Unsteady Airfoil Flow Control via a Dynamically
Deflected Trailing-Edge Flap
Panayiote Gerontakos
Department of Mechanical Engineering McGill University, Montreal, Quebec, Canada February 2008
A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Doctor of Philosophy
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There are many individuals who have been an invaluable resource to me throughout the process of conducting this research and writing this thesis. My success is a measure of their support, encouragement, and guidance. For this I am eternally grateful and appreciative. The supervisor, it should be said, is undoubtedly the most important individual in a graduate student's academic life. In my case, Professor Tim Lee has been more than a supervisor; he has been my mentor. His dedication to the education of his graduate students is exceptional. Professor Lee provided me with an environment in which I could expand my knowledge, prepare for my future career, and grow as an individual. He has provided me with the tools that I will need to be successful in all aspects of my career. My strong work ethic is a direct result of him continually pushing me to my limits, and sometimes even beyond those limits. For all of these reasons, and much more, I would like to convey my deepest gratitude. The Department of Mechanical Engineering at McGill University also has an exceptional support staff. From the administration, Barbara Lapointe has been especially helpful to me. From the Instrumentation Lab, Georges Tewfik and Mario Iacobaccio have always provided me with excellent knowledge and advice with regards to electronics and my experimental setup. Francois DiQuinzio, the network administrator, provided me with computer assistance on numerous occasions. The members of the Machine Tool Lab, most notably Tony Miccosi, Nick De Palma and Mario Sglavo, were very helpful and beneficial to me in terms of model fabrication and machining. The students of the Aerodynamics Laboratory also deserve credit, included David Birch, Mo Wang and Jennifer Pereira, for assisting me in many ways. Be it in lending me a hand with my experimental setup; data acquisition, motion control, and/or data processing programs; assembling electronic components; or even for long discussions regarding my research or fluid dynamics in general. Moral support is just as important as technical support, and sometimes even more important. For this I always turned to my family who provided me with an endless supply. My wife, Carmelina, and my parents, Despina and Vassilios, deserve the majority of my
i appreciation as their encouragement was and still is vital to my success. I truly believe that without the support of people like these, research would not be possible. Financial support throughout my studies was provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Fonds Quebecois de la Recherche sur la Nature et les Technologies (FQRNT). Their support, without which I would not have been able to conduct my graduate studies, is gratefully acknowledged. Lastly, I would like to recognize the Department of Mechanical Engineering and the Faculty of Engineering at McGill University whose nomination granted me the Principle's Dissertation Award during the writing of this dissertation.
ii ABSTRACT
The control of the flow around a harmonically oscillating NACA 0015 airfoil via a dynamically deflected simply-hinged trailing-edge flap was investigated experimentally at a Reynolds number of 2.46 x 105 by using a combination of techniques, including surface pressure measurements, hot-wire wake velocity surveys and particle image velocimetry flowfield measurements. The tests were conducted under deep-stall conditions, with special attention being focused on identifying the changes in the flow structures that led to the observed modified aerodynamic load characteristics, and on the evaluation of the effects of the prescheduled trapezoidal flap motion profile. In addition, light-stall and attached-flow oscillations were also considered, as were static flap deflections and higher harmonic flap motions. The results indicate that a trailing-edge flap imposed an effective camber in the trailing-edge region, and was highly effective in the control of the aerodynamic loads. This was achieved in large part by the manipulation of the lower flap surface pressure distribution via changes to the windward-side flow stream, and was unaffected by the state of the flow above the airfoil. The leading-edge vortex, the predominant flow structure over the airfoil, was only marginally affected in its strength and initiation. The results also revealed that both the flap angle and deflection rate contributed to the above observations, and that the active motion was crucial in preventing the flow separation observed over the lower flap surface for an equivalent static flap, which would have hindered its performance. Furthermore, control was limited to the duration of the flap motion, and, in general, no effect on the flow or aerodynamic loads was observed while the flap was withdrawn to its initial undeflected position. The detailed parametric study showed the characteristics of the flap motion profile to be highly influential on the degree of control. In the application of an optimum flap motion schedule to dynamic stall, the severe nose-down pitching moment decreased by 40%, the performance ratio improved by 30%, and the aerodynamic damping became positive and increased four-fold; this was, however, accompanied by a 20% reduction in the maximum lift.
iii RESUME
Le controle de la circulation autour d'une aile NACA 0015 oscillante par une volet bord de fuite actif a ete investigue experimentalement a Re = 2.46 x 105 par une combinaison de techniques, incluant les mesures de la pression sur la surface, les inspections de la velocite dans le sillage, et les mesures de la circulation par la methode de PIV. Les testes ont ete fait sous les conditions de decrochage profond, avec une attention speciale mis sur 1'identification des changes dans les structures de la circulation qui ont mene aux modifications dans les characteristiques aerodynamiques, et sur 1'evaluation des effets de la profil trapezoidal de motion de la volet. De plus, des motions oscillatoires caracterise par le decrochage leger et la circulation attachee ont ete considere aussi, en plus de deflexions de la volet statique et des motions de la volet a plusieurs harmoniques. Les resultats ont indique que la volet a impose une cambre dans la region du bord de fuite, et a ete tres efficace dans le controle des forces aerodynamiques. Ceci a ete accomplis principalement par la manipulation de la distribution de la pression sous la volet par les changements a la circulation du cote du vent, et a ete non affecte par l'etat de la circulation au-dessus de l'aile. Le tourbillon du bord d'attaque, le structure predominant au-dessus de l'aile, a ete affecte peu dans son puissance et son commencement. Les resultats ont revele aussi que Tangle de la volet et le taux de deflexion ont contribue aux observations ci-dessous, et que le mouvement actif a ete crucial au prevention de la separation de la couche limite en bas de la volet. Par ailleurs, le controle a ete limite a la dure de la motion de la volet, et, generalement, aucun effet sur la circulation ou les forces aerodynamiques ont ete observe pendant que la volet a ete dans sa position initiale. L'etude detaillee a montre les caracteristiques de la profil de motion de la volet d'etre tres influent sur le degre de controle. Dans l'application d'une motion optimal de la volet au decrochage dynamique, le moment severe negatif a ete reduit par 40%, le rapport de la performance a ete ameliore par 30%, et l'amortissement aerodynamique est devenu positif et a ete augment^ quatre fois plus; ceci a ete, cependant, accompagne par une reduction de 20% dans le force soulevant maximale.
iv TABLE OF CONTENTS
ACKNOWLEDGEMENTS i ABSTRACT iii RESUME iv TABLE OF CONTENTS v NOMENCLATURE viii LIST OF TABLES xii LIST OF FIGURES xiii 1. INTRODUCTION 1 2. LITERATURE REVIEW 6 2.1 Pitching Airfoil Flow Topology 7 2.2 Oscillating Airfoil Flow Topology 9 2.3 Dynamic-Stall Flow Mechanism 15 2.4 Parameters Affecting Dynamic Stall 16 2.4.1 Mach and Reynolds Numbers 16
2.4.2 am, Aa and K 19 2.4.3 Pitching Axis Location 21 2.4.4 Three-Dimensionality Effects 22 2.4.5 Boundary-Layer State 23 2.4.6 Airfoil Shape 23 2.5 Theoretical / Numerical Considerations 24 2.6 Flow Control 29 2.6.1 Control Surface 30 2.6.2 Airfoil Shape Deformation 35 2.6.3 Flow Excitation 38 2.6.4 Higher Harmonic Control 44 2.7 Particle Image Velocimetry 45 2.8 Objectives 47
v 3. EXPERIMENTAL METHODS 51 3.1 Flow Facilities 51 3.2 Test Models 53 3.3 Surface Pressure Measurements 57 3.4 Hot-Wire Wake Measurements 60 3.5 Particle Image Velocimetry Measurements 62 3.6 Test Parameters 67 3.7 Experimental Uncertainty 69 4. EVALUATION OF CONTROL METHODS 72 5. RESULTS AND DISCUSSION 76 5.1 Baseline Airfoil 76 5.2 Effect of Trailing-Edge Flap: A Generalized Description 80 5.3 Effect of Flap Motion Parameters 89 5.3.1 Effect of Actuation Duration 90 5.3.2 Effect of Actuation Start Time 94 5.3.3 Effect of Maximum Flap Deflection 98 5.3.4 Effect of Upward Deflection Ramp Rate 103 5.3.5 Effect of Steady-State Time Period 107 5.3.6 Effect of Return Motion Ramp Rate 108 5.4 Guidelines for Control 109 5.5 PIV Results 113 5.5.1 Baseline Airfoil 114 5.5.2 Upwards (Positive) Deflection 121 5.5.3 Downwards (Negative) Deflection 124 5.6 Attached-Flow and Light-Stall Control 127 5.6.1 Attached-Flow Oscillation 128 5.6.2 Light-Stall Oscillation 130 5.7 Passive Flap Control 131 5.8 Higher Harmonic Control 141 5.8.1 Effect of Higher Harmonic Motion 142 5.8.2 Effect of Start Time and Peak Deflection 146
vi 6. CONCLUSIONS 149 6.1 Dynamic Stall Control 150 6.2 Attached-Flow Control 153 6.3 Passive Flap Control 154 6.4 Higher Harmonic Flap Control 155 7. CONTRIBUTIONS 157 8. FUTURE WORK 158 REFERENCES 163 TABLES 1 - 7 171 FIGURES 1 - 73 178
vii NOMENCLATURE b wing model span
Cc section chord force coefficient, = '-/,, ,
Cd section pressure drag coefficient, = 4/ , / Ap^c CH Q-hysteresis factor, = qC/ («)da
Q section lift coefficient, = y,, 2 / Vipw^C
C/,max maximum lift coefficient
Cfa lift-curve slope, = dC//da
p Cm section pitching moment coefficient about %-chord, = /. , , / /zpw^c
Cm,Peak peak negative pitching moment coefficient
C„ section normal force coefficient, = "/. 2 /Vipujs
CD pressure coefficient, -^^°°'/, 2
/Vipu„c
Cw torsional damping factor, = jCm(cc)da
CWjCW clockwise or negative Cw
Cw,ccw counter clockwise or positive Cw Cw,net net Cw value, = Cw,Ccw + Cw,cw = jCm (a)da = jCm (a)da + ccw cw c airfoil chord length d section drag force fc section chord force fn section normal force f0 oscillation frequency / section lift force M Mach number mp section pitching moment vni NP n harmonic of f0 p local static pressure p„ free-stream static pressure q free-stream dynamic pressure, =1/2pul Re Reynolds number based on chord, = u^c/v Rl upward flap deflection ramp rate R2 downward flap deflection ramp rate s airfoil surface distance t time ta flap actuation duration tRi flap upward deflection duration tR2 flap downward deflection duration ts flap actuation start time tss flap steady-state time period u instantaneous streamwise velocity u mean streamwise velocity u' streamwise velocity fluctuation Uc free-stream velocity V two-dimensional velocity vector, = (u,v) v instantaneous transverse velocity v mean transverse velocity v' transverse velocity fluctuation x chordwise or streamwise distance along the airfoil y transverse distance above the airfoil chordline 2 spanwise distance from the wing mid-span a angle of attack ads dynamic-stall angle ara mean angle of attack ocmax maximum angle of attack Omin minimum angle of attack IX C*mp angle at Cm)Peak C*ms moment-stall angle 0»ss static-stall angle Aa oscillation amplitude 5 flap deflection angle C instantaneous spanwise vorticity, -VA % 0 angle between airfoil chord and local surface normal vector K reduced frequency, = coc/2uoo = 7if0c/uoo V fluid kinematic viscosity P fluid density X phase angle, = cot ¥ stream function CO oscillatory radian frequency, = 27tf0 Subscript d downstroke max maximum min minimum u upstroke 00 free-stream conditions Abbreviations CFD computational fluid dynamics CW clockwise CCW counter clockwise DSV dynamic-stall vortex FR flow reversal HHC higher harmonic control LESP leading-edge stagnation point LEV leading-edge vortex x LSB laminar separation bubble NACA National Advisory Committee for Aeronautics n/a not applicable PIV particle image velocimetry rms root-mean-square SLV shear-layer vortex TEF trailing-edge flap TES trailing-edge strip TEV trailing-edge vortex XI LIST OF TABLES Table 1 Chordwise location of the surface pressure taps. Table 2 TEF motion profile characteristics. Table 3 Critical aerodynamic values. Table 4 TEF motion profile characteristics and critical aerodynamic values for PIV experiments. Table 5 TEF motion profile characteristics and critical aerodynamic values for attached-flow and light-stall oscillation cases. Table 6 Critical aerodynamic values for a passively controlled airfoil. Table 7 HHC motion profile and critical aerodynamic values. xn LIST OF FIGURES Figure 1 Rotor blade velocity distribution (reproduced from Ref. 52). Left and right images are for zero and nonzero forward velocities, respectively. Figure 2 Conceptual sketch of the flow structure over a static NACA 0012 airfoil (valid for angles between 6 deg and the static-stall angle). Figure 3 Conceptual sketches of the flowfields during dynamic stall, (a) light stall and (b) deep stall (reproduced from Ref. 61). Figure 4 Angle of attack variations with azimuth angle for a model rotor, oscillating airfoil and ramping airfoil (reproduced from Ref. 34). Figure 5 Selected sequences of boundary-layer events both prior to, during, and post stall at K = 0.1 for a(t) = 10°+l 5°sincot (reproduced from Ref. 46). (a)-(g) flow visualization images; and (h)-(n) conceptual sketches. Figure 6 Dynamic load loops for a(t) = 10°+l 5°sincot at K = 0.1 (reproduced from Ref. 46). Figure 7 3-D representation of the wake mean and fluctuating velocity profiles for a(t) = 10°+15°sin©t at K = 0.1 (reproduced from Ref. 46). Figure 8 Joseph ArmandBombardier wind tunnel, (a) Schematic and (b) photographs. Figure 9 Schematic diagram of the low-speed 0.2 x 0.2 m wind tunnel. Figure 10 Photographs of wing models, (a) 0.254 m chord model and (b) 0.1 m chord model. Figure 11 Schematic diagram of wing model, support structures and oscillation mechanism. Figure 12 Two-dimensionality of the flow over a static wing. xiii Figure 13 Comparison between airfoil motion and sinusoid. Figure 14 (a) Schematic of airfoil with flap and locations of pressure taps, and (b) flap motion profile. Figure 15 Number of cycles for phase-averaging effects on aerodynamic loads. Figure 16 Schematic diagram of the experimental setup and instrumentation system for the surface pressure measurements. Figure 17 Photograph of traverse mechanism for wake scans. Figure 18 Cross hot-wire calibration plots. Figure 19 Schematic diagram of the experimental setup and instrumentation system for the wake velocity measurements. Figure 20 Schematic diagram of the experimental setup and instrumentation system for the PIV measurements. Figure 21 Baseline, or uncontrolled, airfoil, (a) Q, (b) Cm, and (d) Cj; (e) Cp distributions; and (f) wake velocity profiles. Figure 22 Representative baseline airfoil Cp distribution, (a) NACA 0015 airfoil and (b) NACA 0012 airfoil. Figure 23 Dynamic stall function. Figure 24 Cp distributions with representative active control. Figure 25 Wake streamwise velocity distributions with active control. ( , baseline case; , active control) Figure 26 Dynamic Q, Cm and Cd loops with active control. xiv Figure 27 Dynamic Q, Cm and Cd loops for 8max = +16° and ts = On. Figure 28 Variation in the critical aerodynamic values with U for various ts. Dashed line: baseline airfoil; circle: ts ~ -0.57t; square: ts« 0%; and triangle: ts = 0.57t. -1 Figure 29 Dynamic Q, Cm and Ca loops for 8raax = +16° and td = 51 %f0 . Figure 30 Variation in the critical aerodynamic values with ts for various td. Dashed line: baseline airfoil; circle: td ~ 30% fo"1; square: td ~ 50% fo"1; and triangle: td « 70% fo"1. Figure 31 Effect of active flap deflection direction. Figure 32 Difference in the critical aerodynamic values between upwards and downwards flap deflections. Figure 33 Magnitude effects of 5max on (a)-(c) Cp, (d) Q, (e) Cm and (f) critical aerodynamic values. Figure 34 Critical aerodynamic values for various tRi and ts. Figure 35 Effect of tRi on (a) 5 and (b)-(c) Cp distributions at amp. Figure 36 Effect of tss on Q and Cm curves. Figure 37 Flap motion parameters as a function of aerodynamic characteristics. Figure 38 Aerodynamic loads for optimum control case. 4 Figure 39 Static and dynamic Q, Cm and Cd curves for Re = 8.69 x 10 . 4 Figure 40 Cp distributions of baseline airfoil at Re = 8.69 x 10 for (a) static airfoil, (b) upstroke and (c) downstroke. Figure 41 Flowfield around a static airfoil, (a)-(c) streamwise iso-velocity contours, (d)- (f) transverse iso-velocity contours, (g)-(i) iso-vorticity contours, and (j)-(0 xv streamlines. Au/u,*, = 0.1, Av/Uoo = 0.05, and A^c/iic = 5. Solid line: positive; Dashed line: negative. Figure 42 Normalized instantaneous streamwise velocity fields for baseline airfoil. Contour increment AuAu = 0.1. Solid line: positive u; Dashed line: negative u. Figure 43 Normalized instantaneous transverse velocity fields for baseline airfoil. Contour increment Av/m, = 0.05. Solid line: positive v; Dashed line: negative v. Figure 44 Normalized instantaneous spanwise vorticity fields for baseline airfoil. Contour increment A^c/Uco = 5. Solid line: CW; Dashed line: CCW. Figure 45 Normalized instantaneous streamwise velocity fields with dmax = +12°. Contour increment Au/uoo = 0.1. Solid line: positive u; Dashed line: negative u. Figure 46 Normalized instantaneous transverse velocity fields with 8max = +12°. Contour increment Av/u«, = 0.05. Solid line: positive v; Dashed line: negative v. Figure 47 Normalized instantaneous spanwise vorticity fields with dmax = +12°. Contour increment A^c/u*, = 5. Solid line: CW; Dashed line: CCW. Figure 48 Streamline patterns of LEV for (a)-(b) baseline airfoil, (c)-(d) 5raax = +12° and (e)-(f)omax = -12°. Figure 49 Surface pressure coefficient distributions with and without control at Re = 8.69 x 104. 4 Figure 50 Dynamic Q and Cm loops with and without control at Re = 8.69 x 10 . xvi Figure 51 Normalized instantaneous streamwise velocity fields with 8max = -12°. Contour increment Au/Uoo = 0.1. Solid line: positive u; Dashed line: negative u. Figure 52 Normalized instantaneous transverse velocity fields with 8max = -12°. Contour increment Av/iUo = 0.05. Solid line: positive v; Dashed line: negative v. Figure 53 Normalized instantaneous spanwise vorticity fields with 8max = -12°. Contour increment ACp/uo = 5. Solid line: CW; Dashed line: CCW. Figure 54 TEF control of dynamic C/ and Cm loops for a(t) = 12°+6°sincot. 0 0 Figure 55 Cp distributions for a(t) = 12 +6 sincot. Figure 56 Typical wake flow structures for a(t) = 12°+60sincot. Figure 57 TEF control of dynamic Q and Cm loops for a(t) = 14°+6°sincot. Figure 58 Cp distributions for passively controlled airfoil. ( , 8 = 0°; , 8 = +8°; --,8 = -8°) Figure 59 Wake streamwise velocity distributions for passively controlled airfoil, (a) mean component and (b) fluctuating component. ( , 8 = 0°; , 8 = +8°; —, 8 = -8°) Figure 60 Dynamic Q and Cm loops for passively controlled airfoil. Figure 61 Effect of 8 for passive control on Cp distributions. Figure 62 Dynamic Q and Cm loops for passive control of attached-flow regime. Figure 63 Cp distributions for passive control of attached-flow regime. ( , am = 8° & 8 = 0°; , am = 8° & 8 = -8°; —, am = 16° & 8 = 0°) Figure 64 Schematics of HHC motion profiles. xvii Figure 65 Effect of HHC flap motion on dynamic load loops with ts ~ -0.5n and 8max = 16°. Figure 66 Effect of HHC on increment in Q and Cm. Figure 67 Typical Cp distributions for HHC control. Figure 68 Typical wake flow structures for HHC control. Figure 69 Effect of 2P flap motion on Q, AC/ and Cm. Figure 70 Variation of CWjnet with ts and NP for 8max = 16°. Solid symbols denote baseline airfoil. Figure 71 Effect of 3P flap motion on Q, AC/ and Cm. Figure 72 Effect of 4P flap motion on Q, AC/ and Cm. Figure 73 Effect of 8max on Q and Cm for ts ~ -0.57i. xviii CHAPTER 1 INTRODUCTION There are numerous instances, natural or man-made, in which wings and/or blades may be subject to unsteady flows and/or dynamic motions. These include fighter jets, helicopters, wind turbine blades, turbojet engines, dragon flies, bats, hummingbirds, etc. In many situations, this introduces increasing complexity of the flow structures. So much so that the flow may be completely altered causing the wing or blade to behave in unexpected ways. No machine is plagued by such complexities more than the helicopter. To understand why this should be the case, one must first understand the concept behind the articulation of helicopter rotor blades. The principle behind rotor blade articulation is, in fact, quite simple and can easily be illustrated through the following discussion. During forward flight, the combined forward velocity of the craft itself superimposed onto the rotational velocity of the blades causes an asymmetric velocity distribution on the rotor disk; on the advancing side the two velocities combine whereas on the retreating side they subtract (Fig. 1). Consequently, the lift generated, which is proportional to the square of the velocity, is higher on the advancing side than on the retreating side, and results in a rolling moment that would cause the craft to roll if not corrected. To avert this rolling moment, the incorporation of a flapping hinge near the hub allows the blades to flap freely, thus eliminating the moment at the hub but resulting in a flapping motion of the rotor blades that can be interpreted as a cyclic variation in the angle of the incoming flow. In the developmental history of rotorcraft, the articulation of helicopter rotor blades, first suggested by Charles Renard in 1904 and first implemented successfully by Juan de la Cierva in 1923, is the single most revolutionary breakthrough without which stable helicopter flight would not have been possible. However, it also introduced other, perhaps unexpected, complexities in the form of highly unsteady flow over the rotor blades, something helicopter aerodynamicists continue to struggle with to this day. This apparent angle of attack variation complicates the rotor blade aerodynamics and results in a highly unsteady flow, which under certain conditions may lead to a phenomenon referred to as "dynamic stall" to occur on the retreating side. To demonstrate the complexity 1 of the flow past an unsteady airfoil, the flow past a static airfoil is described first. Note that the following discussions apply strictly to a NACA 0012 or NACA 0015 symmetric airfoil as these airfoil sections are traditionally typical for helicopters. The flow past a static airfoil can be described as consisting of a laminar separation bubble (LSB) in the leading-edge region, a region of "dead" flow delimited by laminar separation and turbulent reattachment points, followed by a trailing-edge turbulent separation point, as shown in Fig. 2. Note, however, that at small angles, the laminar boundary layer does not separate and transition occurs via laminar instability. With increasing incidence, the turbulent separation point progresses upstream until the instant at which it encounters the laminar separation bubble, causing it to "burst" and the flow to separate near the leading edge, the result of which is lift and moment stall. Note that the presence and size of the laminar separation bubble is dependent on airfoil geometry as well as Reynolds number. In the absence of a laminar separation bubble, the trailing edge separation point would travel further upstream before stall were to occur leading to a more gradual type of stall. A more detailed description is provided in Ref. 64 by McCroskey and Philippe. In contrast, the flow over an unsteady airfoil has been shown by previous research to be quite complex with the degree of complexity increasing significantly as the angle of attack excursions increase in magnitude. Generally, two categories of unsteady flow are observed depending on the magnitude of the maximum angle of attack: attached-flow and dynamic stall. The attached-flow regime occurs when the airfoil is oscillated within the static-stall angle (i.e. the maximum angle of attack remains below ass). This type of flow is characterized by fully attached flow throughout the cycle with little hysteresis in the loads or deviation from static values. When the airfoil is oscillated such that its maximum angle of attack is well beyond the static-stall angle, the airfoil penetrates the dynamic stall regime. The flow consists of a thin layer of flow reversal in an otherwise attached boundary layer (although this statement may seem contradictory, it is not and will be clarified in chapter 2) which spreads upstream with increasing incidence, followed by a breakdown of the turbulent boundary layer in the vicinity of the leading edge which causes the formation of a large vortical structure, commonly referred to as a leading-edge vortex (LEV) or dynamic-stall vortex (DSV). A nonlinearly fluctuating pressure field is produced by this vortex as it grows and convects over the airfoil to be finally shed into the wake resulting in a drastic stalling of 2 the airfoil; this is the distinguishing feature of dynamic stall. Although the dynamic-stall angle and peak lift coefficient may significantly exceed their static airfoil counterparts, the LEV also induces an excessive nose-down pitching moment, negative work coefficient (i.e. a measure of the aerodynamic damping), increased drag and a significant degree of hysteresis in the aerodynamic loads. These contribute to increased torsional loading of the blades and pitch link loads, reduced aerodynamic damping, excessive vibrations, increased pitch control loads and limited forward flight speed, all of which constrain the performance of modern helicopters. This process is also referred to as deep dynamic stall due to the extreme excursion of the maximum angle of attack beyond the static-stall angle. In the event that the maximum airfoil incidence exceeds the static-stall angle only slightly, a moderate form of dynamic stall, referred to as light stall, occurs. In this case, the flow proceeds similar to dynamic stall, however the leading-edge vortex formation is forced by the deceleration in airfoil pitch motion at the top of the upstroke, and thus is formed prematurely and is of reduced strength. McCroskey [61] provides a sketch of the basic features of the boundary layer over an oscillating airfoil for the light and deep dynamic stall cases, which is reproduced in Fig. 3. An excellent review of unsteady airfoils is given by McCroskey [61], and Leishman's book, Principles of Helicopter Aerodynamics [52], provides an excellent fundamental background in the area of helicopter aerodynamics with chapters focused on unsteady aerodynamics and dynamic stall. There are many other researchers who have contributed immensely to the problem of dynamic stall, including Carr, McAlister, Chandrasekhara, and Jumper. Most recently, a thorough investigation into the flow over an oscillating airfoil was performed by Lee and Gerontakos [46]. Because of the difficulties incurred by the dynamic stalling of rotor blades, much effort has been made to understand the flow topology and the physical mechanisms involved. In general, the most traditional means of studying the dynamic stall phenomenon is through the ramping or sinusoidal oscillation of an airfoil in a laboratory environment. Figure 4 is reproduced from Ref. 34 and demonstrates the angle of attack variations observed on a model rotor as a function of rotor blade azimuth (shown as a solid line). This is also accompanied, for comparison sake, with the angle of attack variations of a typical ramping airfoil (short dashed line) and oscillating airfoil (long dashed line). This figure clearly illustrates why these conditions are simulated in the laboratory using an airfoil subject to either a ramping motion, 3 since it resembles closely the pitch-up motion of the model rotor, or sinusoidal oscillations in pitch, since it models the entire azimuth fairly reasonably. Owing to the severity of the dynamic stalling process that unsteady wings are often subject to, numerous attempts have been made, by both academia and industry, to control the unsteady aerodynamic loads generated by an unsteady airfoil. This is especially true in recent years due to the current increase in popularity of helicopters as a means of transportation. In fact, the Aviation Week & Space Technology publication in their January 28, 2008 issue indicates that "business is booming for rotorcraft manufacturers", and that "demand for helicopters is extraordinarily strong". This has as a result provoked renewed interest in the enhancement of their performance and flight envelope. Both passive and active flow-control concepts capable of minimizing, or eliminating, the detrimental hysteresis in the nonlinear airloads, the excessive nose-down pitching moment and negative aerodynamic damping have been proposed. These methods include pulsating and synthetic jets [15,30,31,32,65,72,85, 90, 91], leading-edge blowing and suction [2, 39, 95, 97], vortex generators [55, 84, 90], plasma actuators [73], leading-edge rotating cylinder [20], higher harmonic motion [67,71, 82, 96], dynamically deformable leading edge [9,10, 80], variable droop leading edge [25, 40, 57], leading-edge slat [97], leading-edge flap [33], trailing-edge strip [26, 88], and trailing-edge flap [18,43,51,76,77,78,89,93,99,100]. In fact, flow control, in particular active flow control, is one of the most studied research topics in applied aerodynamics today. Note that it is the active flow-control schemes, in which relatively small amounts of energy are expensed locally to realize changes in the entire flowfield with significant gains in performance, that show the most promise, as the flow-control device can be designed to affect the flow only on the retreating side of the rotor disk without compromising the performance of the blade on the advancing side. It should also be remarked that the ideal method of flow control would improve upon the deficiencies while at the same time avoiding an adverse influence on favourable characteristics; however this is rarely ever possible. Of all the different control mechanisms, the trailing-edge flap (TEF) dynamic-flow control concept is believed by many researchers to be more feasible and viable considering the severe environment frequently encountered at the leading edge of a rotor blade. Furthermore, its distance from the pitching axis provides it a greater moment arm with which to manipulate the pitching moment effectively. Feszty et al. [18] showed that through a 4 pulsed upwards flap deflection the trailing-edge flap can achieve a significant decrease in the large negative pitching moment during retreating-blade dynamic stall and were able to generate positive aerodynamic damping with which alleviate vibrations. Leishman [51] extended its application and used it to mitigate the advancing side blade-vortex interaction intensity. Recognizing that in addition to dynamic stall there are numerous other sources of rotorcraft vibrations, including blade-vortex interactions, blade-fuselage interactions, main rotor-tail rotor interactions, etc, Liu et al. [100] and Enenkl et al. [99] applied the trailing- edge flap concept to control the vibrations from these other sources which turned out to be fairly successful. In fact, the December 2007 issue of Aerospace America reports that a consortium of academic and commercial institutions, including Techno-Sciences, the University of Maryland, and the Armor Holdings Aerospace and Defense Group, have also recently been exploring trailing-edge flap control technology for rotorcraft performance enhancement, including noise and vibrations. The promise of this technology is so significant that Eurocopter flew a helicopter equipped with trailing-edge flaps in September 2005. 5 CHAPTER 2 LITERATURE REVIEW The significance of the flow over an unsteady airfoil in a variety of both established and emerging applications is obvious from its very extensive reporting in the published literary archives. This review of previous works will constitute a thorough discussion of the many different aspects concerning unsteady airfoil aerodynamics that are relevant to the current work being presented and thus should provide the reader with a strong fundamental understanding of such flows. Research has shown the flow over an unsteady airfoil to have a far more complex structure than that over a static airfoil. In addition, the airfoil motion characteristics have a profound impact on the resulting flow. The primary two categories of unsteady motion that have been studied extensively in the past have been the oscillating airfoil, characterized by a sinusoidal oscillation of amplitude Aa about a mean angle am with reduced frequency K (= TcfoC/uoo, where f0 is the oscillation frequency, c is the airfoil chord and Uoo is the free-stream velocity), and the ramping airfoil, characterized by a motion between starting and stopping angles at a constant pitch rate ac/2u„ (where a is the angular velocity). These two motions (i.e. oscillating and constant pitching), shown in Fig. 4 superimposed onto the motion of a model rotor, are those generally implemented by most researchers to simulate the angle of attack variations observed on helicopter rotor blades and wings during post-stall manoeuvring, respectively. It is fortunate, however, that a ramping airfoil displays many of the dynamic-stall characteristics inherent to the retreating-blade dynamic stall problem of helicopter rotor blades without introducing the additional complications associated with motion time-history effects [94]. For this reason, it is often convenient to introduce the flow over a ramping airfoil prior to focusing on the flow over an oscillating airfoil. Beginning with the ramping airfoil and then continuing with the sinusoidally oscillating airfoil, the first two sections will provide a detailed discussion of the flow topology as well as the fundamental flow characteristics of an unsteady airfoil. This will provide a thorough understanding of the flow over an unsteady airfoil and the dynamic stall process. The third section will focus on the underlying physical mechanism that causes an 6 airfoil to undergo dynamic stall. As there are many parameters which contribute to the character of the fiowfield, including Mach and Reynolds numbers, mean angle of attack, oscillation amplitude, reduced frequency (or pitch rate for a ramping airfoil), pitching axis location, three-dimensional effects, state of the boundary layer, airfoil shape, etc, the fourth section will discuss the impact that each of these parameters has on the fluid structures and aerodynamic load characteristics. Also considered will be certain theoretical models that have been developed and numerical investigations that have been conducted to characterize the flow over an unsteady airfoil, comprising the fifth section. Recent research efforts have vigorously searched for various means of control for a dynamic-stalling airfoil. A comprehensive discussion of various control methods, including their effectiveness and the physical mechanisms behind the flow control, which have been previously implemented, will form the sixth section. The seventh is reserved for a limited review of previous efforts implementing the unique technique of particle image velocimetry to the study of unsteady airfoil flows. The eighth and last section will present the objectives of the current work in light of the present state of the art, clearly indicating how they are unique and contribute to knowledge. 2.1 Pitching Airfoil Flow Topology A survey of the typical research papers concerned with the flow over a ramping airfoil (e.g. Francis and Keesee [19], Jumper et al. [38], Lorber and Carta [53], Jumper et al. [37], Visbal and Shang [94], Shih et al. [83], Schreck and Helin [81], and Robinson et al. [79]) indicate that the overall flow structure over an airfoil subject to a ramping motion between starting and stopping angles is qualitatively universal, as they agree with each other fairly well. Francis and Keesee [19] even show that the observed qualitative features of dynamic stall remain independent of the non-dimensional pitch rate and amplitude provided the stopping angle is sufficiently high, and thus a general description can be formulated through an amalgamation of the results of the above-mentioned articles. For an airfoil pitching from a starting angle well below the static-stall angle, the flow begins with a fully attached upper surface boundary layer. As the airfoil begins the pitching motion, and the angle of attack is increased, a separation point is seen to progress from the 7 trailing edge towards the leading edge of the airfoil, and is associated with a steady increase in lift. The works of Visbal and Shang [94] and Shih et al. [83] have shown that this flow separation is different from that which occurs on a static airfoil; it is in the form of a thin layer of flow reversal (FR) in an otherwise thickened however still attached boundary layer as described by Shih et al.. Figure 3a is a reproduction from McCroskey [61] which shows a schematic diagram of this type of separation. Note that the separated boundary layer follows the airfoil contour, producing a narrow wake. As the separation point reaches a quarter of the chord downstream from the leading edge, Jumper et al. [38] describe a "catastrophic" separation of the flow causing the formation of a large vortex in the leading-edge region, which has been termed the leading-edge vortex (LEV) or dynamic-stall vortex (DSV). The reader should note that these two terms are used interchangeably in this text. The cause for the formation of this vortex, which lies with the breakdown of the turbulent boundary layer, will be discussed in detail in section 2.3. This vortex is seen as a large suction pressure peak in the upper surface pressure distribution [34]. Interestingly, Shih et al. [83] were also able to confirm that the vorticity in the LEV originates in the vicinity of the leading edge. This fact has implications concerning the techniques for dynamic-stall control as will be discussed later in section 2.6. Figure 3b provides a schematic diagram of the LEV-dominated flow. With the formation of the LEV, both the lift and profile drag coefficients, Q and Cd, are observed to increase at a greater rate with increasing airfoil incidence. The formation of a counter-clockwise rotating vortex (i.e. in a sense opposite to the leading-edge vortex) at the airfoil trailing edge, termed the trailing-edge vortex (TEV), as the LEV forms, as well as a shear-layer vortex (SLV) near the mid-chord have also been identified under certain flow conditions [94, 83]. Subsequently, the suction pressure peak is observed to diffuse spatially as well as travel towards the trailing edge. This signals the simultaneous growth of the LEV and its downstream convection over the airfoil and shedding into the wake. The passage of the vortex beyond the pitching axis induces a sudden increase in the negative pitching moment coefficient Cm. This sudden increase in pitching moment is a major source of blade torsional load. As it is shed into the wake, a recovery in the pitching moment and drag force is experienced, however lift stall occurs and the lift generating capability of the airfoil is severely hampered. This results from the fully separated upper surface boundary layer, evidence of which is a flat upper surface pressure distribution. Note however that a 8 fluctuation in the aerodynamic loads is observed once the airfoil attains the maximum angle of attack. Explanation can be found in the repeated flow reattachment and subsequent separation that occurs, as observed from flowfield measurements, until the airfoil motion ends and the flow reaches a steady state consistent with a static airfoil at that angle of attack [83]. Note that the dynamic motion of the airfoil in conjunction with the formation of the leading-edge vortex allowed the lift coefficient and stalling angle to far exceed its static airfoil counterpart, however, the drag and negative pitching moment coefficients were also subject to large increases as well. The above description is in contrast to the flow over the corresponding static, or quasi-steady, airfoil for which trailing-edge flow separation is found to spread upstream with increasing airfoil incidence until which point it either bursts the laminar separation bubble (LSB) that is present, or if no LSB has formed, reaches the leading edge of the airfoil. Further details on the characteristics of laminar separation bubbles may be obtained from O'Meara and Mueller [68]. A schematic diagram of the flow over a generic static airfoil is provided in Fig. 2. Either way, the static-stall angle ass and maximum lift coefficient Qiraax are considerably inferior to the unsteady case. In fact, Jumper et al. [37] found that peak lift could be increased by more than a factor of two and the stall angle delayed 11 degrees. The peak negative pitching moment Cm,Peak however suffers from severe unwanted excursions from the static values. In an effort to expose the mechanisms that contribute to the improved performance of an unsteady airfoil, Ericsson and Reding [16, 17] have developed an extensive semi-empirical theory based on the performance characteristics of a static airfoil. A description of their work is reserved for section 2.5. 2.2 Oscillating Airfoil Flow Topology We now turn our attention to the flow over an oscillating airfoil, which possesses two features that make the flow more complex than that over a ramping airfoil. The first is the variation in the pitch rate, which varies in a sinusoidal manner between positive and negative peak values, and passes through zero pitch rate twice per cycle. The second is the time history effects resulting from the downstroke motion. A review of literature specific to harmonically oscillating airfoils will therefore be presented hereafter. 9 Similar to the ramping airfoil, a review of literature shows that the qualitative flow features of the dynamic stalling of an oscillating airfoil remain generally unaffected by the parameters of the airfoil motion and the flow characteristics [56,62,6,59,58,61,52,41,46, 70]. This permits for the sequence of unsteady boundary-layer events that occur throughout one oscillation cycle to be summarized. Notwithstanding, the quantitative features of the flow are very much influenced by the flow and airfoil motion parameters, and a discussion of these effects will follow in section 2.4. Note that the following discussion applies specifically to a medium thickness airfoil, such as a NACA 0012 profile, subject to angle of attack variations that are in excess of the static-stall angle and thus penetrate into the deep dynamic stall regime. In addition, a distinction should be made regarding the form in which flow separation may present itself between the static and unsteady cases. For a static airfoil, the point after which the boundary-layer fluid begins to reverse direction near the surface coincides with flow separation, where the boundary layer diverges from the airfoil upper surface (Fig. 2). That is, the terms flow reversal and flow separation are synonymous and interchangeable. On the contrary, in the case of an unsteady airfoil, a thin layer of reversed flow may potentially be present over the airfoil surface while at the same time the boundary layer does not separate from the airfoil surface (Fig. 3a). In other words, the boundary layer, despite it being lifted from the surface, continues to follow the airfoil curvature. In such an instance, flow reversal does not coincide with, nor does it imply, flow separation. Sears and Telionis caution that in the case of unsteady flows, vanishing wall shear stress and/or reversed flow are not always indicative of flow separation [64], a view shared by McAlister and Carr [58]. The description which follows is based mainly on the recent and unprecedented in-depth investigation of the temporal and spatial progression of the boundary-layer flow phenomena and their associated aerodynamic loads conducted by Lee and Gerontakos [46] for a NACA 0012 airfoil profile at a chord-based Reynolds number of 1.35 x 105 subject to sinusoidal oscillations characterized by a(t) = 10°+15°sincot and K = 0.1. Although these measurements are not the first of their kind, they do provide unparalleled resolution and detail. In addition, their findings are in good agreement with the results of previous studies. Figures 5 and 6 are reproduced from this paper (i.e. Lee and Gerontakos [46]) and show smoke wire flow visualization images, along with the corresponding 10 schematic flow diagrams, at different points in the oscillation cycle, as well as the dynamic load loops for the above-mentioned oscillation case. During the pitch-up motion, while the angle of attack remained below the static-stall angle, the flow over the airfoil remained completely attached to the airfoil surface, except perhaps in the immediate vicinity of the trailing edge, and the boundary layer was thinner than in the static case. Furthermore, transition was found to be delayed, and progressed upstream at a much lower rate compared to a static airfoil. This improved behaviour did not result, however, in significantly improved aerodynamic loads as they deviated little from the static airfoil during this period (Fig. 6a; between amin and point 1). In addition, a laminar separation bubble was observed in the leading-edge region. As the airfoil incidence surpassed the static-stall angle, the first evidence of a thin layer of flow reversal forming near the trailing edge was observed (Figs. 5a and 5h). The thinning of the boundary layer and delay of flow reversal to large angles of attack is a direct consequence of the airfoil dynamic motion [58]. The flow reversal, which caused a slight thickening of the boundary layer, moved upstream rather gradually with increasing incidence reaching approximately the pitching axis [6, 58, 62]. Flow visualization images showed no strong variations in the boundary-layer thickness or any significant distortion of the external free-stream flow. While the flow reversal advanced upstream (Figs. 5b and 5i), the lift coefficient continued to increase in a linear fashion with the same slope as during the initial first half of the upstroke motion (Fig. 6a; between points 1 and 2). A sudden breakdown of the turbulent boundary layer then occurred, which travelled forward quickly leading to the formation of an energetic leading- edge vortex (Figs. 5c and 5j; marked by point 3 in Fig. 6a). The initiation of stall is marked by a peak in the leading-edge velocity, interpreted by the maximum in the leading-edge suction pressure peak [56]. While the airfoil completed the pitch-up motion, the LEV grew and convected rearward over the airfoil at a speed considerably less than the free stream. The vortex has been found to convect over the airfoil at an approximate speed of 25%Uoo according to Lorber and Carta [53], 30%Uoo according to Chandrasekhara and Carr [8], 35- 40%Ua> according to Carr et al. [6] and McCroskey et al. [62], 45%Uoo according to Lee and Gerontakos [46], and 55%u<» as Ericsson and Reding [17] have cited. McCroskey et al. [62] and Carr et al. [6] affirm that a LEV is always present during the dynamic stalling of an airfoil, and is the defining characteristic. This formation, growth and convection of a LEV 11 coincided with an increased rate of lift generation (Fig. 6a; AQ,LEV between points 3 and 4) as well as the rapid down-turning of the pitching moment coefficient to negative values, the point which marks moment stall (Fig. 6c; between points 2 and 4). McAlister et al. [59] suggest that the strength of the LEV could possibly be linked to the airfoil circulation at the instant of formation. Peak values of lift, drag and negative pitching moment were obtained as the LEV passed over the trailing edge and into the wake, corresponding to lift stall [56,62,6] (Figs. 5d and 5k; marked by point 4 in Fig. 6). Note that the magnitudes of the loads were far superior to those generated on a static airfoil shown by the considerably increased peak in the lift, drag and pitching moment coefficients in Fig. 6 [63]. It should be mentioned here that under certain flow conditions a counter clockwise vortex has been found to form at the trailing edge during LEV convection. Panda and Zaman [69] describe it as forming as a result of the low pressure of the LEV, which pulls fluid with opposite vorticity from the pressure surface. Interestingly, this fluid structure only seems to be present at low Reynolds numbers; many researchers have found that the LEV is the only dominant vortical structure that forms above a Reynolds number of around 5xl04. Subsequent to LEV shedding, the entire upper surface boundary layer was in a state of complete turbulent separation resulting in a severe loss of lift and profile drag, and a rapid recovery in terms of pitching moment (Figs. 5e and 51; Fig. 6 between points 4 and 5). Under certain conditions, a secondary vortex has also been seen to form and convect over the airfoil during the initial portion of the downstroke motion resulting in small but noticeable peaks in the lift and pitching moment coefficient curves [6, 46,56,62,63, 69] (marked by point 6 in Fig. 6a). As the angle of attack reached below the static-stall angle, reattachment of the turbulent boundary layer was initiated near the leading edge and propagated downstream at a rate of about 15-35% of the free-stream velocity [6,46, 62] (Figs. 5f-5g and 5m-5n). The completion of the reattachment process can be identified from the lift and pitching moment coefficient curves as occurring when the loads begin to return to their pre-stalled values [62,6] (marked by point 8 in Fig. 6; Note that in Fig. 6c, the point identified as 8 should be located at the same angle but on the downstroke portion of the oscillation cycle, not the upstroke). Interestingly, when focusing on the instantaneous flow, Rank and Ramaprian [75] did note a nonperiodicity to the reattachment process, in that the flow varied slightly from cycle to cycle during this period. This phenomenon was also observed in the pitching airfoil results of Shih et al. [83]. At even smaller incidence, a return 12 to a laminar state, referred to as relaminarization, was observed in the boundary layer towards the leading edge and spread over the airfoil with decreasing angle of attack. Note, however, that the aerodynamic loads did not return to their pre-stalled values until the beginning of the upstroke. A unique study performed by Kerho [40] compared the results obtained through numerical computation of a sinusoidally oscillating airfoil with the realistic motion of the rotor blade for the UH-60A helicopter. He showed that, compared to a simple sinusoidal airfoil motion, the more realistic motion resulted in larger peak loads (i.e. Q>max, Cd,max, and Cm,peak) as well as a delay in the occurrence of stall. These differences were mainly attributed to the increased pitch rate during the later part of the upstroke motion, thus having the same result as an increase in reduced frequency, which will be discussed further in subsection 2.4.2. On further observation of the unsteady aerodynamic load loops in Fig. 6, one characteristic that should be noted is the hysteresis in the loads between the upstroke and downstroke motions. The observed hysteresis in the unsteady aerodynamic loads was traced back mainly to the hysteresis in the unsteady separation and reattachment points, and to a smaller degree to the transition-relaminarization point hysteresis [64,6]. In other words, the locations of transition and separation are delayed further downstream during the upstroke, and relaminarization and reattachment are promoted further upstream during the downstroke. Ericsson and Reding [17] assign the delayed boundary-layer transition and separation during the upstroke to time lag and boundary-layer improvement effects, which will be further discussed later. Leishman [52] indicates that the lag in the reattachment during the downstroke is due to the "reverse kinematic induced camber effect on the leading-edge pressure gradient." Note that Carr et al. [6] only observed hysteresis when the airfoil oscillated in and out of stall; however, the results of Lee and Gerontakos [46] and Lee and Basu [45] clearly show hysteresis even for attached-flow oscillations, although small in comparison. Panda and Zaman [69], whose experiments were conducted at rather low Reynolds numbers (i.e. 2.2 x 104 and 4.4 x 104) on an airfoil oscillating with 0° mean angle, 7.2° oscillation amplitude, and a reduced frequency of 0.028, attributed the observed hysteresis in the loads to the hysteresis in the laminar separation point. 13 Measurements of the wake flow have also proved to be helpful in characterizing the flow over the airfoil at any given instant. Furthermore, the wake behind an oscillating airfoil is of particular interest owing to its importance regarding the wake-structure interactions that occur on helicopters. Chen and Ho [12] studied the wake of an airfoil undergoing plunging oscillations in the attached-flow regime. Although this type of motion is different, important conclusions were drawn which should also apply to pitch oscillations. Firstly, the wake took the shape of an asymmetric bell, whose width and deficit increased with downstream distance but was self-similar when normalized by the minimum streamwise velocity; the asymmetry was caused by the thicker upper surface boundary layer. Due to the displacement effect, the width was thicker than that of a static airfoil and was on the order of the oscillation amplitude. The trailing-edge pressure differential and v|/ = 0 streamlines, where \|/ is the stream function, indicated that the Kutta condition fails at the trailing edge, which periodically sheds vorticity due to the periodic changes in bound circulation. The experiments of Park et al. [70], who measured the mean and rms (root-mean-square) wake velocity profiles, show that the location of the peak mean velocity deficit follows the motion of the airfoil trailing edge, although a phase lag was present which increased with downstream distance. This occurs due to the time it takes for the flow to reach the sensor in the wake, and therefore demonstrates the need for a compensation scheme, which is provided by Chang and Park [11] and is discussed in chapter 3. The distribution of velocity fluctuations took the form of double peaks, similar to the flow past a cylinder. Park et al. also showed that an increase in the mean angle of attack caused an increase in the velocity defect, wake width and turbulence intensity. Similar to the aerodynamic loads, hysteresis was present in the wake profiles. Lee and Gerontakos [46] acquired detailed wake velocity distribution measurements for the oscillating case a(t) = 10°+l 5°sincot and K = 0.1 in conjunction with surface pressure measurements and upper surface hot-film measurements at a distance of one chord downstream of the trailing edge. This allowed for the wake distributions to be correlated to the upper surface flow structures. Figure 7 illustrates their findings, categorizing the various boundary-layer events into six regions, and the utility of wake measurements to characterize the flow over an unsteady airfoil. Note that the notationy indicates the transverse distance in the airfoil wake. Regions A and B indicate the wakes corresponding to the flow regimes of 14 attached flow and the onset and the end of the upward spreading of the flow reversal, respectively. Note the narrow low velocity deficit with minimal turbulence levels. Region C corresponds to the rapid thickening and breakdown of the turbulent boundary layer, and the subsequent formation and rapid front-to-rear convection of a leading-edge vortex. In this region, the wake width, velocity deficit and turbulence levels increased quickly and significantly. Region D corresponds to the massive separation conditions that occur subsequent to stall with enormous increases in all aspects of the wake flow (i.e. width, deficit and velocity fluctuations). In region E, the wake structures become much less rigorous, representing the beginning and the end of the flow reattachment process during the downstroke motion. During this period, the wake gradually returns to pre-stalled conditions which are finally achieved in the last region, region F. 2.3 Dynamic-Stall Flow Mechanism The mechanism that initiates the formation of the leading-edge vortex and consequently the stalling of the airfoil has been the topic of some controversy in the past. Traditionally it has been proposed that the dynamic stalling of the airfoil results from the bursting of the laminar separation bubble caused by the forward motion of the flow reversal point. Johnson and Ham [34] indicate that as the flow reversal approaches the laminar separation bubble, it causes the reattachment point to be driven upstream along with the inherent promotion of laminar separation with increasing incidence. Despite this upstream motion of the laminar separation bubble [34,59], the net result is a contraction of the LSB; this causes an increased adverse pressure gradient and leads to its bursting and the production of the LEV. This was an interesting point of view as a bubble has little effect on the aerodynamic loads. This hypothesis, however, had been soon after contradicted by the works of McCroskey et al. [56, 62, 6, 59, 63]. They found that it is an abrupt breakdown of the turbulent boundary layer downstream of the LSB near the point of flow reversal that causes the formation of the leading-edge vortex, whose vorticity is supplied by the leading-edge turbulent flow, and not the bursting of the LSB. To substantiate their claim, they performed experiments on a regular NACA 0012 airfoil and then applied a boundary layer trip to eliminate the laminar separation bubble. This simulates the effects of higher Reynolds 15 numbers, where the laminar flow is more susceptible to disturbances, and therefore will most probably transition before it has a chance to separate and form a LSB. In fact, in actual applications a LSB will most probably not form due to the numerous disturbances present, such as vibrations, surface discontinuities and surface contamination. This is the concern of Sunneechurra and Crowther [87], who question the validity of experiments conducted at Reynolds numbers far below those consistent with flight conditions. The results, however, showed very little effect on the basic stall and load characteristics, indicating that the LSB has merely a passive impact on the flow. The more recent work of Lee and Gerontakos [46] corroborate their findings. It is now accepted that the initiation of dynamic stall is triggered by the breakdown of the turbulent boundary layer. 2.4 Parameters Affecting Dynamic Stall Despite the generally common nature of the dynamic stalling process, the parameters describing the flow and especially the airfoil motion do have a significant impact on the quantitative features of the flow [46, 62]. In other words, although the overall sequence of flow events remains unchanged, the instant at which each flow structure occurs may differ and the flow-induced aerodynamic loads may change considerably. The parameters of greatest importance include Mach and Reynolds numbers, mean angle of attack, oscillation amplitude, reduced frequency (or pitch rate for a ramping airfoil), pitching axis location, three-dimensional effects, state of the boundary layer, and airfoil shape. The dependence of the flow and load characteristics on the various parameters will now be explored. 2.4.1 Mach and Reynolds Numbers Beginning with the flow parameters, which include Mach number and Reynolds number, experience has shown their effects, although important, to be overshadowed by those of the airfoil motion. Nonetheless, McCroskey et al. [63], who conducted extensive experiments on oscillating airfoils, performed tests at Mach numbers below 0.3, and found the magnitudes of the aerodynamic loads and stall angles to change. Chandrasekhara and Carr [8], whose experiments were conducted at M = 0.15-0.45, also maintained that the LEV 16 was ever-present, and that only its strength and instant of initiation changed. Furthermore, they discovered that compressibility was an issue for Mach numbers exceeding 0.3 with the LEV formation being promoted considerably; note, however, that none of the Mach numbers resulted in shock waves. The parametric study of Lorber and Carta [53] that varied the Mach number between 0.2 and 0.4 and Reynolds number between 2 x 106 and 4 x 106 suggested that in fact they have a weak influence on the characteristics of the flow over a pitching airfoil, except that at large Mach numbers compressibility effects reduce the strength of the LEV. Concerning Reynolds number effects, Martin et al. [56] concluded, by varying the Reynolds number between one and three million, that increasing Re promotes the onset of stall, increases the peak lift and peak suction pressure, and delays the occurrence of dynamic stall and the peak negative pitching moment. The results of Carr et al. [6] and McCroskey et al. [62] suggest however that Reynolds number effects are small. Panda and Zaman [69] also confirm that Reynolds number effects are of secondary importance. It should be recognized, however, that previous studies of Reynolds number and Mach number effects were not independent. That is, when changing the Reynolds number the Mach number was not kept constant and vice versa. It can therefore not be concluded which effects are a result of the Reynolds number and which are due to the Mach number. Interestingly, the numerical study of Visbal and Shang [94], which assumed laminar flow, and the PIV measurements conducted in a water towing tank at a Reynolds number of 5000 by Shih et al. [83] showed qualitatively similar features as the experiments conducted at Reynolds numbers two to three orders of magnitude larger. From this, it was concluded that the parameters associated with the airfoil motion dominate. Despite the seemingly minor effect that the Reynolds number has on the flow, it should be said that most studies have been conducted at high values of the Reynolds number (on the order of 105 and above) and therefore in the same order of magnitude. It is for that reason important to verify whether the aforementioned flow description still holds for a smaller Reynolds number below 105, where viscous effects may alter the flow behaviour and/or where the nature of the boundary layer (i.e. laminar or turbulent) may be in question. It should be expected that, since, in general, the flow over an airfoil at low Reynolds numbers can maintain a laminar boundary layer for quite some distance whereas for larger Reynolds 17 numbers the flow transitions in the leading-edge region, significant differences be present; this expectation is confirmed by the findings of the few studies conducted at Reynolds numbers below 105. Kim and Park [41] conducted smoke wire flow visualization of the flow past an airfoil undergoing sinusoidal oscillations with 0° mean angle, 7.4° oscillation amplitude, and 0.2 reduced frequency at a Reynolds number of 27000. Although the airfoil does not undergo any type of stall, one important characteristic of a low Reynolds number unsteady airfoil flow is portrayed, and that is the formation of a von Karman vortex-like wake of laminar vortices similar to that behind a cylinder. This indicates that the wake, and therefore the boundary layer, is laminar. They also observed the vortex shedding to persist to the maximum angle of attack, which under static conditions was fully turbulent. This demonstrates the strengthening of the boundary layer during the upstroke due to the unsteady motion. During the downstroke, the wake was found to be largely turbulent, similar to the static airfoil, following a thickening of the boundary layer that led to laminar separation. Similar results were obtained by McAlister and Carr [58] who conducted oscillating airfoil flow visualization tests at a Reynolds number of 21000; however the conditions were characteristic of deep stall. They observed the von Karman vortex shedding to persist up to prior to the dynamic stalling of the airfoil, which they used as evidence of a laminar boundary layer, as opposed to the static airfoil for which transition occurred in the separated boundary layer at only 3°; the vortices originating from the pressure surface were stronger than those from the suction surface. Interestingly, a series of shear-layer vortices formed prior to stall, which coalesced into a single shear-layer vortex. As this vortex reached the trailing edge, the leading-edge vortex was found to form. Based on high-speed movies, they were able to establish that the origin of the vorticity that initially formed the LEV was the forward portion of the airfoil. This finding is supported by the PIV experiments of Shih et al. [83], conducted at a Reynolds number of 5000, who also found the LEV vorticity to originate from the leading edge. It should also be noted that the presence of the shear-layer vortex is limited to very low Reynolds numbers and that above around 5xl04, the LEV is the only dominant vortical structure that forms. Dynamic stall at a low Reynolds number was also studied by Panda and Zaman [69] by oscillating an airfoil between 5° and 25° at Reynolds numbers of 22000 and 44000, and 18 with a large range of reduced frequencies from 0 to 1.6. They conducted both smoke wire flow visualization as well as quantitative wake flowfield measurements using a cross hot wire probe. Their results show that at small angles of attack (a < 8°), both clockwise (CW) and counter clockwise (CCW) vorticity is shed into the wake from the upper and lower surfaces, respectively. As incidence increases, the lower surface continues to shed vorticity; however, the vorticity from the upper surface accumulates near the leading edge leading to the formation of the dynamic-stall vortex. The passage of the DSV into the wake seems to induce a counter-rotating vortex to form at the trailing edge, termed the trailing-edge vortex (TEV), which when in the wake forms a "mushroom" structure. A convection speed of about 60% of the free-stream velocity was observed. It was also observed that the sum of all the vorticity shed into the wake over an oscillation cycle was nearly zero. They did note, however, that the repeatability of their measurements was slightly problematic due to the sensitivity of the laminar boundary layer. 2.4.2 am, Aa and K Focusing now on the more dominant parameters, those describing the unsteady motion of the airfoil, a larger influence on the unsteady airfoil characteristics is observed. The main effect of increasing the mean angle of attack is to shift the flow characteristics from the attached-flow regime, to the light-stall regime and subsequently the deep-stall regime [52]. For small mean angles such that the maximum angle of attack remains below the static- stalling angle, separation of the turbulent boundary layer, if any, is limited to the trailing- edge region; this is termed the attached-flow regime. In this regime, the aerodynamic forces do not deviate significantly from that of the static airfoil. When the mean angle is such that the maximum angle of attack is just around or slightly greater than the static-stall angle, a leading-edge vortex is forcibly formed by the change in pitch direction at the top of the upstroke [58]; this is termed light stall. During light stall, the LEV is less severe as it does not have sufficient time to develop fully. Deep stall, which has been the focus of the previous discussions, occurs for large mean angles and maximum angles that significantly exceed the static-stall angle. In this flow regime, the LEV is the dominant flow structure as it is fully developed [63]. The type of regime that the flow falls into has a significant impact on the 19 aerodynamic damping characteristics of the airfoil. The torsional damping factor Cw is defined as the line integral of the pitching moment coefficient versus angle of attack curve, and is a measure of the degree of vibratory damping the aerodynamic loads impart [61]. If the Cm loop is clockwise, the value of the aerodynamic damping is negative and energy is extracted from the flow causing an unconstrained airfoil to be subject to growth in any pitch oscillations present [61]. A counter clockwise Cm loop is characterized by positive damping and will tend to damping vibrations. With regards to this characteristic, the damping begins positive for small am (i.e. attached-flow), becomes negative once light stall occurs, and then returns to positive values as ara continues to increase and deep stall transpires [63, 52]. Besides contributing to the maximum angle of attack, which controls the flow regime that the flow characteristics will fall, the oscillation amplitude also contributes to the strength and timing of the leading-edge vortex [6]. That is, for large amplitude motions of the airfoil, the LEV becomes stronger and is delayed to larger angles of attack. Note, however, the results of Lee and Gerontakos [46] indicate that the LEV forms in roughly the same location on the airfoil regardless of the value of Act. Also, no significant difference in the peak loads was observed when the oscillation amplitude was changed as long as the maximum angle of attack was kept constant. The role of the reduced frequency has been observed to be the single most dominant parameter. Increasing the reduced frequency results in increased LEV strength and peak load and moment coefficients, increased hysteresis, delayed boundary-layer events and LEV shedding, and increased dynamic-stall angle [56,62,6,59,41,8,69]. In fact, McCroskey et al. [62] were able to cause the airfoil to stall during the downstroke as opposed to the upstroke by oscillating the airfoil with a K = 0.25. Notably, the most important effect of the reduced frequency is to control the degree of unsteadiness. At very low K, below 0.05 for example, the flow is considered quasi-steady. On the other hand, Martin et al. [56] point out that very small oscillation amplitudes and excessively high reduced frequencies are not representative of the dynamic stalling process experienced by helicopters. Therefore, not all investigations into oscillating airfoils are relevant to helicopters, as is the case regarding the work of Bass et al. [3], whose parameters were Act = 1 - 5 degrees and K = 0.5 - 10. In the case of a ramping airfoil, as opposed to an oscillating airfoil, the pitch rate replaces the reduced frequency as the most dominant parameter. The results presented in 20 Refs. 19, 38, 53 and 94 all indicate that increasing the pitch rate causes: 1) a delay in the development of the various flow events to larger angles; 2) a delay in the dynamic-stall angle; 3) a strengthening of the vortex; and 4) increased maximum lift and peak negative pitching moment coefficients. Concerning the lift-curve slope C/0 prior to the formation of the LEV, an important characteristic for a pitching airfoil, there seems to be some conflicting conclusions. Francis and Keesee [19] have determined that the lift-curve slope increases with increased pitch rate, a finding which contradicts the results of Lorber and Carta [53] and Jumper et al. [38], which were determined through experimental and theoretical studies, respectively. Moreover, Lorber and Carta found the convection speed of the vortex to vary from 13% to 33% of the free-stream velocity for non-dimensional pitch rates of 0.001 and 0.02, respectively, but Robinson et al. [79] and Shih et al. [83] found a convection speed on the order of 40% of Uoo. Note, however, that the above-mentioned discrepancies may merely be due to the different Reynolds numbers employed in each of the studies. Interestingly, Francis and Keesee [19] do show that there exists "a point of diminishing returns" and that stall is delayed to a lower degree at higher pitch rates than at lower pitch rates. Also, maximum performance was achieved when the pitching motion does not exceed the dynamic-stall angle (performance is defined as the area between the dynamic lift curve and maximum static lift value). 2.4.3 Pitching Axis Location One aspect of the airfoil motion that has generally been taken for granted has been the pitching axis location. Traditionally, airfoils have been pitched about the %-c location as this is the approximate location of the aerodynamic center for angles below the static-stall angle. It turns out, however, that McAlister et al. [59] showed that the !4-chord location is an appropriate pitch axis since the motion of the center of pressure during the stalled portion of the cycle is centered at about the K-chord. Despite this, by varying the location of the pitching axis, Jumper et al. [37] and Visbal and Shang [94] were able to document its influence on the flowfield. Interestingly, the two investigations gave contradictory results. Jumper et al. found that although there is clearly an effect of pitch location, which is to delay stall as the pitch location is shifted downstream, it is relatively small compared to the effect 21 of pitch rate. Visbal and Shang on the other hand demonstrate a significant delay in LEV formation and reduction in its strength and Q>max as the pitching axis was moved towards the trailing edge. It should be noted, however, that the range of pitch rates that each investigation employed were an order of magnitude different (i.e. Jumper et al. and Visbal and Shang used non-dimensional pitch rates between 0.005-0.06 and 0.03-0.3, respectively). 2.4.4 Three-Dimensionality Effects A study by Schreck and Helin [81] focused on the unsteady vortex dynamics over a finite pitching wing at Re = 69000 to document the effects of a free end on the flow phenomena, in particular the leading-edge vortex. The wing was pitched from 0° to 60° about the 0.33-chord location at non-dimensional pitch rates between 0.05 and 0.2. The surface pressure distributions up to 80% wingspan were measured, and flow visualization in a water tunnel by ejecting dye from a slot machined into the wing along its leading edge was conducted to complement the pressure data and to corroborate their conclusions. Prior to LEV formation, the spanwise normal force distribution indicated a relatively two- dimensional distribution. As the LEV formed, they found the LEV to take on the shape of an arc, being closer to the leading edge at the wing root and tip and slightly further downstream towards the center. The center portion of the LEV filament subsequently became lifted away from the surface of the wing. Evidence of disruptions in the LEV that were precursors to the vortex arching was observed. Moreover, it seems that the LEV became anchored to the same location near the wing tip, as it is observed not to move, while at the root of the wing the LEV convected downstream. In fact, by a = 39.2° the LEV had reached the trailing edge at the root whereas at the wing tip it remained near the leading edge. This caused the wing to stall first in the vicinity of the root and later on near the tip. An accumulation of streamwise vorticity, due to the tip vortex at the wing tip and the junction vortex at the wing root, and the effect of the image of the vortex arc in the splitter plate positioned at the wing root, were determined to be the causes of the halted and accelerated convection of the vortex at the tip and root of the wing, respectively. 22 2.4.5 Boundary-Layer State The consequence of the state of the boundary layer in the leading-edge region on the overall flow over the oscillating airfoil was somewhat unknown until McCroskey et al. [62] and Carr et al. [6] conducted similar experiments with a clean airfoil and one fitted with boundary-layer trips, which promoted transition prior to when laminar separation could occur. Their results show that qualitatively, the flow remains relatively invariant as do the aerodynamic loads, however, quantitatively, there are some observed differences in the dynamic-stall angle, the degree of hysteresis, and the detailed features of the flow separation. 2.4.6 Airfoil Shape Lastly, some effort has been made to characterize the variation in dynamic-stall characteristics with airfoil shape, with the objective of designing an optimum airfoil shape. In Refs. 62 and 6, the leading-edge region of a NACA 0012 airfoil was modified in different ways by reducing the leading-edge radius, sharpening the leading edge, or extending the leading edge with camber. Their goal was to determine the sensitivity of the flow to leading- edge shape. In doing so, they demonstrated that shape is of secondary importance, similar to boundary-layer state, Mach number and Reynolds number. In another attempt, a group of researchers led by McCroskey [63] studied the flow over and the aerodynamic loads on airfoils of various shapes (8 in total), comprising of a range of thickness and camber distributions. They found that during deep stall, the flow is dominated by the leading-edge vortex and therefore any difference between airfoils was deemed insignificant in comparison. They did conclude, however, that the airfoils that showed superior static-stall characteristics were more inclined to behave better when undergoing an unsteady motion. As further proof of the insensitivity of the overall flow structure over a dynamic-stalling airfoil to airfoil shape, Geissler et al. [24] subjected a supercritical airfoil to dynamic stall and noted the same global flow structures as on more traditional airfoils. 23 2.5 Theoretical / Numerical Considerations Despite the highly complex nature of the dynamic stalling process, much progress has been made on the theoretical and numerical fronts. The following section is by no means a thorough treatise on all of the theoretical and numerical studies that have been conducted regarding unsteady airfoils. Rather, a glimpse into different techniques used to model the flow over an unsteady airfoil is provided. This, however, is not to diminish the importance of theoretical and numerical work. In fact, the modelling of dynamic stall is an important step in the evolution of its study and its successful control. It may be said that the theoretical study of oscillating airfoils began with the work of Theodore Theodorsen in his treatise on the determination of the aerodynamic loads on an oscillating airfoil [89]. Based on potential flow theory and the Kutta condition, he was able to express the lift and moment in terms of the parameters describing the airfoil geometry, airfoil motion, and Bessel functions. Limitations to this theory, however, include small amplitude oscillations. Nevertheless, this theoretical solution has been the basis for many other theoretical studies of unsteady aerodynamics, one of which is the work of Rennie and Jumper who profited from the inclusion in Theodorsen's theory of the effect of a trailing-edge flap. Further details are reserved for discussion in subsection 2.6.1. McCroskey [60] used thin airfoil theory to derive simple formulas to describe the inviscid flow over an oscillating airfoil. He found that if the oscillation parameters are such that the boundary layer remains attached (i.e. it does not interact appreciably with the free- stream flow), then the inviscid theory agrees well with experimental measurements in regards to laminar separation. This indicates that under these conditions unsteady viscous effects are minor in comparison to unsteady potential flow effects. This is based on the principle that boundary-layer separation correlates to a unique value of the leading-edge adverse pressure gradient, and that the same boundary-layer process will occur under the same pressure gradient conditions, but at a larger angle of attack. On the contrary, when the airfoil is subject to dynamic-stall oscillations, this hypothesis was found to fail, underestimating the angle at which dynamic stall begins. This shows the importance of viscous effects in delaying dynamic stall. In collaboration with Philippe, McCroskey furthered the above concept to include viscous effects [64]. Using the method in Ref. 60 as a starting point, they modeled 24 the turbulent boundary layer by including eddy viscosity in the time-dependent mean momentum equation. This is a form of the classical thin boundary-layer approach. Viscous- inviscid interactions were excluded, however, from this model. In comparison to experimental results, the limitations of this model were apparent, as it did not predict the formation of the dynamic-stall vortex. This was presumably due to the deficiency in or lack of the modeling of bubble bursting, the turbulent boundary layer, turbulent separation and/or interaction between the boundary layer and free-stream flow. Jumper et al. [37,38] studied the effects of the unsteadiness of the flow (neglecting the wake) and the motion of the airfoil, in both tangent and normal directions to the surface, using a modified momentum-integral method. They validated the results predicted by the model against flow visualization and surface pressure measurements. Their results indicated that the increment in the lift coefficient for a NACA 0015 airfoil pitching at a constant rate about the midchord could be determined using the relation AC, = 3.14 (XND =0.5ca/uoois the non-dimensional pitch rate and t/c is the thickness ratio. This increment is due to the rotation of the airfoil. They also found that the effect of the pitching motion on the lift-curve slope C/a for a flat plate could be estimated by the relation 3 C/a =3.6 + 2.68exp(-aNDXl0 /4.216). This is caused by the vortices being shed into the wake causing a "time lag" thus resulting in a higher lift coefficient in the unsteady case compared to the steady case for a given angle of attack. In their study of the effect of pitching axis location, they found that the slope of the Q curve is independent of the location whereas the increment in the lift coefficient does depend on pitch location. It is of note that the momentum-integral method provides a way of studying the effect of the pitch location on separation. The work of Ericsson and Reding [16,17] constitute one of the many dynamic stall prediction efforts. Their work focuses mainly on the ramping NACA 0012 airfoil. They describe unsteady stall as being composed of or characterized by two different flow phenomena, the first being quasi-steady in nature and the second being transient in nature. The first comprises a delay of stall due to time-lag and boundary-layer-improvement effects. The second involves the forward movement of the separation point and the following "spillage" of a leading-edge vortex. The time-lag effects result from an increase in angle of 25 attack before a variation in the state of the flow can influence the separation-induced aerodynamic loads, or in other words, due to the time that is required to convect the boundary-layer reaction to a change in pressure gradient from the leading edge to the separation point. They suggest that the dynamic overshoot of the static-stall angle can be subdivided into two parts: Aati, which simply shifts the static characteristic in the a(t) frame due to a purely convective flow time-lag effect, and Aas = Aasi + AaS2, which generates the large lift coefficient overshoot over the maximum static value. The contribution of Aocsi comes from the forward motion of the separation point and the AaS2 increment originates from the formation and shedding of the leading-edge vortex. The accelerated flow and moving wall or "leading-edge-jet" effects, as described by Ericsson and Reding, increase the tangential wall velocities and improve the boundary-layer characteristics during the upstroke portion of the oscillation cycle. They both contribute to Aasi, which results in a delay in flow separation to a higher effective angle of attack and a considerable overshoot of static stall. Once the static-stall angle has been exceeded by Aasep = Aotti + Aasi, Ericsson and Reding propose that a massive separation of the boundary layer occurs, caused by the upstream motion of the separation point and the subsequent formation and convection of the leading- edge vortex. This formation and motion of the LEV dominate the lift increase and contributes to AaS2- It is important to note, however, that Ericsson and Reding's model does not predict the presence of a thin layer of flow reversal in a thickened turbulent boundary layer, which has been experimentally identified, nor does it describe the nature of the leading-edge vortex, after its formation, as the cycle ensues. With the goal of making available a simple and practical technique to predict the unsteady airloads on an oscillating airfoil, a method that makes use of the response of an airfoil to a step change in operating conditions using linear aerodynamic theory has been developed. This is termed the indicial response and has been extensively developed by Leishman [48-52]. The premise behind this theoretically based method is that the aerodynamic loads of an oscillating airfoil may be approximated by the superposition of incremental step inputs in angle of attack and pitch rate via Duhamel's superposition principle. A thorough breakdown of this method is provided by Leishman in his book "Principle's of Helicopter Aerodynamics" [52]. The advantage of this method is its computational efficiency and the ease with which it may be included in the aeroelastic 26 analysis of helicopter rotor blades. One main drawback, which limits this method's utility, is its basis in linear aerodynamic theory, thus making it unsuitable for application to any problem involving significant amounts of flow separation, if any, due to the nonlinearity in the behaviour of such a flow. Nevertheless, Leishman has demonstrated good correlation between this method and the results of numerous experimental investigations using different airfoil sections and performed at different flow facilities. Prediction of lift, drag and pitching moment were achieved. This theoretical model is the basis for Nguyen's higher harmonic control studies discussed in subsection 2.6.4 [67]. Another approach is presented by Mateescu and Abdo [98], in which they were able to generate efficient and simple closed form theoretical solutions for unsteady flows past oscillating airfoils by a method using velocity singularities. The basis for this method is the determination of the contributions of the leading edge and ridges, which they define as points on the airfoil where the boundary conditions change, in the form of velocity singularities in the expression of the fluid velocity and pressure coefficient. This method has been developed for airfoils equipped with oscillating ailerons, as well as for flexible airfoils and ailerons. The results match very well those previously reported by researchers elsewhere obtained with different theoretical techniques. Similar to Leishman's approach, however, its basis in linear aerodynamic theory makes it unsuitable for application to any problem involving flow separation. Fairly recently, Ko and McCroskey [42] investigated the effects of using different turbulence models in the simulation of the flow over an airfoil undergoing attached-flow, light-stall and deep-stall oscillations. These are the Baldwin-Lomax model, which is a zero- equation model, the Spalart-Allmaras model, which is a one-equation model, and the k-s model, which is a two-equation model. The Transonic Unsteady Rotor Navier-Stokes (TURNS) code was used to solve the time-averaged, two-dimensional, compressible thin- layer Navier-Stokes equations. Computations were validated using experimental results. In the case of attached-flow, the computed lift, drag and pitching moment curves matched the experimental data rather well no matter which turbulence model was used. This demonstrates that the numerical simulation of the flow over an airfoil oscillating within the static-stall angle (i.e. attached-flow) is well within the state of the art. For light stall, although correlation to experimental data is not as good, it is satisfactory. It does show, however, a 27 preference for the Spalart-Almaras or k-s models. It should be noted that in this case the airfoil does not stall, which normally would not put it in the light stall category. Lastly, in the case of deep stall the results are mixed. Despite the computed aerodynamic loads being unsatisfactory, the computed flowfield does demonstrate the presence of the large vortical structure in the leading-edge region. Oddly, it seems to be attached to the leading edge and does not convect downstream as would be expected. Other numerical works that have been and will be cited in this literature review include those of Visbal and Shang [94], Geissler et al. [24], Ahn et al. [2], Yu et al. [97], Ekaterinaris [15], Joo et al. [36], Sahin et al. [80], Kerho [40], Tang and Dowell [88], Joo et al. [35], and Feszty et al. [18]. Generally speaking, most of these solve the full two- dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations through a variety of methods, details for which can be found in the individual publications. A unique path taken by Yu et al. was to solve the vorticity transport equation for the vorticity field. A very important component to flow modelling concerns the way turbulence is modelled. Visbal and Shang modelled the flow as laminar, doing away with the difficulty of modelling turbulence altogether, and despite this, reasonable qualitative agreement with experimental lift measurements and flow visualization images was achieved. Most others, however, assume a fully turbulent boundary layer flow, choosing to implement one of the following turbulence models: Spalart-Allmaras, k-co shear stress transport model, or Baldwin-Lomax. Most popular is the Spalart-Allmaras turbulence model, as it has been shown to produce results for dynamic stall that agree better with experimental results than others. Moreover, Geissler et al. made an attempt at simulating the location of transition using Michel's criterion, instead of assuming a fully turbulent boundary layer, as most numerical investigations do. Although verification of the location of transition was not made, it was shown that the turbulence and transition modelling could have a profound impact on the results, especially during the downstroke motion, for which most numerical simulations deviate significantly from experimental data. Bousman [4] confirms this fact. Based on a generalization of the results of the above-mentioned numerical investigations, it seems that although most numerical methods have clearly displayed qualitative agreement with experimental results, quantitative agreement still evades attainment, and continues to be the subject of unrelenting research. As the next section will demonstrate, the utility of numerical 28 simulations in studying various flow control methods and applying optimization techniques is great and necessitates continued efforts in discovering new, more accurate and more efficient ways of solving for the flow properties. 2.6 Flow Control The objective of flow control as applied to an unsteady airfoil is to introduce beneficial changes in the flow that improve the airfoil operating characteristics. In the case of an airfoil subject to dynamic stall, the goals would be to delay or completely avoid stall, reduce the negative pitching moment to more moderate values, generate a positive aerodynamic damping, decrease and/or eliminate the hysteresis in lift, all the while maintaining or even enhancing the lift generating capabilities of the airfoil. The various flow control goals, however, are generally in opposition to one another, therefore requiring a difficult compromise to be made [97, 57,26,90]. The nature of the control may be either passive, requiring no energy expenditure, or active, requiring an external source of energy. Furthermore, the benefit gained by the control method preferably should outweigh the cost of implementing the control. Active control systems may also be prescheduled, in that the timing and extent of the control is predetermined, or reactive, in which case the control system responds to the nature of the flow in real-time. Although dynamic stall hinders the aerodynamic characteristics of an airfoil during a significant part of the cycle (i.e. the later portion of the upstroke and the majority of the downstroke), the actual dynamic stall processes or phenomena occur only during a short segment of the oscillation cycle. This suggests, as trends in present research also indicate, that due to the intrinsic inability of passive control schemes to adjust to varying flow conditions, optimum control schemes should be active in nature and should limit their use to a short time period. A detailed review of matters related to flow control is provided by Gad-el-Hak [22] in the article "Flow Control: The Future". In the following section, numerous studies will be presented whose goal is dynamic stall control via a variety of methods. They are categorized into four subsections: those that implement control surfaces, those that deform the airfoil shape, those that excite or energize 29 the flow, and higher harmonic control. Both passive and active control schemes are considered. 2.6.1 Control Surface Flow control via control surface is not a new concept. Fixed wing aircraft have implemented such control schemes for most of their existence in the form of leading-edge slats and trailing-edge flaps of varying configurations. These are fairly efficient in their intended use in quasi-steady flow environments and researchers have found it of interest to study these and other devices concerning their applicability to the unsteady flow environment of oscillating airfoils undergoing dynamic stall. One very simple yet very effective control device is the leading-edge rotating cylinder, which replaces the airfoil leading edge with a motor-driven cylinder that is free to spin. Such devices have been shown in static conditions to delay the stalling of an airfoil to angles of attack in excess of 40°. Freymuth et al. [20] indicate that the concept behind this control scheme is to prevent vorticity production in the leading-edge region and thus avoid flow separation. To verify this, they conducted flow visualization of the flow over a pitching and oscillating airfoil equipped with a leading-edge rotating cylinder. The images showed a minimizing of the wake due to the small amount of separation that was limited to the trailing- edge region. Evidently, the imparting of momentum to the leading-edge flow causes the formation of the LEV to be averted as it was not observed, indicating this technique to be quite effective. Unfortunately, the aerodynamic loads were not measured therefore the precise impact on the lift and pitching moment are unknown. At this point the attitude towards leading-edge flow control as expressed by Sunneechurra and Crowther [87] should be noted. They indicate that the validity and realism of control experiments conducted at Reynolds numbers far below those consistent with flight conditions are questionable. This is due to the presence and lack thereof of a laminar separation bubble at low and high Reynolds numbers, respectively. They also indicate that efforts to trip the boundary layer, and thus avoid the LSB, prove difficult in terms of ensuring turbulence levels representative of flight conditions. Conversely, the results of Shih et al. [83], McCroskey et al. [56, 62, 6, 59, 63], and McAlister and Carr [58] all show that the 30 vorticity in the LEV originates in the vicinity of the leading edge, suggesting that for any technique to control dynamic stall, it must control the leading-edge flow, and therefore be located in the leading-edge region. These facts should be kept in mind during all leading- edge flow control discussions that follow. The extended leading-edge slat has also been studied based on its excellent record of improving the aerodynamic characteristics of a static airfoil. Yu et al. [97] fitted a leading- edge slat to a VR-12 airfoil and conducted tests under deep stall conditions, complementing the measurements with numerical computations of the loads using the ZETA code. They found that similar to a static airfoil, the leading-edge slat delayed the stall angle from around 22° to 24° and reduced the peak negative pitching moment by about 30%. Unlike in the static case, the peak lift was slightly reduced (« 8%); however the post-stall lift coefficient was improved and reattachment promoted, thus reducing the degree of hysteresis. Despite the improved performance, the LEV formation persisted although at a delayed time. Note that qualitative agreement between measured and calculated load coefficients was achieved. This next leading-edge control concept, although not applied to an unsteady airfoil, is still interesting and is therefore included in this review. It consists of a small flap measuring only 4.2% of the airfoil chord in length positioned in the vicinity of the leading edge on the upper surface of a NACA633-018 airfoil [33]. The flap was set to oscillate at various frequencies, amplitudes, mean angles, and motion waveforms. Surface pressure measurements, integrated to yield the lift coefficient, with the airfoil set to a large angle of attack (i.e. 24°) to ensure significant flow separation, show that an excitation frequency corresponding to the vortex shedding frequency in conjunction with rather large flap angles and a symmetric trapezoidal motion was most effective at increasing lift by almost 20% over the airfoil without excitation. The flap works by disturbing the shear layer in such a manner as to result in strong shear-layer vortices that form earlier and remain over the airfoil for a longer period of time due to a slower convection speed. A highly effective control mechanism involving a 25% chord variable drooped leading edge is the subject of a joint experimental/numerical study presented in Ref. 57. One important aspect of this study is the reproduction of typical flight conditions for retreating blade stall on a helicopter, namely M = 0.3 - 0.4 and K = 0.1, which is generally not easily accomplished. The leading edge of the airfoil was set fixed relative to the free-stream flow 31 and therefore relative to the airfoil was seen to be in a continuous oscillatory motion. Results show that this had a profound impact on the flow.Th e reduced leading-edge adverse pressure gradient that the control scheme allows reduced the strength of the LEV considerably, seen as a much reduced pressure footprint, leading to a less severe stalling of the airfoil. Although the peak lift was reduced slightly (8%), both peak drag and peak negative pitching moment were decreased dramatically by an amount of 63% and 31-37% (depending on Mach number), respectively. In addition, the negative aerodynamic damping of the baseline case was completely averted and replaced with positive damping, seen from a single counter clockwise Cm-loop. Not only was the airfoil performance improved relative to the baseline case, it was also better than a fixed drooped leading edge configuration, wherein the leading edge was fixed relative to the airfoil. Notwithstanding, even a fixed drooped leading edge led to improvements by weakening the LEV. Similar results were obtained by Yu et al. [97], for which the LEV formation was completely averted. Like other studies, only qualitative agreement between experimental and numerical results was obtained, although agreement was achieved in the trends of the incremental improvements of the control cases over the baseline case. Changing focus to trailing-edge control concepts, one device that has recently gained attention is the Gurney flap, or more generally referred to as a trailing-edge strip (TES). The Gurney flap, traditionally used on racing car wings to increase down force for added road adhesion during high speed turns, consists of a simple strip mounted normal to the pressure side surface at the trailing edge. Interested in the application of such a simple passive device to the control of the aerodynamic loads on an unsteady airfoil, Gerontakos and Lee [26] fitted a NACA 0012 airfoil with such a device in both normal (i.e. positioned on the pressure surface) and inverted (i.e. positioned on the suction surface) configurations. They found that the trailing-edge strip mounted in the traditional sense (i.e. on the pressure side) led to increases in all components of the aerodynamic loads; that is lift, drag and negative pitching 5 moment all increased. For example, under the conditions used (i.e. Re = 1.06 x 10 , am = 11°, Aa = 5°, and K = 0.05), a 3.2% chord TES led to increases of 26%, 15% and 64% in Q)inax, Cd,max and |Cm,Peak|, respectively. Stall, however, was also promoted to slightly smaller angles. The inverted TES was not capable of alleviating the large negative peak pitching moment to a significant degree, with only a 2% reduction, but did delay dynamic stall, though at the 32 price of a reduced peak lift coefficient (3%) and increased drag (1%). The reason for this is made clear by the important observation that was made, which was the increasingly reduced effectiveness of the inverted TES with increasing angle of attack due to the thickening of the trailing-edge boundary layer in which it operated. This suggests that for an appreciable level of control, an inverted TES should be large enough such that it, at minimum, spans the height of the boundary layer at its thickest. Tang and Dowell [88] continued this work by applying a Navier-Stokes code to investigate numerically this flow control concept. They reproduced the operating conditions of the aforementioned experiments of Gerontakos and Lee. Reasonable agreement was found between the two sets of data. Joo et al. [35] numerically explored the idea of combining two separate control methods with the goal of profiting from each one's benefits. Their simulated airfoil was equipped with a fixed leading-edge droop to benefit from its improved Cm characteristics at the expense of a slightly reduced Q, and a Gurney flap, which improves Q greatly at the expense of a downwards shifting of the Cm curve. Individually, each device behaved as expected from previous studies [57,26, 88]. Their combined effect was to increase lift and the negative pitching moment, to reduce drag, and avoid the formation of a LEV. They used an optimization scheme, using the leading-edge droop angle and length as well as Gurney flap height as parameters, to obtain the best overall performance. Evaluation of the control techniques was based on the peak Q, the minimum Cm near amax, and the minimum Cm near otmin (to account for the unwanted downwards shifting of the whole Cm curve; a potential source of structural problems such as flutter). Their results showed that a 13% increase in Q,max, 60% reduction in -Cm!peak, and 64% decrease in the negative damping area were possible. The works of Rennie and Jumper [77,78] and Rennie [76] focused on the lift control of an unsteady airfoil via a trailing-edge flap and the effectiveness of such a control method. Their basis for control was the theoretical equations for an airfoil equipped with a trailing- edge flap first established by Theodorsen [89]. The theory for a pitching airfoil equipped with a moveable flap was developed and used to preschedule the flap motion, to be verified during experiments. Their findings were that, in fact, the effectiveness of the control surface was greater during motion, nearing the inviscid value, than after it stopped, falling to a steady- state value. This required them to modify the form of the linearized unsteady airfoil theory. 33 By incorporating different coefficients for the during-motion and after-motion portions, the experimental results and theoretical results matched rather well. With this predetermined flap motion, the investigators were able to suppress the increase in normal force caused by an angle of attack ramp of an airfoil from 0° to 7°. On a similar note, Vipperman et al. [93] used a trailing-edge flap to provide gust alleviation as well as flutter boundary extension. Their closed-loop control system, which used the wing pitch and plunging motion as well as the flap position as inputs, successfully achieved these two goals with the flutter boundary being extended by 12.4%. The findings of Rennie and Jumper and Vipperman et al. clearly demonstrate the ability of a trailing-edge flap to control the aerodynamic loads of an airfoil efficiently. Feszty et al. [ 18] therefore undertook the task of conducting a parametric study of the application of this concept to an oscillating airfoil equipped with a trailing-edge flap. They simulated the flow over a NACA 0012 airfoil oscillating with a mean angle of 15°, oscillation amplitude of 10°, reduced frequency equal to 0.173, and at a Reynolds number of 1.46 x 106, using a discrete vortex method. A pulsed motion of the 16% chord flap was used, described by a maximum deflection between +28° and -28°, start time between 0.227t and 0.447c radians, and deflection duration between 22% and 44% of the oscillation period. Comparison of all the results revealed the optimum flap motion, which best alleviated the severely negative peak pitching moment while maximizing lift and minimizing the negative aerodynamic damping, to consist of an upwards flap deflection of significant amplitude (= 20°), short duration (33% of the oscillation period) and a start time at around 0.2571 (i.e. during the second half of the upstroke). This combination of parameters led to a positive aerodynamic damping of 0.25 from a value of-0.17, a reduction of 80% in |Cm,Peak|, and a mere 11% reduction in peak lift. Comparison of the simulated flow between the optimum control and baseline cases revealed this improvement to stem from the weakening of the trailing-edge vortex which, instead of forcing the dynamic-stall vortex to pass over it, is pushed off the trailing-edge by the DSV. This suggests that the TEV plays a vital role where pitching moment is concerned. Recent work at Boeing has focused on the development of a piezoelectric based trailing-edge flap actuator, validating other researcher's efforts on this type of control. Although no aerodynamic measurements were made or presented in Ref. 86, they do indicate that the goals of such a system is to: 1) reduce airframe vibrations by 80%; 2) reduce blade- 34 vortex interaction noise during landing by 10 dB; 3) increase aerodynamic performance by 10%; and 4) alleviate stall so as to improve manoeuvrability. Of significant importance are the pioneering works of Friedmann (see for example Ref. 100), who was first to develop a trailing-edge flap control strategy for the case of a three-dimensional flow. Recognizing that in addition to dynamic stall there are numerous other sources of rotorcraft vibrations, including blade-vortex interactions, blade-fuselage interactions, main rotor-tail rotor interactions, etc, Friedmann did much numerical work to expand the role of the trailing-edge flap using it to control the noise and vibrations caused by not only dynamic stall, but also of the detrimental blade-vortex interaction. Both individual blade control and higher harmonic blade control were investigated. The simulation results demonstrate clear improvements in vibrations and performance and indicate significant benefits obtained from active flap control. This technology has been shown to be so promising that Enenkl et al. [99] also applied trailing-edge flaps for vibration suppression on a full scale rotor, and Eurocopter flew a helicopter equipped with trailing-edge flaps in September 2005. Krzysiak and Narkiewicz [43] extended the idea of flap motion to higher harmonics, oscillating the flap at a frequency twice that of the airfoil. Their combined experimental and theoretical investigation showed that in this situation, the phase shift between the flap and airfoil motions could considerably affect the shape of the aerodynamic loads. However, improvements in the aerodynamic quantities of interest to dynamic-stall control were lacking. Furthermore, in the dynamic stall case, the inviscid theory, as might be expected, did not correlate well with the experimental measurements. 2.6.2 Airfoil Shape Deformation Deformation of the airfoil surface can be a very powerful means of airfoil flow control. This is because small deviations in the airfoil contour, especially in the leading-edge region, can produce large effects on the adverse pressure gradients that form. In addition, the small displacements necessary and the actuators which produce them lend themselves quite readily to active control systems. Three ways in which the airfoil may be deformed will be 35 reviewed in this subsection. These include airfoil thickness variations, deformation of the leading-edge contour, and deflections of the airfoil nose. A numerical investigation on the effect of active thickness variations on the flow over and aerodynamic loads on an airfoil undergoing deep-stall oscillations was conducted by Joo et al. [36]. They simulated an airfoil whose thickness varied between a NACA 0012 profile at the minimum angle of attack and a NACA 0016 profile at the maximum angle of attack. Different rates of thickness transformation were studied. The results show that this type of control was fairly effective at delaying the LEV formation and thus stall. The peak lift and peak pitching moment were also affected, however, in opposite senses. That is, a thickness variation that brought about improved lift (3% increase) also generated increased nose-down pitching moment (5% increase) and vice versa (7.6% reduction in Q,max with a 13% reduction in -Cra,Peak)- Therefore, lift and pitching moment could not be simultaneously enhanced, and the improvements in Cm>peak were rather small. The novel concept of a dynamically deforming leading edge was studied experimentally by Chandrasekhara et al. [9, 10]. Using this technique, the leading-edge pressure distribution could be manipulated by adjusting the leading-edge shape to make it less sharp. With a mere 1.33%c chordwise movement of the leading edge, a 320% change in the leading-edge curvature could be achieved. Flow visualization via point diffraction interferometry indicated that in the case of an "optimally" controlled oscillating airfoil, the formation of a LEV was averted, despite trailing-edge flow separation having reached the leading-edge region. This feat was achieved by reducing the leading-edge flow acceleration, thus lowering the peak suction pressure level, and distributing the pressure gradient, which is indicative of the vorticity production, over a greater area. Note, however, that in order for the flow to respond effectively to changes in leading-edge shape, the change must be done slowly. This work was advanced by Sahin et al. [80], who numerically simulated this control technique. They found that although stall could be delayed somewhat and the flow during the downstroke was greatly improved, stall inevitably happened and improvements in the peak lift and minimum pitching moment were nonexistent. Comparing a dynamically deforming leading edge to the corresponding fixed leading-edge shape, no difference in the aerodynamic loads was found, indicating that it is the shape and not the deformation rate that affects the flow. Note, however, that these results are valid for Mach numbers below 0.4, after which 36 shock-induced dynamic stall occurred and the control case deviated little from the baseline case. Another leading-edge deformation concept that has been developed is that of a drooping nose. The nose of the airfoil is deflected downwards as part of a rigid structure (i.e. there are no joints or gaps in the airfoil surface). Geissler et al. [25] implemented such a device on a numerically simulated oscillating NACA 0012 airfoil. They found that by deflecting the nose downward 10° and back to an undeflected position, a motion spanning the entire oscillation cycle, the peak suction pressure was reduced as a result of a smoothened adverse pressure gradient. This led to a reduction in the DSV strength and a delay in stall. In regards to the aerodynamic loads, the lift was found to change very little while peak drag and minimum pitching moment were both reduced. Somewhat different results were obtained by Kerho [40] who also implemented a leading-edge droop device. Note, however, that the operating conditions were not the same. Geissler et al. simulated a NACA 0012 airfoil undergoing oscillations described by a(t) = 10°+10°sin(cot) at a reduced frequency of 0.3 in a free-stream whose Mach number also varied (M = 0.50-0.23sin(cot)). Kerho on the other hand simulated a Sikorsky SSC-A09 airfoil undergoing oscillations described by a(t) = 100+100sin(cot) at a reduced frequency of 0.075 at both constant and variable Mach numbers (i.e. M = 0.4 or M = 0.40-0.3sin(oot)). Kerho found that with a 10° nose droop angle, which varied between 0° at amin and 10° at amax, stall was delayed significantly and peak lift was also increased, but peak drag and minimum pitching moment increased as well, however were limited to short time periods. Interestingly, by reducing the maximum angle of attack slightly (i.e. to 17° instead of 20°), which brought the flow closer to the light-stall flow regime, and then implementing control, the formation of the leading-edge vortex was completely averted with no loss in the maximum lift coefficient. What's more, by superimposing a reshaping of the leading-edge contour onto the nose droop, a further reduction in the leading-edge suction peak was achieved, which led to the avoidance of LEV formation when nose droop alone was unable to accomplish this. 37 2.6.3 Flow Excitation One concept behind flow excitation is to energize the boundary-layer flow by injecting high-momentum fluid into the boundary layer through blowing, thus allowing it to sustain higher adverse pressure gradients. Conversely, low-momentum boundary-layer fluid may be removed from the flow using suction, which is then replaced by higher momentum free-stream fluid, and thus can sustain larger adverse pressure gradients. Another avenue that researchers have taken is the zero-mass flux periodic excitation, also referred to as synthetic jets. Here, an airfoil is equipped with an internal cavity with either a movable membrane or piston, which alternates between ejecting fluid from the cavity into the boundary layer and removing boundary layer fluid to the cavity. Vortex generators have also been implemented based on their successful application to fixed wing aircraft. Yet another concept is that of the plasma actuator, in which a high ac voltage is applied to a pair of surface mounted copper electrodes separated by a dielectric insulator in order to ionize the surrounding air, forming plasma. These various approaches to flow excitation will now be explored further. The formation of the dynamic-stall vortex is said to occur as a result of the accumulation of reverse flow near the leading edge, owing to the presence of a large adverse pressure gradient, which forces the shear layer to be lifted from the airfoil surface. With the idea that suction in the leading-edge region might avoid the lifting of the shear layer and subsequent vortex rollup by removing the reversed flow, Karim and Acharya [39] studied the effects of leading-edge suction on the flow over a pitching airfoil. Their experiments were conducted over a range of Reynolds numbers, pitch rates, suction timing, and suction-slot size and location. They found that complete suppression of the dynamic-stall vortex is possible; however limitations in the operating conditions often constrained the ability of suction to do so. Ahn et al. [2] numerically studied various control techniques as applied to an oscillating airfoil, of which suction was one. They were able to show that, in contrast to variations in leading-edge nose radius and airfoil thickness which were inadequate in their control of the aerodynamic loads, variable suction (i.e. suction that varied between zero and some predetermined maximum value based on the local Mach number in the leading-edge region or the peak suction pressure) completely averted the formation of the leading-edge 38 vortex and thus dynamic stall. In fact, streamline flow patterns showed no sign of any flow separation. As a result, hysteresis in the aerodynamic loads loops was all but eliminated, peak lift was even increased somewhat, peak drag and peak negative moment were eliminated, and the airfoil never stalled. As stated previously, by injecting momentum into the boundary layer via blowing, the flow may overcome large adverse pressure gradients. The numerical results of Yu et al. [97] indicate that with blowing equivalent to twice and four times the free-stream velocity, the DSV does not form and therefore the airfoil does not undergo dynamic stall. Although drag and pitching moment are mitigated, so is lift unless the injection rate is high. Even with a blowing velocity of four times that of the free-stream, the peak lift matches the uncontrolled case with anything below causing a reduction in C/,max. Furthermore, it is interesting to note that lift during the downstroke exceeds that during the upstroke, an observation that they attribute to a sustained region of separated flow in the trailing-edge region characterized by a rather low pressure, thus contributing to increased lift. An experimental investigation into dynamic-stall control via steady blowing was conducted by Weaver et al. [95]. In this study, conducted at a Reynolds number of 1 x 105, an oscillating VR-7 airfoil was equipped with a blowing slot located at the quarter-chord 2 location, injecting fluid at a mean blowing coefficient C,, (= 2(h/c)(Vs/Uoo) ; where h is the slot height and Vs is the mean slot-exit velocity) up to 0.66. For an airfoil oscillation described by a(t) = 10° + 10°sin(a)t) with K = 0.15 and C^ = 0.56, the effect of control was to delay stall, increase the lift-curve slope of the linear portion of the upstroke (21%) and the peak lift (31%), decrease drag due to the jet thrust caused by the blowing, decrease the peak negative pitching moment (39%), modify the Cm curve such that it is characterized by positive damping, and reduce the extent of the lift-curve hysteresis. Furthermore, increasing the blowing velocity amplified the changes due to control. They also investigated the effects of reduced frequency and airfoil mean angle of attack. Their results showed that, generally speaking, changes in these two parameters only altered the magnitudes of the differences in the aerodynamic characteristics. However, one significant difference observed when a mean angle of 15° was used was that the peak negative pitching moment instead of decreasing was increased relative to the uncontrolled airfoil. Flow visualization pictures suggested to the authors that this might be a result of the formation and trapping of a separation bubble, which 39 was allowed to grow in strength due to its prolonged presence on the airfoil. Eventually, when the blowing was unable to preserve the bubble, it passed over the airfoil and into the wake, causing a sharp drop in pitching moment that exceeded that of the uncontrolled case. To supplement these results, they also conducted some pulsed blowing tests covering a small range of pulse rates. Overlap of the aerodynamic loads showed that 1) variations in pulse rate had very little effect on the loads, and 2) pulsed blowing was slightly superior to steady blowing in terms of maximum lift coefficient and hysteresis level reduction. A numerical investigation into the pulsating jet-flow control of dynamic stall was conducted by Ekaterinaris [15]. The jet velocity was characterized by V(t)jet = V0 + Vacos(27t#) (where V0 is the mean jet velocity, Va is the amplitude andfj is the jet pulsation frequency) with a value for reduced excitation frequency F+ (= jjC/uoo) of 6.3 and an 2 oscillatory blowing momentum coefficient C^ (= 2(h/c)(Vj/u00) ; where h is the slot width and Vj is the jet velocity oscillation amplitude) of 2.5%. Comparison between zero net mass flux (i.e. when V0 = 0) and nonzero net mass flux showed zero net mass flux to be superior mainly due to much improved lift characteristics. Various locations of the jet were also considered, and comparison between jets located at 0, 10 and 70% chord indicated better control of the flow, and thus the aerodynamic loads, by a jet located at x/c = 0.7. In fact, the combined effect of a jet with zero net mass flux located at the 70% chord location, and operating with the above-mentioned values for F+ and C^ was the suppression of the dynamic-stall vortex. This led to much improved lift-curve hysteresis, increased maximum lift coefficient, and significant reductions in the peak drag and negative pitching moment coefficients. Based on the idea that it is not necessary to implement control throughout the entire oscillation cycle, but that it should be limited to as small a time interval as possible, Mochizuki et al. [65] investigated what the appropriate time to start employing control, in the form of a wall jet located at the 4% chord location, on the flow over a pitching airfoil subject to dynamic stall is. They found that a start time prior to a non-dimensional time of 6c/u<» before the occurrence of flow separation, which includes a time lag due to their mechanical apparatus of 4c/uoo, required the same minimum jet velocity to suppress separation, and that anything after this required a significant increase in jet velocity. Also, the minimum energy required to suppress separation was found to be only 10% of the free-stream energy. Their 40 experiments did not include, however, measurements of the aerodynamic loads; therefore the actual effects of the control mechanism on the lift, drag and pitching moment are unknown. A variant of the blowing concept is the pulsed vortex generator jet, which consists of jets of fluid being ejected from the airfoil leading-edge region normal to the surface. The principal behind this method of control is that through these jets, vortices are generated that enhance mixing between the free-stream flow, characterized by high momentum, and the boundary layer flow, characterized by low-energy fluid. The end result is an ability to withstand larger adverse pressure gradients. Magill et al. [55] applied this method using a model-based observer approach to a rapidly pitching airfoil. Their results indicated that a significant mitigation of the leading-edge vortex was possible. Furthermore, it was not necessary for the jets to be active throughout the entire oscillation cycle, but were only required during the second quarter of the cycle between the mean and maximum angles of attack during the upstroke. Improvements on the order of 25-35% in lift in the absence of moment stall were realized. Singh et al. [84] also implemented air-jet vortex generators, however of a constant flow rate, with the intention of impeding the upstream propagation of trailing-edge flow separation (i.e. flow reversal), and thus avoid stall for as long as possible. The configuration used was of a series of rectangular slots along the wingspan at two streamwise locations, x/c = 0.12 and 0.62, with the jet exiting at an angle of 30° and skewed relative to the free-stream flow by 60°. With only the first row of vortex generators activated, a delay in stall of both lift and pitching moment was achieved, along with reductions in peak negative pitching moment (11-20%), negative pitch damping, and lift-curve hysteresis. Furthermore, the leading-edge vortex was weakened, the secondary vortex observed in the baseline case was either averted or very weak, and flow reattachment was promoted. Implementation of the second set of vortex generators further downstream, either on its own or in conjunction with the first set, showed a diminution in performance improvement. Extensive effort to characterize the control of dynamic stall via periodic excitation was put forth by Greenblatt et al. [30,31,32]. In a series of papers, they describe the effects of excitation location, duty cycle, airfoil oscillation reduced frequency, mean angle of attack, momentum coefficient, and excitation frequency. It has been well documented that, due to the extreme sensitivity of shear layers to disturbances, the optimally operated periodic 41 excitation, or synthetic jet, causes a resonance to occur in the shear layer. This leads to the formation of coherent structures at the pulsed frequency, or one of its harmonics, which become discrete vortices who, through merging, grow in size. These larger vortices mix free- stream fluid, characterized by a high level of momentum, with the highly retarded and exhausted boundary-layer fluid, thus energizing it [91]. A detailed characterization of the formation and evolution of synthetic jets is presented by Smith and Glezer [85]. The main conclusions that they draw are: 1) leading-edge excitation increases maximum lift slightly, eliminates lift stall and thus lift-curve hysteresis, and reduces peak negative pitching moment; 2) unlike blowing, that requires a minimum momentum coefficient to be effective, periodic excitation brings about improvements regardless of the momentum coefficient and excitation frequency; 3) intermittent excitation, that is excitation limited to angles above the static-stall angle, has no effect on lift and pitching moment, however it reduces form drag; 4) aerodynamic load dependence on the oscillation frequency is considerably reduced when control is implemented; and 5) flap-shoulder excitation, that is excitation located at the shoulder of the airfoil trailing-edge flap at x/c = 0.75, produces increases in lift that are maintained throughout the entire oscillation cycle and the abolition of moment stall, resulting from the suppression of trailing-edge separation. Similar results were also obtained by Traub et al. [90, 91], who also studied periodic excitation, which they referred to as synthetic jet actuators. They also demonstrate an interesting fact. In contrast to the widely held view that dynamic-stall control should be applied to the leading-edge region, it is the flap shoulder excitation which proves superior. In other words, for the same maximum lift coefficient, the airfoil can operate at a lower mean angle of attack if flap shoulder excitation is used, which leads to less lift-curve hysteresis, a smaller peak negative pitching moment, a reduction in drag, and an increase in C/>max - Q,mi„. A successful implementation of a closed-loop control system, using zero-net-mass- flux actuators, was demonstrated by Pinier et al. [72]. Their control system was based on two concepts. First, they used modified linear stochastic measurement (MLSM) to formulate an accurate representation of the instantaneous velocity field from the measured surface pressures only. They then used proper orthogonal decomposition to construct a set of empirical functions that are fundamental to the flow via the velocity field determined from the MLSM. These functions were then used as inputs to the control system. Pinier et al. 42 describe this method in much more detail, and interested readers should refer to their publications. In using this control system, they were able to demonstrate effective suppression of the trailing-edge flow separation in real time, as applied to both a static and pitching airfoil. They showed that closed-loop control, by using the status of the flowfield to determine whether control is warranted or not and the level of control, provides significant energy savings compared to open-loop control. Moreover, by comparing the level of actuation as a function of angle of attack for open-loop control that is always on (i.e. control is started before the angle of attack is increased) to open-loop control that is turned on after the angle of attack is increased, a disparity in energy requirement is clearly shown. It takes much more effort to reattach a separated boundary layer than to maintain an attached boundary layer, especially near stall, suggesting that although control may not be warranted, it should always be enabled in the case of closed-loop control. Another configuration, which has been used on stationary wings to delay separation, has been implemented on a pitching wing by Traub et al. [90], and that is an array of vortex generators. These delta shaped structures protrude from the airfoil surface forming a zigzag shape along the wingspan. Each one is at a relative angle of 15° with respect to the free- stream flow. They work by generating small streamwise vortices that mix free-stream flow into the boundary layer, thus energizing it. At low airfoil pitch rate, the dynamic-stall vortex formation was promoted and its strength was enhanced; this led to an earlier stall with a higher maximum lift coefficient. Pitching moment, however, was not affected significantly. At higher pitch rate, again DSV formation was promoted, but maximum lift coefficient was reduced, as was the peak negative pitching moment somewhat. A combination of vortex generators with synthetic jet actuators demonstrated the more effective control imparted by the synthetic jet actuators compared to the vortex generators. Lastly, plasma actuators form a unique concept of control. It is thought that by ionizing the air surrounding the actuator, placed at the leading edge, the ensuing plasma will result in a body force due to its interaction with the electric field gradient produced by the asymmetric electrode arrangement. This body force induces a flow in the downstream direction, thus energizing the boundary layer. Post and Corke [73] implemented such an actuator on an oscillating NACA 0015 airfoil. They studied three types of actuation. The first form, steady actuation, seemingly averted DSV formation during the upstroke. This led to the 43 absence of the rapid lift growth due to DSV formation, and growth and the rapid drop in lift at the beginning of the downstroke. However, moment stall, although slightly delayed, still occurred and the peak negative pitching moment remained unchanged. The second form, unsteady actuation, had mixed results depending on the forcing frequency. For low frequency, the lift curve remained essentially unchanged except for the promoted reattachment during the downstroke; however, the pitching moment was modified significantly, with a reduction in the peak negative pitching moment, a delay in moment stall, and a reduction in the overall negative damping. Flow visualization showed a sequence of vortices to have formed on the upper airfoil surface. At a higher frequency, pitching moment followed the uncontrolled curve somewhat closely, but an increase in lift throughout the entire oscillation cycle was observed, especially during the downstroke. Early flow reattachment compared to the baseline case was maintained here as well. The third form consisted of intermittent steady control based on a predetermined schedule. Results for this case showed some improvement in the lift curve, in terms of a more gradual stall and promoted reattachment, but not much of an improvement in the pitching moment. 2.6.4 Higher Harmonic Control Higher harmonic control (HHC) forms the basis of another conceptually different form of control, in which small amplitude motions (i.e. on the order of a couple of degrees or less) at harmonic frequencies above the rotor rotational frequency are superimposed onto the blade motion. For a conventional helicopter, the lack of smoothness, as a result of the variation of local velocity and blade angle of attack, caused by effects other than the swashplate introduced smooth cyclic pitch, could eventually result in vibration. Many researchers have implemented control systems based on this concept with vibration suppression, dynamic stall alleviation, and extended speed limitation in mind. The pioneering analytical study was first performed by Payne [71] who showed the potential effectiveness of HHC in alleviating retreating-blade dynamic stall. He concluded that a combination of higher harmonics (i.e. larger than the second harmonic) could extend the dynamic-stall based limitation in forward speed past the advancing blade compressibility limit. In addition, a second harmonic motion may impart stability improvements. 44 Experiments on a full-scale helicopter equipped with a HHC control system were conducted by Wood et al. [96] throughout the flight envelope to determine the degree of vibration suppression provided by 4/revolution, also referred to as 4P, blade actuation. Improvements in vibration levels clearly were achieved, and reductions in pitch link loads as well as bending moments were also observed with only small implications for aerodynamic performance characteristics; all this with an excitation of only +/- 0.33 degrees. Shaw et al. [82] achieved a condition characterized by the complete and continuous alleviation of hub forces on a dynamically scaled model rotor using 3P HHC pitch variations below +/- 3 degrees. Similar to Wood et al., they only observed a limited impact on the rotor system loads and performance. More recently, Nguyen [67] conducted a numerical investigation to study whether HHC (2P, 3P, and/or 4P) with amplitudes below 1 degree is capable of suppressing dynamic stall. His results show that indeed stall can under certain conditions be suppressed, however that does not imply that rotor performance will simultaneously be improved. Conversely, improvements in rotor performance could be obtained, though at the cost of stall behaviour. Despite all these efforts, however, no detailed dynamic load distributions on the blade were ever reported. 2.7 Particle Image Velocimetry The particle image velocimetry technique has progressed significantly in the past decade becoming an integral part of an experimentalist's tool box to study flows non- intrusively and in a way most other techniques are incapable. PIV provides the entire instantaneous flowfield, in terms of both velocity and vorticity. Moreover, the velocity fields obtained via PIV can be used to evaluate the pressure field from which the aerodynamic forces can be calculated [21,44,66,92]. This is especially valuable in unsteady flows, which require both spatial and temporal information and for which more traditional measurement techniques are less capable of providing the same quantity and quality of data in the same amount of time. In recent of years, advances in computer and imaging technologies have made PIV measurements even simpler in application and the quality of the data much better. Where the PIV technique still encounters some difficulty is in flows where separation is a dominant factor. This is especially true for oscillating or pitching airfoils in the dynamic stall 45 regime. This is confirmed by the relatively few published reports on the application of PIV to these types of flows. As the flow around an airfoil subject to deep dynamic stall with trailing- edge flap control is characterized using PIV in the current investigation, this section is limited to the discussion of two investigations that implemented PIV to study the flow over an unsteady airfoil. First to be discussed are the whole-field measurements of the flow around a pitching NACA 0012 airfoil conducted by Shih et al. [83]. It should be noted, however, that the experiments were carried out at the very low Reynolds number of only 5000. Through the velocity measurements, they identified the difference between the flow separation that occurs on an unsteady airfoil (i.e. a thin layer of flow reversal in an otherwise thickened however still attached boundary layer), and that of a static airfoil. They also identified the formation of a counter-clockwise rotating trailing-edge vortex as the LEV forms, as well as a shear-layer vortex near the mid-chord. Most interesting is their observation that the vorticity in the LEV originates from the separated shear layer at the leading edge. The peak vorticity, however, in the LEV is lower than that found in the separated shear layer, and continues to decrease as the vortex convects over the airfoil and is shed into the wake. This is followed by a reduction in the non-dimensional upper surface circulation from a value of about 1.8 down to 0.8 as it is shed into the wake. Although the aerodynamic loads were not measured, this suggests a likewise reduction in lift. The fluctuating airloads that are often observed once the airfoil attains the maximum angle of attack were also explained via the PIV measurements as resulting from the repeated flow reattachment and subsequent separation that occurs until it reaches a state consistent with a static airfoil at that angle of attack. Lastly, a very important contribution that this work makes is in documenting the reproducibility of the flow. The instantaneous vorticity distributions for four separate experimental runs were presented and show very good agreement, despite small phase differences between them. Also worthy of mention is the work of Rank and Ramaprian [75] who conducted particle image velocimetry measurements of the instantaneous flow velocity around an oscillating airfoil undergoing light dynamic stall conditions. Conducted at a Reynolds number of 1.52 x 105, their experiments implemented a NACA 0015 airfoil model oscillated about its quarter-chord axis with a mean angle of 15 degrees, oscillation amplitude of 4 degrees and reduced frequency of 0.05. It is unfortunate that although the velocity and 46 vorticity fields were measured and computed, respectively, only the instantaneous streamline patterns were presented. Despite this, some valuable information was obtained. The results indicated that a thick layer of slow moving fluid formed over the airfoil, which, just after the airfoil exceeded the mean angle, encompassed recirculating flow (i.e. flow reversal) that propagated upstream. No formation of a leading-edge vortex was experienced during the upstroke and therefore the airfoil did not undergo a catastrophic stall. Immediately as the downstroke began, the flow separated from the leading edge and formed what they referred to as a shear-layer vortex. This vortex, whose vorticity was found to be rather low, convected downstream over the airfoil and was shed into the wake at around the mean angle during the downstroke. It seems, however, that what they describe is indeed a LEV despite their affirmation to the contrary, which they base on the relative weakness of the SLV. Interestingly, they did note a nonperiodicity to the reattachment process, in that the flow varied slightly from cycle to cycle during this period. This phenomenon was also observed by Shih et al. [83] during their low-Reynolds number (i.e. Re = 5000) PIV experiments on a pitching airfoil. 2.8 Objectives Based on the above literature review, it may be concluded that the trailing-edge flap control mechanism has clearly demonstrated its capacity to generate some significant improvements in rotorcraft performance, particularly in manipulating the aerodynamic loads and suppressing vibrations. Despite the significant efforts put forth and advancements that have been made, shortfalls in current research do exist. In this section the objectives of this work will be stated, and will be justified by explaining how they makeup for the shortfalls in current research, are original and contribute to knowledge. Note that although helicopter rotor blades are subject to impulsive loads and vibrations from numerous sources, the main focus of this work will be those only resulting from dynamic stall. 1. To examine the feasibility of using a trailing-edge flap to alleviate the adverse characteristics of a dynamic-stalling airfoil through experiment. Although the trailing- edge flap control of a dynamic-stalling airfoil has been previously studied by Feszty et al. 47 [18], it was a numerical study employing Computational Fluid Dynamics, the findings of which have yet to be verified experimentally. Therefore this work will represent a unique effort to validate the findings of that study without which would remain somewhat questionable. 2. To understand the flow mechanism by which the trailing-edgeflap exerts its control. In their numerical study of the trailing-edge flap control of a dynamic-stalling airfoil, Feszty et al. [18] attribute the ability of the flap to manipulate the aerodynamic loads to a single fluid structure, the trailing-edge vortex that forms in the vicinity of the trailing edge as the leading-edge vortex convects over the airfoil. In general, however, this fluid structure is not always observed, therefore in the absence of a trailing-edge vortex the physical mechanism by which the trailing-edge flap exerts its control over the aerodynamics loads must be different. The true nature of this, however, remains a mystery thus far and requires experimental verification. 3. To document the effect of the flap motion profile, including start time, flap upwards deflection rate, total deflection duration, steady-state time period, flap return motion rate, deflection magnitude and deflection direction, on the effectiveness of the control. Currently, a very detailed parametric study of the effects of the flap motion profile on the effectiveness of the control of the aerodynamic loads does not exist; the study of Feszty et al. [18] was rather limited. This is an essential step in determining which flap motion parameters are most important, and in the definition of an optimum flap motion profile. 4. To define a set of guidelines with which to determine the flap motion profile based on the desired level of control. Most studies in which flow control is the focus, present the data in the form "a change in this control parameter has this effect on the aerodynamic behaviour". A practicing engineer, however, would be more interested in a set of guidelines which dictate how the control system should behave based on the desired effect on the aerodynamic loads. Therefore, the data obtained for the third objective above will be reorganized into this form, thus increasing its usefulness. 48 5. To identify an optimum control strategy for alleviating the adverse effects of dynamic stall. Although Feszty et al. [18] do identify an optimum control strategy, this should be verified experimentally to see if they agree. 6. To use the technique of particle image velocimetry to document the flowfield around the dynamic-stalling airfoil with trailing-edge flap. Few researchers have attempted applying the particle image velocimetry technique to measure the flowfield around an airfoil subject to dynamic stall due to significant experimental difficulties involved. Furthermore, no one has ever done so with an airfoil equipped with trailing-edge flap control. Therefore, not only will this be a unique contribution, it is an essential step in verifying how the dynamic flap control affects the flowfield. 7. To assess the characteristics of flap control as applied to an airfoil undergoing attached-flow oscillations. Previous investigations into flap control have focused on the more complex scenario of dynamic stall. There hasn't been any effort to verify whether the control can also be applied to the more docile attached-flow regime without incurring any adverse consequences. This is useful because if there are no adverse changes in the flowfield, the flap may potentially be used for other purposes when dynamic stall is not a concern, mainly in hover and low speed forward flight. 8. To demonstrate the benefits of a dynamic flap compared to the simpler case of passive flap control Because a passively deflected flap requires no external energy source, it makes it a very appealing control technique. On the other hand, its constant influence on the flow is generally unnecessary and limits its usefulness. Nonetheless, the flow over a dynamic-stalling airfoil with passive flap control has not been previously studied. Furthermore, a comparison between the dynamic flap and passive flap control cases may uncover further insight into the workings of trailing-edge flap control making it worth investigating. 9. To investigate the viability of higher harmonic flap control to manipulate the aerodynamic loads at harmonics higher than the airfoil oscillation frequency. 49 Previously, higher harmonic control meant imparting a small feathering motion to rotor blades at a higher harmonic than the blade rotation frequency. Recently, Liu et al. [100] extended the concept to trailing-edge flaps in which the flap not the blade is actuated at higher harmonics. The aerodynamic loads, however, were not reported; therefore the relation between the flap motion and the variation in the aerodynamic loads remain unknown. Without this information, it remains unclear how the trailing-edge flap higher harmonic control manipulates the aerodynamic loads. It is anticipated that this work will contribute to a deeper understanding of the underlying physical mechanisms involved in the trailing-edge flap control of the flow around and aerodynamic loads generated on an unsteady airfoil, and the efficiency with which it does so. Furthermore, a thorough consideration of the flap motion parameters will provide a strategy with which to relate the degree of control to the flap motion profile. The present work will also provide experimental test data for use with the validation process of computational methods. 50 CHAPTER 3 EXPERIMENTAL METHODS There are two components to the experiments conducted in this investigation. The first part focused on acquiring the surface pressure distributions around and wake velocity profiles behind a trailing-edge flapped oscillating airfoil. From these, the structure of the flow around and behind the airfoil can be determined. This also provided the means for calculating the aerodynamic loads. The second part consisted of employing the particle image velocimetry (PIV) technique to quantify the entire flowfield around a similar unsteady airfoil. This allowed for a more detailed inspection of the fluid structures. This chapter includes a description of the facilities and models used to carry out the experiments, and an account of the measurement techniques implemented as well as the systems used to acquire the data. Note that the two elements of the experiments were carried out in separate flow facilities and airfoil models, each of which are described below. A clear table of experimental parameters that were investigated is also provided, in addition to a reporting of the experimental uncertainties. 3.1 Flow Facilities The main set of experiments, involving the surface pressure measurements and the hot-wire wake surveys, were conducted in the Joseph Armand Bombardier Wind Tunnel, located in the Aerodynamics Laboratory of the Department of Mechanical Engineering at McGill University. A schematic diagram of the tunnel and photographs of the contraction and exhaust are provided in Fig. 8. This is an open-loop suction-type wind tunnel which incorporates a number of enhanced features. The airflow first passes through a honeycomb sheet and four anti-turbulence screens located at the entrance of the three-dimensional contraction, which in combination with the large contraction ratio of 9.05 to 1 results in a high quality flow with turbulence intensity determined to be approximately 0.03% at 35 m/s. The flow then passes through the rectangular test section which measures 0.9m x 1.2m x 2.7m. To compensate for the negative pressure gradient generated by the boundary-layer 51 growth on the walls, the comers of the test section have been contoured with a chamfer that decreases with downstream distance. The test section is also equipped with a static-pitot tube connected to a differential pressure transducer (Honeywell Model DRAL501DN) in order to calibrate the flow speed against the fan speed, precisely regulated by a digital controller. The wind tunnel is capable of reaching a unit length Reynolds number of 3.2xl06/m. Subsequently, the flow passes through a diffuser spanning almost half of the entire wind tunnel length of 18 meters. The motor/fan section that follows is not rigidly attached to the diffuser to avoid transferring any vibrations the motor might generate to the test section. This is done by leaving a small gap between the diffuser and motor/fan section and encircling their flanges with a flexible rubber strap. Lastly, the flow passes through the exit cone, which has been specially designed as an acoustic silencer so as to mitigate the high tone noise. The particle image velocimetry measurements were conducted in a smaller wind tunnel of the same type and configuration as the above-mentioned wind tunnel. Shown via schematic diagram in Fig. 9, this smaller wind tunnel consisted of: 1) a sheet of honeycomb and two anti-turbulence screens placed at the inlet of the 13 to 1 contraction section, resulting in a turbulence intensity on the order of 0.9% at 10 m/s; 2) a 0.2m x 0.2m x 0.56m square test section, whose walls were fabricated from clear Plexiglas to allow for optical access from each of the four walls; 3) a diffuser measuring 28% of the entire length of the tunnel; and 4) a motor/fan section. The airflow was exhausted to the outdoors so as not to contaminate the air inside the lab with the flow seeding particles. In addition, the wind tunnel was located in a dark room to facilitate the PIV measurements. This required the installation of two light-tight vents, which worked with three ventilation vents, to alleviate somewhat the low pressure in the room generated by exhausting the airflow external to the dark room. The value of the free-stream velocity for each part of the experiments (i.e. surface pressure and wake measurements in the first part, and the PIV measurements in the second part) were 15 and 13.2 m/s, respectively. This yielded a chord Reynolds number (based on the model chords of 0.254 and 0.1 m for the separate airfoil models used in the surface pressure/wake and PIV measurements, respectively) of 2.46 x 105 and 8.69 x 104 for the current experiments. With regards to the measurements to be described shortly, no wind tunnel wall interference or blockage corrections were applied due to the uncertainty in such corrections for dynamic airfoil motions [91]. However, the work of Duraisamy et al. [14] 52 does show that even in the case of an airfoil undergoing dynamic stall, the effect of the walls is to increase the aerodynamic loads while maintaining the same flow characteristics. 3.2 Test Models The test model (a photograph of the test model from above and behind the wing, with the leading edge at the top and the trailing edge at the bottom, is provided in Fig. 10a) employed in the pressure and wake measurements consisted of a wing fabricated from solid aluminum with a NACA 0015 airfoil profile and a rectangular planform. This airfoil profile, one of the original airfoil profiles used for helicopter rotor blades, has traditionally been used in the fundamental studies of unsteady aerodynamics due to its simple geometry [6,8,9,12, 41,45,55,56,58,59,60,64,69,70], and for this reason was chosen for these experiments. The model, which had a chord of 0.254 m and a span of 0.38 m, was mounted horizontally in the center of the test section and was supported at both ends (Fig. 11). Although the aspect ratio is rather small, being only 1.5, a two-dimensional flow over the majority of the wing was achieved by placing two 40cm-diameter endplates with sharp leading edges at either end of the wing model. Moreover, Park et al. have found that for an aspect ratio of about 1.62 or greater and K > 0.1 three-dimensionality effects were insignificant [70]. This was verified by scanning a single hot-wire along the span of the wing at a location 30%c downstream of the leading edge and 5 mm above the airfoil surface. The hot-wire output, shown in Fig. 12, demonstrates the flow two-dimensionality with a deviation of only +/- 3% of Uoo near the center portion where the measurements were conducted. Blockage of the flow due to the presence of the wing model was estimated to be less than 4%. A specially-designed oscillation mechanism, located externally to the test section, was used to harmonically oscillate the wing model in pitch about its %-c location in a sinusoidal motion (Fig. 11), as this is the approximate location of the aerodynamic center for angles below the static-stall angle [53]. McAlister et al. [59] found that the '/i-chord location is an appropriate pitch axis since the motion of the center of pressure during the stalled portion of the cycle is centered at about the !4-chord. Articles by Jumper et al. [37] and Visbal and Shang [94] discuss the effect of pitch axis location on dynamic stall, a summary of which is included in the literature review. The apparatus consisted of a four-bar 53 mechanism driven by an Exlar Model DXM340C servomotor and controlled through an Emerson Model FX3161 PCM1 programmable motion controller, which maintained a constant oscillation frequency despite cyclic variations in the loads. The airfoil mean angle of attack was adjusted by varying the relative angle between the wing and the rocker link, and the oscillation amplitude was set by varying the radial distance of the connection between the crank and the coupler link. The zero mean angle was set to within 0.1° by identifying the angle at which the pressure at the leading edge was a maximum and equal to the stagnation pressure. A dial gauge, mounted rigidly to the shaft protruding from the wing, was used to measure the wing angle with an accuracy of 0.1 degrees. The phase angle was measured with an uncertainty of less than 1% by a non-contacting potentiometer (Clarostat Model HRS100SSAB-090) connected to the shaft about which the wing oscillated. Note the long length of the coupler link allowed for an oscillatory motion that was sinusoidal to within 2% (Fig. 13). Monitoring of the oscillation frequency was achieved by connecting the output of the potentiometer to a HP Model 3581A spectral analyser and was measured to an accuracy of ±0.02 Hz. The above-mentioned wing model was modified to incorporate a 25 %c trailing-edge flap which was simply hinged at either end (Figs. 10a, 11 and 14a). To allow free rotation, two modifications were necessary near the 75%c location which caused the airfoil profile to deviate slightly from the NACA 0015 at that location. Firstly, a small gap was introduced between the wing and the flap. This gap, which was less than 0.2 mm wide, came with the risk of allowing the flow to bleed from the pressure side to the suction side. This was prevented by filling the gap with petroleum jelly, a technique used by Rennie and Jumper [76, 77, 78]. Note, however, that measurements conducted with the gap empty, filled with petroleum jelly, and blocked (i.e. a piece of tape was placed over the joint on both the top and bottom surfaces) showed no discrepancy between them in the pressure distribution surrounding the joint, suggesting that in fact this was of no significant concern. Secondly, to allow for a maximum flapdeflectio n of+/-18 degrees, the surface both above and below the joint could not be continuous, as shown in the blown-up portion of Fig. 14a. The effect that this surface discontinuity had on the flow could not be quantified other than by comparing the local surface pressure distribution to that when the joint was covered with tape, which lessened the discontinuity, and showed no disparity. At any rate, a discontinuity such as this 54 located near the trailing edge, where for the current experiments the boundary layer will generally be turbulent and will often be in a state of flow separation, should not be of significant concern; this, in general, would have the effect of tripping the boundary layer and/or promoting separation. In the initial stages of the experimental investigation, a Futaba Model S-3003 servomotor, typically used to actuate the control surfaces of model aircraft, in conjunction with a custom-built controller, was used to actuate the trailing-edge flap. It is with this actuation mechanism that the data for Refs. 27 and 47 were obtained. It was soon realized that this actuation mechanism would not provide the ability needed in defining the flap motion profile with adequate flexibility. This system was then upgraded to a Maxon Model Re-35 servomotor, which was connected to one side of the flap through a direct coupling. The servomotor consisted of a dc motor mated to a 4.3 to 1 ratio gearhead and a 500 cpt (counts per turn) optical encoder. The servomotor was driven by a computer controlled Maxon EPOS 70/10 motion controller. The flap actuation signal was provided once every oscillation cycle by the Emerson Model FX3161 PCM 1 motion controller through one of its externally powered digital outputs and was then input to the Maxon EPOS 70/10 motion controller through its analog input. Note that the duration of the output from the PCM1 controller was insufficient and therefore had to be passed through a BNC Model 7010 digital delay generator, which generated a signal of sufficient duration. A non-contacting potentiometer (Novotechnik Type RSC2201236111102) was attached to the other end of the flap to provide an analog signal with which to monitor the flap motion; the measurement accuracy was +/- 0.35 degrees. The general flap motion profile utilized, shown in Fig. 14b, is trapezoidal. That is, it begins at a certain point in the oscillation cycle, denoted as the start time ts, begins a ramping motion to the maximum deflection angle at a rate Rl that lasts a time tRi, remains at the maximum deflection for a specified amount of time tss, and finally returns back to its undeflected position at a constant pitch rate of R2 during a time tR2. The entire flap motion endures for a total time denoted by ta. Due to the small dimensions of the wind tunnel used for the PIV measurements, a wing model of reduced scale was fabricated. The wing had a N AC A 0015 airfoil profile and rectangular planform, similar to the larger wing; however, the chord and span were reduced to 0.1 m and 0.195 m, respectively (Fig. 10b). It was also mounted horizontally, but was 55 supported from only one side so as not to obscure the camera's view. Endplates were found to be unnecessary as the wing spanned almost the entire test section width, resulting in a flow which was two-dimensional to within 2.7% of u<» across the center of the test section; verified using a single hot-wire probe. The model was spray painted a matte black color to minimize any reflections of the laser light sheet, needed for the PIV measurements, off the polished aluminum surface. Wind tunnel blockage, which was of a concern in the present experiment, was verified by measuring the static pressure at various locations in the streamwise direction along the upper and lower test section walls at mid-span with the airfoil in place at the maximum angle of attack, and was found to be approximately 14%. A smaller four-bar mechanism was designed and fabricated to oscillate the wing in pitch about its VA-C point. A Maxon Model Re-35 servomotor, identical to the one used to actuate the larger wing flap, was used to drive the wing oscillation and was controlled by a Maxon EPOS 70/10 programmable motion controller. The airfoil mean angle of attack was adjusted by varying the relative angle between the wing and the rocker link and the oscillation amplitude was set by varying the radial distance of the connection between the crank and the coupler link. The zero mean angle was set to within ± 0.2° by making the airfoil chord parallel with the wind tunnel upper and lower walls and then verifying, through flow visualization, that the stagnation point was located at the leading edge. A dial gauge, mounted rigidly to the shaft protruding from the wing, was used to measure the mean angle with an accuracy of 0.2 degrees. The phase angle was measured with an uncertainty of less than 1% by a non-contacting potentiometer (Clarostat Model HRS100SSAB-090) connected to the shaft about which the wing oscillated. Similar to the four-bar mechanism used with the larger wind runnel, the small four-bar mechanism generated an airfoil motion that was sinusoidal to within 2% (Fig. 13). The HP Model 3581A spectral analyser was also used in the PIV measurements to monitor and measure to within ±0.02 Hz the oscillation frequency via the potentiometer output. This airfoil model was also fitted with a 25%c trailing-edge flap which was simply hinged at either end at x/c = 0.75. Precautions similar to those previously described were taken to ensure the flow did not leak through the gap between the flap and airfoil. A direct coupling connected one side of the flap to a Maxon Model Re-16 servomotor, which was used to actuate the trailing-edge flap. The servomotor, consisting of a dc motor mated to a 5.4 56 to 1 ratio gearhead and a 512 cpt (counts per turn) optical encoder, was driven by a computer controlled Maxon EPOS 24/5 motion controller. The motor controllers for the flap actuation and wing oscillation were connected to separate computers thus requiring a digital signal to be output from the wing oscillation motor controller once per cycle; this signal was input to the flap motor controller as a trigger for the flap motion. A non-contacting potentiometer (Novotechnik Type RSC2201236111102) was coupled to the motor shaft through a set of spur gears to provide an analog signal with which to monitor the flap motion; the measurement accuracy was +/- 0.35 degrees. 3.3 Surface Pressure Measurements Detailed surface pressure distributions around the 0.254 m chord wing model mid- span were obtained from 48 0.35-mm diameter pressure taps strategically distributed over both the upper and lower airfoil and flap surfaces, which extended up to x/c = 96.5%. The resolution that this quantity of pressure taps provides is greater than that used by many researchers elsewhere [6, 12, 37, 38, 56, 59, 62, 63, 76, 77, 78]. Figure 14a shows schematically the distribution of the pressure orifices, the locations of which are tabulated in Table 1. It should be noted that the origin of the coordinate is located at the airfoil leading edge. Each pressure orifice had a stainless steel tube insert to which a 35-cm long and 0.75- mm i.d. (inside diameter) plastic tubing was connected. The joints between the plastic tube and steel insert, and between the steel insert and airfoil model were sealed using epoxy to avoid any leakage. The plastic tubes were then connected to a 48-port scanivalve system, installed on one of the supports inside the wind tunnel, that used a solenoid-driven adapter to connect each of the tubes one at a time to a Honeywell DC005NDC4 differential pressure transducer (±5" of water head range and dynamic range on the order of 10 kHz), which was calibrated using a water column manometer (WS-Minimeter model A-0702-89). The scanivalve system was modified so that it could be computer controlled to cycle through the 48 ports. The pressure signals were phase-locked ensemble-averaged over 75 to 100 oscillation cycles. A typical total uncertainty in the measured pressure was estimated to be ±0.013 in Cp. 57 When conducting measurements of an unsteady pressure signal for which plastic tubing separates the pressure tap and pressure sensor, which in the current experiment measured 35-cm long with an inside diameter of 0.75-mm, it is important to verify the dampening effect of the plastic tubing on the unsteady pressure signals. A special-purpose acoustically insulated box was constructed and was equipped with a controllable, in both amplitude and frequency, acoustic sound source and a pressure transducer whose input was separated from the inside of the box by the same length of plastic tube. The output level and phase measured by the transducer was then compared to the acoustic source. It was found that a simple constant time delay on all pressure signals with frequency above 2.95 Hz was present, thus limiting the reduced frequency to a value of 0.157 under the current conditions. Details of this method can be found in the work of Chen and Ho [12] and Rennie and Jumper [77, 78]. The unsteady aerodynamic loads, which include lift, drag and pitching moment, were then computed by numerically integrating the phase-locked ensemble-averaged pressure distributions, according to the formulas c Kpulc J pVC c,-= C„ cos(a)- Cc sin(a) (3) cd = Cn sin(a)+ Cc cos(a) (4) _ mP _ f(l/ x/ cm (5) Y2puy >V'4 /c Note that the pitching moment is taken about the quarter-chord pitching axis and that the drag coefficient determined strictly from the pressure distribution, as is done here, does not account for viscous drag. Also, the large number of cycles taken were not necessary to yield accurate results; there is a 0.5% difference between phase-locked ensemble-averaged pressure distributions determined from 25 cycles and 100 cycles. Figure 15 presents the lift, drag and pitching moment coefficients for a typical oscillation case, obtained via numerical 58 integration of the surface pressure distributions over 25,50,75, and 100 cycles. The overlap of the four curves confirms the adequacy of the number of cycles used for phase averaging. In the case of the static airfoil, the mean pressure was calculated for each pressure orifice over a period of 10 seconds, which was then numerically integrated to provide the static aerodynamic loads. A trapezoidal integration algorithm was used to perform the integration. With regards to the accuracy of the computed loads, it may be said that they are slightly underestimated since the pressure measurements extend up to x/c = 96.5% and do not reach the actual trailing edge, however the contribution of the remaining 3.5%c was found to be trivial. The uncertainty in the aerodynamic loads was determined for a representative configuration and was found to be approximately: ± 0.009 in Q, ± 0.004 in Ca and ± 0.0005 inCm. Based on the need for rotor blades to behave in a stable manner, a measure of the aerodynamic damping was adopted to quantify the effect of control. It can be shown that stability for a rotor blade, excluding the effects of structural damping, depends on the direction of the individual moment loop areas. A counter clockwise (CCW) loop is stable, or provides positive damping, and a clockwise loop (CW) is unstable, or provides negative damping. Following the definition in Ref. 7, the work coefficient Cw is calculated according to equation 6. Cw = CCW CW Note the CCW integral is positive and the CW integral is negative. Although this is not the two-dimensional aerodynamic damping coefficient as defined by Carta, they are linearly proportional provided the oscillation parameters, in particular the oscillation amplitude, do not change. In a similar fashion, a measure of the lift-curve hysteresis CH was determined by integrating the lift curve over one oscillation cycle via equation 7. Cff= This is essentially the area bounded by the lift curve, and is used to determine the effect of control on the degree of hysteresis. Data acquisition of the pressure transducer signal, along with the outputs of the two potentiometers (i.e. the wing and flap potentiometers), was conducted using a Pentium II PC equipped with a 16 bit A/D converter board (Measurement Computing CIO-DAS1402/16). 59 Data acquisition programs were written in the QuickBasic programming language. The outputs from the potentiometers required no amplification and were low-pass filtered at 1 kHz to remove random noise. The pressure transducer signal was low-pass filtered at 250 Hz and amplified with a gain of 2 using a multi-channel A A Lab Model G3006 pressure measurement system. The sampling frequency was 500 Hz. The same computer was used to trigger the scanivalve system via an optical relay in a standalone motor controller. A schematic diagram or flow chart of the experimental setup and instrumentation system is presented in Fig. 16. Post-processing of the raw data was conducted on a Pentium IV PC using the Matlab software. 3.4 Hot-Wire Wake Measurements The unsteady wake behind the airfoil at a distance 1.75 chords downstream from the trailing edge along the wing model mid-span was examined using a miniature cross hot-wire probe (Auspex Model AHWX-100) with two Dantec 56C17 constant-temperature anemometers, set to operate with an overheat ratio of 1.6. The probe was mounted on a sting which was extended from a six degree-of-freedom computer-controlled traversing mechanism, displayed in Fig. 17, although only the three orthonormal x,y^ axes were used. The origin of the axes is located at the leading edge of the wing midspan at a zero degree angle of attack. The accuracy with which the origin was located relative to the wing was determined to be less than 0.4%c in all three directions. The position along the vertical axis was accurate to within 5 um. In situ calibration of the cross hot-wire probe was achieved following the technique described by Lueptow et al. [54], which consists of creating a look-up table based on measurements in the wind tunnel free stream for many known speeds and pitch angles. A sample calibration plot of the output from one wire versus the other demonstrating curves of constant speed and constant pitch angle is provided in Fig. 18a. Figures 18b and 18c show the surface plots of the streamwise and transverse velocity components as functions of the two hot-wire outputs, respectively. Note, however, that due to limitations in the sensitivity and accuracy of the probe in the presence of high angularity or reversed flow, there were some data points that fell outside of the calibration range. In these instances, the point in the 60 calibration nearest to the data was adopted. Instantaneous wake velocities, for 70 to 90 cycles of oscillation, were recorded and phase-locked ensemble-averaged to yield the streamwise and transverse mean and fluctuating velocities at various points during the oscillation cycle. Due to the convection time required for the wake flow to propagate from the airfoil to the downstream location of the probe, a phase lag is incurred between the instantaneous probe reading and the airfoil angle of attack at that instant. A compensation scheme, following the work of Chang and Park [11], was implemented, which approximated the convection velocity to be equal to the free-stream velocity, to offset the phase delay. In other words, the measured flowfield at the instantaneous angle of attack of a(t) = ara + Aasin(a)t) was shifted by an amount (p = -xprobe/Uco. The goal of measuring the wake of the airfoil was two-fold. First, it allowed for the nature of the boundary layer to be deduced (i.e., separated or attached depending on the width of the wake, and laminar or turbulent depending on the fluctuation levels). Note, however, this sometimes required added information from the surface pressure measurements since just because the wake is turbulent doesn't necessarily imply the boundary layer is turbulent as the flow could have transitioned while reaching the hot-wire sensor. Second, the extent of the flow separation, in terms of transverse size and velocity deficit, may be inferred. These measurements were important in establishing the effects of the flap control. Data acquisition of the signals from the two wires from the cross hot-wire probe, along with the outputs of the two potentiometers (i.e. the wing and flap potentiometers), was conducted using a Pentium II PC equipped with a 16 bit A/D converter board (Measurement Computing CIO-DAS1402/16). This system was separate from the system used to acquire the pressure data. Data acquisition programs were written in the QuickBasic programming language. The potentiometers required no amplification and were low-pass filtered at 1 kHz to remove random noise. The two hot-wire signals were low-pass filtered at 1 kHz and amplified with a gain of 5. The sampling frequency was 2 kHz. Three motor controllers were also connected to the computer in order to move the traverse. A schematic diagram or flow chart of the experimental setup and instrumentation system is presented in Fig. 19. Post processing of the raw data was conducted on a Pentium IV PC using the Matlab software. 61 3.5 Particle Image Velocimetry Measurements Particle image velocimetry measurements of the flow around the 0.1m chord airfoil equipped with a trailing-edge flap were conducted in the previously described 0.2m x 0.2m wind tunnel. The PIV system is illustrated schematically in Fig. 20. A dual head Nd:YAG laser, composed of two internally aligned laser beams, was used to illuminate the test plane of interest with a laser light sheet. A cylindrical lens was used to expand the beam into a sheet of required width, and an optical configuration consisting of four mirrors was used to guide the sheet towards the test plane. At the center of the test section, the light sheet measured 15.4 cm in width, and was limited to a thickness of 1.7 mm by passing the light sheet through a slit prior to its entry into the test section. The thickness of the light sheet was also measured with a Polaroid film. Simultaneous visualization of the flow on the pressure side of the airfoil was obtained by locating two mirrors above the test section, which were used to reflect the light sheet back onto the airfoil pressure side with no phase lag. The current free-stream velocity, in conjunction with the size of the interrogation region, required a separation in the two laser pulses of 68.1 us. Seeding of the flow was accomplished by using an atomizer to generate particles of measuring on the order of 1 to 3 urn in diameter, according to manufacturer's specifications. The particles were introduced into the flow upstream of the contraction and were exhausted to the outdoors. A custom-built diffuser was designed to shape the output of the atomizer into a highly concentrated 10 mm-thick thin sheet of particles, which was aligned with the laser sheet inside the test section. The two laser light-sheet illuminations of the flowfield, separated by a time delay of 68.1 us, were digitally acquired using a 4 megapixel CCD camera outfitted with a long focal length lens set at f/11 aperture, and located at a distance of about 1.05 m from the light sheet plane. The field of view measured 14 x 12 cm2 with a magnification ratio of 9.7:1. Calibration of the camera was achieved by placing a ruler in the field of view and associating the distance between two points with the number of pixels between them, and was within 0.3%. A two-axis precision traverse was used to position the camera to the flowfield of interest. Note that the origin of the x,y axes was located at the pitching axis so that it remained fixed, in light of the airfoil motion during the dynamic experiments. The particle images were acquired by a 64-bit frame grabber installed in a Dell workstation. Timing and 62 control of the PIV system, which includes the lasers, CCD camera and frame grabber, was accomplished by a programmable synchronizer. Acquisition of the PIV images was synchronized with the airfoil oscillation via a signal from the wing oscillation motor controller passed through a pulse generator. Control of the system components, which includes the lasers, camera, frame grabber and synchronizer, as well as the acquisition, analysis and post-processing of the PIV images, was accomplished using the TSI Insight 3G (version 8.0.4.0) software package. The PIV system parameters were set up following the guidelines detailed in Adrian [1] and Raffel et al. [74]. Special care was taken in the alignment of the laser, mirrors and especially the camera so as to minimize cumulative errors. The procedure described by Drouillard et al. [13] was followed. The various components of the PIV system, including their details, are listed below. 1) a dual-head Continuum Nd:YAG laser, used to illuminate the image plane at 532 nm with consecutive 5-7 nsec 300mJ pulses at a flash rate of 5 Hz (the laser beams are internally aligned to be parallel and to overlap) [23]; 2) a series of four mirrors to guide the beams towards the test plane; 3) a single short-focus cylindrical lens (of a focal length of 100 mm) to expand the beam into a 154mm-wide light sheet; 4) a slit through which the light sheet was passed, limiting the thickness to 1.76 mm, measured with a Polaroid film; 5) two additional redirecting mirrors to illuminate the airfoil pressure side as suggested by Shih et al. [83] (no phase lag between the illumination of the suction side and pressure side was incurred due to the added distance); 6) a TSI 6-jet atomizer (Model 9306), operated with 2 jets at a pressure of 20 psi and a by-pass flow rate of 42.5 cfm, along with a custom-built diffuser to generate a 10 mm-thick sheet of 1 to 3 um-diameter propylene glycol (Fisher P355-1) particles, introduced to the flow upstream of the tunnel contraction and exhausted to the outdoors; 7) a TSI PowerView 4MP Plus CCD camera (Model 630059, 2048 x 2048 pixel resolution, 7.4 urn pixel size, 12 bit dynamic range and 16 Hz maximum frame rate), fitted with a 105 mm focal length lens set to an f/11 aperture, for digital 63 acquisition of the two illuminations, separated by a time delay of 68.1 us, of the 14 x 12 cm field of view at a magnification ratio of 9.7:1 via a 64-bit frame grabber installed in a Dell Precision 690 workstation; 8) a two-axis traverse, on which the camera was mounted, to position the flowfield of interest within the field of view; 9) a TSI LaserPulse programmable synchronizer (Model 610035), which connected and synchronized the operation of the frame grabber, Nd:YAG lasers, camera and computer with a time resolution of 1 ns (the time delay and pulse width could be varied between 0 and 1000 s and 10 ns to 1000 s, respectively). 10) a HP pulse generator (model 8015 A), which acquired a signal from the Maxon EPOS 70/10 motor controller timed with the wing oscillation to provide a signal to the synchronizer to trigger picture acquisition. A two-frame cross-correlation analysis of the PIV images was implemented in the computation of the velocity vectors inside the region of interest, consisting of the field of view less the portion of the image being blocked by the wing and flap. The images were subdivided into square interrogation windows, the second image being shifted relative to the first so as to improve the signal-to-noise ratio, and the correlations were computed using a FFT correlator, requiring the windows to be zero-padded wherever necessary. A Gaussian curve-fit was implemented to determine the location of the correlation map peak with sub- pixel accuracy. A multi-pass scheme was implemented which progressively decreased the size of the interrogation window as well as adjusted the extent of the image shift based on the previously computed velocity vector. During the later passes, this algorithm also deformed each interrogation window to improve measurement accuracy. This yielded more accurate vectors, with the error in velocity for a particle traveling in the free stream being on the order of 1.2%, and a higher percentage of valid vectors. The initial values of the interrogation window size and second image shift were, in pixels, 96 x 96 and 8, respectively. The final size of the interrogation window was set to 40 x 40 (representing a physical size of roughly 2.9 mm). A 50% overlapping of the interrogation windows was implemented and led to a final resolution of 1.5 mm, or 1.5%c. Post-processing of the velocity fields consisted of first vector validation (i.e. removal of erroneous vectors), followed by application of a 3x3 64 Gaussian filter to remove random variations, and finallyinterpolatio n of missing vectors. This method of analysis resulted in 86 to 90% valid vectors in each field;roughl y half of the remaining interpolated vectors were located in the free stream, where a lack of particles in certain regions occurred periodically, and thus do not influence the accuracy of the measurements in the vicinity of the airfoil and wake. The streamwise vorticity fields were computed from equation 8 using a five-pointcentral-differenc e formula (equation 9) in the unbounded flow (i.e. the flow not near a boundary) shown below, A*.) = T^rtA*. -2A)-8/(*. -h) + *f(*. +h)-f(xe+2h)] 4 (9) + — /(5)(£) 30 or a three-point forward-, central-, or backward-difference formula (equations 10,11 and 12, respectively) in the flowfield close to the airfoil surface, depending on the distance and orientation of the surface relative to the location in the flowfield in question. f(x0) = ^-[-3f(x0) + 4f(x0+h)-f(x0+2h)]+^-f^^) (10) 2h 3 i f{x0)=-U-f{x0-h) + f{x0 + h))-^f \^) (11) 2h 6 x i fM = ^7lf( o -2h)-4f(x0-h) + 3f(xo))+^-f \^ (12) 2« 3 In equations 9 through 12, inclusive, x0 is the point at which the differential is being calculated, h is the spacing in-between grid points,/is the variable being differentiated, and f(x0) is the value of the differential at x0. Also, the error in applying these formulas is represented by the last term in each of the equations. Concerning the area of the image surrounding the airfoil, two things should be noted. First, the matte black color of the wing prevented any glare due to the impingement of the light sheet onto the airfoil surface. Second, the tip of the wing model, being closer to the camera than the mid-span where the measurements occurred, causes a region of about l%c surrounding the airfoil to be blocked from the camera's view, precluding any measurements 65 in the direct vicinity of the surface to be made. This is especially true when the flap was deflected. In addition, during the course of the experiments it became very evident that serious attention should be paid to the accumulation of the seeding particles on the airfoil model, as it was found that after a short period of time sufficient particles could accumulate on the surface causing premature transition of the boundary layer, and therefore required periodic cleaning of the airfoil surface. Determination of the angle of attack was achieved by first acquiring images of the static airfoil at various angles of attack between 0 and 20 degrees and identifying the position of the sharp trailing edge in the field of view. This served as a calibration of the airfoil angle of attack as a function of trailing edge location. During the dynamic airfoil experiments, the trailing edge position was pinpointed and the angle of attack was determined via interpolation of the calibration data. In the control cases, where the flap may be in motion and thus the trailing-edge location no longer has any relation to the airfoil angle of attack, the location of the %-chord flap-hinge was used instead. The accuracy of the instantaneous angle of attack was determined to be within ± 0.3 degrees. To determine whether the airfoil was moving in an upstroke or downstroke motion, a low power laser diode was placed outside of the test section on the far end and aimed toward the camera such that it could be seen in the lower corner of the field of view. The laser beam was passed through a filter to lower further the intensity of the beam so as not to damage the CCD chip inside the camera. A digital signal was output from the wing oscillation motor controller that was set to high during the upstroke and low during the downstroke. This created a bright spot in the lower corner of the images when the airfoil incidence was increasing and a dark spot when it was decreasing. With regards to the PIV measurements, the opinion here is akin to that of Shih et al. [83], whose measurements were instantaneous and not phase averaged. The reasoning behind this is that by phase averaging the velocity and vorticity fields, the flow structures tend to be somewhat "smeared", and any subtle flow structures that may be present could become unrecognizable. Shih et al. argue that it should be recognized that a transient flow "is not a featureless average but is built from sharply defined features". For this reason, all flowfields are instantaneous in nature. Due to the cycle-to-cycle variability that is inherent in such a turbulent and unsteady flow as that which is encountered here, numerous images at each 66 phase angle were obtained and analysed, and the most representative image was chosen for presentation. These measurements, which were carried out at a lower Reynolds number than the majority of the experiments due to physical constraints, were complemented by surface pressure distribution measurements conducted on the 0.254 m chord wing model in the 0.9m x 1.2m wind tunnel under the same flow conditions. Note that due to the lower Reynolds number, the static-stall angle of the NACA 0015 airfoil was reduced; the oscillation parameters were therefore adjusted accordingly to match the same type of flow phenomena as that observed during the higher Reynolds number experiments. 3.6 Test Parameters A summary of the experiments, in terms of the test parameters, that were conducted and that will be presented in chapter 5 will now be given. Due to the extensive nature of the investigation, the experimental plan is subdivided into several steps. These include: 1. overview of baseline, or uncontrolled, airfoil • Re = 8.69x104,1.65xl05 and 2.46x105 • am = 8°, 10°, 12°, 14°, 15° and 16° • Aa = 6°, 8° and 10° • K = 0 (i.e. static airfoil), 0.05 and 0.1 2. active TEF control of unsteady aerodynamic loads of an airfoil oscillating in deep stall • Re = 1.65x10s and 2.46xl05 • am=15°andl6° • Aa = 8°andl0° • K = 0.05 and 0.1 • ^ = ±7.5°, ±8°, ±15° and ±16° • td = 30%, 50% and 70%fo"' • ts = -0.57c, 071, 0.127i, 0.257t and 0.571 67 1 • tRi = 8.5% to 43%f0" _1 • tss = 0%, 10%, 25% and 50%fo • tR2 = 8.5% to 43%f0"' 3. PI V measurements of the flow around both an uncontrolled and controlled airfoil • Re = 8.69X104 • ara=12° • Aa = 8° • K = 0 (i.e. static airfoil) and 0.1 • U = 5MU1 • ts =-0.571, On, 0.127tand0.253i • tR^B^/otOSP/ofo-1 1 • tss = 0%andl7.5%fo- 1 • tR2=13.5%to31%f0' 4. control of attached-flow and light-stall aerodynamic loads • Re = 1.65x10s • am=12°andl4° • Aa = 6° • K = 0.1 • 5max = ±7.5° • td = 50% • ts = -0.5JI, OTC and 0.5TC 1 • tRi = 18%^' • t, = 40%^-1 • 1^=18%^ 5. passive flap control • Re = 2.46xl05 68 • am = 8°, 10°, 12° and 16° • Aa = 8° • K = 0.1 • 5 = ±4°, ±8° and ±16° 6. higher harmonic control • Re = 2.46x10s • am=12° • Aa = 8° • K = 0.1 0 • 8max = 8°andl6 • NP = 2P, 3P and 4P • ts = -0.57i, -0.2571, 07t, and 0.27c Note that to simplify the discussion of the results, only a select portion of the entire data set will be presented in chapter 5. 3.7 Experimental Uncertainty In this section, an accounting of the uncertainty involved in each of the parameters relevant to the experiments is made. They are subdivided into seven categories: 1) flow properties and wing models; 2) A/D board; 3) airfoil motion; 4) flap motion; 5) surface pressure measurements; 6) hot-wire wake measurements; and 7) PIV measurements. Those parameters for which two values are given, the values on the left are in regards to the bulk of the experiments conducted in the large wind tunnel (i.e. for the surface pressure and wake measurements), and the values on the right pertain to the PIV measurements. If only a single value is given, it applies to both sets of experiments. 69 Experimental Uncertainty Regarding Flow Properties and Wing Models Parameter Uncertainty Operating Range Free-stream speed, u«, ± 0.2 m/s 15 m/s 13.2 m/s Chord, c ± 0.002 m 0.254 m 0.1m Reynolds number, Re ± 0.05xl05 ±0.26xl04 2.46xl05 8.69xl04 Deviation from 2D ± 3% Uoo ± 2.7% Uoc n/a Flap length ± 0.4% 0.25c Experimental Uncertainty Regarding A/D Board Parameter Uncertainty Operating Range Measurement accuracy ±0.15mV 0-10 Volts Experimental Uncertainty Regarding Airfoil Motion Parameter Uncertainty Operating Range Pitching axis location ± 0.6% 0.25c Sinusoidal motion ±2% n/a Phase angle, x <1% 0-2TC Angle of attack, a ±0.1° ±0.3° 0°-24° 0°-20° Mean angle of attack, am ±0.1° ±0.2° 8°-16° 12° Oscillation amplitude, Aa ±0.05° ±0.1° 8° 8° Oscillation frequency, f0 ± 0.02 Hz 1.88 Hz 4.20 Hz Reduced frequency, K ± 0.003 ± 0.005 0.10 Experimental Uncertainty Regarding Flap Motion Parameter Uncertainty Operating Range Flap angle, 8 ± 0.35° -16°-16° Flap actuation start time, ts ± 0.0271 -0.571-0.57C 1 Flap actuation duration, td ± 2%f0" 30%^ - 70%fo-' 1 1 Flap upward deflection duration, tRi ± 2%f0"' 8%f0- -43%f0" J 1 Flap downward deflection duration, tR2 ± 2%f0" 8%f0"'-43%f0" l Flap steady-state time period, tss ± 2%f0"' 0%U - 50%^' 70 Experimental Uncertainty Regarding Pressure Measurements Parameter Uncertainty Operating Range Pressure coefficient, Cp ±0.013 -6.5 - 1 Lift coefficient, Q ± 0.009 -0.4-2.2 Drag coefficient, Cd ± 0.004 0-1.0 Pitching moment coefficient, Cm ± 0.0005 -0.4 - 0.2 C/-hysteresis factor, CH ±0.29 3-20 Torsional damping factor, CW;net ±0.016 -2.3-1.5 Streamwise distance, x ± 1.3xl0-4m 0 - 0.245 m Experimental Uncertainty Regarding Wake Measurements Parameter Uncertainty Operating Range Streamwise velocity, u ± 0.25 m/s 3-15 m/s Transverse velocity, v ± 0.2 m/s -13-13 m/s (W) = (0,0,0) ± 0.4%c n/a Streamwise distance, x ±20um 1.75c Transverse distance,;; ± 5 um -0.8c-0.8c Experimental Uncertainty Regarding PIV Measurements Parameter Uncertainty Operating Range Magnification ratio ± 0.3% 9.7: 1 Particle size n/a 1 -3 um Time delay, At ±lns 68.1 us Light sheet thickness ±3% 1.76 mm (xy) = (0,0) located at !4-chord ± 0.5%c n/a Streamwise distance, x ±72 um -0.03-0.1m Transverse distance, y ±72 urn -0.035 - 0.06 m Streamwise velocity, u ± 1.2% -11-23 m/s Transverse velocity, v ±1% -13-10 m/s Spanwise vorticity, ^c/ux ±5% -30-45 71 CHAPTER 4 EVALUATION OF CONTROL METHODS The ability to determine whether a control system alters in a favourable and efficient manner the flow over an airfoil requires the identification of the pertinent parameters that quantitatively describe the characteristics of the flow over an airfoil, and provide a measure for evaluating the results of the control tests. Quantities that indicate the effectiveness of the control system may be derived from the aerodynamic performance, in terms of the aerodynamic loads and pitching moments. The physical mechanisms responsible for these improvements/deteriorations are determined from the instantaneous surface pressure distributions, wake velocity profiles, and PIV flowfield measurements, as these are indicative of the various flow structures occurring over the airfoil. This chapter is dedicated to describing the characteristics of the aerodynamic loads that will permit for evaluating the results of the control tests. Be it a steady or unsteady airfoil, there are a number of characteristics, or properties, which can be used to infer the effectiveness of a control scheme. The importance of each of these properties is dependent on the intended goal of the control system, however, and can be quite different. Furthermore, each property is dependent of the others and any attempt to advantageously change a single one may result in changes in the others, either favourably or possibly adversely. Therefore, when determining the effectiveness of the control system, not only should the intended parameters be considered but also those parameters whose deviation was not deliberate, or even desired, but occurred as a consequence of the chosen control. Prior to delving into the methodology behind the evaluation of the control results it would therefore be useful to discuss the benefits put forth by the unsteady airfoil motion and the dynamic stalling process, which we would like to maintain and potentially enhance, as well as the disadvantages, which we would like to mitigate if not completely avoid. Based on the typical unsteady aerodynamic load curves presented in Fig. 6 for a NACA 0012 airfoil oscillating with a(t) = 10°+l 5°sincot and K = 0.1 at a Reynolds number of 1.35 x 105, the following advantages and disadvantages may be identified. 72 Advantages - Q increases linearly beyond ass due to suppressed trailing-edge flow separation (between points 1 and 2) - Substantial overshoot in C/,max due to formation of a LEV (between points 3 and 4) - Stall is delayed significantly beyond ass (point 4) Disadvantages - Post-stall lift loss is severe and occurs abruptly (between points 4 and 5) - Large degree of hysteresis in Q curve due to delay in flow reattachment - Excessive nose-down Cm due to downstream convection of a LEV (point 4) - Presence of a CW loop in the Cm curve resulting in negative aerodynamic damping It can therefore be stated that ideally, favourable control would lead to lift being maintained or increased during the upstroke and increased during the downstroke, the peak negative pitching moment being reduced, and a positive aerodynamic damping. The metrics used to gauge the effectiveness of the control system, which are indicative of the aerodynamic load characteristics, are therefore the maximum lift coefficient C/,max, the peak negative pitching moment coefficient Cm,peak, the work coefficient Cw,net (recall that the work coefficient is a measure of the aerodynamic damping), and the lift-curve hysteresis CH- The combined overall effect on C/)max and Cm,peak may be gauged through the definition of the performance ratlO L/jmax' ^m,peak- Given a set of values for the above-mentioned parameters, namely C/,raax, Cm,peak, Cw,net> CR and C/,max/Cmjpeak, for a single control case, the most straightforward method to determine control effectiveness is to compare these values to those corresponding to the uncontrolled baseline case. These may be plotted as a function of the various parameters 73 describing the flap motion to determine the optimum motion profile. This is the methodology primarily used in this investigation. Another point of view comes from an analysis performed by Bousman [4, 5] of dynamic stall data he collected from numerous sources. In these works, he demonstrated the unique relationship formed between the peak values of the aerodynamic loads due to the formation of the leading-edge vortex and the occurrence of dynamic stall. Furthermore, this apparently universal relation was shown to be a monotonic function. When plotting C/,max versus CmjPeak, all the data points collapsed onto a single curve, described by a second order polynomial, which he designates the dynamic stall function. An example of this for aNACA 0015 airfoil section is provided in Fig. 23. This also applies to Cd,max. The data used to demonstrate this universal character of dynamic stall data covered a wide spectrum of parameters. This included eight different airfoil sections, Mach numbers between 0.05 to 0.3, Reynolds numbers between 0.5 x 106 to 4 x 106, mean angles of attack between 2° and 14°, oscillation amplitudes between 2° and 20°, and reduced frequencies between 0.01 and 0.3. Although there is a certain degree of scatter in the data, none of the parameters that describe the flow or airfoil motion seems to affect the dynamic stall function. In other words, all other things being equal, changing one parameter does not influence the dynamic stall function. For example, the results even show that the data for tests conducted at a Reynolds number on the order of 105 agree with those at 4 x 106. Only a small deviation occurs when different airfoil sections are tested, or when Mach number is changed considerably. Bousman argues that the distinctive nature of the dynamic stall function provides another perspective forjudging the control techniques. The dynamic stall function essentially indicates that for a given airfoil section, the LEV-induced peak lift and peak negative pitching moment are related and follow a predetermined path in which a reduction in one is accompanied by a reduction in the other, and vice versa. As such, only a control mechanism that causes the C/>raax versus Cm,peak data to be shifted relative to the dynamic stall function towards reduced Cm,peak at constant or increased C/)max is deemed an improvement over the uncontrolled airfoil in the opinion of Bousman. The reasoning behind this is that in a helicopter environment a certain amount of lift is required from the rotor blades that the pilot will aim to achieve. If a control system reduces pitching moment at the cost of reduced lift (i.e. the control system moves along the dynamic stall function), then in attempting to 74 achieve the necessary lift, the pitching moment will rise to a value near that of the baseline airfoil, and therefore no gain is realized. This method, however, is very restrictive and does not leave any room for lift to be negatively affected even in the smallest amounts, regardless of the improvements in Cm,peak- In the control investigation of Greenblatt and Wygnanski [32], the methodology used to evaluate whether the periodic excitation flow control was successful or not was based on limits that they set for the pitching moment coefficient. First, the uncontrolled airfoil was oscillated such that the maximum angle of attack was equal to the static-stall angle. Based on the pitching moment curve for this case, they set allowable limits for the pitching moment excursion equivalent to 20% larger than the maximum and minimum Cm for the attached flow case. Bousman [4] also discusses the use of a boundary in Cra that identifies acceptable levels of pitching moment. Based on flight test data for a UH-60A helicopter, the largest Cm,peak observed was -0.15, obtained during maximum forward velocity conditions. Note, however, that this does not account for the extremely high values of Cm)Peak reached by military helicopters during the UTTAS pull-up manoeuvre which he states may attain almost -0.7. Limited use of this method will be made, only applying it to the optimum control scheme determined in chapter 5 section 4. 75 CHAPTER 5 RESULTS AND DISCUSSION This chapter presents and discusses the experimental results obtained via the aforementioned experimental techniques used, namely surface pressure measurements, wake velocity surveys, and PIV flowfield measurements. This chapter is subdivided into eight sections. In the first section, the behaviour of the baseline, or uncontrolled, airfoil, under static and unsteady conditions, is documented and discussed. Note that the terms baseline and uncontrolled are synonymous and are used interchangeably. The effects of trailing-edge flap control on the aerodynamic loads and fluid structures are then introduced in the second section using the results of a typical control case. Particular attention is given to the physical mechanisms involved in the trailing-edge flap control. The third section is further subdivided into six subsections, each of which focuses on the influence of one of the flap motion parameters on the aerodynamic loads. The results of the control tests are summarized and organized into a set of guidelines in the fourth section. The optimum flap motion parameters are also identified here. The results from the PIV measurements of the flowfield are presented in section five with the goal of identifying the physical mechanisms involved in the trailing-edge flap control and confirming the conclusions drawn from the surface pressure measurements. Trailing-edge flap control of the unsteady aerodynamic loads for both attached-flow and light-stall oscillation cases are explored in the sixth section. The seventh section examines the characteristics of passive flap control in comparison to the active flap control. The effects of higher harmonic motion of the flap are discussed in the eighth and last section. 5.1 Baseline Airfoil To set the stage for the control results, a thorough presentation of the baseline, or uncontrolled, airfoil, both static and dynamic, under the current operating conditions is included. Figures 21 a - 21 c present the dynamic Q, Cra and Cd loops of a NACA 0015 airfoil oscillated with ocm = 16°, Aa = 8° and K = 0.1 (solid line). The arrows indicate the upstroke 76 and downstroke directions. Also shown are the static airfoil curves for comparison (denoted by circles). From a glimpse of the aerodynamic loads, the large deviation of the dynamic airfoil, oscillated well beyond the static-stall angle, from the static airfoil is obvious. Figure 21a shows that not only is the dynamic maximum lift coefficient Q,max far superior to the static value by 55% (1.69 compared to 1.09), but the stall angle is significantly delayed by = 5.8° (aas 23.8° compared to ass = 18°). Note that lift stall always occurred after moment stall (i.e. aas > aras), but the peak in Cm was reached just after the peak in Q (i.e. amp > adS). The immense degree of hysteresis in the lift curve, resulting from the hysteretic property of the boundary-layer separation and reattachment points, is also apparent and is quantified by a Q- hysteresis factor CH of 11.9. To put this into perspective, a typical attached-flow oscillation might result in a value of CH on the order of 2. In fact, flow reattachment is delayed until ad ~ 10.6° (recall that the subscript d indicates the downstroke) owing to the lag induced by the reverse kinematic induced camber effect on the leading-edge pressure gradient by the negative pitch rate. The instant of flow reattachment was identified based on when the leading-edge suction peak was re-established (not shown), and coincided with the minimum in C/ during the downstroke. Flow reattachment may also be identified from the hump in the Cm curve (Fig. 21b) during the later portion of the downstroke as pointed out by Yu et al. [97], which is indicative of the reattachment point passing the Vi-chord point during its downstream movement. Cp distributions (not shown) confirm this observation. Of greater significance to the current investigation is the Cm curve shown in Fig. 2 lb, in which a severe nose-down pitching moment is encountered, with a Cm)Peak nearly 7.6 times higher than in the static case. What's more, the shape of the Cm curve is such that the aerodynamic damping is negative, which can potentially lead to a variety of aeroelastic problems on the rotor. It is characterized by a net work coefficient Cw,net of -0.16, due to the large clockwise loop contributing a negative damping of Cw>Cw = -0.41 compared to the other two counter clockwise loops who contribute a combined positive damping of Cw>Ccw = 0.25. Recall that a pitching moment that opposes the direction of airfoil motion will tend to dampen any vibrations, whereas vibrations may by enhanced if the directions of Cm and airfoil motion coincide; this effect being summarized in a single coefficient termed the torsional damping factor, and computed as the line integral of Cm over the oscillation cycle. Lastly, the Cd versus a curve in Fig. 21c demonstrates the 6-fold increase in the drag-at-stall value between 77 the static and dynamic curves. As far as the aerodynamic loads are concerned the current oscillation parameters result in the deep dynamic stall, and are ideal for the application of control. It is of interest to note that there was somewhat of a plateau in the lift coefficient prior to the dynamic-stall angle. In fact, for lower values of reduced frequency and Reynolds number, a double peak was observed [27]. This trend was somewhat unexpected as compared to the rather continuous increase in lift in the dynamic-Q loop of an oscillating NACA 0012 airfoil (dashed line in Fig. 21a). Nevertheless, other researchers have encountered a similar behaviour for a variety of airfoil shapes and Reynolds numbers [40, 32, 57]. This rather unusual sequence of dynamic-stall events can be explained from a careful examination of the surface pressure coefficient distributions on both the NACA 0015 and 0012 airfoils, as shown in Fig. 22. Figure 22a suggests that for an oscillating NACA 0015 airfoil, the upstream movement of the turbulent boundary-layer breakdown, or separation (at ofo ~ 20.9°), was somewhat prolonged and sluggish, compared to a NACA 0012 airfoil [46] (Fig. 22b), before the formation and detachment of a LEV from the airfoil upper surface (at 0Cu « 22.6°). Note that for a NACA 0012 airfoil oscillated with oc(t) = 10° + 10°sinoot, the dynamic-stall mechanism was characterized by the sudden breakdown of the turbulent boundary layer (at Ou = 15.9°) and its rapid upstream movement, which led to an instant disruption of the laminar separation bubble and, subsequently, the initiation of the formation and convection of an energetic LEV (at otu = 17.4°). As a consequence, a single continuous peak in Q prior to dynamic stall at ads = 19.8° was observed. The sequence of events over the airfoil were determined from the three-dimensional views of the phase-averaged surface pressure distributions (Fig. 2Id), and mean and rms streamwise velocity wake profiles obtained at a location 1.75 chords downstream from the trailing edge (Fig. 21e). The observed behaviour is typical of an airfoil subject to dynamic stall. The predominantly attached turbulent boundary layer (AF), ascertained from the strong leading-edge suction peak and the narrow wake of low velocity deficit, persisted up to approximately 12°. During this time, the suction peak increased with increasing incidence, resulting in a linear increase in lift and a decrease in pitching moment (Figs. 21a and 21b). Subsequently, a thin region of reversed flow (FR) formed adjacent to the surface and propagated upstream with increasing incidence until slightly beyond the static-stall angle of 78 18°. Although the presence of flow reversal cannot be directly identified from the surface pressure distributions, its affect on the lift coefficient, in the form of a slight change in lift- curve slope, and on the pitching moment, in the form of an increase, is clearly visible. In addition, the presence of flow reversal results in a slight increase in wake parameters (i.e. width, velocity deficit, and turbulent fluctuations). A breakdown of the turbulent boundary layer is then encountered, which leads to the formation of a LEV, and its subsequent detachment just prior to amax. The turbulent breakdown results in an observed decrease in the peak suction pressure over the airfoil, and the LEV formation is identified by its wide low- pressure footprint that spreads downstream. As a result of the LEV, the wake is seen to abruptly increase significantly in width, deficit, and rms level. The next phase in the flow sequence is characterized by the complete separation of the boundary layer over the upper airfoil surface, resulting in a loss in suction pressure over the airfoil and the persistence of a wide wake of large velocity deficit and turbulent fluctuation (P-S). Finally, the boundary layer begins the reattachment process (RE), indicated by the return of a leading-edge suction peak, and a simultaneous decrease in wake width, velocity deficit and fluctuation levels. The sequence of events described above are characteristic of deep dynamic stall, however in comparison to studies done elsewhere the Reynolds number may be considered relatively low. This may call into question the so-called "quality" of the dynamic stall experienced. That is to say, is it equivalent to that encountered under flight conditions? To establish the utility of the data that will be presented despite the relatively low Reynolds number of 2.46 x 105, use will be made of the dynamic stall function defined by Bousman [4, 5]. His extensive analysis of dynamic stall data from multiple sources, conducted under a wide range of conditions, showed that dynamic stall data may be described by a function characteristic of each airfoil profile that relates the peak aerodynamic load values. In Ref. 5, he provides the relation between C/>raax and CmjPeak for a NACA 0015 airfoil profile derived from data taken at M = 0.3 and Re = 2 x 106. Figure 23 plots the dynamic stall function (solid line) along with the data point for this current investigation (denoted by a circle). The fact that the point lies directly on the curve suggests two things. First, the accuracy with which the data was obtained is fairly high, and second, the current results agree with those obtained under conditions more representative of helicopter flight, and therefore are just as applicable. 79 In fact, the PIV measurements were conducted at an even lower Reynolds number (8.69 x 104) and still agrees well with the dynamic stall function of Fig. 23 (denoted by square). 5.2 Effect of Trailing-Edge Flap Control: A Generalized Description Considering the highly unsteady nature of the flow over a harmonically oscillating airfoil undergoing dynamic stall, it is generally unnecessary and unjustifiable to exercise control continuously over the entire oscillation cycle, and only a brief moment of control within the oscillation cycle should be employed. The questions then become when to begin control, how long should control be applied, and in what form should control take? Essentially, the goal is to determine the ideal flap motion profile for beneficial control of the aerodynamic loads. The motion profile of the trailing-edge flap (TEF), chosen to be genetically trapezoidal in shape, consists of a deflection of the flap initiated at a certain instant in the oscillation cycle (ts), either upwards or downwards, from a position of 0° to a position of 8max at a specified ramp rate (Rl), followed by a period of no motion (U), and completed with a return of the flap to 0° at a specified ramp rate (R2), all of which spans a predetermined total time (ta). Note that an upwards deflection (i.e. towards the suction side) is defined as positive, whereas a downwards deflection (i.e. towards the pressure side) is negative. Prior to discussing the influence that each of the flapmotio n parameters, of which there are six, has on the flow over an airfoil subject to dynamic stall and the associated aerodynamic loads, it is instructive to give an overall description of the effects of trailing- edge flap control using a control case that typifies the entire category of TEF control as applied to dynamic stall. This will lay the foundation with which to understand the effects of each of the parameters. The choice of flap motion parameters to be used in this most crucial step is not arbitrarily chosen and is based on the results which follow, however justification for the choice of flap motion parameters will not be made here; rather it will become apparent in the next section that discusses the results of a parametric study into the effects of each motion parameter. It is of great significance that trailing-edge flap control of the flow around and aerodynamic loads on an unsteady airfoil have never been verified experimentally. 80 The results presented herein will be limited to the single oscillation case described by a(t) =16° + 8°sin(a)t) and K = 0.1. Recall that the Reynolds number for these experiments is 2.46 x 105. The representative flap motion used to establish this foundation is described by an upwards, or positive, flap deflection which begins at ts = On, coinciding with the mean angle of attack during the upstroke motion, reaches a peak deflection of 8max = 16° at au = 21.3° (recall that the subscript u indicates the upstroke) using a ramp rate that endures for tRi = 1 0.116ft , remains at that flap angle for a duration tss = 0.281fo"', or until ad = 20.8°, and returns to a deflection of 0° by aa = 15.4° at a ramp rate that endures for tR2 = 0.116ft,"1; the entire motion takes td = 0.513ft"1 to complete (i.e. about half the oscillation cycle). This case is identified in Tables 2 and 3, which tabulate the values of the flap motion parameter and the critical aerodynamic values resulting from the control, as case #5. A discussion of the effects of TEF control, under slightly different conditions, is provided in Ref. 27. Beginning with the results from the phase-averaged surface pressure distributions, presented in Fig. 24 at selected angles of attack, the effects of the active flap control on the flow over an unsteady airfoil and the aerodynamic loading distribution may be determined from a comparison between the results for the active control case and those for the baseline case. It turns out, however, that this only provides one piece to the puzzle, the other one being provided by a comparison to the results of an oscillating airfoil with a +16° passively, or statically, deflected flap. This combined data set provides a complete appreciation for the effect of active flap control that cannot be achieved otherwise. The Cp distributions for the baseline, active control and passive control cases are represented by the solid, dashed and dotted lines, respectively. The flap motion along with the airfoil oscillation is shown at the end of Fig. 24. Prior to flap actuation, corresponding to au < 16°, the surface pressure distribution of the active control overlaps identically with that of the baseline case. This indicates that while the flow remains attached over the airfoil, which occurs during the initial portion of the upstroke, there does not exist any effect of the ensuing or previous flap control. In other words, although the flap motion lasts until halfway through the downstroke motion, no residual effect of the flap is noticed during the upstroke prior to its reactivation. The reason behind this has to do with the state of the flow during the downstroke motion, and will become evident shortly. This is an encouraging and constructive result, as the concept of an 81 active control system is for the flow to remain unaffected when control is not being employed. This finding supports the potential use of such a control mechanism for the helicopter rotor blade control of various other flow phenomena such as the blade-vortex interaction. Although dynamic stall and blade-vortex interactions are each not limited to a single azimuth angle, they are predominantly observed on the retreating and advancing sides of the rotor disk, respectively, and therefore could possibly implement the same control mechanism if one is discovered that simultaneously mitigates the negative effects of both flow phenomena. During the flap upwards, or positive, deflection between au = 16° and au = 21.3°, the pressure distribution undergoes a deviation from the baseline pressure distribution. On the airfoil lower surface, the motion of the flap lower surface away from the flow induces a reduction in the pressure as a result of higher flow velocities underneath the airfoil permitted by the withdrawal of the trailing edge. In other words, the trailing edge no longer protrudes into the lower flow very much, where the boundary layer is very thin owing to the favourable pressure gradient, thus allowing the flow to maintain a higher velocity. This reduction increases gradually from the leading-edge stagnation point (LESP), which was shifted slightly upstream to a location of x/c = 0.036 from x/c = 0.048, towards the trailing-edge region. Note that the locations of the surface pressure taps in the vicinity of the leading-edge stagnation point are x/c = 0.036 and 0.048, therefore the shift in the stagnation point may be less than implied from the measurements. Regardless, it can be said that a small but distinct upstream shift in the LESP is observed. Near x/c ~ 0.6 the Cp distribution diverged from that of the baseline case more rapidly with downstream distance, reaching a peak suction pressure just downstream of the flap hinge located at x/c = 0.75. The lower flap surface pressure distribution, in an attempt to satisfy the Kutta condition, subsequently increased in pressure to minimize the pressure difference across the trailing edge. On the upper airfoil surface, a reduction in the suction pressure was experienced. The reason for this may be found in the retarded boundary-layer flow, into which the flap now protrudes impeding the flow as it navigates around the flap. In contrast to the lower surface, for which a non-uniform reduction in the positive pressure was observed, the decrease in the upper surface suction pressure was rather evenly distributed fromth e suction peak all the way to the trailing edge. The state of the flow, interpreted solely from the pressure measurements, did not seem to be affected. For 82 example, the laminar separation bubble length and location remained unchanged within the measurement resolution. Among the upper and lower airfoil surfaces, it was the lower airfoil surface, in particular the lower flap surface, which experienced the largest effect on the surface pressure. It is believed that this is due to the local thickness of the boundary layer. On the lower surface, the boundary layer in the trailing-edge region is very thin and a small change in trailing-edge geometry may provoke a large aerodynamic effect, whereas the upper surface trailing-edge boundary layer is thicker and a small change in trailing-edge geometry is less effective in altering the flow. The extent of the deviations from the baseline case as described above increased with increasing flap deflection angle, reaching a maximum once the flap reached its peak deflection of 16°. Note, however, that effect of the flap is not limited to its geometric angle, but also to the rate at which the flap deflects. In comparison to the passive control Cp distribution at au = 21°, the lower flap surface suction peak is superior, indicating the effect of the flap is more than just that of a geometric change in angle, but that the dynamic flap motion also contributes to enhanced loads, similar to that experienced by a pitching airfoil. Rennie [76] and Rennie and Jumper [77,78] also found that the effectiveness of a trailing-edge flap was greater during its motion than after it ceased. More importantly, a comparison between the passive and active control cases at au = 21° and au = 23° indicate that at very large angles the flaps were equally effective. As the discussion of passive flap control in section 5.7 reveals, the above behaviour is indicative of a very important benefit of active TEF control versus passive TEF control. It is demonstrated that for a large static flap upwards deflection, such as 8 = +16°, the boundary layer on its lower surface separated, which significantly hindered the flap's performance. As the presence of a strong suction peak on the lower surface of the active flap indicates that the boundary layer was still attached, it reveals that the dynamic motion of the flap has a crucial role in maintaining an attached lower surface boundary layer. This explains why the lower flap surface suction peak is larger for the active control than for the passive control. For sufficiently high angles of attack though, the boundary layer on the passive flap reattached and therefore its performance mirrored that of the active control case. More details are provided in section 5.7. As a result of the flap deflection, the formation of the LEV (au = 22° and 23°), identified from the formation and growth of a broad suction pressure peak, was slightly 83 delayed and its strength was somewhat reduced. This is observed from its reduced suction pressure footprint, indicating its inferior strength, which is constrained to an area located further upstream, signifying its delayed formation. These two findings are extremely important results as the delayed formation of a weakened LEV will lead to a less severe stalling of the airfoil. This is also important because the current view of researchers elsewhere is that the leading-edge vortex can only be affected by leading-edge devices. The extent of the weakening will become clearer when the aerodynamic load loops will be discussed. Note that the suction pressure beneath the flap has been maintained. In fact, direct comparison between au = 22° and au = 23° shows its magnitude to have increased somewhat. During and subsequent to the shedding of the LEV into the wake (au = 24° and a 84 Inspection of the airfoil wake velocity distributions can also be very informative as they reveal some interesting characteristics that shed light on certain aspects of the flow. In Fig. 25, the non-dimensional mean and rms streamwise velocity wake surveys are presented (i.e. u/uoo and u'/uoo). Prior to the flap motion during the upstroke (i.e. prior to au = 16°) the wake of the actively controlled airfoil agreed in width with the uncontrolled airfoil, however, a marginal increment in both velocity deficit and turbulent fluctuation is noted. During the flap deflection motion, the wake underwent an upwards shifting of its centerline reaching a maximum displacement when it reached its fully deflected position at au ~ 21°. The wake width, deficit and turbulence levels remained unaltered, suggesting that the boundary layer had the same character but was displaced because of the flap. Recall that this was the same conclusion drawn from the pressure measurements. This behaviour continued during the formation of the LEV (au = 22° and 23°). The delay in its formation for the control case is evident from the narrower wake width. The most dramatic effect of the flap on the wake, however, is observed during the post-stall period (see aa = 21°). Although the wake width was the same as the baseline case, suggesting the lower boundary layer remained attached to the surface, the velocity deficit was a great deal reduced, by almost 40%. It is believed this seemingly inconsistent behaviour may be explained as resulting from a more energetic mixing of the accelerated lower surface and retarded upper surface shear layers in the wake. Note that for au = 21°, 22° and 23° the mean and rms u-distributions were biased towards the lower part of the wake, whereas for aa = 21°, they were rather evenly distributed. This suggests that while the upper boundary layer remained attached at the trailing edge, the trailing shear layers continued largely separate from each other without much mixing being involved. Once the massive separation of the upper surface boundary layer occurred, the large turbulent fluctuations enhanced the mixing of the upper and lower shear layers in the wake thus allowing the higher momentum flow emanating from the lower flap surface to energize the highly retarded upper surface flow. This greater mixing continued during the flap return motion (between otd ~ 21° and ad ~ 15°), and thus the wake deficit persisted to be reduced compared to the baseline airfoil. Note that this behaviour is consistent with the Cp results, for which an improved pressure distribution was observed for the control case. In addition, the wake centerline was shifted upwards slightly, but not as much as when the flap was deflected upwards; this owing to the state of the boundary layers in their respective 85 instances. During the later portion of the downstroke (aa =10°) the improved pressure distribution is reflected in an improved wake velocity profile of reduced deficit, albeit at a lower increment. The similarity in the u' distributions confirms the previous deduction that flow reattachment was not promoted, as such an occurrence would entail a reduced wake width with possibly lower turbulence levels, which is clearly not the case. It is interesting to note that although the flap seems capable of significantly altering the mean flow, the fluctuating component consistently remains fairly close to the baseline case. This suggests that, although the relatively quick motion of the trailing-edge flap can alter the overall flow structure, the level of turbulence does not respond in any appreciable way. The consequences of the above-described modifications to the flow on the aerodynamic loads are shown in Fig. 26. The vertical dotted lines separate the upstroke and downstroke motions, and the vertical dash-dot lines identify, in chronological order, the instances of the beginning of flap upwards deflection, end of flap upwards deflection, beginning of flap return motion, and end of flap return motion. The baseline case, depicted with a solid line, is included to serve as a reference for the active control case, represented by the dashed line. In this figure the upstroke and downstroke portions of the load curves are separated so as to avoid the crossing of lines and make the deviations more clear. As the Cp data indicated, prior to the flap deflection during the airfoil upstroke motion there was absolutely no deviation in the lift, drag or pitching moment coefficients from the baseline case, confirming that prior to the flap deflection there was no effect on the flow. As the flap moved towards its maximum deflection, a gradual reduction in lift and drag, and increase in pitching moment are observed. Note that the upward flap deflection made the ordinates of the mean camber line negative in the trailing-edge region. As a consequence, the zero-lift angle became more positive, and the lift and the nose-down pitching moment were reduced for a given angle of attack. The reduction in lift and drag may be traced back to the combined decrease in the upper surface suction and lower surface positive pressures. The increase in nose-up pitching moment, however, was mainly caused by the increased loading on the lower trailing-edge flap surface. During the later portion of the upstroke, the formation and shedding of an energetic LEV is evidenced by the rapid rise and drop in Q and Cra, respectively. Analyzing the Q and Cm curves reveals some interesting facts about the effects of the TEF on the LEV. The timing 86 of the LEV initiation may be gauged by the occurrence of the onset of the rapid drop in Cm and steep increase in Q; these occur at lift and peak negative pitching moment; these occur at au = 23.8° (x = 1.326) and = 1.421) for the baseline case, respectively, and au = 23.9° (x = 1.421) and au = 24.0° (x = 1.484) for the control case, respectively. This represents a delay of only 0.1° or, in terms of phase angle, 0.095 for lift stall and 0.063 for peak moment. This reveals a LEV convection speed over the airfoil that was higher for the control case than for the baseline case. It can therefore be concluded that the initiation of the LEV was delayed compared to the baseline case; however, the presence of the flap caused the LEV to convect over the airfoil at a faster pace. Moreover, the effect on the strength of the LEV may also be approximated from its effect on the aerodynamic loads. The increment in pitching moment coefficient between the instant of moment stall to its peak negative value is 0.3 and 0.27 for the baseline and control cases, respectively. The increment in lift coefficient between the LEV initiation and lift stall is 0.27 and 0.26 for the baseline and control cases, respectively. Although these two measurements can not be used to approximate the actual strength of the LEV, they do suggest a slight weakening of the LEV due to the control mechanism. After the complete separation of the upper surface boundary layer, and during the flap steady-state motion fixed at 8 = 16°, the reduction in lift and drag, and increase in pitching moment was maintained. Notice that the degree to which the lift and drag were decreased was less than that which was observed during the airfoil pitch-up motion, whereas for pitching moment the increases were about the same. For example, comparing the difference in the aerodynamic loads at the beginning of the flap steady-state period (at a„ = 21.3°) to the end of the steady-state period (at aa = 20.8°) ACm is 0.091 compared to 0.095, AC/ is 0.36 compared to 0.22, and ACa is 0.097 compared to 0.039. This confirms that 1) the flap is very effective in controlling the pitching moment, 2) its ability to manipulate Cra is relatively unaffected by the state of the upper airfoil surface flow, and 3) the majority of the effect of the flap originates from the suction pressure formed on its underside. Note that the present explanation of the observed decrease of the undesirable nose-down pitching moment, mainly 87 as a result of the presence of suction pressure on the lower surface of the flap, is, however, in contrast to the mechanism suggested by Feszty et al. [18]. Their CFD results suggest that, for aNACA0012 airfoil oscillated with a(t) = 15°+ 10°sincot and K=0.173 at Re= 1.463 x 106, the alleviation of the nose-down pitching moment was primarily attributed to the trailing- edge vortex (TEV), which caused another suction peak (in addition to the LEV-induced suction peak) over the upper surface of the airfoil in the trailing-edge region, being pushed off of the airfoil by the LEV due to its modified trajectory. During the current experiments, no evidence for a TEV was found. It is possible, however, that this may be due to the much higher Reynolds number and larger reduced frequency at which their computations were conducted. During the flap return motion, a gradual restoration of the loads towards those of the baseline case was observed, however an overshoot occurred resulting in lift and drag levels higher than for the baseline airfoil. This improved lift and unwanted increase in drag are consequences of the improved Cp distribution observed in Fig. 24. This overshoot was maintained until the flow reattachment stage, inferred from the local maximum in the Cra curve at aa = 9.3° which identifies the instant at which the reattachment point passes the quarter-chord pitching axis. At this point the increment gradually decreased until the downstroke motion had ended and the loads coincided with those of the baseline case. In summary, during the upwards deflection of the trailing-edge flap, the flow on the windward side of the airfoil was of a higher velocity due to an effective negative trailing- edge camber and reduced protrusion in the lower flow stream, resulting in a reduction in Cp and an upwards deflection of the shear layer emanating from the flap lower surface causing the wake width to decrease. This deviation in the lower pressure distribution was, however, non-uniform and the majority of the effect was localized in the area surrounding the flap, where a suction peak formed just downstream of the flap hinge. On the upper surface, a uniformly distributed decrease in the surface pressure distribution was observed. The Kutta condition, however, was almost always satisfied, except during LEV shedding, as the trailing-edge pressure differential was minimal. The combined result was a decrease in lift, drag and nose-down pitching moment. Notably, the strength and initiation of the LEV were only slightly affected; its strength was decreased and its initiation delayed. Furthermore, the trailing-edge flap's ability to manipulate Cm was relatively unaffected by the state of the 88 upper surface boundary layer, due to its consistent influence over the lower surface flow. Once the flap returned to its undeflected position, the flow around the airfoil was generally minimally affected if at all, and therefore the aerodynamic loads approached, if not coincided with, those of the baseline, or uncontrolled, airfoil. Of practical interest is the effect of the flap on the peak aerodynamic loads (i.e. C/>max, Cm,peak and Cd,max)5 as well as the global quantities of the aerodynamic damping, or work coefficient Cw, and the lift-curve hysteresis CH- From Fig. 26 it can be seen that despite a 24% reduction in peak lift, the adverse peak negative pitching moment was reduced by 40% and the maximum drag was reduced by 23%. Expressed as a ratio (i.e. C/,max/|Cm;Peak|), which researchers elsewhere have used to define the relative merit of a control concept, a significant improvement is achieved from a value of 6.02 to a value of 7.55; representing an increase of 25%. Of somewhat lesser importance is the Q>maX/C 5.3 Effect of Flap Motion Parameters The previous section gave an overall description of the effects of a dynamic trailing- edge flap on the flow over, wake behind, and aerodynamic performance of an oscillating airfoil under dynamic stall conditions. They were, however, for a single representative flap motion; that is, for a single combination of total duration, start time, deflection magnitude, deflection direction, initial ramp rate, steady-state time period, and return ramp rate. To understand the effects of each aspect of the flap motion, an extensive parametric study was undertaken, in which a wide range of values for each parameter was employed, and the changes in the distinguishing aerodynamic properties was documented. A list of all the different control cases tested, describing the trailing-edge flap motion profile characteristics, is provided in Table 2. The current section will look at the effects of each of these parameters individually, the results of which are presented in tabular form in Table 3. Ref. 28 89 summarizes the results of this investigation into the effects of the flap motion parameters. This comprehensive analysis will then allow for a set of guidelines to be established with which to determine the required values of each flap motion characteristic based on the desired level of control. This, along with a discussion of an optimum control motion, will be discussed in section 5.4. It should be noted that under certain circumstances it is not possible to vary one parameter without altering others. For example, changing the total duration requires a change in at least one of tiu, tss, or tR2. Furthermore, the effects of one variable may depend on the value of another variable. Every effort therefore has been made to consider each parameter in a systematic way with as much detail as possible. 5.3.1 Effect of Actuation Duration To study the effects of the duration of the flap actuation three values for this 1 _1 1 parameter were chosen (i.e. td ~ 30%fo' , 50%fo and 70%fo" ), ranging from a fairly short duration to a rather long duration. Note that f0"' denotes the period of the oscillation frequency (i.e. the time it takes for the airfoil to complete a single oscillation cycle). Anticipating that the influence of td would most probably be largely effected by the start time, since this would control which portion of the oscillation cycle is subject to control, these tests were conducted at three values for ts (i.e. ts ~ -0.5n, OK and 0.57t), corresponding to the beginning of the upstroke amin, the mean angle during the upstroke am, and the top of the upstroke motion amax. In varying the total duration, it is not possible to maintain a constant tRi, tss, and tR2, therefore it was decided to keep tRi and tR2 constant at a selected value, and to change tss to obtain the desired value of td. The choice of tRi and tR2 was based on the decision to divide the flap motion for the shortest duration of around 30%^ approximately into thirds. Therefore the flap pitch-up and pitch-down motions spanned approximately 11% of the oscillation cycle and the stationary portion of the flap motion (i.e. tsS) lasted 30%, 56% 1 _1 1 and 68% of the entire flap motion duration for the td ~ 30%fo' , 50%fo and 70%fo" cases, respectively. In addition, the amount the flap was deflected, as well as the direction in which it was deflected, was chosen to be an upwards deflection of 8 = 16° to best reflect the highest 90 reduction in -Cm,peak and the negative damping. These test cases are identified in Tables 2 and 3 as cases 1 through 9 inclusive. The effects of flap duration on the dynamic Cm-Q-Cd loops are presented in Fig. 27 for a fixed start time of On radians (i.e. starting at am). Recall the three flap actuation durations considered are 30%, 50% and 70% of the oscillation cycle time period f0"\ The baseline oscillating airfoil (solid line) and the static airfoil (dash-dot line) are also included for reference. The arrows indicate the directions of the pitch-up and pitch-down motions. Prior to the beginning of the flap actuation, all three cases demonstrate no effect on the aerodynamic loads, as should be expected. What's more, as the flap deflection ramp rate Rl is the same for all three values of td, the deviation in the loads from the baseline case are almost identical. That is, during the motion of the flap, the reduction in Q and Ca, and the increase in Cm are the same regardless of td. It is evident that the effect of the flap undergoing an upwards deflection is always to increase the effective negative camber in the trailing-edge region of the airfoil thus reducing the overall airfoil circulation and increasing the airfoil's aft loading. In regards to the LEV, the phase angles at which the formation, convection and detachment of the LEV were found to be virtually unaffected by the length of the TEF motion, as evidenced by the same angles of dynamic stall aas and peak in the pitching moment amp (Table 3). Comparing the peak values of pitching moment, lift and drag, occurred during the dynamic stalling of the airfoil, it is found that not much of a variation between the different values of td is encountered. On average, they each result in reductions of 40%, 25% and 23% in -CmjPeak, Q,max and Cd,max, respectively. In contrast, a large difference in the aerodynamic loads during the downstroke motion is observed, and this is where the majority of the influence of td lies (i.e. during the post-stall time period). As td is increased, the increase in Cm and the decreases in Q and Cd are maintained for a longer period of time. This results in a smaller clockwise loop and a larger counter clockwise loop in the Cm curve, leading to a significant increase in the positive aerodynamic damping. In addition, the post-stall drop in Q is also increased with increasing td leading to increasing hysteresis. The instant of flow reattachment, however, was not observed to vary noticeably with td. 91 To further examine the effects of the upward flap deflection duration, and its dependence on the start time, the variation of the critical aerodynamic values, such as C/)raax, Cm,Peak, Cw,net, |C/,ma*/Cm,peak|, CH, and Cd>max, with td at different ts was characterized and is presented in Fig. 28. Also shown in Fig. 28 are the baseline, or uncontrolled, airfoil data, presented as a dashed line. The critical aerodynamic values and the TEF motion profile characteristics are tabulated in Tables 3 and 2 respectively. Figure 28a demonstrates that CmjPeak requires a ts prior to the occurrence of moment stall in order to benefit from a reduction in its peak nose-down value, irrespective of td, since an improvement is only seen for ts < 0.2871. A linear reduction in |Cra;Peak|, compared to a baseline airfoil, with increased td was observed for ts = -0.5TE (or a flap deflected at amin); the longer the flap actuation the less the peak nose-down pitching moment. This resulted from the transition from an undefiected to a fully deflected flap position at the instant when the LEV was traveling downstream over the airfoil as td increased. At ts = On (corresponding to an upward deflection at am during pitch-up), a consistent improvement of about 40% in Cm,peak, effectively insensitive to td, was exhibited as a result of the coincidence of the peak flap deflection with the occurrence of moment stall. It can therefore be concluded that, in regards to Cm,peak, the choice of td is dependent on the choice of t^ an early start time requires a reasonably long td, whereas a later start time can still be effective with shorter durations. However, the value of td is irrelevant if the control motion is begun subsequent to the LEV initiation. In contrast to the virtually unchanged Cm,peak, Fig. 28b indicates that the ts = 0.57c control case persistently provided a significant increase (between 0.52 to 1.27 compared to - 0.16 for a baseline airfoil) in Cw,net (see Table 3); the largest of any ts regardless of td. This is a direct consequence of a significant suction pressure on the flap lower side which persists solely during the downstroke resulting in nose-up pitching moment and contributing to Cw.ccw On the other hand, the ts = -0.57c case presented an increased |CWjCW| resulting in a considerably reduced CW)net compared to a baseline airfoil, as a result of an increased/unchanged Cm during the upstroke/downstroke (except for the longest duration), which translates into slightly smaller counter clockwise loops but significantly larger clockwise loops. The results for ts = Ore fall in-between the other two start times and show a linear increase in CWinet with td as the flap loading extends more into the downstroke; the 92 Cw,net was above the baseline airfoil value for ta > SQVofo'1. Figure 28b therefore implies that _1 for an improved aerodynamic damping, a U < 50%fo requires a minimum ts slightly after On 1 (i.e., the smaller the ta the later the ts required) and a ta > 50%fo" allows for a minimum ts slightly earlier than ts = On. Trends similar to those for Cm)Peak are observed for the peak lift in Fig. 28c. Essentially no reduction in C/,max was observed for the ts = 0.5TC case, since the flap deflection occurred after the LEV was shed into the wake and the instant of peak lift had passed, while for ts = On, a C/>max of about 1.26 compared to 1.69 of a baseline airfoil, was observed; a reduction of about 25%, essentially independent of ta. Furthermore, the peak lift, following the trend in the deflection angle at the moment of lift stall, decreased almost linearly with increasing ta for ts = -0.5TE. In comparison to the ts = On control case, the ts = -0.5JT case 1 generated a larger peak lift for td < SC^/ofo" and a smaller peak lift for ta > 50%fo"'. It is concluded that to minimize the reduction of the peak lift, a shorter duration is desired. The effectiveness of upward-flap control was also evaluated based on the performance ratio of |C/,max/Cm,peak|- Figure 28d shows no noticeable improvement over the baseline airfoil for the ts = 0.57c case for any of the ta tested, proving that the flap deflection occurred too late in the oscillation cycle. Moreover, the earliest start time ts = -0.5TC also _1 showed no improvement until the duration exceeded 50%fo at which point it began to increase. This indicates that for a start time begun at the beginning of the upstroke motion combined with a duration less than SOVoU1, the influence of the flap over lift and pitching moment are the same, however for longer durations the reductions in -Cm,peak outweigh those of C/,max. The highest |C/>max/Cm,peak| ratio was, however, generated by the ts=OTC control case, irrespective of duration. This revealed an advantage of longer durations for early start times (i.e., -0.57C < ts < Ojt) that does not exist for later start times (i.e., OTT < ts < 0.57r). The effect of ta on the lift-curve hysteresis CH was also examined and is displayed in Fig. 28e. Recall that CH is defined as the line integral of the Q -a curve. In comparison to the baseline case, reductions in CH resulted when the flap deflection began earlier, with increased hysteresis occurred for later start times. A consistent trend in ta is not observed, with the ts = - 1 0.571 case displaying a local minimum at ta = 52%f0" , the ts = 0.5TC case displaying a local 1 maximum at ta = 52%f0" , and the ts = 07t being roughly linear as a function of duration, 93 falling in-between the other two start times. This suggests a benefit from earlier start times and/or shorter durations. Finally, the effect on the peak drag coefficient Cd,max was documented in Fig. 28f and is observed to follow very closely the trends in Cm,peak and C/>max. Essentially no reduction in Cd,max was observed for the ts = 0.5TC case, since the flap deflection occurred after the airfoil experienced the peak loads, while for ts = OJI an average Cd,max of about 0.57 compared to 0.74 of a baseline airfoil, was observed; a reduction of about 23%, essentially independent of ta. Furthermore, the maximum drag, following the trend in the deflection angle at the moment of dynamic stall, decreased almost linearly with increasing td for ts = -0.571. In comparison to 1 the ts = OTE control case, the ts = -0.5TI case generated a larger peak drag for td < 65%f0" and a smaller peak drag for td > 65%f0"\ It is concluded that to capitalize on the reduction of the maximum drag, a longer duration is desired. To summarize, the results presented in Figs. 27 and 28 demonstrate that as the duration of the flap actuation is prolonged, so is its effect on the aerodynamic loads. So long as the flap reaches its maximum deflection prior to LEV formation and remains fully deflected during the LEV convection, the actual duration of the flap motion beyond these occurrences is of no importance to the local peak load values. Where td exerts the majority of its influence is on the global characteristics portrayed by Cw,net and CH. For these aerodynamic qualities, the portion of the flap motion spent during the upstroke compared to during the downstroke commands significant influence, and therefore the effects of td and ts are interrelated. This, consequently, leads to the conclusion that a flap actuation duration > 1 SO^ofo" leads to the desired improvements in CraiPeak, Cw,net, |C/,raax/Cm,peak| and Cd,max with a small adverse effect on Q,max and CH. 5.3.2 Effect of Actuation Start Time The effects of the flap actuation start time ts on the dynamic load loops were 1 investigated with td and 8max fixed at 0.5 lfo" and +16°, respectively. Three different ts (= - 0.4771, OK, and 0.46rc radians corresponding to a flap actuation initiated at Ou = 8°, 16° and 23.9°, respectively) were tested (Fig. 29). Again, the baseline oscillating airfoil (solid line) and the static airfoil (dash-dot line) are included for reference, and the arrows indicate the 94 directions of the pitch-up and pitch-down motions. Note that all flap motions were begun during the upstroke motion, as it was deemed unnecessary to initiate the flap during the downstroke, as the focus of the control is the extreme aerodynamic loads caused by the dynamic stalling process, and these occur towards the end of the pitch-up motion. Furthermore, TRI, tR2 and tss were set to the same values as in the td investigation, these being 1 l%f0"' for tRi and tR2, and 56% of td for tsS. As can be seen in Fig. 29, although the two earlier actuations reduced the peak nose- down pitching moment more effectively, they also led to significant loss in the maximum achievable dynamic lift. What's more, the earliest of start times (i.e. ts = -0.477t) caused a massive increase and decrease in the Cm and Q loads during the attached-flow portion of the cycle (Figs. 29a and 29d). This effect is neither desired nor is it beneficial, suggesting that too early a start time has an adverse affect on the aerodynamic loads. The ts = -0A1% case, representing an upward flap deflection covering the entire upstroke motion, basically shifted the lift and moment curves vertically downward and upwards, respectively, during pitch-up and, consequently, rendered a dramatic reduction in C/>max and -Cm,Peak- During the downstroke motion, however, the loads returned rather closely to those of the baseline, or uncontrolled, airfoil. Even though the lift-curve hysteresis and drag levels during pitch-up were dramatically decreased, the negative damping was considerably increased due to what had become a large clockwise loop in the Cm-a curve. With a ts = 07t, this unfavourable effect on the aerodynamic loads during the attached-flow portion of the upstroke could be avoided while still achieving a beneficial reduction in -Cra>Peak, which was even greater than for the ts = -0.477c case. Furthermore, the reductions in C/,max and Cd,max were about the same, but now the single CW Cm-loop was replaced by CW and CCW loops of approximately the same size resulting in only a slight negative damping. The degree of hysteresis in the lift curve was, however, returned to a value on the same order as that of the baseline case, although it was somewhat smaller. Figure 29 also shows that for a TEF deflection actuated towards the end of the pitch-up (i.e., ts = 0.467t), the Q curve remained essentially unchanged during pitch-up, compared to a baseline airfoil, while the post-stall lift loss and the hysteresis were found to increase dramatically. Note also that the value of -Cm!peak was mostly unaffected, however the late actuation cause a large CCW loop to form in the Cra-a curve leading to a large positive value for Cw,net- With regards to the effect of ts on the main flow 95 events, the LEV formation and convection were found to be delayed relative to the baseline case with decreasing ts, and no measurable difference in the angle at which the flow began to reattach could be discerned. The above results are suggestive of a desired start time in a range between the mean and maximum angles of attack during the upstroke. To confirm these, Fig. 30 assesses the effects of the start time, and its dependence on the deflection duration, on the variation of the critical aerodynamic values, such as C/,max, Cra,peak, Cw,net, |C/,maX/Cm,peak|, CH, and Cd,max, with ts at different td. The baseline, or uncontrolled, airfoil data, presented as a dashed line, are also shown. The critical aerodynamic values and the TEF motion profiles for the cases in question are tabulated in Tables 3 and 2 respectively, and are labelled cases 1 through 9. The trends observed in Fig. 30a indicate that for the earliest of start times, td had a profound effect on Cm,peak; short durations did not have much of an alleviating effect, whereas the longest duration resulted in the largest reduction. As the start time was delayed and approached the middle of the upstroke, the reduction in CmiPeak was essentially indifferent to the value of td. This resulted from a transition from an undeflected to a fully deflected flap position at the instant when the LEV was traveling downstream over the airfoil. Moreover, since the flap was fully deflected for all values of td at ts = On, the airfoil experienced the greatest improvement in performance. A further increase in ts caused a reduction in the improvement previously achieved, with the values returning to those of the baseline airfoil when the start time neared amax. This reduction is the same for all the values of td tested, and demonstrates that the Cra,peak requires a ts prior to the occurrence of moment stall. It can therefore be said that the peak value of the negative Cm was found to be insensitive to the magnitude of the flap actuation duration provided that the flap remained deflected during its occurrence. From the results shown here, the conclusion can be drawn that, with respect to Cm>peak, the choice of ts is dependent on the choice of td; an early start time requires a reasonably long td, whereas for a later start time the duration is irrelevant. Figure 30b, which presents the variation of Cw>net with ts, shows a very clear tendency for the damping to increase with increasing start time. Note also that the overall trend seems to be similar for all three values of td. Relative to the baseline case, however, any start time less than or equal to OTC is characterized by a deterioration in performance a propos Cw,net, except for very long durations. Furthermore, the shorter the duration, the later the start time 96 must be to impart a positive effect on the work coefficient. The highest values of Cw,net were obtained for the latest start time (i.e. towards the top of the upstroke), since this led to large CCW loops in the Cm-a curve. This figure consequently proposes a minimum start time around ts = OTC to augment the work coefficient (i.e. to impart a more positive damping) over that of the baseline value. Essentially identical trends, albeit inversed, to those of Cm,peak are observed for Q)max in Fig. 30c. For ts > 0%, almost no difference was seen between the different values of td, and the reduction in Q,max experienced was reduced to almost nothing as ts approached 0.5JT. AS was previously stated, the lack of effect at ts» 0.57c is because the flap deflection occurred after the LEV was shed into the wake. For ts < On:, the curves for each U diverged, with the reduction in Q,max being reduced for short durations and increased further for large durations. Therefore, for the sake of maintaining as much of the original peak lift as possible, a late start time in the second quarter of the airfoil oscillation (i.e. between am and amax) is best. The performance ratio of |C/>max/Cm)peak|, plotted as a function of ts in Fig. 30d, shows the largest improvement in the vicinity of ts = On, and almost no change at the limits of the 1 upstroke motion, except for ts = -0.4771 with td ~ 70%fo~ . Although the effects may be the same for ts ~ -0.5n and ts » 0.57c, the reason behind why no change was experienced is different. For ts ~ 0.5TI it is because neither Q,max nor Cm,Peak were altered from their baseline values, whereas for ts ~ -0.5n it is because the reduction in Cm)Peak was exactly balanced by the reduction in C/>raax. The start time should therefore be kept somewhere near the middle of the upstroke, with no apparent preference as to whether it should be before or after. As the lift-curve hysteresis and the work coefficient are both determined from an area integral of a dynamic load curve it might be expected that the flap motion parameters, especially ts and td, would have similar effects, and indeed this is what is found. Comparison of Fig. 30e with 30b shows that the variation in CH and Cw>net with ts and td are similar. Note however that whereas for Cw,net an increase is desired, for CH a reduction is favourable. This, therefore, would entail a start time prior to OJC to benefit from the reduced lift during the upstroke motion. Be aware, though, that reducing the level of hysteresis would ideally be realized through an increase in lift during the downstroke and not a decrease in lift during the upstroke, as is the case here. 97 As was established when investigating the effect of td, the effect of ts on Cd,max is similar to the trends observed for Cm>Peak and Q,max (Fig. 30f). Essentially no reduction in Cd,max was observed for a flap initiated near amax, since the LEV had already passed. For ts < O71, the curves for each td diverged, with the reduction in Cd,max being reduced for short durations and increased further for large durations. If the desire to reduce the peak level of drag is of importance, the flap motion should be initiated during the first half of the upstroke motion. Note, however, that the earlier the start time, the longer the duration required in order to maximize the improvement. In summary, as the start time of the flap deflection was delayed, so were its effects on the flow and aerodynamic loads. For this reason, selection of the start time depends on which portion of the oscillation cycle is control desired. Starting prior to x ~ O71 will adversely affect the attached-flow portion of the cycle by significantly reducing the lift and torsional damping, and increasing the pitching moment, but simultaneously it does reduce the lift- curve hysteresis, an unwanted attribute of an unsteady airfoil. On the other hand, if the start time is delayed to much after 0%, then the overshoot in the aerodynamic loads generated by the LEV are affected very little, since the flap is not yet fully deflected when the LEV forms, with absolutely no effect if the start time occurs in the vicinity of amax (t = 0.5u), as the LEV has already been shed into the wake. Recall that the initiation of the LEV for the baseline airfoil occurs at x ~ 0.2871. It is therefore desirable that the start time be limited to the range between ts = OTT and 0.2871. Further information regarding data obtained within this range, thus providing even more meticulous preferred-range identification, is provided in subsection 5.3.5. 5.3.3 Effect of Maximum Flap Deflection Up to now, the discussion of trailing-edge flap control has been limited to a single flap deflection magnitude of 16° in the upwards direction. This, however, raises the questions: What if the deflection was, instead of upwards, downwards, and how would the flap control be affected by smaller deflections? It is the goal of this section to answer these questions. The effects of 8max were investigated by, in addition to the upwards 16° peak deflection, first deflecting the flap downwards with the same peak deflection (i.e. 8max - - 98 16°), and then deflecting the flap both upwards and downwards with a smaller 8° deflection (i.e.8max = ±8°). Figure 31 presents the effects that a downwards flap deflection (dotted line) has on the aerodynamic loads, pressure distributions and wake velocity profiles, in comparison to an equivalent upwards deflection (dashed line). The baseline case was also included and serves as a reference (solid line). The flap motion parameters were set to the same values for both types of flap motions; only the direction of deflection was changed. In Table 2, which provides the details of the flap motion, this set of data is identified as tests 4-6 for the upwards deflection and 10-12 for the downwards deflection. Note that although three different start times were studied (i.e. ts ~ -0.571, On, and 0.57t), only the ts = OK case is presented graphically, following the recommendation of section 5.3.2. Initial inspection of the lift and pitching moment coefficient curves (Figs. 31a and 31b) clearly shows the overall outcome of a downwards deflection was to produce the opposite effect of an upwards deflection. That is, instead of reducing Q and increasing Cm during the flap motion, they were increased and decreased, respectively, well beyond the baseline airfoil. In fact, for the current flap motion under consideration here, C/>max and - Cm,Peak were increased relative to the baseline case respectively by 26% and 37%, as opposed to reductions of 24% and 40% for the upwards deflection. The vertical lines in Figs. 31a and 3 lb mark the beginning and end of the flap motion. Although not shown, a similar increase in Cd,max was also observed. Note that prior to flap actuation, no influence on the loads was exerted, similar to the Smax = +16° case. In regards to the LEV, recall that an upwards deflection was found to delay its formation, reduce its strength, and increase its convection speed relative to an uncontrolled airfoil. A downwards flap deflection, however, seems to have the opposite effect. LEV formation and convection were promoted, however, the amount that they were advanced was the same suggesting the convection speed was equivalent to that of the baseline airfoil. Furthermore, the increment in Cm between the instants of moment stall and the peak negative pitching moment was slightly higher than the baseline case, with a value of 0.31 compared to 0.30, suggesting a slight increase in LEV strength. After the return of the flap to its undeflected position (i.e. 8 = 0°), the loads, and therefore the flow, did not return immediately to the baseline characteristics. It was only during the flow reattachment process that the three curves slowly converge. One 99 characteristic that upwards and downwards flap deflections share is that neither seem to be capable of promoting flow reattachment during the downstroke portion of the oscillation cycle. This is determined from the coincidence of the local peaks in the Cm curves at aa = 9.3°. Lastly, it may be anticipated that the modifications to the Q and Cm curves for ts = OK led to a slight improvement in Cw,net and increase in CH; this however is highly dependent on ts and td. The critical aerodynamic values for these flap deflection cases are, again, tabulated in Table 3. The above-described effects on the aerodynamic loads originate from the modifications in the surface pressure distributions shown in Figs. 31 c-31 e. Also presented for added insight are the wake velocity profiles, both mean and rms, in Fig. 3If. Once the flap began to deflect, the loads deviated from the baseline curves as a result of the increased and decreased pressure loading for downwards and upwards flap deflections, respectively. Figure 31c displays a typical surface pressure distribution when the flap was in motion. On the suction surface, an evenly distributed increase and decrease in the suction pressure for the downwards and upwards flap motions, respectively, is visible. The pressure surface was also subject to an increase and decrease in the positive pressure for the downwards and upwards flap motions that was felt over the entire surface, but most predominantly in the vicinity of the flap. It is this that caused the majority of the increased/decreased lift and decreased/increased pitching moment observed for the downwards/upwards flap control cases. Note that the wake profiles shown in Fig. 3 If for au = 20° indicate that both upwards and downwards flap deflections have similar effects on the nature of the wake, and thus the boundary layer, except for the direction of wake deflection prior to LEV formation. Figure 3 Id, showing the suction pressure footprint of the LEV to be higher and further along in its development, confirms the previous supposition that the LEV was promoted in its formation and increased in its strength by a downwards flap deflection. This is in direct contrast to the effects that an upwards flap deflection has. Note the persistence of the deviation in the pressure on the lower flap surface despite the wildly varying upper surface flow. This all contributes to a significant increase/decrease in C/imax and -Cm>peak during the downwards/upwards flap deflections. Also, the downwards flap deflection seems to have resulted in a slightly larger wake of greater velocity deficit and turbulence level (au = 23°). This suggests that the extent of flow separation on the upper surface was slightly increased, 100 as might be expected since the flap was positioned away from the upper surface flow. Lastly, during the post-stall flow condition, it is only the lower surface that contributed to maintaining the deviation in the aerodynamic loads from the uncontrolled case (Fig. 31e). However, the direction of the flap motion greatly influenced the wake (ad = 20°). A downwards deflection led to a much larger wake with increased velocity deficit, but it does not contribute much to increasing the turbulence levels as they were already very high due to the upper surface separated boundary layer. An upwards deflection, on the other hand, reduced the severity of the wake although due to the severe upper surface flow separation did not affect the turbulence level. It is thought that these large differences in the behaviour of the flow were caused by the distance between the upper and lower separated shear layers. For an upwards deflection, the lower surface boundary layer, which remained attached, was closer to the upper shear layer and therefore the large turbulent fluctuations were capable of enhancing the mixing of the two resulting in a mitigated wake deficit. On the other hand, a downwards deflection increased the distance between the two shear layers, increasing the size of the wake and making the mechanism for mixing less efficient than even for the baseline airfoil. The PIV measurements of section 5.5 confirm this notion. The effect of deflecting the flap downwards on the critical aerodynamic characteristics, in relation to an upwards deflection, may be more clearly depicted in Fig. 32, which, similar to Fig. 30, plots the variation in the various aerodynamic points of interest as a function of ts. This also allows for the influence of ts on a downwards deflecting flap to be described. First, comparing the 8max = -16° curve to the 8max = +16° curve in relation to the horizontal dashed line representing the baseline airfoil value shows that they are almost exact opposites. Allowing for some variability and few exceptions, the two control curves are essentially symmetric about the baseline curve for all values of ts. The only significant departure from this trend occurs for the sole value of |C/,max/Cm>peak| at ts = OK. Otherwise, at each value of ts, an increase in any of the aerodynamic characteristics for 5max = +16° is paired with a decrease of equal magnitude for 8max = -16°, and vice versa. The effects of a negative flap deflection (i.e. downwards) can be summed up as being the inverse of the effects of a positive flap deflection as shown in Fig. 32 and Table 3. This entails an increase in the peak loads (i.e. Qimax, -Cm(Peak and C^max) and global quantities (i.e. Cw,net and CH), and a decrease in stalling angle and performance ratio (i.e. |C/imax/Cm>peak|). 101 However, for the global quantities, a start time prior to around the mean angle is necessary otherwise a decrease is observed. It is obvious from these results that a downwards deflection is most valuable when the focus of control is improved lift or reduced lift-curve hysteresis. In relation to the Cm-based parameters, though, it is considered to have a detrimental effect and will no longer be pursued except in the PIV experiments of section 5.5. Attention is now turned to the effect of the magnitude of the deflection. For this, a test case with 8max = +16° is compared to one with 5max = +8°. The choice of deflection amplitude used thus far (i.e. 16°) was based on the physical limitations of the flap mechanism, which was only slightly greater than 16°, and the desire to impart as much an effect on the flow as possible. The choice of a second angle with which to compare was based on the need for the flap deflection to be small enough that the difference between the two control cases would be evident, but not too small so that the effect would be sufficient to discern a difference from the baseline case. To demonstrate the effects of dmax, the actual flap motion parameters were irrelevant as numerous tests showed the overall effect to be a universal one, even for negative flap deflections. Figure 33 therefore presents data for the baseline case and the two control 1 cases, for which ts = 0.247t, t 102 This trend is also reflected in the aerodynamic load curves presented in Figs. 33d and 33e. The solid, thick-dashed, and thin-dashed lines represent the baseline, 8max = +16° and Smax = +8° cases, respectively. It can be seen that throughout the oscillation cycle the thin- dashed line always falls in between the solid and thick-dashed lines. Therefore any improvements or adverse effects of the flap deflection were mitigated by reducing its magnitude. In addition, the relationship between flap angle and its effect is not a constant and seems to vary during the oscillation cycle. The effects of 8max on the critical aerodynamic values, presented as an increment relative to the baseline airfoil (i.e. the value for the baseline airfoil for each parameter is subtracted from the corresponding control case parameters), are shown in Fig. 33f demonstrating again in a different, perhaps more clear, fashion that a reduced 8raax leads to a reduced effect on both the local and global quantities of interest. Furthermore, the non-equidistant spacing between the dotted line marking zero difference and 8max = +8° (denoted by squares), and 8max = +8° and 8max = +16° (denoted by circles) indicates a nonlinear relationship. The only characteristic that was unaffected by the magnitude of the flap deflection was the lift-curve hysteresis. The same value was obtained for both cases. It can therefore be concluded that to augment the benefits obtained by an upwards flap deflection, a large deflection is called for. In this case, the peak deflection of +16° was equal to the mean angle of attack, just below that static-stall angle of 18°, and two- thirds of the maximum airfoil angle of attack of 24°. 5.3.4 Effect of Upward Deflection Ramp Rate The dependence of the aerodynamic characteristics on the overall flap motion, described by ta, ts and 8max, has been documented in the previous three subsections. These command the majority of the influence. The rest of this section is reserved for the effects of the detailed flap motion, which will be shown to contribute considerably to how the aerodynamic characteristics behave. The first of these is Rl, which describes the rate at which the flap is deployed from its initial position at 8 = 0° to its final position at 8 = 8max (i.e. the flap upward ramp rate). For the most part, this parameter will be defined in reference to the time the flap takes to make this transition tRi, presented as a percentage of the airfoil oscillation cycle. Therefore, a 103 decrease in Rl is equivalent to an increase in tRi, and vice versa. For this set of experiments the start time was limited between OTC and 0.25TI to ensure that the flap deflection began during the second half of the upstroke motion, but before the airfoil underwent moment stall at x = 0.287t or a = 22.2° during the upstroke, as suggested in subsection 5.3.2. Three start times, including ts ~ On, 0.12% and 0.25TC, were included in this series of experiments to further narrow down the window for beneficial flap actuation commencement. The flap _1 duration was maintained at around 51%fo and 8max was set to +16°, again following the recommendations previously made in this chapter. The effect of tss, a discussion of which is reserved for subsection 5.3.5, is eliminated in these tests by setting it to zero, and the values of tR2 are determined based on the difference between U and tRi, and vary inversely with TRI so that ta can be kept constant. Details regarding the flap motion profiles are provided in Table 2 (cases 15-29). Figure 34a shows that a greater reduction in the Cm,peak was possible by increasing the upward ramp rate (i.e. decreasing tRi), regardless of the start time. Furthermore, the start time was less effective at inducing a change in Cm,peak at very fast or very slow ramp rates than at a 1 medium ramp rate (i.e., approximately tRi = 25%f0" ). Figure 34a also reveals that to generate the largest improvement in CmjPeak would therefore require an early start time with a fast ramp rate. It is also of interest to note that the fastest ramp rate generated a Cm)peak less than that of a statically deflected flap (Cm>Peak = -0.151 compared to -0.170; Table 3) which suggests the creation of an even stronger suction pressure on the lower side of the flap as a result of the quick flap motion. Regardless of the values of ts and tRi, however, an improved peak negative pitching moment over that of a baseline airfoil was always realized for the current range of test parameters. Truth be told however, this analysis is somewhat incomplete. The nonlinear nature of the observed variation led to an interesting and unexpected find. More on this finding will be provided shortly upon completion of the discussion of the results of Fig. 34. The present results also indicate that a reduction in the ramp rate, equivalent to an increase in tRi, resulted in an increase in the aerodynamic damping that is nearly a linear function of tRi (Fig. 34b). The slope of the relation between Cw,net and tRi decreased as the start time was delayed, with a larger difference occurring between ts ~ 0.1 2TC and 0.25TC than between OTC and 0.1In. Note that all cases generated improvements in the aerodynamic 104 damping except for ts = On at ramp times below 25% of the oscillation cycle, with the largest values of net work coefficient generated by a delayed start time and a slow ramp rate. The reduction of the peak lift coefficient associated with the improvements in Cm,peak and Cw,net induced by an upward deflected flap was also examined in Fig. 34c. This figure shows that as the ramp time tRi was increased, the Q,raax was also increased, however with values always below that of a baseline airfoil, regardless of the start time; an effect brought on by the delay in the full deflection of the flap, similar to the effect a delay in start time would have. As a result, the smallest loss in Q,max is produced by a slow ramp rate, and can be enhanced by delaying the start time. Note, however, that the ramp rate control seems more effective at earlier start times, and the start time is more effective at moderate ramp rates. Consequently, in order to minimize the loss in peak lift, a late start time in conjunction with a slow ramp rate is favoured. The effect of Rl on the performance ratio, combining the effects of both Q>max and Cm,peak, is also summarized in Fig. 34d and shows that all combinations of start time and ramp rate resulted in improvements in |C/imax/Cm)peak|. Due to the slightly linear trend in the C/,max, the trend here is similar to that of Cm>Peak and therefore it is, in general, the earlier start times and the faster ramp rates that generate the higher ratios. The effect of Rl on CH is presented in Fig. 34e displaying similar trends to those of the net work coefficient. CH is an increasing nearly-linear function of TRI, with the slopes of the lines reducing slightly as the start time is delayed. Although, it is only at the fastest ramp rates for the earlier start times that the hysteresis is reduced compared to the baseline case. It is important to note the source of the increased/decreased hysteresis. A reduction of lift during the upstroke contributes to a decrease in Q-hysteresis, whereas during the downstroke the contribution would be positive. It is, therefore, the proportion of flap deflection duration during the upstroke to that during the downstroke that determines whether the hysteresis increases, decreases or remains roughly unchanged. Unfortunately this is not the ideal case, which would be to reduce hysteresis by increasing the lift during the downstroke portion of the oscillation cycle, requiring a negative (downwards) deflection of the flap during the downstroke. This, however, would have a negative impact on CWjnet, which is a much more important parameter. From the above, it can be concluded that the critical aerodynamic values can be subdivided into two categories, those whose performance are improved at early start times 105 and fast ramp rates, which are Cm)Peak, |C/>max/Cm>peak| and CH, and those whose performance are improved at late start times and slow ramp rates, which are C/,max and CW)net. Going back to Fig. 34a, it was stated earlier that the seemingly straightforward trends that are portrayed mask an important finding. Further analysis, however, is required to uncover this behaviour. Comparing the trends for the two extreme start times tested (i.e. ts = O71 and 0.25TT), they indicate the same result; the peak negative pitching moment was reduced as the flap pitch-up motion increased in speed (i.e. tRi decreased). Despite leading to the same conclusion, the cause of this trend is quite different for these two cases. In Fig. 35a, the instantaneous angle of the flap at the moment at which Cm reached its peak negative value (i.e. amp) is plotted for each of the two start times as a function of tRi. For the later start time, the angle of the flap increased with increasing Rl. This is to say that for U ~ 0.2571, the occurrence of Cra,Peak coincided with the pitch-up motion of the flap. Alone, this suggests that the faster ramp rate allowed for a larger flap angle during moment stall, and therefore led to a greater effect on Cm,Peak. This finding would be supported by Fig. 35b, which shows the reduction in the upper surface suction pressure and lower surface positive pressure to increase with decreasing tRi. A reduction in start time would have a similar effect. Nonetheless, this is true only up to a point. Figure 35a shows that for an early start time, such _1 as ts = On, and fast enough ramp up rates (approximately greater than or equal to 21 %f0 ), the flap may be well into its return motion by the time that Cm,peak occurs. This leads to a reduced flap angle compared to larger values of tRi (compare tRi = 10.1 to 25.6), and following the previous logic would hint at a smaller effect on Cm>peak. Clearly this is not the case seen in Fig. 34a. This counterintuitive behaviour can be explained by comparing the Cp distributions at the instant of Cm,peak for each of the values of tRi, as shown in Fig. 35c. It is shown here that the effect of a hastened flap motion was mainly focused on the upper surface pressure 1 1 distribution. As tRi decreased from 42.7%f0" to 25.6%f0" , the lower flap surface experienced a great increase in its suction pressure peak and the upper surface a reduction in suction pressure, as might be expected. This behaviour changed as tRi decreased such that the flap 1 _1 was on its pitch-down motion. Between tRi = 25.6%f0" and 13.1%f0 almost no change in the flap lower surface pressure distribution was observed, while the upper surface suction pressure continued to decrease. It is in the persistence of the upper surface pressure to decrease despite a reduction in flap angle for the faster flap deflections that caused the 106 continued reduction in Cm,peak as tRi decreased. The reason behind this is believed to lie in the flap's effect prior to the occurrence of stall, while the flap was still in its pitch-up motion. Because of the increased flap pitch-up rate, a delay in stall occurred (see Table 3). This also led to a reduced LEV strength. It is this reduced LEV strength that is thought to be at the root of the increased flap effectiveness for the fastest flap pitch-up motions despite being at smaller geometric deflection angles. 5.3.5 Effect of Steady-State Time Period An analysis was also done to determine whether a steady-state portion tss after the flap upwards motion and prior to the return motion is advantageous. For this, complementary tests were carried out for which tss was set to approximately half the 50%fo"' flap duration (cases 4 30-38 in Table 2). Table 3 shows that comparing two cases at fixed ts = On and tiu = 13%f0 , 1 _1 the first with tss = 0%fo" (case #16) and the second with tss = 25%f0 (case #31), it is clear there exists contradictory requirements. Introducing the steady-state portion improved Cm,peak and |C/)max/Cra,peak| to a small degree (39% and 19% versus 34% and 17%), improved Cw,net to a large degree (-18% versus -192%), but reduced Q)imx (27% versus 23%), and did not improve CH as much (9% vs. 12%). Although most differences are small, the significant improvement in the net work coefficient suggests that, in fact, having a steady state portion in between the flap upward and downward deflections is extremely profitable. The increase in CWinet is mainly attributed to the persistence of the flap at is maximum deflection, which maintained the increase in Cm for a longer period of time resulting in a smaller clockwise Cm loop. Similarly, the reduction in Q during the downstroke was also maintained longer _1 causing the increase in CH compared to the tss = 0%fo case. The modifications to the Cra and Q curves caused by the non-zero tss are evident in Fig. 36. The modest reductions in both - Cm,peak and C/,max originate in the angle of the flap during the stalling process. Table 2 indicates that when tss/td = 0,the flap reached its peak deflection by au = 21.9° and had already begun its return motion by the time the airfoil underwent stall, whereas the flap remained at its peak deflection during this time for tss/td = 49%. Therefore, the flap deflection was slightly greater for tss/td = 49% by about 4°; hence the observed reductions. No other differences in the flow are observed between these two cases. Note, however, that incorporating a steady- 107 state portion to the flap motion restricts the flap upwards ramp rate to relatively higher values so as to keep td constant. As it concerns Cmjpeak this is an acceptable if not welcome concession, however the improvement in Cw>net for fast ramp rates is meagre. The advantage of having a slower ramp rate, which is to generate a significant positive Cw,net, could therefore not be fully utilized, and it should be noted that the improvement in Cw>net brought on by a slower ramp rate is more significant than that brought on by having Us £ 0%fo" . In light of this, it is therefore recommended to keep tss small with any time spent in the steady- state motion being removed from the return motion of the flap to its undeflected position at 0° (i.e. decreasing tR2), which will be shown in the next subsection to be of the least important of the flap motion parameters. 5.3.6 Effect of Return Motion Ramp Rate The last parameter describing the flap motion is the rate at which the flap returns from its maximum deflection back to 0°, namely R2. Having studied the effects of all the other flap motion parameters, one comes to the realization that the flap motion parameters have varying levels of control of the aerodynamic characteristics of an oscillating airfoil. It should now be obvious that of primary importance are ts, td and 8max, because these dictate when, how long and how much the aerodynamic loads are being controlled. Next in terms of impact is tiu, because it controls the effectiveness of the flap during the dynamic stalling process. As was just concluded, although the influence of tss is inferior to tRi, it does exert significant control on Cw,net- Therefore, it seems that by default this last parameter (i.e. R2 or tR2) is the least important of all the other parameters. Coupled with the fact that, in general, the downward slope of the flap deflection occurs during the downstroke motion of the airfoil oscillation, during which there are no significant events occurring over the airfoil, and that since td = tRi + tss + tR2, if, as mentioned above, td, tRi and tss are predetermined based on the previously- made recommendations, then tR2 must be chosen to accommodate the values of td, tRi and tss. 108 5.4 Guidelines for Control The previous two sections discussed 1) the nature of the flow over and aerodynamic loads on an airfoil oscillating in the deep-stall flow regime subject to active trailing-edge flap control, and 2) the results of a detailed parametric study into the effects of the flap motion profile. A practicing engineer, however, would be more interested in a set of guidelines which dictate how the flap should be actuated based on what the desired effect on the aerodynamic loads is. This is the goal of the current section, to organize the previous results, not into "a change in this flap parameter has this effect on the aerodynamic behaviour", but rather into "this desired aerodynamic behaviour can be achieved from this flap motion profile". In Fig. 37, the data have been presented in such a way as to easily identify the desired flap motion properties based on the desired effects on control. This may be considered a more compact way of organizing the previously presented data. First, the maximum lift coefficient is plotted versus peak pitching moment coefficient (Fig. 37a), and second the lift- curve hysteresis coefficient is plotted versus the net work coefficient (Fig. 37b). For each of these, six curves representing the effect of each of the flap parameters are provided. Furthermore, on each curve an arrow is superimposed indicating the direction of an increase in the flap parameter. The intersection of the horizontal and vertical dotted lines identifies the location of the corresponding values for the baseline airfoil, dividing the plots into four quadrants. In Fig. 37a, points located in the top right, bottom left, top left or bottom right quadrants are characteristic of improvements in both Q and Cm, neither Q nor Cm, only Q, and only Cm, respectively. In Fig. 37b, points located in the bottom right, top left, bottom left or top right quadrants are characteristic of improvements in both CH and Cw,net, neither CH nor Cw,net, only CH, and only Cw,net, respectively. It should be kept in mind that the following statements are only valid for values of the flap motion parameters within the limits of the experiments conducted. To achieve a decrease in -Cm)Peak, Fig. 37a indicates that a large duration, early start time, large positive flap deflection, fast actuation ramp rate, and moderate steady-state time period, implemented independently or in combination with one another, are required. Note that a positive flap deflection always led to an improved Cm,peak- Furthermore, as the 109 requirements to minimize the loss in C/,max are opposite to those of -Cm,peak, a short duration, late start time, small positive flap deflection, slow actuation ramp rate, and absent steady- state time period, implemented independently or in combination with one another, are required in order to limit the adverse influence on Q,max. In addition, to increase C/,max beyond that of the baseline airfoil, a negative flap deflection is necessary. Note that none of the points fall in the bottom left or top right quadrants, indicating that although trailing-edge flap control will not have a detrimental effect on both Q>max and Cm;Peak, it is unable to improve them both simultaneously, although the improvements in CmjPeak outweigh the degradation of C/>rnax. Figure 37b demonstrates that an improved Cw,net may be obtained by a large duration, late start time, large positive flap deflection, slow actuation ramp rate, and moderate steady- state time period. A relation similar to that between Q,max and Cm,peak also prevails here, where a reduction in CH has requirements in opposition to CWjnet, thus requiring a short duration, early start time, slow actuation ramp rate, and nonexistent steady-state time period. The magnitude of the deflection did not seem to affect CH though. Note that in contrast to C/>max and Cm;Peak, CH and Cw,net generally require a combination of these flap motion requirements to exceed the performance of a baseline airfoil. Furthermore, under certain settings of the flap motion profile, both CH and Cw,net can be improved simultaneously. Based on the above guidelines, an optimum flap motion may be formulated, a discussion of which will be the focus for the remainder of this section. There are a couple of important notions that should be mentioned, however, prior to the expression of this professed optimum flap motion. The first is that the above guidelines and the following optimum control are only claimed to be valid under the current experimental conditions, and that any deviation from these conditions, be it either in the flow (i.e. Reynolds or Mach numbers) or airfoil oscillation (i.e. mean angle, oscillation amplitude or reduced frequency), may likewise cause a deviation in the required trailing-edge flap control. Note, however, the modifications to the flap control motion should not be drastic as the conclusions of the numerical investigation of Feszty et al. [18] agree fairly well with those of this experimental study despite the Reynolds number being an order of magnitude larger, and small differences in the airfoil oscillation parameters. The second comment is in regards to the definition of the term optimum when used in the context of an optimum flap motion. It should be very clear 110 by now that a trailing-edge flap is incapable of generating simultaneous improvements in all aspects of the aerodynamic performance of an unsteady airfoil undergoing dynamic stall. It is, however, very efficient at producing remarkable improvements in the parameters that are at the heart of the goal of unsteady aerodynamic load control as would be applied to a rotor blade (i.e. Cm,peak, Cw,net and |C/>max /Cm,peak|) at the cost of a degradation in the performance of other aerodynamic characteristics (i.e. C/jraax and CH). It is, therefore, in obtaining a practical balance between the improvements and degradations that an optimum flap control motion is defined. Based on the above interpretation of the results, as well as the results of section 5.3, each flap motion parameter may be narrowed down to an approximate single value. We will begin by determining the value of start time and ramp rate since, as subsection 5.3.4 demonstrated, ts and tRi are closely related. We can examine this by comparing two cases; the 1 first with ts = OK and tRi = 25%f0" (case 17) and the second with ts = 0.25K and tRi = 13%^"' (case 26). These two cases are chosen since they both achieve their peak deflections at the same time, near the instant that the peak negative pitching moment is achieved. The first case outperforms the second case in terms of Cm>peak (31% versus 18%), |C/,max/Cm;Peak| (22% versus 13%) and CH (3% vs. -15%), whereas the second case is superior in terms of C/,max (- 7% versus -16%) and Cw,net (+0.53 versus -0.13). A TEF control motion falling somewhere in 1 between the above two cases, such as ts = 0.12K and tRi = 19%f0" , would result in a compromise in performance where Cm,peak, |Q>max/CmiPeak| and CWinet are still very much improved over the baseline case but where the reduction in C/>max and increase in CH are not too severe. With a start time at around 0.12K radians, subsection 5.3.1 indicates that a total 1 actuation duration of greater than around 50%fo" would excessively increase the post-stall lift loss and therefore CH, however durations shorter than this would not improve Cw,net- It is therefore resolved that the value of td should be roughly half of the oscillation cycle (i.e. 1 50%fo" ). Note that in regards to the start time, a more appropriate definition may be to define it relative to the peak aerodynamic loads as this would account for the variation in the instant at which the peak moment occurs caused by a variation in the flow or oscillation parameters. Therefore, the flap motion should be initiated at approximately 0.3 3K radians prior to CmjPeak (i.e. xmp - ts = 0.45K - 0.12K). More obvious is the choice of flap deflection direction and magnitude. Only positive (i.e. upwards) flap deflections improve Cm,peak, with the degree of 111 improvement increasing the larger the deflection is. It should be noted that if the upwards deflection is too high, an excessively large positive pitching moment, which would be just as harmful as the ever-present peak negative pitching moment, would occur. Based on the results, an upwards peak deflection of around 16°, equivalent to two-thirds of the maximum 1 airfoil angle of attack, is appropriate. Lastly, as a total duration of 50%fo" and upwards flap _1 _1 deflection of 19%f0 were chosen, this leaves 3 l%fo for the steady-state portion, deemed in subsection 5.3.5 to be beneficial, and return motion. In an effort to reduce the lift-curve hysteresis obtained by setting tss/ta to 50% while still maintaining a positive damping, tss 1 should be set to a value of around 35% of td (this is equivalent to 17.5%f0" ), leaving the return motion to span 13.5% of the oscillation cycle to make up the required total duration. The values for each of the parameters along with the reasons behind their choice may be summarized in the following list. Parameter Value Reason ts 0.337T prior to Cm,peak Reach 5max prior to LEV shedding td Vi oscillation period Reduce Cw,cw tRi Fast deflection Rapid LEV convection tss Vi total duration Reduce Cw,cw tR2 Least important Occurs during downstroke 2 8max /3ofamax Improve Cm>peak the most The results for an optimum control case, as defined above, is presented in Fig. 38. It demonstrates the significantly improved Cm,peak, Cw,net and |Q,max /Cra)peak| that is possible, along with the accompanying reduced Q,max and slightly increased CH- Quantitatively, the improvements over the baseline airfoil are over 40% in CmjPeak, a four-fold increase in Cw>net resulting in positive damping, 30% in |C/,max /Cm,peak|, with a 20% reduction in Q)max and 8% increase in CH- For completeness, the drag coefficient is also included, showing a considerable reduction in its peak value (25%). Details of the flap motion and critical aerodynamic values are provided in Tables 2 and 3 under the designation case 39. Also included in Fig. 38b are the Cm limits discussed in chapter 4. The two dotted lines, based on the work of Greenblatt and Wygnanski [32], were computed by multiplying the maximum and minimum values of Cm obtained for an attached-flow oscillating airfoil, which for the current investigation is a(t) = 10°+8°sin©t and K = 0.1, by a factor of 1.2. It is obvious that although the pitching moment loads remain within the upper limit, the lower limit is 112 nevertheless exceeded during the dynamic stalling process, albeit for a short time. On the other hand, the peak negative pitching moment of the control case abides almost completely by the limit set by Bousman [4], who determined an acceptable boundary in Cm to be -0.15. 5.5 PIV Results Despite the detailed measurements that have been reported thus far and the hypotheses and conclusions regarding the flow around the airfoil that they have led to, the actual flow around the unsteady airfoil with trailing-edge flap control has yet to be documented, and it would be a valuable addition to this investigation if these hypotheses could be corroborated by actual measurements of the flow around the airfoil. It was therefore undertaken to document the detailed flowfield around an airfoil with and without control via high-density particle image velocimetry (PIV), a task which has yet to be attempted. As was discussed in chapter 3, the PIV measurements were conducted in a smaller wind tunnel on a scaled down airfoil model. This led to a reduction in the Reynolds number compared to the rest of the measurements (i.e. 8.69xl04 compared to 2.46xl05). Recall that the results of other investigations have shown that dynamic stall is to a large degree Reynolds number independent, and the dynamic stalling process has been found to be the same over a large range of Reynolds numbers, within which the above two values fall. The oscillation parameters would, however, have to been adjusted as the aerodynamic properties of the flow over a static airfoil (for example, the static-stall angle) are affected by variations in Reynolds number. It was consequently deemed necessary to reacquire the surface pressure distributions and recalculate the aerodynamic loads for the current conditions. The first step was to document the flow over a static airfoil under the current operating conditions, and to determine the appropriate oscillation parameters to match as closely as possible the character of the flow previously observed. The flow over a baseline, or uncontrolled, airfoil was then documented to serve as a reference for the control tests. The results of these initial tests are presented in subsection 5.5.1. Following the results of section 5.3 and guidelines outlined in section 5.4, control was then applied to the airfoil. A limited range of start times, ramp rates, and steady-state time periods were studied for both upwards and downwards deflections with a single deflection magnitude. As the objective of the 113 current discussion is to support the previous findings, only one combination of the flap motion parameters will be presented here in order to best demonstrate the effects of an upwards (subsection 5.5.2) or downwards (subsection 5.5.3) flap deflection on the flow. It should be noted again that all flowfields presented here are instantaneous in nature, as the effect of phase averaging the velocity and vorticity fields would be a "smearing" of the flow structures potentially causing any subtle flow structures that may be present to become unrecognizable. Shih et al. argue that it should be recognized that a transient flow "is not a featureless average but is built from sharply defined features" [83]. With regards to the presentation of the flowfields, it should be noted that 1) the free- stream flow direction is from left to right; 2) the quantities presented are non-dimensional (i.e. u and v are normalized by u<„, and C, is normalized by uJc); 3) solid and dashed lines denote positive and negative contours, respectively (u, v and C, are positive in the right, upwards and CW directions, respectively, and are negative in the left, downwards and CCW directions, respectively); 4) positive vorticity is in the sense of the airfoil bound circulation; 5) the origin of the coordinates for the PIV results alone was chosen to coincide with the pitching axis so that it remained fixed, in light of the airfoil motion during the dynamic experiments; 6) the lightly shaded region surrounding the airfoil in all figures comprises the region within the fieldo f view that was not observable as it was blocked by the portion of the wing model closer to the camera; and 7) velocity vector fields are not presented since the high vector density makes them undistinguishable. 5.5.1 Baseline Airfoil The variations in Q, Cm and Cd with angle of attack for the static airfoil are presented in Fig. 39 (dotted line). Figure 39a shows that the static airfoil underwent a nonlinear increase in Q prior to its drastic stall at ass = 13°. The pitching moment and drag coefficients were also observed to drop and rise considerably at this angle (Figs. 39b and 39c). The stalling mechanism is characterized by the upstream movement of the turbulent separation point as angle of attack increased (for a < ass) and the bursting of the laminar separation bubble at a < ass- The sudden bursting of the laminar separation bubble accounts for the 114 severe drop in Q, leading to a flat pressure distribution over the airfoil for a > ass (see Fig. 40a). Further details regarding the flow around the static airfoil are available from the non- dimensional instantaneous streamwise u/uoo and transverse vAioo velocity fields, instantaneous spanwise vorticity ^cAi*. fields, and streamlines presented in Fig. 41 for three representative angles of attack (i.e. a = 7°, 12° and 18°). The PIV results demonstrate that prior to the stalling of the static airfoil, the upper surface boundary layer was very thin and the wake was narrow (Fig. 41a); a gradual thickening of the boundary layer and widening of the wake occurred, however, as the angle of attack increased (Fig. 41b). This can also be seen from the streamlines in Figs. 41j and 41k, which show an increased divergence from the surface of the near-wall streamlines at a = 12° compared to a = 7°. Despite the thickness of the boundary layer, as long as it remained attached, the boundary layer and wake had minimal vorticity content (Figs. 41g and 41h). What's more, the increase in the leading-edge suction peak with increasing a may be inferred from the increase in the flow acceleration upstream of the pitching axis (Figs. 41a and 41b). The corresponding iso-v/uoc contours are presented in Figs. 41d and 41e. Subsequent to static stall the character of the flow was completely altered. No longer did the flow accelerate over the leading edge, as the streamwise velocity is on the order of the free stream (Fig. 41c). The upper surface boundary layer separated near the leading edge, forming a thick shear layer on the order of the airfoil maximum thickness, and the lower surface boundary layer separated at the trailing edge (Figs. 41c and 411). This led to a considerably wide wake on the order of half of the airfoil chord. The disorganized turbulent nature of the wake is evident from the disorder found in Fig. 4 If. Lastly, the iso-vorticity contours demonstrate that the majority of the vorticity was located in the upper shear layer, whose intensity decreased with downstream distance due to the vigorous turbulent mixing that took place in the wake (Fig. 41i). Choice of the airfoil oscillation parameters for the dynamic tests was based on a comparison of the static airfoil characteristics between the two Reynolds numbers. At Re = 2.46x105 the airfoil underwent a sharp stall at 18°, and the oscillation parameters used were am = 16°, Aa = 8° and K = 0.1. It was then decided to maintain the same values of oscillation amplitude and reduced frequency, and to adjust the mean angle. Using a simple linear scaling factor (i.e. am/ass), the current static-stall angle of 13° suggested the use of a 12° mean angle 115 of attack. The results of this combination of oscillation parameters at the reduced Reynolds number were then compared to those at the higher Reynolds number, and are discussed next. Figure 39 presents the d, Cm and Q curves for an airfoil oscillating with Lastly, although the values of Qmax and Cm,peak are quite similar, Cd,max does deviate noticeably. Nevertheless, the effects on drag are of secondary importance compared to lift and pitching moment, and will not be considered here. The PIV dataset therefore adequately resembles the previous results due to the similar unsteady boundary-layer improvement and the transient LEV effects. The various unsteady boundary-layer and transient dynamic-stall events corresponding to the low Reynolds number dynamic case were identified from the surface pressure coefficient distributions shown in Figs. 40b and 40c. The Cp distributions reveal that during the majority of the upstroke, corresponding to the attached-flow and flow reversal flow processes, the upper surface suction peak is observed to have increased and decreased in magnitude, respectively, and the presence of a laminar separation bubble is clear from the pressure plateau. Note, however, the size of the LSB was greater than that observed during the higher Reynolds number experiments. This is 116 to be expected, since transition in the shear layer would be delayed due to the lower Reynolds number. In comparison to the static airfoil, transition was delayed as well, due to the boundary-layer improvement effects of the airfoil motion, and the suction peak was noticeably, but minimally, smaller. These two effects seem to offset each other and contribute to the obvious coincidence of the static and dynamic Q curves prior to ass. This behaviour is akin to that observed in Ref. 46 at a higher Reynolds number, and presented in Fig. 6. The downstream shifting of the center of pressure, due to the reduced suction peak and delayed transition, however, led to a nose-down pitching moment during the first half of the upstroke motion. As au = 16.5° was surpassed, the suction pressure began to decrease, however the LEV had yet to form. This resulted in the brief plateau in the Q curve. The increasingly large suction pressure footprint (for example, au = 18°) is indicative of the formation of a LEV, and the downstream motion of its peak (for example, au = 19.5°), or center, signifies it being swept over the airfoil and into the wake. Subsequent to the shedding of the LEV for au > 19.7° (see for example, aa = 17° and 12°), the upper surface flow during the downstroke was in a state of complete separation, evidenced by the flat upper surface pressure distribution. Reattachment of the boundary layer finally began towards the end of the downstroke motion at around aa = 6.5°. During this time period, the upper surface leading-edge suction peak was reformed (for example, aa = 4.7°), growing in magnitude as the airfoil completed the cycle. In summary, the characteristics boundary-layer and LEV events developed on the uncontrolled oscillating airfoil can be readily indicated by points © through © in Fig. 39. The boundary layer remained attached to the airfoil upper surface up to point © (au ~ 13.4°). The flow reversal was present between points © and © (or au ~ 13.4° and 17.8°). Note that the breakdown of the upper surface boundary layer was initiated at ®. The initiation, development and detachment of the LEV took place between points © and © (corresponding to au = 17.8° and 19.7°), while the during-stall and post-stall flow conditions persisted between points © to © (or au = 19.7° to ad = 18.6°) and © to © (or ad - 18.6° to 6.5°), respectively. Note that the separated boundary layer began to attach to the airfoil upper surface at point ®. The identification of these critical flow features are based on the finding of Lee and Gerontakos [46]. As has been demonstrated, despite the reduced Reynolds number, the sequence of events occurring over the airfoil is similar to that observed at higher Reynolds numbers. In 117 fact, the values of C/,max and Cra,Peak fall directly on the dynamic stall function defined by Bousman [5] and presented in Fig. 23 (square symbol). This is a strong indication that the results of the low-Reynolds number experiments are both qualitatively and quantitatively similar to those of the high-Reynolds number experiments. To facilitate the understanding of the influence of the trailing-edge flap on the flow over the oscillating airfoil, the normalized u, v and £ flowfields around the unsteady uncontrolled airfoil at eight representative airfoil incidences (au = 4°, 12°, 18°, 19.5° and 20°; and ad = 17°, 12° and 4.7°) are presented in Figs. 42,43 and 44. The PIV results show that for small angles of attack (for example, 118 thickened, the flow seemed to remain mostly attached. The external flow stream continued to follow the airfoil's contour, and there was no apparent breakaway of the boundary-layer flow from the surface. Unfortunately, this tiny flow reversal region could not be resolved due to the small size of the airfoil model used, resulting in a flow structure whose size was less than the measurement resolution. The previous behaviour of increasing leading-edge flow acceleration, upper surface vorticity production, boundary-layer thickness, and wake width and deficit continued up to the appearance of the LEV over the airfoil, whose formation was initiated at roughly otu ~ 18° by the arrival of a reversing flow which originated at the trailing edge and resulted in a local accumulation of vorticity in the leading edge region [69]. This marks the beginning of the accelerated increase in lift observed in Fig. 39a. Prior to the LEV formation however, the velocity in the leading-edge region reached a maximum, after which it began to decrease. This coincides with the attainment of a maximum leading-edge suction peak and its ensuing decrease. Martin et al. [56] also note that stall is preceded by a peak in the leading-edge velocity, which they interpreted from the peak in the leading-edge suction. The streamwise and transverse iso-velocity, and spanwise iso-vorticity contours are presented in Figs. 42c, 43c and 44c, respectively, at otu = 18°. This angle was chosen so that the LEV could be sufficiently resolved. The initial LEV structure can be identified by the boundary-layer separation near the leading edge and reattachment slightly before the mid-chord (Fig. 42c). This yields a size of about 47%c, which, when compared to the Cp distribution of Fig. 40b, is found to agree extremely well. Figure 44c reveals that, similar to what has been suggested by researchers elsewhere [58,83], the LEV vorticity originated and was supplied by the leading- edge turbulent flow of the separated shear layer, which was characterized by high levels of vorticity. Although the LEV was 47%c long, it had an elongated shape and its height was comparable to the maximum airfoil thickness (i.e. 15%c). As the LEV continued to progress in its development, it grew in both its dimensions (i.e. streamwise and transverse) and its center shifted downstream. By au=19.5° (Figs. 42d, 43d and 44d), the center of the LEV had reached about x/c » 37% along the airfoil chord and it spanned a length of 63%c. Furthermore, the LEV was about a quarter-chord high. Although initially the LEV contained high levels of vorticity (Fig. 44c), its growth caused its peak vorticity to decline. Similarly, the peak suction pressure in the LEV also weakened; however, the growth of the LEV greatly 119 outpaced the decrease in suction pressure resulting in a rapid increase in C/ (Fig. 40b). Moreover, it is the downstream spreading and convection of the LEV that led to the severe nose-down pitching moment (Fig. 39b). Downstream of the LEV the flow was unable to persist in an attached state and separated, becoming much more disorganized and highly turbulent. The LEV reached a size equivalent to the airfoil chord at au = 20° as it was finally shed into the wake (Figs. 42e, 43e and 44e). At this moment, its transverse dimension reached almost 40%c. Note, however, that the more the LEV grew, the smaller its peak vorticity became. On the other hand, the vorticity contained in the separated shear layer emanating from the leading edge maintained the same peak value throughout the LEV formation and convection process. Shih et al. [83] also found the vorticity in the LEV to be inferior to that in the separated shear layer, and that the difference grew with the convection of the LEV over the airfoil. Due to the low pressure formed by the LEV, the shear layer stemming from the lower trailing-edge surface was pulled increasingly upwards into the wake, which can be reflected either from the orientation of the iso-u/Uoo contours in Fig. 42e or the large region of positive vAu in the airfoil's wake seen in Fig. 43e. It is of note that the flow visualization tests of McAlister and Carr [58] indicate that for Reynolds numbers greater than around 5 x 104, the LEV is the only dominant vortical structure that forms, as opposed to the additional formation of a SLV or TEV, a finding which is supported by the current results. Once the airfoil began its pitch-down motion and the LEV had been shed, the upper surface boundary layer was in a state of complete separation. This is displayed for aa = 17° in Figs. 42f, 43f and 44f. Note that the general characteristics of this flow state are similar to the separated flow state of a stalled static airfoil (for example, a = 18° in Figs. 41c, 41f and 41i). In this state, barely any flow acceleration over the leading edge can be discerned. This is accompanied by a flat upper surface pressure distribution (Fig. 40c) and a catastrophic drop in lift (Fig. 39a). Moreover, the only significant vorticity was found in the shear layers, the lower one of which was no longer entrained upwards to mix with the upper surface flow. As the airfoil incidence decreased, the separating shear layer moved closer to the airfoil surface (Fig. 42g and 44g). This led to a smaller wake width with reduced deficit. The upper surface flow, however, was still significantly disturbed (Fig. 43g). As the airfoil reached a sufficiently low angle of attack, the boundary layer began to reattach near the leading edge. 120 Further decreases in a caused this reattachment to progress downstream and the boundary layer became thinner. This caused a narrowing of the wake with improved velocity deficit and a restructuring of the boundary layer and wake flow. By aa = 4.7°, the leading-edge flow acceleration and suction peak had been re-established (Fig. 40c), the wake width and deficit were on their way to returning to pre-stall values, the flow had become more structured, and the boundary-layer vorticity levels had all but vanished (Figs. 42h, 43h and 44h). 5.5.2 Upwards (Positive) Deflection The control of the flow around an oscillating airfoil via an upwards TEF deflection will now be evaluated. As mentioned previously, a limited range of flap motion parameters were used. Parameters that were kept fixed at a singe value include the total duration at 1 around 50%fo" , and the magnitude of the deflection at 12° (this peak deflection was chosen to correspond to the previous measurements where 8max = am). The start time was varied throughout the upstroke motion, and two ratios of tss/ta were studied. In addition, the flap deflection ramp rate was also slightly varied. Of all these cases tested, the details of which are provided in Table 4, a single representative flap motion profile was chosen to demonstrate the effects of an upwards flap control motion. The motion profile is identified as 1 1 case 3 in Table 4, and is described by a 5max = +12°, ts = 0.14u, U = 50.3%fy , tss = 16.1%f0" , 1 1 tRi = 19.6%f0" , and tR2 = 14.6%f0" . These parameters are close to those suggested in the previous section (i.e. section 5.4). The flowfield corresponding to this control case is presented in Figs. 45, 46 and 47 at six angles of attack, selected to demonstrate the differences from the baseline case. The PIV results show that prior to the deflection of the flap (for example, au = 12°), there was little discrepancy between the control and baseline cases. These results agree with the wake surveys previously reported. A comparison of Fig. 45 a to 42b indicates that 1) the same peak leading-edge velocity was attained, 2) the thickening of the boundary layer reached the same upstream location, 3) the boundary-layer thickness was approximately the same, and 4) the wake had roughly the same width and deficit. The transverse velocity distribution also shows minimal differences (Fig. 46a). Similar to the uncontrolled airfoil, vorticity production was small, and separate strips of vorticity emanated from the upper and 121 lower flows at the trailing edge (Fig. 47a). This similarity in the flow prior to ts is also reflected in the Cp distributions (Fig. 49a), and the Q and Cm curves (Fig. 50). The flap motion began at au = 15.4°, therefore the flow at au = 18° is presented so that the flap's influence could be clearly seen. Note, however, that the flap deflection angle at this angle of attack was still fairly small, and therefore only small differences from the baseline airfoil should be expected. On the other hand, changes in the flow are observed that lead to the anticipated modifications to the surface pressure distributions and aerodynamic loads. For example, the streamwise iso-velocity contours underneath the airfoil and flap indicate that at a given location the retardation in the flow was lessened. This can be seen from the fact that, for example, the 0.7, 0.8 and 0.9 iso-velocity contours are located further upstream in Fig. 45b than in Fig. 42c. This faster flow velocity underneath the airfoil and flap consequently led to a reduced lower-surface positive pressure, which can be seen in Fig. 49b. Note, however, that in the vicinity of the trailing-edge, the contours underneath the flap with and without control are the same, suggesting the same local pressure at the trailing edge. This too can be seen in Fig. 49b, where the pressure on the lower surface of the flap rejoins that of the baseline airfoil. This reduction in the lower surface pressure, especially downstream of the pitching axis, results in the observed reduction in Q and increase in Cm (Fig. 50). With regards to the upper surface flow, the LEV seems to have been slightly smaller in its transverse dimension, but it extended slightly further downstream (Figs. 45b and 47b). What's more, Fig. 46b shows the peak transverse velocity in the LEV to be reduced (-0.65 compared to -0.75). All this suggests that the LEV was minutely weaker and slightly promoted in its formation. The upper surface pressure distribution in Fig. 49b supports this conclusion. McAlister et al. [59] suggest that the strength of the LEV could possibly be linked to the airfoil circulation at the instant of formation. If this is true, then it should be no surprise that the LEV seems to have suffered from a slight reduction in strength since lift was also reduced [Fig. 50a]. The peak vorticity inside the shear layer, on the other hand, seems to have been unaffected by the control. The other difference observed is in the wake which, due to an upwards turning of a weaker lower separated shear layer, was narrower. As the LEV continued to grow and the flap deflected further, a greater effect on the flow was observed. At au = 19.5°, the flow underneath the airfoil and flap continued to move faster, and therefore with a lower pressure, than in the absence of control (Figs. 45c and 49c). 122 Moreover, the LEV was still smaller in the transverse direction, and the flow above the airfoil was slightly slower (a peak value of 1.55 compared to 1.63), causing a reduction in the upper surface suction pressure (Figs. 45c and 49c). A more clear view into the effects of the flap on the LEV is given in Fig. 48, which presents the streamline patterns. In comparison to the uncontrolled airfoil (Figs. 48a and 48b), the controlled airfoil with upwards flap deflection (i.e. Figs. 48c and 48d) resulted in a small but clear weakening of the vortex. The reduced increases in Q and -Cm during the LEV formation also hint at a reduced vortex strength (Fig. 50). The earlier convection of the LEV is evident from its further downstream position at au = 20° (Fig. 47d), and agrees with the finding that both peak values in lift and pitching moment were reached 0.2° earlier. Comparison to the higher Reynolds number test case with analogous flap motion parameters (i.e. case 39 in Table 3) also shows a slightly earlier adS, but amp was unaffected. The influence of the flap also translated into a 30% reduction in |Cm,Peak|, a 12% reduction in C/,max, and a 25% increase in |Q,max/Cra,Peak|. During the initial portion of the downstroke motion, the flap remained fully deflected and therefore its influence over the flow underneath the airfoil was consistently present despite the separated upper surface flow. At ad = 17°, a higher streamwise flow velocity beneath the airfoil occurred (Fig. 45e), leading to the persistence of the lower surface increased suction pressure observed in Fig. 49e. In fact, the suction peak on the lower flap surface was equivalent to its highest value. This resulted in the significant deviation from the uncontrolled airfoil aerodynamic loads; Q and Cm were reduced and increased, respectively, by a considerable amount (Fig. 50). As a result, a single large CCW loop in the Cm-a curve formed increasing the positive Cw,net by 188%. Unfortunately, the post-stall lift loss was also increased and CH grew by 8%. The separated flow over the airfoil, on the other hand, resembled the baseline airfoil. The boundary layer separation occurred in the same location, and a layer of reversed flow of equivalent thickness covered the upper surface. It is only due to the upwards turning of the flow that the wake was slightly reduced in width. As the airfoil continued in its pitch-down motion, the flap began to return to its undeflected position. This caused its influence over the flow to decrease. By aa = 12°, the majority of the flap's effects had disappeared, and only remnants were left of its presence in the flow. Although still slightly faster, the lower flow approached that of the baseline airfoil (Fig. 45f). Nevertheless, the excess velocity still caused a slight decrease in the lower surface 123 pressure (Fig. 49f). Above the airfoil, the overall flow was similar; however the aft portion was subject to a restructuring that caused the flow to behave in a somewhat more organized fashion. This is demonstrated best by the v-contours, which showed less variation, and the £,- contours, which were less "messy", over the final 40% of the airfoil chord (Figs. 46f and 47f). This is reflected in an improved upper surface pressure distribution (Fig. 49f). It is believed that this promoted restructuring of the flow is what causes the lift and pitching moment to exceed their corresponding baseline airfoil curves during the second half of the downstroke (Fig. 50). 5.5.3 Downwards (Negative) Deflection To complement the above results and further demonstrate that the findings based on the surface pressure distributions, aerodynamic loads, and wake measurements are clearly reflected in the flowfield, PIV measurements for the case of trailing-edge flap control with a downwards deflection were also conducted. The motion profile chosen for the following discussion is identified as case 12 in Table 4, and is described by a 8max = -12°, ts = 0.0 In, ta = 1 4 1 SO.Srofo" , tss - lS3%f0'\ tRi = 19.6%f0 , and tR2 = D.P/ofo" . These parameters are similar to those of the previous discussion of the upwards flap deflection, except that the start time was chosen to coincide with am. The flowfield corresponding to this control case is presented in Figs. 51,52 and 53 at six angles of attack, selected to demonstrate the differences from the baseline case. The PIV results show that just prior to the deflection of the flap (for example, au = 12°), there was little discrepancy between the downwards control and baseline cases, similar to what was observed previously. A comparison of Fig. 51 a to 42b indicates that 1) the same peak leading-edge velocity was attained, 2) the thickening of the boundary layer reached the same upstream location, 3) the boundary-layer thickness was approximately the same, and 4) the wake had roughly the same width and deficit. The transverse velocity distribution also shows minimal differences (Fig. 52a). Similar to the uncontrolled airfoil, vorticity production was small, and separate strips of vorticity emanated from the upper and lower flows at the trailing edge (Fig. 53a). This similarity in the flow prior to ts is also reflected in the Cp distributions (Fig. 49a) and the Q and Cm curves (Fig. 50). 124 At au = 18° the flap was well on its way to reaching its peak deflection, having started its motion at au = 12.3°. At this angle Fig. 51b shows an additionally hindered flow underneath the airfoil and flap. Contour levels 0.6 through 0.9 are clearly displaced further downstream compared to the uncontrolled airfoil. This led to the increased pressure distribution observed in Fig. 49b on the lower surfaces. This is the leading contributor to the increased lift and decreased pitching moment experienced by the airfoil (Fig. 50). In addition, similar to the upwards flap deflection, the Cp distribution converged with that of the baseline at the trailing edge (Fig. 49b), and is reflected in the flowfield by similar u-contour levels at that location (Fig. 51b). Regarding the upper surface flow, the downwards deflection seems to have had the opposite effect of the upwards deflection. The LEV was larger in its transverse dimension, yet its chordwise dimension was roughly the same as that of the uncontrolled airfoil (Figs. 51b and 53b). Also, the LEV, as shown in Fig. 52b, contained a slightly elevated transverse velocity (-0.77 compared to -0.75). These changes to the LEV are indicative of a stronger vortex that was not affected in the timing of its initiation. The upper surface pressure distribution in Fig. 49b supports this conclusion. The conclusions previously made based on the changes in the surface pressure distributions have therefore been confirmed. Notice that the coincidence of a stronger LEV with an increase in lift also corroborates the suggestion put forth by McAlister et al. [59] that states that the strength of the LEV could possibly be linked to the airfoil circulation at the instant of formation. The only other difference of note is that the lower shear layer originating from the flap lower surface was deflected downwards, causing an increase in wake width. The increase in the strength of the LEV, in addition to the fact that its formation was not affected, is more clear at au = 19.5°. Figure 49c demonstrates that the extent of the suction pressure footprint of the LEV was the same, but that the magnitude of the suction had increased with a negative flap deflection. This is manifested in the flow by the LEV's slightly larger size, and a faster streamwise flow above the airfoil (a peak value of 1.68 compared to 1.63), causing an increase in the upper surface suction pressure (Figs. 51c and 49c). The streamline patterns presented in Fig. 48 also indicate that, compared to the baseline case (Figs. 48a and 48b), the controlled airfoil with downwards flap deflection (i.e. Figs. 48e and 48f) resulted in a slight strengthening of the vortex. On the lower airfoil surface, the reduction in flow speed was maintained (Fig. 51c), as was the consequential increase in 125 pressure (Fig. 49c). These changes to the flowfield and Cp distributions led to a 18% increase in C/>max, but also to a 30% increase in Cm,peak and 9% reduction in |C/>max/Cm>Peak|. Similar observations regarding the flowfield can be made at au = 20°. After the LEV had been shed into the wake and the upper surface boundary layer was completely separated, the effect of the flap on the upper flow was lost, despite the flap still being fully deflected. This is demonstrated in Figs. 52e, 53e and 54e for the angle aa = 17°, where the upper surface flow was found to be similar to that over the uncontrolled airfoil. The boundary layer separation occurred in the same location, and a layer of reversed flow of equivalent thickness covered the upper surface. Nevertheless, the flow external to the shear flow did experience a small acceleration effect, resulting in a higher streamwise velocity and lower upper surface Cp distribution (Figs. 51 e and 49e). The flap's effect on the lower surface flow, on the other hand, was ever-present, as was the downwards deflection of the lower flap surface shear layer (Figs. 51e, 49e and 53e). The flow was persistently of a lower velocity, maintaining the increase in pressure and leading to the observed increase and decrease in C/ and Cm, respectively (Fig. 50). The overall effect was the formation of three loops in the Cm- a curve just like the baseline airfoil, however area from the CCW was shifted to the CW loop. The net work coefficient therefore became negative. On the other hand, the lift-curve hysteresis was reduced by 22%. A reduction in the flap deflection angle occurred subsequently as the airfoil continued in its pitch-down motion, and by aa = 12° had nearly reached its undeflected position. Its influence over the flowfield consequently almost disappeared. The trailing-edge shear layer was no longer deflected downwards, and the flow underneath the airfoil resembled that of the baseline airfoil. Nevertheless, a minute difference in the velocity and Cp distributions were observed (Figs. 5 If and 49f). The flow above the airfoil experienced a noticeable thinning of the boundary layer, similar to the upwards flap control case, but a weakening of the separated leading-edge shear layer (Fig. 53f). The overall effect was to result in values of lift and pitching moment that approach those of the baseline airfoil (Fig. 50). For the remaining portion of the downstroke, the flowfield behaved just as if control had not occurred. 126 5.6 Attached-Flow and Light-Stall Control Thus far the focus has been on deep dynamic stall, as this is the most severe of operating conditions for an unsteady airfoil, therefore making it the most difficult to control. It is also of interest, however, to investigate the applicability and usefulness of trailing-edge flap control as applied to the more tame flow conditions characterized by the light-stall and attached-flow regimes. This next set of experiments was conducted under slightly different operating conditions. The Reynolds number was 1.65 x 105 as opposed to 2.46 x 105 that was used for the rest of the experiments. This led to a slightly smaller static-stall angle of 16.5°, thus the oscillation parameters were adjusted accordingly to a(t) = 120+6°sincot for attached-flow and a(t) = 140+6°sinoot for light-stall cases, both with K = 0.1. The attached-flow and light-stall oscillations were established first from the drastic change in the characteristics of the hysteresis loop, particularly the Cm-a loop, as am was increased from 12° to 14°. For oscillations slightly through ocss (with ocra = 12°), the dynamic C/-oc loop exhibited an attached-flow-like oscillation; i.e., no significant hysteresis was noticed nor a significant increase in the Qmax. Moreover, the airfoil never stalled and a single counter clockwise Cm-a loop was observed. The light-stall oscillation (with am = 14°) introduced a second clockwise Cm loop of negative damping, in addition to the single Cm loop associated with the attached- flow oscillation (with am < 12°), and gave rise to a figure eight-like behaviour. The peak negative pitching moment coefficient and the dynamic-stall angle were found to occur at the end of the pitch-up motion, as a result of the "premature spillage" of the LEV. The flap motion was chosen to follow some of the guidelines established in section 5.4. The total 1 actuation duration was constant at around 50%fo" , and the ramp-up and ramp-down times (i.e. tRi and tR2) were each approximately 18%f0"'. Both upward and downward flap deflections with 8max = ±7.5°, and three start times during the upstroke (i.e. amin, am and amax) were tested. Note that smaller magnitude deflections were chosen, compared to the larger ones used for deep stall, due to the mitigated stall characteristics of light stall. Table 5 lists the parameters that describe the flap motion. The results of this investigation into attached- flow and light-stall control have been summarized in Ref. 47. 127 5.6.1 Attached-Flow Oscillation The effect of upward TEF motions on Qand Cm for an airfoil undergoing attached- flow oscillations was examined first and is presented in Figs. 54a-54d. Similar to the effect that an upward flap deflection would have on a static airfoil, a reduction in Q and increase in Cm for the duration of the flap deflection, as a result of induced negative camber effects, especially in the trailing-edge region, was observed. As the start time shifted from amin to oWx, this C/ reduction and Cm increase also shifted from affecting the entire upstroke motion to the entire downstroke motion. For ts = -0.57T (case #1), the lift during the upstroke was reduced to levels below that of the baseline airfoil during its downstroke motion. In addition, the counter clockwise Cm loop of the baseline airfoil was transformed into a single clockwise loop for the control case (Fig. 54b); a CW)net of-0.43 compared to 0.32 of a baseline airfoil was observed. At the other extreme, a start time at amax (case #3) caused a 220% increase in the positive damping (Fig. 54d), or Cw,CCw, accompanied by a significantly decreased Q during the flap actuation. For the intermediate start time of ts = On (case #2), the later half of the upstroke and first half of the downstroke were equally shifted upwards for Cm and downwards for Q causing an insignificant change in Cw,net or CH- The maximum lift coefficient was, however, considerably reduced. For a downwards deflected TEF, the behaviour of the dynamic load loops were somewhat unexpected; depending on the magnitude of ts, the dynamic Q and Cm loops of an otherwise attached-flow oscillation (characterized by a single CCW Cra loop and a small Q- hysteresis) could exhibit a light-stall-like oscillation. For ts = -0.57E, or a flap actuated at otmin during pitch-up (case #4), the Ci-a curve was shifted upward (Fig. 54e) due to the induced positive camber effects and the subsequent body-conforming flow improvement, especially in the trailing-edge region. A strengthened CCW Cm loop or Cw,ccw compared to a baseline airfoil of greater positive damping was also exhibited (Fig. 54f). The flow, however, still maintained an attached-flow character. On the other hand, for a TEF actuated at On, and amax during pitch-up (cases #5 and #6 respectively) the aerodynamic loads were completely modified throughout almost the entire oscillation cycle, and had the character of a light-stall oscillation. Due to an increased effective ocmax there was the presence of a LEV-induced CW Cm loop (Figs. 54g-54h) and large C/-hysteresis (Fig. 54e) compared to the baseline airfoil 128 oscillation. Note that the LEV was of a weakened strength and was shed prematurely during the initial stages of the downstroke motion. This resulted in a significant negative aerodynamic damping. The strength of the LEV, and the post-stall drop in Q and Cm were most severe for the earlier of the two start times (i.e. ts = On). Although the formation of the LEV caused an increase in the maximum lift coefficient compared to a baseline airfoil, the severe peak negative pitching moment and elevated lift-curve hysteresis were of considerable detriment. Note, however, the Cm hysteresis increased with increasing ts, which seems almost contradictory, until it is observed that during the second half of the upstroke, between ocm and ctmax, Cm is not reduced as it is for ts = Ore, leading to a larger CW loop. Further details regarding the flow, and in particular the unusual presence of a rather weak LEV and its subsequent detachment from the airfoil, can also be demonstrated from the variation in the Cp distributions (Fig. 55) and the associated increase in the wake deficit and width, and fluctuating velocities (Fig. 56). Figure 55 shows the representative surface pressure coefficient distributions at Ou = 18° during pitch-up and oc Also shown are the Cp distributions of a static NACA 0015 at the same angles. For the uncontrolled (i.e. baseline) airfoil and upwards deflection control case, the existence of an attached boundary-layer flow, and the absence of a LEV and flow separation are clearly seen. With control, however, both the suction and positive pressures on the upper and lower airfoil surfaces were decreased while the flap was deflected, especially on the upper and lower surfaces of the flap, compared to a baseline airfoil. The observed manipulation of the Cra curve was due in large part to the presence of suction pressure on the lower surface of the flap. Note the flat Cp distribution of a static airfoil for a > ass. Figure 55c further indicates that during the later portion of the pitch-down motion, when the flap returned to its undeflected position, no noticeable discrepancy in the Cp values was observed, relative to the baseline case, therefore implying that an upward flap motion did not affect the overall flow characteristics. In contrast to an upward TEF, for a downward TEF, the formation of a weak LEV and its detachment from the airfoil upper surface can be clearly identified from the Cp distributions shown in Figs. 55a and 55b. In addition, instead of a suction pressure on the lower flap surface, a positive pressure developed there, similar to the results for the active 129 control of deep stall. Note the presence of a severely hindered upper surface pressure distribution during the downstroke motion (Fig. 55c) caused by the stalling of the airfoil. The influence of the TEF motion on C/, Cm and Cp can also be reflected from the modification of the wake flow structures presented in Fig. 56. The upward TEF motion caused an upwards shifting of the wake, however, the shape of the wake profile was not dramatically altered compared to a baseline airfoil. The deviations in streamwise velocity deficit, wake width, and streamwise velocity fluctuation from the baseline airfoil, were deemed minimal for the majority of the airfoil motion. However, the fluctuation levels were slightly reduced and the wake width was slightly narrowed during the airfoil upstroke motion. The upwards flap deflection also weakened the turbulent kinetic energy and, presumably, the Reynolds stress as well thus decreasing the drag force (see Table 5). Note also the pronounced reduction in the wake width for an oscillating airfoil, as a result of the boundary-layer improvement effects, compared to a static airfoil at the same angle. All of these findings indicate that an upwards flap deflection did not cause the airfoil to deviate from its attached-flow characteristics. In contrast, a substantial increase in the wake width and deficit, and wake velocity fluctuations was observed for a downwards flap actuated at % = On, or am, as a consequence of the formation and premature spillage of a LEV from the airfoil upper surface. Prior to the LEV formation, though, the effect of the negative flap deflection was similar to that of a positive flap deflection, but opposite in effect; the wake was deflected downwards, but this caused the upper and lower separated shear layers to move farther apart causing an increase in wake width. In summary, it can be said that a trailing-edge flap is just as effective at manipulating the aerodynamic loads of an airfoil undergoing attached-flow oscillations as it is for deep stall. However, care must be taken so that the flow is not destabilized into triggering the formation of a LEV, causing the airfoil to stall. This concern is limited to downwards flap deflections only; upwards flap deflections do not suffer from this susceptibility. 5.6.2 Light-Stall Oscillation After investigating the control of light stall, it was found that the results and trends were similar to those of deep-stall control. The only differences were in 1) the strength of the 130 LEV and therefore the induced peak negative pitching moment, which required a much smaller flap deflection magnitude to alleviate its extent; and 2) the presence of only two loop in the Cra-a curve as opposed to the three present in deep stall. As such, a limited discussion on this topic is provided here, with a more detailed treatment of trailing-edge flap control of dynamic stall being found in sections 5.2 through 5.5. Figure 57 presents the aerodynamic loads for an airfoil with TEF control. It is evident from this figure that the effect of the flap operating in the light-stall domain is reminiscent of its effect in the deep-stall regime previously discussed. An upwards flap deflection primarily provided a mitigation of the excessive nose-down Cm produced by the transient LEV effects, accompanied by a reduction in Q. The formation, convection and detachment of the LEV was found to be virtually unaffected by the upward TEF motion. Moreover, the strength of the premature LEV was reduced, as seen by its reduced drop in Cm and jump in Q during the LEV formation and convection, and diminished low pressure signature. A downward TEF motion, on the other hand, induced positive effective camber, shifting the Q and Cm curves upward and downwards, respectively, and causing a considerable increase in C/,max and a substantially intensified peak nose-down Cm. The strength of the LEV was also observed to be intensified. Similar to an upward deflection, however, the dynamic-stall angle 0CdS remained relatively unchanged. The effects on Cw,net and CH are very much ts-dependent. For an upward deflection Cw,net and CH increase with increasing ts. The opposite is found for downwards deflections (i.e. CWjnet and CH increase with decreasing ts). Note that, similar to what has been discussed previously, the effect of the flap is limited to the period in the oscillation cycle during which the flap is active. Outside this, the flow and aerodynamic loads behave very closely to those of the baseline airfoil. 5.7 Passive Flap Control All this talk of active control has, as a consequence, debased passive flap control; however the absence of a required external energy source renders passive control techniques very appealing. Furthermore, they are generally geometrically simple and straightforward to manufacture and implement. On the other hand, it is true that a very important factor limiting the use of passive control devices is their constant influence on the flow, which in a highly 131 unsteady and varying flow may not be necessary and may even be detrimental under certain conditions. Nevertheless, it is possible that certain benefits may be found in such a simple control scheme and this investigation would not be complete if this was not examined. Moreover, further insight into the workings of trailing-edge flap control may be uncovered. The effects of a statically deflected flap on the flow around and aerodynamic loads on an airfoil undergoing dynamic stall oscillations were therefore studied. In the following discussion, the results for an airfoil oscillating in the deep-stall regime (i.e. a(t) = 16°+8°sin(ot and K = 0.1) equipped with a trialing-edge flap set to a constant flap angle of ±8° will be presented. Note that these experiments were also conducted for the light-stall case of ara =12° however the overall effects were similar, and will therefore not be reported. The effects of flap deflection magnitude were also determined by comparing these results to those for 5 = ±16° and will be discussed later on in this section. The critical aerodynamic values for a passively controlled airfoil are tabulated in Table 6. Figure 58 presents the surface pressure distributions at selected angles of attack for an airfoil with (dashed and dotted lines for upwards and downwards pointing flap, respectively) and without (solid line) control. Note that the baseline, or uncontrolled, case is denoted by 8 = 0°. A downwards flap deflection (8 = -8°) can be seen to generally introduce a positive camber to the airfoil: a trend that persists throughout the entire oscillation cycle. Specifically, while the flow remained attached, the suction and positive-pressure pressures on the upper and lower surfaces, respectively, were increased (au = 12°). Furthermore, the observed change in pressure was distributed over the entire airfoil and was not localized in the trailing- edge region as might be expected. As the angle of attack increased, the pressure increase, either suction or positive-pressure on the upper and lower surfaces, respectively, was maintained everywhere except in the immediate vicinity of the upper leading-edge where the suction peak, which at small angles exceeded that of the baseline case, coincided with the baseline case (au = 21°). Make note of the small "bulge" in the pressure distribution which was present just downstream of the laminar separation bubble, identified from the plateau in the suction pressure over the airfoil in the leading-edge region, as it will be discussed shortly. The LEV was found to form during the upstroke slightly prior to that of the baseline airfoil (refer to au = 22°), as seen by the rearward spreading of the broad suction-pressure footprint characteristic of a LEV, and led to a stall that occurred very drastically with a very rapid drop 132 in upper surface suction pressure. This promotion of LEV formation at a smaller incidence occurred due to the positive-camber inducing increased adverse pressure gradient in the leading-edge region. Subsequent to the stalling of the airfoil, referred to as post-stall, the upper surface was encompassed by a separated boundary layer. Due to the complete separation of the upper surface boundary layer, no difference was perceived in the upper surface pressure distribution, relative to the undeflected case (a„ = 24°, ad = 21 °, ad = 16° and aa = 12°). The increased positive pressure on the lower surface was sustained, however, throughout the entire oscillation cycle, especially over the lower flap surface due to the attached nature of the boundary layer underneath the airfoil. The pressure peak underneath the flap is especially clear during the later half of the pitch-down motion. The wake measurements shown in Fig. 59 also identify some interesting characteristics of the flow. As expected, while the flow remained attached the downwards flap deflection caused the wake to be displaced downwards, however, small increases in u and u1 were observed, while the wake width remained essentially unchanged, compared to the baseline case (au =12° and au = 16°). As the phase angle increased and the LEV formed and convected over the airfoil (refer to au = 23° and au = 24°); the increase in velocity deficit was essentially eliminated, since the LEV was highly energetic; the extent of the wake displacement decreased, due to its position above the airfoil; and the turbulent fluctuations matched those of the baseline case, indicating a vortex of similar turbulence levels. These changes endured throughout the remaining portion of the downstroke, except for the mean velocity deficit, which increased beyond that of the baseline case due to the increase in wake width, the difference of which increased as the angle of attack decreased (ad =16°). After reattachment had begun and been nearly completed, the wake returned to its attached-flow characteristics (ad = 8° compared to au = 12°). Contrary to the above, the upwards flap deflection (8 = +8°) imposed a negative camber on the airfoil. In doing so, the pressure differential was reduced over the entire airfoil (Fig. 58). At au = 12°, both the suction and positive pressure pressures on the upper and lower surfaces, respectively, were decreased essentially evenly over the entire airfoil, except for the large reduction in the pressure covering the lower flap surface. The upwards flap deflection led to an acceleration of the flow underneath the flap, due to the divergence of the flap surface from the flow underneath the airfoil, causing a large suction peak to form underneath 133 the flap. Note that the suction peak in the case of an upwards deflection is larger than the pressure peak in the case of a downwards deflection. A reduced leading-edge suction peak and alleviated adverse pressure gradient were also observed. As the airfoil incidence was increased, the reduction, relative to the baseline case, in suction pressure over the airfoil and positive pressure underneath the airfoil was maintained ( The LEV formation and convection was delayed by a small amount (refer to au = 22°), owing to a slightly decreased adverse pressure gradient in the leading-edge region, and once the entire boundary layer had become separated the upper surface experienced no effect of the flap (au = 24°, ad = 21°, a 134 characteristics near the end of the downstroke (aa = 8°) were similar in form to that during the beginning of the upstroke indicating a reattachment of the boundary layer. Figure 60 demonstrates how the aerodynamic loads were modified as a result of the aforementioned effects of the flap. A downwards deflection produced a positive camber which increased the lift and negative pitching moment generation capability of the airfoil, resulting in an overall upwards and downwards shift in Q and Cm, respectively, and a higher C/,max and -Cm>Peak- During the upstroke, the linear portion of the lift curve, whose slope was the same as that of the baseline case, began earlier; however it also ended slightly earlier, due to a promoted LEV formation. The earlier formation of the LEV was presumably due to the increased adverse pressure gradient. The increment in the lift and pitching moment due to the LEV was higher (i.e. 0.36 compared to 0.27 in Q and 0.32 compared to 0.30 in Cm), suggestive of, if not evidence for, a strengthened LEV; however, the slightly earlier shedding of the LEV reduced the stall angle in both lift and pitching moment by 0.2° and 0.1°, respectively. As the airfoil underwent stall, the lift experienced a dramatic drop, increasing the hysteresis, and differed only slightly from the baseline case. During post-stall, the increment in both lift and pitching moment of the control case over the baseline case was recovered slowly as the angle of attack was reduced. Furthermore, the instant at which flow reattachment began was slightly delayed. Note that, except for the earlier moment stall, increased -Cm,Peak» and delayed flow reattachment, the Cm curve had almost the exact same shape as that of the baseline case, which also led to a Cw,net which increased only a little. This suggests that the contribution of the flap remained relatively constant over the entire oscillation cycle. An upwards flap deflection resulted in a more complex interaction with the flow. As the angle of attack during the upstroke increased, the boundary-layer thickness over the later portion of the airfoil, in which the flap operated, also increased. This led to a slightly reduced effectiveness of the flap and a corresponding reduction in the deviation from the baseline curves as the angle of attack increased, seen as an increasing lift-curve slope. Note that the reduction is only slight because the majority of the effect of the flap originates in the lower surface suction peak which is not affected by the upper surface boundary layer. A reduction in lift prior to the LEV formation was observed, similar to the behaviour of an uncontrolled airfoil at a lower Reynolds number [27], indicative of a delay in the formation of a weakened 135 vortex. Comparison of the increment in the lift and pitching moment due to the LEV also shows a weakening of its strength resulting from the negative-camber induced reduction in the upper surface adverse pressure gradient (AC/ = 0.17 compared to 0.27 and ACm = 0.28 compared to 0.30). Consequently, the severity of the moment stall was less significant, as was the post-stall loss in lift, which in turn reduced the lift-curve hysteresis. There was a shift of Cw,ccw to CW;CW resulting in an overall reduction in Cw,net- The similarity in the upper surface pressure distributions between the controlled and uncontrolled cases resulted in the boundary-layer reattachment beginning at roughly the same time. In addition, the persistence of the suction pressure on the lower flap surface resulted in an overall downwards and upwards shifting in the Q and Cm curves, respectively, throughout the entire oscillation cycle. Lastly, except for the duration of the second half of the upstroke, during which the Cm curve deviated slightly from that of the baseline airfoil, the role of the flap remained reasonably constant due to its continual effect on the lower flap surface pressure. To compliment the discussion provided above, the effect of the amplitude of the flap deflection was also investigated to determine the nature of the relation between flap deflection magnitude and flap effectiveness to alter the flow. A quick survey of Fig. 60, which presents the dynamic loads for the control cases along with the uncontrolled case, demonstrates that, as expected, an increase in flap deflection, either upwards or downwards, resulted in an increase in the increment in the loads (i.e. for upwards deflections the increase in lift and decrease in pitching moment was reduced, and for downwards deflections the decrease in lift and increase in pitching moment was reduced). The opposite is true for a decrease in flap deflection. Note, however, that the changes are nonlinear functions of flap deflection angle. More specifically, larger deflections, represented by 8 = ±16°, in comparison to moderate flap deflections, represented by 5 = ±8°, do not have the same effect for upwards deflections as it does for downwards deflections. An increase in the downwards flap deflection, from 8 = -8° to 8 = -16°, is fairly straightforward and did not appear to affect the ability of the flap to increase lift and decrease pitching moment; the 8 = -8° curves fall roughly half-way in between the 8 = 0° and 8 = -16° curves since the moderate deflection was half of the large deflection. In contrast, an increase in the upwards flap deflection, from 8 = +8° to 8 = +16°, showed mixed results. During the upstroke, the additional reduction in lift 136 and increase in pitching moment over that of 8 = +8° was extremely small and indicates that for very large angles the flap was very ineffective. Beginning just prior to LEV formation, the gap between the 8 = +16° and 8 = +8° cases, in both lift and pitching-moment, are observed to diverge, and in fact subsequent to the LEV shedding the 8 = +16° case was equally efficient at reducing lift and increasing pitching moment as the 8 = +8° case. Also note that whereas a deflection of +8° decreased Cw,net and CH, the larger deflection of+16° caused a relative increase in these two parameters. Figures 61a and 61c plot the surface pressure distributions for the 8 = 0°, 8 = +8° and 8 = +16° cases at an instant during the upstroke when the increased flap deflection was very ineffective, and during the downstroke when the increased flap deflection was equally effective. The downwards flap deflection cases are also included for comparison. Figure 61a shows that during the upstroke (au = 16°) there was only a variation in the pressure distribution in the trailing-edge region, and that over the rest of the airfoil the variation was minor, which led to only a small reduction in lift and increase in pitching moment. Furthermore, the suction pressure that normally formed on the flap lower surface was of reduced strength for 8 = +16° than for 8 = +8°, in contrast to what should be expected. During the downstroke (a^ = 16°), the airfoil was stalled and therefore the upper surface pressure distribution did not deviate from the baseline case. On the lower surface, however, the entire pressure distribution was significantly affected, especially in the trailing-edge region where the lower flap surface suction pressure peak, relative to the baseline case, was doubled, and accounts for the increased flap efficiency during the post-stall flow condition. From these observations, it is believed that the divergence of the lower flap surface from the flow underneath the airfoil caused the boundary layer underneath the flap to separate at small angles of attack (i.e. from the beginning of the upstroke motion). This persisted for the majority of the upstroke, despite the favourable conditions caused by the increasing angle of attack, since it is more difficult to reattach a separated boundary layer than to prevent a boundary layer from separating. The lower flap surface boundary layer only reattached towards the end of the upstroke. This is seen in Fig. 61b, which shows that at ocu = 21° the suction peak underneath the flap was larger for 8 = +16° than for 8 = +8° indicating the boundary layer had reattached. The inset is a zoomed in view of the trailing-edge region pressure distribution of the two upwards flap deflection cases shown in Fig. 61a, and is provided for comparison. Since the majority of the effect of the flap 137 originated fromit s lower surface suction pressure, the separation of the boundary layer in this region prevented this from forming, and accounts for the marginal effect of the flap during the upstroke motion. This result is extremely important for understanding the physics behind the effect of a flap for three reasons. First, it demonstrates again, that the majority of the effect of the flapi s derived from its influence on the lower, as opposed to the upper, flow. Second, it shows that, in the case of static upwards flap deflection, if the angle is too large, the boundary layer on its lower surface may separate and significantly hinder the flap's performance. Third, and most important, it reveals that for the previously described active flap control, the dynamic motion of the flap has a crucial role in maintaining an attached lower surface boundary layer, since at no point was the lower surface boundary layer observed to be in a separated state for the same large upwards deflection of 8max = +16°. Despite these findings, it is obvious that applying passive control to an airfoil undergoing dynamic-stall oscillations does not achieve the improvements that active control does. Or, perhaps a change in the operating conditions may lead to a different conclusion. It has been observed that a passively deflected flap can considerably affect the aerodynamic loads without substantially infringing upon the characteristics of the flow. This poses an interesting question: Can a passively deflected flap be applied to an airfoil undergoing attached-flow oscillations in order to replicate the desired large levels of lift characteristic of oscillations with a larger mean angle while at the same time avoiding the unfavourable characteristics of an airfoil subject to dynamic stall? To fully appreciate this approach one must question the motives behind, and advantages of, an unsteady airfoil. When an airfoil is harmonically oscillated in pitch, it is with the intention of varying the loads, specifically the lift force, between two desired values. Depending on what those values are, the mean angle and oscillation amplitude can be chosen to produce the desired loads. Assuming the oscillation amplitude and frequency are predefined (for example, Aa = 8° and K = 0.1), manipulation of the values of the loads can be realized through adjustments in the mean angle. Now, recall that if araax remains below or equal to the static-stall angle, then the airfoil operates in the attached-flow regime, and the loads are characterized by very little hysteresis, the absence of airfoil stall, and a Q that varies between very low and moderately high values; in the case of am = 8°, Q varies between -0.01 and 1.19. In the event, however, 138 that am is increased such that amax exceeds the static-stall angle so as to generate increased loads, as is the case of am =16° where Q varies between 0.48 and 1.69 during the upstroke, the airfoil is subject to dynamic stall and the loads are characterized by significant hysteresis and a very severe Cm,peak due to the formation and shedding of a LEV. The problem boils down to whether it is possible to generate the same high loads as those produced by large mean angles but without generating a LEV, which is responsible for the largely separated flow over the airfoil, the considerable degree of hysteresis and excessive excursions in pitching moment. To illustrate the above concept, Figs. 62a and 62b shows the aerodynamic loads for three baseline cases, corresponding to am = 16° (dynamic-stall regime; thin-dotted line), 10° (attached-flow regime; thin-dashed line), and am = 8° (attached-flow regime; thin-solid line), which will serve as a reference for comparison, and two control cases, corresponding to am = 10° (thick-dashed line) and am = 8° (thick-solid line), both with flap deflections of 8 = - 16°. Note that for direct comparison of the different cases the abscissa is plotted as a-am so that they all fall in the same range. The vertical lines identify the minimum, mean, and maximum angles of attack. Focusing first on the control case of am = 8° with 8 = -16°, it is evident that by a simple constant flap deflection it is possible to reproduce almost completely the peak-to-peak variation in Q of the dynamic stall case (C/,min = 0.56 compared to 0.48 and C/>max = 1-62 compared to 1.69), while at the same time preserving the characteristics of an attached-flow oscillation, which is to say that a LEV does not form. In the absence of a LEV, the airfoil does not stall, and the variations in C/ and Cm are approximately the same as those of the baseline attached-flow case (compare thick and thin solid lines). Additionally, the peak negative pitching moment is much reduced, resulting in a performance ratio twice as high, the aerodynamic damping is positive, and the lift-curve hysteresis is negligible in comparison to the uncontrolled case with am = 16°. This is along the same lines as what was concluded by Greenblatt and Wygnanski [32] who indicated that control located in the trailing-edge region was superior since, for the same maximum lift coefficient, the airfoil could be operated at a reduced mean angle resulting in improved aerodynamic characteristics. The values of the critical aerodynamic characteristics are provided in Table 6. Caution must be taken, however, when choosing the oscillation parameters, as is demonstrated by selecting otm = 10°. In its uncontrolled state, the flow is of an attached-flow type, similar to the am = 8° case. In spite of 139 this, the effect of the passive control on the aerodynamic loads in the case of Cm due to a LEV, the gradual decrease and increase in the downstroke Cm, along with the temporary alleviation of the decrease in Q during the downstroke, do suggest that the flow deviates from its baseline attached-flow nature. To understand how the above results come about, Fig. 63 portrays the surface pressure distribution for the baseline and passive control cases at particular angles of attack (presented as a-am). In comparison to the large mean angle of 16° for which the majority of the load is applied fore of the airfoil %-chord, a reduced mean angle of 8° in conjunction with a 16° downwards flap deflection results in a more evenly distributed pressure loading and an alleviated adverse pressure gradient in the leading-edge region during the upstroke (dashed line). The first and second halves of the airfoil are subject to a reduced and increased pressure differential, respectively. Towards the end of the upstroke (au - am = 7° and au - am = 8°), a LEV is not found to form for the control case therefore avoiding lift and moment stall, and the large degree of hysteresis that would ensue. In fact, the suction peak reaches a maximum at the end of the upstroke and exceeds to a small extent that of the am = 16° case (dotted line). During the downstroke, the control case behaves similar to its corresponding undeflected case (solid line) in that the suction peak and overall pressure differential decrease, leading to a linear reduction in Q and gradual reduction in Cm. The later portion of the downstroke (aa - am = -6°) is characterized by a flow similar to the uncontrolled case, albeit with an increased pressure differential. Up to now it seems that, oddly enough, the characteristics of an airfoil oscillated around a low mean angle of attack and equipped with a passively deflected flap in the negative direction are superior to those of an actively controlled flap. In certain ways this is true; however there is one very important factor that detracts from its prospects as being a viable alternative to active control. In Figs. 62c and 62d, the lift and pitching moment coefficients are presented for the baseline airfoil (with am = 16°; solid line), the optimum 140 active control case presented in section 5.4 (dotted line), and the passive control case (with am = 8° and 6 = -16°; dashed line). With regards to lift, the performance of the passive control case is superior to the active control case, in that the peak lift is relatively unaffected (C/)max = 1.62 for passive control compared to 1.32 for active control) and the lift-curve hysteresis is considerably reduced (CH = 0.6 for passive control compared to 12.8 for active control). Nevertheless, the flaw of the passive control is obvious in the Cm curves of Fig. 62d. Although there is no drastic moment stall present for the passive control case, the downwards flap deflection did shift the Cm curve downwards quite a bit causing the Cm to remain very much negative throughout the entire cycle. Bousman [4] makes known that an airfoil with a large aft camber is not appropriate for application in helicopter rotor blades due to the constant negative pitching moment that results. In fact, Joo et al. [35] include the value of Cm at amin as a criteria in the evaluation of their control to account for the unwanted downwards shifting of the whole Cm curve, which they indicate is a potential source of structural problems such as flutter. In the absence of a method of alleviating this persistent negative pitching moment, it seems that active control still remains the preferred choice over passive control. 5.8 Higher Harmonic Control It was stated in the literature review that higher harmonic control (HHC) has received increasing attention over the last two decades, especially as a means of alleviating the vibratory loads by modifying the rotor blade pitch at harmonic frequencies above the rotor rotational frequency, and consequently the periodic aerodynamic loads such that they no longer produce the detrimental effects. Wood et al. [96] provide a good description of how a 4/revolution HHC system works. Essentially, it consists of an accelerometer that measures the vibrations. This signal is then sent to electronic control unit that separates the sine and cosine 4/revolution vibration components. A computer then determines via mathematical model the blade feathering required to null the vibrations. In other words, the swashplate mechanism it used to alter the aerodynamic loads in a manner that it introduces a vibration of opposite phase to the original vibration thus suppressing it. More recently, Liu et al. [100] applied higher harmonic control using trailing-edge flaps with the goal of reducing vibrations 141 and improving performance. The aerodynamic loads subject to higher harmonic flap control, however, have not been previously reported. It was therefore of interest to apply HHC control via the trailing-edge flap and to document its effects on the aerodynamic loads in order to verify whether it is possible to impart a higher harmonic variation in the aerodynamic loads. In addition, this is a key step in determining the response time of the flow for very quick flap deflections. In this set of experiments, the flap motion, triggered in response to the oscillating airfoil phase angle, was programmed into a series of saw-tooth deflections, described by the start time ts, the peak-to-peak deflection amplitude 8max, and the number of flap deflection cycles per airfoil oscillation cycle NP. Values for these parameters included ts between -0.57t and 0.27t (i.e. Omin and the angle of attack just prior to which the LEV initiates), 8max of 8° and 16°, and NP = 2P, 3P and 4P (i.e. twice, three times, and four times the oscillation frequency). A schematic of the flap motion profile is shown in Fig. 64. Also, it should be noted that the airfoil oscillation parameters were chosen to be a(t) =12°+ 8°sincot and K = 0.1. Subject to these oscillation parameters, the airfoil is observed to undergo light stall and, in fact, airfoil stall occurs during the initial stages of the downstroke motion. The results of this investigation into higher harmonic control have been summarized in Ref. 29. 5.8.1 Effect of Higher Harmonic Motion The influence of the higher harmonic flap motion (i.e., NP = 2P, 3P and 4P), actuated at ts ~ -0.5K (i.e., Ofo = amin or at the beginning of the pitch-up motion) with 8max = 16°, on the dynamic Q and Cm loops was examined first, and provides a sound understanding of this type of control motion. The results were also compared with those of a baseline, or uncontrolled, airfoil. Figure 65 presents the lift and pitching moment coefficients versus angle of attack for each of the three NP values. At first glance, both coefficients seem to deviate wildly from the baseline case in an arbitrary manor. This, however, is not the case as Fig. 66 demonstrates, in which the aerodynamic loads are presented relative to the baseline case. In other words, the deviation in lift AC/ is computed from the difference between the controlled Q|HHC and uncontrolled C/|Baseiine cases. The deviation in pitching moment is similarly computed. The physical mechanisms responsible for the observed modifications in 142 the aerodynamic loads will be illustrated from the detailed Cp distributions (Fig. 67) and the near-wake flow structures (Fig. 68). Figure 65a shows that for a 2P flap motion the Q was reduced for Ou < 14.5° and increased for the remaining upstroke motion, as a result of the negative and positive camber effects, especially in the trailing-edge region, induced by the upward and downward flap deflection, as the airfoil was pitching up. Note, however, that the camber effects are not only caused by the geometric flap deflection angle, but also to the rate of deflection. This was determined from the decrease and increase in Q when the flap was at 0° but deflecting downwards and upwards, respectively (Fig. 66a). During the airfoil pitch-down motion, the upward and downward flap motion was repeated; the Q was first decreased between ow and Od = 13° resulting in an increase in post-stall lift loss, compared to a baseline airfoil, and was followed by a minimal promotion in the pitch-down flow reattachment process and subsequent increase in Q. Figure 67a shows that at oeu = 9° during the pitch-up attached-flow process, the upward flap motion led to an overall reduction in both suction and positive- pressure pressures along the airfoil surfaces compared to a baseline airfoil. Special attention should be given to the significant Cp reduction appeared on both the lower and upper flap surfaces, indicating the majority of the effect of the flap is retained in its vicinity. The wake width and the shape of the wake profile remained unchanged (except for the upward shifting of the wake centerline due to the upwards flap deflection; Fig. 68a), while u' (Fig. 68b) and Reynolds stress distributions (Fig. 68c) across the wake were slightly suppressed, suggesting the boundary layer remained the same in thickness but reduced in turbulence due to the more favourable trailing-edge pressure gradient. Note that, in general, the upward TEF motion was efficient in containing a reduced momentum deficit during the oscillation cycle and resulted in a reduced drag, wake width and u\ At Ou = 19°, the downward flap deflection rendered an advantageous pressure distribution, especially on both the upper and lower flap surfaces (Fig. 67b), and was accompanied by a slightly widened and downward shifted wake with enhanced u' and uV (Fig. 68) across the wake compared to a baseline airfoil. The Cp measurements also indicate that for 2P HHC flap control, the strength of the LEV was not affected by the downwards deflected flap (Figs. 67c and 68), while the "premature" spillage of the LEV was, however, slightly promoted to ad = 19.5° (with C/,max = 1.51) during pitch-down (Figs. 65a, 67d and 68) compared to oca = 19.1° (with Q,max = 1.46) 143 of a baseline airfoil. Figure 66a also shows that during the LEV formation and shedding, the effectiveness of the flap was hindered, this observation being supported by the fairly flat "kink" in the lift variation near the top of the upstroke (i.e. at x « 0.57i). During the post-stall flow condition, the flap-induced reduction in Cp was evident (e.g., at Od = 15°; Fig. 67e). Note that although the upward flap motion (between oca = oc„, and amin) did not significantly promote the pitch-down flow reattachment, it did, however, provide an improved Cp distribution, especially on both the flap surfaces (Fig. 67f), and a moderately more energetic wake with increased u, u' and uV. More importantly, a single CW Cm-oc loop was observed (of CWjCW = Cw,net = -0.66), in contrast to the figure-eight like Cm-oc loops of a baseline airfoil (with Cw,ccw = 0.26 and Cw>cw = -0.68), suggesting an substantially increased negative damping, however the peak negative pitching moment coefficient was slightly reduced (Fig. 65d). The details of the HHC flap motion and the critical aerodynamic values are summarized in Table 7. Figure 65b shows that for 3P flap control an increase in Ci airfoil upper surface can be demonstrated from the Cp distributions at Ou = 20° and oca = 19° (denoted by dashed lines in Figs. 67c and 67d), as well as the wake flow measurements (Fig. 68). Moreover, the delay in LEV convection in combination with a downwards deflecting flap led to the observed increase in C/)max. An increased wake deficit, u' and uV at oca = 19° and oca = 15°, compared to a baseline airfoil with and without 2P flap control, were observed. In fact, these were greater than those of the baseline or 2P cases during their LEV spillage, suggesting the strength of the LEV was somewhat enhanced by the 3P flap motion. The promotion of the flow reattachment (characterized by the reappearance of a laminar separation bubble in the leading-edge region with a higher suction peak; see, for example, Fig. 67f) at around oca = 9.7°, compared to aa = 8.3° of a baseline airfoil, during the pitch- 144 down motion can also be seen from the Cp data. Furthermore, in addition to the observed Q changes, an additional CW Cm-a loop, compared to a baseline airfoil, was also observed in Fig. 65e; the net torsional damping Cw,net = -0.43, however, was found to remained unchanged compared to a baseline airfoil (Table 7). That is, the rather drastic variation in Q, induced by the 3P flap deflection, did not render any additional change in the net negative damping value or nose-down pitching-moment. A slightly reduced -Cm,Peak, compared to a baseline airfoil, while of much higher value than that of 2P flap control was also exhibited (Table 7). For an oscillating airfoil with 4P HHC flap control, an additional CW Cm-a loop (Fig. 65f), similar to the 3P flap control case (Fig. 65e), was exhibited; the CW)net however was again not affected. A noticeable increase in -Cm>Peak was, on the other hand, observed. Also, other than the observed increase and decrease in the Q in response to the downward and upward flap deflections (Figs. 65c and 66c), the onset, subsequent growth and spillage of the LEV was only vaguely promoted (as indicated in Figs. 67c, 67d and 68). In the meantime, the pitch-down flow reattachment (at C6d ~ 13.8°) was found to occur much earlier but more gradually than a baseline airfoil. As such, the flow-reattachment process was found to be characterized by a earlier return to low levels of u, u' and uV. In summary, the 2P flap deflection provided a significant alleviation of Cm>peak, or the large overshoot in nose-down pitching moment, while a higher negative Cw,net, compared to 3P and 4P control cases and the baseline airfoil. The 3P flap motion rendered a somewhat reduced -CmiPeak, a slightly increase C/)max and a virtually unchanged Cw>net compared to 4P flap control and a baseline airfoil. The 4P flap control provided the lowest C/,max (below that of a baseline airfoil) and the highest -Cm,Peak among the three NP tested. Despite certain delays in LEV formation/spillage and/or promotion of flow reattachment, the general sequence of flow structures over the airfoil for all control cases remained akin to the baseline airfoil. Also, for all the HHC flap motions considered, the HHC flap motion only introduced a minor change in the Cd-oc loops and Cd,max (Table 7). Lastly and probably most importantly, the aerodynamic loads were altered and seemed to respond to the flap motion without any noticeable phase lag even for the quickest of flap motions, thus making it a viable alternative to swashplate HHC control. 145 5.8.2 Effect of Start Time and Peak Deflection The effect of the flap actuation start time ts and the peak-to-peak flap deflection 8max on the dynamic Q and Cm loops was also investigated. Figures 69,71 and 72 present the Q and Cm results at different ts for the 2P, 3P and 4P flap control cases, respectively, with the effect on Cw,net being summarized in Fig. 70. The effect of 8max for two values, namely 8° and 16°, are displayed in Fig. 73. Table 7 summarizes the characteristic aerodynamic load parameters for each of the NP, ts and 8max tested. For 2P flap control, four different ts (= -0.46K, -0.15K, On and 0.2JC corresponding to a flap actuation at Ou = 4°, 8.4°, 12° and 16.7°, respectively) were tested, and Fig. 69 shows the results for the case of 8max = 16°. In regards to the lift coefficient, prior to LEV formation, the generation of lift was dominated by the flap motion; therefore a later start time caused a delay in the variation in lift (Figs. 69a and 69b). During the presence of the LEV over the airfoil, the effectiveness of the flap seems to have been somewhat disturbed for all values of ts (Fig. 69b). The overall effect was an increasing C/,max for ts < -0.15n, after which the peak lift began to decrease with increasing ts. The lowest value of Q>max was observed for a flap deflected at ts = 0.2K, and constituted a 12% reduction relative to the baseline airfoil. Note that for a 2P flap deflected at ts = 0.2K or ocu = 16.7° (i.e., at around the end of the upstream propagation of the flow reversal and just prior to the onset of the LEV formation), the magnitudes of Q)max, Cd,max and -Cm,peak were 12%, 16% and 12% below those of a baseline airfoil. This demonstrates again the proportional relation between Q>max and Cd,max, and C/)inax and -Cra>peak, where a reduction in Cd,max or -Cm>peak is accompanied by a likewise reduction in Qmax- On the other hand, the ts = -0.157t case was found to provide the highest combination of C/,max, -Cm,Peak and Cd,max. The values of-Cm,peak were found to increase with increasing ts, except for the latest start time, for which the lowest peak moment coefficient was observed (Fig. 69c). In regards to the net torsional damping Cw,net, presented in Fig. 70, a later actuation initiation benefited from improved damping (i.e. a shift towards less negative values), mainly due to large increases in Cw>Ccw Lastly, the Cp and wake flow measurements (not shown) also indicate that, regardless of ts, the angles of attack at which the formation and detachment of the LEV was found to be slightly affected by the TEF motion, deviating from 146 the baseline values by up to 0.5°. Except for the earliest of start times, the general trend was toward a delay in these activities. The variation of d, AC/, Cm, and Cw,net with ts (= -0.5rc, -0.2571 and -0.06K) for 3P flap control is depicted in Figs. 70 and 71. With 8max = 16°, there was a minor improvement in both C/)tnax and Cm!peak for all values of ts (Figs. 71a and 71c). This behaviour seems to be at odds with the observed trend that C/)tnax and Cm>Peak are inversely related. It is also evident that, at least for large angles of attack (e.g. a > 9°), the degree of hysteresis in the lift curve was considerably reduced for the later two start times. Moreover, the change in the dynamic Q values, compared to a baseline airfoil, presented in Fig. 71b shows that the LEV-induced flap ineffectiveness observed for the 2P control case was not as apparent, except for the earliest of start times. Although the earliest start time led to a delayed LEV initiation and shedding, this effect increasingly disappeared as ts was increased. In fact, for ts = -0.06rc the LEV was somewhat promoted. The Cm curves of Fig. 71c indicate that the large CW loop grew with increasing ts, rendering a decreasing CW)CW relative to the baseline airfoil. Although no specific trend was observed for the CCW loop, they were in general larger than the baseline case, increasing the magnitude of Cw,ccw. Except for the ts = -0.25rc case, the increased |CWjCw| was compensated by an improved Cw,ccw and thus rendered an unchanged net Cw value compared to a baseline airfoil (Fig. 70). Among the three flap start times tested, the ts= -0.2571 control case rendered the lowest -Cm,peak but the highest net negative damping (Table 7). The effect of ts (with ts = -0.571 and -0.267t) for 4P flap motion on the dynamic load loops is investigated in Figs. 70 and 72. In contrast to the 2P and 3P flap control of equivalent ts, the 4P flap motion always rendered a reduced Q,max compared to a baseline airfoil, regardless of ts. The LEV, whose effect on the flap efficiency was re-established and can be seen in Fig. 72c, was not observed to be appreciably promoted or delayed in either its initiation or its shedding; this behaviour differs from both 2P and 3P cases. Also, similar to the 3P case, the later start time reduced the Q-hysteresis. Unlike the 3P or 2P cases, for which -Cra,Peak was always improved or improved with decreasing ts, respectively, the 4P control required an earlier ts to improve -Cm>peak. Despite the significant modifications to the Cm curve, a ts = -0.5TI did not produce significant changes to either CW)CCw or Cw?Cw, whereas a 147 ts = -0.26rc led to reductions in both Cw,ccw and CW;CW resulting in an increased negative damping (Fig. 70). The effect of 5max was also investigated by reducing the deflection by half (i.e. 8max = 8° and 16°) at each of the start times. To illustrate its effect, Fig. 73 presents the Q and Cm dynamic loads for 2P, 3P and 4P cases at a fixed ts«-0.57C. The overall trend detected was that of a reduction in the increment in lift and pitching moment from the 8max =16° control case to the 8max = 8° control case. This implies that any improvements achieved with a larger deflection were lessened, and similarly any deterioration in performance was minimized. This is most true for the 2P case, where the 5max = 8° cases always fell in between the baseline and 5max =16° cases. With even higher harmonics, that is 3P and 4P, there does seem to be sometimes a small phase shift between the flap effects for the two peak-to-peak deflection cases. It was determined that the negligibly small difference in the start time (i.e. - 0.57C for 5max =16° and -0.467U for 8max = 8°) was too small to be the source of the disparity, however the actual cause for this was not clear. The results also showed that (i) for 3P flap control, C/,max was always improved for 8max = 16° in contrast to 8max = 8°, and that Cm,peak and Cw,net were rather similar for the two values of 8max; and (ii) for 4P flap control there was always a minor improvement in Cm,peak for 8max = 8° in contrast to 8max = 16°, and no noticeable difference in Q>raax. The values of the aerodynamic characteristics may be found in Table 7. 148 CHAPTER 6 CONCLUSIONS An experimental investigation into the control of the flow around and unsteady aerodynamic loads developed on a harmonically oscillating NACA 0015 airfoil via a dynamically deflected simply-hinged trailing-edge flap was conducted at a Reynolds number of 2.46 x 105 using a combination of techniques, which include surface pressure measurements, wake velocity surveys, and particle image velocimetry flowfield measurements. A detailed parametric study was performed to evaluate the effects of the flap's prescheduled trapezoidal motion profile, which was found to be highly influential on the degree of control. Although focus was mainly on the dynamic stalling airfoil in the deep- stall regime, both light-stall and attached-flow oscillations were also considered. In addition, the effects of both a static trailing-edge flap deflection and a trailing-edge flap undergoing higher harmonic motions were also considered. The results indicate that a trailing-edge flap imposed an effective camber in the trailing-edge region and was highly effective in the control of the aerodynamic loads, especially the pitching moment, which was achieved in large part by the manipulation of the lower flap surface pressure distribution. In the application to an airfoil subject to dynamic stall, the severe nose-down pitching moment was reduced by up to 40%, the performance ratio (i.e. |C/!max/CmiPeak|) was improved by 30%, and the aerodynamic damping was turned positive and increased four-fold. The leading-edge vortex, the predominant flow structure formed over the airfoil, was affected in its strength and initiation albeit only marginally. Furthermore, control was limited to the duration of the flap motion, and, in general, no effect on the flow or aerodynamic loads was observed while the flap was withdrawn to its initial undeflected position, making this method of control ideal for active systems. Brief conclusions regarding the flow control for both dynamic-stall and attached-flow regimes, as well as passive flap control and higher harmonic flap control are drawn and summarized below. 149 6.1 Dynamic Stall Control The effects of trailing-edge flap control on the flow around an airfoil undergoing dynamic stall oscillations was determined from detailed surface pressure measurements, hot wire wake velocity surveys, and particle image velocimetry flowfield measurements, and can be summarized as follows: a) During the deflection of the trailing-edge flap, the flow on the windward side of the airfoil was of a higher (lower) velocity for a positive (negative) deflection due to an effective negative (positive) trailing-edge camber and reduced (increased) protrusion in the lower flow stream resulting in a reduction (increase) in pressure. This deviation in the lower pressure distribution was, however, non-uniform and the majority of the effect was localized in the area surrounding the flap where a suction (pressure) peak formed just downstream of the flap hinge. On the upper surface, a uniformly distributed decrease (increase) in the surface pressure distribution was observed for a positive (negative) flap angle. The combined result was a decrease (increase) in lift, drag and nose-down pitching moment for a positive (negative) flap angle. The above bias towards the lower surface is believed to come from the local trailing-edge boundary-layer thickness. On the lower (upper) surface, the boundary layer was relatively thin (thick) and therefore sensitive (insensitive) to a small change in trailing-edge geometry. b) The effect of the trailing-edge flap was not limited to its geometric angle, but also depended on its deflection rate, with faster ramp rates resulting in greater effects. In addition, the dynamic flap motion was crucial in preventing the separation of the lower flap surface boundary layer that occurred for an equivalent statically deflected flap, which would have hindered its performance. c) The trailing-edge flap's ability to manipulate the pitching moment was relatively unaffected by the state of the upper surface boundary layer due to its consistent influence over the windward side flow. 150 d) Small changes in the strength and initiation of the LEV, whose vorticity originated and was supplied by the leading-edge turbulent flow of the separated shear layer, were observed. Its strength was decreased (increased) and its initiation delayed (promoted) for positive (negative) flap deflections. These were caused by the alleviated (intensified) adverse pressure gradient in the leading-edge region. e) Boundary-layer reattachment was not affected by the control. f) Despite a large flap deflection the flow attempted to satisfy the Kutta condition as only a minimal trailing-edge pressure differential was observed throughout the entire oscillation cycle, with the exception of the interval of LEV shedding. g) The flap deflected the shear layer emanating from the flap lower surface upwards (downwards) causing the wake width to decrease (increase) for upwards (downwards) flap deflections. h) The flow around the airfoil was generally not affected when the flap was inactive, and therefore the aerodynamic loads coincided with those of the baseline, or uncontrolled, airfoil. Only small deviations were observed subsequent to the stalling of the airfoil. i) Comparable results were observed for both deep- and light-stall flowregimes . The influence of the flap motion parameters on the unsteady aerodynamic loads, computed from numerically integrating the phase-averaged surface pressure distributions, is as follows: a) Only positive flap deflections led to the reduction of the peak nose-down pitching moment, however this was accompanied by a reduction in the maximum lift coefficient. b) A negative flap deflection led to an increase in the maximum lift coefficient; however it also increased the peak nose-down pitching moment, and is therefore inappropriate as this is contrary to the control objectives. 151 c) The larger the flap deflection the larger its effect was, although the relation was not a linear one. d) Variations in U were most influential on the global aerodynamic characteristics (i.e. Cw,net and CH). The peak aerodynamic loads (i.e. Q>max, Cra,peak and Cd,max) were found to be insensitive to U provided the flap reached its maximum deflection prior to LEV formation and remained fully deflected during the LEV convection and shedding. e) The local aerodynamic characteristics (i.e. C/imax, CmiPeak, |C/,max/Cm)peak| and Cd,max) were most influenced by variations in ts and tRi. f) A steady-state time period in-between the flap upward and return motions was found to be advantageous, but should be small so as not to impose an overly fast tRi to the detriment of Cw,net- The flap return motion ramp rate tR2 was determined to be of secondary importance and should be computed from the values chosen for U, tRi and tss. g) For very fast Rl, a reduction in -Cm,peak was still achieved despite a smaller flap angle at the instant of LEV formation and convection. The cause of this increased flap effectiveness for the fastest flap pitch-up motions was found to be rooted in its increased ability to reduce the LEV strength. h) The maximum reduction in severe nose-down pitching moment required a start time near the mean angle (i.e. ts ~ 0%), a large positive deflection (i.e. _1 8max = 0.67araax) and a fast upward flap ramp rate (tRi ~ 10%fo ). i) The maximum lift coefficient was highly sensitive to ts and tRi, requiring a delayed start time towards the maximum angle of attack and/or a slow ramp rate to minimize its reduction, j) The performance ratio was at its highest for the same flap motion parameters as those which achieve the largest reduction in -Cra)Peak. k) The highest net work coefficient was produced by increasing the pitching _1 moment during the entire downstroke (i.e. td ~ 50%fo and ts = 0.57t). 1) The lift-curve hysteresis was most reduced by decreasing the lift during the 1 entire airfoil pitch-up motion (i.e. ts = -0.57E and td ~ 50%fo" ). 152 m) A trailing-edge flap was unable to improve both C/,max and Cm,peak simultaneously. n) Opposing requirements of the aerodynamic characteristics necessitates a compromise to be made. Significant improvements can be made with a 8max ~ 1 0.67amax, ts ~ 0.127c (or 0.3371 radians prior to Cm,peak), td « 50%fo" , tRi ~ 19%^"' and tss ~ 35%td resulting in an improvement over the baseline airfoil of over 40% in Cm,peak, a four-fold increase in Cw>net resulting in positive damping, 30% in |Q>raax /Cm>peak|, with a 20% reduction in C/,max and 8% increase in OH- This experimentally determined flap schedule agrees well with that determined numerically by Feszty et al. [18]. 6.2 Attached-Flow Control The control of the flow around an airfoil oscillating in the attached-flow regime via a dynamically deflected trailing-edge flap was investigated as well, and the findings indicate that: a) The majority of the effect of the trailing-edge flap was due in large part to the presence of suction (pressure) peak on the lower surface of the flap for positive (negative) deflections. b) An upwards flap deflection induced a reduction in the lift and increase in the pitching moment for the duration of the flap deflection, as a result of induced negative camber effects, especially in the trailing-edge region. c) For a downwards flap deflection, depending on the value of the start time, the unsteady boundary-layer flow could become detached from the upper surface and form a LEV, introducing a light-stall oscillation. This, however, is provided that the mean angle of attack is just shy of the value that would prompt light stall. For smaller angles, a downwards flap deflection increased lift and decreased the pitching moment for the duration of the flap deflection, as a result of induced positive camber effects, especially in the trailing-edge region. 153 d) A trailing-edge flap was equally effective at controlling the aerodynamic loads of an airfoil undergoing attached-flow oscillations as it is for deep stall. 6.3 Passive Flap Control Applying a passive flap deflection to control the flow around and the aerodynamic loads on an unsteady airfoil in the deep-stall regime resulted in the following effects: a) A statically deflected flap induced a camber effect throughout the entire oscillation cycle displacing the lift and pitching moment curves downwards (upwards) and upwards (downwards), respectively, and led to decreased (increased) values of Q)max and -Cm;Peak for positive (negative) flap angles. b) The observed changes in the surface pressure were more evenly distributed over the entire airfoil compared to the dynamic trailing-edge flap control, however an increased loading still occurred on the flap lower surface. c) An upwards (downwards) flap deflection delayed (promoted) the formation of the LEV and decreased (increased) its strength as a result of the alleviated (intensified) leading-edge region adverse pressure gradient. d) Flow reattachment was unchanged (delayed) for an upwards (downwards) flap deflection. e) Whereas for a downwards flap deflection, for which a uniform shift in lift and pitching moment were observed, an upwards flap deflection was subject to a slight non-uniform shifting of the lift and pitching moment curves due to a slightly reduced flap effectiveness caused by a thickening of the upper surface boundary layer as angle of attack was increased. f) An excessively large upwards flap deflection angle caused the boundary layer underneath the flap to separate right from the beginning of the upstroke, which persisted for the majority of the upstroke, since it is more difficult to reattach a separated boundary layer than it is to prevent a boundary layer from separating, severely hindering its performance. 154 g) It is possible to reproduce almost completely the peak-to-peak variation in the lift coefficient of the dynamic stall case using a sufficiently reduced mean angle of attack in combination with a negative flap deflection while at the same time preserving the characteristics of an attached-flow oscillation. The peak negative pitching moment is much reduced, the performance ratio is twice as high, the aerodynamic damping is positive, and the lift-curve hysteresis is negligible in comparison to the uncontrolled dynamic stalling airfoil. However, the persistent negative value that the pitching moment maintains throughout the entire cycle makes this inappropriate for application in helicopter rotor blades. 6.4 Higher Harmonic Flap Control A trailing-edge flap actuated at harmonics twice, three times, and four times higher than the airfoil oscillation was studied and resulted in the following effects on the aerodynamic loads: a) The variation in the aerodynamic loads relative to the baseline airfoil adhered closely to the motion of the flap. In other words, as the flap angle increased the lift and nose-down pitching moment decreased, and vice versa. Also, a later start time caused a delay, or shift, in the variation in lift and pitching moment. b) Despite certain delays in LEV formation/spillage and/or promotion of flow reattachment, the general sequence of flow structures over the airfoil for all control cases remained akin to the baseline airfoil. c) During the presence of the LEV over the airfoil, the effectiveness of the flap was somewhat disturbed. d) The 2P flap deflection provided a significant alleviation of the large overshoot in the nose-down pitching moment, while a higher negative work coefficient, compared to 3P and 4P control cases and the baseline airfoil. 155 e) The 3P flap motion rendered a somewhat reduced peak negative pitching moment, a slightly increase maximum lift coefficient and a virtually unchanged work coefficient compared to 4P flap control and a baseline airfoil. f) The 4P flap control provided the lowest maximum lift coefficient (below that of a baseline airfoil) and the highest peak negative pitching moment among the three NP tested. g) A reduction in the peak deflection brought about a reduction in the increment in lift and pitching moment. h) Higher harmonic flap control is a viable alternative to swashplate HHC control. 156 CHAPTER 7 CONTRIBUTIONS Based on the research objectives set out at the beginning of this endeavour and the results which have been obtained, this work constitutes original and novel contributions to knowledge in the following ways: 1. This is the first experimental investigation that sets out to document the trailing- edge flap control of the flow around and aerodynamic loads on a dynamic-stalling airfoil, and to experimentally determine the mechanism through which the dynamic flap exerts its control. 2. This is the first particle image velocimetry (PIV) visualization of the flowfield around a dynamic-stalling airfoil with trailing-edge flap control. 3. This work demonstrates that trailing-edge device can influence the leading-edge vortex albeit in a rather small way. 4. This work provides detailed guidelines with which to determine the required flap motion based on the desired aerodynamic load characteristics. 5. This is the first investigation of the aerodynamic loads on an unsteady airfoil subject to higher harmonic trailing-edge flap control. 6. This work represents an important reference for other researchers of dynamic stall or TEF control, especially those dealing with CFD simulations. 157 CHAPTER 8 FUTURE WORK The results of this dissertation have clearly demonstrated the ability of a dynamically deflected trailing-edge flap to control significantly the aerodynamic loads on a dynamic stalling airfoil. Implementing an upwards TEF deflection led to improvements in the peak negative pitching moment (40%), performance ratio (30%), and aerodynamic damping (four fold increase); however these improvements were plagued by a non-negligible reduction in the airfoil lift-generating capabilities (20%). Furthermore, the trailing-edge flap control was not able to alleviate the strength of the leading-edge vortex to a significant degree; only small variations were observed. Nevertheless, the strong point of this type of control lies in its moment arm, and its ability to manipulate effectively the pitching moment and aerodynamic damping. Unfortunately, the pitching moment and aerodynamic damping both have conflicting requirements of the trailing-edge flap motion than does lift. It has been shown elsewhere that leading-edge flow control, despite its potentially more difficult implementation to rotorcraft due to harsher conditions in the leading-edge region, is more effective at mitigating the leading-edge vortex. Keeping with the same theme of control surface, the variable droop leading-edge concept in particular, developed by Chee Tung and studied, for example, by Martin et al. [57], has been shown to be rather capable of almost eliminating the LEV, leading to a 31% reduction in the peak negative pitching moment and a minor 8% reduction in peak lift. This was achieved through a downwards deflection of the leading-edge flap, which reduced the leading-edge region adverse pressure gradient and consequently prevented massive separation in the form of a LEV. It is therefore proposed that future work should focus on a combined control scheme that would implement both leading-edge and trailing-edge flaps, capitalizing on the strengths of each type of control surface to compensate for their deficiencies. The leading-edge flap is efficient at reducing the strength of the LEV, which in turn results in a reduction in the LEV- induced peak lift and peak negative pitching moment excursions. On the other hand, due to a larger moment arm, the TEF is much more efficient at manipulating the aerodynamic loads without modifying in an appreciable way the overall flow structure over the airfoil. In other 158 words, employing the leading-edge flap would diminish the LEV strength, leading to a slightly reduced peak lift and considerably reduced negative pitching moment. The trailing- edge flap would then be used to impose either a further improvement in the pitching moment, at the small cost of a further reduction in peak lift, or a recovery in the lift, at the cost of a marginally increased negative pitching moment. In either case, the result would be an improvement over the uncontrolled, or solely TEF controlled, airfoil performance. Moreover, this would provide a significant degree of flexibility in terms of having the choice of emphasizing lift or pitching moment given the operating conditions and performance requirements. For such a system to become a viable possibility for implementation onto rotorcraft, however, closed-loop active control is an unavoidable necessity. The possibility of using strategically placed sensors, such as surface mounted pressure transducers and/or hot-film sensors, to characterize the flow structure over the airfoil and to serve as inputs for a closed- loop control system should be explored. Ahn et al. [2] indicate that criteria based on local values are favoured due to the possibility of implementing instantaneous optimization schemes that would allow the airfoil shape to be automatically modified into an optimal configuration given the instantaneous nature of both the airfoil flow and the aerodynamic loads. Previous studies, such as those of Nguyen [67], Magill et al. [55], and Ahn et al. [2], have made use of limited surface pressure information to identify the initiation of the stalling process. The criterion used by Nguyen to gauge imminent leading-edge separation was based on an empirically-determined critical suction pressure in the leading-edge region, which when exceeded marked the initial stages of stall. Magill et al. and Ahn et al. identified when stall was imminent by the dissipation of the leading-edge suction peak. Although this investigation did not explore the form that an active control system might take, specifically the criteria by which to identify the beginning of dynamic stall and with which to trigger control, the data collected does permit a limited analysis of the practicality of the previously mentioned criteria within the limitations of the current experimental conditions. The first, and seemingly the most popular, criteria on which to base dynamic stall is the leading-edge suction peak, as it is generally a measure of the lift on an airfoil. A comparison of baseline airfoil oscillation tests with the mean angle varied between 8° and 16° in 2° increments, covering flow regimes fromattached-flo w to deep stall, shows that the 159 suction peak increased with am reaching a peak value of -6.03 for am = 12°, which corresponds to the first appearance of light stall. However as the mean angle increased further and the flow passed from light stall to deep stall, the maximum suction peak underwent a minor reduction in magnitude. Although the decrease was minimal (-5.89 compared to -6.03 for am = 16° and 12°, respectively), it was sufficient to bring it close to the value of the am = 10° attached-flow case (-5.83). If allowance is made for a certain margin of variability in the magnitude of the maximum suction peak, basing the dynamic-stall criterion solely on the magnitude of the maximum suction peak could be inconclusive under certain conditions, with control being implemented when it may not be warranted, or vice versa. The magnitude of the adverse pressure gradient downstream of the suction peak is also a candidate, since it contributes to the separation of the boundary layer. An evaluation of the maximum adverse pressure gradient downstream of the suction peak shows similar results; the largest peak adverse pressure gradient was experienced by am = 14°, after which it was slightly reduced approaching within 4% the attached-flow case described by 160 The current analysis makes clear that much needed work is required to identify a criterion with which to anticipate the occurrence of dynamic stall reliably and with adequate advanced warning. In addition, these concepts merely identify when stall might occur at which point a pre-determined flap motion is imposed. It would be of greater benefit if the state of the flow throughout the entire airfoil oscillation could be identified, and through appropriate control laws actuate the flap accordingly to achieve the optimum improvement in performance. The ultimate goal of this research topic should be the design of a fully compliant airfoil model equipped with a select number of strategically placed surface mounted sensors, as previously discussed, and whose camber distribution could be actively adjusted via a system of piezoelectric actuators. It is believed that the future lies in airfoils and wings whose shape can be adjusted to the flow conditions resulting in optimum performance over a range of operating conditions. This is a lesson that our feathered friends have mastered very effectively, and future research efforts should follow their lead. This is especially important for rotorcraft, where the rotor blades encounter large variations in their operating conditions from transonic flow on the advancing side to relatively low speed flow on the retreating side, all the while being exposed to interactions with the tip vortices, dynamic stall, and other complications in the flow. In fact, it would be of great advantage if an active control system could be devised and tested that controlled the two most undesirable qualities of helicopter aerodynamics: dynamic stall and blade-vortex interactions. Although dynamic stall and blade-vortex interactions are each not limited to a single azimuth angle, they are predominantly observed on the retreating and advancing sides of the rotor disk, respectively, and therefore could possibly benefit from the same control mechanism. As a TEF has demonstrated its utility in controlling the unsteady aerodynamic loads generated on an airfoil subject to dynamic stall, it should also be studied whether such a mechanism would be equally efficient at alleviating the impulsive loads that are generated when the tip vortex from a rotor blade impacts the following rotor blade. 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Enenkl, B., Kloppel, V., Preibler, D., and Janker, P., "Full scale rotor with piezoelectric actuated blade flaps," Proceedings of the 28th European Rotorcraft Forum, Sept. 2002, Royal Aeronautical Society, London. 100. Liu, L., Friedmann, P. P., Kim, I., and Bernstein, D. S., "Vibration reduction and performance enhancement in rotorcraft using active flaps at high advance ratios," AIAA Paper 2006-1861, May 2006. 170 Table 1 Chordwise location of the surface pressure taps. Tap# x/c Tap# x/c 1 0.963 25 0.000 2 0.901 26 0.002 3 0.860 27 0.007 4 0.825 28 0.015 5 0.796 29 0.026 6 0.652 30 0.036 7 0.624 31 0.048 8 0.570 32 0.071 9 0.520 33 0.146 10 0.470 34 0.178 11 0.421 35 0.221 12 0.371 36 0.272 13 0.321 37 0.345 14 0.272 38 0.421 15 0.248 39 0.468 16 0.222 40 0.519 17 0.179 41 0.569 18 0.151 42 0.624 19 0.118 43 0.653 20 0.092 44 0.796 21 0.073 45 0.825 22 0.049 46 0.862 23 0.028 47 0.903 24 0.006 48 0.960 Notes: 1) x/c = 0 is located at the leading edge. 2) Taps # 1-24 are located on the upper/suction surface, tap #25 is located at the leading edge, and taps # 26-48 are located on the lower/pressure surface. 171 Table 2 TEF motion profile characteristics. Case# "max ts td(%) tss/td tRl (%) tR2 (%) (Xi a2 a3 a4 l +16° -0.5071 32.7 0.29 11.6 11.6 8.0U 10.0U 14.0U 19.6U 2 +16° O.OOTC 31.2 0.31 10.1 11.6 16.0U 20.7U 23.5U 23.4d 3 +16° 0.47TC 31.2 0.29 11.6 10.6 24.0U 22.4d 18.8d 13.6d 4 +16° -0.477C 51.8 0.57 11.6 10.6 8.0U 10.5U 23.1u 23.8d 5 +16° 0.007c 51.3 0.55 11.6 11.6 16.0U 21.3U 20.8d 15.4d 6 +16° 0.46TC 51.3 0.56 11.6 11.1 23.9U 22.6d 10.1d 8.0d 7 +16° -0.47JI 70.3 0.69 11.6 10.6 8.0U 10.5U 22.1d 17.6d 8 +16° 0.007t 69.9 0.67 11.6 11.6 16.0U 21.3U 12.0d 8.4d 9 +16° 0.467c 70.4 0.69 10.6 11.6 23.9U 22.8d 8.7d 12.8d 10 -16° -0.46TC 50.2 0.57 11.6 10.0 8.1u 10.7U 23.0U 23.9d 11 -16° O.OOTC 50.2 0.58 10.6 10.6 16.3U 21.1. 20.6d 15.6d 12 -16° 0.45TC 51.2 0.55 11.6 11.6 23.9U 22.7d 10.4d 8.0d 13 +16° 0.24TC 34.7 0.42 10.0 10.0 21.5U 23.9U 21.9d 17.7d 14 +8° 0.24TC 36.2 0.44 10.0 10.0 21.5U 23.9U 21.4d 16.9d 15 +16° O.OOTC 51.3 0.00 10.1 41.2 16.0U 20.7U 20.7U 15.4d 16 +16° O.OOTC 49.8 0.00 13.1 36.7 16.0U 21.9„ 21.9U 16.1d 17 +16° O.OOTC 51.3 0.00 25.6 25.6 16.0U 24.0d 24.0d 15.4d 18 +16° O.OOTC 51.3 0.00 38.2 13.1 16.0U 21.4d 21.4d 15.4d 19 +16° O.OOTC 51.3 0.00 42.7 8.5 16.0U 19.5d 19.5d 15.4d 20 +16° 0.127i 52.8 0.00 8.5 44.2 19.0U 22.3U 22.3U 11.8d 21 +16° 0.1 2TC 52.8 0.00 13.6 39.2 19.0U 23.5U 23.5U 11.8d 22 +16° 0.1 2TC 51.8 0.00 25.6 26.1 19.0U 23.3d 23.3d 12.2d 23 +16° 0.1 2TC 49.8 0.00 36.7 13.1 19.0U 19.5d 19.5d 13.2d 24 +16° 0.1 2TC 51.2 0.00 41.2 10.0 19.0U 17.4d 17.4d 12.5d 25 +16° 0.25TC 52.8 0.00 9.5 43.2 21.7U 23.9U 23.9U 9.4d 26 +16° 0.25TT 51.3 0.00 13.1 38.2 21.7U 24.0d 24.0d 9.9d 27 +16° 0.2571 51.3 0.00 25.6 25.6 21.7U 21.4d 21.4d 9.9d 28 +16° 0.25TC 51.3 0.00 37.7 13.6 21.7U 15.9d 15.9d 9.9d 29 +16° 0.25TC 51.3 0.00 41.2 10.1 21.7U 14.1d 14.1d 9.9d 30 +16° O.OOTC 49.8 0.50 8.5 16.1 16.0U 20. lu 22.8d 16.1d 31 +16° O.OOTC 51.3 0.49 13.1 13.1 16.0U 21.9U 21.4d 15.4d 32 +16° O.OOTC 49.8 0.51 16.1 8.5 16.0U 22.8U 20.2d 16.1d 33 +16° 0.1 5TC 50.3 0.50 8.5 16.6 19.6U 22.8U 20.2d 12.2d 34 +16° 0.15TC 51.3 0.46 13.1 14.6 19.6U 23.7U 18.8d 11.8d 35 +16° 0.1 5TC 50.3 0.47 16.6 10.0 19.6U 24.0U 17.1d 12.2d 36 +16° 0.22TC 51.3 0.46 10.0 17.6 21.lu 23.8U 18.6d 10.4d 37 +16° 0.22TC 51.3 0.49 13.1 13.1 21.lu 24.0U 16.4d 10.4d 38 +16° 0.23TC 52.3 0.47 17.1 10.6 21.3U 23.8d 14.4d 9.9d 39 +16° 0.1 OTC 50.3 0.32 19.6 14.6 18.5U 24.0U 20.4d 13.4d Notes: 1) 8.0°u denotes a = 8.0° during pitch-up motion. 2) td, tRj and tR2 are given in percent of f0~ . 3) di and 014 are the angles at which flap motion begins and end, respectively. 4) a2 is the angle at which flap reaches peak deflection and steady-state motion begins. 5) 013 is the angle at which flap steady-state motion ends and return motion begins. 6) oscillation case described by a(t) = 160+8°sincot and K = 0.1. 172 O u _ _ II B" w P CO u> to s—^ —• z CD o 4fc ©o CoO oRT tSo o II VI ' ' o p OS W»NWW»UiUi^Ji«000\0\vlH.slUlUiOO\lOWO-J*a-JWM»*»vll!0»>00\«tO VO o a. eno t onc a D- 1 WIOWIOWWMIOWNNtOtONMIONtJIONMWNtONIONMIOIOMMMMMNNIOWN tO o ^c>ibNb>^boboc»^^^b>bsb>b>boc>obocx>cx>cx)boc>o^©^^ro bo 8 CO CD o CD CO o oooooooooooooooooooooooooooooooooooooooo o & £ I I I I I I I I I I I I I I t I I 1 I I I I I I I I 1 I I I I t I I I I I I I I I CO CD o- o o oppppppppooooooooooooopoopoooooooooooooo o ingt h bed b 3. pseo f FH U*OOOOMOOUiM^^«00«-Jfl\Wa\0«MOOU4iUlUiavlJi(H^>0(!OUi«^MJivlO O I CD* WtJK)IOtO(OK)MIO(JNNtOWMWNMWtOWMN)W(OtOMMM(ONtOWMMM(OWNN IsJ *< P CD o P CO T£3 a CO o II o >-i p O H—' p »—* (*r CD o os ^ CD bobs^kJol^^Ln^i^kikj'^bool^^boLnsj^bol^o^NJ^^L^boo^L^ © fp >-! u> o a. S> •guiH-Mwoiwo\**MuuiMvouiauiu-jwjiO\vio-|iauiO\i-'-Jvi^ioui(o*ui^w to O 00 l-f O. +o v; CO CD p S3 S3 f-»o - ^—ca s * P. CD i^^^b>bsl/«l^L/ti^L*^^^b>b>^c^bsi^L/iaNC^b\Lrtl/ibsb>^so^ ^ o s flap CD U00UI>-M>O-J<|VJ4UWWI-VIWO00^«00X1UIIOV00\^UV1V1(0^0\*0000(OUI00H-00 .£. *3 § CO CL P C* * " CD OOOOOOOi— i— OOOOOOOOOOOOOOOOOi— OOOH-OOOOOO o CO OOV1UIUI-JUIUMMWMMMI-MMOUUHO«OUI-OU>-OM UUiOOi-UlO\-|iOOVOvl to i i t i i i i i i i i i i i i OOOOOpOOOOOOOOOOOOOOOOOOOOO>^oP©©»-'©OtOO>-'>-'© © bbbbbb^tow*bbbbbbbbww^bwa^k)^^u2bwbobwN)bbJ^J^ 4*. Uli-(JWUli*M-^OOtOvO-JtOU*0>OOOOOOCeOai^vlOOMM--J>00(O^OOW^VOWW(»i-' -1 >— © J"" P P >—' I © tO P © H- © o •^^©c»boLnl^o^vCo^^Ln^bsl^kJo'„to^-^ji,rft©i-' .^©^^Svbo^'H-toj^bo'*." -J4».-jN)-JCX)^j-~J0000NJV)0>ty, o Z^ 7T, -J bo •- ^ w cs ^ ^-i '•- tjobbcoLobs^uiwbsbolflbswlA'-^ W W ••* vl W M o SB Table 4 TEF motion profile characteristics and critical aerodynamic values for PIV experiments. Case# Omax ts td(%) tss/td tRl (%) tR2(%) ai a2 a3 (X4 1 +12° -0.5071 49.8 0.33 19.1 14.1 4.0U 9.0U 16.9U 20.0d 2 +12° 0.037t 50.8 0.35 19.1 14.1 12.5U 19.6U 17.6d 11.Id 3 +12° 0.1471 50.3 0.32 19.6 14.6 15.4U 20.0d 15.5d 8.5d 4 +12° 0.2771 49.3 0.34 19.1 13.6 18.0U 19.1d 12.4d 6.2d 5 +12° O.OOTI 50.8 0.34 14.1 19.6 12.0U 18.2U 19.4d 11.6d 6 +12° 0.14?t 50.3 0.33 13.6 20.1 15.4U 19.7U 17.8d 8.5d 7 +12° 0.027t 49.8 0.00 19.6 30.2 12.5U 19.7U 19.7U 11.6d 8 +12° 0.1571 49.8 0.00 19.6 30.2 15.6U 19.9d 19.9d 8.5d 9 +12° 0.02TI 49.8 0.00 30.7 19.1 12.5U 19.3d 19.3d 11.6d 10 +12° 0.147t 49.8 0.00 30.7 19.1 15.4U 17.6d 17.6d 8.7d 11 -12° -0.507I 50.3 0.33 20.1 13.6 4.0U 9.5U 17.3U 20.0d 12 -12° O.OlTt 50.8 0.36 19.6 13.1 12.3U 19.6U 17.4d 11.4d 13 -12° 0.257t 51.3 0.35 19.6 13.6 17.7U 19.2d 11.9d 5.9d Case# *W,max ads ^ra.peak OCmp |W,max' ^d,max t-'W.CCW '-'W.CW ^w.net CH ^m.peakl Baseline 1.67 19.7° -0.274 19.9° 6.09 0.64 0.54 -0.12 0.42 12.8 airfoil 1 1.56 19.5° -0.267 19.9° 5.84 0.63 0.18 -0.47 -0.29 8.6 2 1.29 19.6° -0.132 19.8° 9.77 0.49 0.51 -0.02 0.49 11.9 3 1.47 19.5° -0.191 19.7° 7.69 0.53 1.21 0.00 1.21 13.8 4 1.53 19.5° -0.210 19.9° 7.29 0.56 0.82 0.00 0.82 13.1 5 1.27 19.6° -0.151 19.7° 8.41 0.48 0.48 -0.23 0.25 10.7 6 1.26 19.4° -0.137 19.8° 9.20 0.47 0.64 0.00 0.64 11.9 7 1.30 19.5° -0.158 19.9° 8.23 0.49 0.45 -0.22 0.23 11.0 8 1.34 19.5° -0.162 19.8° 8.27 0.49 0.62 -0.04 0.58 12.0 9 1.41 19.5° -0.186 19.9° 7.58 0.52 0.51 -0.11 0.40 11.4 10 1.36 19.5° -0.191 19.8° 7.12 0.68 1.73 0.00 1.73 17.8 11 1.92 19.3° -0.319 19.7° 6.01 0.76 0.53 -0.15 0.38 12.5 12 1.98 19.7° -0.357 19.9° 5.55 0.67 0.33 -0.62 -0.31 10.0 13 1.71 19.7° -0.307 19.9° 5.57 0.93 1.52 0.00 1.52 18.2 Notes: 1) 8.0°u denotes a = 8.0° during pitch-up motion. 2) td, tRi and tR2 are given in percent of f0" . 3) 5) 174 Table 5 TEF motion profile characteristics and critical aerodynamic values for attached- flow and light-stall oscillation cases. -1 Case# Omax ts tdCfo ) tss/td tend a(t) = 12° + 6°sina>t Baseline airfoil 0° 1 +7.5° -0.57C 6°„ 51% 0.40 18°d 2 +7.5° 07t 12°u 51% 0.39 12°d 3 +7.5° 0.5n 18°u 51% 0.40 6°u 4 -7.5° -0.57C 6°» 51% 0.40 18°d 5 -7.5° On 12°u 50% 0.35 12°d 6 -7.5° 0.5TC 18°u 50% 0.36 6°u a(t) = 140 + 6°sincot Baseline airfoil 0° 7 +7.5° -0.57T 8°u 51% 0.38 20°d 8 +7.5° On 14°» 50% 0.37 14°d 9 +7.5° 0.571 20°u 50% 0.36 8°u 10 -7.5° -0.571 8°» 50% 0.35 20°d 11 -7.5° On 14°u 50% 0.36 14°d 12 -7.5° 0.5TC 20°u 51% 0.36 8°u / Case W.max ads ^m.peak l^/.max' cd ,max ^w.ccw ^w,cw '-'w.net CH # ^m,peak| a(t) = 12° + 6°siiK0t BL 1.09 - - - 0.13 0.32 0.00 0.32 1.7 1 1.09 - - - 0.13 0.00 -0.43 -0.43 1.4 2 0.89 - - - 0.09 0.28 0.00 0.28 1.4 3 1.11 - - - 0.13 1.03 0.00 1.03 4.2 4 1.27 - - - 0.16 0.87 0.00 0.87 3.9 5 1.34 18.0°d -0.167 8.02 0.41 0.18 -0.34 -0.16 7.0 6 1.21 17.7°d -0.148 8.18 0.37 0.06 -0.94 -0.88 3.9 oc(f) = 14° + i6°sino) t BL 1.23 19.9°u -0.119 10.34 0.40 0.11 -0.42 -0.31 8.1 7 1.18 20.0°u -0.117 10.09 0.40 0.04 -1.07 -1.03 5.0 8 1.07 19.9°u -0.057 18.77 0.33 0.10 -0.48 -0.38 7.5 9 1.22 19.8°u -0.123 9.92 0.41 0.35 -0.14 0.21 9.5 10 1.35 19.7°u -0.130 10.38 0.42 0.35 -0.09 0.26 10.2 11 1.44 19.8°u -0.213 6.76 0.52 0.12 -0.19 -0.07 9.0 12 1.25 20.0°u -0.181 6.91 0.45 0.04 -0.89 -0.85 6.5 Notes: 1) 8.0°u denotes a = 8.0° during pitch-up motion. 2) tend denotes the end of flap actuation. 3) BL denotes baseline airfoil. 175 Table 6 Critical aerodynamic values for a passively controlled airfoil. 6 *-W,max «ds ^m,peak Otmp ^d,max ^w,ccw *--w,cw ^w,net CH *~-m,peakl 0° 1.69 23.8° -0.280 23.9° 6.02 0.74 0.25 -0.41 -0.16 11.9 +8° 1.45 23.9° -0.228 24.0° 6.36 0.65 0.10 -0.69 -0.59 9.0 +16° 1.22 23.9° -0.170 24.0° 7.19 0.58 0.26 -0.41 -0.15 9.8 -8° 1.96 23.6° -0.340 23.8° 5.76 0.87 0.31 -0.32 -0.01 13.7 -16° 2.15 23.4° -0.390 23.7° 5.52 0.98 0.34 -0.25 0.11 15.0 am 8 *W,max ^/,min ^m,peak v^m 3.1 |W,max' ^w.net CH ™min ^m,peak| 8° 0° 1.19 -0.02 0.000 0.022 - 0.60 0.3 10° 0° 1.31 0.14 -0.001 0.029 - 0.67 0.9 16° 0° 1.69 0.48 -0.280 0.040 6.02 -0.16 11.9 8° -16° 1.62 0.56 -0.123 -0.120 13.17 0.75 0.6 10° -16° 1.63 0.72 -0.117 -0.105 13.93 0.42 2.7 Notes: 1) C/,min is the minimum lift coefficient during the upstroke. 2) ads and amp occur during the upstroke for all cases. 3) oscillation case described by a(t) = 16°+8°sina)t and K = 0.1. 176 *™0 *"0 *T3 ^3 *T3 *™0 *~d *"0 ^3 *"0 *™0 *"0 '"0 *"53 *™0 *^S *^0 *"0 2 to •p*. Ui N) CD (—* ^^ I—» t—» I ^—' "*—' o OS OS OS 00 00 00 00 OS OS OS OS K*3 o o o o 5 o 2_ 2_ i—» CD CD • • * p ol-^ . o o a. OS o o o APPoo©_o© 1 6 P P 6 P 4*. © to £ 1 k) * M ii, O • S) O L^ V : •, © "_ j^ a. OS OS ©©©©©©©pop©©, © © © J- © © © ^^^^-j^Ujosbo^^Uj^oobsbo—© S_O O„N, wb.s I I I I I I I I I I 1 © © op p © © © ppppppppppp o 4^ 4^ as 4^- lo 4*. *• 4^ 4^^ui<^v^-H-pUi4^tOtOUiO\N)OJC\0^4^ aoowwvioouii-oiwvouieoi-' ojuiosto y=180° V|/=180° Retreating Advancing side of disk side of disk \|; = 2700 I y = 90° V = 270° -f v=90° Blade Blade Vtip = £JR Blade azimuth angle, y = 0° \|f = 0° Figure 1 Rotor blade velocity distribution (reproduced from Ref. 52). Left and right images are for zero and nonzero forward velocities, respectively. Reverse Attached Separated Flow Region Turbulent Laminar Laminar Shear Layer Boundary Shear Layer Layer Attached Turbulent Separated Boundary Layer Turbulent Turbulent -LEI Shear Layer Separation Free- I (Geometric S" I / Region Stream "Angle Of Speed I Attack) Figure 2 Conceptual sketch of the flow structure over a static NACA 0012 airfoil (valid for angles between 6 deg and the static-stall angle). 178 (a) Separation Bubble Edge of Viscous Layer Separated Flow Far Wake Laminar Flow Turbulent Flow • Strong Interaction • Viscous Layer = ©(Airfoil Thickness) (b) C^A Ay $ruO /^y^x; • Vortex Dominated • Viscous Layer = ©(Airfoil Chord) Figure 3 Conceptual sketches of the flowfields during dynamic stall, (a) light stall and (b) deep stall (reproduced from Ref. 61). o, deg -to 180 270 f. deg Figure 4 Angle of attack variations with azimuth angle for a model rotor, oscillating airfoil and ramping airfoil (reproduced from Ref. 34). 179 (a) (b) (c) (d) (e) (0 Figure 5 Selected sequences of boundary-layer events both prior to, during, and post stall at K = 0.1 for a(t) = 10° + 15° sinoot (reproduced from Ref. 46). (a)-(g) flow visualization images; (h)-(n) conceptual sketches. 180 2.7 / 2.2 - AC/u?.v l\ 1.7 "Mmax AC({r , AC,„ 1 6 5 Q 1-2 / / ~.„ j ->*•- 0.7 - k: 1 0.2 AOff £^ 8 -0.3 Acttotei -0.8 ". , t 1 ,.,i >, ,.1,, i i < i . i i „ ,,, , -10 -5 0 10 15 20 25 30 1.1 • 4 0.9 - / ; 0.7 - AQ/LEV ^**—rfmax Cd 0.5 - 2 ir®5 0.3 - AQff, *y 1 .. * - -0.1 I „, i 1 i 1 ,1 1 ...1 . 1 i i iii -10 10 15 20 25 30 0.015 -0.045 Figure 6 Dynamic load loops for oc(t) = 10° + 15° sincot at K = 0.1 (dotted line: static airfoil; solid line: upstroke; dashed line: downstroke; reproduced from Ref. 46). 181 -0.5 y/c -0.5 y/c Figure 7 3-D representation of the wake mean and fluctuating velocity profiles for a(t) = 10° + 15° sincot and K = 0.1 (reproduced from Ref. 46). 182 JS Inlet Section with Honeycomb Acoustic /and Anti-turbulence Screens 0.85 x 1.22 Flanged Silencer Test Section OO Top-Hinged Windows Both Sides Top Speed = 265 kph with 125 hp variable frequency drive. Dimensions in meters. Figure 8 Joseph Armand Bombardier wind tunnel, (a) Schematic and (b) photographs. pf-at IBB ** Ik* •H ^^ssta™. Figure 8 cont'd Joseph Armand Bombardier wind tunnel (a) Schematic and (b) photographs. 184 do" c CD ^O C/3 O « Settling Camber with Honeycomb 3 and Anti-turbulence Screens Exhaust to Outdoors o" 20 x 20 Test Section Diffuser Fan Section 5" Contraction CT1Q O 00 72x72 en a & o k> x o k> Dimensions in centimeters. Motor Housing B CD Figure 10 Photographs of wing models, (a) 0.254 m chord model and (b) 0.1 m chord model. 0 Rocker-arm linkage Tunnel wall Counterweight .*—I—*. g—^ Wing support 'J; Servomotor- '• \ driven crank A ^—Airfoil Flap potentiometer Wing potentiometer / / / 1/ Figure 11 Schematic diagram of wing model, support structures and oscillation mechanism. 186 I o o Figure 12 Two-dimensionality of the flow over static wing. , sinusoid , potentiometer output 0.5 -c(Tt) Figure 13 Comparison between airfoil motion and sinusoid. 187 (a) A°5 O,^ T' III III I ' max x/c = 0 © NACA0015 i.T/ocy (b) Wing oscillation motion a max _N4 \ \v% -J \—-J- -f -T a =0. 57T / 0.571 \ 1.571 / 25% \ 3.5TC i / \ / \ \ / a min TEF control motion tR1 t |< >|Hf «s J*&> <> Rl R2 5m:a x 0 K Id Figure 14 (a) Schematic of airfoil with flap and locations of pressure taps, and (b) flap motion profile. 188 0.7 h , 25 cycles , 50 cycles 0.6 , 75 cycles 0.5 , 100 cycles 0.4 0.3 0.2 0.1 0.0 12 16 20 24 a Figure 15 Number of cycles for phase-averaging effects on aerodynamic loads. 189 PC Computer PC Computer Wing BNC Digital Potentiometer Delay Generator Emerson Programmable MaxonEPOS70/10 Model 7010 Motion Controller Programmable Model FX3161 PCM1 Motion Controller I Exlar Servomotor Maxon Servomotor Model DXM340C Model Re-35 4 Bar Pressure Orifices Mechanism 48 Tygon Tubes Flap from Potentiometer Pressure Taps Solenoid Scanivalve System Controller 1 Tygon Tube Power Supply Pressure Transducer Optical Relay in Motor Controller Wing Flap Potentiometer Potentiometer AA Lab model G3006 Pressure Measurement System Analog Filter Terminal Box 16 Lines In 16 Pin Ribbon Cable Out 16 Channel A/D Board Oscilloscope Internal Connection Spectrum Analyser PC/Workstation Figure 16 Schematic diagram of the experimental setup and instrumentation system for the surface pressure measurements. 190 ,i I! £ xm Figure 17 Photograph of traverse mechanism for wake scans. 191 (a) 0 8 - 19m/S^> >>° X 17ms & o o 0 ' ° o V0 15 m/s o (i -\ „ o 13 m s o 0 0 ° llBl/W- on ° 'J ° /A* 6 ° O ', °ouA 9m/;, o > c 0 r °oQ (N 0 ° ° * «^° 7m/sOnODo °oo .a °°n Q0 0 5m/sc D ^ C n 3rv 4 - ^0Ur r °oQ o o * o ,°$ a o Q f> 0 • 3 m/s 6 ft I,I, 0.0 2.0 4.0 6.0 8.0 10.0 Wire 1 (V) (b) u Wire 1 (V) (c) «•*.. Wire 2 (V) Figure 18 Cross hot-wire calibration plots. 192 PC Computer PC Computer Wing BNC Digital Potentiometer Delay Generator MaxonEPOS70/10 Emerson Programmable Model 7010 Programmable Motion Controller Motion Controller Model FX3161 PCM1 Maxon Servomotor Exlar Servomotor Model Re-35 Model DXM340C 4 Bar Mechanism Cross Flap Hot-Wire Potentiometer Probe Power Supply Constant Temperature Anemometer Six-Axis Automated Traversing Mechanism Multi-Channel Wing Flap Low Pass Filter and Potentiometer Potentiometer Amplifier Stepper Motor Controllers Terminal Box Analog Filter 16 Lines In 16 Pin Ribbon Cable Out 16 Channel A/D Board Internal Oscilloscope Connection Spectrum PC/Workstation Analyser Figure 19 Schematic diagram of the experimental setup and instrumentation system for the wake velocity measurements. 193 Spectrum Oscilloscope analyser Jpirror J iiP^-U'Qnel wail Pressurized Analog filter 4 bar mechanism air supply Wing potentiometer 51 Atomizer beam I u\\ er tunnel wall Flap Slit potentiometer I 1IM.T liiilu CCD Power supply SIK-CI camera Mirror*, Maxon servomotor model Re-35 Maxon EPOS 24/5 programmable Maxon servomotor motion controller model Re-16 Mirror^ ¥&& /& Cylindrical lens •** & PC Maxon EPOS 70/10 programmable motion controller PC Dual head Nd:YAG laser h „>A;r. J w Mirror HP pulse generator Q-switch Laser head A power supply and controller Fire Dell workstation TSI LaserPulse (includes frame Q-switch synchronizer Laser head B power grabber and TSI supply and controller Fire 3 Insight Software) * redirects the light sheet from a ** light from a laser pointer placed in field of view horizontal to a vertical orientation to distinguish upstroke from downstroke Figure 20 Schematic diagram of the experimental and instrumentation system for the PIV measurements. 194 (a) 2.0 - NACA0012: ^ift stall a=10°+100sincot;K = 0.1 NACA0015: . a=16°+8°sincot;K = 0.1 0.00 -0.05 £• ^m -0.10 |r -0.15 , NACA 0015; oscillating | -0.20 -°~-,NACA 0015; static (C) cd Figure 21 Baseline, or uncontrolled, airfoil, (a) C/, (b) Cm, and (c) Cd; (d) Cp distributions; and (e) wake velocity profiles. 195 Flow reattachment (d) Suction p< (e) ^'•.*--frt.-:: .*.*»• X(7C) y/c u7u, 0.3. r * , I '-l • ' ^Hp^^-0.5 -0.5 -0-75 Figure 21 cont'd Baseline, or uncontrolled, airfoil, (a) Q, (b) Cm, and (c) Ca; (d) Cp distributions; and (e) wake velocity profiles. 196 -6 Turbulent breakdown / ^ ^_2090 (turbulentbreakdown) V-i -5 - , (Xu = 21.5° (turbulent separation propagation) , otu = 22.0° (turbulent separation propagation) -4 - > , (Xu = 22.6° (LEV initiation) "\-.. , Ou = 23.8° (LEV detachment) SVN , aj = 23.0° (during post-stall) \ C^N^V^LEV initiation Turbulent breakdown , Ou = 15.9° (turbulent breakdown) , Ou = 17.4° (LEV initiation) / -4NVN , (Xu = 18.2° (LEV convection) LEV initiation , Ou = 19.1° (LEV convection) , Ou = 19.9° (LEV detachment) , oed = 18.4° (during post-stall) 21 Figure 22 Representative baseline airfoil Cp distribution. (a) NACA 0015 airfoil and (b) NACA 0012 airfoil. 197 3.5 i 3.0 W,max 1-324 - 0.342Cmjpeak + 3.53oCmpeai{ (from Ref. 5) 2.5 1 U 2.0 1.5 1.0 °,Re = 2.46xl05 D,Re = 8.69xl04 0.5' j i i i_ -0.6 -0.4 -0.2 0.0 -rn,peak Figure 23 Dynamic stall function. 198 «u = 8° Ou=16°: -4 , baseline case -3 , active control , passive control -2 -1 0 1 -5 Ou = 22° -4 -3 flap lower surface -2 CF suction peak -1 0 1 Figure 24 Cp distributions with representative active control. 199 LEV spillage Ou = 24° -2 c ad=15 enhanced suction ad=10° "P 0 , baseline case , active control 1 i ••• i •••'••• i 0.0 0.2 0.4 0.6 0.8 1.0 x/c -0.5K On 0.5rc K l.5n Figure 24 cont'd Cp distributions with representative active control. 200 (a) 0 o o o K = 8° kxu=16°J|au = 21 kxu = 22 )/kxu = 23°j [ad = 21 ]ad=15 |ad=10 ) 0.4 o X 0.0 < -0.4 h -0.8 i, •. v 1111111 i i i i i i i 'i i i i i i i i' , , |i 0.6 0.8 1.0 U/Uoo (b) 0.8 |Ou = 8° lou = 16° K = 21° (Ou = 22° tocu = 23° kxd = 21° = 15° ad=10° 0.4 o X o.o > -0.4 > -0.: 0.00 0.15 0.30 u'/Uoo Figure 25 Wake streamwise velocity distributions with active control. ( , baseline case; , active control) 201 12 16 20 24 20 16 12 a -0.3 12 16 20 24 20 16 12 a (c) o.: 1 i 0.6 i i ' • /' i i Q 0.4 - ' r \ 0.2 !i i! X 0.0 12 16 20 24 20 16 12 a Figure 26 Dynamic Q, Cm and Cd loops with active control. 202 0.2 i (d) 1.8 , baseline airfoil l ,td~30%fo~ -0.3 _l 1 1 L__j u 12 16 20 24 a (e) 0.8 , baseline airfoil ,td = 30%fo"' ,t -50%f 0.6 h d o •,td~70%fo , static airfoil cd 0.4 0.2 0.0 Figure 27 Dynamic Cm, Q and C^ loops for 5max = +16° and ts = 0%. 203 1 td (% V1) tdc/ofo" ) -2.5 25 35 45 55 65 75 25 35 45 55 65 75 td (% fo"1) td(%fo ) 1.85 1.65 h 2 1.45 h U 1.25 1.05 td (% fo"1) td(%fo ) Figure 28 Variation in the critical aerodynamic values with td for various ts. Dashed line: baseline airfoil; circle: ts ~ -0.5rc; square: ts ~ 0.07c; and triangle: ts« +0.5K. 204 0.2 1.8 (a) (d) , baseline airfoil , t = -0.477C 0.1 s , tg = On - * , ts = 0.467t Cm 0.0 — , static airfoil -0.1 , baseline airfoil Q 0.9 -0.2 , ts = -0.4771 , static airfoil -0.3 i . . . -0.3 20 24 0.8 l ; ts = _O.47JC 0.6 , ts - U7t •»— , ts = 0.46n , static airfoil - I'M 0.4 - if - ///v '*' - d/fji 0.2 et^r '' "!>'' i£ks&^^^^- • -' ^**e!2!i&^--' "l— ^t^^^-j^n^L^ • , 0.0 1 , 1 , , . 1 12 16 20 24 a Figure 29 Dynamic Cm, Q and Cd loops for 8max - +16°andtd = 51%f0 . 205 7.5 •1a> &, 7.0 u ~~~* 6.5 a •^-BT 6.0 y. 5.5 u u Figure 30 Variation in the critical aerodynamic values with ts for various t^. Dashed line: baseline airfoil; circle: td ~ 30%fo" ; square: 1 td = SOrofo" ; and triangle: td « 70%fo"\ 206 c) , baseline airfoil , upwards 5 , downiwards 5 0.0 0.2 0.4 0.6 0.8 1.0 x/c 12 16 20 24 20 16 12 a 0.0 0.2 0.4 0.6 0.8 1.0 x/c e) ad = 20° flap lower surface J—i—i—1—i i i I i i i_J i i i L 12 16 20 24 20 16 12 0.0 0.2 0.4 0.6 0.8 1.0 x/c a 0 a,;F2O* J fOu = 23°lf Ou = 20o Ou = 23° Od = 20° 0.4 o X 0.0 -0.4 h -0.1 i i i i i I'I) 0.6 0.8 1.0 0.00 0.15 0.30 "U/Uoo U'/Uoo Figure 31 Effect of active flap deflection direction. 207 -0.5 Figure 32 Difference in the critical aerodynamic values between upwards and downwards flap deflections. 208 (d) 3 = 23.5° 1.6 , baseline 2 i'.-**" ^^ ^ •,8max = +16° 1 > ^max = +8° 1.2 """"""^i^*^ 0 1 \sf\ 1 1 1 1 1 1 1 i i Q 0.0 0.2 0.4 0.6 0.8 1.0 0-8 x/c 1 0.4 - lower flap surface c -/ \\ 1 y^' s v^^jj 0.0 ^/^ a S ad = 22° III! i i i i (e) 0.0 0.2 0.4 0.6 0.8 1.0 0.1 x/c /^ «5^ 0.0 ' J~~"~-"~—_^:S?> ad=13° - ^v \ ri C„ - -0.1 \ 4'\! • \1 ' , baseline airfoil -0.2 ,§max = +16° » "max ~ "*"° 1 1.... i 1 i i i 1 i _l I I I 1 L-J * ' • I I 1 I I 1 L_ -0.3 i i i . i . i 0.2 0.4 0.6 0.8 1.0 12 16 20 24 x/c a (f) & r&£ J" \ °* O? 0^£ o^ Figure 33 Magnitude effects of 8max on (a)-(c) Cp, (d) Q, (e) Cm and (f) critical aerodynamic values. 209 (a) -0.15 (d) 8.0 -0.30 8 14 20 26 32 38 44 14 20 26 32 38 44 tRl tRl (b) 1.1 (e) 16 C U , baseline airfoil •, ts = Ore ,ts = 0.12TI J i I i I ,i I 14 20 26 32 38 44 14 20 26 32 38 44 tRl tRl (C) 1.8 1 2LJ ' l ' l ' I—i i—I_J i i 8 14 20 26 32 38 44 tRl Figure 34 Critical aerodynamic values for various tRi and ts 210 (a) 16 12 to" 8 , ts = On & tss = 0% A— , ts = 0.2571 & tss = 0% l I . I i I . I i L 8 14 20 26 32 38 44 tRlC/ofo"1) (b) tA^' -,tRi=9.5 - , tRi =25.6 -,tRi=41.2 (c) -2 h —,tRi = 10.1 ,tRi=25.6 — , to = 13.1 ~-,tRi=42.7 . Figure 35 Effect of tRi on (a) 8 and (b)-(c) Cp distributions at oc^. 211 a) Q b) 0.1 0.0 ^m -0.1 ,Wtd = 0 ,tss/td = 49% -0.2 -J 1 I I I I L _L i I i i 12 16 20 24 a Figure 36 Effect of tss on Q and Cm curves. 212 2.2 (a) - °,td \. • ,ts 2.0 - \ a , +/- 8 \. • 8 > "max \. °,tR1 3 1.8 - Good C/and \^ Good C/ and • , tss S bad Cm control \ good Cm control u 1.6 - • 1.4 Bad C/ and Bad Q and \J? bad Cm control good Cm control \j<\ 1.2 • • • • i • • • • i • ... -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 *-m,peak (b) 15 Bad CH and Bad CH and bad good CWinet control 14 Cw,net control 13 HI 12 o 11 10 Good CH and Good CH and bad Cw.net control good CWiIiet control I I I— I I I -J 1 1 1 1 L_ -1.00 -0.50 0.00 0.50 1.00 ^w,net Figure 37 Flap motion parameters as a function of aerodynamic characteristics. 213 (a) 1.8 , baseline airfoil , optimum control 12 16 20 24 a (b) o.i Cm -0.1 (c) 0.8 0.6 0.4 cd 0.2 0.0 12 16 20 24 a Figure 38 Aerodynamic loads for optimum control case. 214 (a) 1.6 1.2 Q 0.8 0.4 0.0 4 8 12 16 20 a (b) o.i 0.0 Cm -0.1 -0.2 -0.3 J i i < I < i i I . i . I i i i L 4 8 12 16 20 a (c) 0.8 0.6 Cd 0.4 0.2 0.0 4 8 12 16 20 a 4 Figure 39 Static and dynamic Q, Cm and Cd curves for Re = 8.69 x 10 . 215 ,00=12.0° ,00=16.5° ,Ou=18.0° ,0^=19.5° LEV formation LEV convection (c) -2 ^reattachment ,ad=17.0° , ad=12.0° ,ad = 4.7° 1 JL JL 0.0 0.2 0.4 0.6 0.8 1.0 x/c Figure 40 Cp distributions of baseline airfoil at Re = 8.69 x 10 for (a) static airfoil, (b) upstroke and (c) downstroke. 216 -0.25 0 0.25 0.5 x/c ——•-—•• r 0.5 a == 12°-. N^ ) "' ^,-.o.»"'" ' 0.25 ^ ¥ „ - -«/J. ylc 0 ^ -<"•"• /^ i"*.;»• %.tii nni -0.25 ~"--.-o.i ,0.05—-•''* -0.25 0 0.25 0.5 0.75 x/c (c) . a=18°. 0.5 / Jj^- '"•^=^^^S 0.25 i ylc ::ix 0 sS~~ -0.25 5/ 7. A 0 * -0.25 0 0.25 0.5 0.75 1 x/c Figure 41 Flowfield around a static airfoil, (a)-(c) streamwise iso-velocity contours, (d)-(f) transverse iso-velocity contours, (g)-(i) iso-vorticity contours, and (j)-(l) streamlines. Au/u^ = 0.1, Av/u^ = 0.05 and A^c/u^ = 5. Solid line: positive; Dashed line: negative. 217 (g) 0.5 a=7° • 0.25 • „—.^1 y/c m -^ ~ - 0 ^mii — ^ 0.25 0 o -0.25 0 0.25 0.5 0.75 1 x/c (h) 0.5 a == 12° - 0.25 y/c ^^••mi i*§ -*--f£5 -0.25 -0.25 0 0.25 0.5 0.75 1 -0.25 0 0.25 0.5 0.75 x/c x/c Figure 41 cont'd Flowfield around a static airfoil, (a)-(c) streamwise iso-velocity contours, (d)-(f) transverse iso-velocity contours, (g)-(i) iso-vorticity contours, and (j)-(l) streamlines. Au/u^ = 0.1, Av/u^ = 0.05 and A^c/u^ = 5. Solid line: positive; Dashed line: negative. 218 \, ad=17° / 0.25 mk Slfegi 0 ^71 -0.25 T t -0.25 0 0.25 0.5 0.75 1 Figure 42 Normalized instantaneous streamwise velocity fields for baseline airfoil. Contour increment Au/u^ = 0.1. Solid line: positive u; Dashed line: negative u. 219 au = 4° I (e) ^.. a,u = 20° 0.25 -0.25 -0.25 0 0.25 0.5 0.75 -0.25 0 0.25 0.5 0.75 1 (b) 1 = c 0.5 ..... T ^ 0.25 ^l/k:: ^SM// />;'"' *»-. '"'--- irililA •"•*I|»l»l;.-3".-'* 0/..'..-, • g '--«,. .y' 0 £'. \ Figure 43 Normalized instantaneous transverse velocity fields for baseline airfoil. Contour increment Av/u^ = 0.05. Solid line: positive v; Dashed line: negative v. 220 (a) 0.5 au = 4°. o 0.25 y/c o ^^MBWMM ••• ^^^T"V"-)W V.... —..2-....' ».,,,' , o -0.25 -0.25 0 0.25 0.5 0.75 -0.25 0 0.25 0.5 0.75 >0.5 ad = 12°. 0.25 ^-^i^3jC^o ^ 0 0.25 -0.25 0 0.25 0.5 0.75 1 -0.25 0 0.25 0.5 0.75 1 c (d) au=19.5' a = 4.7 0.5 (h)o.5 d 0.25 0.25 y/c -0.25 -0.25 1 ' -0.25 0 0.25 0.5 0.75 1 x/c Figure 44 Normalized instantaneous spanwise vorticity fields for baseline airfoil. Contour increment A^c/u^ = 5. Solid line: CW; Dashed line: CCW. 221 0.25 0.5 x/c Figure 45 Normalized instantaneous streamwise velocity fields with 5max — +12°. Contour increment Au/u^ = 0.1. Solid line: positive u; Dashed line: negative u. 222 . (a) au=12° , , , a =f 20° 0.5 \ J ;' • u ^~-~~\ \ I i X ,.—• "*15.. 0.25 *KVv /'/.--- '"-v r^N\\ //,/--- 0.2 ^ '"-, y/c ^^MM^^r--^''^^----^ "\ 0 H7"\o --. Mi1 \\'*» ' K•7——•« •Wm^ ry_~---:9,i^ |ji|_iiiiiir-' -0.25 / V"^ * - . &&"— -•"V /-( 3 -0.25 0 0.25 0.5 0.75 -0.25 0 0.25 0.5 0.75 1 x/c x/c au.= 18° (c) """i •' . \ 1 au=19.5° 0.5 \ £ . O.K ! vV"' ^\ \^ \\ V \ L v \ ) / --0.15- \ r y,--0.2s.^ —\\\—«v\*\ >( / ^ N 0.25 y/c M 0 Hi is^m j^^^^^^i -0.25 •A i \ ,^^i* ? / •- •g- • 0 -0.25 0 0.25 0.5 0.75 x/c c Figure 46 Normalized instantaneous transverse velocity fields with 5max — +12 Contour increment Av/u^ = 0.1. Solid line: positive v; Dashed line: negative v. 223 au = 20° Figure 47 Normalized instantaneous spanwise vorticity fields with 5max — +12°. Contour increment A^c/u^ = 5. Solid line: CW; Dashed line: CCW. 224 Figure 48 Streamline patterns of LEVfor (a)-(b) baseline airfoil, (c)-(d) 8max = +12° and (e)-(f) 5max = -12°. 225 (d) -3 Ou=12° ocu = 20° LSB LEV detachment Lower TEF surface 1 J_J I i i i L_J i i I i i i L i i i I i i i I i i i I i i I I i i i L'r0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 x/c x/c (b) au=18° Lower TEF surface // Lower TEF surface ad=17° i i i i i i i i 1.0 _l 1 1™J I l__i l_J l ' ' I I I L_ 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 x/c x/c (c) -3 (f) -1.5 LEV growth -T> -l -and convection 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 x/c x/c Figure 49 Surface pressure coefficient distributions with and without control at Re = 8.69 x 104. 226 (a) z.u [ z1 1.6 •'' / L .•••' y /A /^*<_/ ' 1.2 Q : >< ,i 0.8 0.4 • \\\ \ *Cs^> ^ i * A t\ t , , , i •""" i ~T~ i ... i 12 16 20 a (b) 0.1 0.0 -0.1 ^m -0.2 , static airfoil , uncontrolled airfoil -0.3 , upward TEF , downward TEF -0.4 i i i i i i i i_ 12 16 20 a Figure 50 Dynamic C/ and Cm loops with and without control at Re = 8.69x10 . 227 0.25 0.5 0.75 1 x/c Figure 51 Normalized instantaneous streamwise velocity fields with 5max — 12°. Contour increment Au/uM = 0.1. Solid line: positive u; Dashed line: negative u. 228 /y ...exu = 20° — Figure 52 Normalized instantaneous transverse velocity fields with 8max -12°. Contour increment Av/u^ = 0.1. Solid line: positive v; Dashed line: negative v. 229 0.25 0.5 0.75 1 x/c Figure 53 Normalized instantaneous spanwise vorticity fields with 8max — - 12°. Contour increment A^c/u^ = 5. Solid line: CW; Dashed line: CCW. 230 (a) (e) 1.2 1.6 - baseline airfoil ..;*•"';•! •, baseline airfoil -,t = 0rc 1.0 ts = 07l s 1.2 -,t = 0.57C ts = 0.5TI ..^ ~J s 0.8 ts = -0.57^^" , t. = -0.5i-< Q Q 0.8 0.6 — 0.4 0.4 \^ Omax = +7.5° 0.2 i l—V"" i i i i , i . 1 0.0 10 12 14 16 18 a ts = Ore, 8max = +7.5° I i I u_l i I i I i L 6 10 12 14 16 18 10 12 14 16 18 a (d) a 0.15 ts = 0.57C,8max = +7.5° -m -rn J . I i I i L 10 12 14 16 18 10 12 14 16 18 a a Figure 54 TEF control of dynamic C/ and Cm loops for a(t) =12 +6 sincot. 231 (a) -> au=18" -4 laminar separation bubble (LSB) -3 LEV CP -2 Separated boundary layer TEF lower surface -1 0 (b) ad=17 \ Separated boundary layer ^^LEV spillage \ TEF lower surface I I I L_l I • . . 0.0 0.2 0.4 0.6 0.8 1.0 x/c (C) "3 , baseline airfoil ad = 8 , ts = On & 5max = -7.5° -2 , ts = 0K & 8max = +7.5° , static airfoil ^ - A "•^ .. ^-—v. Xv_.._ v "-—-^5.-;;r : o -~v~ -;=£—& llll i>..; i i , , 0.0 0.2 0.4 0.6 0.8 1.0 x/c o , ^o . Figure 55 Cp distributions for oc(t) =12 +6 sincot 232 , static airfoil; , baseline airfoil; , ts = OTC & ^ = -7.5°; , ts = On & 8max = +7.5°; Figure 56 Typical wake flow structures for a(t) =12 +6 sincot. 233 (a) 1.5 1.0 Q 0.5 Q Q I I I I I I I l_J I I I I L_J 1_ 8 12 16 20 a (b) 0.15 0.05 •na -0.05 -0.15 •, baseline airfoil , ts = On, 8max = +7.5° , ts = On, 8max = -7.5° -0.25 12 16 20 a Figure 57 TEF control of dynamic Q and Cm loops for cc(t) = 14° + 6°sincot. 234 Figure 58 Cp distributions for passively controlled airfoil. ( ,8 = 0°; , 8 = +8° 5 , 8 = -8°) 235 (a) 0.8 c 0 c Ou=12 Ou-16 Ou = 23 Ou = 24° }ad = 23 otd=8° o 0.4 0.0 M -0.4 -0.! ... i, J- L. l.,.t...L -J. I.. .l...l_ff • • • I > ' • l > • • » hull ' • • • ' I • " I I t !ft ' 0.4 0.6 0.8 1.0 (b) 0.8 c au = 12 0Cu=16° [a„ = 23 a* =16° [ad = 8 0.4 o X 0.0 & -0.4 Pi -0.1 i I,I ,i i_ -J I I 1 L_ '0.00 0.15 0.30 U'/lloo Figure 59 Wake streamwise velocity distributions for passively controlled airfoil, (a) mean component and (b) fluctuating component. ( ,8 = 0°; -—, 8 = +8° ; , 8 = -8°) 236 (a) 2.0 1.6 Q 1.2 0.8 0.4 0.0 i i i I i t i I i i i I i i i i i i I i i i I i i i I ~i~"i i 12 16 20 24 20 16 12 a 12 16 20 24 20 16 12 a Figure 60 Dynamic Q and Cm loops for passively controlled airfoil. 237 (a) o -5 rOu=i6 ,6 == 0° i; V, ,8 == +8° -4 \i ..... 5= = +16° ...... g == -8° -3 ,6 == -16° -2 -\ v>\ -1 0 ^HSBS W*". , 1 , , , 1 1 i i i i 0.0 0.2 0.4 0.6 0.8 1.0 x/c (b) 0.0 0.2 0.4 0.6 0.8 1.0 x/c -1.5 (c) ad=16° j Q r>i i i I i i i I i i i I i i i I i i '0.0 0.2 0.4 0.6 0.8 1.0 x/c Figure 61 Effect of 5 for passive control on Cp distributions. 238 a b ( ) OCmin OCm OW Om Omjn ( ) 1.8 n 1 1 1 n 0.1 0.0 Q -0.1 -0.2 -0.3 -404840-4 OC-Om (C) (d) 1.8 . 0.1 1.5 — / Ai \ //' * ;/ \ N 0.0 1.2 - /7 '•-' Q & I ^m 0.9 \ \ -0.1 */ \ \ 0.6 ~r \ \ ^'' 0.3 ~_ , baseline airfoil \ \. | -0.2 , passive control \ ,.-^c.. / 0.0 , active control ^^ I t I I 1 r i i 1 i i i 1 I i r 1 i i I 1 i I I 1 i i I 1 I I I 1 -0.3 -404840-4 -404840-4 Ot-Om a-Om Figure 62 Dynamic Q and Cm loops for passive control of attached-flow regime. 239 Figure 63 Cp distributions for passive control of attached-flow regime. ( ,am = 8°&8 = 0°; — ,am = 8°&8 = -16°; , <*„,= 16°&8 = 0°) 240 Wing oscillation motion i/\ -0L5JI Figure 64 Schematic of HHC motion profiles. 241 (a) (d) 1.7 0.15 , baseline airfoil , 2P HHC 1.4 0.05 1.1 •rn Q 0.8 -0.05 0.5 -0.15 0.2 h , baseline airfoil , 2P HHC -0.1 I,I. L_I_ _i_ -0.25 _1_1 I I I I L_ 4 12 16 20 4 12 16 20 (b) a (e) a 1.7 0.15 , baseline airfoil 1.4 h , 3P HHC 0.05 1.1 •rn Q 0.8 -0.05 0.5 -0.15 V •, baseline airfoil 0.2 , 3P HHC -0.1 _J I I 1 I I I I „-., I 1 U. -0.25 _L _L _L 4 12 16 20 4 12 16 20 (C) a (f) a 1.7 0.15 • , baseline airfoil 1.4 , 4P HHC 0.05 1.1 Q - ^m 0.8 x" -0.05 Si 0.5 /"'' ....-' -0.15 h 0.2 , baseline airfoil , 4P HHC -0.1 1 > ,,!,, Figure 65 Effect of HHC flap motion on dynamic load loops with ts« -0.57C and 8max - 16". 242 (a) (b) -0.3 -0.5 0 0.5 1.0 1.5 X(7C) (c) Figure 66 Effect of HHC on increment in Q and C m- 243 (a) (d) -2.5 Ou = 9 ad=19 LEV spillage Lower flap surface - ad = 15° - Post-stall « A 1 fe^fe -^^^^•-•-^.^.^^ • s§^ 0 - Lower flap surface • f 1 Lower flap surface ' ' • I 1 l I I t 1,1,1 U_l 1,1,1 ' • i i i i i i i i i i 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 jc/c x/c (C) (f) -4.5 -2 oc = 20° a = 9.9u u LSB d -3.5 EV -2.5 bk / -1.5 -0.5 !^r--7^-glfi-jt'"1r7f1* Lower flap surface 0.5 1.5. i ... i 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 x/c x/c Figure 67 Typical Cp distributions for HHC control. 244 , baseline airfoil 4PHHC 0.0 0.1 0.2 U'/Uoo 0.00 0.02 0.04 uVAu, Figure 68 Typical wake flow structures for HHC control. 245 (a) L Q (b) pitch-up .pitch-down -0.6 I I L_ -0.5 0.0 0.5 1.0 1.5 T (n) (c) 0.15 0.05 // •-m -0.05 1/ ..—^_.; baSeline airofil , baseline airfoil -0.15 , ts = -0.46n ,ts = 07t ,t =-0.1571 s , ts = 0.2TC -0.25 I . . i I i I_J L_L_ J_ x_J i i i I i i i I i i i L 12 16 20 4 12 16 20 a a Figure 69 Effect of 2P flap motion on Q, AC/ and Cn v 246 0.9 0.5 ,2PHHC 8:—^- ,3PHHC 0.1 h , 4P HHC --w^et -0.3 h u A~-~.„__ -QS~ , Cwccw ~.~Pr'~ ^y^ 'Cw,cw -0.7" Bi-:^~^^Hlf_ A' Cw'net -1.1 .—J— i —i i i 1 i i i i ~ i i i i !___ -0.50 -0.25 0.00 0.25 ts (n) Figure 70 Variation of Cwnet with ts and NP for 8max = 16°. Solid symbols denote baseline airfoil. 247 (b) , ts = -0.25rc , ts = -0.06JC AC/ o.O -0.3 h pitch-up | pitch-down -0.6 _j i i—i—i i i , I—i * • i • • • -0.5 0.0 0.5 1.0 1.5 (c) 0.1 0.0 c m -0.1 -0.2 0.1 0.0 •rn , baseline airfoil -0.1 — ,ts = -0.25rc J 1 1 1 1 l 1 1 I 1_ -0.2 c o.o Figure 71 Effect of 3P flap motion on Q, AC/ and Cm. 248 (a) 1.6 , baseline airfoil , ts = -0.57T 1.2 Q 0.8 0.4 0.0 i • • i i_ j_ 12 16 20 a (b) 0.15 - - ,' -x /"\ *f*~~*Z<\ s~^ A 0.05 •fim^Z\/ ^ unr"**** 2S&t£r°***°"°°°~^{^ \_ / \ <""a. S\ ^m " -0.05 — V m V ^^5l N iil " %\ 'n " %/| -0.15 -- \ / -0.25 1 1 1 1 1 1 1 1 1 1 1 1 i i i i .. 12 16 20 a •, ts = -0.5K •, ts = -0.2671 pitch-up .pitch-down -0.6 i i i I i i I,I -0.5 0.0 0.5 1.0 1.5 X (71) Figure 72 Effect of 4P flap motion on Q, AC/ and C m- 249 (a) Q ^m (b) Q ••m (c) Q -rn -0.2 Figure 73 Effect of 5max on Q and Cm for ts ~ -0.5TL 250