Active Flow Separation Control of a Laminar Airfoil at Low Reynolds

Home , Flow separation

Active Flow Separation Control of a Laminar Airfoil at

Low Reynolds Number

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

in the Graduate School of The Ohio State University

Nathan Owen Packard, B.S, M.S

Graduate Program in Aeronautical and Astronautical Engineering

The Ohio State University

2012

Dissertation Committee:

Dr. Jeffrey P. Bons, Advisor

Dr. Jen-Ping Chen

Dr. Mohammad Samimy

Dr. Andrea Serrani

Nathan Owen Packard

2012

Abstract

Detailed investigation of the NACA 643-618 is obtained at a Reynolds number of

6.4x104 and angle of attack sweep of -5° < α < 25°. The baseline flow is characterized by four distinct regimes depending on angle of attack, each exhibiting unique flow behavior.

Active flow control is exploited from a row of discrete holes located at five percent chord on the upper surface of the airfoil. Steady normal blowing is employed at four representative angles; blowing ratio is optimized by maximizing the lift coefficient with minimal power requirement. The range of effectiveness of pulsed actuation with varying frequency, duty cycle and blowing ratio is explored. Pulsed blowing successfully reduces separation over a wide range of reduced frequency (0.1-1), blowing ratio (0.5–2), and duty cycle (0.6–50%).

A phase-locked investigation, by way of particle image velocimetry, at ten degrees angle of attack illuminates physical mechanisms responsible for separation control of pulsed actuation at a low frequency and duty cycle. Temporal resolution of large structure formation and wake shedding is obtained, revealing a key mechanism for separation control. The Kelvin-Helmholtz instability is identified as responsible for the formation of smaller structures in the separation region which produce favorable momentum transfer,

i assisting in further thinning the separation region and then fully attaching the boundary layer.

4 Closed-loop separation control of an oscillating NACA 643-618 airfoil at Re = 6.4x10 is investigated in an effort to autonomously minimize control effort while maximizing aerodynamic performance. High response sensing of unsteady flow with on-surface hot- film sensors placed at zero, twenty, and forty percent chord monitors the airfoil performance and determines the necessity of active flow control. Open-loop characterization identified the use of the forty percent sensor as the actuation trigger.

Further, the sensor at twenty percent chord is used to distinguish between pre- and post- leading edge stall; this demarcation enables the utilization of optimal blowing parameters for each circumstance. The range of effectiveness of the employed control algorithm is explored, charting the practicality of the closed-loop control algorithm.

To further understand the physical mechanisms inherent in the control process, the transients of the aerodynamic response to flow control are investigated. The on-surface hot-film sensor placed at the leading edge is monitored to understand the time delays and response times associated with the initialization of pulsed normal blowing. The effects of angle of attack and pitch rate on these models are investigated. Black-box models are developed to quantify this response. The sensors at twenty and forty percent chord are also monitored for a further understanding of the transient phenomena.

Dedicated to Telisha.

iii

Acknowledgments

First, and foremost, I acknowledge my beautiful wife, Telisha. I thank her for standing by my side and supporting me. I thank her for joining me on this difficult yet extremely rewarding experience. I also want to thank my children: Sidney, 6, Owen, 4, and Tanner,

3. I hope to instill in you the desire to get all the education you can, and to never stop learning. I need to thank my parents, Paul and Sherrie, for instilling in me the importance of doing well in school.

I must acknowledge Dr. Jeffrey Bons. He has been an inspiration and guide, both professionally and personally. I thank him for his tireless efforts, and recognize how inadequate this work would be without his assistance.

Lastly, I acknowledge God for his support and direction. To him I owe all that I have and am.

VITA

April 2007……………………………………….B.S. Applied Physics, Minor

Mathematics, Brigham Young

University

August 2009……………………………………..M.S. Mechanical Engineering, Brigham

Young University, Thesis Title:

Numerical Characterization of the

Inlet Flow of Eleven Radial Flow

Turbomachines

PUBLICATIONS

Packard, N. O., Thake, M. P., Bonilla, C. H., Gompertz, K., Bons, J. P., “Active Control of Flow Separation on a Laminar Airfoil,” Under Review, AIAA Journal, Feb. 2012.

Packard, N. O. and Bons, J. P., “Pulsed Blowing on a Laminar Airfoil at Low Reynolds Number,” AIAA 2011-3173, 29th AIAA Applied Aerodynamics Conference, Honolulu, HW, 27-30 June, 2011.

Packard, N. O. and Bons, J. P., “Closed-Loop Separation Control of Unsteady Flow on an Airfoil at Low Reynolds Number,” AIAA-2012-754, 50th AIAA Aerospace Sciences Meeting, Nashville, TN, 9-12 Jan, 2012.

FIELDS OF STUDY

Major Field: Aeronautical and Astronautical Engineering

Specialization: Experimental Fluid Dynamics v

Table of Contents

Abstract ...... i

Acknowledgments ...... iv

VITA ...... v

Table of Contents ...... vi

List of Tables ...... viii

List of Figures ...... ix

Nomenclature ...... xviii

Chapter 1: Introduction ...... 1

Chapter 2: Experimental Setup ...... 9

2.1 Wind Tunnel ...... 9

2.2 Airfoil ...... 9

2.3 Flow Control ...... 10

2.4 Data Acquisition ...... 18

Chapter 3: Results ...... 24

3.1 Baseline Airfoil Characterization ...... 24

3.2 Open-loop Flow Control ...... 30

3.3 Instability Classification ...... 55

3.4 Closed-Loop Separation Control ...... 68

3.5 Transients of the Aerodynamic Response to Flow Control ...... 86

Chapter 4: Future Considerations ...... 112

Chapter 5: Conclusions ...... 119

References ...... 122

vii

List of Tables

Table 1 Combinations of frequencies and duty cycles used in search of dynamic motion ...... 47

Table 2. FOPDT model parameters for 2° ≤ α ≤ 10°, along with a nominal model for

5° ≤ α ≤ 9° ...... 92

Table 3. Comparison of model parameters for the static airfoil versus a dynamic airfoil at nominal pitch rate and double pitch rate for α = 5°, 7° and 9°...... 111

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List of Figures

Figure 1. The flow structure of a laminar separation bubble. Taken from [39]...... 3

Figure 2. Typical surface pressure distributions with and without a separation bubble.

Taken from [5]...... 4

Figure 3. NACA 643-618 airfoil with pressure tap and flow control locations...... 5

Figure 4. Internal structure of the NACA 643-618 airfoil with pressure taps and active flow control...... 10

Figure 5. Streamlines and normalized mean velocity magnitude for BR = 0.5, depicting the domain of slow moving reverse flow formed behind the jet. Taken from [21]...... 11

Figure 6. Streamlines and normalized mean velocity magnitude for BR = 2.5, depicting the advection of the jet far from the wall. Taken from [21]...... 12

Figure 7. Cartoon depicting four types of vortical structures associated with the near- field of a jet in cross flow. Taken from [19]...... 13

Figure 8. Infrared image of 20% span and 20% chord, showing the coherent and independent structures downstream of the normal jets at α = 10° and BR = 0.25. Marks are equally spaced and in-line with the hole locations...... 15

Figure 9. Cartoon of a general Particle Image Velocimetry configuration...... 20

Figure 10. Graphic of a traditional hot-film sensor...... 22

Figure 11. Graphic of a TAO Systems SENFLEX hot-film anemometer...... 23

Figure 12. Graphic of the integration of the surface hot-film sensors employed for closed-loop sensing...... 23

Figure 13(a-c). Comparison of (a) lift, (b) drag and (c) moment coefficients between baseline, steady blowing and the baseline results of Mack et al. [34] at Re = 6.4x104. ... 24

Figure 14(a-d). Surface-oil flow visualization of the baseline flow at (a) α = -1°,

Region I, (b) α = 10°, Region II, (c) α = 16°, Region III and (d) α = 20°, Region IV at Re

= 6.4x104...... 26

Figure 15(a-b). PIV determination of the velocity magnitude for (a) baseline and (b) steady blowing flow (BR ≈ 1.5) at α = -1° and Re = 6.4x104. The dashed white line demarcates two acquisition windows. The white space around the airfoil indicates a mask used in post-processing. (Region I)...... 26

Figure 16(a-b). PIV determination of the velocity magnitude for (a) baseline and (b) steady blowing flow (BR ≈ 0.3) at α = 10° and Re = 6.4x104. (Region II)...... 28

Figure 17. PIV determination of the velocity magnitude for baseline flow at α = 16° and Re = 6.4x104. (Region III)...... 29

Figure 18(a-b). PIV determination of the velocity magnitude for (a) baseline and (b) steady blowing flow (BR ≈ 3) at α = 20° and Re = 6.4x104. (Region IV)...... 30

4 Figure 19. Variation of CL with BR at α = 10° and 20° (Re = 6.4x10 )...... 31

Figure 20(a-b). Power spectral density at (a) x/c = 0.15 and (b) x/c = 0.4 for steady blowing with BR ≈ 1.5 at α = -1° and Re = 6.4x104...... 33

Figure 21. Comparison of time-averaged boundary layer profiles for steady blowing at

BR ≈ 0.3 at five chordwise locations (z/s = 0) for α = 10° with Re = 6.4x104. The baseline

x profile at x/c = 0.4 is obtained from PIV, and being massively separated it is not included at the other locations...... 34

Figure 22. Power spectral density at n/c = 0.003 and z/s = 0 for steady blowing with

BR ≈ 0.3 at α = 10° and Re = 6.4x104...... 36

Figure 23(a-b). Experimental investigation of the fundamental instability frequency of the baseline flow at Re = 6.4x104 and α = 10° at x/c = 0.4. Left (a) is the mean velocity profile, and right (b) is the PSD...... 37

Figure 24. Comparison of the lift coefficient between baseline, steady blowing and zigzag tape at Re = 6.4x104...... 38

Figure 25(a-b). Hot-film investigation of the (a) mean velocity profile and (b) turbulence intensity of the boundary layer at α =10° and Re = 6.4x104 at x/c = 0.12. The turbulence intensity is normalized by the boundary layer edge value...... 40

Figure 26(a-b). Hot-film investigation of the (a) mean velocity profile and (b) turbulence intensity of the boundary layer at α =10° and Re = 6.4x104 at x/c = 0.30, comparing the boundary layer with the flow at α = 16° and x/c ≈ 0.3, where a leading- edge separation bubble has naturally induced transition...... 41

Figure 27. Power Spectral density of flow at α = 10° and x/c = 0.3, comparing the boundary layer with the flow at α = 16° and x/c ≈ 0.3...... 42

Figure 28. Comparison of time-averaged boundary layer profiles for steady and pulsed blowing at four chordwise locations at α = 10° with Re = 6.4x104. Steady blowing at BR

≈ 0.25 and pulsed blowing at BRmax ≈ 0.5, f+ ≈ 1, and DC = 5%. The baseline profile at

xi x/c = 0.4 is obtained from PIV, and being massively separated it is not included at the other locations...... 43

Figure 29(a-b). Variation of CL with pulsing frequency and duty cycle for α = 10° and

4 Re = 6.4x10 , for (a) BRmax = 0.5 and (b) BRmax = 2. The baseline CL at α = 10° is 0.48. 44

Figure 30. Representative jet pulse characterization for varying frequencies with DC =

5% and BRmax ≈ 0.5...... 46

Figure 31. Actuation jet pulse characterization for the parameter combinations defined in Table 1 with peak BR ≈ 0.5...... 48

Figure 32. Lift coefficient versus frequency for the parameter combinations defined in

Table 1 with peak BR ≈ 0.5...... 49

Figure 33. Actuation jet pulse characterization for f = 5 Hz (f+ ≈ 0.12) and DC =

0.625%. The 33 phases investigated with PIV are plotted above the jet time-history. .... 50

Figure 34(a-h). Phase-locked PIV of velocity magnitude (left) and swirl strength

(right). The dashed white line demarcates two acquisition windows. The white space near the airfoil indicates a mask used in post-processing. t/T is indicated on the left...... 52

Figure 35(a-d). Phase-locked PIV of velocity magnitude of four intermediate phases for temporal resolution of the vortex structure and wake interaction...... 53

Figure 36. Comparison of the velocity magnitude of the baseline (top) with the unsteady flow at t/T = 0.069 (middle) and the swirl strength of the same phase (bottom), the phase whereat the separation point has traveled the furthest upstream...... 57

Figure 37. Ascertaining the mean velocity of and distances between swirl structures from the PIV results for the determination of the shear layer shedding frequency, fs...... 58

xii

Figure 38. Frequency spectrum of the wall-normal disturbance velocity at various downstream locations, indicating the preferred shedding frequency in the shear layer of a

4 modified NACA 643-618 airfoil at Re = 6.42x10 and α = 8.64°. Taken from [6]...... 59

Figure 39. Top-view schematic of the airfoil test section showing speaker placement and hot-film placement for the acoustic characterization...... 60

Figure 40(a-b). Velocity profiles of the acoustic control investigation for α = 10° at

(a) x/c = 0.4 and (b) x/c = 0.8...... 62

Figure 41(a-b). Comparison of the velocity profiles of the baseline, acoustically controlled, and jets controlled flow for α = 10° at (a) x/c = 0.4 and (b) x/c = 0.8...... 63

Figure 42. Phase-locked contours of the turbulence intensity for a pulsing frequency of

40 Hz with a 5 percent duty cycle. Re = 6.4x104, α = 10°, and BR = 0.5. The contours are obtained with the hot-film follower device. This phase is approximately t/T ≈ 2/3. The emitted jet has propagated downstream and is interacting with the shear layer. Three shed vortical structures can be seen...... 65

Figure 43. An instantaneous iso-surface of the second invariant of the velocity gradient, Q = 30, displaying the complexity of the JICF. Taken from [35]...... 66

Figure 44. Block diagram of simple closed-loop algorithm...... 69

Figure 45(a-b). Smoke visualization of 643-618 airfoil at high angle of attack, (a) without and (b) with pulsed normal blowing at x/c = 0.05. The hot-film probe at x/c = 0.5 is used for feedback control. Flow is right to left. White outline sketched onto image for identification of airfoil surface...... 73

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Figure 46. Time history of unsteady sensing during airfoil pitch oscillation. From the bottom: angle of attack, pulsed signal to flow control jets, hot-film sensor at 50% chord, surface static pressure tap output. The dashed vertical lines indicate stall and recovery. 74

Figure 47. Hot-film measurements of the leading-edge stagnation line location versus the airfoil lift coefficient for a FlexSys, Inc., Mission Adaptive Compliant Wing, at

Re = 9x105 and 2° ≤ α ≤ 12° (from [43])...... 76

Figure 48. The LE sensor signal for the baseline and controlled flow for both the pitch up and pitch down directions...... 77

Figure 49. Leading-edge sensor outputs versus the lift coefficient of Fig. 13(a) for the

(Fig. 21(left)) baseline flow and (Fig. 52(right)) controlled flow for 6° ≤ α ≤ 20°, validating the use of the leading edge sensor for monitoring the airfoil performance. .... 78

Figure 50(a-b). Application of a linear fit to a set of data. The linear fit is subtracted from the raw signal to obtain the instantaneous deviation, u’, whereby the signal rms is obtained. (a) α = -3° and (b) α = 20°...... 79

Figure 51(a-f). Rms time histories of the surface sensors at (a,c,e) x/c = 0.4 and (b,d,f) x/c = 0.2 for the (a-b) baseline, (c-d) continuously controlled, and (e-f) closed-loop controlled flow through a pitching cycle. These are used for the determination of thresholds in the implementation of control and determination of control parameters in the closed-loop procedure...... 81

xiv displayed. The performance increase while controlling is evident. The algorithm can rapidly detect and institute optimal blowing parameters as determined by the sensed flow.

...... 82

Figure 53. Results of the average performance (20 realizations) of the airfoil under baseline, continuously controlled, and closed-loop control of the continuously oscillating airfoil at the nominal pitch rate and Re = 1.28x105...... 85

Figure 54. Results of the average performance (6 realizations) of the airfoil under baseline, continuously controlled, and closed-loop control of the continuously oscillating airfoil at double the nominal pitch rate...... 85

Figure 55. Representative input (jet actuation) and output (leading edge sensor) signals for Re = 6.4x104 and α = 5°...... 88

Figure 56. Comparison of the average aerodynamic response, measured by the leading edge sensor, for 2° ≤ α ≤ 10°...... 91

Figure 57(a-b). FOPDT models for (a) 2° ≤ α ≤ 10° and (b) 5° ≤ α ≤ 9° compared to a nominal model...... 91

Figure 58. Comparing the transient responses of the surface sensors for α = 2°...... 93

Figure 59. PIV derived velocity magnitude for the baseline and controlled flow at α = -

1°...... 94

Figure 60. Comparing the transient responses of the surface sensors for α = 9°...... 94

Figure 61. PIV derived velocity magnitude for baseline and controlled flow at α = 10°.

...... 95

Figure 62(a-b). Comparison of the sensor responses at (a) 20% and (b) 40% chord for

2° ≤ α ≤ 10°...... 95

Figure 63. Comparison of the phase-locked wake profiles corresponding to the PIV results of Figures 34 and 35 at the (left) most adverse and (right) most favorable portions of the pulsing period...... 96

Figure 64(a-b). Comparison of the LE sensor response at (a) α = 2° and (b) α = 9° for a discrete number of actuation pulses...... 98

Figure 65. Comparison of the LE sensor response at α = 2° for one or two pulses. .... 99

Figure 66(a-b). Close-up view of Fig. 66(a-b), which compares the aerodynamic responses of the (a) 20% and (b) 40% sensors for 2° ≤ α ≤ 10°...... 100

Figure 67. Comparison of the LE response for 20° ≤ α ≤ 24°...... 101

Figure 68. Comparison of the transient responses of the surface sensors for α = 20°.

...... 102

Figure 69. Comparison of the LE sensor responses and corresponding models for α =

20° and 21°, wherein a FOPDT model provides a reasonable estimation of the flow dynamics...... 103

Figure 70. Comparison of the LE sensor response and corresponding model for α =

23°, wherein a SOPDT model is required to provide a reasonable estimation of the response...... 104

Figure 71. Investigation of dynamic control at α = 5° with a view of the unfiltered signal over a full oscillation and (insert) a concentrated view of the filtered signal in the transient region...... 106

xvi

Figure 72. Investigation of dynamic control at α = 7° with a view of the unfiltered signal over a full oscillation and (insert) a concentrated view of the filtered signal in the transient region...... 107

Figure 73. Investigation of dynamic control at α = 9° with a view of the unfiltered signal over a full oscillation and (insert) a concentrated view of the filtered signal in the transient region...... 108

Figure 74. Comparison of the LE sensor response and corresponding model for the oscillating airfoil with actuation engaged at α = 7°...... 108

Figure 75(a-c). Comparison of the LE sensor of the static and dynamic responses at the nominal and twice-nominal pitch rate for (a) α = 5°, (b) α = 7° and (c) α = 9°...... 110

Figure 76. Comparison of baseline and controlled lift coefficient for Re = 6.4x104 and

1.8x105, which express the dependence upon Re for the necessity of active flow control.

...... 116

Figure 77. Basic schematic of the control logic employed in the manipulation of the hysteretic behaviors with respect to the jet blowing ratio. Derived from [9]...... 118

xvii

Nomenclature

BR = blowing ratio, jet velocity normalized by boundary layer edge velocity

CD = drag coefficient

CL = lift coefficient

CP = pressure coefficient [defined in Eq. (2)]

Cµ = momentum coefficient, adjusted for 3-D jet holes [defined in Eq. (1)]

Crit40ON = algorithm trigger ON value of the surface sensor at x/c = 0.4

Crit40OFF = algorithm trigger OFF value of the surface sensor at x/c = 0.4

Crit20 = BR trigger value of the surface sensor at x/c = 0.2

DC = actuation duty cycle

LS = length of suction surface

N = number of actuation holes

Psl = static pressure, local

Ps∞ = static pressure, freestream

PT∞ = total pressure, freestream

Re = Reynolds number based on airfoil chord, ρUc/μ

S = planform area

Srθs = Strouhal number based on conditions at the point of separation (fsθs/Ues)

T = actuation period

Tu* = local turbulence intensity normalized by that at boundary layer edge

Ues = boundary layer edge velocity at the separation location

xviii

U∞ = average freestream velocity c = airfoil chord d = diameter, flow control hole f = oscillation frequency, Hz fs = shear layer shedding frequency f+ = reduced frequency ≡ (fc)/U∞ k = reduced oscillation frequency (k = wc/2U∞) n = wall normal distance from airfoil surface s = spacing, flow control hole (s = 10.667d) t = time from the moment the actuation jet emits from the airfoil surface u = instantaneous hot-film signal magnitude u’ = instantaneous hot-film signal deviation w = pitch oscillating frequency of airfoil x = chordwise distance y = wall normal distance z = spanwise distance

Greek

α = airfoil angle of attack

θs = momentum thickness at the separation location

ν = kinematic viscosity

Subscripts max = maximum

∞ = freestream

xix

Chapter 1: Introduction

Most current commercial and military aircraft operate with turbulent boundary layer flow across the airfoil surface due to its resistance to stall. Airfoils under turbulent flow are highly resistant to separation and are minimally affected by disturbances in the flow because the flow is dominated by inertial forces. Maintaining laminar flow is very difficult in practical applications, and this is the primary reason why most large aircraft operate with turbulent flow. A downside to utilizing turbulent flow is that it has a large velocity gradient near the wall resulting in increased skin friction and viscous drag.

Because of these downsides, there is motivation for a primarily laminar flow airfoil due to the reduced skin friction associated with smooth laminar flow. Reduced skin friction decreases drag thereby lowering the required fuel consumption, a critical factor today with the increasing fuel costs and the pressure to reduce environmental impact [22].

Unfortunately, laminar flow is highly susceptible to boundary layer separation from a strong adverse pressure gradient (e.g. high angle of attack) or transition due to a discontinuity on the surface (e.g. bug deposits or rivets).

1.1 Laminar Airfoil Characteristics

The concept of a laminar airfoil is to create and maintain laminar flow across a majority of the airfoil. To achieve a significant amount of laminar flow on an airfoil, a long run of a favorable pressure gradient (i.e. accelerating flow) must be imposed by locating the

1 maximum airfoil thickness near or aft of mid-chord. This suppresses the growth of two- dimensional Tollmien-Schlichting waves in the boundary layer [25]. The interaction between boundary layer instability growth and adverse pressure gradients (leading to separation) has been studied extensively. Dovgal et al. [16] investigated laminar boundary layer separation and the generation of instability waves. They found that the disturbances which caused transition in the separated flow can be generated upstream of separation at the beginning of the adverse pressure gradient. Amplification of vortical structures was observed in the separation bubble. Diwan and Ramesh [15] performed an experimental and theoretical study of laminar separation bubbles and the associated linear instability mechanisms. Their primary conclusion is that the foremost instability mechanism in the separation bubble is inflectional in nature, and originates upstream of the separation location. They suggest that the instability of the separated shear layer is simply an extension of the instability of the boundary layer upstream of the adverse pressure gradient, and that the laminar-turbulent transition can be avoided if the inflectionality is very weak (e.g. if the inflection point is very close to the wall).

Several researchers have studied the performance and flow structures of laminar airfoils subjected to a low Reynolds number flow to look deeper into the mechanics of separation and control. Mack et al. [34] performed an experimental study on a NACA

643-618 airfoil to investigate boundary layer separation and control at low Reynolds numbers (Re ≈ 6.4x104). Mack et al. showed that at low Reynolds numbers the airfoil was performing below the designed lift coefficient for a majority of the angles of attack due to premature separation. However, at 10 degrees angle of attack there was a sudden

2 increase in lift and decrease in drag which was attributed to a natural boundary layer control mechanism that reattached the separated boundary layer. Mueller and Batill [37] had similar experimental findings on the NACA 663-018 airfoil as well as Brehm et al.

[10] in their computational study on the NACA 643-618 airfoil. All three researchers suggested that the performance improvement was a result of transition from laminar to turbulent flow early in the separated laminar shear layer due to flow instabilities causing the turbulent shear layer to re-energize and reattach to the surface creating a closed separation bubble. Figure 1 reveals the flow structure of a laminar separation bubble.

Figure 1. The flow structure of a laminar separation bubble. Taken from [39].

The flow separates at S-S’’ forming a laminar shear layer, then the shear layer begins the transition process, usually a short distance downstream [5]. The transition is induced by the Kelvin-Helmholtz (K-H) instability, due to disturbance amplification, as the boundary layer decelerates and separates. After transition from laminar to turbulent flow is complete, at T-T’-T’’, entrainment of external fluid causes the shear layer to grow,

3 resulting in a rise in pressure. As the pressure increases to nearly equal to the value for the turbulent flow with no separation bubble (see Fig. 2) the flow reattaches at R-R’’. The area under S-T’-R indicates the separated region [39].

Figure 2. Typical surface pressure distributions with and without a separation bubble.

Taken from [5].

Mack et al. held that the bubble acts as a natural flow control mechanism which only occurs on laminar airfoils and promotes two-dimensional spanwise vortices (i.e. rollers) downstream of R-R’’. These rollers replace the low momentum boundary layer fluid with higher momentum freestream fluid, therefore stabilizing the boundary layer. The spanwise vortices induced by the laminar separation bubble also have the potential to strengthen particular natural flow frequencies depending on the shedding frequencies, which would encourage vortex-merging thus allowing a further increase in wall momentum exchange [10]. 4

Unfortunately, when exposed to a strong adverse pressure gradient, as can be found at a moderate to high angle of attack, laminar flow is highly susceptible to boundary layer separation, dramatically decreasing the overall airfoil performance. As a result, extensive efforts have been made to characterize the effects of flow separation control on aerodynamic performance. Vortex generating jets, fluidic oscillators, plasma actuators of various types, and synthetic jets, among others, have all been investigated. The purpose of these devices, generally, is to maximize the airfoil’s aerodynamic performance for minimal cost.

Experimental and numerical investigations of laminar separation control at low

Reynolds number have been performed at the University of Arizona on the NACA 643-

618 laminar airfoil, with coordinates seen in Fig. 3. Brehm et al. [10] performed two-

(2D) and three- (3D) dimensional simulations of the flow. Wall-normal, harmonic blowing and suction are used at a Re = 6.4x104 and α = 8.64°. Without control, at moderate α, the airfoil performance is reduced considerably due to a massive trailing edge separation. The computational results indicated that placement of the blowing flow control is most beneficial near the leading edge, at 2% chord.

NACA 64 -618 0.2 3 Pressure Tap Locations Flow Control Location

0.1 y/c 0

-0.1 0 0.2 0.4 0.6 0.8 1 x/c

Figure 3. NACA 643-618 airfoil with pressure tap and flow control locations. 5

Mack et al. [34] performed wind tunnel experiments with the same airfoil and Re utilizing active and passive flow control at 40% chord over a wide range of α. For active flow control (AFC), Mack et al. used a plasma actuator strip which pointed downstream and induced a velocity towards the wall which was estimated to be on the order of the free stream velocity (~3.5 m/s). The lift to drag ratio, L/D, was increased 325% over the baseline at 8.3° angle of attack.

Again, with the same laminar airfoil and Re, Plogmann et al. [42] experimentally investigated the effects of forcing amplitude and forcing location on the airfoil performance. Separation control by plasma actuation was implemented at x/c ≈ 0.02 and x/c ≈ 0.4, where x is the chordwise distance and c is the chord, both exclusively and concurrently. Control at x/c ≈ 0.02 was effective for moderate to high α, (5° ≤ α ≤ 18°), preventing separation and extending the stall range. At lower α, where the baseline flow separates well downstream of the leading edge, control was less effective. Forcing at x/c

≈ 0.4 resulted in a nearly opposite trend; improved response was observed at lower to mid

α, yet it was entirely ineffective at higher α. Operating at both locations simultaneously resulted in favorable performance across the entire aforementioned α range, yet this approach is inefficient since more energy is required for the same performance increase that can be obtained by appropriately toggling between actuator locations.

Because the flow and performance characteristics of the uncontrolled NACA 643-618 airfoil are well known, it will be used as the base airfoil for the following flow control investigation on low Reynolds number, laminar airfoils. A fundamental study is conducted where normal blowing near the leading edge is investigated to determine the

6 cause of the delay in separation and increase in performance. Steady normal blowing is initially implemented and compared to the results of previous work. Other efforts in active flow control often optimize actuation for a single configuration (e.g. leading edge stall at fixed Re). However, there has not been significant discussion on the actuation physics and the mechanisms that induce performance enhancement at low Reynolds numbers. Consequently, a delineation of the variation in control effort (BR) and control mechanisms over a range of α is provided. Pulsed blowing is subsequently introduced. A number of actuation parameter combinations (f+, DC, BR) are explored to optimize the aerodynamic response at a moderate angle of attack (α = 10°). Phase-locked boundary layer profiles, wake surveys and full-field laser diagnostics are employed for a characterization of the responsible physical mechanisms. Acoustic excitation is also explored to validate assertions concerning the proposed mechanisms.

The information gained during the open-loop investigations directed the implementation of closed-loop separation control of an oscillating airfoil. While less complex than other recently developed closed-loop approaches, an effective and robust control algorithm is developed. High-speed sensing monitors the flow in real-time and determines the appropriate actuation parameters for improved aerodynamic performance over the desired range of angle of attack.

To assess the ability of the airfoil to respond to the implementation of the jet actuation, the transients of the aerodynamic response are monitored and analyzed. This effort is unique from other similar endeavors as its primary focus is separation control of a laminar airfoil at low Reynolds number at low-to-moderate angles of attack. Further, the

7 introduction of airfoil oscillation provides for the characterization of the effect of angle of attack and pitch rate on the transient dynamics.

Chapter 2: Experimental Setup

2.1 Wind Tunnel

All experiments are conducted in a low-speed wind tunnel at the Aeronautical and

Astronautical Research Laboratory (AARL) of the Department of Mechanical and

Aerospace Engineering at The Ohio State University. This tunnel is an open-loop low speed wind tunnel powered by a centrifugal blower, which pushes the air through a series of flow conditioners and enters a rectangular (0.381 m x 0.362 m) acrylic-walled duct with ±2% velocity uniformity. The wind tunnel is capable of operating at chord Reynolds numbers up to 2x105, based on a 0.152m airfoil chord. The selected Reynolds number for testing is 6.4x104, with a corresponding baseline freestream turbulence level of 0.4%. The airfoil is mounted in the test section with accurate AOA markers between -10 and 25 degrees. The test section has a clear optical view for the use of particle image velocimetry and flow visualization.

2.2 Airfoil

The NACA 643-618 laminar airfoil is the focus of this investigation, with profile seen in

Fig. 3. It has a maximum thickness of 18% at the 37.1% chord location. It has a camber of 3.31% with the maximum deviation point at 51.4% chord. The model spans the 9 entirety of the tunnel and has a chord length of 0.152m. The airfoil is fabricated by milling aluminum ribs, connecting them via strengthening rods and gluing a thin aluminum sheet over the structure, as observed in Fig. 4. Thirty-eight pressure taps (29 on the upper surface, 9 on the lower surface) are drilled into the middle 1/3 span of the airfoil surface, staggered at a 15 degree angle to avoid interference. Figure 3 shows the chordwise locations of the pressure taps and flow control.

Figure 4. Internal structure of the NACA 643-618 airfoil with pressure taps and active flow control.

2.3 Flow Control

2.3.1 Normal Blowing

While it is evident that holes drilled with pitch and skew are more effective AFC devices

[18,55], geometric constraints within the airfoil required that normal holes be utilized.

The flow physics of the two approaches are quite different; an optimally skewed jet of 60 degrees best balances the strength of the vortex and the velocity component in the streamwise direction [18]. The normal jet initially provides zero streamwise velocity; yet 10 depending on the relative strength of the jet, at some distance off the wall it will be turned and entrained into the cross flow.

Near the normal jet hole the interaction with the oncoming flow is quite complex.

Normal blowing has been investigated experimentally by Gopalan et al. [21], and they have demonstrated that two distinctly different flow structures exist in the wake region behind the jet, depending on the jet-to-crossflow velocity ratio (BR). At low blowing ratios (BR < 2), stretching of vorticity in the backside of the jet generates a semi- cylindrical vortical layer or shell. This shell extends from the underside of the jet and connects to the wall, enclosing the domain with slow moving reverse flow. As the flow is advected downstream this reverse flow region is transformed into a “vortex ring”. Figure

5 illustrates streamlines and normalized mean velocity magnitude for BR = 0.5. Within about one hole diameter above the wall the jet has turned into the cross flow direction and entrainment into the crossflow has begun.

Figure 5. Streamlines and normalized mean velocity magnitude for BR = 0.5, depicting the domain of slow moving reverse flow formed behind the jet. Taken from [21]. 11

Gopalan et al. describe that this occurs because the jet experiences different conditions on the forward and rear boundaries at it emerges from the surface. While the back side of the jet shear layer is exposed to slow moving flow the forward face confronts the incoming cross flow. The negative vorticity of the wall boundary layer interacts with the positive jet vorticity on the forward side, yet on the reverse-side the jet vorticity is unrestricted. They conclude that the significant differences between the forward and back sides causes the jet “vortex ring” to stretch vertically along the back side, while mixing with the wall boundary layer vorticity on the front side. As the flow is advected downstream, the semi-cylindrical structure forms [21].

Gopalan et al. identify BR ≈ 2 as a critical value wherein the jet and its vorticity are advected far from the wall. Figure 6 displays streamlines and normalized mean velocity magnitude for BR = 2.5, and it is observed that the jet does not turn into the cross flow direction until approximately three hole diameters above the wall.

Figure 6. Streamlines and normalized mean velocity magnitude for BR = 2.5, depicting the advection of the jet far from the wall. Taken from [21]. 12

Fric and Roshko [19] focused primarily on the high velocity ratio domain (BR > 2), wherein four vortical structures are evident in the near field of a normal jet in cross flow: horseshoe vortices on the wall, jet shear layer vortices at the upstream perimeter of the bending jet, wake vortices extending from the wall to the jet, and a developing counter rotating vortex pair (CVP). Figure 7 illustrates these four vortical structures and their relative size.

Figure 7. Cartoon depicting four types of vortical structures associated with the near-field of a jet in cross flow. Taken from [19].

The CVP is widely regarded as the dominant flow structure downstream of a jet in cross flow [19,29,32]. Particularly in the far field (5-10 diameters downstream of the injection point) the CVP dominates the cross section of the jet. Lim et al. [32] determined experimentally that the CVP are formed directly from the deformation of the transverse- jet shear-layer structure. Yuan et al. [59], along with Majander and Siikonen [35], have confirmed this conclusion computationally. This time-averaged vortical structure is associated with enhanced overall mixing efficiency for the transverse jet.

2.3.2 Hole Configuration and Setup

Previous research concludes that blowing near the separation location is most effective

[27,42,47], since maximum airfoil performance can be attained and then maintained with minimal effort. Seifert et al. [47] state that this approach is not affected by changing the

Reynolds number. However, when employing actuation from a single location for a wide range of angle of attack it is advantageous to do so as close to the leading edge as possible [3,10, 34]. For the present investigation, the near leading edge position is constrained by internal airfoil fabrication, and the control is thus located at x/c ≈ 0.05.

Internally, blowing uses an individual tubing system which uses compressed air.

Externally, round holes are drilled normal to the airfoil surface, which have a diameter, d, of 0.794 mm and a spanwise spacing of 8.467 mm (10.67d). The diameter and spacing are 0.48%LS and 5.13%LS, respectively, where LS is the length of the suction surface, which compares well to the percentages employed in other research [55]. The flow control holes run 95% of the airfoil span.

It has been shown by Kamotani and Greber [28] that if the normal jets are too close (s

< 4d-6d) the initial vortices of the jet are relatively weak (they vanish as smaller spacing approaches a 2-D jet) and the jets interfere with each other’s entrainment of cross flow.

This latter effect results in slower decay of the initial upward momentum flux of the jet.

Consequently for close enough spacing the jets maintain upward momentum longer, and experience only limited deflection due to mutual vortex interaction. However, the spacing used (10.67d) ensures that the jets will not interfere with each other in the near field. At this spacing the normal jet will behave independently, like a single jet in cross flow.

Figure 8 provides a qualitative infrared image of 20% of the span and 20% of the chord, showing that coherent and independent structures travel downstream of the jet in cross flow. The image is obtained using an Electrophysics Silver 420 shortwave infrared camera. The camera has a sensitivity of 0.02°C, due to cryogenic cooling of its detector, to a temperature of 70K. The camera has a maximum frame rate of 100 Hz with a temperature measurement range of 5 to 1500°C. To capture data, the flow is heated and redirected until it reaches steady-state of about 50°C while the airfoil remains at room conditions. The flow is then directed down the wind tunnel and the data is acquired.

10.67d

Flow direction

Normal Jets 0 0.1 0.2 x/c

The hottest locations are indicated by red followed by orange, yellow, green and blue.

The hole spacing is identified on the figure, and it is evident that coherent and independent structures travel downstream of the jet in cross flow (flow direction is left to right). The hot streaks originate from the flow control holes and continue downstream despite the fact that the jet fluid is lower temperature. The hotter streaks appear because the 3-D structures which form from a jet in crossflow are more effective at entraining the hotter freestream flow and convecting that downstream. Distinct structures are present

(minimal spanwise or chordwise mixing/diffusion) until x/c ≈ 0.25, wherein diffusion through viscosity and mixing dampen the effect.

For steady blowing, a rotameter is used to control the volume flow rate, where velocity is calculated from conservation of mass. For pulsed blowing, an inline Parker-Hannifin high-speed solenoid valve (Model: 91-199-900) regulates the normal jet exit velocity. A

General Valve Inc. Iota One (Model: 060-0001-900) pulse driver is used to set the duration of the jet pulse and the time of actuation. The solenoid valve is the limiting factor of the configuration, with a maximum frequency of 100 Hz; the duty cycle can vary from 0.1 to 50 percent. The time history of the jet velocity is measured with a hot- film anemometer; data is acquired using a hot-film situated directly above the jet orifice while issuing jet fluid into quiescent surroundings.

Greenblatt and Wygnanski provide a review of the control of flow separation by periodic excitation [23]. It is well established that pulsed actuation is more efficient then steady actuation, as much less work input is required to achieve a similar performance result. Much of the recent research attempts to identify an optimal frequency which

16 makes the control as effective and efficient as possible by exploiting the natural instability mechanisms of the flow. Recent investigation of the topic is prevalent

[12,40,50].

The actuation jet blowing magnitude is presented as blowing ratio, BR, which is the jet velocity normalized by the local boundary layer edge velocity. The boundary layer edge velocity is calculated based on the local measured pressure coefficient, and the uncertainty of the calculated BR is approximately 8%. As the local fluid dynamics influence the interaction of the jet in cross flow, the prescribed BR accounts for this by normalizing the jet velocity by local freestream velocity, as opposed to the upstream velocity. Jet to free-stream density ratios are approximately unity (ρjet /ρlocal ≈ 1). The jet

2 momentum coefficient, Cµ, is defined as the injected momentum flux (jetUjet ) times the jet area divided by the upstream dynamic pressure times the wing planform area (S). For the general case of an array (N) of unsteady circular jets (diameter “d”) with a duty cycle

(DC) less than or equal to unity this can be written as follows [Eq. (1) also includes a conversion between BR and C for convenience]:

(1)

The airfoil is capable of being oscillated or dynamically pitched about its mid-chord location. The pitching motion is driven by a Leeson DC motor, which has a 20:1 gear ratio and provides 10.2 N.m of continuous torque. It is capable of operating at up to 120 rpm, with the rate driven by a GW Instek power supply. A crankshaft connects the motor

17 to one end of the airfoil. A once-per-revolution optical encoder signal is used to determine the instantaneous position or angle of attack of the airfoil.

2.4 Data Acquisition

2.4.1 Pressure Measurement

All data collection utilizes a PCI-6035E data acquisition (DAQ) card in conjunction with a National Instruments DAQ board. The static pressure distribution along the airfoil surface is obtained by connecting the surface pressure taps to a single 0.5” Druck differential pressure transducer. To utilize a single transducer, all pressure taps are first channeled to a manifold, allowing the user to toggle between pressure ports. The total and static freestream pressures are obtained with an upstream pitot-static probe. The pressure coefficient, CP, is calculated by taking the local static pressure minus the inlet static pressure and dividing by the upstream dynamic pressure, as seen in Eq. 2.

- (2) -

Using the trapezoidal rule to integrate the CP curve, CL is consequently determined [4].

Since pressure data are used exclusively to determine CL, this does not include contributions of the skin friction component. Wake pressures are acquired by traversing a

Kiel probe across the wake along the airfoil centerline, 1.67c downstream of the trailing edge. The drag coefficient, CD, is calculated using the momentum equation in the wake

[4]. These lift and drag values are corrected for wind tunnel effects per the equations developed by Barlow et al. [7], and an uncertainty analysis [14] is performed on the lift

4 coefficients. For a reference, for Re = 6.4x10 at α = 20° the nominal CL is 0.72, with an uncertainty of ±0.03.

2.4.2 Particle Image Velocimetry

Particle Image Velocimetry (PIV) is utilized to investigate the flow character and location of separation at a given angle of attack. A LaVision PIV system is used to obtain two- dimensional velocity data. The camera has a resolution of 1376 by 1040 pixels and is oriented to capture flow phenomena running the full length of the chord. Two image fields are taken, one at the leading edge half and the other at trailing edge half, and meshed together to get a high resolution, full field data set. For the present study, three- dimensional effects are neglected and consequently the PIV images are obtained near

50% span in a plane coincident with the centerline of a flow control hole.

A double pulsed Nd:YAG laser is used to project two consecutive one millimeter thick laser sheets (with a 80µs time separation) in the x-y plane into the test section. Olive oil particles with diameters between 1 and 2µm are inserted into the flow as seed. The laser pulses are synchronized with the high-speed camera to capture two exposures of the light scattered by the olive oil particulate. Figure 9 displays a cartoon representation for further understanding of the configuration.

Eight hundred image pairs are acquired and processed for each measurement. Two 16 x 16 pixel interrogation windows, each one overlapping another by 50%, are used to compute spatial correlation (via FFT) and output velocity vectors. Vector post processing includes a median filter and smoothing. From the PIV analysis several full-field flow

19 characteristics are obtained and used to analyze the flow field. Only the mean velocity results are included here.

Figure 9. Cartoon of a general Particle Image Velocimetry configuration.

In complicated flow fields, regions of considerable shear stress may conceal large- scale structures, making the identification of these structures and their contribution to the flow field difficult to determine. The swirl strength parameter is used with the phase- averaged PIV data to unveil vortical structures, and is calculated through analysis of the eigenvalues of the Jacobian of the velocity field [2,20,60]. In the eigen-analysis of the 2-

D PIV data acquired, there exist either two real eigenvalues or a complex conjugate pair.

Chong et al. [11] propose that a vortex core is a region of space where the rate-of-strain tensor is dominated by the strength of the vorticity and its corresponding rotation tensor, and this is evident when the rate-of-deformation tensor has complex eigenvalues. Hence,

20 the magnitude of the imaginary part of the eigenvalue defines the swirl strength, or the strength of the vortex core.

2.4.3 Surface Oil Flow Visualization

Oil flow visualization is used on the surface of the airfoil using a combination of brake fluid as the viscous transport and blue ink toner as the location identifier. The combination is atomized and sprayed evenly on the upper surface of the airfoil, which is then inserted horizontally into the wind tunnel. The flow is then turned on and images are taken of the airfoil with a camera once the fluid has reached a steady-state condition.

The purpose of oil flow is to demarcate the separation line and regions of laminar and turbulent flow using the properties of shear stress on the surface of the airfoil. Separated regions, where the shear stress is low (indicated by unmoved oil), and regions of large shear-stress gradients (indicated by oil-accumulation lines) can be nicely identified with this approach.

2.4.4 Hot-Film Anemometry

Two different constant temperature hot-film anemometers are employed. A traditional hot-film anemometer is used to obtain boundary layer, wake, and freestream measurements. The film is 50.8 μm in diameter, 1.02 mm long, and has a 100 kHz maximum frequency response. Figure 10 provides a simple cartoon of a standard hot-film sensor. The hot-film signal is low-pass filtered at 10 kHz using an IFA-300 (model:

183100) from TSI and sampled at 20 kHz to eliminate aliasing. When employing the hot-

21 film for boundary layer data acquisition the true wall normal distance is unknown; the author is able to optically determine the nearest wall location to be less than 0.1mm, but any further certainty is undetermined. Therefore the nearest wall location, in all analysis, is set to 0.1mm, and all other distances are adjusted relative to that. Three Tao Systems

SENFLEX SF9902 surface hot-film sensors are employed in the closed-loop control efforts. The individual sensors are on a 120 mm x 20 mm substrate, with nickel elements

0.1 mm wide and 1.45 mm long, as shown in Fig. 11. These sensors are mounted at x/c ≈

0, 0.2, and 0.4 (see Fig. 12). Their locations are determined based on the open-loop characterization of the baseline and controlled flow, in an attempt to minimize the number of sensors required for sufficient closed-loop separation control.

Figure 10. Graphic of a traditional hot-film sensor.

Figure 11. Graphic of a TAO Systems SENFLEX hot-film anemometer.

Surface hot-film elements

Normal jets x/c = 0.2 x/c = 0.4

Figure 12. Graphic of the integration of the surface hot-film sensors employed for closed- loop sensing.

Chapter 3: Results

3.1 Baseline Airfoil Characterization

Before evaluating the characteristics of the NACA 643-618 laminar airfoil, efforts are made to compare the baseline lift and drag coefficients of this investigation with the experimental results of Mack et al. [34]. Figure 13(a-c) displays the lift (a), drag (b) and

4 moment (c) coefficients of the NACA 643-618 at Re = 6.4x10 for the baseline and steady blowing results with the baseline results of Mack et al..

1.4 0.35 Baseline 1.2 Steady Blowing 0.3 Baseline (Mack et al.) 1 0.25 0.8

0.2 L

0.6 D C C 0.15 0.4 0.1 0.2 Baseline Steady Blowing 0.05 0 Baseline (Mack et al.) 2(1+t/c) slope a) -0.2 b) 0 -5 0 5 10 15 20 25 -5 0 5 10 15 20 25   0 Baseline Steady Blowing -0.02

-0.04

M C -0.06

-0.08

c) -0.1 -5 0 5 10 15 20 25  Figure 13(a-c). Comparison of (a) lift, (b) drag and (c) moment coefficients between baseline, steady blowing and the baseline results of Mack et al. [34] at Re = 6.4x104.

It is evident that the airfoil examined in this effort displays similar lift and drag characteristics to the other research effort. For low-to-moderate angles of attack the lift and drag coefficients follows the same slope and magnitude as Mack et al. The major discrepancy is that the data of Mack et al. jump to higher lift and lower drag values at around α = 10°. This corresponds to the formation of the laminar separation bubble, which was discussed in the introduction. The present work does not detect the formation of this laminar separation bubble until nearer to α = 13°. It is assumed that this inconsistency is due to subtle differences in airfoil geometry that are magnified by the extreme sensitivity of this airfoil at low Reynolds numbers. Mack et al. employed a slightly modified NACA 643-618, which has slight differences in thickness and leading edge radius. This causes the laminar separation bubble to form at a slightly different angle of attack. However, it is not critical for this effort that the two airfoils exhibit identical behavior. Rather, the critical feature is the poor performance over the majority of the α sweep due to the low Re flow. In particular, the substantial laminar separation observed in Fig. 13 at moderate α is of great importance.

Initial investigation of the baseline curves and surface oil-flow visualization, displayed in Fig. 14, reveals four regions of unique behavior. Region I corresponds to α < 0°, wherein the airfoil experiences minor laminar separation on the rear portion of the suction surface. Results of oil-flow visualization at a representative angle, α = -1°, are provided in Fig. 14(a). Separation is indicated by the accumulation of oil at x/c ≈ 0.45; upstream of the accumulation the surface is fairly clean of oil, indicating a persistent high shear zone. Further, downstream of the oil accumulation the original coat remains

25 untouched since negligible surface shear stress is present. Figure 15(a) is the corresponding full field display of the mean velocity of the baseline flow obtained from

PIV. The surprisingly poor performance of the airfoil at a negative angle of attack is due to the low Re application of an airfoil originally designed to operate at Re ≈ 1.0x106.

Figure 14(a-d). Surface-oil flow visualization of the baseline flow at (a) α = -1°, Region I, (b) α = 10°, Region II, (c) α = 16°, Region III and (d) α = 20°, Region IV at Re = 6.4x104.

Region II (0° ≤ α < 13°) experiences large regions of separated flow that severely reduce the airfoil performance, as they considerably thicken the effective airfoil shape and wake. This thickening prevents the development of a distinct suction peak near the leading edge, reduces the circulation and lift, and increases drag. The size of the separation region increases with α, and loss is most substantial at 10-13 degrees angle of attack. Here the airfoil is performing at its worst when compared to the ideal 2π(1+t/c) lift slope from airfoil theory [see Fig. 13(a)]. Figure 14(b) shows the surface-oil flow visualization at α = 10°. The separation location (x/c ≈ 0.22) has moved significantly upstream from the previous location. It is important to note a second line of oil accumulation downstream, in the large separated region. This large separation region experiences modest reverse flow and it is proposed that large-scale shear layer shedding is responsible for the second accumulation line evident at x/c ≈ 0.65. PIV data in Fig.

16(a) suggests a comparable separation location and a large recirculating region.

For 13° ≤ α < 19° (Region III) a sudden and dramatic increase in lift is experienced as the laminar separation point shifts upstream toward the leading edge of the airfoil.

Following separation, the boundary layer transitions to turbulent and reattaches just downstream forming a closed separation bubble. This turbulent boundary layer still separates, but much further downstream. Mack et al. [34] conjecture that this natural flow control occurs because the shear-layer instability mechanism of the separated flow is amplified when the angle of attack is increased. The shear-layer (Kelvin-Helmholtz) instability produces spanwise “rollers” which facilitate transition and provide necessary wall-normal momentum exchange which closes the bubble and reattaches the flow.

Figure 16(a-b). PIV determination of the velocity magnitude for (a) baseline and (b) steady blowing flow (BR ≈ 0.3) at α = 10° and Re = 6.4x104. (Region II).

Figure 14(c) shows the oil flow visualization of the baseline flow at α = 16°. Laminar separation is evident at x/c ≈ 0.02. Reattachment, indicated by an absence of fluid, is apparent at x/c ≈ 0.1. For reattachment to occur transition must take place slightly upstream, as indicated. Lastly, turbulent separation, where a less distinct and less uniform accumulation exists, can be seen at x/c ≈ 0.55. While the locations of these phenomena are generally placed in the figure, qualitative agreement with the conclusions of previous investigations [10,34,42] is manifest. The specific chord locations of separation, transition, and reattachment are dependent upon the combination of geometry, angle of attack and Reynolds number [5,38]. Further, while PIV averaging smears out the leading edge separation bubble, the airfoil’s general aerodynamic features are present in Fig. 17,

28 which displays the velocity magnitude determined by PIV. Of significance is the distinct suction peak (x/c ≈ 0.1, y/c ≈ 0.3) observed for this configuration, which corroborates with the naturally obtained performance improvement evident in Fig. 13.

Figure 17. PIV determination of the velocity magnitude for baseline flow at α = 16° and Re = 6.4x104. (Region III).

The final region, IV, (α ≥ 19°) is where strong leading edge laminar separation is evident. With increasing angle of attack the adverse pressure gradient becomes too extreme, the naturally occurring leading edge laminar separation bubble erupts, and separation occurs very close to the leading edge, resulting in a decrease in performance.

Figure 14(d), the oil flow at α = 20°, shows this separation with a clear accumulation of oil at x/c ≈ 0.01 and untouched oil at all locations downstream. All non-uniformity present in the image is the result of gravitational forces. Figure 18(a) confirms these results via PIV.

Figure 18(a-b). PIV determination of the velocity magnitude for (a) baseline and (b) steady blowing flow (BR ≈ 3) at α = 20° and Re = 6.4x104. (Region IV).

3.2 Open-loop Flow Control

3.2.1 Steady Blowing

The control study is performed at one representative angle in each region and is presented throughout at α = -1°, 10°, 16°, and 20°. As evidenced in Fig. 3, the separation location of the NACA 643-618 spans from x/c ≈ 0.45 at low angle of attack to the leading edge at high angle of attack. It would thus be ideal to allow for multiple actuation locations; at low angle of attack the actuation can be employed further downstream, and as the separation location moves toward the leading edge the actuation location can move

30 upstream with it. However, configuring the airfoil for multiple blowing locations can be difficult and expensive; an alternative is to vary the blowing ratio.

Consequently, at each representative α and Re a range of blowing ratios (0 ≤ BR ≤ 3) is investigated in order to optimize the airfoil lift. In some instances a higher blowing ratio did provide some additional lift, yet a lower blowing ratio is taken to be optimal as the marginal increase in lift did not justify the significant increase in required mass flow rate.

This corroborates well with the observation made by Seifert et al. [47] for low Re; that once an effective threshold Cµ is exceeded, additional Cµ fails to be linearly beneficial. A point of diminishing returns is expected, and in some cases the additional Cµ even proves detrimental. An illustrative example is displayed in Fig. 19, a plot of CL versus BR for steady blowing (α = 10° and 20°, Re = 6.4x104).

1.2 Recommended Recommended

0.8 L

C 0.6

0.4

0.2  = 10  = 20 0 0 1 2 3 BR

4 Figure 19. Variation of CL with BR at α = 10° and 20° (Re = 6.4x10 ).

Employing a BR ≈ 0.3 is recommended for α = 10°; any further increase in Cµ provides no additional performance improvement. It is important to note that a lower BR 31 may, in fact, be optimal for this configuration, but BR ≈ 0.3 is the lowest marker on the rotameter available for this study. The combination of low Re and moderate α on this laminar airfoil has a peculiar tendency to allow a positive restructuring of the laminar boundary layer profile with only a very minor perturbation. In contrast, at α = 20° the actuation is submerged within the baseline turbulent shear layer, and a significant BR is required for the normal jet to penetrate the shear layer and influence the flow. At α = 20° the initial conclusion is to set the optimal as BR ≈ 1.5, as it is necessary to double the mass flow rate (BR ≈ 3) to provide an eight percent increase in lift. However, the drag coefficient decreases approximately 10% over the same range. Since the overall aerodynamic performance considers both lift and drag, it is determined that the increased performance at BR ≈ 3 warranted the mass flow increase and the corresponding actuation power (Wi) required.

For α = -1° (Region I), steady blowing optimized at BR ≈ 1.5 slightly delays the separation location (∆x/c ≈ 0.05) and increases the lift. Figure 15(b) displays the PIV results, which highlight the subtle influence of control at this configuration. While the effect is not dramatic, a ΔCL = 0.15CL max is achieved, where CL max is the maximum of the

CL(α) curve for the prescribed Re. A laminar separation bubble begins near 60% chord, which appears to reattach near the trailing edge. Since normal blowing adds no direct streamwise momentum, it is speculated that the effectiveness comes from energizing the boundary layer through large scale, two-dimensional structures which entrain higher momentum freestream flow. The energized boundary layer subtly delays separation and increases the circulation of the airfoil, resulting in an increase of performance. At this

32 moderate blowing ratio it is hypothesized that the steady normal jet penetrates the freestream and forms large vortical structures above the boundary layer edge which encourage favorable momentum transfer toward the wall [66]. The long favorable pressure gradient suppresses the small scale instabilities from growing in the boundary layer, and those disturbances which persist are able to move freestream momentum into the boundary layer and create a fuller velocity profile, although the effect is assumed to be minor. Dovgal and Kozlov [17] noted that when disturbances are generated in the accelerating section they have a minimal effect on the development of the boundary layer downstream because of their strong damping.

The power spectral density (PSD) measured “on-hole” (z/s = 0) at x/c = 0.15 displayed in Fig. 20(a) suggests that the boundary layer is still laminar, like the baseline flow.

-1 -1

10 10

) ) 2

2 -2 -2 /s

/s 10 10

2 2

-3 -3 10 10

-4 -4

10 Baseline 10 Baseline

Energy DensityEnergy (m DensityEnergy (m Blowing: z/s = 0.5 Blowing: z/s = 0.5

-5 Blowing: z/s = 0 -5 Blowing: z/s = 0 a) 10 0 1 2 3 b) 10 0 1 2 3 10 10 10 10 10 10 10 10 Frequency (Hz) Frequency (Hz)

Figure 20(a-b). Power spectral density at (a) x/c = 0.15 and (b) x/c = 0.4 for steady blowing with BR ≈ 1.5 at α = -1° and Re = 6.4x104.

Moving downstream to x/c = 0.4 reveals increased energy content over a band of higher frequencies, suggesting that some instability is causing the flow to be positively perturbed. It is suggested that the long favorable pressure gradient is suppressing full

33 transition, since the PSD at z/s = 0.5 is still closer to the baseline (see Fig. 20(b)). Yet some form of mixing is present and strong enough to improve the boundary layer health.

It is possible that this mixing could be due to 2D longitudinal vortices [66], though they are not explicitly identified.

Within Region II, at α = 10°, steady blowing with BR ≈ 0.3 a dramatic effect on the airfoil performance, as the separation location is delayed about one-quarter chord, and a

ΔCL = 0.44CLmax is achieved. Figure 16(b) displays the performance improvement, and

Fig. 21 displays boundary layer profiles at five chordwise locations.

0.035 x/c = 0.4 Baseline 0.03 x/c = 0.3 Steady Blowing x/c = 0.4 Steady Blowing x/c = 0.5 Steady Blowing 0.025 x/c = 0.6 Steady Blowing x/c = 0.8 Steady Blowing

0.02 n/c 0.015

0.01

0.005

0 0 0.2 0.4 0.6 0.8 1 U/U e

Figure 21. Comparison of time-averaged boundary layer profiles for steady blowing at BR ≈ 0.3 at five chordwise locations (z/s = 0) for α = 10° with Re = 6.4x104. The baseline profile at x/c = 0.4 is obtained from PIV, and being massively separated it is not included at the other locations.

The mechanism for improvement with normal blowing at α = 10° is different than at

α = -1°. Gopalan et al. [21] showed that blowing at a low ratio (BR < 1) creates a small shell around the injection site. The jet is suppressed and small-scale three-dimensional 34 vortices are produced which settle within the boundary layer. The smaller region of favorable pressure gradient at α = 10° allows these vortices to propagate further downstream and effectively suppress separation exploiting turbulent momentum exchange with the freestream. Despite the increased volatility of the boundary layer in this region, a probe reveals that the boundary layer remains laminar until separation begins at x/c ≈ 0.5 (see Fig. 22).

That such a minor perturbation, which occurs over one-quarter chord upstream of the baseline separation location, can provide such an increase in aerodynamic performance while preserving laminar flow is fascinating. Work by Dovgal et al. [16] has shown how this can occur. Two-dimensional vorticity perturbations of initially small amplitude can be enlarged in an adverse pressure gradient, upstream of separation. This amplification causes a rearrangement of the laminar boundary layer through momentum transfer that, while preserving laminar flow, produces a fuller velocity profile which fortifies it against separation. Further, once laminar separation does occur, the instability waves evolving in the pre-separated boundary layer can be transformed into disturbances of the separated flow. This can in turn induce transition and potentially reattachment of the separation bubble near the trailing edge, provided that the instability frequencies of the boundary layer and shear layer overlap sufficiently.

Figure 22 substantiates the overlap at this condition by displaying the power spectral density for this configuration at five chord wise locations. A noticeable peak in the PSD is evident at f ≈ 415 Hz as early as x/c = 0.3. Moving nearer to the separation location (x/c

≈ 0.5) results in an increase in energy near this same frequency. Pushing further into the

35 separated region, x/c = 0.6, amplifies the peak at f ≈ 415 Hz, identifying the frequency of the observed shear layer shedding. This frequency corresponds well to the natural instability frequency, which is measured in the baseline shear layer at x/c = 0.4 for the same angle of attack [see Fig. 23(b)].

0 10

Kolm. -5/3 -1

)

2 /s

2 -2 10

x/c = 0.8 -3 10

x/c = 0.6 EnergyDensity (m

-4 10 x/c = 0.3 x/c = 0.4 x/c = 0.5

-5

10 0 1 2 3 4 10 10 10 10 10 Frequency (Hz)

Figure 22. Power spectral density at n/c = 0.003 and z/s = 0 for steady blowing with BR ≈ 0.3 at α = 10° and Re = 6.4x104.

Region III (α = 16°) exhibits a natural laminar separation bubble at x/c ≈ 0.05, with subsequent transition and reattachment of a turbulent boundary layer. Because it resides near the leading edge, the laminar separation bubble provides a natural control mechanism and significantly increases performance without the need of external actuation. All attempts at further improvement of the lift and drag through blowing techniques in this configuration proved ineffective. In fact, performance decreased with

36 the use of any blowing, suction or passive flow control techniques. The natural size and location of the bubble provide the best performance, and external control suppresses or disrupts the beneficial flow structures induced by the bubble.

0.07 0 10

0.06

-1 10 415 Hz

0.05 ] 2

/s 500 Hz 2

0.04 P2 930 Hz -2

10 y/c 0.03 1400 Hz P1

0.02 EnergyDensity [m -3 10

0.01 P1 a) -4 P2 b) 0 10 1 2 3 0 0.5 1 1.5 10 10 10 U/U  f [Hz]

Within Region IV (α = 20°), blowing with BR ≈ 3 is effective for this region through three-dimensional turbulence which is induced by the high blowing ratio jet. The jet, slightly downstream of the separation location in an extremely adverse pressure gradient, penetrates the separated shear layer bringing high freestream momentum down to the airfoil surface as a turbulent boundary layer. Amitay and Glezer [61] effectively demonstrate this flow mechanism via phase-locked smoke visualization. They show that reattachment of the flow, which is separated at the leading edge, is obtained via jet actuation which encourages mixing of the separated shear layer with the freestream fluid.

In the present effort the resulting fuller boundary layer is able to withstand the adverse

37 pressure gradient and delay separation from the leading edge to x/c ≈ 0.4, and a ΔCL =

0.25CLmax is recorded. Figure 18(b) displays the PIV results. A strong suction peak is evident near the leading edge, as tremendous acceleration is required for the flow to maneuver around the leading edge at high angle of attack, and this is the primary contribution to the lift increase.

In an attempt to separate the active control of separation from the active control of transition, passive flow control is also attempted at each angle of attack. The effects of zigzag tape are investigated through application at x/c = 0.05, the same location as the active control. The dimensions of the tape are taken from Mack et al. [34] and scaled accordingly. Passive control is ineffective in delaying separation at α = -1°, 16°, and 20°, as seen in Fig. 24.

1.5

1.25

0.75

L C 0.5

0.25

0 Baseline Steady Blowing Zig Zag Tape -0.25 0 5 10 15 20  Figure 24. Comparison of the lift coefficient between baseline, steady blowing and zigzag tape at Re = 6.4x104.

To understand why zigzag tape is unable to provide any performance improvement at low alpha an analysis is performed. Tani et al. [67] proposed equations 3 and 4, which are used to determine the effective trip-wire thickness (k) in a low-speed flow. These

38 equations account for the influence of the local pressure gradient by means of the local displacement thickness (δ*) and dimensionless pressure gradient parameter (λ*).

(3)

(4)

To estimate the local displacement thickness the XFLR5 2-D panel code solver was used.

In this manner the angle of attack, Mach and Reynolds number, and trip location directly determined this simulated value. This analysis concludes that in order to ensure transition the boundary layer at α = 1°the zigzag tape should be nearly an order of magnitude larger than was used. Otherwise, the large region of favorable pressure gradient dampens out any instabilities created by the “thin” tape.

At α = 16° the zigzag tape resulted in a performance loss, as did the active flow control techniques. At α = 20° the zigzag tape is submerged in the separated shear layer near the leading edge and is incapable of producing the required perturbations necessary for separation control.

At 10° the configuration is such that the perturbation imposed by the zigzag tape provided substantial performance improvement. The resulting boundary layer profiles are nearly as healthy as the active control counterparts, and PIV showed similar overall results as well. Since the tape has a positive effect on the flow, experience suggests transition occurs shortly downstream of the tape. However, a measured boundary layer profile at x/c = 0.12 showed the “passively” controlled boundary layer to be less turbulent 39 than that of the “active” blowing approach, or even the baseline flow. Fig. 25(a-b) compares the (a) mean velocity and (b) normalized turbulence intensity profiles of the flow for the baseline, steady blowing and zigzag tape configurations. The turbulence intensity is normalized by the boundary layer edge value to show how the turbulence intensity changes with respect to the freestream.

1.1 Baseline Blowing: z/s = 0 1 ZigZag Tape

0.9

0.8

0.7

 0.6 y/

0.5

0.4

0.3

0.2

0.1 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2 U /U Tu* avg 0.99 Figure 25(a-b). Hot-film investigation of the (a) mean velocity profile and (b) turbulence intensity of the boundary layer at α =10° and Re = 6.4x104 at x/c = 0.12. The turbulence intensity is normalized by the boundary layer edge value.

Another probe at x/c = 0.30 showed the “passively” controlled boundary layer to be experiencing increased turbulence intensity (perhaps transitioning), but not yet turbulent.

Further, an obvious difference is observed in the boundary layer (see Fig. 26(a-b)) and power spectral density profiles (see Fig. 27) when compared to the naturally transitioned flow at α = 16°. These data suggest that the zigzag tape may cause transition near x/c ≈

0.35 or 0.4. However, it appears that the tape creates instabilities which are not strong 40 enough to induce transition but are strong enough to instigate mixing and improve performance. Likewise, it is evident that the mechanism for active separation control through the application of steady blowing at α = 10° is not boundary layer transition.

1.1  = 10 -- Blowing: z/s = 0 1  = 10 -- ZigZag Tape  = 16 -- Natural Transition 0.9

0.8

0.7

0.6

 y/ 0.5

0.4

0.3

0.2

0.1

0 0 0.2 0.4 0.6 0.8 1 1.2 0.5 1 1.5 2 2.5 U /U Tu* avg 0.99

Figure 26(a-b). Hot-film investigation of the (a) mean velocity profile and (b) turbulence intensity of the boundary layer at α =10° and Re = 6.4x104 at x/c = 0.30, comparing the boundary layer with the flow at α = 16° and x/c ≈ 0.3, where a leading-edge separation bubble has naturally induced transition.

Based on the findings above, a few key conclusions can be made regarding the benefits of steady blowing and the effect of the actuation amplitude. At low Re, the lift curve can be modified, through the implementation of active flow control, to remove abrupt changes in performance while increasing overall performance. Low blowing ratios are sufficient only for unique configurations where small disturbances are easily amplified, whereas higher blowing ratios are required when large separation is evident.

At moderate angles of attack a minor perturbation results in significant performance improvement, all while maintaining a laminar boundary layer.

It is important to note that normal, steady blowing, in general, is not the most energy efficient. Pulsing has the potential to amplify unstable frequencies and introduce vorticity such that reduced mass flow may be required.

0 10  = 10 -- Blowing  = 10 -- ZigZag Tape  = 16 -- Natural Transition

10-1

) 2

/s -2 2 10

10-3 Energy Density (m

10-4

-5 10 100 101 102 103 104 Frequency (Hz)

Figure 27. Power Spectral density of flow at α = 10° and x/c = 0.3, comparing the boundary layer with the flow at α = 16° and x/c ≈ 0.3.

3.2.2 Pulsed Blowing

Further investigation of the controlled flow at α = 10° is conducted with detailed boundary layer profiles of the flow while employing steady and pulsed normal blowing.

Figure 28 compares the velocity profiles for steady and pulsed actuation at four

42 chordwise locations. The ordinate is indicated as “n/c”, the wall normal distance to the airfoil surface normalized by the airfoil chord, to differentiate it from y/c used in previous figures.

0.05 0.05

x/c = 0.4 Steady x/c = 0.5 Steady 0.04 x/c = 0.4 Pulsed 0.04 x/c = 0.5 Pulsed x/c = 0.4 Baseline

0.03 0.03

n/c n/c 0.02 0.02

0.01 0.01

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 U/U U/U   0.05 0.1 x/c = 0.6 Steady x/c = 0.8 Steady x/c = 0.6 Pulsed x/c = 0.8 Pulsed 0.04 0.08

0.03 0.06

n/c n/c 0.02 0.04

0.01 0.02

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 U/U U/U  

Figure 28. Comparison of time-averaged boundary layer profiles for steady and pulsed blowing at four chordwise locations at α = 10° with Re = 6.4x104. Steady blowing at BR ≈ 0.25 and pulsed blowing at BRmax ≈ 0.5, f+ ≈ 1, and DC = 5%. The baseline profile at x/c = 0.4 is obtained from PIV, and being massively separated it is not included at the other locations.

The appeal of pulsed blowing is evident as a reduction in required mass flow provides equivalent (or better) performance. The steady blowing results are for BR ≈ 0.25, whereas the pulsed results are for a frequency of 40 Hz (f+ ≈ 1), duty cycle of five percent, and

-4 -5 BRmax ≈ 0.5. Cµ values for the two cases are 1.29x10 and 2.97x10 , respectively, with

43 corresponding CL values of 1.06 and 1.14. The boundary layer profiles displayed in Fig.

28 are time-averaged. These, along with corresponding phase-locked wake surveys, reveal the flow with pulsed actuation to have very little dynamic motion at f+ ≈ 1. The drag calculated from the wake momentum thickness remains within ±11 percent of the mean drag through the duration of the pulsing period.

As pulsed actuation is shown to be a more efficient mechanism for separation control, the range of effectiveness is of great importance. Accordingly, the time-averaged lift coefficient is measured versus actuation frequency for a combination of duty cycles and blowing ratios. Figure 29 displays the effectiveness of pulsed actuation with varying pulsing parameters.

1.2 1.2

1.15 1.15

1.1 1.1 L

L 1.05 1.05

C C

1 1 5% DC 5% DC 0.95 50% DC 0.95 50% DC Steady, BR=0.5 Steady, BR=2 a) 0.9 b) 0.9 0 20 40 60 80 0 20 40 60 80 f (Hz) f (Hz)

Figure 29(a-b). Variation of CL with pulsing frequency and duty cycle for α = 10° and Re 4 = 6.4x10 , for (a) BRmax = 0.5 and (b) BRmax = 2. The baseline CL at α = 10° is 0.48.

Of note is the observation that with the low BR the aerodynamic performance exhibits a frequency preference, which is not present while actuating with a higher BR. While the results are not presented here, a full-field investigation revealed that the higher blowing causes the jet fluid to penetrate the boundary layer, roll up into the freestream and 44 develop into a large scale structure above the airfoil surface. This structure entrains high momentum flow down towards the wall which interacts with the wake and moves the separated region downstream with it. The jet fluid of the low BR configuration, however, stays much nearer to the airfoil surface, being redirected downstream by the freestream flow before it can penetrate deep into the freestream. Consequently, a dynamic interaction between the pulsed jet and the laminar boundary layer occurs at the separation location. Apparently, the receptivity of the boundary layer to this disturbance has a frequency preference near 40 Hz (f+ ≈ 1). This agrees well with Plogmann et al. [42], who found that when actuating from near the leading edge of the NACA 643-618 at α >

10°, forcing at f+ = 0.88 is found to be the most effective in increasing the maximum lift.

Another feature of Fig. 29 is the near independence of CL on duty cycle. Only at f = 5

Hz does the parameter have a significant effect. While the 50% duty cycle configuration always outperforms steady blowing in terms of aerodynamic performance and mass flow requirement, the 5% duty cycle case sees nearly a 10% drop in lift coefficient for both a low and high blowing ratio at f = 5 Hz. At this low frequency a higher mass input is required to produce enough momentum transfer to maintain performance.

To ensure that the frequency dependency observed in Fig. 29 for BRmax ≈ 0.5 is not due to variation in the pulsed jet waveform with actuation frequency, data is acquired using a hot-film situated directly above the jet orifice while issuing jet fluid into quiescent surroundings. A representative phase-locked characterization of the jet pulses is displayed in Fig. 30, which reveals a near-constant waveform of comparable peak velocity and primary structure.

Figure 30. Representative jet pulse characterization for varying frequencies with DC = 5% and BRmax ≈ 0.5.

The phase lag of the internal plumbing is nearly constant with varying frequency circa

40 Hz (f+ ≈ 1), as fluid is first sensed leaving the jet orifice about 4ms after the solenoid valve receives the TTL pulse. Since the duty cycle is constant, the pulse width changes with the actuation period. Further, while the pulse driver transmits a square wave with

DC = 5%, the internal dynamics of the actuation cause a smearing of the jet pulse, particularly at the higher actuation frequencies. For example, at f = 80 Hz, the jet orifice has BR > 0.1 for approximately 25% of the pulsing period, or DC ≈ 25%, while for f = 5

Hz, BR > 0.1 for the expected 5% of the pulsing period. Since duty cycle is found to have very little effect on performance in Fig. 30, the variations in the jet pulses are not considered to be significant.

Physical Mechanisms

With an understanding of the range of effectiveness in terms of frequency, duty cycle, and BR dependence, the next pertinent investigation is to seek an understanding of the physical mechanisms involved. Yet the lack of significant dynamic motion in the boundary layer or wake for the pulsed actuation cases outlined in the previous section makes this difficult. Using phase-locked wake surveys with the hot-film the movement of the mean flow are tracked while reducing the frequency and duty cycle. For each iteration the frequency and duty cycle are halved, thus maintaining a constant TTL pulse width, or

“on-time”, while doubling the “off-time”. The intent is to allow more time for the flow to respond between pulses. This iterative process continues until large scale unsteady behavior is visualized. Table 1 compares the on- and off-times for each of the frequency and duty cycle combinations investigated.

Table 1 Combinations of frequencies and duty cycles used in search of dynamic motion f f+ (fc/U∞) DC (%) T (ms) On-Time (ms) Off-Time (ms) Cµ (Hz)40 0.95 5 25 1.25 23.75 2.97x10-5 20 0.475 2.5 50 1.25 48.75 1.48x10-5 10 0.238 1.25 100 1.25 98.75 7.41x10-6 5 0.119 0.625 200 1.25 198.75 3.71x10-6

Again, care is taken to quantify the variance of the jet pulse with changing parameters.

Figure 31 displays the phase-average of the jet pulse for the four parameter combinations defined in Table 1. While minor variation is observed in the peak velocity, the pulse is nearly identical in all cases, employing an “on-time” of 1.25ms throughout.

0.7

0.6 5 Hz 10 Hz 0.5 20 Hz 40 Hz 0.4

BR 0.3

0.2

0.1

0 0 5 10 15 20 25 time (ms)

Figure 31. Actuation jet pulse characterization for the parameter combinations defined in Table 1 with peak BR ≈ 0.5.

Figure 32 tracks CL with varying frequency for the parameter combinations defined in

Table 1. Comparing these results to those obtained with a constant 5% DC (Fig. 29), as the frequency and corresponding duty cycle decrease the time averaged lift coefficient continues to drop. This is expected when considering the importance of the duty cycle parameter at low frequency and blowing ratio. Results in Fig. 29 indicate that while decreasing the frequency to 5 Hz (f+ ≈ 0.12) results in a noticeable drop from the 25 Hz

(f+ ≈ 0.62) configuration, maintaining a fifty percent duty cycle provides a time-averaged lift coefficient above that produced with steady blowing. It is when dropping the duty cycle to five percent that a significant reduction in the time-averaged performance is observed. This result, in combination with that of Fig. 32, suggests that while frequency plays an important role, this role is dependent upon maintaing a Cµ substantial enough for sufficient control. Thus for the majority of the parameter combinations explored in Fig.

29 (the combinations that would be employed for effective active separation control) the critical Cµ is maintained and emphasis can be appropriately directed toward the influence 48 of frequency and blowing ratio. In these instances the blowing ratio directly determines how the jet-in-crossflow will interact with the boundary layer. For low BR, where the jet fluid is quickly mixed into the passing boundary layer, the pulsing frequency can clearly influence the time-average performance (Fig. 29(a)). In contrast, for high BR the jet fluid penetrates deep into the freestream and the airfoil suggests no clear frequency preference within the investigated range (Fig. 29(b)).

1.2

1.15

1.1

L 1.05 C

1 Pulsed 0.95 steady

0.9 0 10 20 30 40 50 f (Hz)

Figure 32. Lift coefficient versus frequency for the parameter combinations defined in Table 1 with peak BR ≈ 0.5.

Significant dynamic motion is not evident until actuating with a frequency of 5 Hz

(f+ ≈ 0.12) and duty cycle of 0.625%, for a TTL “on- time” of just 1.25ms and an “off-

th time” of 198.75ms. This configuration has a Cµ that is 1/8 of the 5% duty cycle configuration at the top of Table 1.

Phase-locked PIV of 800 different realizations is employed with these parameters for full-field analysis. It is obtained by synchronizing the laser firing and image acquisition to specific times within the period of pulsed jet actuation by specifying a time delay.

Eight hundred image pairs are acquired with a constant time delay, then processed and averaged to obtain flow information at one time step. This process is completed for 33 unevenly spaced phases within the period, with an increased temporal density during the most dynamic portions of the period. Two data acquisition windows combine to span from 0 ≤ x/c ≤ 1.2, and a view of the wake from 0 ≤ y/c ≤ 0.4.

A low forcing frequency (f+ = fc/U∞ ≈ 0.12) and duty cycle (DC = 0.625%) are employed for pulsed actuation; a pulse time history of the jet is shown in Fig. 33. The thirty-three unevenly spaced phase positions are indicated along the top of the figure, indicating the regions of increased emphasis, wherein the critical features of the physical mechanisms are made manifest.

0.6

0.5

0.4

0.3 BR

0.2

0.1

0 0 0.25 0.5 0.75 1 t/T

Figure 33. Actuation jet pulse characterization for f = 5 Hz (f+ ≈ 0.12) and DC = 0.625%. The 33 phases investigated with PIV are plotted above the jet time-history.

Figure 34(a-h) displays velocity magnitude and swirl strength contours for eight phases of the pulse period. Time increases from top to bottom, spanning from the moment the TTL signal is received from the pulse generator (t/T = 0) to t/T = 0.925. A

50 white dashed line demarcates the two acquisition windows, which is the cause for some discontinuity evident in the images, particularly in the swirl strength. Note that the

PIV acquisition windows are oriented in line with the blade coordinates, so while the airfoil is physically set to α = 10°, the images appear without rotation. Figure 35(a-d) displays velocity magnitude contours only for four closely spaced phases of the pulse period, to provide additional temporal resolution.

The actuator is pulsed at t/T = 0 (Fig. 34(a)), and the resulting disturbance convects downstream toward the separation point. As shown by Dovgal et al. [16], the disturbances are amplified as they encounter the adverse pressure gradient, which begins near the leading edge. The receptivity of the boundary layer upstream of separation is significant, and an amplification of vortical strucutures in the shear layer results, due to a

Kelvin-Helmholtz (K-H) instability. The first evidence of large scale separation control is observed as a ripple in the shear layer at t/T = 0.087, and it is more patent at t/T = 0.104

(Figs. 35(a) & (b)). Significant motion in the shear layer develops at t/T = 0.139. As seen in Fig. 35(c), a large pocket of high velocity fluid at x/c ≈ 0.8 and y/c ≈ 0.3 is interacting with the low momentum fluid in the shear layer, causing it to deform and convect downstream (Fig. 35(d)). This causes the “wake structure” to separate from the blade between 0.208 < t/T < 0.313 (Figs. 34(d) & (e)), taking a large region of low momentum flow away from the airfoil in the process. Thus ensues a period of increased circulation and reduced drag. It is believed that this is the primary mechanism for separation control in the present configuration.

0.4

0.3 a) t/T = 0.001 0.2

0.1

0 0.4

0.3 b) t/T = 0.069 0.2 Normal Velocity at t/T = 0.001 Axial Velocity at wake location at t/T = 0.001 0.6 5 9 0.1 8 0.5 4 0 7 0.4 0.4 6 3 0.3 0.3 5

c) t/T = 0.1390.2 4

2 y/c 0.2 3 0.1 Normal Velocity at t/T = 0.069 Axial Velocity at wake location at t/T = 0.069 0.6 5 9 Axial Velocity (m/s) 2 0.1 1 0 8 0.5 1 4 70 -0.1 0 0 0.4 0.4 -16 Controlled wake -0.2 3 Baseline Wake 0.3 -1 -25 0 0.3 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x/c x/c d) t/T = 0.2080.2 4

2 y/c 0.2 3 0.1 Normal Velocity at t/T = 0.139 Axial Velocity at wake location at t/T = 0.139

0.6 5 Axial Velocity (m/s) 29 0.1 1 0 18 0.5 4 07 -0.1 0 0 0.4 0.4 -16 Controlled wake -0.2 3 Baseline Wake 0.3 -1 -25 0 0.3 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x/c x/c e) t/T = 0.3130.2 4

2 y/c 0.2 3 0.1 Normal Velocity at t/T = 0.208 Axial Velocity at wake location at t/T = 0.208 0.6 5 9 Axial Velocity (m/s) 2 0.1 1 0 18 0.5 4 07 -0.1 0 0 0.4 0.4 -16 Controlled wake -0.2 3 Baseline Wake 0.3 -1 -25 0 0.3 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x/c x/c f) t/T = 0.4170.2 4

2 y/c 0.2 3 0.1 Normal Velocity at t/T = 0.313 Axial Velocity at wake location at t/T = 0.313 0.6 5 Axial Velocity (m/s) 92 0.1 1 0 81 0.5 4 70 -0.1 0 0 0.4 0.4 -16 Controlled wake -0.2 3 Baseline Wake 0.3 -1 -25 0 0.3 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x/c x/c g) t/T = 0.5560.2 4

2 y/c 0.2 3 0.1 Normal Velocity at t/T = 0.417 Axial Velocity at wake location at t/T = 0.417 0.6 5 9 Axial Velocity (m/s) 2 0.1 1 0 18 0.5 4 07 -0.1 0 0 0.4 0.4

0.4 -16 Controlled wake -0.2 3 Baseline Wake 0.3 0.3 -1 -25 0 0.3 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 h) t/T = 0.925 x/c x/c 0.2 4 2 g) t/Ty/c = 0.9250.2 0.2 3 0.1 Normal Velocity at t/T = 0.556 Axial Velocity at wake location at t/T = 0.556 0.6 5 9 Axial Velocity (m/s) 2 0.1 1 0 0.1 18 0.5 4 0 07 -0.1 0 0 0.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -16 Controlled wake -0.2 x/c 3 x/c Baseline Wake 0.3 -1 -25 0 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x/c x/c 0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 4 0.1 0.2 0.3 0.4 0.5 2 y/c U/U Swirl Strength  3 0.1 Normal Velocity at t/T = 0.925 Axial Velocity at wake location at t/T = 0.925 0.6 5 9 Axial Velocity (m/s) 2 Figure 34(a-h). Phase-locked PIV of velocity1 magnitude (left) and swirl strength (right). 0 8 0.5 1 The dashed white line demarcates two 4 acquisition windows. The white space near the 70 -0.1 0 0.4 airfoil indicates a mask used in post-processing. t/T is-16 indicated on the left. Controlled wake -0.2 3 Baseline Wake 0.3 5 -1 -2 0 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x/c 52 4 x/c 0.2

2 y/c 3 0.1

Axial Velocity (m/s) 2 1 0 1

0 -0.1 0

-1 Controlled wake -0.2 Baseline Wake -1 -2 0 0.2 0.4 0.6 0.8 1 1.2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x/c x/c 1.6 0.3 a) t/T = 0.087 0.2 1.4 0.1

0 1.2

0.3 b) t/T = 0.104 0.2 1 U/U 0.1  0.8 0

0.3 c) t/T = 0.139 0.6 0.2

0.1 0.4

0 0.2 0.3 d) t/T = 0.185 0.2 0 0.1

0 0 0.2 0.4 0.6 0.8 1 x/c

Figure 35(a-d). Phase-locked PIV of velocity magnitude of four intermediate phases for temporal resolution of the vortex structure and wake interaction.

The underlying physical mechanism responsible for this control is observed in the swirl strength contours of Fig. 34. At this frequency-duty cycle combination the attached shear layer has time between pulses to begin separating, and the separation point moves quickly up the airfoil. Just when the separation point reaches its maximum upstream location, comparable to that of the baseline configuration, the free shear layer starts to swing outward (away from the airfoil) to resume its baseline location (Fig. 34(g) & (h)).

The jet is then pulsed at x/c = 0.05 (Fig. 34(a)). As fluid from the jet in cross flow convects downstream the perturbations imposed by the jet grow in the shear layer at the separation location, via excitation of a Kelvin-Helmholtz (K-H) instability.

Smaller scale structures are first identified in the swirl strength contours at t/T = 0.069

(Fig. 34(b)), 3ms before any motion in the shear layer is detected. While the large structures further above the airfoil surface are interacting with each other there are 3-4 small structures present on the airfoil surface. The average frequency of these structures is on the order of 450 Hz. The K-H undulations of the free shear layer produce favorable momentum exchange such that the free shear layer begins to approach the wall. The wake contracts until t/T = 0.417 (Fig. 34(f)), and the proximity to the wall dampens out the K-

H instability and the boundary layer fully attaches. The wake and the corresponding drag are at a minimum. The boundary layer stays attached until t/T ≈ 0.5; this is the phase lag or “inertia” of the airfoil circulation. In time, the boundary layer begins to detach and separate (0.5 < t/T < 0.069); yet there is no evidence of the K-H instability until the jet perturbation arrives again. It is important to reiterate that the swirl strength is evaluated for the phase-averaged PIV data. The fact that the observed structures survive the averaging of eight hundred image pairs is remarkable. The structures lock into the forcing, despite the order of magnitude difference in the forcing and shedding frequencies.

It is anticipated that higher frequency forcing may not exhibit the same dynamics as for f+ ≈ 0.12 shown in Figs. 34 and 35. If pulsing at f+ ≈ 1 is initiated during stall, the first pulse will behave like control with f+ ≈ 0.12, but subsequent pulses operate on a much thinner separation zone that has not recovered due to the phase lag. The unsteady dynamics at f+ ≈ 1 are far less pronounced, with hysteresis regulating the flow long enough for the proceeding jet pulse to fire. The actuation is occurring rapidly enough that

54 the wake does not have time to relax toward the baseline configuration. It is expected that since the separation zone has been subdued, each jet pulse will not result in the large scale structure-wake interaction evident at f+ ≈ 0.12. Furthermore, the disturbances created by the jet-in-crossflow interaction must travel a greater distance before encountering the separated shear layer. Despite this increased distance, it appears that the disturbances are still substantial enough to cause a K-H instability (see Fig. 45), resulting in momentum exchange and, ultimately, separation control.

3.3 Instability Classification

The observed shear-layer instabilities in Fig. 34 warrant further investigation. It merits repetition to note how remarkable it is that the flow can lock into coherent shear-layer shedding on the order of 450 Hz resulting from a 5 Hz forcing frequency. Further, it is remarkable that this locking is coherent enough to survive the averaging of eight hundred image pairs. This phenomenon can be explained by concluding that the observed structures are not the byproduct of the pulsing itself, but are the result of the perturbations which are imposed by the jet-in-crossflow (JICF). To verify this hypothesis, the ensuing section will justify the following:

1) That the observed structures should be classified as a K-H instability.

2) That the natural instability frequency is of the same order as the instability

frequency measured in the structures of Fig. 34.

3) That the structures are independent of the 5 Hz forcing frequency, and that the

frequency content necessary to trigger the K-H instability is a byproduct of the

complex interaction of the jet-in-crossflow.

4) That the imposed perturbation originating near the leading-edge is capable of

initiating the K-H structure formation observed at least x/c = 0.3 downstream.

Item 1: It is suggested above that the coherent shedding is regulated by the Kelvin-

Helmholtz mechanism in the shear layer. Justification of this classification is accomplished through the correlation introduced by McAuliffe and Yaras [36]. They utilize a dominant instability Strouhal number, Srθ, to correlate the vortex shedding mode to the K-H instability. This is calculated via Equations 5-6

(5)

(6)

where θs is the momentum thickness [56] at the separation location and Ues is the boundary layer edge velocity at the separation location. These secondary parameters are calculated via boundary layer profiles interpolated from the PIV contours, as shown by the representative vertical lines in Fig. 36. These interpolated boundary layer profiles confirm that the observed structures are indeed originating at the baseline separation location. It is important to note that while the separation location recovers the baseline position, the wake will take longer (than 200 ms) to resume its baseline extent. More time

56 is required for the circulation “inertia” to dissipate, allowing the wake to swing outward from the airfoil surface. The shear layer shedding frequency, fs, is determined by ascertaining Uavg, the mean velocity of, and D, the distances between, swirl structures observed in the PIV results (see Fig. 37). All information is based on the flow of Fig.

37(b) at the separation location, corresponding to the origin of the small structures first evident in the actuation period.

0.3

0.2 y/c 0.1

0.3

0.2 y/c 0.1

0.3

0.2 y/c 0.1

0 0.2 0.4 0.6 0.8 1 1.2 x/c Figure 36. Comparison of the velocity magnitude of the baseline (top) with the unsteady flow at t/T = 0.069 (middle) and the swirl strength of the same phase (bottom), the phase whereat the separation point has traveled the furthest upstream.

The calculated frequency is proposed to be the most-amplified instability frequency of the inflectional velocity profile. McAullife and Yaras assert that the associated instability of the laminar separation bubble on an airfoil surface is likely convective in nature and that growth of the most-amplified instability frequency results in the formation of vortices having a direction consistent with the shear layer vorticity. The present study

57 concludes that Srθs = 0.015, which compares well to McAullife and Yaras’ value of

0.011. In fact, a review of the instability Strouhal numbers identified in several other experimental and numerical studies involving shear layers with inflectional velocity profiles reveals a range of 0.005 ≤ Srθs ≤ 0.016. A previous survey by Thomas [65] supports this proposed range. His supplementary review of open literature revealed values of Srθs in the range of 0.009 to 0.018.

0.2 1.5

0.1 1 y/c 0.5 0 0 0.2

0.4 0.1 y/c 0.2

0 0 0 0.2 0.4 0.6 x/c Figure 37. Ascertaining the mean velocity of and distances between swirl structures from the PIV results for the determination of the shear layer shedding frequency, fs.

Item 2: The natural shear-layer shedding frequency at this configuration is obtained experimentally by investigating the power spectral density (PSD) of the baseline flow.

Recall Fig. 23(a-b), which shows the results for Re = 6.4x104 and α = 10°; the two curves correspond to two locations in the shear layer near the point of maximum skewness. A distinct frequency preference is observed at f ≈ 415 Hz, a comparable value to the observed structures in Fig. 34 (fs ≈ 450 Hz). 58

Complementary to the experimental investigation, a numerical investigation of the natural shedding characteristics has been performed at the University of Arizona. Balzer and Fasel [6] performed Direct Numerical Simulation (DNS) on a “modified” NACA

4 643-618 airfoil at Re = 6.42x10 and α = 8.64°. This configuration is very similar to the experimental arrangement executed in the present work. They performed a discrete

Fourier transform (DFT) of the wall normal disturbance velocity at three downstream locations, sSL = 0.4, 0.5, and 0.6, as indicated in Fig. 38. From this analysis a fundamental frequency is identified. Utilizing F+ ≈ 8.5, which is on the upper end of the identified band in Fig. 38, corresponds to a natural shedding frequency of f ≈ 400 Hz.

Figure 38. Frequency spectrum of the wall-normal disturbance velocity at various downstream locations, indicating the preferred shedding frequency in the shear layer of a 4 modified NACA 643-618 airfoil at Re = 6.42x10 and α = 8.64°. Taken from [6].

Acoustic excitation is employed to further substantiate that the natural instability frequency is near the frequency of the structures measured via PIV. The use of acoustic excitation is proposed as a precise method of control that allows for specific excitation of instability frequencies without involving the turbulent physics of normal jets.

The effect of acoustic excitation is investigated with velocity profile measurements, in the same location as the baseline (Fig. 38(b)). Acoustic excitation is applied using a Pyle

Dryver Pro (Model: PDIC60) ceiling speaker for frequencies above 65 Hz and a Klipsch subwoofer (Model: SW - 350) for frequencies below 65 Hz. Both can be mounted flush on the ceiling of the wind tunnel with the center of the speaker located 1.7c upstream of the airfoil leading edge, as shown in Fig. 39. The ceiling speaker is amplified using a

Sony amplifier (Model: STR-DH100). The input frequency is set with an Agilent signal generator (Model: 33521A).

Figure 39. Top-view schematic of the airfoil test section showing speaker placement and hot-film placement for the acoustic characterization.

Due to the speaker geometry and the associated electronics, the actuation amplitude imparted into the flow varies as a function of frequency. Since the purpose of this study is to address purely the effect of frequency receptivity on the boundary layer, it is important that the excitation amplitude is held constant over the frequency range to determine the most optimal frequencies. To characterize the speaker and subwoofer, a hot-film sensor is placed at midspan in the tunnel aligned with the leading edge of the airfoil. The flow is

60 turned on to match the test conditions of Re = 6.4x104. The sensor is placed in the freestream midway between the airfoil suction surface and the tunnel wall (see Fig. 39).

The amplifier settings are held constant and the input voltage from the signal generator is used to control the sound amplitude. For a given input voltage, hot-film measurements are taken for a range of frequencies. This is repeated for seven input voltages. The frequency coefficient at the excited amplitude is taken as the excitation amplitude for each frequency and input voltage. This creates a look-up table that can be used to maintain constant excitation amplitude for any given frequency.

Velocity probes are taken for the peak frequencies shown in the PSD (Fig. 23(b)), shown in Fig. 40(a). The 415Hz is the most effective in adding near wall momentum, and the 500Hz frequency demonstrates significant improvement as well. The low frequency of 100Hz and the two higher frequencies of 930Hz and 1400Hz each appear ineffective in changing the airfoil performance. A second set of velocity profiles are taken at x/c = 0.8

(Fig. 40(b)) with actuation at 415Hz and 500Hz. At this downstream location, it is shown that the 415Hz frequency is much more effective at energizing the boundary layer. It is interesting to note that the frequencies within a narrow range of the K-H instability frequency are the only frequencies that have any effect. The strong laminar characteristics of this airfoil are thought to result in the strong preference to the K-H instability.

It is hypothesized that pulsed flow control takes advantage of the natural K-H instability frequencies that have been determined in this study (Item 1). The jet structure initiates small scale turbulence and streamwise vorticity within the boundary layer which

61 has been shown to further increase control effectiveness through momentum exchange between the free-stream flow and the boundary layer.

0.04 0.12 Baseline Baseline 0.035 f = 100Hz f = 415Hz f = 415Hz 0.1 f = 500Hz f = 500Hz 0.03 f = 930Hz f = 1400Hz 0.08 0.025

0.02 0.06

y/c y/c

0.015 0.04

0.01

0.02 0.005

a) b) 0 0 0 0.2 0.4 0.6 0.8 1 1.2 0.4 0.6 0.8 1 1.2 U/U U/U  

Figure 40(a-b). Velocity profiles of the acoustic control investigation for α = 10° at (a) x/c = 0.4 and (b) x/c = 0.8.

Figure 41(a-b) shows a comparison between the acoustic control and pulsed-jet control. The mean velocity profiles at x/c = 0.4 suggest that acoustic control at 415Hz is comparable to the pulsed-jets at 40Hz. This supports the hypothesis that the pulsed-jets are exciting the natural K-H instability of the free shear layer. At x/c = 0.8 the jets show a slight benefit with added momentum near the wall over the acoustic control. This benefit may be attributed to the physics of the pulsed jet that creates turbulent structures and streamwise vorticity that enhance momentum exchange down towards the airfoil surface.

0.04 0.12 Baseline Baseline Acoustic, f=415Hz Acoustic, f=415Hz 0.035 Jets, f=40Hz Jets, f=40Hz 0.1

0.03

0.08 0.025

0.02 0.06

y/c y/c

0.015 0.04

0.01

0.02 0.005 a) b) 0 0 0 0.2 0.4 0.6 0.8 1 1.2 0.4 0.6 0.8 1 1.2 U/U U/U  

Figure 41(a-b). Comparison of the velocity profiles of the baseline, acoustically controlled, and jets controlled flow for α = 10° at (a) x/c = 0.4 and (b) x/c = 0.8.

Item 3: The present experimental efforts agree well with the numerical analyses of Balzer and Fasel [6] with regards to the natural instability frequency of the separated shear layer.

Further, the correlation by McAuliffe and Yaras suggests that this measured shedding frequency is the fundamental instability frequency, the K-H mechanism. Evidence is now required to verify that the perturbations imposed by the jet-in-crossflow interaction are responsible for the coherent high frequency shedding, and that it is independent of the 5

Hz forcing.

Recall Fig. 22, which plots the PSD at x/c = 0.3, 0.4, 0.5, 0.6, and 0.8 for the implementation of steady blowing with BR = 0.5. At x/c = 0.4 a noticeable peak in the

PSD is evident at f ≈ 415 Hz. Moving nearer to the separation (x/c ≈ 0.5) location results

63 in an increase in energy near this same frequency. Pushing further into the separated region, x/c = 0.6, further amplifies the peak at f ≈ 415 Hz. Thus steady blowing causes the consistent shear-layer shedding with a frequency similar to that of pulsed-blowing. Recall from Fig. 34 that the structures are only evident for the portion of the pulsing period.

They are first observed shortly after the jet is emitted from the actuation holes, and only survive until they are dampened by near-wall viscous effects. In contrast, the shear layer

PSDs in Fig. 22 indicate that steady blowing causes repeated coherent structures to form in the shear layer.

Independence of the shedding structures of the 5 Hz pulsing is further verified through

Fig. 42. This looks at the phase-locked contours of the turbulence intensity for a pulsing frequency of 40 Hz with a 5 percent duty cycle. The contours of turbulence intensity are obtained with the hot-film follower device, for Re = 6.4x104, α = 10°, and BR = 0.5. This particular phase image is approximately t/T ≈ 2/3. The emitted jet has propagated downstream and is interacting with the shear layer. Three shed vortical structures can be seen. Calculation of shedding frequency, as performed above, results in an approximate shedding frequency on the order of 400 Hz. This indicates that some critical information is produced by the JICF that propagates downstream and interacts with the shear layer. It appears to not be dependent on a particular forcing frequency, nor does it require that forcing even be unsteady. Regardless, the complex interaction is such that the dominant instability frequency is perturbed and allowed to amplify as the fluid convects downstream and interacts with the shear layer.

Figure 42. Phase-locked contours of the turbulence intensity for a pulsing frequency of 40 Hz with a 5 percent duty cycle. Re = 6.4x104, α = 10°, and BR = 0.5. The contours are obtained with the hot-film follower device. This phase is approximately t/T ≈ 2/3. The emitted jet has propagated downstream and is interacting with the shear layer. Three shed vortical structures can be seen.

Item 4: It is left to explain how the JICF is capable of producing the bandwidth necessary for the above phenomenon to occur. Steady normal blowing from a discrete hole located in a boundary layer results in a complex interaction. Gopalan et al. [21] experimentally observed that at low blowing ratios (BR < 2) stretching of vorticity in the backside of the jet generates a semi-cylindrical vortical layer or shell. This shell extends from the underside of the jet and connects to the wall, enclosing the domain with slow moving reverse flow. Recall Fig. 5, which illustrates streamlines and normalized mean velocity magnitude for BR = 0.5.

Within approximately one hole diameter above the wall the jet has turned into the cross flow direction and entrainment into the crossflow has begun. The jet momentum is not large enough to penetrate deep into the freestream, but instead results in the majority of the jet fluid being entrained into the boundary flow and interacting downstream with 65 the surface shear layer. Gopalan et al. describe that this occurs because the jet experiences different conditions on the forward and rear boundaries at it emerges from the surface. While the back side of the jet shear layer is exposed to slow moving flow the forward face confronts the incoming cross flow. The negative vorticity of the wall boundary layer interacts with the positive jet vorticity on the forward side, yet on the reverse-side the jet vorticity is unrestricted. They conclude that the significant differences between the forward and back sides causes the jet “vortex ring” to stretch vertically along the back side, while mixing with the wall boundary layer vorticity on the front side.

Figure 43 displays instantaneous iso-surfaces of the second invariant of the velocity gradient, and is calculated via Large Eddy Simulation by Majander and Siikonen [35].

Despite employing a higher blowing ratio (BR = 2.3), the results of their work are employed to provide additional insight to the complexity of the jet-in-crossflow interaction.

Figure 43. An instantaneous iso-surface of the second invariant of the velocity gradient, Q = 30, displaying the complexity of the JICF. Taken from [35].

The jet-in-crossflow interaction produces a complex perturbation which, in this instance, results in coherent shedding in the downstream separated shear layer. However, a review of open literature determined that it remains unknown precisely how this is done. With an understanding of the potential disturbances resulting from the JICF it is not unreasonable to assume that this interaction is capable of producing a broad frequency band of perturbations on the order of the fundamental instability frequency. Future efforts should be made to validate this presumption. A detailed investigation of the frequency content of the perturbations could be measured at a number of different locations.

Measurements in the near wake could characterize the perturbations as it originates.

Ancillary measurements at multiple downstream locations could subsequently track the propagation and potential transformation of the perturbation as it navigates the adverse pressure gradient and interacts with the shear layer.

Even though the interaction of the JICF is capable of producing such a perturbation, additional assistance is needed for the fundamental frequency to produce the observed structures in Fig. 34. Dovgal et al. [16] state that there are two means for the excitation of disturbances in the flow. First, the more commonly observed, is the generation of disturbances at separation. Second, and the proposed mechanism for the current investigation, the disturbance waves evolving in the pre-separated boundary layer are transformed into the disturbances of the separated flow. In this case, the receptivity of the boundary layer upstream of separation is critical. Despite the small blowing amplitude, disturbances originating upstream with frequency content at or near the fundamental

67 instability frequency propagate downstream. The disturbances evolving in the pre- separated boundary layer are transformed into the disturbances of the separated flow.

In summary, the coherent structures in Fig. 34 are correlated to the Kelvin-Helmholtz instability through the procedure outlined by McAuliffe and Yaras [36]. The correlated frequency compares well to the measured and simulated natural instability frequency.

Coherent structures of a comparable shedding frequency also occur with steady blowing, and pulsed blowing at 40 Hz. The K-H mechanism does not appear to be dependent on the pulsing frequency, nor does it require the forcing to even be unsteady. The jet-in- crossflow interaction has been shown to be extremely complex [19,21,29,32,35,57] with intense mixing and vorticity generation downstream of the actuation jet. It is hypothesized that this interaction produces a perturbation at or near the fundamental instability frequency. Lastly, Dovgal et al. [16] experimentally observed that the interaction with the shear layer may cause a transformation of the disturbances within the pre-separated boundary layer into the disturbances of the separated flow. It is thus conclusive that the Kelvin-Helmholtz mechanism plays a significant role in the observed shear layer dynamics of Fig. 34.

3.4 Closed-Loop Separation Control

The fundamental principle behind closed-loop, or feedback, control is that real-time measurements of a physical system are recorded, analyzed, and used to make real-time adjustments to the control input. This is done in an attempt to maximize performance and minimize effort. Figure 44 is a block diagram of a simple closed-loop algorithm.

Input Output Actuator Plant

Sensor

Figure 44. Block diagram of simple closed-loop algorithm.

A number of general closed-loop control (CLC) approaches have been implemented recently. Reduced-Order Modeling (ROM) has been the most prevalent approach over the last decade. The ROM approach is physically based, yet since the flow physics are too complex to be modeled in their entirety, reduced-order models are employed. The most common application of ROM has been with Proper-Orthogonal Decomposition (POD) in conjunction with some form of Linear Stochastic Estimation (LSE). While the details of this approach are not pertinent to this work, the following references contain an overview of the principles and their application [1,26,33,41]. While this approach has merit, and has been effectively utilized over a wide range of configurations [13,24,31,41,46,49,51], it may be considered overly complicated for a number of applications.

While less prevalent and complex than ROM, a number of other approaches may be more practical. Despite their simplicity, they may provide an equally effective result.

Two of these CLC techniques include extremum seeking and slope seeking. In some applications, the reference-to-output map has an extremum and the objective of the control algorithm is to select the set point to keep the output at the extremum value [8]. In other applications the controller seeks to identify an optimal forcing frequency, which is intended to utilize the natural growth mechanisms resulting from instabilities in the 69 boundary or shear layer [30,42]. With slope seeking the plant is considered to have a static input-output map; the control algorithm seeks to achieve and maintain a reference slope of the steady state map [8-9]. Another CLC technique includes black-box models, which are only interested in the input-output behavior; classical step response experiments can be easily performed to find the coefficients for the model which can then be used in CLC [57].

Lastly, direct feedback algorithms triggered by predetermined thresholds have also been employed. Poggie et al. [43] employed surface hot-film sensors for stagnation-line- sensing for a direct feedback control procedure with a slowly pitching airfoil. The on- surface sensors are capable of monitoring the unsteady flow at the airfoil surface, and when placed near the leading edge (LE), expose a strong correlation between the stagnation line location and airfoil lift. For a fixed geometry at low-to-moderate α, lift is a monotonic function of stagnation line location, which indicates that a lift sensing system could be derived from an array of LE sensors. Unfortunately for Poggie et al., the closed- loop control algorithm did not employ the LE sensors. The α regime of interest for the closed-loop investigation exceeded the range of the installed array of leading edge hot- film sensors, and precise resolution of the stagnation line could not be achieved.

Consequently, separation was sensed with a hot-film sensor on the trailing-edge flap, located downstream of the actuators, and this separation detecting sensor acted as the trigger for initiating actuation. The airfoil pitch was increased from α = 12° until a predetermined signal threshold was satisfied, whereupon the airfoil ceased pitching and actuation-on data was measured for a period of time.

Nishizawa et al. [38] also looked at separation control for an airfoil pitching up from pre- to post-stall. A trailing-edge, suction-surface sensor acted as separation indicator, which, when triggered, initiated the actuation. While the sensor effectively monitored suction-surface separation at a given chordwise location, it provided no other means for assessing aerodynamic performance. Other measurement devices, namely an off-surface hot-film sensor and chordwise pressure sensors, were required. Benard et al. [9] utilized a surface mounted pressure sensor at x/c = 0.22, the sensor nearest the LE, which was the most sensitive in terms of variation in CP between attached and detached flow states. This upstream location also permitted the anticipation of the flow changes compared to sensors located further downstream. Accordingly, this sensor was employed first as a direct feedback threshold sensor, and later as a predictor of separation, by monitoring the

RMS of the sensor signal. All closed-loop control investigations, however, were performed at a constant angle of attack. Rethmel et al. [45] also explored closed-loop separation control on an airfoil. At a constant α they attempted to obtain a relative estimate of the stagnation point location near the LE of the airfoil, which is approximately correlated to the lift coefficient, CL. They used their nearest LE sensor, which was on the pressure side at x/c = 0.11, and although their sensor location was sub- optimal, it was the best possible scenario. Yet it was clear that employing a sensor nearer to the LE would provide a much more clear understanding of the LE dynamics, and hence overall airfoil performance.

Post and Corke [44] attempted closed-loop control on a periodically oscillating airfoil, yet the closed-loop algorithm was activated in selected portions of the airfoil’s oscillatory

71 cycle, and was based on angle of attack feedback. The predetermined ranges of operation were well chosen, defined from open-loop control as a range of α where the actuation was intended to augment the lift. They accounted for hysteresis, formation of a dynamic vortex, stall prevention, etc. However, the input to the control algorithm was the measured α, and not a measured flow variable. Sometimes flow is oscillatory (i.e. helicopter rotor) and α can be used for direct feedback, but the majority of the time the unsteadiness is random (i.e. gust response) so a flow measurement is needed for robust and dependable control. For robustness, closed-loop actuation should be determined by the instantaneous sensing of flow conditions.

Closed-loop separation control is initially demonstrated experimentally using an off- body hot-film sensor for feedback control to actuate a row of pulsed normal jets near the leading edge of the 643-618 airfoil. Unsteady flow conditions are generated by continuously oscillating the airfoil in a nominal periodic cycle of α = 10°+14°sin(0.20t),

-3 4 reduced frequency k = 2.4x10 , in a constant freestream of Re = 6.4x10 (U∞ ≈ 6.5 m/s).

The hot-film is located at x/c = 0.5, which is the center of rotation; thus the sensor remains a nearly constant distance above the airfoil surface. Further, placing the sensor at x/c = 0.5 provides a satisfactory demarcation between mild and strong separation. If the flow separates downstream of the sensor the aerodynamic performance is considered adequate; increasing the angle of attack causes the separation location to creep forward, eventually triggering the sensor and activating flow control when the performance is less than satisfactory.

Figure 45(a-b) shows representative smoke visualization of the flow (a) without and

(b) with flow control at a high angle of attack. Without control, the flow separates at the leading edge and a large three dimensional separation bubble is evident, as seen by the rapid diffusion of the smoke lines. Autonomous application of separation control reattaches the flow; the performance improvement is noticeable as the smoke lines remain distinct further downstream.

(a) No control (b) Control

Figure 46 shows a time history of the angle of attack oscillation as well as the actuator, sensor, and surface pressure time response. The top plot from the pressure sensor lags the hot-film due to its very slow response. The dark blue line in the top two plots is the baseline performance with no control. While pitching up, the hot-film indicates that both when 8° < α < 12° and when α > 18°, the airfoil stalls (identified by vertical and horizontal dashed lines in Fig. 46). The green line indicates the performance when the pulsed actuation (normal blowing at 40Hz) is continuous. Finally, the red line indicates 73 the performance when the hot-film sensor output is used as a direct feedback into the actuation.

stall recover stall recover 2

1 -Cp

0 HTW Vel 0.5c (m/s)

10 Baseline Continuous Blowing 5 Closed-Loop

0 Signal Generator (V)

30 20 10 0

Angle of Attack (deg) -10 0 5 10 15 20 25 30 Time (seconds)

When a stalled condition is sensed by the hot-film at x/c = 0.5, the feedback loop actuates the pulsed jets for a user-defined period of time (1000ms). Then the control is turned off, the flow is evaluated, and the process repeats. Decreasing the on-time of the actuators provides a more rapid response to changes in the flow, yet also introduces noticeable unsteadiness due to the repeated on/off actuation. Note that, when controlling, the red and green lines in the hot-film signal are nearly coincident, indicating similar airfoil performance.

Of major significance is the observation that the feedback loop control requires less than 50% mass flow rate compared to the continuous actuation. Also, it should be noted that hysteresis is evident both with increasing vs. decreasing α and initiation and termination of actuation. While this is an effective, introductory effort in closed-loop separation control, there are two significant limitations. First, the off-surface flow sensor is impractical for integration on an aircraft, and its chordwise placement is severely limited by this configuration. Second, while open-loop separation control revealed four α regions of varying aerodynamic performance, with associated optimal blowing parameters in each region, this effort is limited to a single set of blowing parameters.

While closed-loop control reduced the required actuation power by only controlling over a necessary portion of the oscillation period, a further reduction in power can be realized if the flow sensors can delineate the α regions and then optimally control. Lastly, it is non-ideal for the actuation to be turned off in order to re-evaluate the flow performance; continuous performance monitoring and actuating should be occurring simultaneously.

Use of surface hot-film sensors for more practical and efficient feedback control has, consequently, been demonstrated. These devices can be used for the identification of flow features, such as separation, and are placed at x/c ≈ 0, 0.2 and 0.4, as seen in Fig. 12. A more dynamic pitching cycle of α = 10°+14°sin(0.57t), reduced frequency k = 6.7x10-3 is now employed. As has been shown [43,45], the flow near the LE can provide an excellent indication of the overall airfoil performance, as the airfoil lift and stagnation line location are nearly linear functions of angle of attack [see Fig. 47]. Further, it has been observed

75 that an observed shift in the LE flow can be correlated to changes in the static pressure distribution, and subsequently CL.

Figure 47. Hot-film measurements of the leading-edge stagnation line location versus the airfoil lift coefficient for a FlexSys, Inc., Mission Adaptive Compliant Wing, at Re = 9x105 and 2° ≤ α ≤ 12° (from [43]).

Consequently, an open-loop study “calibrated” the hot-film sensors at fixed α, comparing surface flow dynamics in the stagnation region to the aerodynamic performance of the airfoil. Figure 48 displays results for the baseline and controlled flow.

For the “pitch up” data the wind tunnel is initiated with the airfoil fixed at α ≈ -5°, wherein the time mean of 100k samples (20 kHz sampling rate) provides the data point for that location. The angle of attack is manually moved to the next location, and the process is repeated. For the “pitch down” data, the process is the same, except that the wind tunnel is initiated at fixed α ≈ 25°, with the angle subsequently moved down through the α range. This approach is taken to observe hysteresis effects that may be present while continuously oscillating.

3.5 3.5 Baseline Flow Controlled Flow 3 3

2.5 2.5

2 2

1.5 1.5 LE Sensor SignalSensorLE (volts) 1 SignalSensorLE (volts) 1

0.5 pitch up 0.5 pitch up pitch down pitch down 0 0 -5 0 5 10 15 20 25 -5 0 5 10 15 20 25 Angle of Attack (deg) Angle of Attack (deg)

Figure 48. The LE sensor signal for the baseline and controlled flow for both the pitch up and pitch down directions.

Nevertheless, while a minimum is present in each case at α ≈ 2-4°, indicating the stagnation location, a similar trend is observed between the LE sensor signal (Fig.

48(left)) and the lift coefficient (Fig. 13(a)) as a function of angle of attack. In each case a sudden and significant increase is observed at α ≈ 15°, which is indicative of the initiation of the natural laminar separation bubble observed in previous efforts [42, 52, 53].

Following the increased region both signals drop suddenly at α ≈ 19°, as the natural laminar separation bubble erupts due to the increasingly adverse pressure gradient.

Lastly, it is observed that the profiles for the controlled case (Fig. 48(right)) behave similarly to the data points for the controlled flow in Fig. 13(a). To validate the use of the

LE sensor, Fig. 49 displays a plot of the correlation curve for 6° ≤ α ≤ 20°.

Note that the CL(α) curve suggests the performance-enhancing, leading-edge separation bubble occurs at α = 14°, while the leading-edge sensor data suggests that this phenomena did not occur until α = 15°. It is hypothesized that this shift is the result of the surface hot- film placed at the leading edge, since it was not yet installed for the Fig. 48

77 data. Accordingly, the data in Fig. 48(left) is shifted down by one degree for the correlation in Fig. 49. The correlation between LE signal and CL is evident throughout the range, with some scatter near stall.

1.4 14° 1.2 16° 18° 18° 1 10° 20°

0.8 20°

L C 0.6 12° 10° 8° 0.4  = 6° 0.2 baseline controlled 0 0 0.5 1 1.5 2 2.5 3 3.5 LE Signal (V)

Figure 49. Leading-edge sensor outputs versus the lift coefficient of Fig. 13(a) for the (Fig. 21(left)) baseline flow and (Fig. 48(right)) controlled flow for 6° ≤ α ≤ 20°, validating the use of the leading edge sensor for monitoring the airfoil performance.

While the LE sensor tracks the instantaneous aerodynamic performance, the surface sensor at x/c ≈ 0.4 is utilized as an indicator of separation, and the sensor at x/c ≈ 0.2 is used to demarcate between flow regions, identifying when certain blowing parameters should be employed for optimal control. The unsteady signal from each of these sensors is continuously measured at a sampling rate of 20 kHz with the airfoil oscillating at the

11 second period, to document the baseline response. The signals are then analyzed to obtain the instantaneous rms as follows:

1) Evaluate the sensor data in 1000 sample packets (50ms of data).

2) Apply a linear fit to the samples. [Fig. 50(a-b) shows two representative sample

packets and their linear fits, of the baseline flow, at (a) α ≈ -3° (pre-stall) and (b)

α ≈ 20° (post-stall)].

3) Subtract the linear fit from the raw data to obtain the instantaneous fluctuating

component of the signal, u’

4) Calculate the rms of this packet of data, rms = sqrt(sum((u’)2)).

5) Repeat for subsequent data packets, yielding rms(t).

4.63

4.62

4.61

4.6 40%Sensor(volts) 4.59 40% sensor Linear Fit a) 4.58 0 0.01 0.02 0.03 0.04 0.05 Time (sec)

5 40% sensor 4.8 Linear Fit

4.6

4.4

4.2

4 40%Sensor(volts)

3.8

b) 3.6 0 0.01 0.02 0.03 0.04 0.05 Time (sec)

With the hot-film signal rms histories documented, the control algorithm is applied as follows:

The rms-level from the sensor at 40% chord determines whether the actuation is on or off, with Crit40ON user-defined at a value of 0.75 based on Fig. 51(a). Figure 51(a-f) displays the rms time histories of the signal sensors at (a,c,e) x/c = 0.4 and (b,d,f) x/c =

0.2 for the baseline, continuously controlled, and closed-loop controlled flow, respectively, through a pitching cycle. If rms40 > Crit40ON, control is implemented

(i) Once control is implemented, rms40 is continuously monitored to determine if

rms40 < Crit40OFF = 2.5 [see Fig. 51(c)], at which point control is terminated.

(Note that Crit40OFF > Crit40ON). If Crit40OFF = Crit40ON the control will never

turn off, because of the induced unsteadiness in the boundary or shear layer due to

the pulsed actuation. Overall, the airfoil performance improves as actuation is

employed, and the expectation is for the unsteadiness to drop accordingly.

However, the pulsed actuation produces such a high rms that it masks the reduced

separation unsteadiness.

o While rms40 > Crit40OFF, perform the following logic (rms20 is user-

defined at a value of 3.6, as seen in Fig. 51(d)):

. If rms20 < Crit20 then pulse at BRlow = 0.5

. If rms20 > Crit20, then pulse at BRhigh = 2

(ii) For rms40 < Crit40OFF, terminate control and resume rms40 monitoring per step (i)

x/c = 0.4 x/c = 0.2  (deg)  (deg) -1 3 7 11 15 19 23 23 19 15 11 7 3 -1 -1 3 7 11 15 19 23 23 19 15 11 7 3 -1 7 7

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LE SensorLE(V) 2 2 No Control No 1 1 a) b) 0 b) 0 0 2 4 6 8 10 0 2 4 6 8 10 time (sec) time (sec)

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1 1 Closed e) 0 f) 0 0 2 4 6 8 10 0 2 4 6 8 10 time (sec) time (sec)

Figure 52 displays the average performance of 20 airfoil oscillations (beginning at α ≈

-4°, pitching up toward α ≈ 24°, returning to α ≈ -4°, and repeating) for the baseline,

81 continuously controlled, and closed-loop controlled performance. The average recommended BR is also displayed, and identifies which portions of the cycle the actuators are active, and also the magnitude of blowing, as determined by the rms20 sensor criterion.

 (deg) -1 3 7 11 15 19 23 23 19 15 11 7 3 -1 5

LE Sensor (V) and BR and (V) Sensor LE 1 Baseline 1 Baseline

LE Sensor (V) andSensorLEBR (V) Continuous Control Closed-LoopControlled Control BlowingClosed-Loop Ratio 0 Blowing Ratio 00 2 4 6 8 10 time (sec)

Figure 52. Results of the average performance (20 realizations) of the airfoil under baseline, continuously controlled, and closed-loop control of the continuously oscillating airfoil at nominal conditions. The desired BR, as determined by the algorithm, is also displayed. The performance increase while controlling is evident. The algorithm can rapidly detect and institute optimal blowing parameters as determined by the sensed flow.

As the airfoil pitches up from α ≈ -4°, the 40% sensor criterion is satisfied, on average, at around α ≈ 5°, and the flow control is engaged at f = 40 Hz, DC = 0.25, and BR = 0.5.

Soon after this, the leading edge sensor records the closed-loop performance transition from the baseline to the continuously controlled trajectory. The actuation parameters remain constant until α ≈ 15°, wherein the 20% sensor criterion indicates that the 82 actuation parameters should be toggled to f = 80 Hz, DC = 0.5, and BR = 2.0. The increased BR delivers time-averaged performance improvement at the higher angles of attack. Increasing the frequency and duty cycle reduces the unsteadiness of the resulting shear layer. No noticeable disturbance is observed in the leading edge sensor response, indicating a smooth transition between actuation parameters. Satisfactory aerodynamic performance improvement is maintained as the airfoil pitches to a maximum angle of attack of α ≈ 24°. Hysteresis effects are observed as the airfoil pitches back down. At α ≈

15° the algorithm determines that the actuation parameters should revert back to the low

BR configuration. Controlled is turned off, on average, at α ≈ 4°.

The application of closed-loop control at a constant BR ≈ 2 requires approximately

67% of the total mass flow necessary for continuous, open-loop control over one oscillation period. By employing the real-time BR optimization, only 45% of the total mass flow from open-loop control is required.

With each airfoil oscillation the algorithm responds in a unique way, yet a trend of initiating control at α ≈ 4°, maintaining significant performance increase through moderate and high angles of attack, and then releasing control at α ≈ 4° is observed. The figure displays the capability of the sensors to perform two critical functions. First, the capability of the LE sensor to monitor the airfoil performance as the airfoil experiences unsteady flow conditions. There is an obvious aerodynamic benefit throughout the majority of the controlled period, wherein the pulsing amplitude is greater than zero, and is expressly evident during the crucial range of 5° ≤ α ≤ 24°. Second, the downstream sensors enable the algorithm to demarcate between small/moderate and high angles of

83 attack, and more importantly, the associated flow phenomena. Previous efforts revealed optimal blowing ratios change with each stall regime [24]. The effectiveness of the closed-loop approach is exhibited as the airfoil performance is augmented during the regions of moderate and heavy stall (α > 15°), and that the algorithm desires to employ, for the most part, a lower BR at moderate α while a higher BR is only employed at high α.

The robustness of the control algorithm, with respect to the freestream Reynolds number, is investigated by increasing the Reynolds number to twice that of the nominal.

The nominal pitch rate and all control algorithm parameters are maintained. The actuation pressure and dimensional forcing frequency are adjusted to maintain the BR and reduced forcing frequency at the increased freestream velocity. Twenty realizations of the full airfoil oscillation are run with the baseline, continuously controlled and closed-loop controlled flow for Re = 1.28x105. Figure 53 displays the average performance.

Most importantly, the algorithm prevented separation at high angles of attack. At around seven degrees a noticeable change in the performance is evident, and this performance is maintained well beyond the stall location. While the algorithm may engage the actuation longer than is necessary on either side of the stall location, it correctly increases the BR in the desired region and successfully navigates the massive separation present in the baseline curve.

The effectiveness of the algorithm with varying pitch rates is tested by doubling the oscillation rate. In this instance only six realizations are recorded and averaged. Figure 54 displays the average performance. The average performance is detected, and the closed- loop algorithm provides excellent aerodynamic benefits across the regions of interest.

 (deg) 5 -1 3 7 11 15 19 23 23 19 15 11 7 3 -1

4 4

3 3

2 2

LE Sensor (V) and BR and (V) Sensor LE 1 Baseline LE Sensor (V) and BR and (V) Sensor LE Continuous Control 1 Closed-Loop Control Blowing Ratio 0 0 2 4 6 8 10 time (sec) 0 Figure 53. Results of the average performance (20 realizations) of the airfoil under baseline, continuously controlled, and closed-loop control of the continuously oscillating airfoil at the nominal pitch rate and Re = 1.28x105.

 (deg) -1 3 7 11 15 19 23 23 19 15 11 7 3 -1 5

2 LE Sensor (V) and BR and (V) Sensor LE LE Sensor (V) and BR and (V) Sensor LE 1 Baseline 1 Contrinuous Control Closed-Loop Control Blowing Ratio 0 00 1 2 3 4 5 time (sec) Figure 54. Results of the average performance (6 realizations) of the airfoil under baseline, continuously controlled, and closed-loop control of the continuously oscillating airfoil at double the nominal pitch rate. 85

3.5 Transients of the Aerodynamic Response to Flow Control

The focus of this section is to further elucidate the physical phenomena associated with active separation control via pulsed normal blowing. Particular emphasis is placed on comprehension of the transient response at the onset of actuation. There are inherent dynamics associated with the specific actuation configuration employed, and also with the aerodynamics characterisitics of the chosen airfoil. Airfoil oscillation further complicates these dynamics. Understanding how the lift responds to actuation at a given angle of attack while stationary or pitching will provide insight into the physical phenomena associated with each condition.

Developing static (fixed α) and dynamic (oscillating α) models of the aerodynamic response of the airfoil to actuation will help quantify these effects. Further, it is valuable to determine the variation in the models with angle of attack and pitching rate, as this will shed light on the range of operating conditions which a nominal model can adequately model. Understanding these dynamics, including the extent of the actuation effectiveness and how quickly the airfoil responds to a desired control input, will help determine the potential robustness of the closed-loop control algorithms and the extent of its application to real problems.

Black-box models are interested in the input-output behavior of the control system; classical step response experiments can be performed to find the coefficients for a model which can then be used in CLC. Williams et al. [57] employed black-box models to successfully mitigate fluctuations in airfoil lift amidst unsteadiness in the freestream velocity (simulating longitudinal gusts), but at a constant angle of attack. The models

86 were experimentally developed and utilized for closed-loop control; they found that their actuation jet exhibited a first-order dynamic response with a time delay. Further, the dynamic models of the lift response to actuation were also well represented in the mean by a first-order model with a time delay. They highlight that while active flow control techniques are well established for steady-state conditions, the introduction of unsteady flow, due to maneuvering or gusting flow conditions, results in deviations. These deviations appear as time delays and differences in amplitudes of the lift relative to the steady predictions, and they must be modeled for successful control. They note that the dependence of the plant, and the corresponding models for unsteady aerodynamics, on angle of attack has not been addressed, and that a nonlinear control system would likely be required for inclusion of these effects.

3.5.1 Modeling the Static Airfoil (Fixed α)

Models of the aerodynamic response at a fixed angle of attack are investigated. The surface hot-film sensors placed at x/c = 0, 0.2 and 0.4 are monitored simultaneously, along with the output of the IOTA One pulse driver. Data is collected at 20 kHz with a low-pass filter of 10 kHz to eliminate aliasing. Actuation parameters are set to those used in the closed-loop control algorithm. For low and moderate angles of attack f = 40 Hz,

DC = 25% and BR = 0.5. Control is configured near the performance peak observed in

Fig. 29 and seeks to maximize aerodynamic performance with minimal power input. For high angles of attack f = 80 Hz, DC = 50% and BR = 2.0. A higher frequency/duty

87 cycle/blowing ratio combination is required to achieve maximum separation control while reducing unsteadiness in the separated shear layer.

Experimental data applied toward the model development is obtained by collecting leading edge sensor data of the baseline flow for 4 seconds, initializing the actuation and maintaining control for 4 seconds, followed by another 4 seconds of baseline flow. This process is repeated twenty times, and these twenty realizations are averaged. Figure 55 provides a representative data set, specifically the average leading edge sensor response of the fixed airfoil at α = 5°. Also plotted is the general form of the actuator input, indicating when the flow control actuation system is engaged.

0.6 LE Sensor Output Actuator Input 0.5

0.4

0.3

0.2 Input or Input Output or (V) 0.1

-0.1 -3 -2 -1 0 1 2 3 4 5 6 7 Time (sec)

Figure 55. Representative input (jet actuation) and output (leading edge sensor) signals for Re = 6.4x104 and α = 5°.

In the figure, and throughout the present section, the time t = 0 is always indicative of the instant that the jet fluid ejects from the airfoil surface. This is determined by

88 monitoring the TTL input waveform to the pulse driver, and then accounting for the

2.55ms time delay repeatedly measured in the jet time-histories. This procedure decouples the airfoil aerodynamic response from the internal dynamics and time delay of the actuation system.

While the sensors at x/c = 0.2 and 0.4 are monitored and explored for details regarding the transients of flow separation control, only models of the leading edge sensor are developed. Recall that it is the leading edge sensor that correlates well with the overall airfoil performance (see Fig. 49). Models of the input-output response are obtained using the System Identification Toolbox in MATLAB. In all cases the data are preprocessed by removing the mean. This normalizes the data and assists the toolbox in isolating the input-output relationship. The System Identification Toolbox (SIT) enables the user to employ a number of models, including black-box models of various orders, linear parametric models, and nonlinear models, among others. A fundamental and commonly used black-box model is exercised here, a first-order plus dead-time (FOPDT) model from step response. This transfer function has one real pole and accounts for a time delay.

Its basic structure is observed below

(7)

where K is the system gain, Td is the time delay, and Tp is the time constant. The time delay is theoretically determined by when the output exhibits its first clear response to the input. The time constant is the “how fast” variable, and is the time beyond the time delay that elapses before the output reaches 63% of the total response. The parameters are 89 determined via the SIT which iterates until the least square error is minimized. They can be determined manually, yet the System Identification Toolbox provides some particular advantages. Most beneficial to the user is the benefit of time; a large number of data sets are investigated and the SIT accelerates the process dramatically. Most beneficial to the integrity of the work is the objectivity of the algorithm. User bias or error can be removed by allowing the SIT to determine the parameter fit that best represents the data. This can be particularly important in instances where the baseline flow is quite unsteady, even after averaging twenty realizations. In these instances it can be difficult to determine where the output exhibits its first clear response to the input. The SIT is repeatable and eliminates user subjectivity.

Comparison of the aerodynamic response (as monitored by the leading edge sensor) over a range of α sheds light on the phenomena associated with the implementation of control. Figure 56 displays the average response of the LE sensor for 2° ≤ α ≤ 10°.

Corresponding models are created and displayed in Fig. 57(a). The gain is normalized to isolate the variation in the time delay and time constant, respectively. The model parameters are quantified in Table 2. In the figure solid lines are applied to 5° ≤ α ≤ 9° to identify the range of α wherein the model parameters are very similar. A nominal model can be fashioned which adequately simulates the model parameters over this α range.

This is accomplished by averaging the model parameters, rather than averaging the output of the models themselves. The result can be found in the last column of Table 2, as well as in Fig. 57(b). That a nominal model provides an excellent approximation of the response for this subset of α provides encouragement for the future use of black-box

90 models in closed-loop control applications. This can greatly simplify the control strategy.

Further, this validates the initial demarcation of the regions within Fig. 13.

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2 deg 0.2 4 deg 5 deg 0.1 6 deg LE Sensor Response(V) SensorLE 7 deg 8 deg 0 9 deg 10 deg -0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (sec)

Figure 56. Comparison of the average aerodynamic response, measured by the leading edge sensor, for 2° ≤ α ≤ 10°.

1 1

0.8 0.8

0.6 2 deg 0.6 4 deg 5 deg 5 deg 0.4 6 deg 0.4 6 deg 7 deg 7 deg 0.2 8 deg 0.2 8 deg

9 deg 9 deg

SimulatedLE Sensor Response SimulatedLE Sensor Response 10 deg Nominal a) 0 b) 0 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 Time (sec) Time (sec)

Figure 57(a-b). FOPDT models for (a) 2° ≤ α ≤ 10° and (b) 5° ≤ α ≤ 9° compared to a nominal model.

Table 2. FOPDT model parameters for 2° ≤ α ≤ 10°, along with a nominal model for 5° ≤ α ≤ 9° Model Nominal α = 2° α = 4° α = 5° α = 6° α = 7° α = 8° α = 9° α = 10° Parameter (5°-9°) K 0.420 0.491 0.547 0.511 0.478 0.442 0.438 0.397 0.465 Td 0.038 0.047 0.038 0.037 0.034 0.034 0.036 0.028 0.036 Tp 0.075 0.044 0.058 0.058 0.056 0.058 0.055 0.056 0.057

A more detailed understanding of the transient response can be found through investigation of the sensors at x/c = 0.20 and 0.40. Figure 58 displays the response of the three sensors for α = 2°. At this lower angle of attack the amplitude of the 20% response is smaller than that of the 40% sensor. The flow at α = 2° is similar to that present at α = -

1°, which was investigated previously with PIV. Figure 59 was presented beforehand, but is offered here for the reader’s convenience. It displays the velocity magnitude for the baseline and steady blowing flow. The baseline separation location is x/c ≈ 0.5, and while the separation location shifts downstream only slightly with control, the proximity to the furthest aft sensor produces a more substantial response amplitude. As seen in the PIV, the increase in circulation is minimal. Thus the local velocity at 20% does not change substantially, and the magnitude of the sensor response is small.

Figure 60 displays the response of the three sensors for α = 9°. Here the amplitude of the 20% sensor is more substantial than that of the 40% sensor. Figure 61 displays the results from PIV at α = 10°, wherein a substantially more dramatic effect is produced by the jet actuation. The 40% sensor is now submerged within the baseline separation region, and is straddled by the baseline and controlled separation locations. Thus despite the major flow changes near the 40% sensor, the magnitude of the steady state response is not as large as that of the 20% sensor. It is not clear what is responsible for the large 92 excursion seen early on. However, the author suggests that this may be due to the initial roll-up of the separated shear layer as observed in Fig. 35. The sensor at x/c = 0.20 measures dramatic change. This is due to the circulation increase observed via the PIV.

The effective airfoil shape and wake are considerably thinned. This thinning causes an increase in circulation, which allows the development of a distinct suction peak near the leading edge. This rapid acceleration is readily detected by the sensor at 20% chord, and is responsible for the stronger response.

0.8 LE Sensor 20% Sensor 0.6 40% Sensor

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0 0.1 0.2 0.3 0.4 Time (sec)

Figure 58. Comparing the transient responses of the surface sensors for α = 2°.

Comparison of the changes of the two sensors with varying angles of attack can be seen in Fig. 62(a-b). It is evident that the response amplitudes transition from low-to- moderate angles of attack. This variation allows an investigator to estimate the size and strength of the separation region while increasing from low to moderate angles of attack.

It also agrees well with trends observed in the performance curves of Fig. 13. Further, the monotonic mean response with alpha validates the use of these two aft sensors in the

93 closed-loop control algorithm of Section 3.4. It is evident that these sensors provide excellent real-time observation of the local flow conditions, and that without or with the implementation of flow control they can adequately monitor the aerodynamic performance.

No Control

Control

Figure 59. PIV derived velocity magnitude for the baseline and controlled flow at α = -1°.

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Figure 60. Comparing the transient responses of the surface sensors for α = 9°.

No Control

Control

Figure 61. PIV derived velocity magnitude for baseline and controlled flow at α = 10°.

0.6 0.8 0.5

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Figure 62(a-b). Comparison of the sensor responses at (a) 20% and (b) 40% chord for 2° ≤ α ≤ 10°.

At each pre-stall angle of attack the sensors at x/c = 0.2 and 0.4 exhibit a substantially shorter time delay than the LE sensor. Table 2 shows a nominal LE sensor time delay of

~36ms. The 20% and 40% sensors record average time delays of approximately 4.6ms and 11.2ms, respectively. These values are on the order of the expected convective time for the jet fluid to emit from the surface, bend downstream and travel x/c = 0.15 or 0.35

(the full chord convective time is ~23ms). Thus approximately one convective time beyond the time delay of the 40% sensor elapses before the leading edge sensor measures a noticeable response to the actuation.

The reason for the long time delay recorded by the leading edge sensor can be found by returning to the PIV results of Section 3.2.2 (Figs. 34 and 35). The aerodynamic benefits of pulsed normal blowing are investigated at α = 10°. Actuation is executed at f =

5 Hz (f+ ≈ 0.125), DC = 0.625% and BR = 0.5, resulting in a 1.25ms jet pulse on-time, followed by 198.75ms off-time. The flow has enough time to transition through a nearly fully baseline to fully controlled to fully baseline sweep before the onset of the subsequent jet pulse. Figure 63 compares the phase-locked downstream wake at the (left) most adverse and (right) most favorable portions of the pulsing period.

Figure 63. Comparison of the phase-locked wake profiles corresponding to the PIV results of Figures 34 and 35 at the (left) most adverse and (right) most favorable portions of the pulsing period.

It was stated previously, but is worth recalling, that it is anticipated that higher frequency forcing (f+ ≈ 1) may not exhibit the same dynamics shown in Figs. 34 and 35.

If pulsing at f+ ≈ 1 is initiated during stall, the first pulse will likely behave like control with f+ ≈ 0.12, but subsequent pulses operate on a much thinner separation zone that has not recovered due to the phase lag.

The time delay and overall response of the LE sensor to actuation at f+ ≈ 1 corroborates well with this claim. Figures 34 and 35 authenticate the time delays measured at both x/c = 0.2 and 0.4, as changes in these regions are detected in the PIV results at comparable times. The surprising leading edge time delay of ~36ms is also justified therein. A significant interaction between the jet pulse and the separating shear layer occurs as early as ~11ms after the introduction of the jet pulse. However, the actuation causes a “roll-up” in the shear layer. Thus while significant change has occurred near x/c = 0.4, the airfoil wake and corresponding effective airfoil thickness do not diminish until t/T ≈ 0.2 (≈ 40ms/ 200ms pulse period) [see Figs. 35(d) and 34(d)].

This sustained “thickness” inhibits the development of circulation, thus maintaining the overall airfoil performance for a surprisingly long time delay.

Further interrogation of the transients associated with reattachment is performed through measurement of the aerodynamic response corresponding to a discrete number of actuation pulses. The three sensors are monitored whilst the actuation is initialized and executed for a discrete number of pulses, namely one, two, five and ten. The magnitude and temporal dynamics of the responses are compared to that of a two second pulse train.

Comparison of the LE sensor response for the five signals at α = 2° and 9° is displayed in

Fig. 64(a-b). Five jet pulses are required for the signal to obtain 90% of the steady state response. Also, while a single pulse produces a relatively substantial aerodynamic

97 benefit, the time delay is large enough that the effect is not even detected until after a second jet pulse would have occurred.

0.5 2 seconds 10 shots 5 shots 0.4 2 shots 1 shot

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0 a)

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0 b)

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (sec) Figure 64(a-b). Comparison of the LE sensor response at (a) α = 2° and (b) α = 9° for a discrete number of actuation pulses.

Lastly, Fig. 65 displays the LE sensor response for both a single actuation pulse and for two actuation pulses, with the actuation input included to provide temporal perspective.

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Figure 65. Comparison of the LE sensor response at α = 2° for one or two pulses.

For each of the aft sensors shown in Fig. 62, an interesting feature occurs immediately after the time delay. These are not detected by PIV, due to the lack of near-wall spatial or temporal resolution. The 20% sensor signal displays a short period of reducing voltage before beginning its anticipated trajectory up to the fully controlled magnitude. Fig. 66(a) provides a close-up look of the initial transients in Fig. 62(a). This feature may be the result of a momentary reduction in the airfoil circulation. The insertion of the first jet pulse into the baseline boundary layer temporarily causes the “effective thickness” of the airfoil to increase. For a moment the boundary layer is thickened, the local velocity decreases, and the sensor outputs a corresponding voltage reduction.

A more perplexing feature is observed in the transient dynamics of the 40% sensor output. A close-up look at Fig. 62(b) is displayed in Fig. 66(b). A peak of variable time and strength occurs after the convective time delay. For low angles of attack the delay is slightly longer than at higher α, ranging from 13 to 17ms. The separation location moves

99 upstream as angle of attack increases. Thus a shorter convective time elapses before the emitted actuation jet interacts with the shear layer and starts causing aerodynamic changes at the sensor location. The complexity of the peak increases with α; for 7° ≤ α ≤

10° a second peak is detected. The temporal span also increases, with a maximum breadth of approximately 50ms. It appears that the troughs of the 9° profile (at time = 0.038 and

0.063 seconds) align with the pulsing period of 25ms. It is suggested that the first pulse provides a noticeable disturbance which improves the aerodynamics. However, the cause of the reduction and subsequent peak are unknown at this time. Yet after two pulsing periods the transients begin to resolve and tend toward the steady state condition.

0.6 0.6 2 deg 2 deg 0.5 4 deg 0.5 4 deg 5 deg 5 deg 0.4 6 deg 0.4 6 deg 7 deg 7 deg 0.3 0.3 8 deg 8 deg 9 deg 9 deg 0.2 0.2 10 deg 10 deg 0.1 0.1

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20%Sensor Response (V) 40%Sensor Response (V)

-0.1 -0.1 a) b) 0 0.02 0.04 0.06 0 0.02 0.04 0.06 Time (sec) Time (sec)

Figure 66(a-b). Close-up view of Fig. 62(a-b), which compares the aerodynamic responses of the (a) 20% and (b) 40% sensors for 2° ≤ α ≤ 10°.

It is encouraging that the sensors at x/c = 0.2 and 0.4 exhibit a faster time delay than the leading edge sensor. This validates their use as monitors for the closed-loop control algorithm employed previously. Use of the leading edge sensor as a control input algorithm could have inhibited the temporal robustness and accuracy of the procedure.

100

For α ≥ 20°, significant variation in the gain and the complexity of the response is evident. Figure 67 displays the leading edge sensor response for 20° ≤ α ≤ 24°.

0.5 20 deg 21 deg 0.4 22 deg 23 deg 24 deg

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LE Sensor Response LE (V) Sensor Response 0.1

0 0.05 0.1 0.15 0.2 0.25 Time (sec)

Figure 67. Comparison of the LE response for 20° ≤ α ≤ 24°.

The time delay is approximately 0.5ms, which is dramatically shorter than values of the pre-stall configuration (36ms). The time-history of the three sensors at α = 20°, in particular, are shown in Fig. 68. While the LE sensor responds immediately, the sensors at 20% and 40% reveal time delays of 6.4 and 11.9ms, respectively. However, though the leading edge sensor detects a noticeable change first, it does not reach its steady state value until after both the sensors at 20% and 40% have done so. The flow nearest the leading edge is first affected by the jet penetration of the shear layer at x/c = 0.05, and consequently responds first. Yet the overall airfoil performance does not reach a steady state until the fluid dynamics of the whole airfoil have settled.

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1.2 LE Sensor 20% Sensor 1 40% Sensor

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0.2

-0.1 0 0.1 0.2 0.3 0.4 0.5 Time (sec)

Figure 68. Comparison of the transient responses of the surface sensors for α = 20°.

Both the 20% and 40% sensors record a transient peak directly after the initial response, similar to what is observed in Fig. 66(b). However, at this configuration neither signal reverts fully to the baseline value before increasing again. The sensor at x/c = 0.40 only drops for 9ms, whereas the sensor at 20% drops for nearly 30ms before rising again.

This delay accounts for nearly 2.5 convective times (80 Hz actuation), and is followed by a substantial and rapid increase up to the steady state magnitude. What causes these dynamics is unknown, yet the time consumed during these phenomena is likely to limit the temporal effectiveness of the control. Eliminating these events may improve the time response and the robustness of the control process.

A FOPDT model provides a reasonable simulation of the response at α = 20° and 21°, as seen in Fig. 69. In addition to the lower time delay the LE response has time constant of approximately 0.030, which is nearly fifty percent faster than the pre-stall value.

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LE Sensor Response LE (V) Sensor Response 0.1 20 deg Experimental Data 20 deg Simulation 0 21 deg Experimental Data 21 deg Simulation

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (sec)

Figure 69. Comparison of the LE sensor responses and corresponding models for α = 20° and 21°, wherein a FOPDT model provides a reasonable estimation of the flow dynamics.

Although the FOPDT model provides a reasonable estimation of the transient dynamics at α = 20° and 21°, it is apparent that higher order dynamics are beginning to develop. Increasing the angle of attack requires at least a second-order plus dead-time

(SOPDT) model to better simulate the more complex response. The general form of the

SOPDT model is shown below

(8)

where Tω is a time constant, and δ is the damping coefficient. Fig. 70 displays the experimental day and the generated model [K = 0.253, Tω = 0.0302, δ = 0.2714, Td = 0] for α = 23°. The fit of the model is less than satisfactory, further revealing the increased complexity associated with the aerodynamic responses of such flows.

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0.1 LE Sensor Response(V) SensorLE 0.05

0 Experimental Data Simulation -0.05 0 0.1 0.2 0.3 0.4 0.5 Time (sec)

Figure 70. Comparison of the LE sensor response and corresponding model for α = 23°, wherein a SOPDT model is required to provide a reasonable estimation of the response.

An in-depth understanding of the physical mechanisms responsible for control at post- stall angles of attack has not been obtained here. A few other efforts have investigated the transient response to pulsed actuation at high angles of attack [58,61,62]. However, these have all been performed at a relatively high Reynolds number and with an actuation configuration and parameter combination much different from this effort. Thus it is recommended that a detailed investigation via PIV and wake surveys be undertaken, similar to that performed in Sections 3.2.2 and 3.3. Even though details are not fully understood, it is evident that when fully entrenched in deep stall the physical mechanisms for control must be different from those at low-to-moderate angles of attack.

Considering the results of this section, it is clear that nonlinearity is evident within the black-box models employed across the entire range of angle of attack. This nonlinearity confirms previous assertions by Williams et al. [57] and throws caution to future efforts to utilize these models in more complex control algorithms.

104

3.5.2 Modeling the Dynamic Airfoil (Oscillating α)

Dynamic models of the aerodynamic response are obtained for a select subset of the angle of attack span. Particular focus is placed in the region where the closed-loop control algorithm tends to initiate control while dynamically oscillating (α = 5°, 7° and

9°). LabVIEW is used to execute precise control of the pitching airfoil, which initially pitches at the nominal rate [~8.5°/sec]. An optical encoder tracks the pitch position and engages the actuation at precisely the same angle of attack for each pitch oscillation.

While pitching down the code is initialized, which tracks the optical encoder until the airfoil has stopped moving. The data collection begins and the airfoil starts to pitch up from α ≈ -3.5°. The encoder measures when the airfoil has reached a prescribed angle of attack, at which point control is initialized and data is collected until the airfoil reaches the top of the pitch oscillation. The process is repeated 20 times to obtain the average response.

Figures 71-73 compare the baseline, continuously controlled and dynamically controlled signals throughout an average pitch oscillation, with control initialized at (Fig.

71) α = 5°, (Fig. 72) α = 7° and (Fig. 73) α = 9°. The angle of attack is indicated on the top of each figure. Time is also monitored on the figure bottom. In the same manner as the static tests, t = 0 indicates the moment the actuation jet ejects normal to the airfoil surface. A large, full scale view is displayed, with a zoomed-in view inserted in the lower right. The signals in the insert are low-pass filtered at 50 Hz to clarify the extent of the transient response.

105

Angle of Attack (deg) -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 4.4

4.35

4.3

4.25 Angle of Attack (deg) 4 5 6 7 8 9 4.254.25

4.2 4.24.2

4.154.15

System Response (V) Response System 4.15 LE Sensor Response (V) Response Sensor LE

4.14.1

4.1

System (V) Response LE Sensor Response LE (V) Sensor Response

4.054.05 Baselinebaseline 4.05 ContinuousControlled Control Baseline DynamicDynamic Control 44 Continuous Control -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Dynamic Control Time (sec) 4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 Time (sec)

Figure 71. Investigation of dynamic control at α = 5° with a view of the unfiltered signal over a full oscillation and (insert) a concentrated view of the filtered signal in the transient region.

Quantifying the dynamic response proves more difficult than with a fixed angle of attack. The baseline, continuously controlled and dynamically controlled signals each vary with angle of attack (time), both in magnitude and in the rate of change.

Consequently, the response is quantified as the difference between the dynamically controlled and the baseline signals, normalized by the difference between the continuously controlled and baseline signals, as shown below

(9)

For a quantifiable comparison of the static and dynamic responses, the static gain

(determined from the static modeling process) is applied to the corresponding dynamic 106 model. As with the static models, first-order plus time delay models are created using the

System Identification Toolbox in MATLAB. The dynamic response and corresponding model at α = 7° are shown in Fig 74.

Angle of Attack (deg) -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 4.4

4.35

4.3

4.25 Angle of Attack (deg) 6 7 8 9 10 11 4.3

4.2 4.25

4.2

System Response (V) Response System 4.15 LE Sensor Response (V) Response Sensor LE

4.15

4.1

System (V) Response LE Sensor Response LE (V) Sensor Response

4.1 Baselinebaseline 4.05 ContinousControlled Control Baseline DynamicDynamic Control 4.05 Continuous Control -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Dynamic Control Time (sec) 4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 Time (sec)

Figure 72. Investigation of dynamic control at α = 7° with a view of the unfiltered signal over a full oscillation and (insert) a concentrated view of the filtered signal in the transient region.

107

Angle of Attack (deg) -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 4.4

4.35

4.3

4.25 Angle of Attack (deg) 8 9 10 11 12 13 4.35

4.2 4.3

4.25

System Response (V) Response System 4.15 LE Sensor Response (V) Response Sensor LE

4.2

4.1

LE Sensor Response LE (V) Sensor Response LE Sensor Response LE (V) Sensor Response

4.15 baseline 4.05 Controlled Baseline Dynamic 4.1 Continuous Control -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Dynamic Control Time (sec) 4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 Time (sec)

Figure 73. Investigation of dynamic control at α = 9° with a view of the unfiltered signal over a full oscillation and (insert) a concentrated view of the filtered signal in the transient region.

0.6

0.5

0.4

0.3

0.2

0.1 LESensor Response (V) Experimental Data 0 Simulation

0 0.1 0.2 0.3 0.4 Time (sec)

Figure 74. Comparison of the LE sensor response and corresponding model for the oscillating airfoil with actuation engaged at α = 7°.

108

To determine the effect of pitch rate on dynamic separation control, the process is repeated at an increased pitch rate of approximately twice that of the nominal [~17°/sec].

As before, actuation is engaged at prescribed α locations, and the dynamic sensor response is recorded and modeled. The simulated time responses of the LE sensor for the static, nominal pitch rate and double pitch rate are compared in Fig. 75(a-c) for (a) α = 5°,

(b) α = 7° and (c) α = 9°. Table 3 contains the model parameters.

Trends concerning the simulated time delay are inconclusive. However, there is a common trend that the response time decreases with increasing pitch rate. In all cases the introduction of airfoil oscillation reduces the response time, and in two cases doubling the pitch rate provided further reduction. A minimum reduction in the response time of 30% is observed. Ghosh Choudhuri and Knight [68] show that increasing the pitch rate decreases the strength of the adverse pressure gradient. Doubling the pitch rate caused the surface pressure coefficient to become more negative over the front 75% of the suction surface. Walker et al. [69] confirms this result. Using surface pressure measurements they found that the pressure coefficient, and consequently CL,max and dCL/dα, increased with increasing pitch rate. These two efforts provide some explanation for the observed trends of Fig. 75(a-c). While pitching up the decreased adverse pressure gradient slows down the development of the baseline reversed flow region. The pressure gradient causes the separated region to be less averse to being manipulated, and this augments the ability of the jet fluid to actively control the flow separation.

109

0.6

0.5

0.4

0.3

0.2

0.1 5deg Static 5deg Nominal Pitch

SimulatedLE Sensor Response (V) 0 5deg Double Pitch

a) 0 0.1 0.2 0.3 0.4 Time (sec) 0.6

0.5

0.4

0.3

0.2

0.1 7deg Static 7deg Nominal Pitch

SimulatedLE Sensor Response (V) 0 7deg Double Pitch

b) 0 0.1 0.2 0.3 0.4 Time (sec) 0.6

0.5

0.4

0.3

0.2

0.1 9deg Static 9deg Nominal Pitch

SimulatedLE Sensor Response (V) 0 9deg Double Pitch

c) 0 0.1 0.2 0.3 0.4 Time (sec)

Figure 75(a-c). Comparison of the LE sensor of the static and dynamic responses at the nominal and twice-nominal pitch rate for (a) α = 5°, (b) α = 7° and (c) α = 9°. 110

Table 3. Comparison of model parameters for the static airfoil versus a dynamic airfoil at nominal pitch rate and double pitch rate for α = 5°, 7° and 9°. α = 5° α = 7° α = 9° Pitch Rate K Td Tp K Td Tp K Td Tp Static 0.5462 0.0378 0.0578 0.4777 0.0342 0.0555 0.4373 0.0358 0.0548 Nominal -- 0.0411 0.0407 -- 0.0440 0.0383 -- 0.0415 0.0422 Double -- 0.0383 0.0379 -- 0.0402 0.0391 -- 0.0446 0.0347

111

Chapter 4: Future Considerations

The fundamental motivation for developing models in Section 3.5 was to further the understanding of the physical mechanisms inherent in the control process. These efforts validate the observation of Williams et al. [57] that a nonlinear control system is likely required for the inclusion of the effects of angle of attack in a closed-loop control algorithm. Variation in the leading edge sensor response is evident not just across the whole α span, but even within subsets of this range (e.g. 20° ≤ α ≤ 24°). However, the implementation of nonlinear models in the closed-loop is well beyond the scope of this work. Yet the groundwork for this endeavor is laid, and may be pursued further. One limiting factor in the implementation of the developed black-box models is that at low-to- moderate angles of attack there is no opportunity to vary in control input (blowing ratio).

Unlike the work by Williams et al., the improvement in aerodynamic response is not dependent upon the magnitude of the control input. Figure 19 shows how a substantial variation in the blowing ratio provided no additional performance improvement at α =

10°. The independence of the response upon the control input eliminates the advantages of implementing a black-box control algorithm. For α ≥ 20° there may be an opportunity for input variation due to amplitude modulation, yet this needs to be explored further.

112

The presence of the relatively substantial time delays of the aerodynamic response at low-to-moderate angles of attack presents reasonable concern. Palmor [63] states that two major consequences result from the presence of time delays in a control process. First, the analysis and design of the feedback controller becomes much more complicated. Second, it is more difficult to achieve satisfactory control. As the time-delay approaches the time constant, the maximum gain, Kmax, for maintaining closed-loop stability is reduced. In theory, as Td/Tp → 0 (the process is void of dead-time) Kmax → ∞. Yet when Td/Tp → 1,

Kmax is dramatically reduced to approximately 2.26. As the relative magnitude of time delay increases, maintaining stability requires the controller gain to be reduced. In most cases this results in poor performance and sluggish response [60].

Substantial dead-time can be compensated for through the implementation of a Smith

Predictor. This algorithm calculates the predicted process change in response to a control action as if there is no time delay [64]. The process variable absorbs this change, and persuades the controller to “believe” that the corrective action actually took effect immediately. This modification allows the controller to be tuned aggressively (high Kmax) such that satisfactory control can be achieved. However, despite the implementation of the Smith Predictor, it is always beneficial to reduce the physical dead-time of a process.

Lessening the burden of the corrective measures within the closed-loop algorithm will provide improved accuracy and stability.

Further repercussions arise with the built-in phase lags of the aerodynamic response.

The relatively substantial dead times at low-to-moderate angles of attack pose a direct threat to resolving and responding to perturbations occurring on the order of or faster than

113 the convective time. An even greater response time further delays the effect of the imposed actuation. This conundrum is not easily resolved, as it is clear that the control bandwidth is limited solely by the ability of the fluid to physically respond to the imposed actuation, and not by the actuation itself. Therefore, efforts should be made to minimize the time restraints articulated in Section 3.5. A couple of approaches may provide improved response.

Implementation of actuation further downstream would eliminate the convective time delay. At its most adverse configuration (α = 10°), the baseline separation location is at x/c ≈ 0.35. However for α = 2° the separation location moves back to x/c ≈ 0.5. Plogmann

4 et al. [42] demonstrated on the NACA 643-618 at Re = 6.4x10 that actuation at x/c = 0.4 can provide substantial aerodynamic benefit across this range of angle of attack. Hence one can be confident that placing pulsed blowing near these separation locations would provide the desire flow separation control, all while eliminating the time delay required for the actuation jet fluid to travel over thirty percent of the chord length. At a minimum this should reduce the time delay by approximately 7ms, a reduction of nearly twenty percent. However, it is unclear if it would remove a larger percentage of the ~36ms time delay. It is also unclear what effect it would have on the time constant associated with the

“speed” of the aerodynamic response. It may be that the pressure gradients imposed at α

= 9° require an inherently longer time constant, irrespective of the associated time delay.

Regardless, the functionality to toggle between a near-leading edge and downstream actuation location, dependent upon the detected real-time separation, could provide benefit both to the stability of the controller and to the effectiveness of the actuation.

114

The introduction of pitched and skewed jets could further diminish the dead-time of the flow separation control. Holes drilled with pitch and skew are more effective active flow control devices [18], yet the benefit here could depend on the additional streamwise momentum imparted. This added streamwise momentum could propel the jet fluid downstream at a faster rate, causing the critical flow control mechanisms to occur at an earlier time. Further, this effect could be magnified by implementing control at a very high blowing ratio (BR ≈ 10) for a brief moment, directly upon the initiation of control.

This high BR would be employed only long enough to combat the undesirable time delay, after which the actuation can revert to the configuration for optimal control in the steady state.

The application of more surface hot-film sensors could provide better resolution of the magnitude of the separation region. This would better allow the control logic to be used for the selection of the optimal control parameters and for improved response (by potentially employing the developed response models). However, practical implementation is limited by the number of anemometers available for data acquisition.

The desired estimation precision introduces excessive costs, which could outweigh the benefit of the closed-loop control.

It may also be advantageous to move the leading edge sensor slightly downstream on the suction surface. In its current position it records a minimum at α ≈ 3°-5°. If the sensor were moved slightly downstream it would put the minimum nearer to α ≈ -5°. This would alter the curve of Fig. 48 to look more like the CL(α) curve of Fig. 13(a). The magnitude

115 of the leading edge sensor would provide an estimation of the aerodynamic performance.

A corresponding reference voltage could then be used to drive the control logic.

The knowledge gained in this work could be transitioned toward a number of different applications.

1) One opportunity lies in maintaining the aerodynamic performance over a range of

freestream Reynolds numbers. Figure 76 conveys the effect of Reynolds number

on the aerodynamic performance over a range of angle of attack.

1.4

1.2

0.8

L 0.6 C

0.4

0.2 Baseline 64k Control 64k 0 Baseline 180k Control 180k 2(1+t/c) slope -0.2 -5 0 5 10 15 20 25 

Figure 76. Comparison of baseline and controlled lift coefficient for Re = 6.4x104 and 1.8x105, which express the dependence upon Re for the necessity of active flow control.

Increasing Re to 1.8x105 results in a significant change in lift magnitude for nearly

all α. More importantly, note the absence of the loss-bucket and sudden spike in CL

resulting from the naturally forming laminar separation bubble. Instead, a more

commonly observed CL-α is evident, with the opportunity for performance

improvement via active flow control limited to the post-stall regime (α > 14°).

Consequently, at a fixed angle of attack a reference leading edge sensor voltage

could be set which determines the necessity of active flow control as the

freestream Reynolds number oscillates over a prescribed range. Tracking the 116

output of the leading edge sensor would provide a real-time indication of the

overall airfoil performance. When control is required the actuation would be

engaged, employing optimal control parameters. The developed static response

models provide insight into how quickly the airfoil could respond to the introduced

actuation, and the prevention of reduced aerodynamic performance.

2) A similar type analysis could be performed at a fixed α and fixed Reynolds

number, yet with varying freestream turbulence levels. Increased levels of

freestream turbulence induce transition and subsequent aerodynamic performance

improvement for approximately 5° ≤ α ≤ 12°. Variations in the freestream

turbulence levels would be akin to a noisy aerodynamic environment, as would be

encountered if the sensor was in the wake of a maneuvering fuselage, for example.

3) Another interesting avenue is the investigation of potential hysteresis effects.

While a certain blowing ratio is required to obtain control over the separated flow,

the blowing ratio can subsequently be reduced without compromising

performance. This is particularly significant at post-stall angles of attack, wherein

a relatively substantial BR is required to penetrate the shear layer and initiate

control. Yet once control is maintained it is suggested that the blowing ratio could

be moderately reduced while maintaining desired performance requirements. At

low-to-moderate α, the measured minimal blowing ratio of BR = 0.25 was limited

by the limits of the rotameter used. It is suggested that the actual minimal BR

required is lower than this, particularly after separation control is achieved. Figure

77 provides a basic representation of how this procedure could be implemented.

117

The concept is derived from Benard et al. [9]. However, fundamental differences exist in the input (BR of pulsed normal jets vs. voltage of plasma actuators), the tracking method (LE hot-film vs. pressure transducer at x/c = 0.22), and Reynolds number (6.4x105 vs. 1.9x105).

Step Increase in BR

VLE – VLE,ref < Margin

YES

Step Decrease in BR

Figure 77. Basic schematic of the control logic employed in the manipulation of the hysteretic behaviors with respect to the jet blowing ratio. Derived from [9].

118

Chapter 5: Conclusions

The suction side of a laminar airfoil is susceptible to laminar separation at low Reynolds number, significantly diminishing the airfoil performance. Application of flow control can extend the stall limit and improve performance by energizing the boundary layer, delaying separation and increasing circulation. Particle Image Velocimetry, hot film anemometry, surface-oil flow visualization, infrared imaging and surface pressure measurements were used to investigate flow over a NACA 643-618 airfoil at a Reynolds number of 6.4x104 over a wide range of angle of attack. The baseline flow of the NACA

4 643-618 airfoil at Re = 6.4x10 reveals four distinct regions of flow behavior, ranging from -5° to 25° angle of attack. Steady blowing with varying optimal blowing ratios reveals that significant performance improvement can be made in discrete α ranges, and that natural separation control is maintained over the 13 ≤ α ≤ 19 range via a laminar separation bubble along the suction surface leading edge. Four representative angles of attack were investigated in detail for the characterization of the airfoil performance and boundary layer features. Results were conclusive that the baseline flow exhibited behavior suggested by Mack et al. [34]. Further, active flow control, through normal blowing and suction, and passive flow control, via zigzag tape, were utilized at each angle of attack. Significant increases in lift were observed over a broad range through

119 open loop optimization. It is observed that the flow physics and optimal flow control configurations change greatly with angle of attack.

Pulsed actuation is employed to provide comparable performance improvement while reducing the actuation mass flow requirement. The range of effectiveness of the pulsed blowing is investigated while actuating over a range of reduced frequency, duty cycle and blowing ratio. The time averaged lift coefficients are sustained above that for steady blowing for all parameter combinations except for pulsed blowing at low frequency and duty cycle.

To understand the separation control mechanisms at α = 10° the actuation frequency and duty cycle were reduced from the nominal configuration of f+ ≈ 1 and DC = 5% to f+ ≈ 0.12 and DC = 0.625%. At this low frequency, phase-locked PIV was employed for full-field diagnostics. It was shown that the primary control mechanism is the result of a

Kelvin-Helmholtz instability in the shear layer, resulting from the disturbances which are imposed by the jet pulse and amplified in the adverse pressure gradient. The consequent interaction with the wake increases the airfoil circulation by momentum exchange and wake removal. A secondary control mechanism is evident in the separation zone, where a

Kelvin-Helmholtz instability induces smaller undulations of the free shear layer which produce supplementary favorable momentum exchange and cause the free shear layer to approach the wall. This action further reduces the separation zone and increases circulation, improving the separation control.

Two attempts at closed-loop separation control of a continuously oscillating airfoil have been demonstrated. The first approach utilized an off-surface sensor, and while

120 effective, was limited in practicality, efficiency and the ability to satisfactorily monitor the airfoil performance. An off-surface sensor is not practical for real applications, and the efficiency of the system was limited in that the BR and duty cycle cannot be varied between α regions.

The controller over-compensates at lower α to ensure that control can be maintained over the whole α sweep, and thus requires more actuation power than is necessary.

Further, the employed sensor provided limited understanding of the real-time performance of the airfoil. To remedy these limitations, three surface hot-film sensors were placed along the suction side for increased practicality, control efficiency and monitoring ability. The LE sensor provided a good indication of the instantaneous airfoil performance, while the sensors at x/c = 0.2 and 0.4 were employed for real-time flow sensing and determination of the control parameters. Significant performance improvement is obtained by preventing stall over a significant portion of the angle of attack sweep, even as the controller determines appropriate control amplitudes. The algorithm is shown to be fairly robust, and capable of maintaining flow separation control over a range of operating conditions.

The transients of the aerodynamic response to flow control were investigated. Black- box models were created to help quantify the aerodynamic response. The effects of angle of attack and pitch rate on the simulation models were investigated. To implement these models in the closed-loop may require nonlinear control processes. However, other suggestions have been made to improve the accuracy and robustness of future control applications.

121

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