AN EXPERIMENTAL INVESTIGATION OF LIFT AND ROLL CONTROL USING PLASMA ACTUATORS. A Dissertation. Submitted to the Graduate School

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1 AN EXPERIMENTAL INVESTIGATION OF LIFT AND ROLL CONTROL USING PLASMA ACTUATORS A Dissertation Submitted to the Graduate School of the University of Notre Dame in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Alexander N. Vorobiev Mark R. Rennie, Co-Director Eric J. Jumper, Co-Director Graduate Program in Aerospace and Mechanical Engineering Notre Dame, Indiana July 2010

2 AN EXPERIMENTAL INVESTIGATION OF LIFT AND ROLL CONTROL USING PLASMA ACTUATORS Abstract by Alexander N. Vorobiev This work describes an experimental investigation into the use of plasma actuators for lift and roll control. The use of plasma actuators for flow-control applications has been demonstrated extensively in recent years, for example, to postpone flow separation or eliminate Karman shedding behind bluff bodies. The current research describes a unique application of plasma actuators in which the actuators were placed near the trailing edge of a wing or airfoil in an effort to directly control circulation. Experimental data are presented showing the effect that the actuators have on lift, pitch, roll-moment and pressure distribution as a function of angle of attack and wind speed. The experiments are performed in the range of Reynolds numbers Re = 30, ,000 and the angle-of-attack range = -3 to +10. The results indicate that the performance of the actuators is strongly influenced by Reynolds number effects. The implications of the results on the application of plasma actuators as lift and roll-control devices are discussed.

3 CONTENTS Figures... v Nomenclature... xii Chapter 1: Motivation Summary Chapter 2: Introduction to Flow Control Using Plasma-produced Forces Near a Surface Introduction Electro-Hydrodynamic Force Based Actuators DBD Plasma Actuators Flow Control with Plasma Actuators Boundary Layer Separation Control Flow Control around Bluff Bodies Flat Plate Boundary Layer Control Airfoil Circulation Control Summary Chapter 3: Lift Control Experiment Three-Dimensional Wing Experiments Data Acquisition and Analysis Two-Dimensional Airfoil Experiments Lift and Pitch Moment Measurements Surface Pressure Distribution Measurements LDA Measurements Actuators Chapter 4: Lift Control Results Baseline Aerodynamic Behavior Aerodynamic Forces with Plasma Actuation Center of Pressure Roll Control Reynolds Number Effects Chapter 5: Detailed Investigation of The Reynolds Number Effects Airfoil Surface-Pressure Distributions ii

4 5.2 Collation of Force-Balance Results LDA Measurements Re = 107,000. Positive Lift Enhancement Re = 207,000. Negative Lift Enhancement Re = 361,000. Positive Lift Enhancement Summary of LDA Results Effect of Electric Power Discussion of Power Scaling Considerations Effect of Electric Power Lift Enhancement with Tripped Boundary-Layer Summary Chapter 6: Lift Enhancement With Multiple Actuators Single-Actuator Operation Multi-Actuator Operation No Additional Lift Enhancement Produced: < Multi-Actuator Case Produces Lower Lift Enhancement: 2 to Multi-Actuator Case Produces Increased Lift Enhancement: > Discussion of Multiple-Actuator Results Estimated Lift and Roll Control with Multiple Actuators Current Actuator Arrangement and Design Chapter 7: Conclusions and Recommendations Contributions of this Dissertation Research Reliable Experimental Data for the Effect of Trailing-Edge Mounted Actuators Influence of Reynolds Number Roll Control Estimate of Current Lift- and Roll-Control Capabilities Recommendations for Future Work Detailed Investigation of Very-Low Reynolds-Number Behavior Detailed Investigation of Higher Reynolds-number Behavior Appendix A: Navion Airplane Wing Geometry Appendix B: Calibration and Accuracy of Measurements B.1 Regression of Calibration Data and Instrumental Precision B.2 Random Error B.3 Calibration Procedure and Results B.3.1 Nonlinearity B.3.2 Hysteresis B.3.3 Summary of Calibration B.4 Other Factors Influencing the Measurement Accuracy B.4.1 Influence of the High-Voltage Cables in SWT B.4.2 Misalignment of Applied Load iii

5 B.5 Effect of Plasma Discharge on Load Cell Signal B.5.1 Lift Load Cell B.5.2 Pitching Moment Load Cell Appendix C: Corrections of experimental data for effect of test section walls C.1 Correction on Wind Tunnel Walls Boundary Layer C.2 Correction on Solid Blockage C.3 Correction on Wake Blockage C.4 Correction on Streamline Curvature C.5 Summary of Wind Tunnel Measurements Corrections Bibliography iv

6 FIGURES Figure 1.1: Lift curve for NACA 0009, U = 15.2 m/s [19]... 2 Figure 1.2: Smoke visualizations of upstream oriented plasma actuators (top). Smoke visualizations of downstream oriented plasma actuators (bottom) [75] Figure 1.3: CFD Simulations of an upstream oriented actuator in a flow [75] Figure 1.4: CFD simulations of a downstream oriented actuator in a flow [75] Figure 1.5: Doublet model of an upstream oriented actuator in a free-stream [29]... 5 Figure 1.6: Doublet model of a downstream oriented actuator in a free-stream [29]... 5 Figure 1.7: Effect of reducing the ratio of doublet strength to the magnitude of the free-stream velocity. Reproduced from Hall [29]... 6 Figure 1.8: The constant- approach and the experimentally observed trend for C l versus [29]... 7 Figure 1.9: Lift versus angle of attack using the doublet model at U = 15.2 m/s. [29].. 10 Figure 1.10: Calculated change in lift coefficient versus doublet model chord position [29] Figure 1.11: Wing with multiple plasma actuators, NACA 0009 airfoil [29] Figure 2.1: Schematic of SDBD plasma actuator Figure 2.2: Plasma panel design concepts. (a) Symmetrically staggered, (b) asymmetrically staggered, (c) symmetric planar lower electrodes. (Roth et al. [89]) Figure 2.3: Top view photograph of a SDBD actuator with plasma discharge on a quartz glass as a dielectric v

7 Figure 2.4: Voltage and current time histories for SDBD plasma discharge (one electrode is insulated) Figure 2.5: Schematic illustration of the charge build-up on the dielectric surface. (Enloe et al. [23]) Figure 2.6: Synchronized voltage, current, horizontal velocity (u) and vertical velocity (v) of the SDBD-induced velocity versus time [25] Figure 2.7: Effect produced by SDBD actuator on boundary layer profiles [5] Figure 2.8: SDBD body force at different freestream velocities and ac frequencies [5].. 27 Figure 2.9: Comparison of lift coefficient with plasma on and off, at U = 20 m/s and Re = 158,000. (Post and Corke [72]) Figure 2.10: Wake mean velocity profiles with plasma actuator on and off, for = 16, U = 20 m/s and Re = 158,000. (Post and Corke [72]) Figure 2.11: Effect of steady and unsteady SDBD actuation on lift coefficient at U = 30 m/s and Re = 257,000, Corke et al. [18] Figure 2.12: Smoke visualization around a cylinder with SDBD plasma actuators. (Thomas et al. [105]) Figure 3.1: Schematic of roof-mounted balance system used for lift and moment measurements on three-dimensional wing model Figure 3.2: System of coordinates and planform view of the wing model. A plasma actuator; B exposed electrode. Direction of the flow is from left to right Figure 3.3: Photograph of wing model mounted in the test section of AWT. Flow direction is from top to bottom of figure Figure 3.4: Schematic of the strain-gauge force balance with model of airfoil. Adopted from [62] Figure 3.5: Flowchart for data acquisition of lift and pitch moment Figure 3.6: Photograph of the SWT setup with the airfoil model mounted in the test section. 1 airfoil model, 2 force balance, 3 high voltage power source, 4 power amplifiers, 5 data acquisition system vi

8 Figure 3.7: Flowchart for measurement of static pressures Figure 3.8: Diagram of (a) plasma actuator and (b) power amplification circuit Figure 3.9: Representative actuator voltage and current time histories Figure 4.1: Lift curve for NACA 0009 airfoil, U = 10.1 m/s, Re = 135, Figure 4.2: Lift curves for wing with NACA 0009 profile and AR = Figure 4.3: Lift curves for NACA 0009 airfoil from Selig et al. [97] and current research Figure 4.4: Lift curve for NACA airfoil [61] Figure 4.5: Visualization of boundary layer on the suction side of NACA 0009 airfoil with smoke for different angles of attack. Re = 130,000 (U = 9.7 m/s). A) = 0; B) = 2; C) = Figure 4.6: Oil flow visualization on the suction side of NACA 0009 airfoil for different angles of attack. Flow direction from left to right, Re = 130,000 (U = 9.7 m/s). A) = 0; B) = 2; C) = Figure 4.7: Surface flow visualization. Re = (U = 9.7 m/s), = 5. 1 separation of the flow; 2 reattachment of the flow Figure 4.8: Contour plot showing baseline airfoil lift (Cl/2πα) over the tested range of angles of attack and Reynolds numbers Figure 4.9: Approximate locations of laminar separation and reattachment of the boundary layer versus angle of attack from oil-flow visualization data. Re = (U = 9.7 m/s) Figure 4.10: Effect on aerodynamic forces and moments, both left and right plasma actuators operating. U = 6.1 m/s, Re = 83, Figure 4.11: Comparison of measured increase in lift enhancement with difference in lift curve from inviscid behavior Figure 4.12: Visualization of the flow near trailing edge of NACA 0009 airfoil: A) plasma off; B) plasma on. Re = 83,000, = vii

9 Figure 4.13: Roll moment produced by operation of a single actuator Figure 4.14: Example of the lift and roll moment for combined and independent operation of left and right plasma actuators Figure 4.15: Effect on aerodynamic forces and moments, single actuator operation Figure 4.16: Aerodynamic force and moment dependence on wind speed/ Reynolds number. Single actuator operation, = Figure 4.17: Lifting-line prediction of lift distribution for constant wing twist over a spanwise distance matching the extent of the right-hand-side plasma actuator Figure 4.18: Variation of dimensional lift enhancement with wind speed Figure 4.19: The plasma lift versus angle of attack for airfoil (SWT) and wing (AWT). Data for wing are corrected for downwash and for difference in dissipated power Figure 4.20: Lift enhancement produced by plasma versus with wind speed for airfoil in SWT Figure 4.21: Contours of plasma lift increment in SWT, N Figure 5.1: Pressure distribution over NACA 0009 airfoil with plasma on and off. Re = 84,000 (U = 6.2 m/s), = Figure 5.2: Pressure difference for Plasma ON and Plasma OFF over NACA 0009 airfoil. Re = 84,000 (U = 6.2 m/s), = Figure 5.3: Pressure difference for Plasma ON and Plasma OFF over NACA 0009 airfoil; Re = 267,000 (U = 20 m/s), L = -0.6 N, = 0 (note: L = -0.6 N) Figure 5.4: Contours of Cl/2π with the region of negative lift enhancement (contained within the contour marked 0 ) Figure 5.5: LDA measurements of mean velocity (top) and velocity fluctuations (bottom) near the trailing edge of NACA α = 1, Re = 107,000, U = 8 m/s Figure 5.6: LDA measurements of mean velocity (top) and velocity fluctuations (bottom) near the trailing edge of NACA α = 1, Re = 207,000, U = 15.4 m/s viii

10 Figure 5.7: LDA measurements of mean velocity (top) and velocity fluctuations (bottom) near the trailing edge of NACA α = 1, Re = 361,000, U = 26.8 m/s Figure 5.8: Plasma-off boundary-layer shape factor for suction side NACA 0009 airfoil at = Figure 5.9: Near-wall velocity probability density function from LDA measurements. U = 8 m/s, Re = 107,000, z/c = 0.001, x/c = Figure 5.10: Effect of plasma discharge on the skin friction coefficient. U = 7.95 m/s, Re = 107, Figure 5.11: Effect of plasma discharge on the boundary layer displacement thickness. U = 7.95 m/s, Re = 107, Figure 5.12: Near-wall velocity pdf. U = 15.4 m/s, Re = 207,000, z/c = 0.001, x/c = Figure 5.13: Near-wall velocity pdf. U = 15.4 m/s, Re = 207,000, z/c = 0.001, x/c = Figure 5.14: Effect of plasma discharge on the skin friction coefficient. U = 15.4 m/s, Re = 207, Figure 5.15: Near-wall velocity probability density function. U = 15.4 m/s, Re = 207,000, z/c = 0.001, x/c = Figure 5.16: Effect of plasma discharge on the boundary layer displacement thickness. U = 15.4 m/s, Re = 207, Figure 5.17: Effect of plasma discharge on the skin friction coefficient. U = 26.8 m/s, Re = 361, Figure 5.18: Effect of plasma discharge on the boundary layer displacement thickness. U = 26.8 m/s, Re = 361, Figure 5.19: Actuator thrust as a function of dissipated power (per length of actuator) for 2 khz positive ramp signal (6.35-mm thick quartz), Thomas et al. [106] Figure 5.20: Effect of varying plasma discharge power on lift increment. U = m/s, Re = 98, , ix

11 Figure 5.21: Lift enhancement linearly scaled by the plasma discharge power. U = m/s, Re = 98, , Figure 5.22: Lift curves for NACA 0009 with boundary layer tripped and developing naturally Figure 5.23: Plasma effect for clean airfoil and with boundary layer tripped Figure 6.1: Schematic of 3-plasma actuators airfoil. Flow direction is from left to right Figure 6.2: SDBD effect for airfoils with different plasma actuators configurations. U = 10 m/s, Re = 140, Figure 6.3: Effect of multiple SDBD. U = 8.3 m/s, Re = 110, Figure 6.4: Effect of multiple SDBD. U = 10 m/s, Re = 140, Figure 6.5: Estimated roll moment for the multiple actuator wing with AR = Figure 6.6: Estimated aileron deflection angle due to plasma actuator Figure A.1: Planform view of the Navion airplane [94]. A aileron, F flap (all dimensions are in meters) Figure A.2: Navion airplane wing geometry [45] (flap is not shown). All dimensions are in meters Figure B.3: Residuals for linear regression model Figure B.4: Mean value of residuals at different directions of load Figure B.5: Lift load cell calibration for 3-th order polynomial regression model Figure B.6: Residuals for 3-th order polynomial regression model Figure B.7: Load produced by high-voltage wires on lift load cell Figure B.8: Effect of high-voltage wires on lift load cell x

12 Figure B.9: Offset on lift load cell created by plasma discharge RF noise at different loads Figure B.10: Offset of pitching moment load cell created by plasma discharge RF noise at different loads Figure C.11: Correction in SWT free-stream wind speed on test section walls boundary layer Figure C.12: Corrected and uncorrected lift in SWT test section xi

13 NOMENCLATURE A wing planform area AR wing aspect ratio, AR = b 2 /A b c C l C L wing span wing chord section lift coefficient wing lift coefficient C l section lift-curve slope C L wing lift-curve slope C M C p C R wing quarter-chord pitch moment coefficient (M P /qac) pressure coefficient, (p - p )/q wing roll moment coefficient, (M R /qab) C f skin friction coefficient, C f τ = w q H boundary layer shape factor, H = δ θ L lift force M P quarter-chord pitch moment M R roll moment P P ~ electric power dissipated by plasma actuator electric power dissipated by plasma actuator per unit span of the actuator xii

14 p q Re St u e pressure dynamic pressure Reynolds number based on chord Strouhal number (f c/u) velocity of external flow U free-stream velocity V x x CP y y CP z boundary air ν L0 * voltage chordwise coordinate chordwise location of the center of pressure, nondimensionalized by chord c spanwise coordinate spanwise location of the center of pressure, nondimensionalized by wing span b normal to wall coordinate angle of attack zero lift angle of attack boundary layer displacement thickness aileron deflection angle layer momentum thickness doublet strength, viscosity density kinematic viscosity, ν = µ ρ u w wall shear stress, τ w = µ y y=0 xiii

15 CHAPTER 1: MOTIVATION Single dielectric barrier discharge (SDBD), or plasma actuators, have recently become an important new tool for aerodynamic flow control applications. Although dielectric barrier discharges have been studied since at least 1857 and used in industrial processes for several decades [10, 99, 116, 117], the utility of plasma actuators for flow control has only been recognized and investigated in the past few years. These investigations have focused largely on employing plasma actuators as boundary-layer control devices, where typically the velocity perturbation produced by the actuator is used to influence the global character of the flow by delaying or preventing boundarylayer separation at strategic locations [15, 73, 77, 67, 75]. The advantages inherent to plasma actuators suggest that they could also be usefully employed in other kinds of aerodynamic flow-control applications. In particular, to satisfy man-portable requirements, new small-scale unmanned aerial vehicles (UAV s) are being designed that incorporate folding or inflatable wings. The need to break the aircraft down into a compact, storable configuration makes it difficult or impossible to design in conventional aerodynamic control surfaces employing standard mechanical actuators and linkages; as a substitute, plasma actuators have been proposed to control aerodynamic forces and moments for these aircraft. This application of plasma actuators, i.e., to effect control of flight-vehicle aerodynamic forces and moments via direct control 1

16 of wing circulation, represents a subtle but important deviation from typical applications of plasma actuators in which the actuators are used to directly influence boundary-layer development (which may then indirectly influence aerodynamic forces and moments). As such the question arises: what is the nature and effect that plasma actuators can have on the circulation of a wing or airfoil? Figure 1.1: Lift curve for NACA 0009, U = 15.2 m/s [19] Recent efforts that have been initiated to answer this question have consisted of both experimental [19, 113] and theoretical [29] investigations. In [18, 19], plasma actuators constructed from copper foil electrodes and using a Kapton film dielectric were mounted near the trailing edge (x/c = 0.75) of a 0.2 m chord, m wide, end-plated airfoil with NACA 0009 profile. Lift and drag data were acquired as a function of angle of attack and at two wind speeds. These data showed that the plasma actuators produced a measurable amount of lift enhancement. In particular, the landmark finding of these initial experimental investigations was that, for a given plasma-actuator arrangement and 2

17 dissipated power, the lift enhancement generated by the actuators remained constant as a function of both angle of attack and wind speed (Figure 1.1). As such, the change in lift coefficient C L produced by the actuators was found to drop off as the square of the wind speed, which appears in the denominator of C L as part of the non-dimensionalizing dynamic pressure term: 1 C L (1.1) U 2 A theoretical investigation to interpret the experimental results in [18, 19] was next carried out by Hall [29]. After considering both experimental and computational results of the effect of the SDBD discharge on the flow [18, 19, 75], Hall noticed that the effect of plasma actuation on flow streamlines from flow-visualization studies bore a close resemblance to the effect produced by a doublet in the presence of a freestream flow. Figure 1.2 shows the effect of plasma actuation using smoke visualization over a set of actuators. Two situations are shown: first, the actuators are placed in an upstream orientation (jetting upstream) creating small bubble-like regions over the points of actuation; in the second, the actuators are oriented downstream (jetting downstream), resulting in sharp dips in the smoke at the points of actuation [75]. Corresponding CFD results, which were performed by including a body force in the flow calculations at the point of actuation (the theory demonstrating that a plasma actuator produces an effective body force on the flow is reviewed in Chapter 2), are shown in Figure 1.3 and Figure 1.4 [75]. The upstream-oriented actuator computation shows the same bubble-like effect on the flow as observed in the smoke visualizations (Figure 1.2). Likewise, the CFD predicts 3

18 Figure 1.2: Smoke visualizations of upstream oriented plasma actuators (top). Smoke visualizations of downstream oriented plasma actuators (bottom) [75]. Figure 1.3: CFD Simulations of an upstream oriented actuator in a flow [75]. Figure 1.4: CFD simulations of a downstream oriented actuator in a flow [75]. 4

19 the same dips in the flow that were shown by the smoke when the actuators were operated with a downstream orientation. Figure 1.5: Doublet model of an upstream oriented actuator in a freestream [29]. Figure 1.6: Doublet model of a downstream oriented actuator in a freestream [29]. In Figure 1.5 and Figure 1.6 the streamlines from the doublet model are plotted for upstream- and downstream-oriented actuators. The similarity of the experimental (Figure 1.2) and CFD (Figure 1.3 and Figure 1.4) results with the computed streamlines 5

20 for the simple potential-flow, doublet-and-free-stream combination shown in Figure 1.5 and Figure 1.6 is readily apparent. Figure 1.7: Effect of reducing the ratio of doublet strength to the magnitude of the free-stream velocity. Reproduced from Hall [29]. In Figure 1.7, the potential-flow streamlines are shown for several different ratios of doublet strength to the magnitude of the free-stream velocity, showing how this ratio changes the overall flow structure and affects the appearance of the flow field [29]. This figure demonstrates the importance of correctly determining the ratio of doublet strength to free-stream velocity in order to produce meaningful results. 6

21 To compute the effect that a plasma actuator has on airfoil lift, Hall next incorporated the doublet potential-flow approximation of the plasma actuator into a Smith-Hess panel method [32, 79]. This was done by superposing a doublet with downstream orientation (Figure 1.6) onto the airfoil s panel surface at the same location of the plasma actuator employed in the experimental investigations (x/c = 0.75). In his initial approach to the problem, Hall attempted to reproduce the experimental results of Figure 1.1 by using a constant doublet strength at all angles of attack; the assumption being that a plasma actuator with constant dissipated power should be modeled using a doublet with constant. As shown in Figure 1.8, this approach failed to reproduce the experimental results. Figure 1.8: The constant- approach and the experimentally observed trend for C l versus [29]. Following the failure of the constant- assumption, Hall took a more systematic approach to the problem. He made the important assumption that a plasma 7

22 actuator with constant dissipated power produces a constant body force (cf. Chapter 2) and incorporated this into the Euler equation: 1 U U = p + f ρ (1.2) where f represents the actuator-induced body force, U velocity and p pressure. Integrating along a streamline from infinity to a control point gives: U 2 2 ε U 2 2 ε = fds pds γ ε (1.3) where the right hand side of the equation has been defined as. Taking into consideration the two scenarios where the plasma actuator is on and off, he introduced γ - the difference in the integral (3) for those two scenarios: γ = γ P ε ε 2 2 γ 0 = Uε Uε = f ds ppds + p ds (1.4) p o 0 ε where subscripts P and 0 correspond to actuator-on and actuator-off conditions respectively. The quantity γ is assumed to be constant for a particular plasma actuator with a constant dissipated power. Putting U P = U 0 + U, Hall next expanded the velocity-squared difference term in Eq. (1.4): U 2 ε p 2 εo ( U + U U + U ) U = 2U U + U U = (1.5) ε o 2 ε ε ε ε ε ε ε o o o where the plasma s effect is found in the term U. Although the velocity at all control points on the airfoil will be changed with the plasma on compared to the plasma-off case, to first order, the effect of the plasma at the point p can be computed by superposition. 8

23 As such, Hall assumed that the effect of the plasma, U, to first order, would be the effect of the doublet alone at a distance downstream from the doublet position: µ U ε = U (1.6) 2 ε Eq. (1.4) becomes: 2 µ µ U (1.7) 4 ε 2ε 2 γ = ε U 0 + U 2 For a given airfoil and actuator configuration, Eq. (1.7) contains 3 unknowns:, and. However, Eq. (1.7) is in a form in which these three unknowns can be determined using experimental data; in effect, the panel method is calibrated using two distinct experimental data points (which could be, for example, the lift enhancement at two different angles of attack, wind speeds, etc.). For each of these experimental data points, the value of is adjusted until the lift increment C L produced by the doublet and panel method matches the experimental results. Since γ is constant for a particular plasma actuator and dissipated power, the quantities on the right-hand side of Eq. (1.7) can be set equal for the two experimental data points, and the resulting equality solved for the control-point location : ε = µ U µ U µ 1U ε 2µ 01 2U ε 02 (1.8) where the subscripts 1 and 2 corresponds to the two different experimental data points. With ε determined, the doublet strength for any other point in the experimental data set can be computed and used in the panel method to calculate the corresponding lift increment due to the plasma actuator. An example of the results obtained using this 9

24 process is shown in Figure 1.9, which shows the lift increment computed using the paneland-doublet method once the method was calibrated using two points from the experimental data shown in Figure 1.1. As shown in Figure 1.9, the panel/doublet method precisely reproduces the constant lift-enhancement effect observed in the experimental results, once the body-force effect of the plasma actuators has been properly incorporated into the method. This result was one of the first to rigorously confirm the body-force effect that plasma actuators have on the flow. Figure 1.9: Lift versus angle of attack using the doublet model at U = 15.2 m/s. [29] Hall also used his doublet actuator model to predict some performance characteristics of the plasma actuators. He showed that the actuators have a greater effect the closer they are to the airfoil trailing edge (Figure 1.10). Further, Hall showed that the doublet model predicts that the effect of two actuators is equal to the sum of them operating individually. This result was observed experimentally by Post [75] and confirmed lately by Forte [25] and indicates that more than one actuator could be used on an airfoil without diminishing the effectiveness of either actuator. 10

25 Figure 1.10: Calculated change in lift coefficient versus doublet model chord position [29]. Figure 1.11: Wing with multiple plasma actuators, NACA 0009 airfoil [29]. Finally, Hall extended his model to the case of three-dimensional flow and examined roll moments produced by the plasma actuators using Prandtl s lifting line theory [44]. He considered a configuration with multiple plasma actuator as shown in Figure 1.11, where each of the actuators could operate individually or simultaneously with others. Hall showed that this actuator array with discretely-operating elements was able to produce roll-moment coefficients C R in the range from up to For 11

26 comparison, the roll-moment coefficients for a Navion airplane with the ailerons deflected at various deflection angles are summarized in Table 1.1 [63]; these data show close agreement with the range of roll moments that can be produced using the plasmaactuator array shown in Figure 1.11, and illustrate the possibility of using plasma actuators as roll-control devices. TABLE 1.1 NAVION AIRCRAFT ROLL MOMENT COEFFICIENTS C R FOR VARIOUS AILERON DEFLECTION ANGLES a. [63] a.(deg) C R

27 1.1 Summary The experimental data of [19, 18] showed that plasma actuators can be used to directly control the lift of an airfoil. Further, Hall s doublet actuator model was able to reproduce the experimentally-observed constant lift increment produced by plasma actuators. As part of his theoretical approach, Hall showed that the constant liftenhancement results of [19] were a natural outcome of the constant momentum addition, or body force, that plasma actuators impart to the flow. Using his model, Hall demonstrated that roll moments sufficient to control an airplane should be possible with present plasma-actuator technology. The motivation of the experimental investigation described in this dissertation was therefore twofold: to repeat and verify previous results documented in Corke [19, 18], and to experimentally verify the use of plasma actuators as lift- and roll-control devices. 13

28 CHAPTER 2: INTRODUCTION TO FLOW CONTROL USING PLASMA-PRODUCED FORCES NEAR A SURFACE 2.1 Introduction Active flow control consists of manipulating a flow to effect a desired change [27]. A definition of flow control provided by Flatt [24] regarding wall-bounded flows (but which can also be applied to almost any type of flow) is as follows: boundary-layer control includes any mechanism or process through which the boundary layer of a fluid flow is caused to behave differently than it normally would, were the flow developing naturally. In aeronautics, flow control is used to achieve a wide range of purposes, including the delay of laminar-to-turbulent transition, prevention of flow separation, and suppression or promotion of turbulence. Eliminating or delaying laminar-to-turbulent boundary-layer transition is desirable since the skin-friction drag of a laminar boundary layer (BL) under certain conditions can be an order of magnitude lower than for a turbulent boundary layer [17]. Similarly, improving the flow-separation characteristics of an airfoil can increase the maximum lift and stall characteristics of a wing and improve many aspects of an aircraft s performance, including reducing the take-off and landing distances. Conventional flow-control devices such as slats and flaps have long been used on wings to prevent separation at large angles of attack; more recently, researchers are 14

29 exploring the possibility of replacing leading edge slats and flaps with active flow-control devices such as synthetic jets and plasma actuators [18, 65]. Finally, flow control can be used to manage turbulence, for example, to promote better flow mixing in the case of mixing layers, or to suppress or reduce aerodynamic noise. In aero-optics for instance, flow control has been shown to favorably modify the optical aberrations imposed by compressible shear layers [80, 81]. An extensive review of aerospace-specific flowcontrol strategies, research, and applications can be found in Gad-El-Hak et al. [27]. 2.2 Electro-Hydrodynamic Force Based Actuators Among active flow-control methods is a relatively new technology using lowtemperature glow-discharge plasmas to manipulate the flow over surfaces. Although mechanical devices may be effective, they have several drawbacks; in particular, mechanical devices add weight and volume, are sources of noise and vibration, and are composed of mechanical parts that may wear off and break down. Another disadvantage of mechanical actuators is that they usually require linkages and control rods that cannot be broken down into a storable configuration as required by the man-portable UAV s [11, 12] which are a primary motivation for this research. Many of these drawbacks can be avoided with plasma actuators, which directly convert electrical energy into the kinetic energy of a near-wall jet without involving moving mechanical parts. Plasma actuators also have a very short response time, enabling real-time control at high frequencies. A disadvantage of plasma actuators is their low efficiency of energy conversion [23, 60, 68, 82], although work is ongoing to raise their performance; this is particularly true in the 15

30 case of the SDBD, where the performance of this type of plasma actuator has been increased by an order of magnitude in the past few years [106]. Non-thermal plasmas at atmospheric pressure may be produced by a variety of electrical discharges; those which are used for flow-control purposes are usually a corona discharge, a dielectric barrier discharge, or a combination of both (the consideration of high-temperature plasmas is beyond the scope of this work). These plasma discharges release some amount of heat into the air, but temperature change is not the mechanism for flow control [16]. Briefly, the formation of the discharge in non-thermal plasmas is based on the Townsend mechanism [108], or electron avalanche; that is, the multiplication of electrons in a cascade ionization. Under an electric field, these electrons are accelerated towards the anode and ionize the gas by collisions with neutral molecules as given by: + A + e A + 2e (2.1) where A is a neutral particle and A + a positive ion. An avalanche develops as the multiplication of electrons proceeds along their path of motion from the cathode to the anode. More details about the physics of non-thermal plasmas may be found in [26, 49, 84, 86, 95]. Though the first flow-control experiments were done using corona discharges, and research studying this type of discharge for flow control is ongoing, detailed consideration of the corona discharge is beyond the scope of this work. Only a brief review of results obtained with this type of discharge is given here. A history of electric wind research is given in [83]. The phenomenon of coronadischarge induced ionic wind was reported for the first time in 1709 by Hauksbee and the 16

31 first explanation was given by Faraday in The first papers dealing with flow control employing electrohydrodynamic (EHD) forces were published in 1966 by Mhitaryan et al. [57] and 1968 by Velkoff and Ketchman [112]. In the first paper, the authors demonstrated separation control of the boundary layer of an airfoil using near-surface corona discharge, where the free-stream velocity in this experiment was about 20 m/s. In the second paper by Velkof et al. [112] it was demonstrated that the transition point on a flat plate could be affected by the application of an electric field. Bushnel [9], Malik et al. [50] and Soetomo [100] studied the drag reduction effect induced by corona discharges along a flat plate, but free-stream flow velocities were extremely low, about 1-2 m/s. Among recent results is the work of Labergue et al. [47], who used a low-frequency square wave corona discharge to reattach a naturally detached airflow along a 17 inclined wall. Control of the flow separation on an airfoil has also been reported in [101, 102, 103], although the reported wind speeds and Reynolds numbers are very low. In 1997, Noger et al. [66] used a point-to-plane configuration in order to manipulate the airflow around a cylinder; this study was continued in [2, 3]. Finally, Hyun and Chun [36] investigated control of the wake flow behind a circular cylinder using a dc corona discharge actuator. An extensive review of the published literature on flow control using corona discharge actuators is given in [59] DBD Plasma Actuators Although the corona-discharge actuator can induce an electric wind of several m/s close to a wall surface (the maximum velocity ever measured to date was 5 m/s [59]), one of the main disadvantages of the corona-discharge actuator is the glow-to-arc transition which limits the maximum voltage and induced velocity. This transition may be 17

32 prevented if the discharge is driven by a pulsed (from a few nanoseconds to several microseconds) high voltage. Another approach is to use a dielectric barrier in the discharge gap, which stops the electric current and prevents spark formation. This type of discharge is called the dielectric barrier discharge (DBD). Because of the dielectric barrier, a DC voltage cannot be used to drive the discharge, since charge buildup in the dielectric rapidly counteracts the applied DC voltage. Instead, DBDs are usually excited by an AC or pulsed high-voltage source, with frequencies between 50 Hz and 500 khz [26, 73]. DBD devices have been widely used in industrial processes since the 20 th century and exist in many configurations; cylindrical or planar for example [26]. Among many recent publications concerning the physics of the DBD, the fundamental and experimental works of Yokoyama et al. [118] and Massines et al. [52, 53] deserve particular mention, as well as the reviews of Wagner et al. [114], Fridman et al. [26], Kogelschatz [46] and Schütze et al. [95]. Figure 2.1: Schematic of SDBD plasma actuator. Based on the research of Kanazawa et al. [42, 118], Roth et al. [91, 92] developed volume-type atmospheric-pressure DBD s in They protected this device by a patent 18

33 and called it the One Atmosphere Uniform Glow Discharge Plasma (OAUGDP TM ). Realizing that this discharge could induce a secondary airflow of several m/s, they proposed a modification of this actuator for airflow control in 1998 [85, 89]. This geometry is now commonly referred as the single dielectric barrier discharge (SDBD) [22] and is distinct in that it employs only a single dielectric to separate the electrodes, which are placed asymmetrically on both sides of the dielectric. The most basic SDBD actuator arrangement is shown in Figure 2.1, which shows a single SDBD actuator composed of two planar electrodes flush-mounted on both sides of a dielectric plate with a gap g between the electrodes. The figure shows the most common actuator arrangement in which one of electrodes is insulated. In these conditions a plasma sheet appears on one side of the actuator near the exposed electrode that induces a jet in the surrounding air. If both electrodes are exposed then a plasma discharge ignites on both sides of the actuator. The direction of the flow induced by the actuator is shown schematically in the figure. The geometries of multi-actuator SDBD concepts investigated by Roth et al. [90] are shown in Figure 2.2. Figure 2.2: Plasma panel design concepts. (a) Symmetrically staggered, (b) asymmetrically staggered, (c) symmetric planar lower electrodes. (Roth et al. [89]) Other geometrical configurations of surface DBD actuators have also been proposed; however, the remainder of this review chapter will focus on the SDBD 19

34 actuator. Considering the case of a single SDBD plasma actuator (Figure 2.1), if an AC voltage above the ignition voltage V 0 (usually a sine or saw-tooth waveform from a few kv to several tens of kv) is applied between the electrodes of the SDBD, a glow discharge plasma appears. The electrical and mechanical characteristics of the plasma depend strongly on different parameters, such as electrode width, electrode gap, dielectric thickness and the nature of the dielectric. However, in most cases, these parameters are as follows: an exposed electrode width of a few mm, an insulated electrode width of a few cm (typically about 2 cm), an electrode gap equal to zero or a few mm and a dielectric made of Teflon, kapton, glass, ceramics or Plexiglas. The best candidates for the dielectric material are quartz glass and Teflon [87], since dielectric losses in quartz and Teflon are the lowest among the available materials, which minimizes the amount of electrical power dissipated by heating of the dielectric. Machinable ceramics (such as the material marketed under the trade name Macor ) are also commonly used as a lessexpensive substitute for quartz, but the dielectric losses in Macor are higher. Dielectric thickness are typically between 0.1 mm and a few mm. Typical parameters of the driving voltage are a magnitude from a few kv to several tens of kv and a frequency f between several hundred Hz and a few tens of khz. Figure 2.3 shows a picture of an activated surface SDBD with a quartz glass dielectric and zero gap g between the electrodes. Typical behavior of the discharge current versus time is presented in Figure 2.4 for an SDBD driven by a sine waveform. For the case shown in Figure 2.4, the actuator consisted of two copper foil electrodes flush-mounted on each side of a 2 mm thick Macor ceramic plate with an insulated lower electrode and an electrode gap of g = 0 mm. Figure 2.4 shows that the discharge current 20

35 is composed of a set of microdischarges appearing at the beginning of each inversion of polarity and that the plasma is different during the negative and the positive half-cycles of the driving voltage signal. Further, the discharge current pulses are positive during the positive voltage half-cycle and negative during the negative one. Figure 2.3: Top view photograph of a SDBD actuator with plasma discharge on a quartz glass as a dielectric Voltage Current Voltage (kv) Current (ma) Time (ms) Figure 2.4: Voltage and current time histories for SDBD plasma discharge (one electrode is insulated). In [21, 22, 23], Enloe et al. performed optical measurements that revealed that the structure of the plasma is different in both space and time and showed that there is a noticeable difference between the two halves of the AC cycle (forward and backward strokes). The authors showed that the plasma is not uniform as it appears to the unaided 21

36 eye, but rather consists of a series of individual filaments or microdischarges occurring in rapid sequence. During the forward stroke, the microdischarges happen in rapid succession, whereas during the backstroke there are a relatively small number of microdischarges. a b Figure 2.5: Schematic illustration of the charge build-up on the dielectric surface. (Enloe et al. [23]) More importantly, Enloe et al [22] also experimentally demonstrated that the direction of the induced flow does not depend on the polarity of the driving AC voltage, but rather, is in the same direction, that is, from the exposed electrode towards the encapsulated electrode (Figure 2.1) for both positive and negative AC voltage cycles. This observation has important implications on determining a viable model that describes the way in which the SDBD actuators work. A simple physical explanation of the operation of the surface SDBD proposed by Enloe et al. [23] is summarized in Figure 2.5. The half-cycle for which the exposed electrode is negative and emits electrons is illustrated in Figure 2.5(a). Because the discharge terminates on the dielectric surface, the build-up of surface charges opposes the applied voltage, and the discharge shuts itself off unless the magnitude of the applied voltage is continually increased. When the voltage reverses, the charge transferred 22

37 through the plasma is limited to that deposited on the dielectric surface, Figure 2.5(b). In the plasma itself, the plasma acts to nullify the electric field by pulling the ions and electrons apart to counter the applied field. All of the force imbalance interactions take place in a thin layer surrounding the plasma volume where there is an imbalance of charge; this region is the so-called Debeye region with a thickness equal to the Debeye thickness, as it is known from a number of basic plasma-physics texts [56, 78]. According to Enloe et al [23] this phenomena is responsible for producing a body force on the nearby fluid, which is the result of the force on the Debeye region of the plasma by the applied electric field. This force causes the charged particles to be pulled toward the exposed electrode s corner nearest the covered electrode and then to force them away from the exposed electrode in the direction of the actuator asymmetry. The force also confines the resulting flow to a narrow strip close to the surface; the overall effect is to pull fluid in toward the actuator and expel it (from the exposed electrode towards the encapsulated electrode) as a wall jet. The outcome of this explanation is that, unlike explanations that posit an ionic wind being responsible for the effect on the fluid (which then must argue that the force on the fluid is opposite for opposite polarities), the Enloe model correctly predicts the observed constant force direction regardless of the particular polarity of the cycle of the applied AC voltage to the electrodes. A more detailed description of this model is given in [15, 16]. 23

38 Figure 2.6: Synchronized voltage, current, horizontal velocity (u) and vertical velocity (v) of the SDBD-induced velocity versus time [25]. Support for the Enloe et al. model of the SBDB operation was provided by laser Doppler velocimetry measurements performed by Forte et al. [25]. Figure 2.6 presents the instantaneous velocity (x- and z-components) induced by a surface SDBD (2 mmthick glass as a dielectric, V = 18 kv, f = 700 Hz) simultaneously with the actuator voltage and current. The measurements were made at a location 2 mm downstream of the exposed electrode at a 1 mm height above the dielectric surface in a wind tunnel with a free-stream flow of 2 m/s ( the local wind speed at the point of measurement was 1.2 m/s due to the effect of the boundary layer). The figure clearly shows that the discharge does not behave exactly the same during the positive and the negative half-cycles; in particular, the negative half-cycle induces more horizontal velocity (3.5 m/s) than the positive one (2.3 m/s). Moreover, the vertical velocity shows negative values during the positive half cycle (and positive values during the negative voltage cycle), which implies that the streamline above the actuator contracts and expands during each voltage cycle. 24

39 The data show, however, that both the negative and positive cycles of the discharge produce a jetting effect in the same direction, as follows from the model of Enloe et al. [23]. The SDBD electrical power consumption was studied in [87, 22, 69]. Pons et al. [69] computed the electrical power as a function of several parameters. They measured the electrical charge Q on one of the actuator electrodes by placing a capacitor between the electrode and ground, and computed the electrical energy per AC voltage cycle. Their data showed that the electrical power consumption versus voltage increases as a parabolic function P = C ( V V ) 2 (2.2) 0 The same result has been reported in [87] for other geometrical and electrical configurations. Enloe et al. reported, however, a different behavior of the power consumption [22, 23]. Enloe showed that the power dissipated in the plasma actuator increased as the applied voltage to the power of 7/2: P 7/ 2 = C V (2.3) He measured the actuator current with an inductive sensor and voltage with high-voltage probe. The dissipated power was then calculated as the integral of the product of the instantaneous current and voltage over the discharge period. The difference in power versus voltage behavior in these measurements can possibly be attributed to differences in the dielectric material and thicknesses that were employed: Pons s SDBD actuator was made with a 5-mm glass dielectric while Enloe s actuator used Kapton tape with

40 0.64 mm thickness. Roth et al. [87, 88] investigated the amount of electrical power that is dissipated by heating of the dielectric. They found that this depends highly on the dielectric, the applied voltage and the waveform frequency. The same V 7/2 dependence was also observed by Post [70, 71] for the plasma induced velocity: 7/ 2 u ~ V (2.4) In these experiments, the maximum plasma-induced velocity was inferred from PIV measurements for various applied voltages. It should be noted that there are other studies demonstrating different dependence of the plasma-induced velocity on the applied voltage, from linear to asymptotically increasing [25, 87]. Nevertheless, if the applied voltage is increased too much then the plasma discharge becomes filamentary; the entire current is concentrated within a few filaments and the total thrust produced by the SDBD does not increase and sometimes even decreases with increasing voltage [87]. Numerous recent papers have also been published concerning the SDBD-induced velocity distribution [87]. Stationary and non-stationary velocity measurements induced by SDBD actuators are presented for example in [25, 74, 77]. The momentum induced by plasma actuators versus various parameters such as frequency, voltage and free-stream flow velocity was investigated by Baughn et al. [5]. An example from this work showing the effect produced by a plasma actuator on boundary layer profiles is presented in Figure 2.7. The velocity profile measurements in Figure 2.7 were made using a Pitot probe at a location 5 cm downstream from the exposed electrode of the plasma actuator at different free-stream flow velocities. 26

41 plasma off plasma on 10 y, mm u/u Figure 2.7: Effect produced by SDBD actuator on boundary layer profiles [5] body force, N/m khz 10 khz 20 khz U, m/s Figure 2.8: SDBD body force at different freestream velocities and ac frequencies [5]. 27

42 Baughn et al. [5] also calculated the body forces produced by the SDBD using a control-volume momentum balance analysis. These results are presented in Figure 2.8 for different free-stream velocities and discharge frequencies. For these measurements, the discharge voltage at different frequencies was adjusted to deliver the same electric power to the actuator. One of the conclusions made by the authors was that the body force is not affected by the free-stream velocity, at least in the range from 4 to 8 m/s. Post [74] also showed that plasma actuators placed in arrays had an additive effect; in particular, two actuators placed in serial created a plasma-induced jet in which the momentum of the two actuators was twice the momentum from a single actuator. This characteristic was also observed by Forte et al. [25] in their Pitot probe and LDV measurements. 2.3 Flow Control with Plasma Actuators Boundary Layer Separation Control Separation control over airfoils with SDBD was studied in 2003 by Post et al. [70, 77]. In this study, two methods of control were compared: a passive method using mechanical vortex generators and a plasma-based active method. The airfoil had a profile with a chord c = 12.7 cm. Two actuators were used: the first one was placed at the leading edge (x/c = 0) and the second one at x/c = 0.5 (50% of the chord). The airfoil was instrumented for surface pressure measurements in order to calculate lift coefficients. Mean velocity profiles downstream of the airfoil were used to determine drag coefficients. Measurements were performed over a range of free-stream velocities 28

43 from 10 to 20 m/s, (Re = 77, ,000). The actuators were found to lead to boundary-layer reattachment for angles of attack that were 8 past the stall angle, accompanied by full pressure recovery on the airfoil suction side and up to a 400% increase in the lift-to-drag ratio. The authors demonstrated that the most effective actuator location to achieve reattachment of the leading-edge flow separation was at the exact leading edge. Figure 2.9: Comparison of lift coefficient with plasma on and off, at U = 20 m/s and Re = 158,000. (Post and Corke [72]) In [71, 72] Post and Corke reported on a large number of experiments concerning separation control at high angles of attack using plasma actuators, for both a stationary and periodically-oscillating NACA 0015 airfoil, and for steady and unsteady actuator operation. Figures 2.9 and 2.10 show the effect on the airfoil lift curve and downstream velocity profile for a case in which steady actuation was used on a stationary airfoil at a free-stream velocity of 20 m/s. The experimental data showed that the actuation induces a pressure recovery near the airfoil leading edge resulting in improved lift and downstream wake behavior (and concomitant drag reduction) shown in Figures 2.9 and

44 Figure 2.10: Wake mean velocity profiles with plasma actuator on and off, for = 16, U = 20 m/s and Re = 158,000. (Post and Corke [72]) Figure 2.11: Effect of steady and unsteady SDBD actuation on lift coefficient at U = 30 m/s and Re = 257,000, Corke et al. [18]. In [18], Corke et al. compared the effect of unsteady versus steady actuation, and the influence of the position of the actuator, on the ability of an SDBD actuator to 30

45 reattach the boundary layer of an airfoil. The goal of the investigation was to mimic the effects of wing leading-edge slats and trailing-edge flaps. The airfoil had a NACA 0015 profile with a chord of 12.7 cm. The flow-control tests were conducted at 21 and 30 m/s, corresponding to a maximum Reynolds number of Re = 257,000 (307,000 if corrected for tunnel blockage effects). The results showed that unsteady actuation was more efficient; specifically, steady actuation was able to reattach the flow for angles of attack up to 19, which was 4 past the normal stall angle, while unsteady actuation was able to reattach up to 9 past the normal stall angle. In steady actuation, the waveform frequency of the plasma driving AC voltage usually is sufficiently high compared to any relevant frequency of the baseline flow that the associated body force could be considered effectively steady. For unsteady actuation, the actuator is modulated at a much lower frequency f U, which could be chosen to be comparable to some relevant frequencies of the flow around the airfoil. Detail and summaries of investigations into this kind of unsteady actuation can be found in [14, 71, 72, 73]. The most efficient results were obtained when the unsteady actuation period corresponded to the airfoil flow-passing time, that is, when the Strouhal number f U c/u was equal to one. The duty cycle of the unsteady actuation was only 10%, which means that the unsteady power consumption was only 2W instead of the 20W used in the steady case; this result highlights the increase in performance that can be achieved using unsteady flow control with wisely-chosen actuation frequencies. Zavialov et al. published two papers dealing with boundary-layer reattachment using plasma actuators on the suction side of a 9 cm chord NACA 0015 airfoil, for velocities up to 110 m/s [119, 120]. The actuator was composed of three successive 31

46 SDBDs, spaced from the airfoil leading edge to the trailing edge. The results showed that, beyond the stall angle at 12 and up to an angle of attack of 20, the actuation was very effective, leading to a strong increase in the pressure distribution along the suction side of the airfoil. The authors concluded that they could significantly change the flow only at the separation point, where the velocity was relatively low and most susceptible to the actuator s jetting effect. As an interesting side note, Roupassov et al., repeated the same measurements [93] but with a stream-wise oriented actuator, resulting in an actuator jet direction perpendicular to the free air stream. They obtained similar results, indicating that the discharge effect which induces reattachment does not necessarily have to be in the direction of the main flow. Jolibois et al. [38] published a paper investigating the most-efficient location of the actuator for airfoil flow reattachment. Seven independent actuators along the suction side of a 1 m chord NACA 0015 airfoil were mounted from x/c = In this study the boundary layer was transitioned at the airfoil leading edge using a trip-surface. Flow visualizations and PIV measurements showed the physical effect of each actuator, as a function of the flow separation point which depends on the angle of attack. The authors investigated the ability of the SDBD actuators to displace (upstream and downstream) the position of the separation point, by reattaching naturally detached airflows or, inversely, by detaching naturally-attached airflows. The main result was that, whatever the angle of attack and the location of the separation point, the actuator must act at the separation point to be the most efficient with a minimum input power. In [111], Van Dycken et al. looked at the effect of a plasma actuator installed on a blade of a gas turbine blade cascade. Flow separation was detected via surface pressure 32

47 measurements and loss of stagnation pressure via Pitot pressure measurements. Their results showed that flow separation was eliminated and stagnation-pressure losses were reduced by 50% at 3 m/s (Re = 30,000) for an input power of 45 W. A similar problem was studied by Huang et al. [33, 34] with steady and unsteady SDBD actuation for controlling flow separation on turbine blades in the linear cascade of a generic low-pressure turbine stage. The Reynolds number in these experiments varied from 10,000 up to 50,000 (U = m/s). The authors used surface pressure, LDV, and hot-wire measurements to locate the region of separated flow on the suction side of one of the blades and to study the effect of actuation. It was demonstrated that both steady and unsteady actuation resulted in reattachment of the flow, but unsteady actuation was found to be more effective and required less power compared to steady actuation. The optimum excitation frequency to reattach the flow with unsteady actuation corresponded to a Strouhal number St = 1, with Strouhal number based on the chord length and free-stream velocity (as found by Corke et al. [18], cf above). They showed also that the steady plasma actuator was the most effective when the actuation was applied slightly upstream of the separation line. The authors suggested that the mechanism for the steady actuators was turbulence tripping, whereas the mechanism for the unsteady actuators was to generate a train of spanwise structures that promoted mixing. Among the most recent and potentially very promising ideas is the concept of a plasma flow-control optimized airfoil proposed by Corke et al. [14]. This concept uses a laminar airfoil design that maintains a favorable pressure gradient over as much of the upper surface as possible and incorporates a separation ramp at the trailing edge that can 33

48 be manipulated by a plasma actuator in order to control lift. At lower angles of attack, such as during cruise flight, a laminar boundary layer is maintained until it reaches the trailing-edge separation ramp. The separation in this case is a laminar one which can easily be controlled with an unsteady plasma actuator at very low power levels. This concept was investigated through numerical simulations and lift-control experiments using steady and unsteady SDBD plasma actuators mounted on a HSNLF(1)-0213 airfoil. The experiments showed a nearly constant change in the lift coefficient at U = 21 m/s (Re = 215,000) for angles of attack from -2 up to stall and a shift in the drag polar, consistent with an increase in airfoil camber. The authors demonstrated with numerical simulations that for a constant actuator amplitude, the change in lift is nearly constant to approximately Re = 300,000, beyond which point the C l drops off as Re -1. It should be noted that, although this concept is directed at airfoil lift-control using plasma actuators, the primary intent of the plasma actuators for this case is to control the airfoil boundary layer, with changes in the airfoil forces and moments resulting indirectly from the boundary-layer control. In other words, the increase in lift in these experiments is the result of a recovery of lift lost due to flow separation at the trailing-edge ramp. As such, this study is different from the goal of this research, in which the intent is to directly manipulate the circulation of the airfoil by using plasma actuators to alter the inviscid flowfield of the airfoil. Further, the Reynolds-number variation of the lift enhancement -2 determined by the numerical simulations in this study do not contradict the C l U result found in [19, 29, 30] (Equation (1.1)) since, again, those investigations consider the effect of the plasma actuators on the airfoil inviscid flowfield. 34

49 Further investigations related to the concept of a plasma flow-control optimized airfoil were done by He et al. [31]. The authors performed numerical and experimental studies of the turbulent flow separation over a wall-mounted hump model and separation control using plasma actuators at Re = 290,000. The plasma actuator configurations investigated included both spanwise and streamwise orientations, and both configurations were found to increase the pressure level in the separation region and to significantly reduce the size of the separation bubble. The authors suggested the use of a spanwiseoriented plasma actuator with unsteady operation for laminar separation control and unsteady operation for turbulent separation control. For the streamwise-oriented plasma actuator, the actuator can be placed upstream of the separation location and may be more useful for separated flows in which the separation location changes with flight conditions. Nelson et al. [65] demonstrated the ability of plasma actuators to produce roll control on a scaled 1303 UAV configuration. The flow over the suction surface of a scaled 1303 UAV model was found to be highly three-dimensional. As it was demonstrated the SDBD plasma actuators located near the leading edge of the 1303 wing was very effective in controlling the lift and roll moment in the high angle of attack regime, by controlling boundary-layer separation on the wing suction surface. The results are reported for a range of angles of attack from 10 to 30 and free-stream velocities from 10 to 30 m/s (Re = 150, ,000) Flow Control around Bluff Bodies In the case of flow control around bluff bodies the goal is typically to manipulate the wake by preventing or provoking boundary-layer separation. The result may be 35

50 modification of the vortex shedding, or reduction or enhancement of the pressure drag, as demonstrated in the following. Plasma off Plasma on Figure 2.12: Smoke visualization around a cylinder with SDBD plasma actuators. (Thomas et al. [105]) Figure 2.12 presents an example of bluff body flow control by a surface SDBD at U = 4 m/s [105]. Four plasma actuators are located at ±90 and ±135 with respect to the approach flow direction, inducing a jet tangential to the cylinder surface. With the actuators off, the flow undergoes separation leading to a large-scale separated flow region, accompanied by unsteady vortex shedding (Figure 2.12, left). With the SDBD actuation (Figure 2.12, right), there is a substantial reduction of the separated flow region, resulting in an elimination of the associated vortex shedding. Steady actuation has been shown to drastically reduce flow separation and the associated Karman vortex shedding is eliminated. The authors used unsteady actuation also, and showed it was very effective. For both steady and unsteady actuation, near-field sound pressure levels were reduced by 13.3 db in a frequency band centered on the Karman shedding frequency and turbulence levels in the wake downstream the cylinder were reduced by 50%. McLaughlin et al. [55] used SDBD actuators to manipulate the flow separation and wake behavior downstream of a circular cylinder at a Reynolds numbers Re

51 The purpose of this work was to show that the vortex shedding frequency could be driven to the forcing frequency of the unsteady SDBD plasma actuator. This research was continued in [54] but at higher velocities (up to 90 m/s, Re = 300,000). They showed that the plasma actuator was capable of triggering vortex shedding at the actuator forcing frequency within approximately ±10% of the Karman shedding frequency. Asghar et al. [4], performed an experimental study dealing with the use of plasma actuators to phase synchronize vortex shedding from two side-to-side circular cylinders, in the Reynolds number range Re = 16,700 76,000 (U = 30 m/s). The plasma actuators were placed at ±90 from the forward stagnation point of each cylinder, along the full span. The vortex shedding phase between the two cylinders was determined from unsteady velocities measured by two hot wires, located behind the cylinders. The study showed the effectiveness of the plasma actuators in synchronizing the vortex shedding Flat Plate Boundary Layer Control A paper dealing with the manipulation of a flat-plate boundary layer using plasma actuators was published by Roth et al. [89] in It was demonstrated that plasma actuators could be used to alter the wall turbulence and drag. The authors investigated the influence of the body force direction with respect to the direction of the freestream and showed that the drag is reduced when the SDBD-induced jet and the free air stream are in the same direction, whereas it increases otherwise. Several researchers worked on the separation control on flat plates. For example, Hultgren and Ashpis [35] studied the control of boundary-layer separation using a SDBD actuator, for 50,000 < Re < 300,000 and various free stream turbulence intensities (from 37

52 0.2% to 7%). The results suggested that the actuator works by promoting early transition in the shear layer above the separation bubble thus leading to rapid reattachment. Jukes et al. [40, 41] tried to reduce skin-friction drag by applying a span wise oscillation in the near-wall region of a turbulent boundary layer, using a SDBD. The experiments were performed at low velocity (1.8 m/s) and consisted of flow visualization and velocity measurements Airfoil Circulation Control There are two experimental studies dealing with the use of SDBD plasma actuators to control airfoil or wing circulation: Corke et al. [19] and Nelson et al. [64]. The use of plasma actuators to control the circulation on wing sections without flow separations was first described in Corke et al. [18] (cf Chapter 1). For this investigation, plasma actuators were placed near the trailing edge of a NACA 0009 airfoil and operated in a steady mode. The actuators were found to produce a shift to negative angles of the zero-lift angle-of-attack, L0, while maintaining the same lift-curve slope, C l. The effect was equivalent to that of a positively deflected trailing edge flap. More detailed consideration of the work by Corke et al. [19] is given in Chapter 1. The use of SDBD plasma actuators to provide circulation control was also investigated in experiments by Nelson et al. [64]. This work dealt with improving the performance of wind- turbine blade airfoils using distributed plasma actuators, where the aim of the study was to provide digital control that would produce discrete changes in lift in response to dynamically changing wind conditions. Experiments were done with two airfoil sections: S827 and S822, designed for wind power generation applications. Two different approaches were explored: separation control and circulation control. The 38

53 modified S822 section shape had separation ramps that could be manipulated by the plasma actuators to produce different pressure distributions near the trailing edge, and thereby control the overall lift. It was shown that unsteady plasma actuation recovered the lift loss due to separation of the flow over the ramp at angles of attack in the range For the circulation-control experiments, the authors used the S827 section shape with a steady SDBD plasma actuator at x/c = The actuator resulted in a positive shift in the lift coefficient of approximately C l = 0.08 at a free-stream velocity of 20 m/s (Re = 404,000). This increase in lift is equivalent to a change in the angle of attack of approximately = 0.7 and is equivalent to a 2 deflection of a plane flap. 2.4 Summary SDBD plasma actuators have been shown to be effective flow-control devices in many different aerodynamic applications. The advantage of the SDBD over other electrohydrodynamic actuators is its stability; specifically, the SDBD can sustain a large volume discharge at atmospheric pressure without arcing. Other operational advantages of SDBD plasma actuators include: no moving parts, they can be recessed into the airfoil surface, with no bumps or gaps, they can be operated only when necessary, the actuators can be operated in both steady and unsteady modes, the actuators have a very fast response time, enabling real-time control at high frequencies. 39

54 The main disadvantage of SDBD actuators is their low efficiency of energy conversion and limited amount of induced momentum; however, even relatively low power input into the flow can be very effective, especially with unsteady actuation. Very good results have been obtained for low-velocity subsonic airflows (typically U < 30 m/s), while some promising results have also been achieved at higher velocities. Most commonly, SDBD plasma actuators have been used to modify or control boundary layers where, as shown in the above literature review, they can have significant effects, including initiation or delay of transition or elimination of separation. The effectiveness of SDBD actuation is due not only to the direct momentum addition of the actuator jet, but also to how it is spatially and temporally applied. Far fewer investigations have been devoted, however, to the concept of using plasma actuators for circulation control. In this case, the objective is to use the plasma actuator jet to directly control the circulation on an airfoil operating in the attached-flow regime, thereby directly influencing airfoil forces and moments. This application differs from other studies in which the actuator is used to, for example, reattach a normally separated boundary layer on the airfoil which then indirectly influences the airfoil aerodynamic characteristics. The purpose of current work is a detailed investigation of circulation enhancement produced by SDBD actuators via momentum injected into the flow. 40

55 CHAPTER 3: LIFT CONTROL EXPERIMENT At the outset of this project the objective seemed quite simple: to attempt to verify the claim made in [19] that the effect of spanwise plasma activation on the aft-chord suction side of a wing gives a constant lift augmentation independent of angle of attack and free-stream speed. A further objective was to attempt to verify Hall s [29] lifting-line predictions of the roll-moment effects of span-asymmetric plasma actuation. The first objective was motivated by a desire to improve confidence in the Corke et al [19] data by better accounting for RF interference created by the plasma actuators. Performing the experimental measurements to achieve the project objectives proved, however, far more difficult than anticipated. In the following section describing the three-dimensional-flow experiments, the experimental setup reported is actually the third generation of attempts to measure the aerodynamic forces and moments on the wing. In the first attempt at performing these experimental measurements, mechanical scales were used due to their immunity to the RF interference created by the plasma actuators; however, problems in collecting sufficiently-unbiased data in what was a slightly unsteady flow in order to produce statistically-significant results eventually led to the use of electronic scales, which were themselves affected by RF interference from the plasma actuators. At the start of this dissertation research, this RF noise problem was solved by changing over to the specially-shielded scales described below. In addition, the 41

56 electrical circuit was modified to reduce RF effects. In the end, even this measurement system had a small RF noise component; however, this RF noise was repeatable and accountable. Once the RF issue was overcome, additional problems were encountered. As will be reported, the aerodynamic response that was measured was far from simple as suggested in [19], and the heat created by electromagnetic losses in the actuators, albeit small, was sufficient to slightly warp the thin trailing edge of the wing model over long actuation periods, which added a slight camber to the wing and incorrectly showed a slow change in lift augmentation. All of these complications, and others not mentioned here, led to a very slow progress over the first few years of work. Nonetheless, all of these problems were eventually sorted out, identified, and dealt with in a manner that led to the repeatable data with accurately-placed error bars shown in the results presented in Chapter 4. The reliable and repeatable data that were obtained then revealed the initiallybaffling aerodynamic behavior reported in the next chapter. In the chapters that follow, the results are presented in a way that does not convey this unexpected behavior but rather, presents the results in a rational progression of discovery that now seems almost self evident; however, it should be noted that many of the early results shown in Chapter 4 were actually obtained late in this investigation in order to sort out a number of hypotheses proposed to explain the peculiar behavior found. 42

57 3.1 Three-Dimensional Wing Experiments Measurements of the lift and moments in 3-dimensional flow over the wing were made in the University of Notre Dame Atmospheric Wind Tunnel (AWT). The AWT is an open circuit, indraft wind tunnel with test-section dimensions of 1.8 m 1.8 m. The tunnel turbulence intensity level is less than 2%, and maximum wind speed is approximately 9 m/s. Figure 3.1: Schematic of roof-mounted balance system used for lift and moment measurements on three-dimensional wing model. The wing used for the lift-enhancement investigations was made out of epoxy and had a NACA 0009 profile. The wing had a 0.2 m (8 in) chord, and a span of 0.91 m (36 in), giving it an aspect ratio of 4.5:1. Since the objective was to measure lift and moments in 3-dimensional flow, end plates were not used; however, thin, 25 mm wide aluminum bars were attached to the tips of the wing in order to suspend the wing (upside down) from the roof-mounted balance system. Aerodynamic loads acting on the wing were transmitted to the scales by steel wires attached to the aluminum wingtip-mounted 43

58 support bars. To increase the signal-to-noise ratio of the force-measurement system, the aerodynamic loads transmitted to the scales were mechanically amplified by a factor of 3 using lever arms. The forces measured by the four scales were resolved into lift, pitch and roll moments. Drag force was not measured; rather, the wing was restricted from moving in the streamwise direction by thin steel wires attached to the wing tips at the ¼ - chord location. A schematic of the roof-mounted aerodynamic balance system is shown in Figure 3.1. The planform view of the wing model with plasma actuators and the system of coordinates are shown in Figure 3.2, and a photograph of the wing model mounted in the AWT test section is shown in Figure 3.3. Y 0.5b A 0 B 0.75c -0.5b 0 1.0c X Figure 3.2: System of coordinates and planform view of the wing model. A plasma actuator; B exposed electrode. Direction of the flow is from left to right. 44

59 Figure 3.3: Photograph of wing model mounted in the test section of AWT. Flow direction is from top to bottom of figure. Two separate and independently-controllable 0.4 m long actuators were installed on the left and right sides of the wing to enable lift enhancement (actuators operated concurrently) and control of the wing roll moment (actuators operated independently). The geometry of the actuator installation can be seen in Figure 3.2. Additional details on the plasma actuators are presented in Section 3.3. Power cables leading from the wing-mounted actuators to amplifying circuitry located outside the test section were loosely hung from the model s wing tips. Measurements of the wing s aerodynamic forces made with the power cables attached and removed showed that the aerodynamic behavior of the wing was not influenced by the presence of the cables Data Acquisition and Analysis Initial tests showed a slight drift in the aerodynamic effect of the plasma actuators during long runs, which was attributed to thermal deformation of the model due to heating by the plasma discharge. As such, measurement sets were acquired by measuring the aerodynamic forces over many short-duration runs, rather than over a single run of 45

60 longer duration. Each run consisted of a measurement made with the plasma off followed immediately by one with the plasma on, with the aerodynamic effect of the actuators reported as the difference between the plasma on/off states. An additional source of measurement error was the radio frequency (RF) noise emitted by the actuators and high voltage wires during operation. This RF noise was especially noticeable in the AWT experiments, due to the much larger size of the set-up and, consequently, longer high-voltage lines. To minimize the effect of RF noise on the data, in the AWT experiments a novel force-measurement system was employed using four electronic scales mounted on the roof of the AWT test section. The scales were specially shielded for operation in high-frequency electromagnetic noise conditions, and the length of the wires was kept as short as possible to minimize the effect of RF noise. Despite efforts to minimize the influence of the plasma discharge on the dataacquisition system, the RF noise of the plasma discharge still created a small offset in the scale output. The lift increase measured for the plasma actuators therefore consisted of two terms: L = L + (3.1) RAW L RF where the first term in Eq. (3.1) is the lift produced by the plasma actuator while the second term is the lift offset produced by the RF noise of the plasma discharge, typically in the range of 0.02 N for the AWT tests. The RF noise influence was found to be constant when the plasma power was not changed; as such this noise-induced offset was accounted for by taring the balances prior to data acquisition, with the plasma actuators energized and the wind tunnel off. 46

61 3.2 Two-Dimensional Airfoil Experiments Measurements were also performed using two-dimensional airfoil models. These measurements were made in one of Notre Dame s low-speed Subsonic Wind Tunnels (SWT), and were designed to evaluate the performance of the plasma actuators at higher Reynolds numbers than could be achieved in the Atmospheric Wind Tunnel, and to clarify the details of the interaction between the plasma actuator and the airfoil boundary layer. The Notre Dame Subsonic Wind Tunnels are open circuit, indraft wind tunnels with a 0.6 m x 0.6 m test section and mean turbulence level below 0.1%. These tests also employed a NACA 0009 profile with 0.2 m chord. Although end plates were not installed, the models were built to span the test section in order to minimize end effects and generate a more 2-dimensional flow. The two-dimensional airfoil tests included liftforce and pitching-moment measurements using a strain-gauge force balance, measurements of the pressure distribution on the airfoil, velocity measurements inside the airfoil boundary layer using a Laser Doppler Anemometer (LDA), and smoke flow visualization, at wind speeds up to 30 m/s. The aerodynamic force data were corrected for the wake blockage, as well as solid blockage and the streamline curvature using the approach suggested by Allen and Vincenti [1] and the blockage due to boundary layer growth on the test section walls (see Appendix C). The loss in lift due to wing tip clearance leakage was estimated according to [48] as being below 3% and was not corrected Lift and Pitch Moment Measurements The aerodynamic forces were measured using an external 3-component straingage force balance equipped with load cells for measuring lift and drag forces and a 47

62 moment sensor which was used to measure pitch moment. The force balance was placed on the top of the test section with the airfoil model suspended vertically on the force balance sting in the middle of the test section. Figure 3.4: Schematic of the strain-gauge force balance with model of airfoil. Adopted from [62]. A schematic of the force balance with the model is shown in Figure 3.4 (only the moment sensor is shown). The force balance also was equipped with a servomotor which enabled control of the angle of attack of the airfoil. Calibration of the force balance was 48

63 performed by applying weights of known mass using a cable pulley system. More details about this aerodynamic force balance can be found in [62]. One 0.6 m long plasma actuator was installed on the airfoil model covering 95% of the wing span. The wires for the plasma actuator were passed through a small hole in the floor of the test section; although these wires applied a small tension to the airfoil, the effect of this tension did not affect the accuracy of the measurements of the SDBDproduced forces (see Appendix B.4.1. The dynamic pressure of the flow was measured using a pitot-static probe mounted in the wall of the test section upstream of the model and connected to a Setra differential pressure transducer. The output signals of the dynamic pressure sensor and load cells were digitized by a data board manufactured by Measurement Computing, model USB-1616FS. Data acquisition was controlled using a LabView program which provided simultaneous measurements of lift, drag, pitch and dynamic pressure as well as control of the plasma actuators and angle of attack. The input parameters to this program included the atmospheric pressure and air temperature which were used to calculate air density [39]. The plasma driving signal was generated using an Agilent Technologies, model 33220A Function/Arbitrary Waveform generator, which was also controlled by the data acquisition program over a USB link. Finally, control of the airfoil angle of attack was performed using the stepper motor attached to the balance; during data acquisition the stepper motor was switched to idle to avoid undesirable vibrations produced by motor. As mentioned above, it was found that energization of the plasma actuator for long periods of time would heat and deform the airfoil model, resulting in significant errors in the measured aerodynamic forces. This problem was circumvented by 49

64 performing the plasma-on tests in short runs that were only a few seconds in duration. Each run consisted of a plasma-off measurement followed immediately by a plasma-on measurement, and the effect of the plasma for the run was reported as the plasma-on to plasma-off difference in the aerodynamic forces. The mean effect of the plasma, and measurement uncertainty, was then determined using a data set of up to 30 such runs. This method of measuring the plasma effect over short runs was found to produce consistent data sets that avoided possible extraneous influences on the measurements, such as would be produced by a gradual deformation of the airfoil model if longer runs had been employed. A flowchart of the data-acquisition procedure is shown in Figure 3.5. The delays 1 and 2 shown in Figure 3.5 were introduced to allow for the decay of transient responses after changing the angle of attack and turning on the plasma actuators. The lower limits of the delays 1 and 2 were estimated from the requirement: 1 1 c τ >> = (3.2) f St 0. 2 U where f St is the Strouhal or reduced frequency and a Strouhal number of 0.2 was assumed. At the lowest wind speed of 8 m/s used in the tests, Equation (3.2) gives the condition that the time delays 1 and 2 must be greater than 0.1 s. As such, the delay time 2 following activation of the plasma was set at 0.2 s; this delay time was sufficiently long to allow transients due to activation of the plasma to die out while still minimizing the amount of time that the plasma was on, thereby reducing the heating and possible deformation of the airfoil model. The delay time 1 after changing the airfoil angle of attack, was set to 1 s. An additional delay time 3 was added after extinguishing the 50

65 Specify output data file, number of data acquisition cycles (N), input file with angles of attack, atmospheric pressure and ambient temperature Initialize loop variable, j = 1 Move airfoil to the next angle of attack Switch servomotor controller to the idle mode Delay τ 1 Turn plasma actuator ON No Is j odd? Yes Delay τ 2 Delay τ 3 Dynamic pressure and load cells data acquisition Turn plasma actuator OFF No Is j odd? Yes j = j+1 j > N? No Yes Is this the last angle of attack? No Yes Save data file Figure 3.5: Flowchart for data acquisition of lift and pitch moment. 51

66 plasma and before starting the plasma-off measurements to allow additional time for the plasma actuators to cool off between runs was also set to 1 s. Data were acquired as the 1-second averages of the load cells and pressure transducer signals sampled at an 8 khz rate. As shown in Figure 3.5, for each angle of attack a series of N one-second data samples were taken, where every even sample was taken with the plasma actuator turned on and every odd sample with plasma actuator off. The typical number of samples N taken was 31. Figure 3.6: Photograph of the SWT setup with the airfoil model mounted in the test section. 1 airfoil model, 2 force balance, 3 high voltage power source, 4 power amplifiers, 5 data acquisition system. A photograph of the setup with the airfoil model mounted in the test section is shown in Figure 3.6. The angle of attack = 0 was determined as the angle of zero lift in preliminary measurements with the plasma actuators off. 52

67 3.2.2 Surface Pressure Distribution Measurements A second NACA 0009 airfoil model incorporating pressure taps was constructed to measure the airfoil static pressure distributions with and without SDBD actuators. This airfoil model also spanned the test section with approximately 10 mm gaps between the wing tips and the side walls of wind tunnel. The airfoil had a chord of 0.2 m and had 36 pressure taps near the midspan of the model: 16 on the suction (actuator) side, 19 on the pressure side, and one pressure tap at the leading edge. The pressure taps were connected via 1.3 mm internal diameter plastic tubes to a Scanivalve pressure switch (model JS4-48) which was connected to a pressure transducer. The Scanivalve with its solenoid drive and drive controller, model CTLR2/S2-S6, were shielded from electromagnetic interference from the plasma discharge by a metal enclosure. The pressure transducer used for the static pressure measurements was either a Validyne pressure transducer with a dynamic range of 22 mm of H 2 O, or a Setra pressure transducer with a dynamic range of 140 mm of H 2 O, depending on the wind speed. The freestream dynamic pressure measurements in the tunnel were made using a pitot-static probe which was connected to a Setra model 339H differential pressure transducer with a range of mm H2O. The plasma actuator circuit, Scanivalve controller, and static and dynamic pressure data acquisition for the pressure-distribution measurements were controlled in a LabView program through a Measurement Computing model USB-1616FS analog and digital I/O board. A flowchart of the LabView program is shown in Figure 3.7. In this experiment, the time delays 1 and 2 in Figure 3.7 were introduced to allow the flow to settle after turning the plasma actuator on or off, as well as allowing the pressures to stabilize in the static pressure lines. After additional testing it was found that good results 53

68 Specify output data file, number of data acquisition cycles (N), atmospheric pressure, ambient temperature and angle of attack Bring Scanivalve to port #1 Initialize loop variable, j = 1 Step Scanivalve to the next port Turn plasma actuator ON No Is j odd? Yes Delay τ 1 Delay τ 2 Static pressure and dynamic pressure data acquisition Turn plasma actuator OFF j = j+1 j > N? No Yes Is this the last Scanivalve port? No Yes Save data file Figure 3.7: Flowchart for measurement of static pressures. 54

69 were obtained using s at a wind speed of 9 m/s. The delay 2 was set at 1 s to allow additional time for the airfoil model to cool after extinguishing the plasma. The data were acquired over a sampling period of 1 s at 8 khz sampling frequency. Zero angle of attack was determined from additional measurements as the angle of zero lift LDA Measurements Flow velocity measurements inside the boundary layer of the NACA009 airfoil model were made using a Dantec Dynamics FiberFlow 2D Laser Doppler Anemometer (LDA) System with BSA F60 signal processor. The measurements were made using the same airfoil model that was used for the static pressure tests (see Chapter ). The LDA transmitting/receiving optics was installed on a 3-axis remotely-controlled traverse system. To obtain better spatial resolution of the boundary layer, the 160 mm focusing lens was used, which provided a probe volume with dimensions of 0.08 mm in both the streamwise (X-axis) and normal-to-wall (Z-axis) directions. Since the primary interest of the experiment was the boundary layer behavior, only the streamwise velocity component was measured. The boundary-layer profiles were measured at streamwise locations x/c = 0.6, 0.65, 0.7 and so on up to x/c = In the wall-normal Z direction, measurements were made starting typically at 0.1 mm from airfoil surface. The spanwise location of the measurements was dictated by the focal length of the optics, and was approximately ¼ of the test section width from the side wall of the wind tunnel. The average data rate of the LDA signal varied from 5 to 10 khz, except for the locations of mm above the airfoil surface where the data rate was as low as Hz. Seeding of the flow was performed using an oil atomizer that generated particles with a mean size of approximately 1 µm. 55

70 The LDA data were acquired over a 1-minute sampling period. During this sampling period, the plasma actuator was alternately turned on and off with 1-second intervals to prevent heating and possible distortion of the airfoil model. The plasma-on data were then compiled from these 1-second data intervals, after eliminating the initial, transient portion of each interval. 3.3 Actuators The plasma actuators used in the wing (Section 3.1 ) and the airfoil tests (Section 3.2 ) were identical, and were constructed using thin electrodes made of copper foil tape attached to a glass-ceramic dielectric (trade name Macor). This type of dielectric is particularly well suited to plasma-actuator applications because of its superior ability to withstand high voltage plasma discharges. A schematic showing the construction of the plasma actuators used in this investigation is shown in Figure 3.8(a). The thickness of the Macor dielectric used in the actuators was 2 mm; the actuators were recessed into the suction side of the models so that no steps or gaps existed with the actuators installed. The streamwise extent of the actuators was approximately 40 mm and the upstream (exposed) electrodes were typically situated at x/c = This location for the plasma actuators was selected based on previous studies [19, 29, 30] which showed that aerodynamic force and moment control improves as the actuators are mounted further rearward on the wing. Additional experiments with multiple SDBD plasma actuators were also performed with the actuators located at x/c = 0.38, 0.58 and A diagram of the circuit used to drive the plasma actuators is shown in Figure 3.8(b). The key element is the 150:1 transformer shown in the center of the diagram that 56

71 (a) Exposed Electrode (copper tape) Macor Dielectric 40 mm Embedded Electrode (copper tape) (b) Signal generator Power amplifier Current probe A Transformer C L C Plasma actuator High voltage probe V Figure 3.8: Diagram of (a) plasma actuator and (b) power amplification circuit. Voltage, kv Current, ma time, msec Figure 3.9: Representative actuator voltage and current time histories. was used to step up the low-level driving signal to the kilovolt levels required by the plasma actuators. An additional LC filter was put in the high voltage side of the circuit to suppress RF noise. The plasma actuators were driven by a positive saw-tooth signal with a frequency of 2.9 khz for both the wing tests in the AWT and the airfoil tests in the 57

72 SWT; as shown in [22], the sawtooth driving signal is more efficient than, for example, a sinusoidal one. The voltage and current of the signal driving the plasma actuator were measured using high-voltage and inductive current probes. Representative actuator voltage and current time histories over three cycles of excitation are shown in Figure 3.9. The meancycle power dissipated by the actuator was computed by integrating the product of the instantaneous voltage and current over a full cycle, and then averaging over 128 cycles, Eq P = V ( t) I( t) dt, N N T NT = 128 (3.3) All plasma-on data presented were acquired using a constant mean dissipated power of 33 W per actuator (65 W total power in experiments with both actuators and 33 W in experiments with a single actuator) in experiments in the AWT and 40 W in experiments in the SWT. 58

73 CHAPTER 4: LIFT CONTROL RESULTS 4.1 Baseline Aerodynamic Behavior The NACA 0009 profile used in the experiments was chosen to enable comparison with results reported in [19], but also because it is a fundamental profile that is simple to manufacture. This profile, however, undergoes considerable and rapid changes in its flow physics at the low Reynolds numbers relevant to small-scale UAV s. The strong Reynolds-number dependence of the NACA 0009 airfoil is clearly evident in Figure 4.1, which shows a lift curve measured using the two-dimensional airfoil model at a Reynolds number of 135,000 (corresponding to a wind speed U = 10.1 m/s). In order to make the behavior of the lift curve more discernable, the figure includes a linear lift curve of 2π/rad slope. As shown in Figure 4.1, the section lift curve exhibits a reduction in slope in the range 3 to 9 followed by stall between the angles of attack of 9 to 10 ; this kind of behavior of the lift curve is well known and is caused by the increased importance of viscous effects at higher angles of attack, specifically, the thickening and eventual separation of the turbulent boundary layer on the suction surface of the wing. A more unusual feature of the lift curve is the dip in the angle-of-attack region from roughly 0 to 1.5 angle of attack. This dip in the section lift curve was observed at all Reynolds numbers below approximately 200,

74 Re = 135,000 2π α C l α, deg. Figure 4.1: Lift curve for NACA 0009 airfoil, U = 10.1 m/s, Re = 135, Re = 28,000 Re = 83,000 Re = 125, /deg C L α, deg Figure 4.2: Lift curves for wing with NACA 0009 profile and AR =

75 Three low-reynolds-number lift curves for the three-dimensional wing model are shown in Figure 4.2, which also includes a lift curve computed using lifting-line theory that accounts for wind-tunnel wall effects; Figure 4.2 shows that the wing model lift curve exhibited the same dip at low angles of attack as was observed for the airfoil model Re = 112,000 Re = 101,000, Selig et al. 2π α C l α, deg. Figure 4.3: Lift curves for NACA 0009 airfoil from Selig et al. [97] and current research. The reduction in lift at low angles of attack, shown in Figures , is actually a fairly common phenomenon for many airfoil profiles at low Reynolds numbers [61, 97]. As discussed in [61], this behavior is caused by laminar boundary-layer separation on the airfoil surfaces. In particular, at close to 0º angle of attack, the adverse pressure gradient on both sides of the airfoil is sufficiently strong to induce laminar boundary layer separation on both the upper and lower airfoil surfaces. As the airfoil angle of attack 61

76 increases, the adverse pressure gradient on the suction surface of the airfoil increases, moving the separation point on the suction surface forward and leading to a reduction in lift. In extreme cases, the airfoil can exhibit negative lift at small positive angles of attack; see, for example, Figure 4.4, which shows the lift curve for a NACA profile at nearly the same Reynolds number (130,000) shown in Figure 4.1 [61] C l Smooth Grit Roughness α, deg. Figure 4.4: Lift curve for NACA airfoil [61]. Depending on the local pressure gradient and the Reynolds number, the separated laminar boundary layer can stay separated or it can reattach as a turbulent boundary layer, forming a separation bubble on the airfoil surface. As pointed out in [13], the longitudinal size of the separation bubble (the distance from separation to reattachment points) can be determined from the following simple estimation: that the Reynolds number based on its length is approximately 50,000. As such, if the point of boundary-layer separation is far enough upstream of the trailing edge to fit the separation bubble on the airfoil, then 62

77 boundary-layer reattachment occurs leading to a significant increase in the circulation and lift on the airfoil due to a more rigorous enforcement of the Kutta condition. This kind of abrupt increase in lift at angles of attack just above the dip in the lift curve is clearly visible in Figures 4.1 and 4.2. As the Reynolds number increases, the size of the separation bubble becomes smaller [28], and this reduces the angle-of-attack range of the dip in the lift curve. This effect can be seen in Figure 4.2; for example, at Re = 28,000 the dip is roughly between 0 to 6 while at Re = 83,000 the dip is only between 0 to 4. For the Re = 125,000 data in Figure 4.2, the region of decreased C L is unnoticeable due to the low resolution in angles of attack, but its existence was observed in more detailed measurements using the airfoil. A further unusual characteristic of the airfoil lift curve shown in Figure 4.1 is that the measured lift in the range 2º to 4º is substantially greater than the theoretical lift curve. This phenomenon of elevated C l at low Reynolds numbers at certain angles of attack is not uncommon and can be found in a number of published experimental investigations [97, 98, 96, 107, 37]. For example, Figure 4.3 shows that published liftcurve data for the NACA 0009 airfoil [97] at a similar Reynolds number compares closely to the measured lift curve shown in Figure 4.1. The above explanation for the low-reynolds-number behavior was verified by smoke and oil-flow visualization measurements that were made at Reynolds numbers ranging from Re = 80,000 up to Re = 210,000 (U = m/s). The measurements were performed using the two-dimensional airfoil model to reduce end effects and improve the visualization results. The oil used for the surface flow visualization tests was 63

78 a mixture of kerosene, mineral oil and fluorescent dye, which emits visible light under ultraviolet illumination. Figure 4.5: Visualization of boundary layer on the suction side of NACA 0009 airfoil with smoke for different angles of attack. Re = 130,000 (U = 9.7 m/s). A) = 0; B) = 2; C) = 3. Smoke flow-visualization data for the airfoil model at angles of attack of 0, 2, and 3 are shown in Figure 4.5, for essentially the same Reynolds number as the lift curve shown in Figure 4.1 (Re = 135,000). At 0 angle of attack (Figure 4.5 A), the smoke streaklines clearly indicate boundary-layer separation near the airfoil trailing edge; note that the vortical structures that appear near the airfoil trailing edge in Figure 4.5 A are a typical characteristic of laminar separated-flow regions [110]. At = 2 (Figure

79 B), the laminar separation region appears to transition to turbulent flow just upstream of the airfoil trailing edge, while at = 3 (Figure 4.5 C), the boundary layer above the suction surface of the airfoil becomes turbulent by the trailing edge; note, however, that the inset to Figure 4.5 C shows a small region that appears to be a laminar separation bubble at the mid-chord location of the airfoil. As such, the smoke-flow visualization data in Figure 4.5 generally agree with the corresponding lift-curve data of Figure 4.1, which shows a dip from recovery in lift value at = 0 to 1.5 caused by laminar separation, followed by a = 1.5 that indicates boundary-layer reattachment near the airfoil trailing edge. Oil-flow measurements for the NACA 0009 are shown in Figure 4.6; these show essentially the same behavior as the smoke-flow visualization data in Figure 4.5. At 0 angle of attack (Figure 4.6 A), the accumulation of oil near the airfoil trailing edge shows that the skin friction has reduced to zero in this region indicating boundary-layer separation. In Figure 4.6 B and C ( = 2 and 3 ), the region of oil accumulation moves upstream towards the mid-chord location, while the trailing edge of the airfoil is now clear of oil; the lack of oil around the airfoil trailing edge at = 2 and 3 shows an increased skin friction in this region indicating reattachment of the boundary layer and formation of a separation bubble. Figure 4.7 shows that at = 5, the separation bubble has moved to just downstream of the airfoil leading edge, with a turbulent boundary layer on most of the downstream part of the airfoil suction surface. 65

80 Figure 4.6: Oil flow visualization on the suction side of NACA 0009 airfoil for different angles of attack. Flow direction from left to right, Re = 130,000 (U = 9.7 m/s). A) = 0; B) = 2; C) = 3. It should be noted that the smoke-flow visualization results (and the results of LDA measurements which will be presented in Chapter 5) show that the flow in the boundary layer near the separated-flow region is unsteady at low angles of attack, which agrees with the results of [6, 8]. Because of this flow unsteadiness, the location of zero 66

81 skin friction is not a single point but rather a range. This explains the difference in the oil accumulation pattern in the separated-flow regions in Figures 4.6 and 4.7. In particular, rather than a sharp accumulation line separating regions of direct and reverse flows, as in Figure 4.7, the region of zero skin friction appears as a wide range of gradual accumulation of oil in Figure 4.6. Figure 4.7: Surface flow visualization. Re = (U = 9.7 m/s), = 5. 1 separation of the flow; 2 reattachment of the flow Based on the preceding discussion, a good summary of the way in which the airfoil boundary layer affects its lift can be obtained by compiling the lift-curve data measured at all Reynolds numbers into a single contour plot, Figure 4.8. This plot shows contours of the ratio C l /2πα to reveal the angle of attack Reynolds number regions where the lift coefficient is suppressed or increased. As such, the depression in the lift contours in Figure 4.8 at low angles of attack and Reynolds numbers is caused by trailing-edge laminar boundary-layer separation, while the increased lift surrounding this depression is associated with reattachment of the boundary layer and formation of a 67

82 separation bubble in the trailing-edge region of the airfoil. The preceding statements are supported by Figure 4.9, which shows the approximate locations of laminar separation and reattachment of the boundary layer at Re = 130,000; these data were taken from the oil-flow visualization results, along with a predicted separation location calculated using a panel code and Thwaites method [104]. Finally, the drop off in the lift contours in Figure 4.8 as the angle of attack increases is due the thickening and eventual separation of the turbulent boundary layer on the airfoil suction surface No Data α, deg U, m/s , Re Figure 4.8: Contour plot showing baseline airfoil lift (Cl/2πα) over the tested range of angles of attack and Reynolds numbers. 68

83 7 6 5 Separation, Thwaites Separation Reattachment α, deg x/c Figure 4.9: Approximate locations of laminar separation and reattachment of the boundary layer versus angle of attack from oil-flow visualization data. Re = (U = 9.7 m/s). In summary, the lift-curve and flow-visualization measurements show that the baseline performance of the wing and airfoil models used in the investigation compares closely to previously established results [61, 97]. In particular, over the low-reynoldsnumber range of the investigation, the NACA 0009 airfoil is susceptible to both laminar boundary-layer separation and the formation of a suction-surface separation bubble. It will be shown later that these characteristics have an important effect on the response of the airfoil to trailing-edge plasma actuation. 69

84 4.2 Aerodynamic Forces with Plasma Actuation 0.1 C L 0.08 C M C R 0.06 Coefficient α, deg Figure 4.10: Effect on aerodynamic forces and moments, both left and right plasma actuators operating. U = 6.1 m/s, Re = 83,000. Once the baseline performance of the wing and airfoil models had been established, measurements were next performed using the wing model to determine the effect of the plasma actuators on wing lift, pitch and roll moments. An example of the angle-of-attack dependence of the wing aerodynamic force coefficients is shown in Figure 4.10; these data are shown for the three-dimensional wing model with both left and right plasma actuators operating. As described in Section 3.1, the data are presented in Figure 4.10 as the difference between the plasma-on and the plasma-off results. The data were acquired at a wind speed of 6.1 m/s (Re = 83,000) and a total plasma power of 65 W (33 Watts to each actuator). The figure shows that the plasma actuators increased 70

85 the lift coefficient of the wing while imparting a nose-down quarter-chord pitch moment. The fact that the actuators had no discernable effect on the wing roll moment indicates that the lift forces imparted by the left and right actuators were well balanced. One of the landmark findings of previous investigations [29, 30] was that plasma actuators impart a fixed momentum to the flow, so that trailing-edge mounted plasma actuators should produce a lift enhancement that is constant with both wind speed and angle of attack. Figure 4.10 shows, however, two distinct deviations from constant lift enhancement, consisting of a peak in C L at an angle of attack of = 1.5, and a gradual increase in C L as the angle of attack increases from around = 4 to = 10. After further investigation, it was noticed that the regions of increased C L enhancement in Figure 4.10 match almost exactly the regions in which the baseline lift of the wing is depressed below the theoretical, linear lift curve (cf Figure 4.2). This matching of the plasma lift enhancement with the baseline wing lift curve suggests that the deviations from constant C L are due to the interaction of the plasma actuators with the viscous flow field of the wing; in effect, the plasma actuators are counteracting depressions in the C L - curve by suppressing viscous effects. The above ideas are more clearly illustrated in Figure 4.11, which shows: the excess lift enhancement taken from Figure 4.10, computed as the difference between the measured C L enhancement at each angle of attack and the minimum C L measured at 3.5 angle of attack (circles); the influence of viscous effects on the wing plasma-off C L - curve, estimated as the difference at each angle of attack between the straight lifting-line lift curve and the measured C L data at the same Reynolds number Re = 83,000, taken from Figure 4.2 (squares). The good agreement between the two data sets up to an angle of attack of approximately 6 supports the supposition that the excess lift enhancement is elevating the lift up to the 71

86 theoretical, inviscid limit in this angle-of attack range. Beyond = 6, the excess lift enhancement is less than the drop off of the C L from the theoretical lift curve; however, this merely indicates that the plasma actuators were not powerful enough to fully compensate the reduction in lift due to viscous effects at high angles of attack as the airfoil approaches stall Deviation from constant lift enhancement, C L min( C L ) Difference in C L from straight lift curve, πα C L 0.06 C L α, deg Figure 4.11: Comparison of measured increase in lift enhancement with difference in lift curve from inviscid behavior. The supposition presented above and shown in Figure 4.11 was more fully investigated by performing smoke flow-visualization measurements around the trailing edge, Figure The photographs were taken using the two-dimensional wing model at the same Reynolds number as the data shown in Figure 4.10, and at an angle of attack of 2, which corresponds roughly to the peak in the lift-enhancement ( C L ) data shown in Figure With the plasma actuators turned off, the flow visualization shows what 72

87 Figure 4.12: Visualization of the flow near trailing edge of NACA 0009 airfoil: A) plasma off; B) plasma on. Re = 83,000, = 2. appears to be laminar boundary-layer separation upstream of the trailing edge. Activation of the plasma actuators eliminates this separated-flow region, resulting in a more rigorous enforcement of the airfoil Kutta condition with concomitant increase in the airfoil lift closer to the theoretical limit. Overall the lift-curve data shown in Figure 4.10 and Figure 4.11, as well as the flow visualizations shown in Figure 4.12, strongly indicate that the plasma actuators increase the wing lift due to a flow-control suppression of viscous flow effects [76, 77]. Whether the actuators also increase the wing lift due to an inviscid-like interaction with the wing Kutta condition, as described in [30], cannot be definitely 73

88 concluded at this point; more detailed measurements showing how the actuator interacts with the wing/airfoil trailing-edge flow will be shown in Chapter Center of Pressure The chordwise center of pressure x CP for the lift enhancement was computed from the lift and moment data acquired at all wind speeds. The resulting values for x CP were found to be invariant with wind speed, and the mean location of the center of pressure, averaged over all tested wind speeds, was x CP 0.40±0.06. This location of x CP, rearward of the quarter-chord point, indicates that the plasma actuators produced a noticeable modification to the pressure distribution over the wing. For comparison, the center of pressure of a plain mechanical flap with hinge line at x/c = 0.75 (the location of the upstream electrode of the plasma actuators) is x CP = The fact that the plasma actuators produce a rearward shift of the wing loading indicates that the actuators do not behave as simple circulation-enhancement devices but rather, shows that they also modify the loading distribution on the airfoil; this finding is similar to results reported in [14] Roll Control In addition to investigating the lift-enhancement capabilities of plasma actuators, another objective of the research was to determine their suitability as roll-control devices. As discussed above, two independently-operable actuators were installed on the wing model, and roll control was affected by operating one or the other actuator independently, Figure

89 Induced Roll Moment Figure 4.13: Roll moment produced by operation of a single actuator C L 0 0 C M 0.05 Lift Coefficient Roll Coefficient Plasma off Both Left Actuators Actuator Right Actuator 0.01 Figure 4.14: Example of the lift and roll moment for combined and independent operation of left and right plasma actuators. A simple illustration of the lift and roll dynamics possible with the wing/actuator system is presented in Figure The figure shows the measured change in wing lift and roll moment for 4 cases: actuators off, both actuators operated together, and each actuator operated independently. As shown in the figure, for the same test conditions, each actuator produced approximately half the lift enhancement that was generated when both actuators were run together, and each actuator produced an equal but oppositedirected roll moment when operated independently. These results conform to intuitive 75

90 expectations for the effect of the actuators, and show that the two actuators were well balanced in terms of the lift enhancement that they produced Coefficient C L C M C R α, deg Figure 4.15: Effect on aerodynamic forces and moments, single actuator operation Coefficient C L C M C R Wind Speed, m/s Figure 4.16: Aerodynamic force and moment dependence on wind speed/ Reynolds number. Single actuator operation, = 4 Aerodynamic force coefficients measured during operation of a single actuator are summarized in Figure 4.15 and Figure These figures show similar behavior to the two-actuator performance data shown in Figure 4.10, discussed above. 76

91 The location of the wing s spanwise center of pressure, y CP, during single-actuator operation was calculated from the measured lift enhancement and roll moment produced by the actuator: y CP C C R = (4.1) L These computations gave a constant value for the spanwise center of pressure that was independent of wind speed and angle of attack and equal to 18.5% of the wing span (i.e. y CP /b = 0.185) from the wing centerline. For comparison, a spanwise location for the center of pressure was also computed using lifting line theory [58]. For this calculation, the lifting-line equation was solved using a constant value for the zero-lift angle of attack over the spanwise region corresponding to the location of the plasma actuator on the experimental model. The resulting lift distribution is plotted in Figure The spanwise center of pressure for this computed lift distribution is y CP = 0.175, which closely matches the experimentally-measured value given above. This result indicates that the plasma actuators give constant lift enhancement across their spanwise dimension, but that the lift enhancement is modified by wing downwash. In Equation (4.1), y CP is a constant that depends on the wing geometry and the location of the actuators used for roll control which, as shown by Figure 4.17, can be computed using lifting-line theory assuming that the actuator produces a constant effect across its span. Because of the fact that the spanwise center of pressure for the plasma-on case does not vary with angle of attack or wind speed, the roll moment C R induced by a plasma actuator is related by a simple constant to the lift increment C L ; as such, the 77

92 remainder of this dissertation focuses on an examination of the lift-enhancement behavior of the actuators, since roll behavior can be simply determined using Eq. (4.1) y CP = Fraction of Lift y/b Figure 4.17: Lifting-line prediction of lift distribution for constant wing twist over a spanwise distance matching the extent of the right-hand-side plasma actuator Reynolds Number Effects The variation of the lift enhancement with wind speed/reynolds number was also measured and is shown in Figure 4.18 for three angles of attack. The figure shows that, like the angle-of-attack data shown previously, the lift enhancement also varied significantly with wind speed. This result differs from results reported in [19], which showed constant lift enhancement; however, the data reported here spanned much lower Reynolds numbers than that reported in [19]. 78

93 α = 2 α = 4 α = L, N U, m/s , Re Figure 4.18: Variation of dimensional lift enhancement with wind speed. Figure 4.18 shows two distinct variations of the lift enhancement with wind speed; first, a general drop off of the lift enhancement to zero occurs as the wind speed decreases to 0 m/s for all angles of attack. Second, at = 2, the lift enhancement undergoes a sudden dip in lift enhancement in the wind speed range 6 9 m/s. The fact that this dip in lift enhancement occurs within the 1 to 4 angle-of-attack range over which the NACA 0009 airfoil exhibits laminar trailing-edge boundary layer separation (cf Section 4.1) suggests that this effect may be the result of an interaction of the plasma jet with the boundary layer separation. At angles of attack = 4 and greater, the lift enhancement asymptotes to a constant value as the wind speed increased to the maximum tested value of 9.5 m/s. To further investigate the results shown in Figure 4.18, additional measurements were performed using the two-dimensional airfoil model in the SWT. Since the SWT has 79

94 a much higher maximum wind speed than the AWT, the objective of these tests was to better clarify the Reynolds-number variation of the lift enhancement over a larger range of Reynolds numbers. Prior to investigating the airfoil lift enhancement over the full wind speed range of the SWT, measurements were first performed with the airfoil at low wind speed. The purpose of these measurements was to determine how well the lift enhancement measured using the airfoil compared to the lift enhancement measured using the wing at the same airspeeds. To perform this comparison, the following corrections were first applied to the wing lift-enhancement results: First, an attempt was made to correct the 3-dimensional wing results to the equivalent lift enhancement that would have been obtained on a 2-dimensional airfoil. In essence, the objective of this correction was to remove the reduction in L caused by downwash in the 3-dimensional wing measurements. This correction was estimated by computing the lifting-line-theory prediction [43] of the lift enhancement for a constant angle of attack over the extent of the plasma actuator, and then comparing this to the lift enhancement that would result for the same angle of attack in 2- dimensional flow. For the aspect ratio 4.5 wing, this correction comes out to be Next, the data were corrected for differences in the electrical power used to drive the actuators. This correction was applied by assuming that the lift enhancement produced by the actuators scales linearly with the dissipated power of the actuator. In reality, the effect of the actuators at different powers can also depend on the state of the boundary layer in the vicinity of the actuator. The way in which the actuator lift enhancement depends on the dissipated power will be more fully treated in Chapter 5.4, which presents a more detailed investigation into Reynolds number effects; however, for the purpose of this comparison between the wing and airfoil results, it is adequate to assume at this point that the lift enhancement scales linearly with dissipated power (cf. Chapter 5). As such, correcting the wing results, which used 65 W of power, to the airfoil results, which used 40 W of power, gives a correction factor of The net equation used to correct the wing results to equivalent airfoil results was therefore: L = L = L (4.2) airfoil wing wing 80

95 A comparison of airfoil lift-enhancement results to corrected results for the wing is shown in Figure 4.19 for the same range of angles of attack and comparable wind speeds U = 7.8 m/s, Re = 105,000, wing, corrected U = 9.3 m/s, Re = 125,000, wing, corrected U = 8.04 m/s, Re = 108,000, airfoil U = 9.98 m/s, Re = 134,000, airfoil 0.3 L, N α, deg Figure 4.19: The plasma lift versus angle of attack for airfoil (SWT) and wing (AWT). Data for wing are corrected for downwash and for difference in dissipated power. The figure shows that the lift-enhancement results for the 3-dimensional wing and 2- dimensional airfoil compare very closely when the data are corrected for downwash effects and differences in dissipated power. Lift-enhancement results measured using the airfoil for a wider range of wind speed are plotted in Figure As can be seen, the lift enhancement produced by the plasma actuator varies significantly over the tested wind-speed range, and at some angles of attack and wind speeds, the lift enhancement produced by the plasma actuator actually becomes negative; for example, at an angle of attack of = 2 negative lift enhancement is produced from approximately U = 8 to U = 17 m/s. Lift-enhancement results are 81

96 L, N α = 0 α = α = 2 α = α = 6 α = U, m/s , Re Figure 4.20: Lift enhancement produced by plasma versus with wind speed for airfoil in SWT summarized in Figure 4.21, which shows the plasma lift increment plotted as a function of wind-speed and angle of attack. In Figure 4.21, the region of negative lift enhancement is contained within the contour labeled 0, which shows that negative lift enhancement occurred near zero angle of attack and was not observed for > 3. At angles of attack > 3, the lift enhancement slightly increases with the angle of attack. The fact that negative lift enhancement occurs only at low angles of attack where the NACA 0009 airfoil undergoes laminar boundary-layer separation strongly indicates that the phenomenon is the result of an interaction of the plasma jet with the development of the suction surface boundary layer. The physical cause of the negative lift enhancement results shown in Figure 4.20 are investigated in further detail in Chapter 5. In summary, the results presented in this chapter show that the lift enhancement produced by the actuator is strongly influenced by Reynolds number effects. As such, a 82

97 more detailed investigation was conducted that looked specifically into the unusual Reynolds-number behavior of the actuators; this investigation is described in Chapter 5. No Data Figure 4.21: Contours of plasma lift increment in SWT, N. 83

98 CHAPTER 5: DETAILED INVESTIGATION OF THE REYNOLDS NUMBER EFFECTS Previous experimental [19, 113] and theoretical [29] investigations indicated that the use of plasma actuators mounted near the trailing-edge of a wing or airfoil should produce a constant lift enhancement that is independent of wind speed or angle of attack. In several instances, results presented in the preceding chapter have shown that this is clearly not the case. In fact, at certain Reynolds numbers and angles of attack, the effect of the plasma actuators was actually a net reduction in the airfoil lift compared to the plasma-off case. This section presents an investigation into the Reynolds-number dependence of the lift-enhancement results and a discussion of the possible causes. 5.1 Airfoil Surface-Pressure Distributions Reynolds-number effects on the lift-enhancement results were first investigated via measurements of the airfoil surface-pressure distribution. As discussed in Section 3.2.2, the pressure at each pressure port of the airfoil was measured as the average of approximately 30 short runs in which a 1-second measurement with the plasma on was immediately followed by a measurement with the plasma off; this procedure was adopted in order to avoid any thermal deformation of the airfoil that would result from longer runs. 84

99 Example airfoil pressure distributions with the plasma on and off are shown in Figure 5.1. The wind speed and angle of attack for the results shown in Figure 5.1 correspond to a situation in which the plasma actuators produced positive lift enhancement. The absence of pressure data near the trailing edge of the suction surface of the airfoil is due to the presence of the plasma actuator, which covered the airfoil surface in this region C p actuator (suction) side pressure side actuator side, SDBD on pressure side, SDBD on x/c Figure 5.1: Pressure distribution over NACA 0009 airfoil with plasma on and off. Re = 84,000 (U = 6.2 m/s), = 1. The effect produced by the plasma actuators is more clearly shown in Figure 5.2, which plots the difference in the airfoil pressure distributions (i.e. C P ) between the plasma on and off cases shown in Figure 5.1. The figure shows that the plasma actuator affects the pressure distribution over the entire airfoil and on both sides of airfoil, most noticeably near the leading edge of the airfoil and in the region of the plasma actuator itself. In particular, an increase in overall airfoil circulation is indicated by the increased 85

100 pressure loading over the entire airfoil chord, and by the increase in the leading-edge suction peak. Similarly, the presence of a suction peak in the vicinity of the actuator also shows that the actuator has a local pressure-loading effect with a rearward shift of the airfoil center of pressure. These observations agree with results presented in Chapter 4 regarding the effect of the actuators on the airfoil circulation and center of pressure actuator (suction) side pressure side C p x/c Figure 5.2: Pressure difference for Plasma ON and Plasma OFF over NACA 0009 airfoil. Re = 84,000 (U = 6.2 m/s), = 1. The change in pressure distribution C P caused by the plasma actuator for an angle of attack and Reynolds number in which the actuator produced negative lift enhancement is shown in Figure 5.3. The negative effect of the plasma actuator on the lift is evident from the fact that the actuator produced an increase in pressure on the suction surface of the airfoil, and a decrease in pressure on the pressure surface; this situation is the reverse of that shown in Figure 5.2, in which the actuator produced positive lift enhancement. More importantly, Figure 5.3 shows that the actuator most strongly affects 86

101 the loading in the trailing-edge region of the airfoil. The figure also shows that the actuator changed the pressure distribution over the entire airfoil surface; this implies that the negative lift enhancement effect must be associated with a modification of the airfoil Kutta condition that changes the airfoil circulation. Both of these effects on the airfoil pressure distribution indicate that the actuator strongly influences the flow at the trailing edge of the airfoil C p actuator side "pressure" side x/c Figure 5.3: Pressure difference for Plasma ON and Plasma OFF over NACA 0009 airfoil; Re = 267,000 (U = 20 m/s), L = -0.6 N, = 0 (note: L = -0.6 N). In summary, the airfoil pressure distribution measurements show that in all cases, the plasma actuator changes the pressure distribution over the entire airfoil surface. In particular, cases in which the actuator produces negative lift enhancement cannot be explained only by a localized change in the airfoil loading, and points to a more-detailed investigation of the trailing-edge flow. 87

102 5.2 Collation of Force-Balance Results Further insight into the Reynolds-number variation of the lift enhancement can be obtained by a more-detailed analysis of the force-balance data already presented in Chapter 4. Specifically, Figure 5.4 shows a comparison of the lift-curve data for the baseline airfoil shown in Figure 4.8, with the lift-enhancement data from Figure In Figure 5.4, only the contour of zero lift enhancement is shown, that delineates the angleof-attack and wind-speed region where the actuator produces positive lift enhancement from the region where the actuator produces negative lift enhancement. The comparison presented in Figure 5.4 reveals that the region of negative lift enhancement occurs just outside the region where the dip in the lift curve (eg. Figures 4.1, 4.2) occurs at low angles of attack and wind speeds on the baseline (plasma-off) airfoil. In Section 4.1 it was shown that this dip in the lift curve is caused by laminar boundary-layer separation at the airfoil trailing edge, and that the dip ends when the angle of attack and/or wind speed increases to the point that the separated boundary layer reattaches as a separation bubble. As such, Figure 5.4 shows that negative lift enhancement occurs when a separation bubble forms on the actuator side of the airfoil; in particular, the fact that the zero lift-enhancement contour lies in a narrow band just outside the region of laminar boundary-layer separation suggests that negative lift enhancement occurs specifically when a separation bubble has just formed in the trailing-edge region of the airfoil. In summary, the collated force-balance data show that the strongest changes in the lift enhancement, from positive to negative values, occurs when a separation bubble exists in the trailing-edge region of the airfoil in the plasma-off case. This finding supports the results of the pressure-distribution measurements in the sense that it also points to the 88

103 trailing-edge region of the airfoil as the origin of the strongest Reynolds-number effects on the lift enhancement. Furthermore, it suggests that the Reynolds-number variation of the lift enhancement is associated with the state of the boundary layer at the airfoil trailing edge α, deg U, m/s , Re Figure 5.4: Contours of Cl/2π with the region of negative lift enhancement (contained within the contour marked 0 ). 5.3 LDA Measurements Based on the force-balance and airfoil surface-pressure results, it seems clear that the negative lift phenomenon is associated with the state of boundary layer near the wing or airfoil trailing edge and its effect on the Kutta condition. As such, Laser Doppler Anemometer measurements were made in the trailing-edge region for several flow conditions corresponding to negative and positive lift enhancement. The measurements were made at an angle of attack of 1 and at wind speeds of approximately 8, 15.4 and 89

104 26.8 meters per second (Re = 107,000, 207,000 and 361,000); as shown in Figure 4.20, these cases corresponded to situations in which the lift enhancement was positive, negative and positive, respectively. The evolution of the boundary layer mean velocities and velocity fluctuations along the trailing edge of the NACA 0009 airfoil suction surface (x/c = ) are presented in Figures for all three tested Reynolds numbers. The profiles are plotted for the cases of the naturally-developing boundary layer (denoted SBDB off ) and the BL in the presence of forcing with the plasma actuator (SDBD on). The boundary layer behavior for the plasma-off case is also summarized in Figure 5.8 which shows the shape factors for all tested Reynolds numbers. As discussed in Section 3.3, the exposed electrode of the plasma actuator was located at x/c = The results at each Reynolds number are discussed in detail in the following sections Re = 107,000. Positive Lift Enhancement. The LDA data acquired at Re=107,000 are shown in Figure 5.5. For these data, the separation of the naturally-developing boundary layer at the trailing edge is clearly indicated by the negative mean velocities (i.e. flow reversal) close to the airfoil surface in the region 0.8 < x/c < 0.98 (top of Figure 5.5). Furthermore, flow in the boundary layer for the naturally-developing case is also highly fluctuating in this region, as shown by the u /U results (bottom of Figure 5.5) as well as the probability density functions (pdf) of the velocity in the boundary layer, shown in Figure 5.9; these flow fluctuations also indicate flow separation from the airfoil trailing edge. 90

105 SDBD on SDBD off u/u SDBD on SDBD off u /U x/c Figure 5.5: LDA measurements of mean velocity (top) and velocity fluctuations (bottom) near the trailing edge of NACA α = 1, Re = 107,000, U = 8 m/s z/c z/c 91

106 SDBD on SDBD off u/u 0.01 z/c SDBD on SDBD off u /U 0.01 z/c x/c Figure 5.6: LDA measurements of mean velocity (top) and velocity fluctuations (bottom) near the trailing edge of NACA α = 1, Re = 207,000, U = 15.4 m/s 92

107 SDBD on SDBD off u/u 0.01 z/c SDBD on SDBD off u /U 0.01 z/c x/c Figure 5.7: LDA measurements of mean velocity (top) and velocity fluctuations (bottom) near the trailing edge of NACA α = 1, Re = 361,000, U = 26.8 m/s 93

108 6 5 4 Re = 107,000 Re = 207,000 Re = 361,000 Laminar BL (Thwaites) H x/c Figure 5.8: Plasma-off boundary-layer shape factor for suction side NACA 0009 airfoil at = SDBD on SDBD off relative counts u/u Figure 5.9: Near-wall velocity probability density function from LDA measurements. U = 8 m/s, Re = 107,000, z/c = 0.001, x/c =

109 In contrast, the mean velocity profiles for the plasma-on case shown in Figure 5.5 clearly indicate attached flow at the airfoil trailing edge. Furthermore, the velocity fluctuations in the boundary layer are largely suppressed in the plasma-on case, especially near the trailing edge, with u /U reduced from approximately 30% for the plasma-off case to 5% for the plasma-on case at x/c = A significant reduction in the velocity fluctuations is also shown by the probability density function for the LDA velocity measurements shown in Figure 5.9. To better show the effect that the plasma discharge had on the boundary layer, skin friction coefficients were also computed from the LDA data. The friction coefficient at the wall was computed using two methods; first, C f data were computed directly from the measured velocity profiles using: C f = w ρu z z= 0 ρu 2 τ = 2 µ u (5.1) Second, since there may be some error in estimating the wall velocity derivative u z from the measured velocity profiles, C f results were also determined using the z=0 von Karman momentum integral equation [58]: 1 dθ θ due C f = + (2 + H ) (5.2) 2 dx ue d x As can be seen from Eq.(5.2), determination of C f using the momentum integral equation involves the computation of integrated values such as * and and therefore may give more accurate results than Eq. (5.1), which relies on the estimation of the velocity derivative at a single point. 95

110 20 x SDBD on SDBD off SDBD off (IE) Thwaites 10 C f x/c Figure 5.10: Effect of plasma discharge on the skin friction coefficient. U = 7.95 m/s, Re = 107,000. The skin friction coefficient results for the Re = 107,000 data are summarized in Figure The figure shows C f results for the plasma-off case computed using Eq. (5.1) (squares) and using the momentum integral equation, Eq. (5.2) (asterisks). Figure 5.10 also shows C f results for the plasma-on case computed using Eq. (5.1) (circles) For the plasma-off case, the figure shows good agreement between the wall shear-stress (Eq.(5.1)) and momentum-integral (Eq.(5.2)) results; both these approaches give negative C f values starting at x/c = 0.8 indicating trailing-edge boundary-layer separation. On the other hand, the plasma-on results show a sharp increase in C f, with a maximum value at x/c = 0.8, slightly downstream of the exposed electrode of the plasma actuator (x/c = 0.75). Downstream of this C f peak at x/c = 0.8, Figure 5.10 shows that the plasma-on skin friction rapidly decreases; however, the C f results indicate that the flow still remains 96

111 attached right up to the airfoil trailing edge. Figure 5.10 also includes a calculation of C f using Thwaites method [58, 104] (solid line) computed using the potential flow solution that was determined with a panel method [43]. This simple method by Thwaites gives reasonably good results for laminar boundary layers and was used in this work to estimate the characteristics of the boundary layer in the laminar part of the flow SDBD on SDBD off Thwaites δ * /c x/c Figure 5.11: Effect of plasma discharge on the boundary layer displacement thickness. U = 7.95 m/s, Re = 107,000. The effect produced by the plasma discharge on the boundary layer also is also demonstrated in Figure 5.11, which shows the boundary layer displacement thickness *, calculated from the LDA data for the plasma-off and plasma-on cases. The growth of the separated boundary layer up to the trailing edge of the airfoil in the plasma-off case and the significant reduction of the boundary layer displacement thickness by the plasma 97

112 discharge illustrate the effect of momentum injected by the plasma, leading to a more attached flow. In summary, the LDA results obtained at Re = 107,000 show that the plasma actuator eliminates a laminar boundary-layer separation that normally exists in the plasma-off case. The elimination of this laminar boundary layer separation leads to increased circulation on the airfoil due to a more rigorous enforcement of the airfoil Kutta condition Re = 207,000. Negative Lift Enhancement. The LDA velocity profiles for the plasma-off and plasma-on cases at Re = 207,000 (U = 15.4 m/s) are displayed in Figure 5.6. As can be seen in Figure 5.6, boundary-layer separation occurs at roughly the same location, x/c 0.8, as in the Re = 107,000 data shown in Figure 5.5. Although the velocity profiles in Figure 5.6 may not show distinct reversals of the flow direction, it should be noted that the figure displays time-averaged velocity data. Instances of flow reversal can be seen in the LDA probability density functions shown in Figure 5.12 (x/c = 0.8) and 5.13 (x/c = 0.9). For the plasma-off case, the LDA data at Re = 207,000, as well as the C f calculations presented in Figure 5.14, also indicate reattachment of the boundary layer at the airfoil trailing edge. As shown in Figure 5.14, the C f data computed using the wall shear-stress approach, Eq. (5.1) (squares) and the momentum-integral equation (asterisks) both show positive C f values at the airfoil trailing edge; as discussed above, the larger trailing-edge C f value obtained using the momentum-integral equation may be more accurate than the value obtained using the shear-stress approach due to the integrated parameters used in the momentum-integral equation, and therefore reduced sensitivity to 98

113 local measurement errors. The existence of laminar boundary-layer separation and reattachment near the airfoil trailing edge at this angle of attack and Reynolds number agrees with the results of the baseline airfoil performance presented in Section relative counts SDBD on SDBD off u/u Figure 5.12: Near-wall velocity pdf. U = 15.4 m/s, Re = 207,000, z/c = 0.001, x/c = 0.8. Figure 5.6 also shows the effect of the plasma actuator at Re=207,000. The figure shows that the actuator re-energizes the boundary layer and eliminates the separation in the region x/c = that exists in the plasma-off case. However, Figure 5.6 shows that when the flow reaches the point x/c =0.95, the re-energizing effect of the plasma actuator is no longer evident and the mean plasma-on and plasma-off velocity profiles are nearly identical. Farther downstream at the x/c = 0.98 station, the plasma-on boundary layer is in fact less energetic that the plasma-off boundary layer, and is actually separated. The preceding interpretation is supported by the skin friction data shown in Figure 5.14, 99

114 which show a rapid drop off in C f to a negative value at the airfoil trailing edge. The LDA probability density functions for the near-wall velocity also indicate boundary-layer separation at x/c = 0.98 in the plasma-on case, as shown by the mostly negative u/u results (Figure 5.15). 30 relative counts SDBD on SDBD off u/u Figure 5.13: Near-wall velocity pdf. U = 15.4 m/s, Re = 207,000, z/c = 0.001, x/c =

115 10 8 SDBD on SDBD off SDBD off (IE) Thwaites 6 C f x/c Figure 5.14: Effect of plasma discharge on the skin friction coefficient. U = 15.4 m/s, Re = 207, SDBD on SDBD off relative counts u/u Figure 5.15: Near-wall velocity probability density function. U = 15.4 m/s, Re = 207,000, z/c = 0.001, x/c =

116 8 7 6 SDBD on SDBD off Thwaites δ * /c x/c Figure 5.16: Effect of plasma discharge on the boundary layer displacement thickness. U = 15.4 m/s, Re = 207,000. In summary, the LDA measurements at = 1 and Re = 207,000 show that the effect of the plasma is to re-energize the boundary layer at the airfoil trailing edge thereby eliminating a reattached separation bubble that normally exists in the plasma-off case. As such, the negative lift-enhancement effect of the plasma actuator can be attributed to the fact that the actuator actually worsens the condition of the boundary layer in the airfoil trailing-edge region, by preventing the formation of a separation bubble and reattachment as a turbulent boundary layer. Instead, the actuator re-energizes the laminar boundary layer, which then rapidly grows and separates by the airfoil trailing edge; this laminar boundary-layer separation at the airfoil trailing edge lowers the overall airfoil circulation due to a reduction in the effectiveness of the airfoil Kutta condition. The negative lift enhancement effect might also be explained by the boundary-layer displacement thickness in the plasma-on case, shown in Figure As pointed out in 102

117 [58], the displacement thickness indicates how the boundary layer effectively modifies the shape of the airfoil; as such, the rapid increase in * near the airfoil suction-surface trailing edge in the plasma-on case might be considered to have the same effect as a small, negatively-deflected flap Re = 361,000. Positive Lift Enhancement. The boundary layer profiles at the Re = 361,000 test condition are presented in Figure 5.7. At this relatively-high Reynolds number, the boundary layer in the vicinity of the plasma actuator is expected to be turbulent [58], and this is indicated by the u /U data shown in Figure 5.7 (bottom) as well as the baseline airfoil data presented in Section 4.1. In fact, the shape factor distribution for the plasma-off case, shown in Figure 5.8, indicates a typical transition to a turbulent boundary layer. At this Reynolds number, the plasma actuator does not produce considerable effect on the shape of boundary layer velocity profiles or on the skin friction coefficient (Figure 5.17) or the boundary-layer displacement thickness (Figure 5.18). The effect of the plasma on the velocity fluctuations (Figure 5.7, bottom) is more noticeable, although its near-wall effect is mainly localized near the point x/c =

118 10 x SDBD on SDBD off SDBD off (IE) Thwaites C f x/c Figure 5.17: Effect of plasma discharge on the skin friction coefficient. U = 26.8 m/s, Re = 361, SDBD on SDBD off Thwaites δ * /c x/c Figure 5.18: Effect of plasma discharge on the boundary layer displacement thickness. U = 26.8 m/s, Re = 361,

119 5.3.4 Summary of LDA Results At the two lower Reynolds numbers that were tested, the boundary layer approaching the plasma actuator from the upstream side was laminar, and the momentum added to the boundary layer by the actuators was sufficient to prevent a separation of the laminar boundary layer that occurred in the plasma-off case. At the lowest Reynolds number tested (Re = 107,000), the LDA data for the plasma-on case showed that the boundary layer downstream of the actuator remained attached right to the airfoil trailing edge, resulting in a stronger enforcement of the airfoil Kutta condition that produced positive lift enhancement. However, at a slightly higher Reynolds number of 207,000, the laminar separation in the plasma-off case normally reattaches as a separation bubble just upstream of the trailing edge; in this case, the actuator actually worsened the state of the boundary layer at the airfoil trailing edge by preventing the formation of this laminar separation bubble. Instead, for the Re = 207,000 case, the actuator locally re-energized the laminar boundary layer, which then rapidly grew downstream of the actuator until it separated just upstream of the airfoil trailing edge; as such, the net effect of the actuator in this case was a reduction in the airfoil lift. At the highest Reynolds number tested, Re = 361,000, the boundary layer approaching the actuator was turbulent; in this case, the actuator did not significantly affect the state of the boundary layer compared to the plasma-off case. In summary, the LDA data show that the lift-enhancement effect of the actuators depends on the state of the boundary layer in the trailing-edge region of the airfoil. In particular, the lift enhancement of the actuators is strongly affected by instances in which 105

120 the actuator prevents (or causes) a boundary-layer separation that exists (or doesn t exist) in the plasma-off case. This suggests that the effect of the actuators should be greatest at the angles of attack and wind speeds where the boundary-layer is just separated or nearly attached, and this is in fact the case in the lift-enhancement results shown above and in Chapter

121 5.4 Effect of Electric Power The force-balance, surface-pressure and LDA measurements presented above have shown that the lift enhancement of the actuators depends on the state of the boundary layer in the airfoil trailing-edge region, and strongly varies in operating conditions where the boundary layer is close to separation. The lift enhancement effect of the actuators was also measured as a function of discharge power, and it will be shown here that these results are consistent with the Reynolds-number behavior of the actuator determined in the preceding sections Discussion of Power Scaling Considerations Thrust, N/m khz Ramp Power dissipation, W/m Figure 5.19: Actuator thrust as a function of dissipated power (per length of actuator) for 2 khz positive ramp signal (6.35-mm thick quartz), Thomas et al. [106]. 107

122 The way in which the effect of a plasma actuator depends on dissipated power was investigated by Thomas et al. [106], who measured the thrust produced by an actuator as a function of power. The investigation showed that the thrust produced by the plasma actuator increased with increasing voltage until saturation occurred, after which point an increase in the applied voltage no longer produced an increase in thrust. Furthermore, Thomas et al. showed that, up until saturation, the thrust is close to a linear function of the dissipated power. The variation of the thrust produced by the plasma actuator versus the dissipated power is shown in Figure 5.19 [106]. For the results presented in Figure 5.19, the plasma actuator was driven by a positive ramp signal, the same type of waveform which was used in the current research. Figure 5.19 shows that for powers greater than approximately 500 W/m, an increased in the applied power produced no further increase in thrust. According to Hall [29, 30], the lift increment is proportional to the momentum, transferred by the plasma discharge into directed motion of the fluid, or the plasma actuator thrust. As such, if the plasma actuator operates below the saturation level, then the lift enhancement due to the plasma actuator should be proportional to the dissipated power: L ~ P (5.3) In accordance with these considerations, the scaling parameter for the plasmaproduced lift was chosen as the dissipated power. As discussed above, Equation (5.3) is valid up to the saturation power, after which point an increase in the dissipated power produces no additional thrust or, presumably, lift enhancement. The Equation (5.3) can be rewritten as: 108

123 L ~ P ~ b (5.4) where P ~ is the power per unit span of the actuator. Equation (5.4) makes it possible to estimate the maximum effect of a particular plasma actuator: ~ PSAT LMAX = L ~ (5.5) P In Equation (5.5), P ~ SAT is the power per unit span of the actuator at which the actuator performance becomes saturated. For example, in the current research, a typical value for the lift increment is L = 0.2 N for a dissipated power of P = 40 W and 0.6 m span, or P ~ = 67 W/m. If the saturation level for this particular dielectric material were P ~ SAT = 200 W/m, then the estimated value of the maximum lift enhancement would be approximately L = 0.6 N. The exact value of P ~ SAT depends on the thickness and dielectric properties of the material, the driving waveform, etc., and should be determined experimentally. As can be seen in Figure 5.19, [106] P ~ SAT for 6.35-mm thick quartz and a 2 khz positive sawtooth signal is about 500 W/m. In summary, when operating below the saturation level, Equation (5.3) shows that the lift enhancement should scale with the dissipated power; however, when determining the maximum performance that can be achieved using a particular actuator, Equation (5.4) shows that the maximum lift enhancement scales only with the length of the actuator, b. 109

124 5.4.2 Effect of Electric Power P = 40 W P = 20 W P = 10 W P = 5 W 0.2 L, N α, deg Figure 5.20: Effect of varying plasma discharge power on lift increment. U = m/s, Re = 98, ,000. The effect of discharge power on the lift increment at a wind speed of U = 7.5 m/s is shown in Figure In these experiments, the plasma discharge power was varied by changing the driving voltage, and the plasma lift enhancement and dissipated power were measured. Figure 5.20 shows that the lift enhancement effect of the actuator increased as the discharge power was increased, but that the underlying trend of the behavior is the same as shown previously, for example, in Figure The data in Figure 5.20 are re-plotted in Figure 5.21, this time with the lift enhancement scaled by the plasma power. Figure 5.21 shows that linearly scaling the liftenhancement results by the discharge power collapses the data onto a single curve, except in the low angle-of-attack region, 0 to

125 P = 40 W P = 20 W P = 10 W P = 5 W 0.01 L/P, N/W α, deg Figure 5.21: Lift enhancement linearly scaled by the plasma discharge power. U = m/s, Re = 98, ,000. As established in Section 4.1, the 0 to 4 range at this Reynolds number corresponds to laminar boundary-layer separation with a possible formation of a separation bubble in the trailing-edge region. As such, Figure 5.21 shows that the way in which the lift enhancement varies with power is also influenced by Reynolds-number effects in the same manner as the force-balance, surface-pressure and LDA data presented in the preceding sections. The way in which the lift-enhancement results in Figure 5.20 and 5.20 vary with power is also consistent with preceding discussions. For example, Figure 5.20 shows that the lift enhancement in the 0 to 4 range increases with actuator power; this can be attributed to the fact that the more-powerful actuator adds additional momentum to the laminar boundary layer in the trailing-edge region, improving the airfoil trailing-edge flow further. In particular, in the 2 to 4 range where the actuator normally produces negative lift enhancement, Figure 5.21 shows that 111

126 the lift enhancement actually becomes positive at a discharge power of 40W; in this case, even though the actuator disrupts the trailing-edge separation bubble that normally forms in the plasma-off case, the actuator is likely powerful enough to maintain an attached laminar boundary layer right to the trailing edge of the airfoil so that positive lift enhancement results. It should also be noted that Figure 5.21 shows that the scaled power results become less dependent on angle of attack as the power increases. This result makes sense in that an extremely powerful actuator should be able to override the effect of the airfoil boundary layer and produce the same trailing-edge flow at all angles of attack. Figure 5.21 suggests that the scaled lift enhancement per unit power would asymptote to a value of approximately L/P 0.005N/W if the actuator power were increased indefinitely. It should be noted, that increase of plasma actuator dissipated power above saturation level does not increases plasma actuator performance and, therefore, will not increase lift. 5.5 Lift Enhancement with Tripped Boundary-Layer The fact that the lift enhancement is strongly influenced by the presence of laminar boundary-layer separation in the trailing-edge region suggests that a more constant actuator effect could be produced by tripping the boundary layer upstream of the actuator. With the boundary layer tripped, the boundary layer approaching the actuator would be turbulent and attached up to the airfoil trailing edge, thereby eliminating the cause of the low angle-of-attack variations in the lift enhancement. This supposition is supported by the airfoil lift data in Figure 5.22, which shows the airfoil lift curve with the 112

127 boundary layer tripped and developing naturally. For these tests, the boundary layer was tripped using a 1.5 mm high strip located at x/c = 0.25 on both sides of the airfoil [7]. Figure 5.22 shows that the trip eliminates the dip in the lift curve that is produced by trailing-edge laminar boundary-layer separation, and results in a more linear lift curve Laminar BL, Re = 112,000 Tripped BL, Re = 110,000 2π α C l α, deg. Figure 5.22: Lift curves for NACA 0009 with boundary layer tripped and developing naturally. Figure 5.23 shows the effect of the plasma actuator with the boundary layer tripped; for these tests, the boundary layer was tripped on the actuator side of the airfoil only. The figure shows that the boundary-layer trip effectively removed the large variation in lift enhancement at low angles of attack. In particular, as shown in Figure 5.23, the trip strip had essentially no effect on the lift enhancement for 4 ; however, with the boundary layer tripped, the plasma produced essentially constant, positive, lift enhancement for angles of attack less than 2. As such, the tripped boundary-layer results 113

128 shown in Figure 5.23 confirm the results of the preceding sections of this chapter: that the large variations in actuator effect are caused by an interaction of the actuator with the separated laminar boundary layer that normally exists in the plasma-off case L, N U = 8.0 m/s, Re = 108,000 U = 10.0 m/s, Re = 134,000 U = 27.4 m/s, Re = 368,000 U = 9.9 m/s, Re = 133,000, Tripped BL U = 8.2 m/s, Re = 111,000, Tripped BL U = 27.2 m/s, Re = 366,000, Tripped BL α, deg Figure 5.23: Plasma effect for clean airfoil and with boundary layer tripped. 114

129 5.6 Summary Reynolds-number effects on the lift-enhancement were investigated by forcebalance, surface-pressure and LDA measurements. These tests consistently showed that the way in which the plasma actuator affects the lift on the airfoil depends on the state of the boundary layer that exists in the trailing-edge region of the airfoil in the first place. Three cases were investigated: i. If the boundary layer in the trailing-edge region of the airfoil is laminar, then the actuator re-energizes the boundary layer, thereby preventing or alleviating trailingedge laminar boundary layer separation. In this case, the actuator produces substantially more lift than the plasma-off case due to a more rigorous enforcement of the airfoil Kutta condition. ii. At slightly higher Reynolds numbers or angles of attack than case i above, the separated laminar boundary-layer in the plasma-off case reattaches in the trailingedge region of the airfoil to form a separation bubble. The reattached, turbulent boundary layer results in significantly greater lift, as shown in Section 4.1. In this case, the actuator, by re-energizing the laminar boundary layer and preventing the formation of the separation bubble that exists in the plasma-off case, results in a thicker, or separated, laminar boundary layer at the airfoil trailing edge. As such, the actuator actually worsens the boundary layer at the airfoil trailing edge, leading to a reduction in the airfoil lift. 115

130 iii. If the boundary layer in the trailing-edge region of the airfoil is turbulent, then the actuator effect on the boundary layer is not as discernable as it is when the boundary layer is laminar. In this case, lift enhancement is once again positive. In summary, these results lend further support to the findings of Section 4.2, that the lift enhancement produced by the plasma actuator in the studied Reynolds number range is strongly affected by laminar boundary-layer separation at the trailing edge of the wing or airfoil. As such, for low-reynolds-number applications, such as lift and roll control on small-scale UAV s, the interaction of the actuator with the wing boundary layer must be carefully considered. 116

131 CHAPTER 6: LIFT ENHANCEMENT WITH MULTIPLE ACTUATORS 0.38 c 0.58 c 0.78 c Figure 6.1: Schematic of 3-plasma actuators airfoil. Flow direction is from left to right. As discussed in Chapter 1, one of the objectives for this investigation was to verify the predictions of the effect of multiple plasma actuators made by Hall [29]. The additive effect of multiple plasma actuators has been reported by a number of authors; all of these studies showed that the effect produced by multiple actuators was greater than that produced by a single actuator [25, 74, 106]. To investigate the claim of [29], a second two-dimensional airfoil model was built that incorporated three plasma actuators that could be operated simultaneously or individually. The airfoil had the same 117

132 dimensions as the single-actuator airfoil described in Section 3.2 and had the same NACA 0009 profile. The plasma actuators were constructed using the same method described in Section 3.3, and were flush-mounted on the same side of airfoil with their exposed electrodes oriented in the spanwise direction. The chordwise locations of the plasma-actuator electrodes are shown in Figure Single-Actuator Operation The performance of the 3-actuator airfoil was first checked by comparing the lift enhancement measured using the 3-actuator airfoil to results obtained using the singleactuator airfoil described in Chapter 3 and presented in Chapters 4 and 5. For this comparison, only the plasma actuator closest to the trailing edge of the 3-actuator airfoil was used; as shown in Figure 6.1, this actuator was located at x/c = 0.78, which is essentially at the same location as the plasma actuator installed on the single-actuator airfoil, x/c = 0.75 (cf Chapter 3). The measured dissipated power for the actuators was the same for both airfoils, approximately 40 W. Figure 6.2 shows a comparison of lift-enhancement results measured using the two airfoils (with single-actuator operation) at a Reynolds number of 140,000, and shows that the lift enhancement for the two airfoils was essentially the same, except for discrepancies over the angle-of-attack range of approximately 1 to 3, and at = 9. At = 9, the difference in the lift enhancement is within the uncertainty of the measurements and therefore may be attributed to experimental error; note that fluctuations in the measured lift are large in this angle-of-attack region due to intermittent 118

133 boundary-layer separation which starts at 9. On the other hand, the discrepancy in lift enhancement over the range 1 to 3 is greater than the uncertainty associated NACA 0009, 3 PA airfoil, single PA operated NACA 0009, 1 PA airfoil, single PA operated 0.3 L, N α, deg. Figure 6.2: SDBD effect for airfoils with different plasma actuators configurations. U = 10 m/s, Re = 140,000. with the two sets of measurements. This angle-of-attack range corresponds, however, to the negative lift-enhancement range of the airfoil where, as shown in Chapter 5, the actuator interacts with a laminar separation bubble that normally forms in the trailingedge region of the airfoil in the plasma-off case. As such, the lift enhancement in this angle-of-attack range is likely to be highly sensitive to the state of the boundary layer at the trailing-edge region of the airfoil, so that small differences in the two airfoils would be expected to produce noticeable differences in lift enhancement. Possible differences in the airfoils that might produce different lift-enhancement results include, for example, the small difference in the location of the plasma actuators (i.e. x/c = 0.78 for the multi- 119

134 actuator airfoil versus x/c = 0.75 for the original, single-actuator airfoil). More significantly, the installation of the 3 actuators on the multi-actuator airfoil may have slightly altered the shape of the airfoil surface, or introduced small steps and gaps on the airfoil surface. Figure 6.2 shows, however, that despite local discrepancies, the overall behavior of the lift enhancement for the two airfoils is essentially the same. This similarity in the lift enhancement shows that the multi-actuator airfoil is undergoing the same flow physics as the single-actuator airfoil used in Chapters 4 and 5, and that the multi-actuator airfoil can be used to build upon results already presented in this dissertation. 6.2 Multi-Actuator Operation The multi-actuator airfoil was next tested with all three plasma actuators running, and the resulting lift enhancement was measured. For these tests, the actuators were driven by a 25.8 kv peak-to-peak sawtooth signal. The measured total dissipated power for all three actuators was 120 W, compared to 42 W for the single actuator case (see Section 6.1). Lift-enhancement results for the multi-actuator airfoil with all three actuators operating are compared to the results for the multi-actuator airfoil with only the mostdownstream actuator (x/c = 0.78) operating, in Figures 6.3 and 6.4. From these two figures it is possible to make the following observations: i. Up to an angle of attack of approximately 2, the operation of all 3 actuators produces no additional lift enhancement compared to the lift enhancement obtained using just the trailing-edge actuator. 120

135 ii. Over the angle-of-attack range 2 to 5, the three-actuator case produces lower lift enhancement compared to the single, trailing-edge actuator. iii. For angles of attack greater than approximately 5, the three-actuator case produces greater lift enhancement compared to the single-actuator case. Each of these observations is discussed in further detail in the following sections No Additional Lift Enhancement Produced: < 2 Figures 6.3 and 6.4 show that for angles of attack less than approximately 2, the three-actuator airfoil has essentially the same lift enhancement effect as the single, trailing-edge actuator. This result contradicts the expectation that multiple actuators should produce an increased lift-enhancement effect [29]. It has to be noted, however, that as shown by the results of Chapter 5, in this angle-of-attack range, and at low Reynolds numbers, the lift enhancement is strongly affected by the laminar boundarylayer separation at its trailing edge. As such, the multi-actuator results shown here contribute additional insight into the findings of Chapter 5, which showed that in the range of angles of attack < 2 and Re = 100, ,000 the trailing edge actuator eliminates a laminar separation that normally exists in the plasma-off case, thereby better satisfying the airfoil Kutta condition and increasing the airfoil circulation. It seems reasonable to assume that once the trailing-edge separation has been eliminated, then the effect of the additional upstream actuators in the 3-actuator case would be to increase the lift still further. The fact that the three-actuator airfoil does not produce any additional lift enhancement compared to the single-actuator airfoil shows, however, that this assumption is clearly not valid. 121

136 PA 1 PA L, N α, deg. Figure 6.3: Effect of multiple SDBD. U = 8.3 m/s, Re = 110, Triple PA Single PA 0.4 L, N α, deg. Figure 6.4: Effect of multiple SDBD. U = 10 m/s, Re = 140,

137 6.2.2 Multi-Actuator Case Produces Lower Lift Enhancement: 2 to 5 As shown by Figures 6.3 and 6.4, in the range 2 to 5, the airfoil with 3 actuators generally produced lower lift enhancement than the airfoil with a single, trailing-edge mounted actuator. As such, like the low angle-of-attack results discussed above, the three-actuator lift-enhancement results in this angle-of-attack range also contradict the concept of the increased effect of multiple plasma actuators. In Chapter 5, it was shown that the lift enhancement in this angle-of-attack range for a single, trailing-edge mounted actuator depends primarily on the interaction of the actuator with a laminar separation bubble that normally exists in the trailing-edge region of the NACA 0009 profile in the plasma-off case. As such, the fact that the three-actuator airfoil produced less lift enhancement in the 2 to 5 range may come as less of a surprise, since the lift characteristics of the NACA 0009 profile in this range have already been shown to be strongly influenced by boundary layer behavior. In Chapter 5, it was shown that, for a single, trailing-edge mounted actuator, reduced or even negative lift enhancement is produced when the actuator prevents formation of a laminar separation bubble and concomitant transition to turbulence just upstream of the airfoil trailing edge. As such, in the actuator-on case, the boundary layer remains laminar and rapidly grows until it separates upstream of the trailing edge, resulting in a reduction in lift compared to the actuator-off case due to a less rigorous application of the airfoil Kutta condition. The essential point of the preceding discussion is that reduced, or negative, lift enhancement occurs when the actuator eliminates a laminar separation bubble that normally exists near the location of the actuator in the plasma-off case. As such, with actuators located over the range x/c = 0.38 to 0.78 (Figure 6.1), it is it is expected that the 123

138 three-actuator airfoil will disrupt the formation of a laminar separation bubble over almost its entire suction surface. This means that the three-actuator airfoil will disrupt the formation of a separation bubble over a larger range of than the airfoil with a single, trailing-edge mounted actuator; this extended range of reduced lift compared to the single-actuator case is clearly visible in Figures 6.3 and 6.4. Figure 4.9 shows that at an angle of attack of 5, the separation bubble reaches the leading-edge of the airfoil, upstream of any of the actuators located on the three-actuator airfoil; where, at 5 and above, the actuators no longer interfere with the formation of the separation bubble on the airfoil suction surface so that, as shown in Figures 6.3 and 6.4, reduced lift enhancement is no longer produced. In summary, the reduced lift enhancement for the three-actuator case over the range 2 to 5 is caused by the greater extent of plasma actuators on the airfoil suction surface, so that formation of a separation bubble and concomitant transition to a turbulent boundary layer is prevented over a larger range of angles of attack Multi-Actuator Case Produces Increased Lift Enhancement: > 5 As shown by Figures 6.3 and 6.4, for angles of attack larger than approximately 5, the airfoil with 3 actuators generally produced greater lift enhancement than the airfoil with a single, trailing-edge mounted actuator; as such, in this angle-of-attack range, the experimental results show the most agreement with the predictions of Hall [29]. In this angle-of-attack range, the boundary layer on the suction surface of the airfoil, and in the vicinity of all of the actuators on the three-actuator airfoil, is turbulent (cf Section 4.1). According to Hall s model, the total lift-enhancement effect of three equalstrength actuators with the geometry shown in Figure 6.1 is approximately 2.8 times the 124

139 effect of a single actuator located at x/c = 0.78 [29]. In Figures 6.3 and 6.4, the experimentally-measured lift enhancement for the three-actuator airfoil for > 5 varies from approximately 1.4 to 1.7 times the lift enhancement using the single, trailing-edge actuator, which is considerably smaller than Hall s prediction of Discussion of Multiple-Actuator Results The results presented above show, once again, that the lift enhancement produced by the plasma actuators is strongly influenced by the state of the boundary layer and the existence of boundary-layer separation on the airfoil (or wing). Perhaps the most surprising result of the multiple-actuator tests was that for angles of attack less than approximately 2, the multiple-actuator airfoil does not produce any more lift enhancement than the single-actuator airfoil, in contradiction to the predictions of Hall s inviscid model [29]. This lack of additional lift enhancement for < 2 is likely due to the existence of a laminar boundary layer on the suction surface of the airfoil at the tested Reynolds numbers, as well as laminar trailing-edge boundary-layer separation, which means that the flow physics is not modeled by Hall s inviscid model. The precise mechanism underlying the experimental lift-enhancement in this angle-of-attack range is not known, but it can be assumed that the manner in which the actuators interact with a laminar boundary layer, which may also be approaching separation in an adverse pressure gradient, is an important part of the response. The reduced lift enhancement produced by the multi-actuator airfoil over the range 2 to 5 is a less unexpected outcome of the multiple-actuator tests, since the lift enhancement in this angle-of-attack range has already been shown to be sensitive to an interaction of the actuator flowfield with a separation bubble that exists in the vicinity 125

140 of the actuator. The greater angle-of-attack range over which reduced lift is produced with the multi-actuator airfoil is in agreement with the results of the negative liftenhancement investigation presented in Chapter 5. Finally, Figures 6.3 and 6.4 show the multi-actuator airfoil produces greater lift enhancement compared to the single-actuator case for angles of attack > 5 ; as such, the experimental results show the closest agreement with Hall s inviscid prediction method [29] in conditions where the boundary layer on the suction surface of the airfoil is fully turbulent. This finding may make some sense, since turbulent boundary layers have a thinner displacement thickness and therefore produce a smaller modification of the airfoil aerodynamic response away from inviscid-like behavior. At the Reynolds numbers tested, the experimentally-measured lift enhancement for the three-actuator airfoil varies from approximately 1.4 to 1.7 times the lift enhancement using the single, trailing-edge actuator, which is considerably smaller than Hall s prediction of Estimated Lift and Roll Control with Multiple Actuators As discussed in Chapter 1, one of the motivations for this investigation was to determine how well the lift and roll of a small Unmanned Aerial Vehicle (UAV) could be controlled using plasma actuators. In this regard, Chapter 1 presented results from an inviscid panel-code study [29] that showed that a wing with the plasma-actuator arrangement shown in Figure 1.11 could produce a maximum roll-moment coefficient C R of In [29], it was further shown that this value of C R = corresponds to the kind of roll moment that would be produced on a small aircraft by an aileron deflection of slightly greater than 10 (Table 1.1), and was therefore judged adequate for control. In 126

141 this section, maximum lift and roll coefficients, and equivalent flap deflection angles, for a realistic actuator configuration are estimated based on the results of the experimental investigation presented in this dissertation. The estimates presented in this section were made for the actuator configuration shown in Figure 6.1. Since roll coefficients are needed, the estimates were performed for a three-dimensional wing. To perform the estimates, the multi-actuator results obtained using the two-dimensional airfoil in Section 6.2 were corrected to equivalent threedimensional wing results using Equations (4.1) and (5.4). Assuming that the triple plasma actuator configuration shown in Figure 6.1 gives 1.6 times the performance of the single plasma-actuator case (Section 6.2.3), the roll moment was calculated from Eq. (4.1) as: ~ 1 P bwing 1 ycp Cl (6.1) b wing CR =.6 ~ 1.52 Pairfoil airfoil In Equation (6.1) the factor is the correction for downwash. The term ~ ~ P b ) ( P b ) is introduced to scale the multiple-actuator results for ( wing wing airfoil airfoil differences in the plasma-actuator dissipated power (cf Chapter 5.4). Both of these assumptions were shown to be valid by the close comparison of wing and airfoil results shown in Figure 4.19, in which the airfoil results were scaled using Eq. (4.2) Current Actuator Arrangement and Design The estimates were also computed assuming that the plasma actuators were constructed and operated in the same manner as the actuators used in this dissertation, and therefore have the same performance. For the purpose of roll-coefficient estimates, it was assumed that the actuators were mounted on a three-dimensional wing with aspect 127

142 ratio of 4.5:1 (the same as the aspect ratio used for the wing tests discussed in Chapter 4), and that the actuators were separated into independently-operable left and right sides C R U, m/s Figure 6.5: Estimated roll moment for the multiple actuator wing with AR = 4.5. The value of lift increment for single plasma actuator L airfoil was chosen as 0.2 N, which corresponds to the representative value of the lift enhancement measured at all angles of attack with the boundary layer tripped (cf Figure 5.23). A lift enhancement of 0.2 N is also a typical value for the actuator effect in the range of angles of attack 4º to 8º when the boundary layer was not tripped (cf Figure 4.20). The roll-moment results C R estimated using Eq. (6.1) for this nominal value of L airfoil = 0.2 N are presented in Figure 6.5 for the free-stream velocity range U = 5 30 m/s. The roll-moment estimates shown in Figure 6.5 were next compared to the kinds of roll moments that are produced due to the deflection of ailerons on an actual airplane, 128

143 specifically, the Navion aircraft [63]. In general, the deflection of an aileron by an angle a results in a roll moment given by: C R dc δ R = a (6.2) dδ a dcr where, for the Navion aircraft = deg -1 [63]. The Navion airplane basic dδ a geometry and geometry of the wing are presented in Appendix A. As such, the estimated roll moments shown in Figure 6.5 correspond to the equivalent aileron deflections plotted in Figure 6.6. As can be seen from Figure 6.6, the estimated roll performance for the multi-actuator wing produces equivalent aileron deflections greater than 10º at low wind speeds; however, since the actuators produce a constant roll moment (rather than a constant roll-moment coefficient), the equivalent aileron deflection decreases rapidly with wind speed to a value of only 0.45º at a wind speed of U = 30 m/s. It should be noted, however, that the plasma actuators used in this research were not designed for high power, and so better performance could be obtained using more-powerful actuators; in this case, the resulting roll moment would scale with the maximum possible power as shown in Equation (6.1). 129

144 δ a, deg U, m/s Figure 6.6: Estimated aileron deflection angle due to plasma actuator. 130

145 CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS This dissertation has reported on an experimental investigation into the use of trailing-edge mounted plasma actuators to control the lift and roll of small UAV s. The work was motivated by new designs for small, man-portable UAV s that incorporate folding or inflatable wings [11, 12]. Compared to conventional control surfaces and their associated mechanical linkages and actuators, plasma actuators appear to be an ideal alternative for controlling these kinds of UAV s due to their low weight, instant response and relatively-small size. As shown in Chapter 2, there are a multitude of flow-control applications involving plasma actuators in which the primary intended effect of the actuator is to modify an existing boundary-layer flow. As such, perhaps the most innovative idea tested by this research is the concept of attempting to influence the circulation of a wing or airfoil in an direct manner; that is, by mounting the plasma actuators near the wing/airfoil trailing edge so that they can have a direct effect on the wing or airfoil Kutta condition. This concept was first shown by the inviscid, numerical investigation described in [29], which was partly supported by experimental data presented in [19], although these data were fairly limited in scope. As such, one of the major contributions of this research is to provide experimental insight into the concept of inviscid control using plasma actuators. In general, the support for this inviscid-control concept that has been provided by the experimental data 131

146 presented in this dissertation must be considered questionable at best. Instead, the results presented in this research have shown consistently that the effect of the actuator is strongly influenced by Reynolds-number effects. In particular, the LDA data presented in Chapter 5 showed that the actuator always has an effect on the on the trailing-edge boundary layer, and this effect could fully account for the lift-enhancement effect of the actuator in all cases. Furthermore, it is possible to give an alternate explanation for the liftenhancement effect of the actuator that is fully framed in the context of the effect that the actuator has on the trailing-edge boundary layer. First, if the actuator prevents trailingedge boundary-layer separation, then the lift enhancement can be attributed to a reinforcement of the airfoil Kutta condition, leading to increased circulation; this effect has already been discussed in Chapter 5. On the other hand, even if the boundary-layer is already attached in the plasma-off case, the actuator still adds momentum to the boundary layer, and this addition of momentum reduces the displacement thickness * of the boundary layer. As pointed out in [58] (and other aerodynamics texts), the boundarylayer displacement thickness modifies the effective shape of the airfoil, in such a way that the airfoil behaves as though its surface is extended outward by a distance equal to the displacement thickness. This displacement-thickness effect usually acts in such a way as to reduce the airfoil lift; for example, if the airfoil is at a positive angle of attack, then the boundary layer is usually thicker on the suction surface of the airfoil due to the moreadverse pressure gradient there, and this large * at the suction-surface trailing edge effectively makes the airfoil appear to be at a lower angle of attack. In this case, the actuator, by reducing *, produces an increase in lift on the airfoil. Whether the preceding 132

147 concepts of separation and displacement-thickness control can explain the effect of trailing-edge mounted plasma actuators in all situations is outside the scope of this research and may be a suitable subject for a follow-on investigation; however, it is apparent that the experimental lift-control results presented in this dissertation can all be explained in the context of boundary-layer control (i.e., viscous control ). In summary, although Hall s inviscid model provided the motivation for this research, the validity of Hall s inviscid lift-control model cannot be considered to be supported by the experimental results presented in this dissertation research. The remainder of this chapter summarizes the major findings of this dissertation research, in the context of identifying elements of the research that are considered to be contributions to the field. Following this summary, recommendations for future work are presented. 7.1 Contributions of this Dissertation Research Reliable Experimental Data for the Effect of Trailing-Edge Mounted Actuators One of the major contributions of this research is simply the fact that repeatable experimental data have been acquired showing the effect that trailing-edge mounted plasma actuators have on the lift and roll moment of a wing and/or airfoil. To the knowledge of the author, this kind of data has never been acquired before. The types of measurements that have been made are extensive, and include force-balance, pressure, smoke- and oil-flow visualization, and LDA. The quality of the data is shown by the fact that all of these measurement approaches support the same conclusions. 133

148 The dissertation has also produced useful techniques for the acquisition of reliable data with plasma actuators. As shown throughout this work, plasma actuators can present considerable challenges to the experimenter including, for example, radio-frequency noise output that can interact with data-acquisition circuits, and actuator heating that can deform the model. As such, the shielding and data-acquisition procedures that were developed to deal with the problems presented by the actuators will prove useful for follow-on investigations Influence of Reynolds Number Perhaps the most significant scientific contribution of the research has been to determine the influence of Reynolds number on the effect of trailing-edge mounted plasma actuators. The investigation has shown how the actuator flowfield interacts with the laminar, turbulent, attached or separated boundary layer in the trailing-edge region of the wing or airfoil, and how this interaction influences the lift-enhancement effect of the actuator. These findings are useful for any trailing-edge flow-control application, using either plasma actuators or other blowing techniques Roll Control A further contribution of the research has been to characterize the effect of trailing-edge mounted plasma actuators when used for roll control. In particular, the research showed that the actuators produce a constant lift-enhancement effect across their spanwise length so that, when used on a three-dimensional wing, the roll-moment of the actuators can be accurately modeled using lifting line theory in which a constant angle of attack is applied across the spanwise extent of the actuator. As such, the roll-control 134

149 capabilities of a given actuator configuration can be simply and accurately estimated from two-dimensional lift-enhancement data, without the need for specialized wing measurements Estimate of Current Lift- and Roll-Control Capabilities Finally, an estimate of the effect that trailing-edge mounted actuators can have on the lift and roll-moment of a wing for a realistic configuration has been produced. The estimate has indicated that the actuators would only be marginally adequate for control of a UAV, although the estimate was made for fairly standard plasma-actuator technology with regards to actuator power and size. As such, more powerful and compact (i.e. so that more actuators could be mounted on the wing) actuators may result in adequate control forces; however, the estimate provided in this research gives an indication of the improvement that is needed. 7.2 Recommendations for Future Work The research presented in this dissertation has also uncovered some questions that warrant further investigation, described below Detailed Investigation of Very-Low Reynolds-Number Behavior The initial Reynolds-number behavior presented in Chapter 4 showed that the liftenhancement effect on the wing model decreased to zero as the wind speed U decreased to 0 m/s; the exact reason for this drop off in lift enhancement was not determined in this research. This wind speed range corresponds to very low Reynolds numbers, less than 135

150 approximately 60,000. Although Reynolds numbers below 60,000 may be too low for the kinds of UAV s that motivated this research, investigation into the behavior of the trailing-edge mounted actuators at near zero wind speeds would provide useful insight into the behavior of plasma actuators in general Detailed Investigation of Higher Reynolds-number Behavior The multiple-actuator results presented in Chapter 6 showed that the combined lift-enhancement effect of multiple actuators improved as the Reynolds number increases. The maximum Reynolds number tested in this research was approximately 400,000, which is still relatively low. Future investigations should measure the lift enhancement produced by the multiple-actuator configuration at higher Reynolds numbers, to determine if additional performance can be obtained. 136

151 APPENDIX A: NAVION AIRPLANE WING GEOMETRY A F F A 8.35 Figure A.1: Planform view of the Navion airplane [94]. A aileron, F flap (all dimensions are in meters). 137

152 FUSELAGE CENTERPLANE SPAR No. 8 PLANE AILERON HINGE PLANE SPAR No. 12 PLANE MOMENT CENTER % OF THE CHORD PLANE Figure A.2: Navion airplane wing geometry [45] (flap is not shown). All dimensions are in meters. 138

153 APPENDIX B: CALIBRATION AND ACCURACY OF MEASUREMENTS Accuracy of measurements was considered to be contributed by instrumental precision and random error [20]. The instrumental precision of differential pressure sensors, mercury barometer, thermometer etc was taken according to specifications of manufacturer of an instrument. Calibration and calculation of instrumental precision of the lift load cell is presented below. B.1 Regression of Calibration Data and Instrumental Precision Calibration fit curves were calculated from calibration experiment data with least squares method using polynomial model. Vector of coefficients b of the polynomial fit of order of m was calculated as a solution of matrix equation [115]: T 1 T b = ( X X) X y (B.1) where y = K is an n-by-1 vector of responses to the loads x, T ( y1, y2, y3, yn ) x = K, T ( x1, x2, x3, xn ) b = K is a (m+1)-by-1 vector of polynomial fit T ( b0, b1, b2, bm ) coefficients and X the n-by-(m+1) matrix, which, for the case of polynomial regression model, is: 139

154 140 = m n n n m m m x x x x x x x x x x x x K K K K X (B.2) The standard error of prediction of responses y * was calculated from the calibration data as [115]: * 1 T T * * ) ( 1 ˆ ) ( x X X x y + = σ SE (B.3) where x * is a matrix of loads and σˆ is the standard error of regression: ν σ = T ˆ (B.4) and is the vector of residuals of response: y y C = (B.5) which is the difference between the observed response, y, and calculated from regression model, y C : b X y = C (B.6) and ν is the number of degrees of freedom in calibration experiment: ( +1) = m n ν (B.7) The term 1 T 2 ) ( ˆ X X σ in equations above is the covariance matrix of regression model coefficients b:

155 var( b0 ) cov( b0, b1 )... cov( b0, bm ) cov( b1, b0 ) var( b1 )... cov( b1, b ) 2 T 1 m ˆ σ ( X X) = (B.8) cov( bm, b0 ) cov( bm, b1 )... var( bm ) where var(b i ) is the variance of b i and cov(b i,b j ) is the covariance of b i and b j. Instrumental precision u B was calculated as the calibration confidence interval at 95% level [20]: u B = t ( ˆ σ x (B.9) T T 1 ν, 0.95 SE y* ) = t ν, x* ( X X) * where t ν,0. 95 Student's t - distribution inverse cumulative function value for number of degrees of freedom ν and 95% confidence level. Quality of the regression model is illustrated on figures with residuals, defined as a difference between predicted by regression model value and the actual load: r x = f 1 ( y) x (B.10) where f 1 (y) is a inverse function of regression model, Eq. A.6, or in equivalent notation: y = f(x) (B.11) B.2 Random Error Random error u A was calculated as [20]: u A ν,0. 95 = t s (B.12) where s is a sample standard deviation: 141

156 s = n 1 ( x i x) n 1 i 2 Accuracy of measurements was calculated as sum of squares of instrumental precision and random error: u u A + u B 2 2 = (B.13) B.3 Calibration Procedure and Results Calibration of load cell balance was done with the balance placed on the top of the test section with the wing model (weight 1.3 kg) installed. The channels of measurement of lift, drag or torque were calibrated as the appropriate assembly of load cell, signal conditioner channel and channel of A/D converter of the data acquisition board. As the load sensors for lift and drag were used strain gauge load cells (Transducer Techniques, models MLP-10 for lift and MLP-50 for drag) and the torque sensor (RTS- 500) for pitch. The load cells can be employed for both tension and compression loads. Some precision related specifications of load cells are presented in the Table B.1 [109]. In a majority of experiments the load cell balance orientation was chosen to measure the lift with the 44 N load cell as providing better accuracy of the lift and especially of the plasma produced lift and, consequently, the drag was measured with 220 N load cells. 142

157 TABLE B.1 LOAD CELLS SPECIFICATIONS Lift Drag Pitch MLP-10 MLP-50 RTS-500 Capacity 44 N (10 lbs) 220 N (50 lbs) 3.5 N m (500 oz in) Nonlinearity: (0.1% of F. S.) 0.04 N 0.2 N 3.5 mn m Hysteresis: (0.1% of F. S.) 0.04 N 0.2 N 3.5 mn m Nonrepeatability: (0.05% of F. S.) 0.02 N 0.1 N 2 mn m Temp. Effect on Output: (0.009% of Load/ C) N/ C at full load 0.02 N/ C at full load 0.3 mn m at full load Temp. Effect on Zero: (0.009% of F. S./ C) N/ C 0.02 N/ C 0.3 mn m The cable pulley system of the force balance allows applying loads in two opposite directions to provide a calibration in the range of positive and negative loads. In lift calibration procedure the calibration pulley at negative lift side of the balance was preloaded with 1.0 kg (9.8 N) weight. Positive lift side of the balance had a harness (0.8 N) and variable loads ranging from 0 to 5.5 kg (55 N) with 0.5 kg (4.9 N) increments. The calibration weights masses were known with 0.2 gram (0.002 N) uncertainty. Presented below are the data for several cycles of load cell calibration taken with intervals from 2 to 24 hours. Every cycle of calibration consisted of 2 parts: increasing the load from -1.0 to 5.5 kg (-9.8 N to +45 N) and unloading the cell in opposite order. B.3.1 Nonlinearity The nonlinearity of the lift load cell used in current study is illustrated in Figure B.3. The figure shows residuals as the difference between applied load and value predicted by the linear regression model versus load magnitude. The nonlinearity limits of ±0.04 N provided by the load cell maker are shown in Figure B.3 as well. To take into 143

158 account the load cell nonlinearity the model of regression was chosen as the polynomial one of order of residuals, Load Predicted Value, N Residuals Nonlinearity margins Load, N Figure B.3: Residuals for linear regression model. B.3.2 Hysteresis This effect of hysteresis is illustrated in the Figure B.4. Residuals are calculated with polynomial regression model of order of 3. Data points on this figure are the averaged over all calibration cycles separately for loading and unloading directions. As it can be seen the effect of hysteresis for this particular load cell is not as high as it declared by maker (±0.04 N) and in fact is within the limits of non-repeatability (±0.02 N). 144

159 residuals, Load Predicted Value, N Loading Unloading Nonrepeatability margins Load, N Figure B.4: Mean value of residuals at different directions of load. 6 5 y = x x x Output, Volts Load, N Figure B.5: Lift load cell calibration for 3-th order polynomial regression model. 145

160 residuals, Load Predicted Value, N Residuals 95% confidence interval Load, N Figure B.6: Residuals for 3-th order polynomial regression model. B.3.3 Summary of Calibration Summarizing, the lift load cell exhibit good repeatability and high accuracy. Calibration data and least squares fit curve for 3-rd degree polynomial regression model are presented on the Figure B.5. Residuals are shown in Figure B.6. Confidence interval of calibration at 95% level of confidence is calculated from Eq. B.8 and displayed also. According to load cell maker (Table A.1) combined instrumental precision of lift load cell including non-repeatability and hysteresis is ±0.05 N or ±0.07 N if nonlinearity is taken into account. Assuming that effect of nonlinearity is decreased with the proper choice of regression model, the value of instrumental precision u B = ±0.03 N obtained with calibration of particular load cell and calculated from Eq. B.9 is unexpectedly low but does not unrealistic. Explanation to this result lies in lower magnitude of hysteresis, as shown in the Figure B

161 B.4 Other Factors Influencing the Measurement Accuracy B.4.1 Influence of the High-Voltage Cables in SWT In experiments with SDBD, the measured loads were affected by tension of highvoltage cables. The cables for driving plasma discharge were passed through a small hole in the floor of the test section near one quarter of the chord giving a small tension which was dependent on the angle of attack. This extra component of lift, drag and pitch moment can be accounted with taring the balance against the variation of angle of attack and no flow. In fact, the mean values of lift, drag and pitch coefficients were obtained in separate experiments with no cables attached to aerofoil. As to the increments of lift, drag and pitch produced by SDBD, these quantities were not subjected by this kind of error. The effect produced by plasma was calculated as the difference in aerodynamic loads between the plasma on and off states while the angle of attack was kept the same. Since there was no change in angle of attack, the load created by high-voltage cables at both plasma on and off states were the same and taking a difference between plasma off and plasma on made this component of error to vanish. Typical example of load produced by high-voltage wires in lift direction without flow is presented in Figure B.7 and residuals for corresponding fit are presented in Figure B

162 L = *α 0.1 Load, N α, deg Figure B.7: Load produced by high-voltage wires on lift load cell Residuals 95% confidence interval Residuals, N α, deg Figure B.8: Effect of high-voltage wires on lift load cell. 148

163 B.4.2 Misalignment of Applied Load The angle of misalignment of applied load and the load cell in a procedure of calibration and in the process of measurements was estimated as = 2 deg, giving the error of 0.1% of measured load. ε AL 2 2 2(1 cos( δ )) L δ L (B.14) 2 Error in drag due to misalignement of drag load cell ( 1) and lift load cell ( 2): 1 ε AD 2(1 cos( δ1)) D + sin( δ 2) L δ1 D δ 2 L (B.15) B.5 Effect of Plasma Discharge on Load Cell Signal B.5.1 Lift Load Cell 6 4 zero order fit 95% confidence offset by SDBD, mv offset by SDBD, N load, N Figure B.9: Offset on lift load cell created by plasma discharge RF noise at different loads. 149

164 B.5.2 Pitching Moment Load Cell 2 0 zero order fit 95% confidence offset by SDBD, mv offset by SDBD, mn m load, mn m 3.4 Figure B.10: Offset of pitching moment load cell created by plasma discharge RF noise at different loads. 150

165 APPENDIX C: CORRECTIONS OF EXPERIMENTAL DATA FOR EFFECT OF TEST SECTION WALLS The wind tunnel data were corrected for effects due to presence of solid boundaries (test section walls) as test section boundary layer, solid and wake blockages and streamlines curvature. C.1 Correction on Wind Tunnel Walls Boundary Layer The free-stream velocity is not the same at different cross-sections of the wind tunnel as a result of growth of the boundary-layer along the tunnel walls which essentially makes the tunnel cross-section area smaller. In SWT experiments the freestream velocity was measured with Pitot-static pressure tube installed approximately 0.75 m upstream of the model and the free-stream velocity at the model location was slightly underestimated. The curve for correction coefficient at different velocities was obtained by replacing the model with a second Pitot probe and measuring wind speed simultaneously in two cross-sections. The resulting velocity correction for boundary layer on wind tunnel walls is shown in Figure C

166 K BL = U U corr / U U, m/s Figure C.11: Correction in SWT free-stream wind speed on test section walls boundary layer. C.2 Correction on Solid Blockage Solid blockage correction according to [1] was calculated as ε SB = Λσ (C.16) where 2 2 π c σ = = (C.17) 48 h here h wind tunnel height, c chord and Λ - solid body shape factor (Λ = for NACA 0009 airfoil, [1]) Resulting value for solid blockage correction coefficient was found to be: 152

167 ε = (C.18) SB C.3 Correction on Wake Blockage Effect of wake blockage leads to increase of wind speed in the closed type test section due to blockage of tunnel cross-section with the wake behind the model. Wake blockage coefficient was calculated according to [51] as: c ε WB = C d u (C.19) 2h C.4 Correction on Streamline Curvature Flows around the model in open space and in presence of the solid walls are different and likewise the aerodynamic loads are. For closed wind-tunnel sections, the presence of solid walls results in an increase in lift, pitching moment at the quarter-chord, and angle of attack. Corrections due to solid walls were calculated according to [1] as: C = σ C (C.20) lw l 57.3σ α W = ( C l + 4Cm ) (C.21) 2 π C mw 1 = Cmu + σ Clu (C.22) 4 153

168 C.5 Summary of Wind Tunnel Measurements Corrections Corrected wind speed was calculated as: U = K BL ( 1+ ε + ε ) U (C.23) SB WB u Corrected lift, drag and pitch coefficients: C l 1 σ = 2 (1 + ε SB + εwb ) C l u (C.24) C d 1 ε SB = 2 (1 + ε SB + εwb ) C d u (C.25) C m Cmu σ (1 σ ) Cl = (C.26) 2 (1 + ε + ε ) SB WB Corrected angle of attack: 57.3σ α = αu + ( C l u + 4 Cmu ) (C.27) 2 π 154

169 1 0.8 C l, uncorrected C l, corrected 2π α 0.6 C l α, deg. Figure C.12: Corrected and uncorrected lift in SWT test section. Corrected and uncorrected lift curves are presented Figure C.12. In this experiment the uncorrected wind speed was: U = 9.71 m/s, (Re = 131,000) and after applying corrections for solid and wake blockages wind speed was: U = 10.1 m/s, (Re = 135,000). 155

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