Active Control of Flow Over an Oscillating NACA 0012 Airfoil

Active Control of Flow over an Oscillating NACA 0012 Airfoil

Dissertation

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

David Armando Castañeda Vergara, M.S., B.S.

Graduate Program in Aeronautical and Astronautical Engineering

The Ohio State University

2020

Dissertation Committee:

Dr. Mo Samimy, Advisor Dr. Datta Gaitonde Dr. Jim Gregory Dr. Miguel Visbal Dr. Nathan Webb c Copyright by

David Armando Castañeda Vergara

2020 Abstract

Dynamic stall (DS) is a time-dependent flow separation and stall phenomenon that occurs due to unsteady motion of a lifting surface. When the motion is sufficiently rapid, the flow can remain attached well beyond the static stall angle of attack. The eventual stall and dynamic stall vortex formation, convection, and shedding processes introduce large unsteady aerodynamic loads (lift, drag, and moment) which are undesirable. Dynamic stall occurs in many applications, including rotorcraft, micro aerial vehicles (MAVs), and wind turbines. This phenomenon typically occurs in rotorcraft applications over the rotor at high forward flight speeds or during maneuvers with high load factors. The primary adverse characteristic of dynamic stall is the onset of high torsional and vibrational loads on the rotor due to the associated unsteady aerodynamic forces. Nanosecond Dielectric Barrier

Discharge (NS-DBD) actuators are ﬂow control devices which can excite natural instabilities in the ﬂow. These actuators have demonstrated the ability to delay or mitigate dynamic stall.

To study the effect of an NS-DBD actuator on DS, a preliminary proof-of-concept experiment was conducted. This experiment examined the control of DS over a NACA 0015 airfoil; however, the setup had significant limitations. The NS-DBD showed significant promise as a means of reducing the unsteady loads associated with dynamic stall, despite limitations of the proof-of-concept experiment. The limitations/issues with the preliminary set up were rectified by designing an upgraded experimental setup for examining dynamic stall flow control using NS-DBD plasma actuators on a NACA 0012 airfoil. The upgrade

ii included installing a modular, vertically-mounted airfoil driven by a direct-drive servomotor in combination with a multi-axis force and torque transducer, all of which was controlled by a real-time data acquisition device. In addition, the airfoil (in the proof-of-concept experiment) imposed a high tunnel blockage when at large angles of attack. This issue was ameliorated by reducing the airfoil chord length and aspect ratio. End plates were added to prevent tip vortex formation and to reduce tunnel sidewall interference.

Baseline data were obtained using the upgraded setup. Force and moment data from the load cell were acquired for all cases to obtain aerodynamic loading data. The results showed signiﬁcantly lower uncertainty levels when compared with the data obtained from the previous setup due to the increased repeatability of the airfoil motion and the direct measurement of aerodynamic forces (which includes the effect of any potential ﬂow three- dimensionality).

After baseline experiments, a series of ﬂow control tests on dynamic stall were performed using NS-DBD plasma actuator installed at the leading edge of the NACA 0012 airfoil. A combination of three chord-based Reynolds numbers (300,000, 500,000, and 700,000) with reduced frequencies from 0.025 to 0.075 was used. Two excitation schemes were used: continuous excitation (excitation at a given frequency continuously throughout multiple oscillation cycles, as typically done in the literature) and a new method: Excitation in Parts of the Oscillating Cycle (EPOC). EPOC is excitation over a selected portion of the oscillating cycle or a variation of the excitation in the oscillation cycle. From load cell and PIV results, it is concluded that continuous excitation for deep and light stall produces signiﬁcant changes in lift, drag, and moment during the oscillating cycle. Excited cases exhibit a reduction in lift hysteresis, peak drag, and negative damping compared with baseline due to the effects of excitation-triggered coherent structures. Results for light and deep dynamic stall using

iii EPOC control showed that it is possible to improve a particular beneﬁt (e.g. reduction in lift hysteresis, negative damping or drag ) with targeted control and the use of a particular excitation timing during the oscillating cycle. Different EPOC schemes can be used for different situations depending on the application requirements.

iv Dedicated to my family and all my good friends!

v Acknowledgments

Dr. Samimy, I express my gratitude to you for your guidance and patience during all

these years and for showing me that in science, we must be humans ﬁrst and then scientists.

Dr. Nathan Webb, thanks for sharing all your experience and knowledge in the ﬁeld of

experimental ﬂuid dynamics and for the support as a friend outside the laboratory routine.

For Achal Singhal, thank you for helping me with this project and for your honest

feedback in the last years.

Nicole Whiting, I am grateful for your dedication and your contribution to this project.

Thank you for being an example of a good team worker!

Josh Gueth, thanks for being the master of the tools and for your help during all the

stages of this project.

My highest appreciation to Jeffrey Barton and Dr. Matthew McCrink for your help with

the NS pulser.

I also want to thank to Benjamin Egelhoff for your collaboration and efﬁciency making

the components for the experimental set up.

To all the labmates who have shared your time with me, I am all gratitude.

Finally, Colciencias, Fulbright, and the Ohio State University thanks for the support all

these years.

vi Vita

December 2008 ...... B.S. Aeronautical Engineering Universidad de San Buenaventura Bogota, Colombia March 2011 ...... M.S. Mechanical Engineering Universidad Nacional de Colombia Bogota, Colombia 2012-2013 ...... Lecturer Universidad de San Buenaventura Bogota, Colombia 2013-2018 ...... Fulbright Fellow The Ohio State University Columbus, Ohio, USA 2018-present ...... Graduate Research Associate The Ohio State University Columbus, Ohio, USA

Publications

Conference Publications

David Castañeda, Nicole Whiting, Nathan Webb, and Mo Samimy. Design and Character- ization of an Experimental Setup for Active Control of Dynamic Stall over a NACA 0012 Airfoil In AIAA Aviation 2019 Forum, AIAA 2019-3212, doi:10.2514/6.2019-3212. June 2019.

Nicole Whiting, David Castañeda, Nathan Webb, and Mo Samimy. Control of Dynamic Stall over a NACA 0012 Airfoil Using NS-DBD Plasma Actuators In AIAA SciTech 2020 Forum, AIAA-2020-1568. January 2020.

vii Achal Singhal, David Castañeda, Nathan Webb, and Mo Samimy. Unsteady Flow Separa- tion Control over a NACA 0015 using NS-DBD Plasma Actuators In 55th AIAA Aerospace Sciences Meeting,AIAA 2017-1687, doi:10.2514/6.2017-1687. Jan 2017.

Archival Publications

David Castañeda, Nicole Whiting, Nathan Webb, and Mo Samimy. Design, validation of a facility and its preliminary results for light dynamic stall ﬂow control. In Experiments in Fluids, will be submitted in 2020 .

David Castañeda, Nathan Webb, and Mo Samimy. Strategies for ﬂow control in deep dynamic stall using plasma actuators. In Physics of Fluids , will be submitted in 2020.

Achal Singhal, David Castañeda, Nathan Webb, and Mo Samimy. Control of dynamic stall over a NACA 0015 airfoil using plasma actuators In AIAA Journal, doi:10.2514/1.J056071. Sep 2017.

Theses

David Castañeda. Design and Construction of a Windpump System Based on a Bioinspired Rotor (In Spanish). Universidad Nacional de Colombia, Bogota, Colombia, Dec 2010.

David Castañeda et al. Detailed design of a Supersonic wind tunnel for its implementation at the University of San Buenaventura (In Spanish). Universidad de San Buenaventura, Bogota, Colombia, Dec 2007.

Fields of Study

Major Field: Aeronautical and Astronautical Engineering

Studies in: Aerodynamics, Experimental Techniques, Flow Control, Fluid Mechanics, Optical Diagnostics, Turbulence

viii Table of Contents

Page

Abstract ...... ii

Dedication ...... v

Acknowledgments ...... vi

Vita ...... vii

List of Tables ...... xii

List of Figures ...... xiv

1. Introduction ...... 1

1.1 Thesis Overview ...... 3

2. Background and Related Work ...... 4

2.1 Static Stall ...... 8 2.2 Comparison between Thin and Thick Airfoils ...... 12 2.3 Flow Characteristics over an Oscillating Airfoil ...... 15 2.4 Flow Characteristics of Dynamic Stall ...... 17 2.4.1 Parameters that inﬂuence Dynamic Stall ...... 22 2.4.2 Aerodynamic Damping ...... 23 2.5 Flow Control in Dynamic Stall ...... 25 2.5.1 Initial Work in Dynamic Stall Flow Control at GDTL ...... 28

3. Redesigned Experimental Setup ...... 34

3.1 Redesigned Experimental Set up Components ...... 36 3.1.1 Subsonic Wind Tunnel Facility ...... 36

ix 3.1.2 Airfoil Model ...... 38 3.1.3 Plasma Actuator ...... 41 3.1.4 Load Cell Transducer ...... 43 3.1.5 Direct Drive Servomotor ...... 44 3.1.6 Data Acquisition System ...... 45 3.2 Particle Image Velocimetry (PIV) ...... 47 3.3 Experimental set up capabilities ...... 51

4. Baseline Static and Dynamic Experiments ...... 52

4.1 Discussion of Motion profile, End Plates, and Aspect ratio effects . . . . 53 4.1.1 Motion Profile ...... 53 4.1.2 End plates effects ...... 54 4.1.3 Aspect ratio influence ...... 56 4.2 Static Baseline ...... 58 4.3 Dynamic Baseline ...... 61 4.3.1 Filtering process ...... 61 4.3.2 Dynamic Stall Results ...... 65 4.4 Effect of plasma actuator installation ...... 71

5. Excitation Results and Discussion ...... 74

5.1 Light Dynamic Stall Regime ...... 76 5.1.1 Baseline Results for Light Dynamic Stall Cases ...... 77 5.1.2 Continuous Excitation in Light DS Cases ...... 79 5.1.3 EPOC in Light DS Cases ...... 89 5.1.4 PIV results in Light Dynamic Stall regime ...... 102 5.2 Deep Dynamic Stall Regime ...... 113 5.2.1 Continuous Excitation in Deep DS Cases ...... 113 5.2.2 EPOC in Deep DS Cases ...... 123 5.2.3 PIV results in Deep DS regime ...... 131

6. Conclusions and future work ...... 141

6.1 Future work ...... 144

Appendices

A. Additional results ...... 145

A.1 Baseline for Light DS Cases ...... 146 A.1.1 Light Dynamic Stall at Reynolds number of 500,000 ...... 146

x A.1.2 Light DS at Reynolds number of 700,000 ...... 148 A.2 Continuous Excitation in Light DS Cases ...... 151 A.2.1 Continuous Excitation in Light DS at Reynolds number of 500,000 ...... 151 A.2.2 Continuous Excitation in Light DS at Reynolds number of 700,000 ...... 157 A.3 EPOC in Light DS Cases ...... 164 A.3.1 EPOC cases in Light DS at Reynolds number of 500,000. . . . . 164 A.4 Continuous Excitation in Deep DS Cases ...... 171 A.4.1 Continuous Excitation in Deep DS at Reynolds number of 500,000 ...... 171 A.4.2 Continuous Excitation in Deep DS at Reynolds number of 700,000 ...... 178 A.5 EPOC in Deep DS Cases ...... 185 A.5.1 EPOC cases in Deep DS at Reynolds number of 500,000. . . . . 185

Bibliography ...... 193

xi List of Tables

Table Page

3.1 Representative wind-tunnel installations for nominally 2-D dynamic stall studies ...... 40

4.1 Aerodynamic Characteristics for NACA 0012 AR 2 at different Reynolds numbers ...... 59

5.1 Reynolds number and reduced frequency combinations selected for excitation cases ...... 75

5.2 Negative damping values for light dynamic stall at Reynolds number of 300,000...... 77

5.3 EPOC cases during the upstroke (from 4◦ to 16◦) for light dynamic stall at Reynolds number of 300,000...... 89

5.4 EPOC cases during the downstroke (from 16◦ to 4◦) for light dynamic stall at Reynolds number of 300,000...... 95

5.5 EPOC cases for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 124

A.1 Negative Damping Values for Light Dynamic Stall at Reynolds Number of 500,000 ...... 146

A.2 Negative Damping Values for Light Dynamic Stall at Reynolds Number of 700,000 ...... 148

A.3 EPOC cases during the upstroke for light dynamic stall at Reynolds number of 500,000...... 164

xii A.4 EPOC cases for deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 185

A.5 EPOC cases for deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 185

xiii List of Figures

Figure Page

2.1 Airfoil geometry. From reference [4] ...... 4

2.2 Starting vortex development. From reference [21] ...... 6

2.3 Streamlines around an airfoil at increasing angle of attack. From reference [2] 6

2.4 Section view of laminar separation bubble. From reference [55] ...... 9

2.5 Flow characteristics for different types of stall in low speed airfoil. From reference [13]...... 11

2.6 Low speed stalling characteristics of airfoil sections correlated with Reynolds number and the upper-surface ordinates of the airfoil sections at the 0.0125 chord station. From reference [23] ...... 12

2.7 Types of pure static stall. From reference [60] ...... 13

2.8 Lift curves comparison between thin and thick airfoils. From reference [23] 14

2.9 The events of dynamic stall on NACA 0012 airfoil. From reference [8] . . . 19

2.10 Flow ﬁeld during dynamic stall. From reference [44] ...... 21

2.11 Aerodynamic Damping: Clockwise and Counterclockwise Loops for pitching motion cycle ...... 24

2.12 DBD plasma actuator schematic. It is composed of two electrodes separated by a dielectric barrier. Plasma is formed over the covered electrode when an AC or DC voltage is applied to the electrodes. From reference [63] . . . . . 27

xiv 2.13 Previous experimental setup at GDTL, showing airfoil conﬁguration and timing belt and pulley oscillating mechanism. From reference [67] . . . . . 29

2.14 Swirling strength, during the airfoil’s pitch-up motion, for the baseline and low and high Strouhal number excitation cases for Reynolds number of 300,000 and reduced frequency (k) of 0.05. From reference [67] ...... 31

2.15 Phase averaged lift and moment curves for NACA 0015 during excitation at low and high Strouhal number excitations for Reynolds number of 300,000 and reduced frequency (k) of 0.05. From reference [67] ...... 33

3.1 Subsonic Recirculating Wind Tunnel ...... 37

3.2 Current Wind Tunnel Test Section ...... 38

3.3 Estimated Solid Blockage Ratio comparison for NACA 0015 in the Initial Experimental Set Up and NACA 0012 in the Redesign Experimental Set Up 39

3.4 Cross sectional view of Aluminum airfoil with Delrin leading edge. . . . . 41

3.5 Cross sectional view of Delrin leading edge with Plasma Actuator installed. 42

3.6 Pulser output signals for voltage and current with power and energy estimation. Input frequency of 2000Hz...... 43

3.7 Airfoil, Load Cell, Servomotor Assembly in Re-designed Experimental Set Up ...... 45

3.8 Data Acquisition System Components ...... 46

3.9 Oscillating Airfoil PIV Set Up in a Plane (2D2C) ...... 48

3.10 Range of Reduced Frequencies for Redesigned Experimental Set up . . . . 51

4.1 Comparison of airfoil motion plotted against time for initial (a) and upgraded ◦ ◦ (b) experimental setup (α0 = 13 ,α1 = 5 , f = 3.48Hz) at Re =300,000. For initial setup, 5 cycles are shown and for upgraded setup, 43 cycles are shown 54

4.2 Effect of end plates on lift coefﬁcient of the NACA 0012 AR=2 airfoil at Reynolds number 500,000. Reference Critzos et al. (1955) [12] used. . . . 55

xv 4.3 Comparison between AR=2 and AR=3 with 0.46m (18in) diameter end plates. Reynolds number 500,000 ...... 57

4.4 Lift coefﬁcient for Reynolds numbers 300,000, 500,000 and 700,000 . . . . 58

4.5 Moment coefﬁcient about quarter-chord for Reynolds numbers 300,000, 500,000, and 700,000 ...... 60

4.6 Spectra of Fx data for the aspect ratio of three airfoils with end plates at oscillation frequencies of f = 1Hz (a), f=3Hz (b), f=3.5Hz (c) ...... 63

4.7 Effect of system weight on the inertial normal force (Fx) frequency spectrum 64

4.8 Cycle-to-cycle (Fx) load variations for an oscillating airfoil run ...... 65

4.9 Global lift coefﬁcient for NACA 0012 oscillating airfoil at two different reduced frequencies k=0.05 and k=0.075 at Reynolds number 300,000. . . 67

4.10 Global moment coefﬁcient for NACA 0012 oscillating airfoil at two different reduced frequencies k=0.05 and k=0.075 at Reynolds number 300,000. . . 68

4.11 Global lift coefﬁcient for NACA 0012 oscillating airfoil at different Reynolds number 300,000, 500,000 and 700,000 at a reduced frequency k=0.05 . . . 69

4.12 Global moment coefﬁcient for NACA 0012 oscillating airfoil at two different Reynolds number 300,000, 500,000 and 700,000 at a reduced frequency k=0.05 ...... 70

4.13 Lift coefﬁcient for NACA 0012 airfoil AR 2 with and without the exposed electrode. Reynolds number 500,000...... 72

4.14 Lift coefﬁcient for NACA 0012 airfoil AR 2 with and without the exposed electrode. Reynolds number 300,000.and reduced frequency k=0.05 . . . . 73

◦ 5.1 Lift coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number= 300,000 and reduced frequency k=0.05 ...... 78

5.2 Moment coefﬁcient comparison between different motion amplitudes, 10◦ + α1 . Reynolds number = 300,000 and reduced frequency k=0.05 ...... 79

xvi 5.3 Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 81

5.4 Lift hysteresis for various excitation Strouhal numbers. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 82

5.5 Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 84

5.6 Negative damping for various excitation Strouhal numbers. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 85

5.7 Cycle damping for various excitation Strouhal numbers. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 85

5.8 Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 87

5.9 Drag reduction for various excitation Strouhal numbers. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 88

5.10 Phase-averaged lift coefﬁcient for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt). 90

5.11 Lift hysteresis for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 91

5.12 Phase-averaged moment coefﬁcient for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 92

5.13 Negative damping for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 93

5.14 Cycle damping for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 93

5.15 Phase-averaged drag coefﬁcient for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt). 94

xvii 5.16 Drag reduction for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 95

5.17 Phase-averaged lift coefﬁcient for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt). 97

5.18 Lift hysteresis for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 98

5.19 Phase-averaged moment coefﬁcient for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 99

5.20 Negative damping for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).... 100

5.21 Cycle damping for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 100

5.22 Phase-averaged drag coefﬁcient for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 101

5.23 Drag reduction for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 102

5.24 Baseline case. Swirling strength for phase-locked PIV.Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt) ...... 104

5.25 Baseline case. Streamwise mean velocity for phase locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt) ...... 105

5.26 Excitation cases. Swirling strength for phase locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt) ...... 108

5.27 Excitation cases. Streamwise velocity for phase locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt) ...... 109

5.28 Phase-averaged lift coefﬁcient for light DS at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 110

xviii 5.29 Phase-averaged moment coefﬁcient for light DS at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 111

5.30 Phase-averaged drag coefﬁcient for light DS at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 6◦sin(ωt)...... 112

5.31 Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 117

5.32 Lift hysteresis for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 118

5.33 Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 119

5.34 Negative damping for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 120

5.35 Cycle damping ffor various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 120

5.36 Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 121

5.37 Drag reduction during the upstroke for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 122

5.38 Drag reduction during the downstroke for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).... 122

5.39 Phase-averaged lift coefﬁcient for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 ...... 125

5.40 Lift hysteresis for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 ...... 126

5.41 Phase-averaged moment coefﬁcient for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 . . 127

5.42 Negative damping for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 ...... 128

xix 5.43 Cycle-averaged damping for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 ...... 128

5.44 Phase-averaged drag coefﬁcient for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 . . 129

5.45 Drag reduction for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 ...... 130

5.46 Drag reduction for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5 ...... 130

5.47 Baseline case. Swirling strength for phase-locked PIV.Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt) ...... 132

5.48 Baseline case. Mean streamwise velocity for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt) ...... 133

5.49 Excitation cases. Swirling strength for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt) ...... 136

5.50 Excitation cases. Mean streamwise velocity, u, for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt) ...... 137

5.51 Phase-averaged lift coefﬁcient for deep dynamic stall at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 138

5.52 Phase-averaged moment coefﬁcient for deep dynamic stall at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 139

5.53 Phase-averaged drag coefﬁcient for deep dynamic stall at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 140

◦ A.1 Lift coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number = 500,000 and reduced frequency k=0.05 ...... 147

A.2 Moment coefﬁcient comparison between different motion amplitudes, 10◦ + α1 . Reynolds number = 500,000 and reduced frequency k=0.05 ...... 148

xx ◦ A.3 Lift coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number = 700,000 and reduced frequency k=0.05 ...... 149

A.4 Moment coefﬁcient comparison between different motion amplitudes, 10◦ + α1 . Reynolds number = 700,000 and reduced frequency k=0.05 ...... 150

A.5 Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 152

A.6 Lift hysteresis for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 153

A.7 Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 154

A.8 Negative damping for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 155

A.9 Cycle damping for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 155

A.10 Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 156

A.11 Drag reduction for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 157

A.12 Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 158

A.13 Lift hysteresis for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 159

A.14 Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 160

A.15 Negative damping for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 161

A.16 Cycle damping for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 161

xxi A.17 Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 162

A.18 Drag reduction for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 163

A.19 Phase-averaged lift coefﬁcient for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 165

A.20 Lift hysteresis for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 166

A.21 Phase-averaged moment coefﬁcient for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 167

A.22 Negative damping for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 168

A.23 Cycle damping for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 168

A.24 Phase-averaged drag coefﬁcient for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 169

A.25 Drag reduction for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt)...... 170

A.26 Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 172

A.27 Lift hysteresis for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 173

A.28 Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 174

A.29 Negative damping for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 175

xxii A.30 Cycle damping for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 175

A.31 Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 176

A.32 Drag reduction during the upstroke for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 177

A.33 Drag reduction during the downstroke for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).... 177

A.34 Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 179

A.35 Lift hysteresis for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 180

A.36 Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 181

A.37 Negative damping for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 182

A.38 Cycle damping for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 182

A.39 Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 183

A.40 Drag reduction for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 184

A.41 Phase-averaged lift coefﬁcient for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 187

A.42 Lift hysteresis for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 188

A.43 Phase-averaged moment coefﬁcient for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 189

xxiii A.44 Negative damping for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 190

A.45 Cycle damping for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 190

A.46 Phase-averaged drag coefﬁcient for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 191

A.47 Drag reduction for EPOC cases during the upstroke in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 192

A.48 Drag reduction for EPOC cases during the downstroke in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt)...... 192

xxiv Chapter 1: Introduction

The phenomenon of dynamic stall is present in many applications: maneuvering aircraft, wind turbines, natural ﬂyers, helicopters, and others. In helicopters, dynamic stall typically

occurs at high forward-ﬂight speed when the rotor blades dynamically pitch to counteract the

lift dissymmetry due to the vehicle forward motion. Under these conditions, the retreating

blade pitches to a higher angle of attack than the static stall angle, thereby generating

the conditions for ﬂow separation and stall [46]. The large unsteady aerodynamic loads

associated with dynamic stall subject the rotor to high torsional loads and excessive vibration

[38]. Analysis of dynamic stall is more complex than static stall due to the number of

parameters involved and their interactions. These parameters are related with intrinsic

characteristics of ﬂow (Reynolds number, Mach number), airfoil geometry and surface ﬁnish,

motion characteristics (reduced frequency of oscillation, axis of rotation, angle of attack

range), and overall arrangement characteristics (wall interference, and three-dimensionality

effects, e.g. tip vortex , sweep angle, and aspect ratio) [7, 46].

Methods of active or passive ﬂow control to mitigate the adverse consequences of

dynamic stall in rotors have been widely researched. The beneﬁts of such control include

the reduction of loads in the blades and the increase of forward speed ﬂight, thereby the

increased utility and potentially reducing the maintenance of helicopters. The common

requirements for these control methods are robustness of control authority, durability, and

1 ability to withstand high centrifugal forces. Other necessary characteristics include low weight, required power, and cost [38]. Multiple actuator technologies have been proposed

and explored for use in dynamic stall ﬂow control including zero-net-mass-ﬂux synthetic

jets, piezoelectric ceramics, ﬂuidics, electromechanical devices, and plasma actuators. Due

to their weight, robustness, power use, and resistance to high centrifugal forces, plasma

actuators are an excellent candidate for ﬂow control and mitigation of dynamic stall in

helicopter blades. Preliminary results documenting the use of plasma actuators [59, 68] in

dynamic stall are promising.

The ﬂow phenomena that can be important in dynamic stall include boundary layer

growth, separation, unsteadiness, shock/boundary layer and inviscid/viscous interactions, vortex/body and vortex/vortex interactions, transition to turbulence, and ﬂow re-laminarization

[69]. Therefore, the ﬂow physics behind unsteady ﬂow presents plenty of details to examine

and further comprehend. A key element is the onset of the dynamic stall vortex (DSV), which has been studied by many authors [7, 22, 42, 49]. To avoid the adverse effects of

dynamic stall, the DSV needs to be weakened or suppressed. The use of an NS-DBD

plasma actuator is proposed for this purpose. The hypothesis behind the use of an NS-DBD

plasma actuator is that the periodic excitation of the ﬂow at low amplitude will excite the

Kelvin-Helmholtz instability in the separation shear layer, thereby generating vortices and

removing accumulated vorticity from the leading edge. This will weaken the eventual DSV

and reduce the magnitude of the concomitant lift and moment peaks. As the control authority

of the NS-DBD actuator depends on proper leveraging of existing ﬂow physics, the study of

dynamic stall ﬂow physics, in combination with this ﬂow control technique, is crucial.

2 1.1 Thesis Overview

In chapter 1, an introduction to the speciﬁc research topic for the thesis is presented.

In chapter 2, a literature review covering static and dynamic stall over airfoils is presented.

Previous implementations of ﬂow control aimed at diminishing the negative effects of dynamic stall are discussed, including previous work done in The Ohio State University’s

Gas Dynamics and Turbulence Laboratory (GDTL).

In chapter 3, the modiﬁcations performed in the experimental set up are presented. These modiﬁcations were made to diminish the level of uncertainty in the results. Experimental set up capabilities for the upgraded facility are also discussed.

In chapter 4, the baseline results from static and dynamic stall experiments are presented as well as a discussion about the effect of end plates and the aspect ratio of the airfoil.

In chapter 5, the results from excitation cases in both schemes: continuous excitation and Excitation in Parts of Oscillating Cycle (EPOC) are presented and discussed. Additional results are presented in appendices.

Finally, the conclusions of this thesis and some suggestions for future work are included.

3 Chapter 2: Background and Related Work

An airfoil is any more or less flat surfaces producing or experiencing lift in a direction normal to the relative flow direction [31].The geometry of an airfoil section can be described by its chord, camber line, and thickness distribution (see figure 2.1).

Figure 2.1: Airfoil geometry. From reference [4]

The ﬂow characteristics over an airfoil are dominated by the Reynolds number and Mach number. In the description of the ﬂow in the current work, large Reynolds number and subsonic Mach number with negligible compressibility effects are assumed. Additionally, airfoils with a rounded leading edge and sharp trailing are the object of this work.

4 When the relative motion between the ﬂow and the airfoil at small angle of attack starts,

the ﬂow near to the airfoil follows the curvature of the airfoil in both sides from leading

edge to trailing edge. At the trailing edge, the ﬂow can no longer follow the sharp turn, it

separates, and a starting vortex forms [73]. The starting vortex is shed downstream and the

upstream ﬂow follows a smooth path around the curvature of the airfoil (See ﬁgure 2.2).

Under these conditions, the ﬂow creates a thin boundary layer near the airfoil surface as well as a thin wake downstream [74]. In addition, the regions around the airfoil can be

classiﬁed as either a low viscous effect region or a high viscous effect region. First, the low viscous effect region is outside of the boundary layer and the airfoil wake. The low viscous

region ﬂow streamlines are still affected by the presence of the airfoil (See ﬁgure 2.3). Due

to the streamlines being curved by the airfoil, a pressure gradient across the streamline is

generated and the pressure increases in the direction away from the center of curvature [2];

hence a pressure distribution around the airfoil is established. There exists a difference

between pressure distribution on the upper and lower surface of the airfoil. This contributes

to lift and drag forces experienced by the lifting surface. Second, in the high viscous effect

region, the most appreciable viscosity effects in the airfoil occur in the boundary layer. It

has been observed that the pressure gradient normal to the surface in the boundary layer

is negligible [4]. Therefore, pressure gradient along the boundary layer dominates and

according to the momentum equation, it is inﬂuenced by the inertial and viscous terms.

5 Figure 2.2: Starting vortex development. From reference [21]

Figure 2.3: Streamlines around an airfoil at increasing angle of attack. From reference [2]

The airfoil boundary layer can transition from laminar to turbulent regime due to disturbances in the ﬂow. These disturbances can be from pressure gradients, surface roughness, compressibility effects, surface temperature, suction, blowing at the surface, or free-stream turbulence [4]. In the case of a pressure gradient along the suction surface, the increase to positive values of angles of attack strengthens the pressure gradient that the boundary layer

flow needs to overcome due to the change in the curvature of streamlines. The generation of this adverse pressure gradient promotes flow instabilities (Tollmien–Schlichting waves) that start the transition process to the turbulent flow. In addition, strong adverse pressure

6 gradients contribute to ﬂow separation of the boundary layer. At the separation point, the

shear stress on the surface is equal to zero and the ﬂow direction is reversed. The ﬂow leaves

the surface and recirculating ﬂow is generated downstream of the separation point [38]. At

a certain angle of attack, massive separation of the airfoil boundary layer occurs on the

suction surface, creating a large zone of recirculating ﬂow. This dramatically changes the

pressure distribution, considerably reducing the lift force and augmenting the drag force

(See ﬁgure 2.3).

7 2.1 Static Stall

Stall in an airfoil at low speed subsonic ﬂow is the ﬂow condition which follows the

first lift curve peak [51]. Massive flow separation on the upper surface creates a significant

loss in lift and increase in drag. As the angle of attack increases, the ﬂow on the suction

side undergoes the following events: a negative peak in the pressure distribution at or near

the leading edge, a strong adverse pressure gradient between the negative pressure peak

and trailing edge, and thickening of the boundary layer. There are two potential spots for

boundary layer separation, in which stall is to be expected; one at the leading edge, due to

momentum deﬁcit and other close to the trailing edge due to boundary layer thickening [31].

Another ﬂow feature that can contribute to airfoil stall is a laminar separation bubble. A

laminar separation bubble is a region of separated ﬂow that results from the separation

of the laminar boundary layer near the airfoil leading edge. The separated shear layer

experiences transition followed by turbulent regime in a short distance after separation,

ﬁnally it reattaches to the airfoil upper surface as a turbulent boundary layer [32]. See ﬁgure

2.4.

8 Figure 2.4: Section view of laminar separation bubble. From reference [55]

According to McCullough [51] and Gault [23], for low speed airfoils without high-lift

devices and smooth surfaces, there are three types of pure stall: thin airfoil stall, leading

edge stall and trailing edge stall. There are two additional types of stall that can be added to

this list: re-separation stall and combined stall [13]. This classiﬁcation of different airfoil

stall depends on the section shape, thickness ratio, and the Reynolds number based on chord.

They are all shown in ﬁgure 2.5 and described below:

1. Thin airfoil stall or leading edge-long bubble stall. It is characteristic of some sharp-

edged airfoils and thin airfoils (thickness ratio of 0.09 or less) with a rounded-leading

edge. First, a long laminar separation bubble is observed. The ﬂow separation starts at

the leading edge with a reattachment point downstream that moves to the trailing edge

with the increase of angle of attack. Static stall occurs when the reattachment point is

at the trailing edge and any subsequent increase in the angle of attack reduces the lift.

9 2. Leading edge stall or leading edge-short bubble stall. It is characteristic of most airfoil

sections of moderate thickness (symmetric section with thickness ratio from 0.09

to 0.15). The laminar ﬂow separation occurs after the leading-edge pressure peak

is formed and then transition and reattachment occur through a laminar separation

bubble. As the angle of attack increases the pressure peak, and laminar separation

point, move closer to the leading edge. The length of laminar separation is reduced

compared with its size at lower angles of attack. After a certain angle of attack,

the separation point is moved so far forward that reattachment is not possible after

transition and a complete disruption of the ﬂow over the suction side occurs.

3. Trailing edge stall or thick airfoil stall. It is characteristic of thick airfoil sections

(thickness ratios of 0.15 or greater). It results from the turbulent separation that moves

gradually from the trailing edge as the angle of attack increases. When turbulent

separation appears, the lift-curve slope starts to diminish. The separation continues to

the point where the slope is zero and the airfoil is stalled.

4. Re-separation stall: This is an alternative leading edge stall where after the reattach-

ment point of the short laminar separation bubble, sudden separation can occur [13].

5. Combined stall: This stall is a mix between the leading edge stall that involves

separation bubble bursting and trailing edge separation. An abrupt decrease in lift can

be observed after the maximum lift coefﬁcient.

10 Figure 2.5: Flow characteristics for different types of stall in low speed airfoil. From reference [13].

11 2.2 Comparison between Thin and Thick Airfoils

The comparison between thin and thick airfoils is established by the behavior of the airfoil during the stall development. Thick airfoils (thickness ratio (t/c) of 0.15 or more) are prone to experience trailing edge stall. However, thin airfoils (thickness ratio (t/c) of 0.09 or less) are prone to experience thin airfoil stall or leading edge-long bubble stall. Although the thickness ratio is a simple parameter to establish a difference between flow characteristics in an airfoil, a more specific criteria is defined by correlating Reynolds number and an airfoil geometry parameter as a common upper-surface ordinate in the curve of the airfoil [23](See

ﬁgure 2.6).

Figure 2.6: Low speed stalling characteristics of airfoil sections correlated with Reynolds number and the upper-surface ordinates of the airfoil sections at the 0.0125 chord station. From reference [23]

12 Figure 2.7 summarizes the ﬂow characteristics of thin and thick airfoils.

Figure 2.7: Types of pure static stall. From reference [60]

A notable characteristic of thin airfoils is the large static stall hysteresis in the aerodynamic loads which produces different results in aerodynamic coefficients depending on the angle of attack at the flow starting. In addition, evidence shows thin airfoils and leading-edge airfoils flow stall are more sensitive to change in the airfoil shape compared to trailing-edge stall airfoils [38]. In addition, the maximum lift capability is an important aspect for comparison between thin and thick airfoils. Thin airfoils tend to have a lower

13 maximum lift coefﬁcient than thick airfoils due to the growth of the long separation bubble that progressively reduces leading edge suction peak [13]. See ﬁgure 2.8.

Figure 2.8: Lift curves comparison between thin and thick airfoils. From reference [23]

14 2.3 Flow Characteristics over an Oscillating Airfoil

An oscillating airfoil is one of the classical problems in unsteady aerodynamics [44].

The oscillating airfoil problem can be divided into translational oscillation normal to ﬂow

direction (plunging motion), longitudinal oscillation, and pitching oscillation. For this

dissertation, the ﬂow characteristics for an incompressible viscous ﬂow around a sinusoidal

pitching oscillating airfoil are considered.

The sinusoidal pitching oscillations of the airfoil are about an axis within the chord

length and varies with angle of attack

α(t) = α0 + α1sin(ωt) (2.1)

where α0 is the mean angle of attack, α1 is the amplitude, and ω = 2π f is the angular

frequency of the oscillation and f is the physical motion frequency [48].

The ﬂow characteristics over an oscillating airfoil are dominated by these parameters:

Reynolds number, Mach number, and reduced frequency. In this case, the reduced frequency

for sinusoidal oscillation is deﬁned by

ωb π f c k = = (2.2) U∞ U∞ where f is the frequency of the forced oscillation, b is half of the airfoil chord c, and

U∞ is the free-stream velocity. In general, the reduced frequency is the ratio between

c 1 the convective time scales 2U and the time scale of the forced oscillation ω [15]. The unsteadiness of the flow can be defined by the reduced frequency. For k = 0, the flow is

steady [18], if 0 ≤ k ≤ 0.05, the ﬂow is considered quasi-steady, where the unsteady effects

are small. For k > 0.05, the ﬂow is considered unsteady with signiﬁcant hysteresis in the

aerodynamic loads and if k > 0.2, the ﬂow is highly unsteady, acceleration effects dominate

the air loads and the ﬂow around the moving airfoil is similar to bluff body ﬂow [38, 56].

15 The unsteady effects in an oscillating airfoil flow are seen in the boundary layer. The unsteady response of the boundary layer will either lead or lag the quasi-steady behavior depending on the fluctuations in free stream flow or the pressure gradients [43]. In addition, unsteady separation is delayed by these unsteady effects. According to Ericsson and

Reding [18], unsteady airfoil stall is characterized by the delay of stall due to time lag and boundary layer improvement effects and a transient effect which is determined by the forward movement of the separation point and the spillage of leading-edge vortex.

16 2.4 Flow Characteristics of Dynamic Stall

Dynamic stall is a time-dependent ﬂow separation and stall phenomenon that occurs due

to accelerated motion of a lifting surface. Before the stall, the ﬂow will remain attached

at angles greater than the typical static stall angle of attack. This delay of the onset of

separation is the result of the following elements:

1. The circulation shed into the wake at trailing edge of airfoil that generates the un-

steadiness of the main ﬂow hence a reduction of lift and adverse pressure gradient

compared with the static case for the same angle of attack.

2. The kinematically induced camber effect that decreases the leading edge pressure and

pressure gradients for a given value of lift during the positive pitch rate.

3. The boundary layer flow reversal without any significant flow separation during the

positive pitch rate in response to pressure gradients.

4. The acceleration of boundary layer due to moving wall effect or Magnus effect created

by the motion of the leading edge

Items 1 to 3 are described in reference [38] and item 4 in reference [19].

After the delay of separation, the onset and development of the dynamic stall vortex

(DSV) occurs. The onset of dynamic stall is dictated by different mechanisms that depend

on Reynolds and Mach numbers, these mechanisms are the bursting or breakdown of the

laminar separation bubble, an abrupt breakdown of the boundary layer, reverse ﬂow within

the separation bubble, and boundary layer-shock interaction that causes ﬂow separation [11].

Any of those mechanisms triggers the release of the boundary layer vorticity accumulated

at the airfoil leading edge with the subsequent formation of a vortex structure. When the

17 DSV is formed, it convects along the upper surface of the airfoil generating a moving low pressure region, which causes the maximum lift value to exceed the maximum static value, and a more negative pitching moment (nose down) is experienced. Eventually, the DSV reaches the trailing edge and then the ﬂow is fully separated followed by an abrupt loss of lift. [42]. As the airfoil decreases its angle of attack during the downstroke, the ﬂow starts to reattach to the airfoil near the static stall angle and it progresses until it is fully attached [1].

Figure 2.9 summarizes the stages in the ﬂow.

18 Figure 2.9: The events of dynamic stall on NACA 0012 airfoil. From reference [8]

Other features to highlight the dynamic stall phenomena are discussed here. First, the convective velocity of the dynamic stall vortex is between one third and one half of the free stream velocity [5, 24, 49]. Second, the moment stall always occurs before the lift stall because of the change in the pressure generated by the DSV on the upper surface. This

19 pressure change develops an imbalance in the moment with respect to the quarter-chord that results in a large nose-down moment. Third, there is a significant lag for the reattachment of the flow due to the reorganization of the separated flow and the kinematic induced camber effect on the leading edge pressure gradient by the negative pitch rate. The lag in the reattachment stage generates the hysteresis in the unsteady aerodynamic forces. Dynamic stall is divided by McCroskey [49] into four categories: no stall, stall onset, light stall, and deep stall. According to Corke and Thomas [11] the characteristics for each of the categories are:

1. No stall: The airfoil trajectory remains below the static stall angle of attack. Under

these conditions, the aerodynamic loads are predicted well by quasi-steady aerody-

namic theory.

2. Stall onset: Stall onset is the regime in which the airfoil trajectory reaches the static

stall angle of attack. This condition produces the maximum useful lift without

excessive drag or pitch moment. Again, under these conditions, the aerodynamic

loads are predicted well by quasi-steady aerodynamic theory.

3. Light stall: The light stall regime marks the ﬁrst development of a dynamic stall

vortex. The onset, growth, and convection of the vortex are sensitive to the airfoil

chord, Reynolds number, and free-stream Mach number, as well as the unsteady

parameters, including the pitching reduced frequency, k, the mean angle of attack

α0, and the amplitude α1. Lift and moment stall peaks are less severe in this regime.

The ﬂow separation region size is on the order of the airfoil thickness. The boundary

between stall onset and light stall is abrupt and can be identiﬁed by the ﬁrst appearance

of moment stall (see ﬁgure 2.10)

20 4. Deep stall: A strong dynamic stall vortex is developed. The aerodynamic loads

ﬂuctuate dramatically through the pitching cycle with large peak forces and strong

hysteresis. The aerodynamic loads exhibit little sensitivity to Reynolds number, airfoil

geometry, or pitching motion. The ﬂow separation region size in this case is on the

order of the airfoil chord length.(See ﬁgure 2.10)

Figure 2.10: Flow ﬁeld during dynamic stall. From reference [44]

21 2.4.1 Parameters that inﬂuence Dynamic Stall

The dynamic stall process in a pitching airfoil is a complex phenomenon that can be

inﬂuence by various parameters. The main parameters include the airfoil shape, Reynolds

number, reduced frequency, mean angle of attack, amplitude of motion, and pitch axis

location.

The airfoil shape inﬂuences the nature of the initial boundary layer separation, then the

type of airfoil stall, which strongly affects the dynamic stall behavior [50]. In addition, an

airfoil shape with high static lift capability should show these characteristics during dynamic

conditions, although static airfoil performance metrics as maximum static lift coefﬁcient or

low static pitching moments will not predict the same behavior for a dynamic airfoil [38].

The effect of Reynolds number at moderate and high values is negligible for the leading

edge vortex shedding in dynamic stall [46]. Also, the effect is minor for the force and moment variation with angle of attack as well as the delay in reattachment [8]. For oscillating airfoils

such as NACA 0012 and 0015 at moderate Reynolds numbers, an increase in Reynolds

number, reduces the size of laminar separation bubble located at the leading edge due to the

movement of the LSB transition and reattachment point upstream [3, 66].

The oscillating motion that produces dynamic stall is deﬁned by reduced frequency,

mean angle of attack α0 and amplitude α1. These parameters have a major inﬂuence in

the development of the dynamic stall events. Increasing the reduced frequency produces a

delay in the ﬂow reversal and the subsequent development of stall events [8]. This augments

the magnitude of the suction peak induced by the dynamic stall vortex, the strength of

this structure, and the peak aerodynamic loads [15, 42]. The mean angle and amplitude

determine the degree of dynamic stall (no stall, stall onset, light stall, or deep stall) and the

associated unsteadiness for a given oscillation frequency [42].

22 The effect of moving the pitch axis location aft of the leading edge is to increase the

dynamic stall angle of attack but decrease the lift coefﬁcient peak [16, 30].

2.4.2 Aerodynamic Damping

In an oscillating airfoil, the aerodynamic work per cycle is deﬁned by

I W = Mdα (2.3) where M is the moment at quarter-chord. A positive work means energy exchange from the

ﬂow to the airfoil, hence an unstable motion; negative work means the energy exchange is

from the airfoil to the ﬂow, hence a stable motion. A more precise term that deﬁnes how the

energy from oscillations is dissipated or collected by the airfoil is the aerodynamic damping.

If the system is a single degree of freedom structure (i.e. a helicopter blade) and is subjected

to harmonic forcing in uniform air stream, its aerodynamic damping in each cycle is deﬁned

by [54] 1 I Ξcycle = − Cmc/4 dα (2.4) πα1 where Cmc/4 is the moment coefﬁcient at quarter-chord. From equation 2.4, if the aerodynamic damping is negative, the oscillating lifting surface is prone to self-excited oscillations

known as ﬂutter, which are ampliﬁed and could lead to an unstable system state. Flutter

always requires an energy supply and a zero or negatively damped system [54]. With positive

aerodynamic damping, the induced oscillations are dissipated, implying a stable system.

Overall, the aerodynamic damping deﬁnes the stability of the system.

To demonstrate aerodynamic damping under dynamic stall condition, an airfoil moment

coefﬁcient curve at quarter-chord for a pitching motion cycle is shown in ﬁgure 2.11. The

counterclockwise loops in the ﬁgure contribute positively to aerodynamic damping, therefore

in these regions the airfoil oscillations are damped, and the system is stable. The clockwise

23 loop in the ﬁgure contributes negatively to aerodynamic damping. If the cycle-averaged aerodynamic damping is negative the system is unstable.

Figure 2.11: Aerodynamic Damping: Clockwise and Counterclockwise Loops for pitching motion cycle

24 2.5 Flow Control in Dynamic Stall

Efforts to mitigate or avoid the adverse consequences of dynamic stall (DS) on rotors have been developed using passive and active ﬂow control. The overall beneﬁts of such control could include the reduction of unsteady loading on the blades, elimination of the potential for

flutter, and the increase of potential forward flight speed and utility of the helicopter. Passive techniques like vortex generators installed on the leading edge have achieved a reduction of peak moment coefficient and reduced the moment hysteresis loops [29]. The combination of transonic glove and vortex generators has been shown to reduce the maximum moment experienced from dynamic stall [41] in the compressible flow regime. However, these passive flow control devices have several disadvantages: they modify the shape of the lifting surface, they can add weight, they prove ineffective at off-design operating conditions, and they become a source of noise and vibration.

Previously explored active techniques include the use of momentum injectors, zero-net- mass-ﬂux devices, and plasma actuators. Muller-Vahl et. al. have examined the use of high momentum blowing to eliminate rapid, transient changes in lift force for a pitching NACA

0018 airfoil [53]. Greenblatt and Wygnanski found the use of zero net mass flux devices an effective means of DS control in light-stall as well as deep-stall cases [25]. Visbal [71], in a computational study of DS flow control with high-frequency excitation, using a zero- net-mass-flux blowing/suction slot located on the airfoil lower surface, concluded that for light DS, actuation is capable of maintaining an effectively attached flow during the entire oscillatory pitching cycle. It inhibited the formation of large-scale leading edge and shear-layer vortical structures. For deep DS, high-frequency excitation is found also to be effective at eliminating leading-edge separation and the formation of the DSV. For both cases, actuation provided a significant reduction in the cycle-averaged drag and in

25 the force and moment excursions. Unfortunately, momentum injectors are not able to

maintain a broad operating range because, as the speed is increased, signiﬁcantly more

momentum is required to sustain control efﬁcacy. Post and Corke [58] used an Alternating

Current Dielectric Barrier Discharge (AC-DBD) plasma actuator operated in both steady

and unsteady modes to control leading-edge ﬂow separation and the DSV of an oscillating

airfoil. They concluded that when the plasma actuator was operated in steady actuation

cases, the lift was increased throughout the entire cycle except at the peak angle of attack where it suppressed the DSV. Primarily, the steady actuation acted to eliminate the sharp

drop in the lift coefﬁcient at the start of the pitch down phase. Unsteady plasma actuation

produced a signiﬁcant improvement in the lift coefﬁcient during the pitch-down phase of the

cycle, especially at the minimum angle of attack. A closed-loop control actuation approach

produced the greatest improvement in the lift cycle with the highest integrated lift and

elimination of the sharp stall past the maximum angle of attack. While AC-DBD plasma

actuators showed promising results, the ion density in the region of the electric charge

restricts the momentum production and thus the efﬁcacy at higher ﬂight speeds [63]. Due to

their low weight, resistance to high centrifugal forces [58], small energy requirements, and

lack of moving parts [39], plasma actuators are excellent candidates for ﬂow control and

mitigation of DS on helicopter blades (See ﬁgure 2.12).

26 Figure 2.12: DBD plasma actuator schematic. It is composed of two electrodes separated by a dielectric barrier. Plasma is formed over the covered electrode when an AC or DC voltage is applied to the electrodes. From reference [63]

Unlike AC-DBD plasma actuators, which generate body force and inject momentum into the flow, the Nano-Second Pulsed Dielectric Barrier Discharge (NS-DBD) plasma actuators produce localized thermal perturbations to excite and control instabilities in flow over airfoils. This thermal effect excites the Kelvin-Helmholtz instability in the free shear layer which amplifies the perturbation over a wide bandwidth. The Kelvin-Helmholtz instability excited by NS-DBD plasma actuator has an inviscid nature which means that as Reynolds number increases, the instability becomes less sensitive to its effect. There are two frequencies associated with the Kelvin-Helmholtz instability excited by NS-DBD perturbation. There exists a most amplified frequency for the free shear layer that generated the maximum amplification of the perturbations. The most amplified frequency is obtained using a first length scale which is the shear layer momentum thickness. The shedding frequency is obtained using a second length scale, in this case is the airfoil chord. This shedding frequency is used to study the airfoil performance during excitation and its values are much smaller than the values of obtained with first length scale related with shear layer. As mentioned in Samimy et al. [65]., “this second length scale plays an even more

27 important role in the growth of perturbations and the development of ensuing large-scale

ﬂow structures than the local momentum thickness”.

The characteristics of these structures including size, organization, and entrainment capabilities are controlled by the excitation frequency of the perturbations. NS-DBD actuators produce relatively high-amplitude, high-bandwidth perturbations for effective instability-based flow control and they have the possibility of excitation of natural flow instabilities over a wide range of flow speeds and Reynolds numbers [64].

Another application of NS-DBD for dynamic stall ﬂow control is found in the computational work from Visbal and Benton [72] where low-amplitude, very-high-frequency forcing excites convective instability mechanisms present in the LSB. The excitation of

LSB instability delays ﬂow separation close to leading edge, and the DSV formation. The excitation frequencies are associated with the LSB separation instability and they are very high compared with excitation frequencies used for NS-DBD. In summary for both works,

NS-DBD actuators can used targeting two different control mechanisms for the reduction of unsteady loads during the oscillation of an airfoil.

Previous ﬂow control efforts using NS-DBD plasma actuators in the Gas Dynamics and Turbulence Laboratory research group at OSU have included static and dynamic cases.

During static cases, it was found large structures generated by excitation contributes to ﬂow reattachment and lift recovery in a similar manner than in dynamic cases. [20, 67, 68].

2.5.1 Initial Work in Dynamic Stall Flow Control at GDTL

In the proof-of-concept setup, a NACA 0015 airfoil was driven by an oscillating mechanism following a sinusoidal proﬁle. This previous work at The Ohio State University’s Gas

Dynamics and Turbulence Laboratory (GDTL) included the development of an experimental

28 setup for preliminary investigation of DS ﬂow control [67, 68]. The setup used a recircu-

lating wind tunnel with an optically clear acrylic test section. The test section has a 61 x

61 cm cross-section and a 122 cm length. A NACA 0015 airfoil with a 20.3 cm chord was

installed and an NS-DBD plasma actuator was used for ﬂow control. The airfoil oscillation

mechanism was designed to maximize optical access and consisted of two acrylic disks

secured in aluminum rings (See ﬁgure 2.13). The airfoil’s ends were mounted to these disks

and thin ball bearings were used to mount the airfoil support rings to the tunnel sidewalls.

The aluminum rings were driven by a servo via timing belts. An array of static pressure

taps near the airfoil centerline was used to measure the surface pressure and calculate the

aerodynamic forces. Motion-locked PIV measurements were acquired at various motion

and excitation conditions. In motion-locked PIV, images are taken at the same motion phase

during all cycles. The results obtained by Singhal et al [68] using this experimental setup

are brieﬂy described below.

Figure 2.13: Previous experimental setup at GDTL, showing airfoil conﬁguration and timing belt and pulley oscillating mechanism. From reference [67]

29 Detailed PIV images showed that ﬂow excitation resulted in the formation of large-scale

ﬂow structures, the scales of which inversely proportional to the excitation Strouhal number, when the ﬂow is stalled. Perturbations generated by the actuator over a large range of

Strouhal number are ampliﬁed by the instability of the shear layer formed over the separated

zone and rolled up into ﬂow structures. Figure 2.14 shows swirling strength, used to identify

ﬂow structures from PIV measurements, for the baseline (Ste = 0), one low Strouhal number

(Ste = 0.35), and one high Strouhal number (Ste = 9.9) excitation case during the airfoil’s

pitch-up motion.

30 Figure 2.14: Swirling strength, during the airfoil’s pitch-up motion, for the baseline and low and high Strouhal number excitation cases for Reynolds number of 300,000 and reduced frequency (k) of 0.05. From reference [67]

At low Strouhal number excitation, the structures are quite large, and the convection and eventual shedding of these structures increases the unsteadiness in the lift and moment forces. As the excitation Strouhal number increases, the structures become smaller, develop

31 further upstream, and breakdown quickly. This results in partial, but relatively steady,

reattachment that signiﬁcantly reduces unsteadiness. The results clearly show the changes

in the nature of the structures as the excitation Strouhal number is changed. Figure 2.15

shows phase-averaged lift and moment coefﬁcients for the baseline (Ste = 0), two low

frequency (Ste = 0.3 and Ste = 0.78), and one high frequency (Ste = 9.9) excitation cases.

An important effect of high Strouhal number excitation is the reduction of the DSV strength

that is evidenced by the reduction in lift peak during the upstroke. The reduction in DSV

strength contributes to the decrease in the magnitude of the lift and moment coefﬁcients. A

lower strength of the DSV is due to a reduction in the vorticity accumulation at the airfoil

leading edge during the pitch-up motion, as can be observed from ﬁgure 2.15. Excitation

creates vortices before the ejection of the DSV that carry away some of the accumulated vorticity. This effect at high excitation Strouhal numbers eliminates the DSV. These results

indicate that NS-DBD actuators are an effective means of ﬂow control for unsteady ﬂow [68].

The results also showed that excitation, especially high-frequency excitation, contributes to

the reduction of the lift and moment hysteresis, as shown in ﬁgure 2.15 , and decreases the

negative damping coefﬁcient [68]. In addition, the signatures of the structures in the low

frequency excitation case can be seen in the downstroke.

32 Figure 2.15: Phase averaged lift and moment curves for NACA 0015 during excitation at low and high Strouhal number excitations for Reynolds number of 300,000 and reduced frequency (k) of 0.05. From reference [67]

33 Chapter 3: Redesigned Experimental Setup

This chapter details the upgrades adopted for each component in the redesign of the

experimental setup and the improvements obtained. The results obtained with the NACA

0015 airfoil driven by a timing belt and pulley oscillating mechanism were used to prove

the efﬁcacy of NS-DBD plasma actuator on an oscillating airfoil. While a reduction in the vibratory and torsional loads during dynamic stall (DS) due to excitation were observed, this

experimental set up had some drawbacks that caused signiﬁcant issues with the repeatability

of the results and increased their uncertainty. The drawbacks for this initial facility were

poor repeatability of the motion, poor motion and pressure signal synchronization with a

low temporal resolution, high solid blockage in the test section with wall boundary layer

interaction for the model and questionable load calculations given by surface pressure taps

conﬁguration. The poor motion repeatability was evidenced by changes in the angular

position of up to one degree between the cycles of one run. A non-consistent motion pattern

introduced variability in the entire dynamic stall process which could generate a ﬂow ﬁeld

different from the sinusoidal oscillating airfoil ﬂow ﬁeld. The synchronization process

between motion and pressure signal was also poor due to the lack of a universal sample

clock for data acquisition of all the sensor signals. This limitation generated different lags

in the signals that, despite the synchronization corrections, the motion of the airfoil and

the pressure data were only synchronized to within 5ms for low oscillating frequencies. In

34 consequence, there was greater uncertainty in the aerodynamic load results. A low sampling

rate, limited by the pressure transducers, added to the synchronization issue by limiting the

acquisition of detailed time dependent ﬂow features at the dynamic stall vortex onset and

subsequent convection.

Another issue in the initial facility was a high blockage ratio in the test section expe-

rienced by the model. Due to high blockage ratio, the magnitudes of maximum lift and

moment coefﬁcients were larger than the results reported in the literature [26, 47]. Addition-

ally, the ratio h/c (where h is the distance from the wind tunnel wall to the surface of the

airfoil at zero angle of attack) was 1.5 for a chord length (c) of 20.32 cm (8 in). According

to Duraisamy et al. [17], for h/c < 3, signiﬁcant lift augmentation can be expected. Many

researchers have used a value of h/c around 2 or above [22, 26, 47, 57, 59]. In addition to the

effects of blockage, the airfoil span used in this initial experimental set up covered the entire

span of the test section, which left the airfoil susceptible to wall boundary layer effect. Due

to the spatial resolution of surface pressure taps on the airfoil, the measured lift was affected

(especially near the leading edge). Speciﬁcally, the distribution did not allow the details of

the DS vortex evolution to be captured during the fastest oscillating case. Moreover, this

single line of pressure taps at the mid-span of the airfoil only captured the pressure changes

in the ﬂow that occurred in this area neglecting any three-dimensionalities in the ﬂow.

In order to diminish the uncertainty in the DS data, modiﬁcations in the airfoil, motion

system, and data acquisition system were made and are described below.

35 3.1 Redesigned Experimental Set up Components

The experimental setup was redesigned in order to improve the overall quality of the

experimental results. Modiﬁcations to the airfoil, motion system, and data acquisition

system are described below. The adoption of these modiﬁcations permits experiments in the

range of reduced frequencies from 0.02 to 0.2 at Reynolds numbers up to 750,000.

3.1.1 Subsonic Wind Tunnel Facility

The experimental setup was installed in the optically clear acrylic test section of the

subsonic recirculating wind tunnel at the Gas Dynamics and Turbulence Laboratory (GDTL), within the Aerospace Research Center at The Ohio State University. The test section has a

61cm x 61cm (2ft x 2ft) cross-section and a 122cm (4ft) length. The ﬂow velocities that

can be reached in the test section vary from 15m/s-95m/s (50ft/s-310ft/s) (See ﬁgure 3.1).

Flow velocity is estimated using free stream static and stagnation pressure (p∞ and po) from

two rings of pressure taps placed at both ends of the converging section. Each pressure tap

ring is connected to a pressure transducer. A thermocouple located downstream of the test

section, before the turning vanes, is used to monitor freestream temperature T∞. Ambient

temperature Tamb is measured using the same thermocouple, prior to tunnel startup. Ambient

pressure pamb is collected from METARs data reported by the OSU Airport (KOSU). With

all these input data, the velocity is estimated using Bernoulli’s Equation: s p − p U = 2 o ∞ (3.1) ∞ ρ

For more details about this wind tunnel facility, see reference [39].

36 Figure 3.1: Subsonic Recirculating Wind Tunnel

Due to the structural requirements for the servomotor mounting, the test section ﬂoor was changed from an acrylic plate to a black anodized aluminum smooth plate. (See ﬁgure

3.2)

37 Figure 3.2: Current Wind Tunnel Test Section

3.1.2 Airfoil Model

The airfoil was changed from a NACA 0015 to a NACA 0012 model which is a more

typical airfoil for rotorcraft research. The NACA 0012 airfoil is ideal for rotorcraft applica-

tions due to near ideal behavior at the center of pressure with varying incidence below stall which minimizes the pitching moment and maximizes the lift coefﬁcient which contributes

to diminishing blade twisting and torsional loads [27,38]. In addition, the NACA 0012 is

selected due to the broad amount of studies which have been done at different conditions for

rotorcraft applications [28, 37, 42, 45].

For the redesigned experimental set up, the airfoil chord and span lengths were changed

to diminish the solid blockage ratio effects and to increase the h/c parameter. Also, these

dimensional modiﬁcations help to provide a balance between parameters that affect the DS

ﬂow control experiments which include: range of chord-based Reynolds numbers, maximum

38 excitation Strouhal number, and airfoil mass which influences the inertial loads and natural frequencies of the oscillating assembly. Following the aforementioned parameters balance, the initial NACA 0015 airfoil with aspect ratio (AR) of 3 with a chord of 8in was replaced by a NACA 0012 airfoil with aspect ratio (AR) of 2 and a chord of 7in. With this modification, the first benefit obtained was a reduction in solid blockage ratio. For example, at an angle of attack of 20 degrees the blockage decreased from 16 percent for the NACA 0015 with AR of 3 to almost 10 percent in the NACA 0012 with AR of 2 (see figure 3.3) with end plates included. Details about end plate implementation are discussed in the chapter 4.

Figure 3.3: Estimated Solid Blockage Ratio comparison for NACA 0015 in the Initial Experimental Set Up and NACA 0012 in the Redesign Experimental Set Up

39 The airfoil chord reduction from the initial 8 inches to 7 inches also contributed to

increase in the wall distance factor h/c to 1.7, which is still less than the recommended value

of 3 [17], but an improvement which reduces lift augmentation due to wall interference

effect. The span and aspect ratio reduction from 24 inches (AR=3) to 14 inches (AR=2)

diminished the effect of solid blockage ratio and airfoil mass. The aspect ratio of 2 is in the

range of other representative experimental studies listed in Table 3.1.

Reference AR h/c ratio McAlister, Carr, and McCroskey (1978) [42] 1.75 1.25 McCroskey et al. (1982) [47] 3.5 2.5 Karim and Acharya (1994) [35] 2.0 1.0 Gardner et al. (2013) [22] 3.3 1.67 Muller-Vahl et al. (2016) [53] 1.75 1.4 Ramasamy et al. (2016) [62] 1.8 2.5

Table 3.1: Representative wind-tunnel installations for nominally 2-D dynamic stall studies

The airfoil was mounted vertically to eliminate the effect of the weight on the airfoil

bending moment and to increase the optical access for ﬂow visualization experiments

using PIV. This optical access was reduced by oscillating aluminum rings installed in the

previous experimental setup. The airfoil is composed of two interchangeable pieces, a

Polyoxymethylene (POM) (Delrin) leading edge, to which the NS-DBD plasma is applied to

insulate it from the metal airfoil, and the aluminum main airfoil (see ﬁgure 3.2 and 3.4). This

two-piece design was adopted (rather than the composite airfoils used in similar previous

experiments) due to the structural requirements of the cantilevered arrangement.

40 Figure 3.4: Cross sectional view of Aluminum airfoil with Delrin leading edge.

3.1.3 Plasma Actuator

The NS-DBD plasma actuator was installed on the airfoil leading edge (Delrin portion)

(see ﬁgure 3.5) and covered the entire span of the airfoil. This plasma location is similar

to the previous set up and the purpose of this location is to excite instabilities in the shear

layer that appear during the leading-edge ﬂow separation. To build the leading edge plasma

actuator, the copper tape ground electrode, which is a 0.09 mm thick and 12.7 mm wide,

is attached to a recess in the Delrin piece; it is then covered with three layers of Kapton

tape, each 0.09 mm thick with a dielectric strength of 10 kV. There is also a recess in the

airfoil metal portion to minimize discontinuities in the airfoil shape after the addition of

the Kapton tape. Finally, the copper tape exposed electrode, 0.09 mm thick and 6.35 mm wide, is attached to the airfoil lower surface completing the plasma actuator. Plasma forms

at the juncture of the copper electrodes, which is located at the leading edge of the airfoil. A

schematic of the plasma actuator is shown in ﬁgure 3.5.

41 Figure 3.5: Cross sectional view of Delrin leading edge with Plasma Actuator installed.

The actuator is connected to and powered by a pulse generator, which was custom

designed and built at Ohio State University. A magnetic compression circuit in the pulser

creates, a high voltage-current waveform for the actuator, producing up to a 10kV pulse with a pulse width around 200ns. Details about the pulse generator can be found in

references [40,70]. A sample of the pulser output signals for voltage and current, and power

and energy estimation for the actuator can be observed in ﬁgure 3.6. They were calculated

using the procedure taken from reference [14] .

42 Figure 3.6: Pulser output signals for voltage and current with power and energy estimation. Input frequency of 2000Hz.

3.1.4 Load Cell Transducer

A six-axis force and moment load cell transducer was used to directly measure aerodynamic forces on the airfoil and eliminate the phase delay that existed due to long plastic tubing between the pressure taps and transducers in the previous experiment. In addition, this load cell device allows any potential ﬂow three-dimensionality to be accounted for in

43 the aerodynamic force and moment coefﬁcients and signiﬁcantly increases the temporal

resolution of the measurements to have a better description of dynamic stall time events. In

the previous work, any potential three-dimensionalities in the ﬂow were not accounted for

since pressure taps were used only along the centerline. Forces and moments were acquired

using an ATI Industrial Automation Six-Axis Force/Torque Delta 660-60 transducer. This

transducer can obtain forces and moments in the ranges required for the reduced frequencies

and Reynolds numbers selected. The transducer was installed above the servomotor using

an adapter made out of stainless steel and connected to the airfoil with one Delrin and two

metal adapter pieces. This complex setup was decided upon because Delrin insulates the

high voltage discharge in the airfoil from the load cell transducer and servomotor. The center

of the transducer was aligned with the quarter-chord axis of the airfoil. This is in accordance with common literature practice [37, 46, 49, 52, 57] as well as the previous preliminary work [67].

3.1.5 Direct Drive Servomotor

A direct drive motor for the motion system was selected to improve the motion repeata-

bility. More details about repeatability of the motion are given in chapter 4. The motion was provided by a Kollmorgen Housed Direct Drive Rotary (DDR) motor DH063M-13, which can deliver a peak torque of 160 N-m and a maximum rotational velocity of 500

rpm. The servo control was established using a combination of an AKD servo drive with a

National Instruments Compact Reconﬁgurable Input and Output system (NI-cRIO) model

9035 through NI Softmotion using EtherCAT communication protocol. The AKD drive

quadrature encoder signals were used to control and record the airfoil angular position from within a Field Programmable Gate Array (FPGA) module. The force measurement and

44 airfoil motion systems are now synchronized extremely well using a new data acquisition

system, which is a real-time controller for the servomotor, load cell transducer, and actuators

to be used for ﬂow control. A CAD rendering of the load cell and servo assembly with the

airfoil mounted is shown in ﬁgure 3.7.

Figure 3.7: Airfoil, Load Cell, Servomotor Assembly in Re-designed Experimental Set Up

3.1.6 Data Acquisition System

The data acquisition system for the redesigned experimental setup was selected to

have real-time and synchronization capabilities and it is composed of the sensors, data

acquisition hardware, and a computer with programmable software. The sensors are a load

cell transducer, encoder for servomotor, and two pressure transducers which are part of the wind tunnel instrumentation. These sensors are connected to a National Instruments 9220

Analog Input card which is installed in a NI-cRIO model 9035. Additionally, the servomotor

45 drive communicates with the NI-CRIO via EtherCAT. The NI-cRIO 9035 chassis has a processor running NI Linux Real-Time, a FPGA, and modular I/O with vision, motion, and display capabilities. The cRIO controller contains a timing controller that synchronizes data acquisition from all connected I/O modules and the FPGA for high performance and highly deterministic control [34]. A schematic of the data acquisition system is shown in ﬁgure

3.8. The data acquisition hardware is controlled by a series of custom-made graphical user interface programs designed with LabVIEW and they run on a host computer connected via

Ethernet to the NI-cRIO module.

Figure 3.8: Data Acquisition System Components

46 3.2 Particle Image Velocimetry (PIV)

The diagnostic technique known as particle image velocimetry (PIV) is based on the

determination of the velocity of tracer particles added to the ﬂow. To obtain the velocity, the

displacement of the tracer particles and the displacement time are required. First, a pair of

images is acquired with a speciﬁc time delay. Then the displacement of particles is obtained via image processing using computational tracking algorithms based on correlation methods.

Finally, the entire velocity ﬁeld is resolved with the combination of the displacement of each

particle and the recorded time delay. For two velocity components in a plane, a common

PIV system consists of a single camera that captures the images, a laser in combination with

optical lenses provides the illumination of tracer particles generated by a particle seeder,

a timing device that provides the synchronization between camera and illumination and a

computer with data acquisition and image processing software. Details of the current PIV

apparatus used in these experiments are recorded below.

Two components of velocity in a single plane were resolved (2D-2C). The camera set

up used two (to extend the ﬁeld of view) LaVision Imager sCMOS 16-bit camera with a

resolution of 2560 x 2160 pixel. Each camera had Nikon Nikkor 55mm f /2.8 lens installed.

The cameras lenses were at 710mm from the laser sheet and the camera center-to-center

horizontal distance was 150mm. The camera acquired data at 24.5Hz a multiplier of the

motion frequency. For each baseline and excitation phase, 500 image pairs were taken.

47 Figure 3.9: Oscillating Airfoil PIV Set Up in a Plane (2D2C)

The illumination was generated with a Quantel Evergreen HP Laser system with two

laser heads. Each laser head is a frequency doubled Nd:YAG laser (wavelength 532 nm) that

can deliver 312 mJ per pulse in a frequency range between 24Hz to 26Hz. The laser beam

is transformed into a sheet using a set of two plano-concave lenses in combination with a

spherical lens to reduce the sheet thickness, and the noise in the images. The laser sheet

had a thickness of approximately 2mm and it was located at the mid-span of the airfoil. The

tracer particles were olive oil droplets generated in a Six-Jet Atomizer 9306. The atomizer was set to a pressure of 35psi to have the ﬂow particle density to obtain good correlation for

the images.

48 The PIV camera control and image processing was done using Davis 8.3 software which is commercially available from LaVision. Before the acquisition of the images, the

software requires a calibration procedure. This calibration was performed in the software

using the two-camera stereo conﬁguration mode and a type 31 LaVision calibration plate.

The software also controlled the programmable timing unit (PTU) which synchronizes the

cameras with the laser. This PTU was externally cyclically triggered to synchronize the

airfoil motion frequency with the camera image acquisition rate. Phase-locked images were obtained through this procedure. Six trigger pulses were generated in each motion

cycle. Each pulse corresponded to a selected phase in the motion. The reference time in the

software was changed to create a delay in the trigger signal and in consequence a new set of

phases.

The image processing using Davis software started with a time ﬁlter to reduce the noise

in the raw images and to improve the correlation values. Then the raw image is covered with a geometric mask in the areas not illuminated by the laser sheet to avoid wasting

computational time in this area. A sequential, FFT based multi-pass cross-correlation

algorithm was employed to generate the vector ﬁelds. The ﬁrst pass used a 64 x 64-pixel

interrogation window with 50% overlap between adjacent interrogation windows. The

next two passes used a 24 x 24-pixel interrogation window with 75% overlap. These windows sizes determined the spatial resolution of the velocity ﬁeld. To reduce the spurious vectors, during the passes, an allowable vector range 10 m/s +/- 50 m/s was enforced in

combination with a 3 x 3 vector-smoothing ﬁlter. After the processing, the two vector ﬁelds

from the cameras were merged. Calculation of the statistics and swirling strength as a vortex identiﬁcation method was performed in Davis. Swirling strength was selected due

49 to its availability in the software and ease of implementation. The results were exported to

MATLAB to improve the visualization the plots.

50 3.3 Experimental set up capabilities

The current experimental set up using an aluminum airfoil of AR of 2 and chord of 7

inches allows the current experimental apparatus to achieve a range of reduced frequencies

at different Reynolds numbers that can be seen in ﬁgure 3.10.

The Reynolds numbers selected were 300,000, 500,000 and 700,000. The reason for

this selection was to have a broad range of Reynolds number achievable in the subsonic wind tunnel to test the NS-DBD plasma actuator and to be able to compare baseline results with literature. On the other hand, the reduced frequencies selected were chosen due to the

limitations of the servo motor power and load cell capacity. Moreover, it was desirable to

test the NS-DBD actuator in quasi-steady and unsteady conditions.

Figure 3.10: Range of Reduced Frequencies for Redesigned Experimental Set up

51 Chapter 4: Baseline Static and Dynamic Experiments

This chapter describes the baseline results for static and dynamic tests using the redesigned experimental setup. First, a discussion of motion proﬁle, end plates and aspect ratio is shown. Second, the static results for NACA 0012 airfoil at Reynolds numbers of

300,000, 500,000 and 700,000 are presented. Finally, this chapter shows a description of the dynamic baseline including its data processing and the results for NACA 0012 airfoil.

52 4.1 Discussion of Motion proﬁle, End Plates, and Aspect ratio effects

4.1.1 Motion Proﬁle

The new experimental setup improved the repeatability of the motion. Improving the

repeatability limits the source of uncertainty to the stochastic nature of dynamic stall (DS).

A comparison of motion proﬁles between the initial and the upgraded experimental

setup is shown in ﬁgure 4.1. Both graphs show the cycle-to-cycle variation for the same

◦ ◦ sinusoidal airfoil motion (α0 = 13 ,α1 = 5 , f = 3.48Hz) at a Reynolds number of 300,000.

The left plot shows the initial experimental setup motion repeatability and the right plot

shows the upgraded setup motion repeatability. The left plot includes 5 motion cycles and

the right plot shows 43 motion cycles. However, in the upgraded setup, the cycles match so well that they overlay each other perfectly. The individual cycles in the initial experimental

setup varied by approximately 1 degree and in the current experimental setup this variation

is less than 0.01 degree, according to the direct drive servomotor measurements from the

encoder. With this signiﬁcant improvement, the deviation in the averaged cycle-to-cycle

aerodynamic coefﬁcients was reduced as well as in angle of attack deviation that inﬂuences

the phase-averaged PIV results.

53 Figure 4.1: Comparison of airfoil motion plotted against time for initial (a) and upgraded ◦ ◦ (b) experimental setup (α0 = 13 ,α1 = 5 , f = 3.48Hz) at Re =300,000. For initial setup, 5 cycles are shown and for upgraded setup, 43 cycles are shown

4.1.2 End plates effects

To minimize the interaction between the test section wall boundary layer and the ﬂow

over and in the wake of the airfoil, as well as produce a more two-dimensional ﬂow and

thereby simulate more accurately an inﬁnite wing, circular end plates were designed, built,

and installed on the airfoil. The end plate diameter, material, and thickness selection were

based on guidelines and designs found in literature [6,36,37, 61] while also balancing the

desire to minimize the solid blockage ratio in the wind tunnel. According to Kubo et al. [36],

to minimize the effect of the wake vortex, the downstream portion of the end plate should

be greater than 4.28 times the model depth, and for circular end plates, the diameter should

be larger than 8.5 times the testing body depth. Experiments were performed to explore the

effect of end plate diameter with a 7 in chord airfoil which had an aspect ratio of two and

clean leading edge (no recess and one airfoil piece). Two different acrylic circular end plate

54 diameters 0.46 m (18 in) and 0.33 m (13 in) were tested using the previously mentioned

design parameters.

The measured results using the upgraded setup can be seen in ﬁgure 4.2 where they

show the effect of end plates on the NACA 0012 clean airfoil with AR=2 lift coefﬁcient.

Due to the more two-dimensional ﬂow around the airfoil, the slope of the lift coefﬁcient and

maximum lift coefﬁcient vs. angle of attack curve signiﬁcantly increase when end plates

are installed. The results with the two different diameter end plates show no signiﬁcant

differences in slope or stall angle/stall characteristic between them. This allows the 13-inch

end plates to be used, which reduces the blockage from 10 % to 9 % at 18◦ angle of attack while retaining the majority of the beneﬁts offered by the end plates.

Figure 4.2: Effect of end plates on lift coefﬁcient of the NACA 0012 AR=2 airfoil at Reynolds number 500,000. Reference Critzos et al. (1955) [12] used.

55 4.1.3 Aspect ratio inﬂuence

In order to understand the effect of airfoil aspect ratio, a comparison between the lift

characteristics of two NACA 0012 airfoils with two different aspect ratios AR=3 and AR=2

using end plates of 0.46 m (18 in) diameter is shown in Figure 4.3. This is essential to

understanding the effect of tunnel blockage, one of the main concerns with the initial setup.

At the highest angle of attack, 18◦, the AR=3 airfoil has a 13% blockage whereas the

AR=2 airfoil only has a 10% blockage. Besides reducing the tunnel blockage, reducing

the AR also reduces the airfoil weight and total forces produced, which allows for higher

Reynolds numbers and reduced frequencies to be tested. Overall, both aspect ratios produce

similar results, except for the change in the maximum stall angle. Therefore, an airfoil with

AR=2 was used with an end plate diameter of 0.34 m (13.5in) to eliminate the problems

associated with a high blockage ratio and allow for experiments with a larger range of

Reynolds numbers and reduced frequencies.

56 Figure 4.3: Comparison between AR=2 and AR=3 with 0.46m (18in) diameter end plates. Reynolds number 500,000

57 4.2 Static Baseline

Load cell measurements were acquired to establish the static baseline aerodynamic loads for the AR=2 NACA 0012 airfoil with a plasma actuator installed; this was done at Reynolds numbers of 300,000, 500,000 and 700,000 using 34 cm (13.5 in) diameter end plates in a range of angles from 0 to 20 degrees. Figure 4.4 and table 4.1 displays some aerodynamic characteristics for the chosen Reynolds numbers. As the Reynolds number increased from

300,000 to 700,000, the maximum lift coefﬁcient also increased, as expected. A gradual change in the lift curve followed by an abrupt stall (in lift) is also observed. This stall behavior could be an indication of a combined trailing-edge and leading-edge stall for this

Reynolds number range [23,33]. The maximum lift coefﬁcient, Cl and the stall angle for each Reynolds number case, are also shown in table 4.1.

Figure 4.4: Lift coefﬁcient for Reynolds numbers 300,000, 500,000 and 700,000 .

58 Reynolds number Max. Lift Coefﬁcient Static Stall AoA 300,000 0.86 14 500,000 0.98 15 700,000 1.03 15

Table 4.1: Aerodynamic Characteristics for NACA 0012 AR 2 at different Reynolds numbers

In Figure 4.5, values for the moment coefﬁcient about the quarter-chord axis are reported.

The moment coefﬁcient values are close to zero up to stall. Massive separation of the ﬂow

from the upper surface of the airfoil then causes the large drop in moment associated with

the stall. These results make intuitive sense based on the airfoil characteristics and due to

load measurements, which include any three-dimensionality that might be present under

incipient stall conditions and that might be missed by a centerline pressure-tap array.

59 Figure 4.5: Moment coefﬁcient about quarter-chord for Reynolds numbers 300,000, 500,000, and 700,000 .

60 4.3 Dynamic Baseline

To obtain dynamic stall results, the airfoil is oscillated in a sinusoidal fashion about the

quarter-chord axis. Equation 4.1 describes the motion.

α(t) = α0 + α1sin(ωt) (4.1)

where α0 is the mean angle of attack, α1 is the amplitude, ω is the angular frequency

π f c dictated by the selected reduced frequency, k. The reduced frequency is deﬁned as k = U where f is the physical frequency of the motion, c is the airfoil chord, and U is the freestream velocity. The total forces measured by the load cell include the aerodynamic forces as well

as the inertial forces from the acceleration and mass of the setup. To account for the inertial

loads, two sets of data are taken for each dynamic stall case one with the wind on, capturing

the total forces, and one with the wind off, capturing just the inertial forces. The data is

acquired using the NI-cRIO system at a sampling rate of 20kHz over a minimum of forty

cycles. Before the data is phase averaged and subtracted from inertial forces to get the phase

averaged pure aerodynamic forces, it is ﬁltered using a 3rd order Chebyshev type II digital

filter in combination with a zero phase filter which is used to reduce the influence of noise

and the natural frequencies of the test stand. The ﬁltering process, is discussed with greater

detail below. Finally, the lift, drag, and moment coefﬁcients are obtained from the phase

averaged aerodynamic forces.

4.3.1 Filtering process

The load cell used requires one end of the airfoil to be free to avoid corruption of the

measured forces by reaction forces from the opposite wall mounting. This conﬁguration

signiﬁcantly reduces the natural frequency of the setup. Therefore, for aerodynamic forces

61 measured using a load cell transducer, it is essential to ﬁlter out the natural frequency of

the full setup and high-frequency noise (associated with higher frequency modes from the

experimental setup and wind tunnel fan noise) while preserving as many harmonics of the

oscillation frequency as possible and the frequency associated with the convection of the

Dynamic Stall Vortex (DSV). The frequency associated with the convective time scale of

the DSV can be approximated using equation 4.2 where rv is the ratio of the DSV velocity

(UDSV ) to the freestream velocity (U∞), estimated to be between 0.3 and 0.5 [5,10,24,46,49].

U r U f = DSV = v ∞ (4.2) c,DSV c c

To eliminate the loads associated with the natural frequency of the system, two ﬁlters are

ultimately required: a band-stop and a low-pass ﬁlter. The band-stop ﬁlter is used to eliminate

the natural frequency of the system while the low-pass ﬁlter is used to eliminate high

frequency noise. To determine the natural frequency of the setup, a fast Fourier transform was performed on the data (using a Hann window) in order to obtain the frequency spectrum.

The ideal frequency spectrum, with no interference from the natural frequency of the setup, would include the oscillation frequency (or two times the oscillation frequency, depending

on which load component is being examined) as the largest peak and the harmonics of the

oscillation frequency, with decaying amplitudes as the frequency is increased. However,

in Figure 4.6, which shows as an example the normalized inertial frequency spectrum for

inertial normal force, Fx, (the force in the direction perpendicular to air ﬂow) this is not the

case. The largest peak is at the oscillation frequency and the amplitudes of the harmonics

initially decrease but then start to increase again. This portion of the frequency spectrum

is contaminated by vibrations near the natural frequency of the system. As the oscillation

frequency increases the affected frequency band does not change, only the magnitudes of

62 the amplitude peaks in the natural frequency band increased. This provides more evidence that these peaks are not related to the oscillation frequency but are rather due to the natural frequency of the setup.

Figure 4.6: Spectra of Fx data for the aspect ratio of three airfoils with end plates at oscillation frequencies of f = 1Hz (a), f=3Hz (b), f=3.5Hz (c)

The effect of the system’s weight on the natural frequency was also investigated by altering the test set up; the results for the inertial loads in the x-direction oscillated at a frequency of 1Hz are shown in figure 4.7. As the weight of the setup increases, the natural frequency (and therefore the contaminated band) of the setup decreases. It is important that the contaminated band does not overlap with the first few harmonics of the oscillation frequency or the convection frequency of the DSV as this would render it very difficult to filter the natural frequency of disturbances without affecting the aerodynamic forces associated with dynamic stall. The lighter the airfoil, the more beneficial is for experiments

63 since it allows more harmonics of the oscillation frequency to be preserved as well as reducing the tunnel blockage.

Figure 4.7: Effect of system weight on the inertial normal force (Fx) frequency spectrum

The cycle-to-cycle load variations are minimal for two reasons: ﬁrst, the repeatability of the motion in the redesigned experiment and second, the measured loads are integrated loads over the entire airfoil, rather than based on a using a line of pressure probes, as often done in the literature. As example, the variation of Fx aerodynamic load (lift related) in 50 cycles is observed in ﬁgure 4.8 for Reynolds number of 300,000 and k=0.05 during deep dynamic stall .

64 Figure 4.8: Cycle-to-cycle (Fx) load variations for an oscillating airfoil run

4.3.2 Dynamic Stall Results

The dynamic tests motion proﬁle for the baseline is described by α(t) = 10+10sin(ωt):

this motion results in deep dynamic stall. Figure 4.9 and Figure 4.10 show the global lift and

moment coefﬁcients (i.e. not merely sectional but including 3-D effects), respectively for the

airfoil at a Reynolds number of 300,000 and two different reduced frequencies k=0.05 and

k=0.075, which correspond to physical frequencies of 2.4Hz and 3.6Hz. During the upstroke

in both cases, the lift force increases with the angle of attack. Lift increases beyond the static

stall angle of attack due to the delay in the boundary layer separation. Then, the ejection

of vorticity through the DSV is seen in both curves with the abrupt lift augmentation. The

maximum lift coefﬁcient and lift curve slope increase as reduced frequency increases due to

the induced camber effect and stronger DSV shedding. In the moment curve, ﬁgure 4.10,

the convection of the DSV generates the moment stall due to the imbalance of pressure in

65 the upper surface of the airfoil which produces a shift in the center of pressure to trailing edge. A large negative moment peak is seen for both curves. The negative peak in moment is increased as the reduced frequency for the same reason that lift peak is increased. When the DSV leaves the airfoil and the ﬂow is fully separated, lift stall occurs. A sharp drop in lift is seen in ﬁgure 4.9.

During the downstroke, the airfoil motion reduces the angle of attack and the flow starts to reattach at the leading edge. The flow reorganizes at slower rate than the change in the angle of attack. This delay in the flow produces the hysteresis in the lift curve. Also during the reattachment, there is a pressure imbalance in the airfoil upper surface which produces a shift in the center of pressure. The center of pressure moves toward leading edge generating a positive nose up moment as it seen in figure 4.10.

The moment coefﬁcient curves during down stroke follow a similar trend to the static moment curve. The trends shown in the results for the current motion are qualitatively similar to the results in the literature [47].

66 Figure 4.9: Global lift coefﬁcient for NACA 0012 oscillating airfoil at two different reduced frequencies k=0.05 and k=0.075 at Reynolds number 300,000.

67 Figure 4.10: Global moment coefﬁcient for NACA 0012 oscillating airfoil at two different reduced frequencies k=0.05 and k=0.075 at Reynolds number 300,000.

Figure 4.11 and Figure 4.12 show lift and moment coefficients for the airfoil at three different Reynolds numbers with the same reduced frequency of k = 0.05. As the Reynolds number increases the airfoil develops higher peak suction levels and stall is delayed to a higher angle of attack, resulting in an increase in the peak lift coefficient and in the peak negative moment coefficient.

68 Figure 4.11: Global lift coefﬁcient for NACA 0012 oscillating airfoil at different Reynolds number 300,000, 500,000 and 700,000 at a reduced frequency k=0.05

69 Figure 4.12: Global moment coefﬁcient for NACA 0012 oscillating airfoil at two different Reynolds number 300,000, 500,000 and 700,000 at a reduced frequency k=0.05

70 4.4 Effect of plasma actuator installation

In Figure 4.13, the effect of the plasma actuator’s exposed electrode on the lift coefficient curve is shown. Both curves show the same trend with the same type of sharp stall at different stall angle (16◦ with clean and 15◦ with exposed electrode). When the exposed electrode is used, it creates a slight change in the leading edge shape and a small discontinuity. These changes could explain the variation in lift coefficient values and stall angle between exposed electrode and no exposed electrode case. Though its presence appears to affect the flow, the baseline cases to which the excited results are compared with were collected with the exposed electrode installed to provide the most appropriate comparison. In the dynamic case shown in figure 4.14, a slight increase in the lift peak is also seen for the airfoil with the plasma actuator installed. The reason for the observed changes is not clear at this time.

71 Figure 4.13: Lift coefﬁcient for NACA 0012 airfoil AR 2 with and without the exposed electrode. Reynolds number 500,000.

72 Figure 4.14: Lift coefﬁcient for NACA 0012 airfoil AR 2 with and without the exposed electrode. Reynolds number 300,000.and reduced frequency k=0.05

73 Chapter 5: Excitation Results and Discussion

This chapter provides excitation results in both light and deep dynamic stall in the form

of aerodynamic force coefﬁcients as well as PIV measurements. Two excitation schemes were investigated. The ﬁrst is continuous excitation during the entire oscillating cycle, which

is normally used in the literature and in GDTL laboratory. The second, a novel approach, is

targeting speciﬁc parts of the cycle with excitation. The objective of excitation in parts of

the oscillating cycle (EPOC) is to combine the beneﬁts (e.g. reduction in DSV strength, lift

hysteresis, and negative damping) of different excitation frequencies, by targeting speciﬁc

segments, during the upstroke and the downstroke. For EPOC, the excitation is locked to

the airfoil motion, so that the pulses always come at the same phase angle.

The cases selected to study the inﬂuence of NS-DBD plasma actuators are listed in the

table 5.1. They include various combinations of Reynolds numbers and reduced frequencies

for light and deep dynamic stall. The selection was limited by the load cell maximum

moment capacity and the range of experimental set up natural frequencies.

74 Reynolds number Reduced Frequency, k 300,000 0.025, 0.045, 0.05, 0.075, 0.1, 0.125 500,000 0.025, 0.045, 0.05, 0.075 700,000 0.025, 0.045, 0.05

Table 5.1: Reynolds number and reduced frequency combinations selected for excitation cases

Due to the large amount of cases explored, and to give a concise idea of the ﬁndings,

this chapter only focuses on the Reynolds number of 300,000 with a reduced frequency of

0.05 for load cell data and PIV. Other results show similar trends that are summarized in this

chapter by the case mentioned above. Details for Reynolds number of 500,000 and 700,000

can be found in the appendix A.

75 5.1 Light Dynamic Stall Regime

According to McCroskey et al. [50], the conditions for light dynamic stall occur com-

monly in helicopter applications. When light dynamic stall develops, lower values of

aerodynamic damping are more likely than in deep stall. Therefore, rotorcraft applications

are more prone to ﬂutter during light dynamic stall. To better understand and minimize

this problem, the effect of NS-DBD plasma actuators on airfoil performance during light

dynamic stall regime is explored in this section.

The differences between light dynamic stall and deep dynamic stall are established by

the duration and severity of the separation phenomenon. For light DS regime, the ﬂow

separation region size is on the order of airfoil thickness while in the deep DS regime, the

ﬂow separation region size is on the order of airfoil chord [50]. The development of the

DSV during light DS depends on Reynolds number, Mach number, reduced frequency and

motion amplitudes. In deep DS, the DSV development is the most important element during

the development of the process.

Light dynamic stall can occur for αmax = α0 + α1 slightly above the airfoil’s static stall

angle of attack. Based on this understanding, different motion amplitudes with reduced

frequency of 0.05 were tested and load-cell data collected to determine the light dynamic

stall cases for the airfoil. A representative case for light dynamic stall, in each Reynolds

number, was chosen based on the motion amplitude that produced the highest negative

damping coefﬁcient. With the selected cases, the NS-DBD actuators were tested with various excitation frequencies.

76 5.1.1 Baseline Results for Light Dynamic Stall Cases 5.1.1.1 Light Dynamic Stall Results at Reynolds number of 300,000

At Reynolds number of 300,000, the static stall angle observed was 14◦ and thus three

◦ ◦ ◦ different motion amplitudes were selected, corresponding to αmax of 15 , 16 and 17 values.

These three cases established the possible light DS motion cases for the oscillating airfoil

◦ motion as can be seen in table 5.2: here the mean angle was taken α0 = 10 following

◦ reference cases in [50] . Finally, the case αmax = 16 which is 2 degrees above the static

stall, was selected because it had a moment curve with the lowest negative damping (i.e. the

highest tendency for ﬂutter).

◦ ◦ ◦ ◦ ◦ ◦ Values for αmax = α0 + α1 10 + 5 10 + 6 10 + 7 Negative Damping Values -0.85 -2.2 -1.9

Table 5.2: Negative damping values for light dynamic stall at Reynolds number of 300,000.

77 ◦ Figure 5.1: Lift coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number= 300,000 and reduced frequency k=0.05

In ﬁgure 5.1, the motion amplitude case αmax = 15 shows the maximum lift coefﬁcient minimal hysteresis and no stall. A large hysteresis can be seen in the lift curves beyond

◦ αmax = 15 with a noticeable lift peak, which is an evidence of the strengthen of the DSV. In

◦ the the motion amplitude case αmax = 17 , the lift peak is the largest between the three cases.

In ﬁgure 5.2, the appearance of the moment stall establishes the transition from stall onset

◦ ◦ ◦ regime at the αmax = 15 case to light DS regime in the αmax = 16 case. In the αmax = 16 case, the peak moment occurs during the downstroke, this is typical for light dynamic stall as the DSV shedding is triggered by the change in airfoil direction.

78 ◦ Figure 5.2: Moment coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number = 300,000 and reduced frequency k=0.05

5.1.2 Continuous Excitation in Light DS Cases 5.1.2.1 Continuous Excitation in Light DS at Reynolds number of 300,000

To evaluate the effect of continuous excitation using the NS-DBD plasma actuator on lift, drag, and moment coefﬁcient during light DS, load-cell data was collected for multiple excitation frequencies. Results and discussion are presented for a Reynolds number of

300,000 with k = 0.05. Similar trends for lift, drag, and moment can be seen in Reynolds numbers of 500,000 and 700,000. The results for these cases are shown in the Appendix A.

In ﬁgure 5.3, a comparison of lift-coefﬁcient for baseline and different excitation Strouhal numbers are shown. During the upstroke, the baseline shows the lift augmentation and the

DSV signature. In the upstroke, the changes due to continuous excitation are primarily

79 in the reduction of peak lift. This could possibly be because the incipient ﬂow separation

and its associated free shear layer instability, is affected by the perturbations produced by

the plasma actuator. The effect of the DSV is mitigated through structures generated by

excitation. As the excitation frequency is increased, the gradual vorticity release is more

effective contributing to the reduction of the DSV strength and the ﬂow reattachment close

to leading edge. PIV results will show more details about this process.

During the downstroke, signiﬁcant change in the lift curves at different excitation

Strouhal numbers is observed because there is separation (i.e the K-H instability is present).

The effect of excitation is more pronounced at high excitation Strouhal number and its effect

on lift is quantiﬁed using lift hysteresis. This is deﬁned here as the maximum distance

between the upstroke and the downstroke of the lift curve. Lift hysteresis is important

because it offers an idea of the magnitude of the vibratory loads. As can be seen in ﬁgure 5.4,

high excitation Strouhal numbers (above Ste = 3) help reduce the lift hysteresis which causes

the abrupt change in lift during an oscillating cycle. An explanation of this effect during high

excitation frequencies is the production of smaller structures that generates a more consistent

reattachment of the ﬂow close to leading edge during the downstroke. Evidence of this can

be seen in the PIV results section, which will be presented and discussed later. Another

point to consider is that there exists an optimum excitation frequency for lift hysteresis and

it is close to 1. The reason could be that at this frequency there is a balance between the

number of structures generated that contribute to ﬂow reattachment and the time before

these structures starts to disintegrate and lose their effectiveness for reattachment.

80 Figure 5.3: Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

81 Figure 5.4: Lift hysteresis for various excitation Strouhal numbers. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

In ﬁgure 5.5, the moment coefﬁcient results for excitation at light DS are shown. During

the upstroke baseline, there exists a slight increase in the moment, product of the center of

pressure shift which is also increased with the DSV convection. This part of the moment

is intercepted by the nose up moment in the downstroke forming counterclockwise loops which contribute positively to the aerodynamic damping. The counterclockwise loops in

the moment are eliminated as the excitation frequency is increased. During downstroke the

moment coefﬁcient shows its abrupt stall when the DSV convects along the airfoil’s upper

surface. There is a reduction of peak moment after stall for the excited cases, this is good as

one of the primary objectives is to reduce the unsteady loading. As the excitation frequency

is increased, the moment peak has a tendency to decrease as shown in the ﬁgure. This

behavior could be explained by the release of vorticity generated by the actuator due to the

82 flow structures that contribute to the weakening and eventual elimination of the DSV. Also, the effective reattachment of the flow due to the flow structures generated by the excitation causes the positive moment recovery seen in the figure 5.5. Negative damping, which is generated by the moment clockwise loops of the figure 5.5, decreases as the excitation frequency increases as shown in figure 5.6 and figure 5.7. A saturation of this excitation effect at high excitation Strouhal numbers (above Ste = 3) is also seen. In summary, the reduction in the negative damping due to excitation makes the airfoil less susceptible to

ﬂutter.

83 Figure 5.5: Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

84 Figure 5.6: Negative damping for various excitation Strouhal numbers. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

Figure 5.7: Cycle damping for various excitation Strouhal numbers. Re=300,000, k=0.05, ◦ ◦ and motion: α(t) = 10 + 6 sin(ωt). 85 The drag results are shown in ﬁgure 5.8. Signiﬁcant reduction of drag is seen during the

downstroke which is part of the objective of reducing unsteady loading. The ﬂow structures

that are formed due to excitation during the downstroke help mitigate or suppress ﬂow

separation. As, the separation increases pressure drag this causes the observed reduction

in drag. Figure 5.9 shows that as the Strouhal number increases the reduction of drag is

considerable. It is also observed in the drag ﬁgure that there exists an optimum excitation

frequency for lift hysteresis and it is close to 3. The reason could be excitation at this

frequency balances the number of structures generated that contributes to ﬂow reattachment

(which mitigate the pressure drag) and the time before these structures begin to disintegrate

and lose their effectiveness for reattachment.

86 Figure 5.8: Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

87 Figure 5.9: Drag reduction for various excitation Strouhal numbers. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

In summary, for continuous excitation in light dynamic stall at the three different

Reynolds numbers, the results shows:

1. Excited cases exhibit a reduction in lift hysteresis, peak drag, and negative damping

when compared with baseline.

2. High excitation Strouhal numbers generate the most considerable beneﬁts for oscillat-

ing airfoil performance in all Reynolds numbers tested.

3. Small change in lift, drag, or moment due to continuous excitation was seeing during

the upstroke part of the oscillating cycle, only excitation during the downstroke has a

considerable effect on the airfoil performance.

88 5.1.3 EPOC in Light DS Cases

The excitation during different parts of the oscillating cycle (EPOC) was used in light

DS cases at the selected Reynolds numbers. Due to the very large amount of combinations

for EPOC, only schemes based on previous results obtained with continuous excitation were tested. Two main EPOC cases for light DS cases were used: excitation only during

the upstroke and only during the downstroke. In the following pages, the results of EPOC

excitation for Reynolds number of 300,000 are shown. For Reynolds number of 500,000,

see appendix A.

5.1.3.1 EPOC cases in Light DS at Reynolds number of 300,000. (Excitation only during the upstroke )

Ste = 0.2 Ste = 0.5 Ste = 3 Ste = 8 Ste = 13.5 EPOC upstroke G1 case G2 case G3 case G4 case G5 case

Table 5.3: EPOC cases during the upstroke (from 4◦ to 16◦) for light dynamic stall at Reynolds number of 300,000.

Shown in ﬁgures 5.10, 5.12, 5.15, the effect of excitation during the upstroke on the

airfoil’s aerodynamics is small. The excitation may be slightly affecting the DSV shedding

timing and thus, even though there is no excitation during the downstroke, there is a change

due to the alterations to the DSV. These changes are observed in the lift, drag, and moment

plots. The effect of the DSV is mitigated through structures generated by excitation, which

release part of the vorticity accumulated. None of the metrics (lift hysteresis, negative

damping or drag reduction) changed signiﬁcantly (see ﬁgures 5.11 to 5.14) because the

small effect of excitation on the ﬂow during the upstroke.

89 Figure 5.10: Phase-averaged lift coefﬁcient for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

90 Figure 5.11: Lift hysteresis for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

91 Figure 5.12: Phase-averaged moment coefﬁcient for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

92 Figure 5.13: Negative damping for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

Figure 5.14: Cycle damping for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

93 Figure 5.15: Phase-averaged drag coefﬁcient for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

94 Figure 5.16: Drag reduction for EPOC during the upstroke for different cases in table 5.3. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

5.1.3.2 EPOC cases in Light DS at Reynolds number of 300,000. (Excitation only in downstroke )

Ste = 0.2 Ste = 0.5 Ste = 3 Ste = 8 Ste = 13.5 EPOC downstroke G6 case G7 case G8 case G9 case G10 case

Table 5.4: EPOC cases during the downstroke (from 16◦ to 4◦) for light dynamic stall at Reynolds number of 300,000.

EPOC cases with excitation during the downstroke had a signiﬁcant inﬂuence on the

flow as can be seen from figure 5.17 to figure 5.23. Excited cases exhibit a reduction in lift

hysteresis, peak drag, and negative damping compared with baseline. The best lift hysteresis

95 and negative damping reduction is obtained for G8 and G9 because small scale structures established a more consistent ﬂow reattachment, which also contribute to a rapid nose-up moment recovery during the downstroke.

During these EPOC tests, the effect of EMI was larger than in the continuous excitation tests. The reason is that EPOC generates an abrupt change in excitation frequency which affects the current and voltage variation in the pulse and this effect is responsible for the

EMI.

The main conclusion was that only excitation during the downstroke has a signiﬁcant effect for light DS. The EPOC results were nearly the same as the continuous excitation cases, which means the EPOC method produced a 50% saving in the power consumption of the actuator.

96 Figure 5.17: Phase-averaged lift coefﬁcient for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

97 Figure 5.18: Lift hysteresis for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

98 Figure 5.19: Phase-averaged moment coefﬁcient for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

99 Figure 5.20: Negative damping for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

Figure 5.21: Cycle damping for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

100 Figure 5.22: Phase-averaged drag coefﬁcient for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

101 Figure 5.23: Drag reduction for EPOC during the downstroke for different cases in table 5.4. Re=300,000, k=0.05, and motion: α(t) = 10◦ + 6◦sin(ωt).

5.1.4 PIV results in Light Dynamic Stall regime

This section details the baseline PIV results for light dynamic stall. PIV experiments phase locked to the airfoil motion were performed at Reynolds number of 300,000 with a reduced frequency of 0.075. This reduced frequency was chosen to match the motion to the laser frequency. The motion for light dynamic stall was α(t) = 10◦ + 6◦sin(ωt). Images in eleven phases were acquired and the following description only focuses on the most relevant phases.

Figures 5.24 and 5.25 show the baseline swirling strength results for light dynamic stall. During the upstroke, the ﬂow remains attached in angle of attack (α = 14.4◦ ) above the static stall angle of attack (α = 14◦). At α = 15.3◦ (upstroke), it can be seen how an incipient reversed ﬂow begins at the airfoil’s trailing edge. When α = 15.9◦, vorticity

102 accumulated at the leading edge is released. When ﬂow separation eventually occurs over a signiﬁcant part of the airfoil, the separation size is on the order of the airfoil thickness.

Despite the fact that the figure does not show a well-defined DSV, its effect is evidenced in the small lift peak and the large moment drop observed in figures 5.28 and 5.29. A possible explanation is the stochastic nature of DS process that makes that DSV is not capture by

PIV motion locked images. During the downstroke, at α = 15.5◦ and α = 14.7◦, a fully separated flow region forms over the airfoil as can be seen in figure 5.25. As the angle of attack is reduced during the downstroke, the flow starts to reattach at the leading edge as can be seen at α = 12.8◦.

103 Figure 5.24: Baseline case. Swirling strength for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt)

104 Figure 5.25: Baseline case. Streamwise mean velocity for phase locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt)

5.1.4.1 Light dynamic stall excited cases

The excitation results for light dynamic stall are shown in ﬁgures 5.26 and 5.27. As shown in ﬁgure 5.26, all the excited cases show the appearance of coherent structures, the number of which is proportional to the Strouhal number. At low Strouhal number ( around

105 Ste = 0.5), the vortical structures created at the leading edge are large, and in contrast, at higher Strouhal numbers (above Ste = 3) the structures created by the effect of excitation are smaller.

PIV data and load-cell data shown in ﬁgures 5.26, 5.27, 5.28 and 5.29 complement each other very well. During the upstroke, load-cell data at the representative phase 15.8◦ in

figure 5.28 shows that there is a small effect (a few percent increase in peak lift) during the upstroke due to excitation. The same phase in PIV data shows that excitation acts over the separated flow region close to leading edge as shown in figure 5.27 and produce multiple structures during the upstroke that release the vorticity accumulated at the leading edge, see figure 5.26. The production of these structures close to leading edge generates a small increase in lift due to flow reattachment caused along the airfoil.

During the downstroke, the instability of the shear layer produced by flow separation is excited by the plasma actuator, generating coherent structures from the leading edge as can be seen in figure 5.26. At low Ste, large coherent structures are formed while at high Ste, small coherent structures appear. As seen in figure 5.28, an effective lift recovery during the downstroke is obtained because of the coherent structures created by excitation. At Ste above 1, the lift recovery effect generated by increasingly smaller structures is in invariant due to their close spacing and the small order of flow separation found in light DS. The close spacing in structures guarantees the same number of structures passing over the leading edge which maintain the flow entrainment on this small region of flow separation. If the separated flow region were larger, the effect of the relatively small structures would not be effective. The lift recovery produced by excitation contributes to the reduction in lift hysteresis as shown in previous light DS results.

106 In figure 5.29, moment curves are shown. During the upstroke, the reduction in moment is due to effective flow reattachment of a small separated region (size of the airfoil thickness order for light DS). During the downstroke, the peak moment magnitude reduction is more noticeable as the Strouhal number increases, due to the DSV mitigation through structures generated that release the vorticity accumulated. This mitigation reduced the DSV strength and its effect on the center of pressure shift. In addition, these structures generate a more consistent reattachment as seen in figure 5.27. The center of pressure is shifted towards leading edge, creating the force imbalance with respect to the quarter chord, contributing to the nose up moment and reducing the negative damping in the moment curves.

In the drag results, shown in figure 5.30, a reduction in drag is seen during the oscillating cycle. The flow structures formation seen in figure 5.26 during the downstroke mitigates or suppress flow separation, a main contributor to increase pressure drag.

Additionally, the excitation appears to be changing the separation characteristics as it is observed in ﬁgure 5.27. The separation region size is reduced by excitation at low Ste and it becomes trailing edge (rather than leading edge) separation in the high Ste cases.

107 Figure 5.26: Excitation cases. Swirling strength for phase locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt)

108 Figure 5.27: Excitation cases. Streamwise velocity for phase locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 6◦sin(ωt)

109 Figure 5.28: Phase-averaged lift coefﬁcient for light DS at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 6◦sin(ωt).

110 Figure 5.29: Phase-averaged moment coefﬁcient for light DS at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 6◦sin(ωt).

111 Figure 5.30: Phase-averaged drag coefﬁcient for light DS at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 6◦sin(ωt).

112 5.2 Deep Dynamic Stall Regime

5.2.1 Continuous Excitation in Deep DS Cases 5.2.1.1 Continuous Excitation in Deep DS at Reynolds number of 300,000

The effect of continuous excitation using NS-DBD plasma actuator on lift, drag, and

moment coefﬁcient during deep DS was evaluated. To do this, load-cell data was collected at various excitation frequencies during each experiment. Results and discussion are presented

for a Reynolds number of 300,000 with k = 0.05. Similar trends for lift, drag and moment

can be seen for Reynolds numbers of 500,000 and 700,000. The results for these cases are

shown in the appendix A.

In ﬁgure 5.31, the effect of excitation with different frequencies on lift is shown. Both

stages, the upstroke and the downstroke, of deep dynamic stall experienced the effect.

During the upstroke, the lift augmentation and its peak, a consequence of DSV evolution, is

diminished by the excitation. Strouhal numbers from 3 to 8 generated the best reduction

in DSV vortex strength as determined by the peak lift. The mechanism of this reduction is

explained using PIV results presented later. During the downstroke, structures generated by

the plasma actuator reattach the ﬂow, which enables lift to be recovered. Low excitation

Strouhal numbers are more effective for this recovery than high excitation numbers. A cause

is the effectiveness of large coherent structures generated at low Strouhal numbers to reattach

the ﬂow during the downstroke similar to having multiple DSVs in the downstroke. This is

different from light dynamic stall because of the separation size. In addition, ﬁgure 5.32

shows a summary of the excitation effect on lift using lift hysteresis. The best lift hysteresis

reduction is close to an excitation Strouhal number of 1. When excitation Strouhal numbers

increase above Ste = 1, the effect on lift hysteresis reduction. This behavior could be caused

by the loss of effectiveness for ﬂow reattachment in the increasingly smaller structures. In

113 addition, the high excitation Ste number cases outperform the low Ste late in the downstroke.

A possible reason is that for high Ste, the small structures formed disintegrate faster than

the large structures produced at low Ste, so small structures maintain their effect over in a

smaller portion of the airfoil upper surface compared with large ones.

The effect of continuous excitation on the moment curve is seen in ﬁgure 5.33. In deep

DS, the peak moment occurs during the upstroke as observed in the baseline. During the

upstroke, the actuator generates a reduction in negative peak moment which is a consequence

of the DSV strength reduction also seen in lift. During the downstroke, the effect of excitation

creates an increase in the nose-up moment coefﬁcient. This increase in nose-up moment is

more effective when the Strouhal number is increased, due to the increasingly large number

of structures generated the center of pressure is shifted towards the leading edge due to

ﬂow reattachment in that region. The combination of these effects during the upstroke and

downstroke has an effect on the clockwise moment loops related to negative damping. In

ﬁgures 5.34 and 5.35, the negative damping is reduced and the cycle-averaged-damping

becomes more positive as the excitation Strouhal number is increased, assuring that the

airfoil is less and less prone to ﬂutter. While there is an optimum excitation frequency

for increasing (algebraically) the negative damping, when the whole cycle is accounted

for, the effect of the moment recovery (and the change in the counter clockwise moment

loops) causes the trend in overall damping to be monotonic. Additionally, the baseline case

outperforms the low frequency excitation cases early in the downstroke. A possible reason is

that the large structures generated at low Ste delay the natural center of pressure shift towards

leading observed in the baseline during their convection along the upper surface. These

structures act as other DSVs during the downstroke. This behavior at low Ste increases the

clockwise loop size having a detrimental effect on the negative damping coefﬁcient. In light

114 DS, this effect at low Ste is not observed due to the DSV timing because part of the DSV convection occurs in the downstroke. Any excitation effect on the DSV in light DS affects the downstroke part of the cycle. A reduction in the DSV strength, reduces the downstroke moment peak in light DS.

The effect of continuous excitation on drag is seen from ﬁgures 5.36 to 5.38. During the upstroke, drag is reduced by the effect of excitation. An explanation is that excitation diminishes the strength of the DSV which contributes to the generation of pressure drag. A reduction of the DSV strength limits its effect on drag. Figure 5.37 shows that the best drag reduction occurs between Ste = 1 and Ste = 6. Above Ste = 6, the effect of excitation on drag is attenuated as the DSV strength is recovered as evidenced in the lift curves. During the downstroke, despite the detrimental effect of excitation on drag in this stage, between

Ste = 1 and Ste = 6 the negative effect is not as signiﬁcant. This may be due to the structures formed during excitation reattaching the ﬂow and thereby reducing the the pressure drag over the airfoil.

PIV results will show more details about the ﬂow physics during excitation and will support the aforementioned explanations.

In summary, continuous excitation in deep dynamic stall at the three different Reynolds numbers shows,

1. Signiﬁcant change in lift, drag, or moment due to continuous excitation was seen

during both parts of the oscillating cycle. The mechanism of excitation reducing the

DSV strength during the upstroke is not well understood from load cell data but can

be explained using PIV results, which will be shown and discussed later.

2. Excited cases exhibit a reduction in lift hysteresis, peak drag, and negative damping

compared with baseline.

115 3. Low excitation Strouhal numbers (close to 1) beneﬁt the lift hysteresis reduction in all

Reynolds numbers tested.

4. Excitation at high Strouhal numbers generates the most considerable beneﬁts for

negative damping at all Reynolds numbers tested.

5. Moderate excitation Strouhal numbers (Ste = 1 − 6) contribute to drag reduction

during the oscillating cycle of the airfoil.

6. The control with NS-DBD is saturated at high values of the excitation frequency due

to the limited effect of the structures on the ﬂow reattachment generated by their

disintegration during their passing over the airfoil.

116 Figure 5.31: Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

117 Figure 5.32: Lift hysteresis for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

118 Figure 5.33: Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

119 Figure 5.34: Negative damping for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Figure 5.35: Cycle damping ffor various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

120 Figure 5.36: Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

121 Figure 5.37: Drag reduction during the upstroke for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Figure 5.38: Drag reduction during the downstroke for various excitation Strouhal numbers for Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

122 5.2.2 EPOC in Deep DS Cases

EPOC excitation was used in deep DS for Reynolds numbers of 300,000 and 500,000.

Different schemes were used during various parts of the oscillating cycle to attain the beneﬁts of reducing lift hysteresis, drag and negative damping. Due to the very large number of possible combinations for EPOC, only schemes based on previous results obtained with continuous excitation were tested.

5.2.2.1 EPOC cases in Deep DS at Reynolds number of 300,000.

For a Reynolds number of 300,000 and reduced frequency of k = 0.05, the following schemes were used. A summary of the results is given in the next paragraph. Only EPOC cases which include excitation in both the upstroke and the downstroke are detailed.

1. EPOC during the upstroke : The excitation was implemented during the upstroke part

of the cycle. Low, moderate, and high excitation frequencies were tested. The effect

of excitation on the upstroke for deep DS is seen in the reduction of the DSV strength.

This reduction follows the trends found in continuous excitation during the upstroke.

2. EPOC during the downstroke: The excitation was implemented during the downstroke

part of the cycle. Low, moderate, and high excitation frequencies were tested. The

effect of excitation in the downstroke for deep DS is seen on the lift recovery due

to ﬂow reattachment, negative damping, and drag reduction. The reduction of this

strength follows the trends found in continuous excitation during the downstroke.

3. EPOC in the upstroke and the downstroke to combine the beneﬁts seen during the

previous test and with continuous excitation, EPOC in the upstroke and the downstroke

123 with different excitation frequencies were performed. Two representative cases are

detailed in table 5.5.

Upstroke Downstroke Downstroke Ste = 3 Ste = 0.5 Ste = 13.52 Case E1. Two portions. 14◦ - 20◦ 20◦ - 0◦ N/A Case E2. Three portions. 14◦ - 20◦ 20◦ - 15◦ 15◦ - 0◦

Table 5.5: EPOC cases for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

The cases in table 5.5 used different frequencies at different parts of the upstroke and the

downstroke. The selection of the parts and the frequencies was based on the results of the

continuous excitation approach. For case E1, a combination of two frequencies at different

parts of the cycle was used. The excitation number Ste = 3 was used during the upstroke

part where the DSV evolves to obtain a considerable DSV strength reduction based on the

continuous excitation results. Ste = 0.5 produces the best ﬂow reattachment in most of the

downstroke as seen for continuous excitation, contributing to lift hysteresis reduction. For

case E2, an additional frequency was used in the downstroke to improve lift recovery as

seen in continuous excitation cases. Figure 5.39 and 5.40 shows that both cases achieved

a lift hysteresis reduction, for the case E2 the second part of excitation does not show the

improvement expected, possibly due to for the timing of the excitation. Although the lift

hysteresis reduction goal is reached, drag reduction and negative damping are compromised

under theses EPOC schemes as can be seen from ﬁgures 5.41 to 5.46.The reason for the

signiﬁcant decrease in damping is that EPOC is destroying the counterclockwise loop.

124 It can be concluded that EPOC schemes due to the vast number of frequency combinations and timing, demand an optimization approach that is beyond the focus of this dissertation. This is part of the suggested future work for control in DS.

Similar to EPOC tests in light DS, EMI effect during these tests was larger than in continuous excitation tests.

Figure 5.39: Phase-averaged lift coefﬁcient for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

125 Figure 5.40: Lift hysteresis for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

126 Figure 5.41: Phase-averaged moment coefﬁcient for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

127 Figure 5.42: Negative damping for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

Figure 5.43: Cycle-averaged damping for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

128 Figure 5.44: Phase-averaged drag coefﬁcient for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

129 Figure 5.45: Drag reduction for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

Figure 5.46: Drag reduction for deep dynamic stall at Re=300,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt). EPOC cases in table 5.5

130 5.2.3 PIV results in Deep DS regime 5.2.3.1 Deep dynamic stall baseline results

The PIV baseline results for deep dynamic stall are shown in this section. Phased-locked

PIV experiments were performed at Reynolds number of 300,000 with a reduced frequency

of 0.075. This reduced frequency was chosen to match the motion to the laser frequency.

The motion for deep dynamic stall was α(t) = 10◦ + 10◦sin(ωt). PIV images in eleven

phases were acquired and the following description only focuses on the most relevant phases.

The baseline results show the evolution of DS during the oscillating cycle. Figures

5.47 and 5.48 show swirling strength and mean streamwise velocity in several angle of

attack cases during the upstroke and the downstroke. During the upstroke, the ﬂow remains

attached to an angle of attack (α = 14.5◦ ) above the static stall angle of attack (α = 14◦).

At α = 14.5◦ (the upstroke), the ﬂow remains attached and it has been mentioned in the

literature that circulation is shed into the wake at the trailing edge causing a delay of

separation due to the reduction of the adverse pressure gradient [9, 38]. At α = 17.8◦, vorticity accumulated at the leading edge is released when ﬂow separation starts to occur.

After this event, a shear layer is formed and rolls up into the DSV. At α = 19.2◦, during the

upstroke, the DSV convects downstream over the upper surface of the airfoil during upstroke

and its vortex pair at the trailing edge appears. During the downstroke, at α = 18.9◦ and

α = 17.5◦, a fully separated ﬂow region is seen over the airfoil. As the angle of attack

is reduced, the ﬂow starts to reattach at the leading edge and reorganized over the upper

surface as can be seen at α = 14.2◦.

131 Figure 5.47: Baseline case. Swirling strength for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt)

132 Figure 5.48: Baseline case. Mean streamwise velocity for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt)

5.2.3.2 Deep dynamic stall excited cases

The excitation results for deep dynamic stall are shown in ﬁgures 5.49 and 5.50. As seen in ﬁgure 5.49, all the excited cases show the appearance of coherent structures in number proportional to the Strouhal number. Their coherence diminishes as they move downstream

133 over the upper surface of the airfoil. At low Strouhal number (around Ste = 0.5), the vortical structures created at the leading edge maintains their coherence along the airfoil upper surface and seem to be phase-locked to the structures generated at the trailing edge. At high Strouhal number (around Ste = 8), the structures created by the effect of excitation are smaller and less coherent than the ones generated by low excitation frequencies.

The relationship between PIV results and load cell results can be established based on

ﬁgures 5.49, 5.50, 5.51 and 5.52. During the upstroke, load cell results at the representative phase 19.2◦ shows a reduction of DSV strength for the excitation cases as can be seen in

figure 5.51. The same phase in PIV results shows that excitation acts over the separated flow region close to leading edge as shown in figure 5.50 and produces multiple structures during the upstroke that release the vorticity accumulated at the leading edge, see figure 5.49. This controlled release of vorticity diminishes the strength of the DSV in the upstroke.

During the downstroke, the instability in shear layer produced by ﬂow separation is excited by the plasma actuator generating coherent structures from the leading edge as can be seen in ﬁgure 5.49. At low Ste, large coherent structures are formed while at high Ste, small, closely spaced coherent structures appear. The actuator does not control the structure size, but rather the spacing. The structure spacing limits how much they grow. Closely spaced structures do not grow as much as structures that are spaced more widely.

As seen in figure 5.51, at low Ste, a more effective lift recovery during the downstroke is obtained because of the large-scale structures. This can be explained by the average size of the flow attachment region generated by large-scale structures and their persistence over the upper surface of the airfoil. At high Ste, the flow reattachment effect along the airfoil generated by small structures is not as persistent as the one produced by large structures because small structures disintegrate faster. With the lift recovery produced by excitation, a

134 reduction in lift hysteresis is achieved as shown in previous results. In contrast, for light DS,

the smaller structures still have sufﬁcient entrainment capability to reattach the separation,

in the more severe DS separation, they lack that ability thus, the structures need to be large

enough to entrain ﬂow, yet closely spaced enough to maintain consistent reattachment.

For the moment curves in ﬁgure 5.52, during the upstroke the reduction in peak negative

moment is due to diminished DSV strength through the vorticity release generated by

excitation as explained for lift. During the downstroke, a nose up moment recovery is more

noticeable as the Strouhal number increases. An explanation (see in ﬁgure 5.49) where the

Strouhal number is higher, the number of structures close to the leading edge is augmented which generate a more consistent ﬂow attachment in this region (see ﬁgure 5.50) . The

negative pressure in the region close to leading edge creates the force imbalance with respect

to the quarter chord that contributes to the nose up moment. This effect also helps to reduce

the negative damping in the moment curves.

The effect of excitation during the upstroke reduces the overall drag (see ﬁgure 5.53)

due to decrease in the strength of the DSV, as seen in ﬁgure 5.49. During the downstroke,

although the effect of excitation on drag is detrimental compared to drag at the baseline,

there is reduction due to structures formed that reattach the ﬂow momentarily and reduce

the airfoil’s pressure drag.

135 Figure 5.49: Excitation cases. Swirling strength for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt)

136 Figure 5.50: Excitation cases. Mean streamwise velocity, u, for phase-locked PIV. Re=300,000, k=0.075, and motion:α(t) = 10◦ + 10◦sin(ωt)

137 Figure 5.51: Phase-averaged lift coefﬁcient for deep dynamic stall at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 10◦sin(ωt).

138 Figure 5.52: Phase-averaged moment coefﬁcient for deep dynamic stall at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 10◦sin(ωt).

139 Figure 5.53: Phase-averaged drag coefﬁcient for deep dynamic stall at Re=300,000, k=0.075, and motion: α(t) = 10◦ + 10◦sin(ωt).

140 Chapter 6: Conclusions and future work

Dynamic stall (DS) is a time-dependent ﬂow separation and stall phenomenon that

occurs when a lifting surface undergoes rapid pitching motion. One of the main adverse

characteristics of DS, especially in helicopters, is the imposition of high torsional and vibratory loads on the rotor. This can lead to structural fatigue and eventual failure. Attempts

to reduce or eliminate these adverse consequences have been made using both passive and

active ﬂow control.

Passive ﬂow control devices are disadvantageous because they can add weight, are

normally ineffective at off-design operating conditions, and could become a source of noise

and vibration. Active ﬂow control, primarily using momentum-based control devices, has

shown promising results but is unable to sustain control efﬁcacy at high speeds. NS-DBD

plasma actuators produce localized thermal perturbations to excite and control instabilities

in the ﬂow (instead of adding momentum) thus allowing them to maintain control efﬁcacy

in high-speed, high Reynolds number ﬂows. Additionally, they minimally alter the rotor

blade geometry, thereby avoiding the detriments of passive ﬂow control devices.

Initial work using NS-DBD plasma actuators to better understand DS ﬂow physics and

its control had been carried out in Ohio State’s Gas Dynamics and Turbulence Laboratory.

While promising results had been obtained, the experimental setup had issues related to the

repeatability of the motion, the synchronization of pressure and encoder signals, and high

141 solid blockage (i.e. test-article to wind-tunnel area ratio). The aerodynamic coefﬁcients

had also been calculated from data acquired using 35 static pressure taps located along the

center chord line, effectively ignoring three-dimensional effects in the ﬂow.

To address these issues, the DS experimental setup has been upgraded. Solid blockage was reduced by reducing the airfoil chord and aspect ratio. Endplates were added to prevent

tip-effects and interaction with the wall boundary layer from altering the results. The

motion repeatability and synchronization issues were addressed by the use of a direct drive

servomotor and a real-time control system to pitch the airfoil. A load cell transducer was

installed to allow the aerodynamic forces to be measured directly, including the effects of

any potential three-dimensionality in the ﬂow.

The upgraded experimental setup showed less uncertainty in the data due to the increased

repeatability of the airfoil motion and data/motion synchronization. The static aerodynamic

coefﬁcients were documented to validate the new experimental arrangement against literature.

The detailed baseline (i.e. no control) dynamic stall results were also presented and discussed.

It was found that, in addition to a wind-off subtraction to eliminate the measured inertial

forces, the natural frequencies present within the experimental arrangement necessitated

spectral ﬁltering to isolate the aerodynamic forces. A characterization of the baseline

dynamic stall results for Reynolds numbers 300,000, 500,000, and 700,000 was performed.

The results showed that the trends for the DS aerodynamic coefﬁcients are similar to results

available in the literature.

After the baseline validation, a series of tests with continuous excitation and excitation

in parts of oscillating cycle (EPOC) was performed. The tests were divided into light and

deep DS cases in combination with Reynolds numbers of 300,000, 500,000, and 700,000

and reduced frequencies of 0.025, 0.05, and 0.075. For continuous excitation and EPOC,

142 only results for a reduced frequency of 0.05 were discussed in this dissertation. For PIV data, only results at Re=300,000 and a reduced frequency of 0.075 were discussed.

Load cell and PIV results for deep and light stall showed a signiﬁcant change in lift, drag, and moment due to continuous excitation during the oscillating cycle. Excited cases exhibited signiﬁcant reductions in lift hysteresis, peak drag, and negative damping compared to the baseline cases. At low Ste, large coherent structures were formed while at high

Ste, small coherent structures appeared, with very different development, entrainment, and disintegration characteristics.

For light dynamic stall, high excitation Strouhal numbers generated the most considerable beneﬁts for oscillating airfoil performance in all Reynolds numbers tested. Small change in lift, drag, or moment due to continuous excitation was observed during the upstroke part of the oscillating cycle, only excitation during the downstroke had a considerable effect on the airfoil performance.

For deep dynamic stall, low excitation Strouhal numbers (close to 1) beneﬁted the lift hysteresis reduction in all Reynolds numbers tested. High excitation Strouhal numbers generated the most considerable beneﬁts for negative damping in all Reynolds numbers tested. Moderate excitation Strouhal numbers (Ste = 1 − 6) contributed to drag reduction during the oscillating cycle of the airfoil.

EPOC for light and deep dynamic stall showed that it is possible to improve a particular beneﬁt (reduction in lift hysteresis, in negative damping or in drag ) with an speciﬁc excitation timing during the oscillating cycle. A combination of different excitation schemes during EPOC could be used to achieve a better control of airfoil performance depending on the application requirements.

143 6.1 Future work

A list of activities for future work is shown below.

To expand the capabilities of the current experimental set up to further increase the

Reynolds number and reduced frequency and to address the issue of the natural frequency

of the system possibly generated by the servo controller. In addition, to explore the use of

other motion proﬁles for applications like wind turbines.

To upgrade the current airfoil to a composite airfoil with a series of pressure transducers

inside that in combination with load cell that can provide more detailed data on the dynamic

stall process during the use of the NS-DBD plasma actuator.

To study the mechanism of DSV strength reduction by the plasma actuator during the

upstroke part of the cycle in an oscillating airfoil.

To study 3D dynamic stall vortex evolution and the effect of NS-DBD plasma using

stereo PIV along the airfoil’s span.

To explore the extremely large parameter space of excitation over parts of the oscillation

(EPOC) approach at different timing in the cycle using experimental and computational

tools.

144 Appendix A: Additional results

Additional results for baseline and excitation cases in Reynolds numbers 500,000 and

700,000 are presented in this section.

In the section A.1, the baseline results for light DS cases for Reynolds numbers 500,000

and 700,000 are detailed.

In the section A.2, the results for continuous excitation cases in light DS cases for

Reynolds numbers 500,000 and 700,000 are detailed.

In the section A.3, the results using Excitation in Parts of Oscillating Cycle (EPOC) in

light DS for a Reynolds number of 500,000 are presented and discussed.

In the section A.4, the results for continuous excitation cases in Deep DS cases for

Reynolds numbers 500,000 and 700,000 are detailed including their metrics.

In the section A.5, the results using Excitation in Parts of Oscillating Cycle (EPOC) in

deep DS for a Reynolds number of 500,000 are presented and discussed.

145 A.1 Baseline for Light DS Cases

A.1.1 Light Dynamic Stall at Reynolds number of 500,000

At Reynolds number of 500,000, the static stall angle observed was 15◦ and thus three

◦ ◦ ◦ different motion amplitudes were selected corresponding to αmax of 16 , 17 , and 18 values.

The 17◦ case which is 2 degrees above the static stall was selected for detailed measurements

because it had a moment curve with the highest negative damping.

◦ ◦ ◦ ◦ ◦ ◦ Values for αmax = α0 + α1 10 + 6 10 + 7 10 + 8 Negative Damping Values -1.54 -5.71 -4.15

Table A.1: Negative Damping Values for Light Dynamic Stall at Reynolds Number of 500,000

146 ◦ Figure A.1: Lift coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number = 500,000 and reduced frequency k=0.05

◦ In ﬁgure A.1 large hysteresis in lift curves is observed after αmax = 16 and there is not a clear lift peak signature as in Reynolds number of 300,000 , which is possibly due to the dominance of the low oscillation frequency effect over the DSV effect. In this case, a low reduced frequency at this Reynolds number produces a low effect of unsteadiness which reduces the DSV signature compared to Re = 300,000. However, the expected signiﬁcant

◦ lift augmentation is noticeable. In ﬁgure A.2, the abrupt moment stall at αmax = 17 is the signature of the light DS regime.

147 ◦ Figure A.2: Moment coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number = 500,000 and reduced frequency k=0.05

A.1.2 Light DS at Reynolds number of 700,000

At Reynolds number of 700,000, the static stall angle observed was 15◦ and thus three

◦ ◦ ◦ different motion amplitude cases were selected corresponding to αmax of 16 , 17 and 18 values. The 17◦ case which is 2 degrees above the static stall was selected because it had a

moment curve with the highest negative damping.

◦ ◦ ◦ ◦ ◦ ◦ Values for αmax = α0 + α1 10 + 6 10 + 7 10 + 8 Negative Damping Values -3.35 -4.39 -2.44

Table A.2: Negative Damping Values for Light Dynamic Stall at Reynolds Number of 700,000

148 ◦ Figure A.3: Lift coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number = 700,000 and reduced frequency k=0.05

◦ In figure A.3 large hysteresis in lift curves is observed after αmax = 16 and there is no noticeable lift peak signature as in Reynolds number of 300,000, possibly due to the influence low oscillation frequency effect over DSV effect. In this case, a low reduced frequency at this Reynolds number produces a low effect of unsteadiness then the DSV signature is not as strong as observed in Re = 300,000. However, the expected significant lift

◦ augmentation is clear. In ﬁgure A.4, the abrupt moment stall at αmax = 17 is the signature of the light DS regime.

149 ◦ Figure A.4: Moment coefﬁcient comparison between different motion amplitudes, 10 + α1 . Reynolds number = 700,000 and reduced frequency k=0.05

150 A.2 Continuous Excitation in Light DS Cases

A.2.1 Continuous Excitation in Light DS at Reynolds number of 500,000

Similar trends for lift, drag, and moment as seen in at a Reynolds number of 300,000 are evidenced during excited cases in figures from A.5 to A.11. Similarities in this Reynolds number with Re=300,000 are: Excited cases exhibit a reduction in lift hysteresis, peak drag, and negative damping when compared with baseline. High excitation Strouhal numbers generate the most considerable benefits for oscillating airfoil performance in all Reynolds numbers tested. Small change in lift, drag, or moment due to continuous excitation was seeing during the upstroke part of the oscillating cycle, only excitation during the downstroke has a considerable effect on the airfoil performance. No significant difference in the excited cases trends at 300,000 and 500,000 were seen.

151 Figure A.5: Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

152 Figure A.6: Lift hysteresis for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

153 Figure A.7: Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

154 Figure A.8: Negative damping for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

Figure A.9: Cycle damping for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt). 155 Figure A.10: Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

156 Figure A.11: Drag reduction for various excitation Strouhal numbers. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

A.2.2 Continuous Excitation in Light DS at Reynolds number of 700,000

Similar trends for lift, drag and moment as seen in Reynolds numbers of 300,000 are observed during excited cases in figures from A.12 to A.18. Similarities in this Reynolds number with Re=300,000 are: Excited cases exhibit a reduction in lift hysteresis, peak drag, and negative damping when compared with baseline. High excitation Strouhal numbers generate the most considerable benefits for oscillating airfoil performance in all Reynolds numbers tested. Small, but statistically significant, changes in lift, drag or moment due to continuous excitation were seeing during the upstroke part of the oscillating cycle, only excitation during the downstroke has a considerable effect on the airfoil performance. A small difference in the excited cases trends between 300,000 and 700,000 is in the lift

157 hysteresis. There is a continued and slight downward trend with increasing excitation frequency in contrast to what was seen in the Re 300,000 results. This is possibly due to more intense vorticity release at Re=700,000 during the excitation used on weaker DSV.

Figure A.12: Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

158 Figure A.13: Lift hysteresis for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

159 Figure A.14: Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

160 Figure A.15: Negative damping for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

Figure A.16: Cycle damping for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt). 161 Figure A.17: Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

162 Figure A.18: Drag reduction for various excitation Strouhal numbers. Re=700,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

163 A.3 EPOC in Light DS Cases

A.3.1 EPOC cases in Light DS at Reynolds number of 500,000.

Upstroke Downstroke Ste = 3 Ste = 8 L5 case N/A 17◦ - 3◦ L6 case 14◦ - 17◦ 17◦ - 3◦

Table A.3: EPOC cases during the upstroke for light dynamic stall at Reynolds number of 500,000.

EPOC in both cases L5 and L6 reduce lift hysteresis, peak drag, and negative damping

compared with the baseline. The L6 case produces the best reduction of negative damping

as can be seen in ﬁgure A.22. The reason could be the EPOC timing for L6 case where

the effect of excitation during last part of the upstroke generates structures that reach the

downstroke immediately as it begins.

164 Figure A.19: Phase-averaged lift coefﬁcient for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

165 Figure A.20: Lift hysteresis for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

166 Figure A.21: Phase-averaged moment coefﬁcient for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

167 Figure A.22: Negative damping for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

Figure A.23: Cycle damping for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

168 Figure A.24: Phase-averaged drag coefﬁcient for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

169 Figure A.25: Drag reduction for EPOC during the upstroke for different cases. Re=500,000, k=0.05, and motion: α(t) = 10◦ + 7◦sin(ωt).

170 A.4 Continuous Excitation in Deep DS Cases

A.4.1 Continuous Excitation in Deep DS at Reynolds number of 500,000

Similar trends for lift, drag, and moment as seen in Reynolds numbers of 300,000 are

evidenced during excited cases in ﬁgures from A.26 to A.33. In summary: signiﬁcant change

in lift, drag, or moment due to continuous excitation was seen during both the upstroke and

the downstroke. Excited cases exhibit a reduction in lift hysteresis, peak drag, and negative

damping compared with baseline. Low excitation Strouhal numbers (close to 1) beneﬁt the

lift hysteresis reduction in all Reynolds numbers tested. High excitation Strouhal numbers

generates the most considerable beneﬁts for negative damping in all Reynolds numbers

tested. Moderate excitation Strouhal numbers (Ste = 1 − 6) contribute to drag reduction

during the oscillating cycle of the airfoil.

A difference in the excited cases trends at 300,000 and 500,000 were seen in the drag

reduction. There is a negative effect at low frequencies during the upstroke. This is possibly

due to the pressure drag generated by large structures at low excitation Strouhal numbers.

The effect of low excitation on drag surpasses the values that DSV can generate for this

case. In contrast, at Re=300,000, the effect of the DSV on drag prevail over any other effect

generated by structures due to the DSV strength observed.

171 Figure A.26: Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

172 Figure A.27: Lift hysteresis for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

173 Figure A.28: Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

174 Figure A.29: Negative damping for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Figure A.30: Cycle damping for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

175 Figure A.31: Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

176 Figure A.32: Drag reduction during the upstroke for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Figure A.33: Drag reduction during the downstroke for various excitation Strouhal numbers for Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

177 A.4.2 Continuous Excitation in Deep DS at Reynolds number of 700,000

Similar trends for lift, drag, and moment as seen for a Reynolds number of 300,000 are

observed during excited cases in ﬁgures from A.34 to A.40. In summary: signiﬁcant changes

in lift, drag, or moment due to continuous excitation were seen during the upstroke and the

downstroke. Excited cases exhibit a reduction in lift hysteresis, peak drag, and negative

damping compared with baseline. Low excitation Strouhal numbers (close to 1) beneﬁt the

lift hysteresis reduction at all Reynolds numbers tested. High excitation Strouhal numbers

generate the most considerable beneﬁts for negative damping at all Reynolds numbers tested.

Moderate excitation Strouhal numbers (Ste = 1 − 6) contribute to drag reduction during the

oscillating cycle of the airfoil. At a Reynolds number of 700,000 there is evidence of the

inﬂuence of the natural frequency issue that reduces the number of harmonics available for

the reconstruction of the aerodynamic force curves. As an example in the moment curve the

three distinctive loops are not seen in any of the cases. However, the comparison between

baseline and excited cases is done under the same (ﬁltered) conditions.

A difference in the excited case trends at 300,000 and 700,000 was seen in the drag

reduction. There is a negative effect at low frequencies during the upstroke. This is possibly

due to the pressure drag generated by large structures at low excitation Strouhal numbers.

The effect of low Strouhal number excitation on drag surpasses the values that the DSV can

generate for this case. In contrast, at Re=300,000, the effect of the DSV on drag prevail over

any other effect generated by structures due to the DSV strength observed.

178 Figure A.34: Phase-averaged lift coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

179 Figure A.35: Lift hysteresis for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

180 Figure A.36: Phase-averaged moment coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

181 Figure A.37: Negative damping for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Figure A.38: Cycle damping for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

182 Figure A.39: Phase-averaged drag coefﬁcient for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

183 Figure A.40: Drag reduction for various excitation Strouhal numbers for Re=700,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

184 A.5 EPOC in Deep DS Cases

A.5.1 EPOC cases in Deep DS at Reynolds number of 500,000.

Upstroke Downstroke Downstroke Ste = 3 Ste = 0.5 Ste = 8 D1 case. Two portions. 15◦ - 20◦ 20◦ - 0◦ N/A D2 case. Three portions. 15◦ - 20◦ 20◦ - 14◦ 14◦ - 0◦

Table A.4: EPOC cases for deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Upstroke Downstroke Ste = 3 Ste = 3 D3 case. Two portions. 14◦ - 20◦ 20◦ - 0◦

Table A.5: EPOC cases for deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Three EPOC cases were studied following the trends seen in continuous excitation. For

case D1, a combination of two frequencies at different parts of the cycle was used. Ste = 3 was used during the upstroke part to obtain a considerable DSV strength reduction based

on the continuous excitation results. Ste = 0.5 produces the best ﬂow reattachment in most

of the downstroke as seen in continuous excitation, contributing to lift hysteresis reduction.

For case D2, an additional frequency was used in the downstroke to improve lift recovery as

seen in continuous excitation cases. For case D3, only two parts in the cycle were used with

a moderate excitation frequency, the objective was to reduce negative damping. Figure A.41

185 and A.42 show that all three cases achieved a lift hysteresis reduction, for the case D2 the

second part of excitation does not show the improvement expected possibly for the timing

of the excitation. Although the lift hysteresis reduction goal is reached, drag reduction and

negative damping are compromised under these EPOC scheme as can be seen from ﬁgures

A.42 to A.48. For case D3, the reduction in negative damping is achieved and it is best of

the three cases as expected. Figures A.44 and A.45 show the improvement in negative and

cycle-averaged damping. Due to the instantaneous response of NS-DBD plasma actuator,

EPOC approach offers multiple control options depending in the performance goal required

for the oscillating airfoil.

186 Figure A.41: Phase-averaged lift coefﬁcient for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

187 Figure A.42: Lift hysteresis for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

188 Figure A.43: Phase-averaged moment coefﬁcient for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

189 Figure A.44: Negative damping for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Figure A.45: Cycle damping for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

190 Figure A.46: Phase-averaged drag coefﬁcient for EPOC cases in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

191 Figure A.47: Drag reduction for EPOC cases during the upstroke in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

Figure A.48: Drag reduction for EPOC cases during the downstroke in deep dynamic stall at Re=500,000, k=0.05, and motion: α(t) = 10◦ + 10◦sin(ωt).

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