to modern aircraft and will be discussed further in Section 1.3. At low speeds or under gusty wind conditions, the exible feathers on a bird wing pop up at both leading and trailing edges, as seen in Figure 1.6. Liebe [27] postulated that once separation begins to develop, reverse ow causes the feathers on the upper surface to be pushed up preventing separation from moving forward. Wind tunnel experiments on wings with a passive ap inspired by this mechanism found an 18% increase inC L;max [28]. Flight tests were conducted on a Stemme S10 motorized glider and found a 3.5% reduction in minimum ight speed with the application of passive aps [29, 30]. For a single feather, aeroelastic forces cause the nose of the feather to droop. This eectively changes the camber of the feather. This variation in camber causes a wide range of C L values with little variation in C D [31]. Bird feathers and wings are relatively rough in comparison to most manufactured wings. Lentink and de Kat [33] and van Bokhorst, et al. [34] found that surface 9 a) b) Figure 1.6: Passive a) leading edge ap on an eagle [32] and b) trailing edge ap on a skua [29]. roughness of a swift wing at Re< 3:6 10 4 reduced ow separation. The rough wings cause small, well-contained recirculation zones within the valleys between feather structures keeping the ow attached [34]. Additionally, feathers are permeable. This permeability has no directional bias from dorsal to ventral; however, there is large variation in the permeability dependent upon the feather type and location on the feather [35]. Force measurements made on the foremost primary feather of the White Stork (Ciconia ciconia) with and without an air seal showed an increase in lift to drag ratio when air could pass through the feather [31]. The aerodynamics at moderate Re are very sensitive to small details of boundary layer movement, which can have large eects on the global ow. Several active and passive control strategies have been identied. One passive modication that could be eective is in allowing some ow through the airfoil surface creating small disturbances, which in turn would stabilize the sensitive boundary layer. 10 1.3 Bio-inspired Flight With biological systems, it is dicult to decouple the often multifunctional aspects of a structure or behavior. For example, feathers are necessary to provide lift for a bird, but it also keeps the animal warm; therefore, the feature may not be optimal for one or the other. Therefore, engineered systems provide control over the specic parameters wished to be studied in comparison to measurements made on living or deceased animals. Takeo Climb Cruise Climb Cruise Mission Segment Loiter Descent Landing Dive Cruise Descent f Figure 1.7: Sample ight mission with various ight segments. Every ight is divided into mission segments, as shown in Figure 1.7. Conventional aircraft are typically optimized for only one or two segments and only exhibit small- scale morphing, such as landing gear retraction or slat and ap deployment. During o-design mission segments, the aerodynamic performance of the aircraft is reduced [36, 37]. As discussed above, birds can adapt their planform shape for optimal gliding ight [26], or many mission segments. Similar planform changes could be benecial to the aerodynamic performance and control of UAVs. 11 Signicant changes in chord and span can reduce the fuel consumption in an aircraft at variable ight speeds, but often increases the weight of the aircraft [38]. For planes only intended for limited mission segments, this weight penalty often negates the aerodynamic benet. As more tasks and roles are added to requirements, the feasibility of morphing grows. For instance, wing sweep has a strong in uence on pitching moment and could be used to reduce control surfaces [39]. By using wing sweep for both control and ight envelope extension, morphing capability may be desired despite the weight and complexity penalties. Figure 1.8: Avian inspired morphing aircraft with a retracting wing [40]. Di Luca, et al. [40] constructed a UAV with a feather like outer wing, as seen in Figure 1.8. When the outboard wing was retracted, the total planform area was reduced by 41%. This allowed for increased lift during slow ight and reduced drag in high speed ight. To control roll, the wing was asymmetrically deployed. Similar shape changes on both the inboard or outboard sweep angles of the aircraft could lead to a small turn radius and crosswind rejection [42]. The gull-wing conguration 12 Figure 1.9: Gull wing conguration based on seagull dihedral changes[41]. in Figure 1.9, named after the similar out of plane shape changes by seagulls, caused a reduction in glide ratio, which would be benecial for a steep dive [41]. Wing twist on the outboard sections of the same aircraft provided increased roll authority over ailerons. Wind tunnel experiments on a sh bone inspired camber changing wing, shown in Figure 1.10, exhibited similar lift generation with signicant drag reduction in comparison to a wing with a discrete ap [43]. Additional concepts can be found in Barbarino, et al. [36] and Weisshaar [37]. Though research aircraft have implemented bio-inspired shape changes, distinctly non-biomimetic, telescoping wings represent a practical solution to the numerous possible mechanisms for ight envelope extension. A typical telescoping wing design leads to stepwise discontinuities in the planform. Experiments suggest that the aero- dynamic eects may be small[44, 45] while maintaining controllability[46, 47]. These results seem to have empirical support in observations of nonuniform lifting and/or 13 Figure 1.10: A sh bone inspired camber changing airfoil [43]. propulsive wings/ns of certain birds and marine life. Humpback whales (Megaptera novaengliae), for example, have regular scallops on their ipper leading edge. It is hypothesized that these structures not only do no harm, but also induce streamwise vorticity which re-energizes the boundary layer, thus delaying separation[48]. 1.4 Historical Porous Wing Studies Barslow, et al. [49], Nuber and Needham [50], and Dannenberg and Weiberg [51]. completed some of the earliest studies into porous airfoils; however, they focused on cases with suction under the permeable surface at Re> 10 6 . Suction causes a reduction and delay in separation [49, 50], which can be used to increase C L;max and stall [51]. This suction technology was not further developed, partly due to power required, as well as the potential weight penalty of the requisite pump for any aircraft using suction. 14 As ight speeds are increased, the uid cannot be approximated as incompressible. The Mach number, Ma, is the ratio of U to the speed of sound in the medium, a, or Ma = U a : (1.4) Flows at Ma < 0:3 are considered incompressible, while at 0:8 < Ma < 1, it is transonic. At transonic speeds, the local ow velocity over a wing will reach Ma = 1, and a shockwave, discontinuity in pressure and density, may form leading to a signicant increase in drag. Savu and Trifu [52], Nagamatsu, et al. [53], and Hartwich [54] all examined porous airfoils at transonic speeds. A porous surface with a cavity underneath on the aft portion of the wing, shown in Figure 1.11, was studied by these authors. While Savu and Trifu's [52] simulations had the plenum pressure prescribed, Nagamatsu, et al. [53] and Hartwich [54] held the plenum at no particular pressure in their experiments and computations, respectively. The presence of porosity on the top surface either removed the shockwave or weakened its intensity. This was attributed to the boundary layer downstream of the shockwave being ingested into the plenum and injected upstream of the shockwave. At low Ma, the porosity caused an increase in drag; however, the wave drag at higher Ma was reduced so signicantly that total drag was decreased in some cases by 46%[53, 55, 56]. Barakat [57] completed a theory-based study of porous sails and airfoils in inviscid, incompressible ow. He found that the pressure dierence between top and bottom surface diminished with increasing porosity. This causes a decrease inC ` as shown in 15 Figure 1.11: NACA 0012 with porous strip and cavity below[54]. Figure 1.12. Similarly, the aerodynamic center (AC) moves aft as a greater portion of the airfoil is porous [58]. Additionally, lift and pitching moment decrease with increased porosity [59, 60]. Iosileveskii [61] made estimates of the drag due to uid seeping through the porous material and found that a specic porosity creates a peak in drag. Interestingly, a potential ow model on an airfoil with a porous top surface on the forward portion at Re = 6 10 6 showed a 10% increase in lift [62]. a) b) Figure 1.12: a) Pressure dierence over a parabolic plate. b) C ` divided by for a at plate (A) and two dierent cambered plates (B, C). is the porosity coecient, where = 0 is a solid surface and sigma = 1 is completely transmissive. Adapted from Barakat[57]. 16 Geyer, et al. [63] made measurements on a modied SD7003 out of materials with various resistivity, r, dened as, r = p d (1.5) where d is the thickness of a sample of the porous material. At 3:8 10 5 <Re< 8:5 10 5 , increasing r, i.e. less permeable, lead to increases in lift, bringing values closer to that of inviscid ow theory, as shown in Figure 1.13 [63]. A similar trend was observed when the forward portion of the wing was taped over. Additionally, hotwire measurements observed increases in turbulent boundary layer and wake decit with decreasing r [64]. Not only does lift decrease and drag increase with porosity, AC moved forward andC L decreased with increasing porosity when a honeycomb surface was used [65]. Figure 1.13: Lift versus drag normalized by lift and drag at = 0 for the solid case respectively. r is given to the left of each curve[63]. Iosileveskii [59] predicted the reduction in C L and hypothesized that this could be useful in gust and turbulence alleviation. A more gradual lift slope leads to smaller 17 jumps in lift with a sudden change in . Dahdi, et al. [66] ran 2D Unsteady RANS (URANS) simulations on a WTEA-TE1 airfoil with holes cut into the top and bottom surfaces with separate plenums underneath at Re = 6 10 6 and Ma = 0.3. Like Hartwich [54], they found that that uid entered the plenum aft and was expelled forward. They also found that for certain turbulence test cases, a reduction in peak C L during a gust was accomplished with increasing porosity; however, this was not true for all test cases, and diminished lift performance for all in steady-state ight was observed. Comparable computations made by Eljack, et al. [67] came to similar conclusions. 1.5 Objectives The aerodynamics at moderate Re are often complex and counter-intuitive in comparison to higher Re ows; however, this allows for unconventional solutions to the design of aircraft. This study will quantify the aerodynamic benets of plan- form variations, including bio-mimetic and telescoping wing changes, by creating a ight mechanics based model, and determine the key parameters aecting vehicle performance. Because some telescoping wing designs introduce discontinuities in the wing planform, static wind tunnel experiments will be conducted on stepped wings to determine any adverse eects of such planforms at moderate Re. PIV measure- ments will be used to understand the uid dynamical reasoning for any similarities or dierences observed in force balance testing. While this rst portion used planform 18 changes to aect a highly three-dimensional oweld, the nal piece of this work will focus on the eect of small changes in porosity on the boundary layer of a NACA 0012 at Re= 5 10 4 , known to have odd lift performance at small. The underlying mechanisms behind performance changes will be determined through qualitative dye visualizations and quantitative PIV measurements. Though biology in a similar Re regime was used as inspiration for this work, the intention was to understand the underlying aerodynamic principles for a given form than to directly replicate nature. 19 Chapter 2 Methods and Materials 2.1 Wind Tunnel Experiments 2.1.1 Facility All wind tunnel experiments were conducted in the Dryden Wind Tunnel at the University of Southern California. The regular octagonal test section, pictured in Figure 2.1, has a width of 1.37 m. Turbulence levels were < 0:035% for frequencies between 10 and 1000Hz for velocities between 4 and 20 m/s. The excellent ow quality is attributed to 11 anti-turbulence screens upstream of the long and gradual 8:1 contraction ratio converging section. It was assumed that the freestream ow was aligned with the walls. To align models, a camera above the model, normally used for Particle Image Velocimetry (PIV), was leveled and aligned with the bottom of the wind tunnel. Then, the model was aligned by eye using the camera. The uncertainty 20 of alignment is estimated to be 0:3 . was varied using the rotary table, on which the model and balance were assembled. Camera Endplates Shrouded Sting Force Balance Rotary Table Laser Sheet y x z Figure 2.1: Dryden Wind Tunnel experimental setup. 2.1.2 Force Balance Calibration and Testing A shrouded sting rested upon a custom, three-component, cruciform shaped force balance[68]. The balance was mounted to a rotary table, which set . Axial and normal arms were calibrated by statically applying a range of expected loads. A cal- ibration was completed before each test producing a 3-by-4 calibration matrix. This matrix was then averaged with 2 previous matrices, which was used for experimental data collection. The measurement uncertainty of the balance in the axial direction was 5 mN and 15 mN in the normal direction. Before each test, zeroing forces were recorded corresponding to the weight of the model, on the order 20 mN and 10 mN in axial and normal directions respectively. Each experiment consisted of 5 forward and backward sweeps. For stepped wing 21 experiments, was varied between3 and 15 in 1 increments. Experiments com- paring porous and solid wings varied from5 and 12 in 0:5 increments. Once these measurements were completed on the porous or solid wing, a ner sweep in 0:1 increments was conducted at small. In every case, the ow was allowed to settle for 10 s after was changed. Data was sampled at 1kHz for 10 s and averaged producing a single measurement. 10 measurements were then averaged yielding a single data point for each . The maximum of the measurement standard deviation, percision, and device uncertainty was considered the uncertainty of the data point. 2.1.3 Stepped Wing Models a) b) Figure 2.2: 3D printed wings a without and b with sweep. Mounting rods are not shown. Three half-span wings were 3D printed using PLA lament on a Raise3D Pro2 Plus, which has a 12.5 mmx-y resolution and 10 mm layer thickness. All wings had a NACA 0012 prole with c r = 10 cm and c t = 7 cm, root and tip chords respectively, and b = 42 cm, span. The congurations considered were 3 steps, 7 steps, and 22 continuous, as shown in Figure 2.2a. Wing sections were arranged so the thickest portion of the wing, or 0:3c, was at a constantx location alongy. For stepped wings, the wing was sectioned into rectangular segments of equal span, while the continuous wing had a trapezoidal planform. Such geometric constraints meant that all wings had the same planform area, S, of 357.0 cm 2 and aspect ratio,A, dened as, A = b 2 S : (2.1) The semispanA = 2:5 for all models. The mean aerodynamic chord,c, was computed by c = 2 S Z b=2 0 c 2 (y)dy ; (2.2) and was found to be within 0.1 cm of 8.7 cm for all models. An 8 mm steel rod was epoxied into each wing at c=4, which also corresponded with c r =4, to mount the models within the tunnel. To replicate a sideslip angle, three additional models were printed on the same 3D printer. Pictured in Figure 2.2b, the geometry from the rst set of experiments was swept by 10 from the leading edge and the corresponding area removed from the wing. The new area was approximately S = 348:3 cm 2 . Swept models were arranged on the print bed so that layers were deposited in the same orientation as the unswept models so as to keep the direction of surface roughness similar to that of the unswept 23 models. To ensure forces were applied at similar location with respect to the force balance, the 8 mm steel mounting rod was placed at c=4, which was further aft than c r =4. Experiments were conducted at U = 12:7 m/s, or Re 74 10 3 . Because experiments were conducted at a moderate Re, the top surface of all six wings were tripped at 0:1c. Based on at plate estimates, the laminar boundary layer = 5:2x=Re x 1=2 = 0:57 mm at the root chord trip location. Because there is an adverse pressure gradient, the boundary layer is expected to be thicker than this prediction. Boundary layer trips were created by layering 8 strips of 0.07 mm thick tape; therefore, the trip height was 0.56 mm or 0:99 lam at the root chord. The tape had a width of 6.30 mm, or 60%t, where t is the maximum chord thickness at c. Mirror Laser Sheet Rotary Table Endplate Shrouded Sting Force Balance Camera y x z Figure 2.3: Wind tunnel test section with force balance and PIV experimental setup. Note, the mirror was not present during force balance experiments, and the balance was removed for PIV. To create a quasi-full-span ow, an endplate was mounted at the root of the wing, as seen in Figure2.3. The endplate had dimensions of 8:18c in x by 4:09c in z and 24 a thickness of 0:15c. To allow for the mounting rod, a slot in the plate was placed at 2:48c in x and at the center in z. Based on the longest distance from the leading edge of the end plate to the leading edge of the model, was estimated to be 2.3 mm. The gap between the model and the endplate was less than 1 mm, or 0.43. From projected areas the blockage in the test section was estimated to be 2.5% so the comparative data were not corrected. 2.1.4 Porous Wing Models TwoA = 4 rectangular NACA 0012 prole wings of c = 15 cm, and b = 60 cm, were 3D printed from PLA. U was set to 5 m/s corresponding to Re= 5 10 4 . The solid wing was printed in three sections on a PrintrBot Replicator 2 with layer and x-y positioning resolution of 100 mm and 11 mm respectively. For the porous model, a Prusa i3 MK2 printer, which has a 50 mm layer resolution and 10 mm x-y position resolution. Due to build volume constraints, the porous model was printed in 5 sections. Seams for both models were sealed with 1.3 cm wide, 72%t, and 0.20 mm thick, 1:1%t, duct tape. Both models were not sanded but had similar surface roughness due to being printed on comparable resolution machines. A Comparison of surface roughness is given in Appendix A. A 0.8cm steel rod was inserted in the models at c=4 to be used for mounting in the wind tunnel. The porous model was printed with 1 mm, 0.67% c, holes oriented perpendicular to the chord line. The holes were arranged in a rectangular pattern starting at 10% 25 Figure 2.4: CAD model of porous wing with zoomed image of the leading edge. c from the leading edge and spaced 10% c apart along the chord line. Holes were placed starting at 10% b and evenly spaced by 10% c in the spanwise direction, as shown in Figure 2.4. In total, the porous wing had 297 holes. Estimating porosity, , as the ratio of the area of the holes, S H , to the total planform area, S, = 0:010. To create a quasi-2D ow, endplates were mounted on either side of the model. The endplates had dimensions of 4:74c inx by 2:37c inz and a thickness of 0:08c. The laminar boundary layer thickness was estimated to be = 3:6 mm at the leading edge of the model. The gap between the model and the endplate was less than 1 mm, or 0:27. A slot in the lower endplate at 1:44c from the plate leading edge and centered in the z direction allowed for the mounting rod to pass through. Based on projected areas, the wind tunnel had 3.4% blockage at highest , and again the comparitive data was not corrected. 26 2.2 Flow Visualization 2.2.1 Particle Image Velocimetry To conduct PIV measurements, the tunnel was lled with a glycerin-based smoke with particle diameters typically 0.2-0.3 mm. Images were acquired with a LaVision Imager sCMOS camera, which has 25602160 pixels and 16 bit digital output. A laser sheet was generated by a Quantel EverGreen double-pulsed Nd:YAG laser. Mod- els were painted with Stuart Semple Black 2.0 acrylic paint on the suction surface to minimize light re ections. 200 image pairs were captured for each and wing conguration at a sample rate of 9.6 Hz. To obtain velocity eld estimates, images were processed in LaVision's DaVis software. A multi-pass algorithm with two ini- tial passes of 4848 pixel interrogation windows and three passes with window size of 3232 pixels and 50% window overlap was used. The 200 instantaneous vector elds were averaged to create a time-averaged velocity eld. The vorticity eld was computed using the MATLAB function, curl. 2.2.1.1 Cross-stream Plane PIV on Stepped Wings As shown in Figure 2.3, the image was re ected into the camera by a 30 cm by 30 cm mirror mounted 66 cm downstream of the model trailing edge. Total blockage is estimated to be 7.3% of total test section area. The laser sheet was position 6.5 cm downstream of the model, or 0.75c. The camera was mounted with a Nikon 50 mm 27 a) b) Figure 2.5: a) Rear and b) top views of the PIV eld of view. NIKKOR lens, and camera eld of view in relation to the wing is shown in Figure 2.5. A time delay of 250ms between images of a pair was used. The spatial resolution of the vector eld was also 16 pixels. Due to large eld of view, this was a spatial resolution of 1.88 mm or 0.022c. The uniform background ow was subtracted leaving just the time-averaged perturbation velocities. To reduce low level noise, vorticity elds had a threshold set to 5% of peak value. 2.2.1.2 PIV on Porous Wings The camera was mounted with a Nikon 70-210 mm f/4-5.6 NIKKOR AF lens. The time delay between the rst and second image of a pair was 120 ms. The laser sheet was position at mid span of the porous wing. The window overlap gave a spatial resolution of 16 pixels, which is 0.98 mm or 0.0065c, for the vector eld. 28 Figure 2.6: Camera eld of view for porous wing PIV data acquisition. Only one surface of the wing could be illuminated because the laser sheet inter- sected the model and cast a shadow. Suction and pressure surfaces were imaged for a given by collecting data at then rotating the model to to image the recip- rocal side. This was viable because the wing has a symmetric cross-section. Note in Figure 2.7 that there is a region in the wake where overlapping data is available from both pressure and suction surface measurements. To splice elds into one image for a given, thex andz coordinates of the trailing edge were computed from x TE = 3c 4 cos +C 1 ; (2.3) and, z TE = 3c 4 sin +C 2 ; (2.4) where C 1 and C 2 are necessary constants due to the airfoil being rotated about c=4 and the origin prescribed by DaVis being arbitrary. The image was cut at the grid location closest toz TE for both surfaces. Then, the suction surface image was ipped 29 u U x c z c Figure 2.7: Sample PIV eld of velocity magnitude of the porous wing at = 0 . The black box in the wake is the region where data is available for both pressure and suction surfaces when splicing elds together. 30 along the x-axis and both images were spliced together. This process is accurate to within a grid point, which is 0.98mm, or 0.0065c. Data from the overlapping wake region, shown in Figure 2.7, were averaged. 2.2.2 Porous Wing Dye Traces The water channel at USC has a rectangular test section of height 61 cm and width of 89 cm. With a maximum achievable ow speed of 70 cm/s, the channel still maintains turbulence levels of < 1%. Experiments were conducted at a water height of 48 cm. To maintain the same Re as wind tunnel experiments, the channel was run at U = 16:7 cm/s, following sizing constraints described below. TwoA = 1:5 rectangular NACA 0012 prole wings were machined out of acrylic with c = 30 cm and b = 45 cm. The porous model had 2 mm diameter holes, still 0:67%c, drilled in the same orientation and chordwise locations as the wind tunnel model. Nondimensionalized spanwise spacing remained the same, but holes began from 1.5 cm, 3:33%b, from the wingtip. Though = 0:013 for this model, the geometry and hole placement are similar by a factor of 2; therefore, the physics must be similar to that of the wind tunnel model. As seen in Figure 2.8, a at plate of dimension 2:54c inx and 2:96c inz with 0:04c thickness was mounted above the wing to create quasi-2D ow as well as remove any free-surface eects. A hole was drilled in the center of the plate to allow for the wing mounting hardware. The bottom of the wing was ush with the bottom of the 31 Laser Sheet Camera α Positioning Figure 2.8: Water channel experimental setup showing camera and laser sheet place- ment, as well as positioning hardware. channel. To set , a pin was used to align a rotor plate with a stator plate with known angles; was also cross-checked from the images in postprocessing. Bright Dyes Fluorescent FWT Red 25 dye was diluted with water by a ratio of 40:1. The dye was injected from the leading edge at center span. A 5.14 W, 532 nm wavelength CNI wave laser was used to create a laser sheet that would illuminate the dye. Mounted below the channel, a Mako U-130 camera (1280 1024, 10 bit) with a Rainbow H6mm 1:1.2 lens was used to acquire ow visualization images. All images were post-processed to improve contrast, black levels, and invert colors. To to account for perspective between the wingtip and imagining planes, the wingtip was masked out and an airfoil image of the correct length and streamwise location was placed. 32 Chapter 3 Flight Mechanics 3.1 Biomimetic Wing Sweep Before wind tunnel experiments were conducted, the focus was rst on examining large planform changes to aerodynamically improve ight performance of a UAV. To determine what could be achievable, a MATLAB script was developed on the basis of aerodynamic theory. The code assumed an aircraft, which would maintain straight and level ight at sea level. A rectangular base wing was folded at midspan, referred to as Simple Sweep (SS), as well as at both mid- and quarter-span, referred to as M Sweep (MS), which are shown in Figure 3.1. The former is similar to planform changes achieved by the F-111 ghter airplane, while the latter is more similar to changes made by birds. The code neglected the body of the aircraft and any eects from the joints. , sweep angle for SS, and in and out , the inboard and outboard sweep angles for MS respectively, were varied from 0 to 45 in 1 increments, and S andA were 33 U U out in Figure 3.1: Base wing deformed into both Simple Sweep and M Sweep congurations with the angles dening each. calculated for each conguration. Using a brute force method, U was incremented from 7 m/s to 60 m/s in 0.1 m/s increments andC L was calculated for each congura- tion at each ight speed by replacingL withW , weight, in Eqn 1.2. IfC L was above a value of 1.2, the conguration was considered stalled, and removed from the set of viable congurations for the given ight speed. Then the induced drag coecient, C Di , was calculated using C Di = C 2 L eA : (3.1) where e is the Oswald eciency factor, assumed to be 0.7. With complex planform geometry changes, e is unlikely to remain constant for all congurations; however, this was assumed in order to create a preliminary estimate of morphing benets. The zero lift drag coecient, C D0 , was assumed to have a constant value of 0.006, based on experimental data for a NACA 0012 at Re> 10 6 [69]. Again, this was used for 34 preliminary estimates. D 0 andD i , zero lift and induced drag forces respectively, were calculated for each U and conguration by, D 0 =qSC d0 (3.2) and D i =qSC di : (3.3) The total drag, D, was computed by adding D e and D i together. Then D was multiplied by U to calculate power required, P req . The optimal conguration for SS and MS were chosen for each U given that it minimized P req . b, c, and W are user inputs; however, the bounds of U could be easily modied if the user desired. Total 0 i U (m/s) U (m/s) S (m 2 ) P req (%) D (N) Base MS SS Figure 3.2: By sweeping the wing, a reduction in D and P req is observed due to a reduction in area. In the top plots,D e ,D i , andD are represented by dotted, dashed, and solid lines respectively. 35 A representative result is given in Figure 3.2. At lower U, D is mostly due to D i , therefore the baseline conguration is ideal because both SS and MS reduceA. Past the design point of D min ,D 0 dominatesD, andS reductions become benecial, even though D i is increased. MS provides a greater area reduction than SS, which in turn leads to a greater reduction in D. This can lead to a decrease in P req of 20%, or more; however, in application, this would be less dramatic due to weight penalties. Such ndings are not limited to SS and MS but could be achieved by simple telescoping of both the span and chord. This model provides some insight, but neglects any aerodynamic eects created by the discontinuities in the planform as well as interaction of the wing when folded close to the body, which can only be examined with experiments or computationally expensive CFD simulations. 3.2 Morphing Aircraft Design Tool 3.2.1 Mathematical Method Arrays of varyingc,b, andU are generated, andS,A,C L , are calculated for each conguration. From Raymer[70], the zero lift drag, C D0 , is estimated by: C D0 =c f S wet S (3.4) given that c f is the skin friction coecient and S wet is the total wetted surface area of the aircraft. It is assumed that the fuselage and tail have the same shape and 36 their areas are scaled proportionally to the square of the inputted length of the body. The induced drag, C Di , is given by Equation 3.1 and the Oswald eciency factor is estimated by, e = 1 kA + 1 (3.5) given a shape term, k, which has been estimated here to be 0.0235 for moderate Re airfoils. Adding C D0 and C Di together, and multiplying by qS gives the total drag of the aircraft, D, in dimensional units of N or lbs. By dividing W by D, the lift to drag ratio, L=D, is computed. Based on these results, physically impossible congurations, such as unachievable C L values required to y, or ones that do not conform to user prescribed constraints, such as largerA, are removed from the set of viable options. The baseline congu- ration is chosen so L=D is maximized at the baseline ight speed. Eight more ight speeds are examined without constraint on maximum span at speeds slower than the baseline. Again, the conguration that maximizes L=D is chosen as optimal for the given ight speed. This may be a local and not global maximum for the conguration. Once the baseline conguration is chosen, the maximum root bending moment for the baseline is estimated by, M max = n(0:9W )b 8 ; (3.6) 37 wheren is the maximumg-loading that the user has prescribed for the baseline. This is under the assumption that the wings only account for 10% of the aircraft weight. In Equation 3.6, the only parameter that is varied between congurations isb; therefore, morphing allows for greater g-loading for the same structural bending moment limit as the baseline. With this, the maximum allowable g-load for each conguration is scaled proportionally to the baseline. The minimum turning radius,R min , for a given maximum g-loading, N, is given by, R min = U 2 g p N 1 : (3.7) From this, the maximum turn rate, ! max , is computed as ! max = U R min (3.8) The range, R, for an electric aircraft is estimated as, R =E tot 1 g L D W bat W (3.9) where E is the mass specic energy content, total is the eciency of the entire aircraft, and W bat is the weight of the battery[71]. 38 Figure 3.3: Screenshot of Morphing Aircraft Design Tool displaying default inputs. 3.2.2 Telescoping Wing Predictions Building on the previous code, a design tool was created to further explore the design space of morphing aircraft. MATLAB was still used as the programming lan- guage; however, a GUI, shown in Figure 3.3, was developed. A variety of parameters and ranges are selected by the user. Simple aerodynamic theory, described in the previous subsection, is used to determine performance measures such as range and maximum turn rate. As with the earlier code, a brute force method was used. Note, all shape changes considered are only with telescoping in b and c; however, fuselage and tail drag were integrated into calculations. Results discussed in this section are for the default input parameters; however, they do extend to general design principles. Two key parameters that the user must enter to provide realistic results areA max and C L;max . The former prevents excep- tionally highA, which may have undesirable structural and aeroelastic properties, 39 Figure 3.4: Necessary C L values to maintain steady level ight for varying b and c wing congurations. b and c axes have been rotated for clarity. being preferred by the algorithm. The necessity of removing largeC L values is shown in Figure 3.4. At moderate Re,C L values in excess of 1.3 are improbable; thus, these congurations were removed when determining an optimum. The user still has the exibility to input larger C L;max if they are considering higher Re applications. For a given base conguration, represented by the orange curve in Figure 3.5, there is a maximum L=D value at a certain U. IfA is held constant, but S is allowed to increase, the maximum L=D can be shifted to a lower U, shown by the dark blue curve. At higher U, such as U = 22 m/s, decreasing S, considering the dark red curve, leads to anL=D benet compared to the baseline vehicle, despite ying below the conguration's optimal L=D. As S decreases, D e of the wing decreases, but D becomes dominated by the drag of the body and tail, which produces close to no L. This leads to a decrease in maximum L=D as S decreases with a constantA. 40 Figure 3.5: Comparison of L=D for various wing congurations. Figure 3.6: Change of R with U for dierent wing congurations. Examining Equation 3.9, R is directly related to L=D; therefore, it follows that the curve for R is proportional to the curve for L=D, as shown in Figure 3.6. 41 A Figure 3.7: Variation of L=D withA and U given a constant b. A Figure 3.8: Variation in L=D withA and U given a constant c. For a given constantb orc, the same trend betweenL=D,A, andU is present, as seen in Figures 3.7 and 3.8. For a givenA, there is aU which will yield a maximum L=D. AsA decreases, (L=D) max also decreases but its location shifts to a higher U. 42 In contrast to the range of the aircraft, the maneuverability of the aircraft may also be of interest, especially in military applications. R min and! max are parameters that quantify this aspect of an aircraft. From Equations 3.7 and 3.8, it is clear that! max is inversely proportional toR min . In other words, a tighter turn allows for the aircraft to change heading at an increased rate, as shown in Figures 3.9 and 3.10. These gures seem to indicate that reductions inS lead to faster, tighter turns; however,A is held constant in all these congurations. Figure 3.9: The minimum turn radius as a function of U for various wing congura- tions. In Figure 3.11, the b-c plane represents the possible congurations of the wing geometry. The lowc, lowb corner represents minimumS, and the highc, highb corner is the maximumS. R min shows no dependence onc, but has a linear relationship with b. Therefore, reductions in S will not necessarily lead to increased maneuverability, 43 Figure 3.10: The maximum turn rate as a function of U for various wing congura- tions. as could be incorrectly deduced from Figures 3.9 and 3.10. b is the limiting parameter because it is directly proportional to M max . If c is held constant, variations inA represent changes in b and by extension S. At low speeds, R min is not sensitive to variations in b, as shown in Figure 3.12. However, as U increases, R min becomes increasingly sensitive to b. Thus, spanwise wing morphing is necessary to improve vehicle maneuverability at high speeds. When compared to the baseline conguration, the morphing aircraft will have increased weight due to the mechanisms that enable shape changes. The MATLAB tool presented here allows for the user to input their estimate of this weight penalty. For the 22.2 N aircraft used in the presented estimates, the weight of servomotors, a more complex spar, pulleys, and overlapping wing sections was approximated to be 44 Figure 3.11: Surface plot of R min at a constant U with b and c as independent variables. A Figure 3.12: Comparison of R min toA and U given a constant c 2.5 N. Estimates ofP req for the base conguration, the orange curve in Figure 3.13, did not consider this additional weight; however, all other curves in that plot accounted 45 for this weight. AtU = 8 m/s, the morphing capability allows for a 6.5% reduction in P req with respect to the baseline conguration. WhenU is increased to 25 m/s, there is a 26% reduction in P req . Only for the range from U = 10 to 17 m/s is there no P req benet due to the additional power needed to y a heavier aircraft. Therefore, if large variations in U are expected, there are P req benets despite having a heavier aircraft. Figure 3.13: P req as a function ofU. The orange curve represents the base congura- tion with no additional weight to enable morphing. The operator must consider trade-os when determining what conguration to use for a given mission. For example, for greatest R, the wings should be at the highest A and U chosen to maximize L=D. Another possible scenario is the approach of an enemy vehicle, which may warrant dash cruise and high maneuverability. In this 46 situation, S and b should be minimized to increase the L=D performance at high speeds and maximize ! max . In summary, bio-mimetic planform changes provided some aerodynamic benets at high speeds; however, such shape changes did not allow for large variations in ight performance. This was due to the inability to drastically changeS. Telescoping wings, however, allow for large variations in S andb, which improves performance in o-design ight conditions, as compared to a non-morphing aircraft. 47 Chapter 4 Aerodynamic Consequences of Discontinuous Wing Planforms From the previous chapter, it was determined that telescoping wings are desirable due to the ability to signicantly change bothb andS leading to performance benets at o-design conditions. Allowing wing sections to nest within one another greatly simplies the design of a telescoping wing, but introduces discontinuities in both c and t. The following experiments were aimed at determining and explaining any benecial or adverse eects of such discontinuities while considering the consequences on wing design. 4.1 Force Balance Lift and Drag Measurements Time-averaged force data presented in Figures 4.1 and 4.2 show no measurable dierence in C L , C D , and L=D between the stepped and smooth wing shapes at 48 below stall. Despite a boundary layer trip on the suction surface, the C L () curve at small show some non-linearity. Near stall, the continuous wing generates a hysteresis loop. Greater lift and less drag were produced when the continuous wing was pitching up, in comparison to the wing pitching down. The 3 step wing abruptly stalled at = 11 , while the continuous wing stalled suddenly near = 13 when pitching up and = 11 when pitching down. The 7 step wing, however, experienced a gradual stall at about = 11 . The dierence in stall behavior may be attributed to the presence of streamwise vortices shed at the steps. Under a cross ow, the eect of these vortices may change. The in uence of a cross ow on time averaged forces is estimated in Figures 4.3 and 4.4. No measurable dierence was observed inC L orC D before the onset of stall. Both the 3 step and 7 step wings showed a more gradual stall, and the hysteresis loop in lift of the continuous wing shrunk. The stall angle remained roughly the same between the swept and unswept cases though the stall angle was higher for the continuous wing in pitch-down. Because a ight vehicle will likely experience a cross ow, this robust stall behavior is desirable for vehicle design. 49 a) d) b) e) c) f) Figure 4.1: Comparisons of C L (left) and C D (right) versus between 3 step and continuous (a and c), 7 step and continuous (b and d), and 7 and 3 step wings (e and f) at Re= 7:4 10 4 . Data are plotted with shaded uncertainty envelopes. 50 a) d) b) e) c) f) Figure 4.2: Comparisons of L=D versus (left) and C L versus C D (right) between 3 step and continuous (a and c), 7 step and continuous (b and d), and 7 and 3 step wings (e and f) at Re= 7:410 4 . Data are plotted with shaded uncertainty envelopes. 51 a) d) b) e) c) f) Figure 4.3: Comparisons of C L (left) and C D (right) versus . 3 step (a and d), 7 step (b and e), and continuous (c and f). 52 a) d) b) e) c) f) Figure 4.4: Comparisons of L=D versus (left) and C L versus C D (right). 3 step (a and d), 7 step (b and e), and continuous (c and f). 53 4.2 Flow Visualization Figure 4.5: Starting vortex creation and the generation of circulation about an airfoil according to Kelvin's circulation theorem[72]. According to Kelvin's circulation theorem, the total circulation about an enclosed contour must remain constant with time. Consider the airfoil in Figure 4.5a. At rest, the total circulation, 1 , enclosed by curve C 1 is 0. When the airfoil begins to move with a uniform velocity, the circulation within C 2 , 2 , must remain 0 in order to obey Kelvin's circulation theorem. A starting vortex will form with circulation 3 . Curve C 3 encloses the starting vortex while C 4 encompasses the airfoil, which has a circulation of 4 . Curves C 3 and C 4 are subdivisions of C 2 ; therefore, 3 + 4 = 2 . This means that 3 = 4 . 54 This bound circulation, , at a given spanwise location is related to the lift per unit span, L 0 , by the Kutta-Joukowski theorem, or L 0 (y) =U(y) ; (4.1) L 0 is normalized by the dynamic pressure and local c, yielding the local coecient of lift, C ` , or C ` (y) = L 0 1 2 U 2 c : (4.2) Combining Equations 4.1 and 4.2 relates C ` to , or C ` (y) = 2 Uc : (4.3) Prandtl's lifting line theory extended this to 3D wings by assuming this bound cir- culation is a vortex element from y =b=2 to y = b=2. According to Helmholtz's second theorem, a vortex lament cannot end in a uid, but must either form a closed path or extend to the boundaries of the uid. Prandtl, therefore, assumed the vortex lament continues downstream as two free vortices at the wingtips which continue to innity. This vortex is called a horseshoe vortex due to its shape resembling a horseshoe. For a wing with a nonuniform lift distribution, as shown in Figure 4.6, the superposition of horseshoe vortices is used to generate the desired distribution. 55 Figure 4.6: Horseshoe vortices are superpositioned along a lifting line to create a nonuniform lift distribution[72]. When there is a change in , this theory predicts that vorticity must be shed into the wake. For the wings presented in this chapter, will vary directly with c. Therefore, will decrease linearly from the root to tip on the continuous wing. As shown in Figure 4.7a, it is expected that vorticity will be shed along the entire span of this wing. Because the 3 and 7 step wings have step-wise variations in c, it is expected that will also be a step-wise function. Because will only vary at the steps, it is expected that vorticity will only be shed at the steps, as seen in Figure 4.7b. PIV measurements attempted to detect this shed vorticity at the planform discontinuities. Under conditions where a large fraction of the bound circulation is deposited into a wake which then rolls up into a concentrated vortex, then concentrations of streamwise vorticity can be integrated over selected areas, A, to estimate a wake circulation, which may then be related to the total circulation and hence lift on the wing: 56 ! x a) ! x b) Figure 4.7: Prediction of shed vorticity,! z , and circulation, , distribution for the a) continuous and b) 3 step wings. w = Z ! x dA : (4.4) Here, we may compare estimates of w in windows that encompass the tip vortex alone, or all measurable shed vorticity. In principle, streamwise vorticity is shed into the wake wherever there is a spanwise (or timewise) change in , as shown in Figure 4.7. With large local c at the discontinuities of the 3 and 7 step wings, there will be a large , which may lead to a recognizable structure in the wake. In order to visualize the ow, a large mirror was mounted 7:6c downstream of the wing, likely causing a pressure gradient upstream. Current Dryden Wind Tunnel PIV assembly limited the maximum distance between the mirror and wing trailing edge. The largest distance was chosen to minimize these adverse eects. Additionally, all measurements were used comparatively, therefore, any undesirable ow eects will be a component of systematic error. 57 a) b) c) Figure 4.8: Cross-stream plane of streamwise vorticity 0:75c downstream of the a) 3 step, b) 7 step, and c) Continuous wings at = 5 . X mark denotes wing discontinuity locations. PIV measurements presented in Figures 4.8 and 4.9 show the presence of a con- centrated wingtip vortex at y=b = 1 at both . At higher , the tip vortex is larger, commensurate with the higher total lift on the wing. One may also observe traces of a distinct vortical structure at the discontinuity of the 3 step wing at y=b = 0:67. This structure becomes larger when is increased. No clear vortices were observed behind the discontinuities of the 7 step wing at = 5 . In Figure 4.9b, there are bulges in the ! x near the two steps closest to the wing tip. Though their amplitudes of ! x are similar to vorticity shed in the same regions on the continuous wing, these concentrations of vorticity indicate the formation of a distinct structure. Streamwise 58 a) b) c) Figure 4.9: Cross-stream plane of streamwise vorticity 0:75c downstream of the a) 3 step, b) 7 step, and c) Continuous wings at = 9 . X mark denotes wing discontinuity locations. vorticity was shed along the entire span of the continuous wing in the observation window at = 9 . All measurements are at x=c = 0:75 from the wing trailing edge, and the viscous roll-up process is unlikely to be complete. Based on the PIV measurements and Equation 4.4, estimates of =Uc, are given in Table 4.1. The likely measurement uncertainty, , was estimated from the maximum of the precision of any sequence of between multiple PIV data sets of a given conguration, and evaluated to = 0:005. As a reference, the resolution in setting any specied is about 0:3 . For a wing with a lift slopeC L = 2 A A+2 , the expected variation in C L is0:02, and through Equation 4.3 the variation in =Uc would 59 be on the order of 0.01. Within these uncertainty limits, none of the wake vortex strengths and circulations vary as wing geometry changes; however, an increase in is accompanied by a measurable increase in . From the force balance data, C L is expected to double from = 5 to 9 . Though is lower than expected, still roughly doubles from = 5 to 9 . Given the dispersed distributions of ! x and the thresholding operation that will neglect all low-amplitude components, the wake circulations would be under-estimates of wing circulation, and we use them here only in a comparative way. = 5 = 9 Wing Tip Inboard Total Tip Inboard Total 3 Step 0.038 0.025 0.063 0.094 0.050 0.145 7 Step 0.032 0.023 0.055 0.101 0.053 0.154 Cont. 0.048 0.023 0.071 0.099 0.051 0.151 Table 4.1: Estimates of circulation for the three wings based on PIV data. for the wingtip, area inboard of the tip, and total area were computed separately, and that was nondimensionalized by Uc. Uncertainty for all measurements is estimated to be 0.005. The only measured dierences in the wings above from force balance data was in stall behavior. The hysteresis loop shown in both the unswept and swept cases of the continuous wing is typically associated with the formation and bursting of laminar separation bubbles. This was unexpected due to the boundary layer trip on the suction surface. Wing tip vortices induce a spanwise ow, and stall can be delayed can by preventing the spanwise boundary layer from developing, such as the use of wing fences[73]. Possibly, the presence of vortices at the wing discontinuities induced spanwise ow, similar to that of a wing tip vortex, preventing the formation of these 60 bubbles. When the continuous wing was swept, the hysteresis loop may have shrunk due to the presence of spanwise ow. Additional PIV experiments would be needed to conrm this hypothesis. 61 Chapter 5 Eect of Porosity on Wing Performance at Moderate Re Whereas the previous chapters focused on the wing planform, the quasi-2D aero- dynamics of an airfoil are studied here. In contrast to synthetic systems, birds and bats occupy a moderate Re regime; therefore, they must account for the previously mentioned ow sensitivities. Bird wings are characterized by their exibility, poros- ity, and wide range of morphability. While the eects of exibility have been widely studied and morphability was examined earlier, the in uence of porosity is less well- known. Here, low porosity was introduced on a NACA 0012 airfoil at Re= 5 10 4 to determine any aerodynamic performance changes in comparison to a solid wing. 62 5.1 Permeability and Porosity The uid velocity, v, through a medium, where inertial eects are negligible and Stokes ow occurs within the pores [74], is given using Darcy's Law as, v = rp ; (5.1) where is the permeability, rp, is the pressure gradient, and is the dynamic viscosity. is a dimensional parameter and has units of m 2 . This was derived experimentally by Darcy in 1856 and later theoretically conrmed by Whitaker [75]. Consider channel ow with a permeable lower wall aty = 0 and an impermeable wall aty =h with a uniform pressure gradient across both the channel and the permeable material. This creates a slip velocity at the interface of the ow. Beavers and Joseph [76] postulated that this slip velocity diers from the mean velocity within the porous medium, as seen in Figure 5.1. They believed that this is due to the transmission of shear eects into the body of the material through a boundary layer region. Thus, laminar friction over a porous wall is less than that over a solid wall. Brinkman [77] expanded Darcy's Law to v + ~ v =rp (5.2) where ~ is the eective viscosity. Neale and Nader [78] concluded that the boundary layer thickness within the porous material is quite small but can have a signicant 63 Figure 5.1: Velocity prole of channel ow with a permeable lower wall (y = 0) and an impermeable upper at (y =h) [76]. eect in the external ow of thin channels. Furthermore, Darcy's law is valid far away from the interface [79]. ~ is believed to be related to the porosity of the medium [80], where Porosity, , is dened as the ratio between V V , the void volume, and V T , the total volume, of the medium, or = V V V T : (5.3) The relationship between porosity and permeability is not simple and requires knowledge of the size, distribution and spatial arrangement of pores [81]. The Kozeny- Carman model [82, 83] is most widely accepted; however, it is beyond the scope of this body of work. Zagni and Smith [84] conducted open-channel experiments over 20 dierent porous surfaces composed of spherical particles. A thin plate weir and a pitot tube were used to measure the ow rates and velocity proles. They determined that the friction fac- tor was higher for permeable beds compared to impermeable beds with similar surface 64 roughness when a turbulent boundary layer is considered. This was attributed to mo- mentum exchange across the bed interface leading to energy dissipation. This theory is supported by hotwire measurements made by Ru and Gelhar [85]. Similarly, Kong and Schetz [86] concluded permeability could lead to a 30-40% increase in skin friction relative to an impermeable wall with comparable roughness. Zippe and Graf [87] also observed increases in skin friction in their wind tunnel experiments. Figure 5.2: DNS results of wall normal vorticity elds normalized by (u p ) 2 = at z=H = 0:5, whereu p is the friction velocity at the permeable wall andH is the height from the top of the porous material to the top wall of the channel. Negative and positive vorticity isocontours are represented by dotted and bold lines respectively. was considered to be linearly proportional to a) = 0 b) = 0:8 and c) = 0:95[88]. 65 These experiments show that permeability aects turbulence dierently than sur- face roughness; therefore, it is implied that the dynamics and the structure of tur- bulence are changed by permeability [88]. Direct Numerical Simulations (DNS) by Breugem, et al. [88] and PIV measurements by Suga, et al. [89] point to permeability allowing for wall normal velocity uctuations to not be completely damped. This yields to higher shear stress on the permeable wall [90]. Quasi-streamwise vortices are seen in Figure 5.2 for the nonpermeable wall. When the porosity,, is increased to 0.8, irregular structures begin to appear. For = 0:95, all streaky structures disappear. With such a great eect on turbulent boundary layers and the slip boundary condition in laminar ows, porosity may potentially lead to benets on moderate Re airfoils. 5.2 Force Balance Lift and Drag Measurements Time-averaged lift and drag proles for the NACA 0012 at Re = 5 10 4 are given in Figure 5.3- 5.6, which also show previous reference data from the same prole shape in the same tunnel[23], which rst established the phenomenon of negative lift at positive . The observation of the 'N'-shaped curve around = 0 requires a very smooth geometry and quiet ow conditions, and is very sensitive to small disturbances. The C ` () is qualitatively similar but with local peak amplitudes in C ` of about one half the reference values at 0:5. Dierences in surface roughness between the machined wing of Ref. [23] and the 3D printed article here likely account 66 for the dierences in C ` , both at small and for > 4. The important point is that all curves in Figures 5.3 and 5.4 are qualitatively similar, with previously remarked characteristic features of sensitive dependence on the appearance and fore- or aft- motion of laminar separation bubbles. Finally the wing aspect ratio, b=c =A = 4, and in Ref. [23],A = 6:5 so end eects will be more in uential here. a) b) Figure 5.3: a) C ` and b) C d with uncertainty envelopes for a quasi-2D NACA 0012 at Re= 5 10 4 for the solid airfoil (red) with comparison to Tank, et al.[23] (blue). As discussed in Tank, et al.[23], there is little agreement of NACA 0012 lift data between facilities due to the sensitivity of the ow to facility turbulence levels and variations in wing geometry, making repeatable measurements dicult. Such qualita- tive agreement indicates that any dierences observed between the solid and porous wings are not due to any additional surface roughness or geometry irregularities as a result of the 3D printing process. Also, while making careful comparison with the ref- erence case, there was no attempt to make a specially smooth nish on the 3D printed 67 a) b) Figure 5.4: a) L=D versus and b) drag polar for comparison between the solid airfoil (red) and Tank, et al.[23] (blue). a) b) Figure 5.5: a) C ` and b) C d versus of a solid (red) and porous (purple) quasi-2D NACA 0012 wing at Re= 5 10 4 . wing because the main comparison is not with Ref. [23], but will be with a similar wing with porous features. This comparison is given in Figure 5.5 and Figure 5.6. Figure 5.5a shows that the presence of holes in the porous wing almost com- pletely straightens out the C ` () curve around = 0, removing the characteristic local positive and negative lift peaks. At the same time, there is no dierence in 68 a) b) Figure 5.6: a) L=D versus and b) drag polar for solid (red) and porous (purple) wings. C d (Figure 5.5b). There is a small decrease in C ` at higher but overall, within measurement uncertainty, L=D is equal to, or superior to the baseline wing at all (Figure 5.6). The porous wing always performs better than the solid one. 5.3 Dye Traces When = 0:0 , von K arm an vortex streets are observed in the wake of both air- foils, shown in Figure 5.7. Similar structures are observed at = 0:2 , commensurate with the similar values of C ` at small . The uid close to the trailing edge of the porous airfoil at = 0:4 begins to form small eddies, slightly disrupting the main wake eddies. Meanwhile, the ow about the solid wing shows no equivalent desta- bilizing disturbances on the von K arm an vortex street. As increases, the regular alternating wake feature is more clearly contaminated with smaller scale features and at = 0:8 the amplitude of the vortex street de ections is much reduced compared 69 with the solid wing counterpart. The small-scale eddies that eventually disrupt the von K arm an street seem to originate in the boundary layer on both upper and lower wing surfaces. Pixel values were averaged over 1,300 images for each producing images such as Figure 5.8. The streamwise separation location, x s , dened as the chord location of Figure 5.7: Instantaneous dye images for = [0:0; 0:2; 0:4; 0:5; 0:6; 0:8 ]. Images on the left are of the solid airfoil; those on the right are of the porous airfoil. 70 separation normalized by c, was estimated from the time-averaged images for each and plotted in Figure 5.9. Above = 2 , x s of the porous airfoil separates further downstream than that of the solid airfoil for a given . The range of higher x s coincides very closely with the range of measurably-dierent C ` () between the solid and porous wings (see Figure 5.5a). C ` may be lower ( 2 ), or higher (2 < 10 ). The most practical consequence is that the lift slope,C ` , is much more uniform over the entire range. Close to = 0 , the separation locations are quite similar. The airfoil-driven pressure dierence itself drives a ow disturbance that leads to small-scale features that promote later boundary-layer separation. Though the force measurements and time-averaged dye images that lead to mean separation location measurements lend themselves to time-averaged interpretation, the ow towards the trailing edge, and so the pressure dierence that causes the small perturbations, are never steady. Figure 5.8: Three instantaneous ow elds at = 3:0 . Below, is the time-averaged image of 1,300 frames. Solid on left; porous on right. 71 Figure 5.9: Streamwise separation location, estimated from time-averaged dye images for the solid and porous NACA 0012 at Re= 5 10 4 . The small eddies formed in the boundary layer and wake of the porous airfoil, shown in Figure 5.7, will lead to small perturbations to the uid ow. These pertur- bations, somehow, lead to the straightening of the lift curve seen in Figure 5.5a near = 0:0 . As shown in Figure 5.10, the pressure dierence between the suction and pressure surfaces may be imagined to induce a ( uctuating) uid ow through the wing, causing a local disturbance to the boundary layer at the pore. 5.4 Through Flow Model Some quick estimates of the magnitude of the pressure disturbance and subsequent wall-normal ow may be made, and XFOIL[91], a panel code, was used to compute 72 p Figure 5.10: Mechanism of pressure driven porous airfoil ow. the pressure distributions on a solid NACA 0012 at Re= 5 10 4 . Despite XFOIL's simplicity in comparison to CFD with turbulence models, it is the only code that predicts the in ection point of the NACA 0012 C ` () curve about = 0 . The pressure coecient, C p , is dened as, C p = pp 1 q ; (5.4) where p and p 1 are the local and freestream static pressures, respectively. The change of C p between both surfaces at the chordwise locations of the pores, C p , was estimated. Then, the ow through a given pore may be approximated by the Darcy-Weisbach equation, p =f l i d u 2 ? 2 ; (5.5) 73 wherel i andd are the length and diameter of the pore, respectively. It is assumed the pore is suciently small, so p does not vary over the face of the pore. The friction factor, f, is dened as, f = 64 Re d ; (5.6) and Re d = u ? d : (5.7) Combining and rearranging Equations 5.5-5.7 produces, u ? = d 2 32l i p : (5.8) Nondimensionalizing Equation 5.8 by U, q, and c produces, u ? U = (d=c) 2 64(l i =c) ReC p : (5.9) Note, l i =c is a function of the chordwise location of the pore, and d=c is a constant. Seen in Figure 5.11, the pores aft of midchord exhibit a more negativeu ? at low than pores closer to the leading edge. The suction at the pore will perturb the boundary layer normal to the wall. These perturbations lead to the global lift changes observed in Figure 5.5a. 74 0.1c 0.2c 0.3c 0.4c 0.5c 0.6c 0.7c 0.8c 0.9c u ? U Figure 5.11: u ? =U computed using Equation 5.9 and XFOILC p results at Re= 510 4 . For a permeable medium, the volume ow rate due to a pressure dierence is determined by Darcy's law, or, Q = S t p ; (5.10) where , a dimensional parameter, is the permeability. Q can also be estimated for a porous wing by multiplying Equation 5.8 by the pore area and summing over all pores yielding, Q =m d 4 128 p n X i=1 1 l i : (5.11) m and n are the number of holes in the spanwise and streamwise directions, respec- tively. Combining Equations 5.11 and 5.10 and simplifying produces, = d 2 t 32n n X i=1 1 l i : (5.12) 75 Assuming l i t, simplies Equation 5.12 further to, = d 2 32 : (5.13) is estimated to be 80mm 2 and 390mm 2 for the wind tunnel and water channel models, respectively. Because is a dimensional quantity, it should vary with geometry changes despite Re being held constant. u ? , however, is consistent between both wind tunnel and water channel experiments meaning the ow physics are similar. Low values of are to be expected because the majority of the airfoil is solid, yet this still has a signicant eect on the airfoil performance. Figure 5.12: Comparison of boundary layer prole with and without uniform suction. Given a 2D at plate, the Blasius boundary layer can be described by the following equations: 76 u(x;y) =Uf 0 () (5.14) v(x;y) = 1 2 r U x [f 0 ()f()] (5.15) given f 000 +f 00 f = 0 (5.16) and =y r U 2x : (5.17) A similar at plate with uniform suction will have a velocity prole describe by, u(x;y) = 1 exp u ? y U (5.18) As shown in Figure 5.12, the boundary layer is thinned with the presence of uniform suction. This will eect the transition and separation locations of the suction surface of the airfoil. In comparison to the Blasius result, the uniform suction case will have greater shear stress near the wall due to a steeper gradient in u. This would imply a higher drag on the porous airfoil; however, the momentum decit is lower 77 for this conguration. Therefore, it follows that the measured drag in force balance experiments were comparable between solid and porous cases. 5.5 PIV Visualization The model proposed in Section 5.4 predicts a perturbation velocity normal to the chord line. To test this is indeed the mechanism leading to the performance dierences observed in force balance measurements, a set of PIV experiments were conducted on the aft section of the wing. This portion of the wing was selected because the model predicted the maximum value of u ? =U to be 3% at = 1 and x=c = 0:7. Due to intense re ections despite a matte surface nish, the boundary layer could not be fully imaged without the risk of burning camera pixels. As seen in Figures 5.13 and 5.14, there is a nonphysical discontinuity in velocity at the trailing edge, and is a byproduct of the image splicing outlined in the Sec- tion 2.2.1.2. Note thatjuj = p u 2 +w 2 . Because these velocity elds were imaged at small , the w component of velocity is an order of magnitude smaller than the u component; therefore,juj is dominated byu. For this reason, Figures 5.13a and 5.14a appear relatively the same. Examining the u eld, the wake shape is relatively unaf- fected with increasing. Similar can be said about the vorticity elds in Figure 5.13b except for = 0:2 . At = 0:2 , there are two weak counter-rotating vortices. Looking at the w eld at this, there is upwash at the trailing edge followed by a region of downwash 0:04c 78 downstream. The net eect of this ow feature is a downwash close to 0, which is observed in force balance data presented in Figure 5.5a. Notably absent for all is the presence of signicant w at the pores, which would correspond to u ? . Because the expected perturbation velocity was only 3% of freestream and boundary layer was not imaged close to the wing, this feature may have dissipated before it could be imaged. Typically, the delay time between PIV images in a pair are chosen so particle displacements are between 2 to 3 pixels. High pixel displacements can lead to an averaging eect. With the time delay of 120 ms used, the pixel displacements were on the order of 3 to 5 pixels in the portion of the boundary layer that was imaged. Larger time delays were not possible without further increasing pixel displacements in this portions of the boundary layer. Therefore, the maximum expected pixel displacement for u ? was < 0:5 pixels. The region that could not be imaged close to the surface, dead , was about 1.6 mm thick. Laminar and turbulent at plate boundary layer approximations are given by lam = 5:2x p Re and turb = 0:37x Re 1=5 , respectively. At the trailing edge, dead = 0:73 lam and 0.25 turb . With such a small pixel displacement and a large portion of the boundary layer not visible, it was quite dicult to capture u ? before it dissipated. Future PIV experiments may successfully image this ow feature. 79 juj U ! y c U z c z c z c z c z c z c x c x c Figure 5.13: PIV derived elds of velocity magnitude (left) and spanwise vorticity (right) for = 0 to 1 in 0:2 increments. 80 u U w U z c z c z c z c z c z c x c x c Figure 5.14: PIV derived elds of u (left) and w components (right) for = 0 to 1 in 0:2 increments. 81 5.6 Sealed Pore Force Balance Testing According to the theoretical results in Section 5.4, the aft pores will have the greatest eect on the boundary layer because they produce the largest suction ve- locities along the chord. PIV measurements in the previous section were unable to conrm the existence of these perturbations. To determine if the aft pores are respon- sible for lift performance dierences, experiments were repeated with the pores sealed with 0.07 mm thick tape; therefore, the added thickness was 0.4% t. The width of the tape was 6.3 mm, or 0.35t. a) b) Figure 5.15: a)C ` and b)C d versus of a solid (red) and all pores sealed (dark blue) qausi-2D NACA 0012 wings at Re= 5 10 4 . Experiments were rst conducted with all pores sealed to ensure the tape did not signicantly aect the ow. These results were compared with previous force balance data of the solid 3D printed wing in Figures 5.15 and 5.16. There was no measurable dierence in C d or L=D. Examining small about = 0 , the local 82 maximum and minimum values ofC ` were equal for both solid and sealed cases. The sealed wing crossed C ` = 0 at 1:0 while the solid wing crossed at 0:8 . At small positive , both crossed at 0:6 . These discrepancies could arise from slight asymmetries due to the 3D printing process. Measurements ofC ` were in good agreement at larger . a) b) Figure 5.16: a) L=D versus and b) drag polar of a solid (red) and all pores sealed (dark blue) wings. With the ve aft pores unsealed, the in ection point in C ` about = 0 was attened, as shown in Figure 5.17a. In comparison to the airfoil with porosity along the entire chord, the C ` curve was not straightened. Therefore, porosity is necessary closer to the leading edge to have the eect observed in Figure 5.5a. The model discussed in Section 5.4 did predict suction along the entire chord at small , but larger values of u ? closer to the trailing edge. This, however, was based on pressure distributions calculated in XFOIL. Though, XFOIL does capture the nonlinear lift behavior of the solid NACA 0012 at Re= 5 10 4 , it may not be correctly modeling 83 a) b) Figure 5.17: a)C ` and b)C d versus of a solid (red) and ve aft pores open (green) qausi-2D NACA 0012 wings at Re= 5 10 4 . a) b) Figure 5.18: a) L=D versus and b) drag polar of a solid (red) and ve aft pores open (green) wings. 84 the boundary layer dynamics. Furthermore, the integrated eect of perturbations at pores from the leading to trailing edges and not at a specic pore could be responsible for the straightening of the lift curve. 85 Chapter 6 Closing Remarks 6.1 Conclusions The goal of this study was to predict, quantify, and explain any benets of several unconventional solutions for moderate Re aircraft design. First, a ight mechanics model was developed to determine the benets of planform morphing. It was demon- strated that bio-inspired shape changes could provideD, and in turnP req , benets at high speeds by reducing D 0 in a greater proportion to D i . Birds have been shown to optimize their wing planforms for various ight conditions in a similar fashion[24{26]. The code was further developed and examined performance benets of a telescop- ing wing. It was found that S can be tailored to give increased L=D in o-design ight conditions, such as high-speed cruise. Also, b can be selected to increase the maneuverability of the aircraft. In the moderate Re regime, the aerodynamics of airfoils and nite wings are known to be sensitive to small ow and geometry perturbations. Therefore, focus was then 86 turned to wind tunnel experiments of atypical wing and airfoil geometries in order to take advantage of these sensitivities. Because viscous and inertial forces are in a ne balance in this regime, results may not always be applicable to higher or lower Re regimes. First, stepped and continuous wings were studied at Re 7:410 4 . Force balance measurements revealed no performance degradation for 3 step or 7 step wings com- pared with a continuous, tapered wing for typical of aircraft cruise. Experiments were repeated for wings swept 10 to examine the eect of a sideslip angle. The hys- teresis loop in the lift curve of the continuous wing shrunk, while the stepped wings showed a more gradual stall in a cross ow. A vortical structure was found at the discontinuity of the 3 step wing in the wake but no similar structures were measur- able in the wake of the 7 step wing. Though step discontinuities were associated with shedding of streamwise vorticity, the integrated eect across the span was negligible, in agreement with direct force balance measurements. Since the boundary layers were tripped, these results may extend to higher Re. Because nonuniform planforms exist in nature, such as humpback whale at higher Re ippers[48], or barn owl feathers at lower Re [92], there is precedence for the benet of these geometries. Finally, wind tunnel experiments measuredC ` () andC d () on a quasi-2D NACA 0012 at Re= 510 4 with both solid and porous surfaces. The solid airfoil showed qual- itative agreement with a previous, comparable study. At small, positive , negative lift is produced, a counterintuitive result. When low porosity between the pressure 87 and suction surfaces is introduced, the anomalous behavior is removed without a measurable drag or L=D penalty. Dye visualization combined with XFOIL analysis show that porosity can allow a ow through the airfoil to perturb the boundary layer, sucient to cause signicant changes in the lift prole; however, PIV measurements were unable to conrm this analysis. The intrinsic ow sensitivity can lead to ampli- cation of disturbances, which may be used deliberately for eective control, either passive or active. Therefore, the permeability of avian feathers may act as a passive ow control mechanism. 6.2 Future Work The current study concentrated on the time averaged aerodynamics of unusual and changing wing geometries; however, controllability must must be addressed to build practical ying devices. This is especially relevant when addressing the use of telescoping wings. If unexpected ow features develop, this may lead to unstable ight conditions making the morphing capability impractical. Additionally, telescop- ing allows for unique aircraft control over conventional control surfaces. For example, the left wing could be extended more than the right, causing greater lift and drag generation on the left wing. This, in turn, would cause a rolling moment; therefore, the need of a conventional aileron may be unnecessary. Also, additional PIV exper- iments are need to conrm that spanwise ow is responsible for dierences in stall behavior of planforms with discontinuities. 88 Furthermore, airfoil design for these wings at moderate Re is still little understood. The addition of porosity showed lift benets at low , but more work is needed to determine proper applications. PIV experiments should be repeated with the aim to visualize the boundary layer close to the airfoil surface in order to conrm or refute the model presented in Section 5.4. Force balance measurements should also be repeated with aft pores sealed and pores close to the leading edge left open. This would determine if the forward pores are most important or if porosity is necessary along the entire chord. In comparison to the circular holes presented here, feathers have complex pore geometries. Future studies should examine other pore geometries such as square or oval. 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[91] Drela, M., \XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils," Low Reynolds Number Aerodynamics, Springer-Verlag Berlin, Heidel- berg, 1989, pp. 1{12. [92] Weger, M., and Wagner, H., \Morphological variations of leading-edge serrations in owls (Strigiformes)," PloS one, Vol. 11, No. 3, 2016, p. e0149236. [93] Bunker, R. S., \A review of shaped hole turbine lm-cooling technology," J. Heat Transfer, Vol. 127, No. 4, 2005, pp. 441{453. 98 Appendix A Surface Roughness Estimation a) b) Figure A.1: a) Spanwise and b) chordwise prolometer traces of machined NACA 0012 wing used in by Tank, et al.[23]. Wing roughness measurements were made using an Ambios XP-2 prolometer. This machine drags a needle across the sample surface and measures the height as a function of position. Examples of the prolometer output is given in Figures A.1 and A.2. The regular shape observed in Figure A.2a are the individual layers from the fused deposition modeling (FDM) printing process. In the spanwise direction, 99 a) b) Figure A.2: a) Chordwise and b) spanwise prolometer traces of the NACA 0012 model printed on the PrintrBot machine. measurements were averaged to give h. A spline, ~ h, was tted to the data in the chordwise direction to account for the curvature of the geometry. The deviation of the surface height, Z, as a function of x, was calculated as, Z =yh (A.1) in the spanwise direction, and, Z =y ~ h (A.2) in the chordwise direction. The arithmetic mean and root mean square of Z, R A and R q respectively, are taken as quantitative measures of surface roughness. Values for R A and R q are given in Table A.1 for wind tunnel models that did not have surface 100 treatments after 3D printing and the machined wing from Ref.[23]. Uncertainty of these measurements are estimated to be 0.1 mm. Spanwise Chordwise 3D Printer R A [mm] R q [mm] R A [mm] R q [mm] Prusa 11.8 15.0 0.8 1.0 PrintrBot 17.6 21.2 0.3 0.4 Raise3D 8.3 10.2 0.8 1.5 Machined Wing (Ref. [23]) 2.0 2.6 2.0 2.7 Table A.1: Roughness measurements of wing samples. All samples had a NACA 0012 prole. 101

Abstract (if available)

Abstract Recently, there has been a push towards smaller unmanned air vehicles (UAVs) due to decreased size and weight of available electronics and actuators. These new vehicles occupy a Reynolds number (Re) regime from 10⁴ to 10⁵. At these scales, the aerodynamics of airfoils and finite wings yield nonlinearities in the lift curve and are sensitive to small perturbations in the flow and/or geometry. These sensitivities at once make measurement, prediction and control difficult and at the same time allow for new control strategies. The design space of small wings can readily expand to unusual geometries and mechanisms, and as advanced materials are developed, there is renewed interest in large- and small-amplitude shape changing properties. ❧ With the design of wings and aircraft in this moderate Re regime being little understood, this work aimed to predict, quantify, and explain any benefits of several planform and airfoil design strategies. First, a MATLAB model based on aerodynamic theory was created to determine the potential flight performance benefits of span and chord variations. These included lift to drag ratio optimization for a given flight speed and maneuverability parameters, such as turn radius. It was determined that telescoping wings potentially provide greater flight performance benefits in comparison to biomimetic morphing. ❧ Absent any special matching shield, the neighboring segments on a telescoping wing introduce stepwise discontinuities in thickness and chord. Direct force balance data and PIV flow measurements of continuous, 3 step, and 7 step wings were made at Re ≈7.4×10⁴ to determine any beneficial or adverse effects of such planforms. Furthermore, the wings tested had boundary layer trips on the suction surface

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Asset Metadata

Creator Hanna, Yohanna George Tewfik (author)

Core Title Biomimetics and bio-inspiration for moderate Reynolds number airfoils and aircraft

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Aerospace Engineering

Publication Date 02/20/2020

Defense Date 01/24/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag aircraft,airfoil,biomimetics,discontinuous,moderate Reynolds number,morphing,OAI-PMH Harvest,planform,porous

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Spedding, Geoffrey (committee chair), Flashner, Henryk (committee member), Nutt, Steven (committee member), Uranga, Alejandra (committee member)

Creator Email yhanna@usc.edu,yohanna.hanna.phd@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-272780

Unique identifier UC11674692

Identifier etd-HannaYohan-8196.pdf (filename),usctheses-c89-272780 (legacy record id)

Legacy Identifier etd-HannaYohan-8196.pdf

Dmrecord 272780

Document Type Dissertation

Rights Hanna, Yohanna George Tewfik

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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