Flow Control of Compressible Dynamic Stall using Vortex Generator Jets
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University
By
Shawn Christopher Naigle
Graduate Program in Aeronautical and Astronautical Engineering
The Ohio State University
2016
Master's Examination Committee:
Professor Jeffrey P. Bons, Advisor
Professor James W. Gregory
Copyright by
Shawn Christopher Naigle
2016
Abstract
Dynamic stall is an airspeed and maneuver limiting event which occurs on helicopter retreating blades at high advance ratios and is associated with aerodynamic flutter and large negative pitch moments. The potentially violent dynamic stall sequence amplifies pitch link stress and can lead to loss of aircraft control. Steady Vortex
Generator Jet (VGJ) blowing has proven to delay the onset of dynamic stall. This work presents results of an experimental investigation into active flow control of a Sikorsky
SSC−A09 airfoil undergoing periodic pitching motion in a variety of flow conditions including, steady incompressible, steady compressible, and time-varying compressible freestream, representative of a helicopter rotor system in flight. The airfoil was evaluated at reduced pitching frequencies of 0.025≤ k≤0.050 with a nominal angle of attack schedule, α=9.5°−10.5°cos(ωt). Flow conditions were at steady Mach numbers of M=0.2 and M=0.4 and time-varying phase-locked freestream oscillations at Mach number
M=0.4+0.07cos(ωt), at Reynolds numbers 1.5×106≤ Re≤3.0×106. Flow control was achieved through a spanwise row of jets located at 10% chord, oriented normal to the surface, with an effective activated control width of 75% airfoil span. Blowing flow control was evaluated at a jet mass flux ratio 0.002≤ Cq≤0.005.
Flow control enhancements evaluated include stall penetration, lift and moment improvements, reduction in negative damping, and flow reattachment angle. Quantitative
ii measurements of lift and moment coefficients were calculated through the integration of airfoil surface pressure taps. Qualitative, time-resolved Background Oriented Schlieren
(BOS) supplemented surface pressure measurements to assess spanwise averaged dynamic stall vortex progression as well as shock interaction.
No optimal mass flux ratio completely controls dynamic stall, but VGJs delayed boundary layer separation, consistently improved cycle average moment, and increased cycle average lift. VGJs triggered an earlier flow reattachment which reduced hysteresis and circuits of clockwise rotation on the CM curve related to negative damping. BOS imagery confirmed the presence of leading edge shock formation and showed VGJ capability to delay shock-induced flow separation. The effectiveness of VGJ flow control is primarily a function of maximum angle of attack, pitching frequency, and freestream compressibility.
A comparison of VGJ flow control evaluated on a pitching airfoil in a steady compressible freestream at M=0.4 versus a pitching airfoil in a time-varying compressible freestream at M=0.04+0.07cos(ωt) at matched mean reduced frequency and Reynolds number, experienced similar quantitative improvements. Comparison of BOS imagery reveal the same physical VGJ to shear layer interaction between the steady and time- varying freestream cases. Thus, performance measurements based on active VGJs in a steady compressible freestream provide a good prediction of the expected performance measurements when blowing is applied to an airfoil in a low amplitude, time-varying compressible freestream. At low freestream oscillations, airfoil pitching frequency is the dominant factor influencing VGJ effectiveness.
iii
Dedication
To my loving wife, Laura, beautiful daughter Vera, and fellow students.
iv
Acknowledgments
This thesis would not have been completed without the assistance and support from all of my co-workers at The Ohio State University Aerospace Research Center. To my fellow students, thank you for your tutelage on the systems, software, and general concepts; especially Matthew Frankhouser, Kyle Hird, Kevin Disotell, and Kevin
Williams. Your extra efforts were invaluable. A special thank you to Josh Gueth for assistance in component manufacturing and ensuring resources were always available for completion of this study. I would be remiss if I did not recognize the critical professional guidance, patience, and mentorship from Dr. James Gregory and my advisor, Dr. Jeffrey
Bons. Thank you both for challenging me and helping me grow throughout the entire graduate school experience. Thank you to the Department of the Army for not only offering me the opportunity to attend The Ohio State University, but also to the Army
Research Office for funding this investigation. Most importantly, thank you to my family, especially my wife, Laura. From the late-night dinners for study groups at the lab to re-teaching me calculus, your unwavering support did not go unnoticed and this thesis is as much yours as it is mine. Lastly, to my little girl, Vera, thank you for being an unrelenting, but wonderful distraction – I love my ladies.
v
Vita
2000 ...... Diploma, Centreville High School
2005 ...... B.S. Mechanical Engineering, United States
Military Academy
Fields of Study
Major Field: Aeronautical and Astronautical Engineering
vi
Table of Contents
Abstract ...... ii
Dedication ...... iv
Acknowledgments ...... v
Vita ...... vi
List of Tables...... ix
List of Figures ...... x
Nomenclature ...... xvi
Chapter 1: Introduction ...... 1
Section 1.1: Rotorcraft Mechanics and Dynamic Stall ...... 2
Section 1.2: Flow Control of Dynamic Stall ...... 13
Section 1.3: Normal Oriented Vortex Generator Jets Flow Control ...... 17
Chapter 2: Experimental Methodology ...... 23
Section 2.1: Experimental Facility ...... 23
Section 2.2: Data Acquisition ...... 29
Section 2.3: Test Article ...... 31
Section 2.4: Tunnel Instrumentation ...... 34
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Section 2.5: Dynamic Compensation ...... 36
Section 2.6: Vortex Generator Jets ...... 37
Section 2.7: Background Oriented Schlieren ...... 40
Section 2.8: Measurement Uncertainties ...... 44
Chapter 3: Results and Discussion ...... 46
Section 3.1: Static Airfoil in a Steady Freestream ...... 48
Section 3.2: Airfoil Pitch Oscillations in a Steady Freestream ...... 58
Section 3.2.1: Airfoil Pitch Oscillations in an Incompressible Freestream ...... 59
Section 3.2.2: Airfoil Pitch Oscillations in a Compressible Freestream ...... 69
Section 3.3: Airfoil Pitch Oscillation in a Time-Varying Compressible Freestream .... 86
Section 3.4: Time-Resolved Background Oriented Schlieren ...... 102
Chapter 4: Conclusion ...... 119
References ...... 123
Appendix A: Dynamic Compensation Modeling ...... 128
Appendix B: Non-Optimal Results ...... 133
viii
List of Tables
Table 1: Bergh-Tijeman tubing and sensor geometry...... 128
Table 2: Amplification and phase delay of airfoil model...... 132
ix
List of Figures
Figure 1: Schematic of rotorblade relative velocity in forward flight [2]...... 3
Figure 2: Diagram of rotor disc lift regions in forward flight [2]...... 3
Figure 3: Hypothetical rotorcraft pitch angle in high speed forward flight [2]...... 4
Figure 4: Hypothetical pitch amplitude difference between advancing and retreating blades at various phases of flight [2]...... 6
Figure 5: Retreating blade stall and lift producing regions [2]...... 6
Figure 6: Stall sequence of a pitching airfoil vs. stall sequence of a static airfoil [4]...... 7
Figure 7: Helicopter flight test results depicting stall regions on the retreating blade as seen from above [8]...... 8
Figure 8: CL orbit of steady and unsteady freestream at k=0.05 [20]...... 12
Figure 9: Normal jet vortex generation [31]...... 19
6 Figure 10: PSP CP distribution of 3D flow around VGJs at M=0.3; Re=0.53×10 ; k=0.05,
α=13±7° during stall. a) α=14.2° b) α=15.5° c) α=16.7° d) α=17.7° (i) No blowing (ii)
Blowing at Cμ=0.12 [36]...... 21
Figure 11: Schematic of OSU 6"×22" unsteady transonic tunnel [13]...... 25
Figure 12: Operating limits of OSU 6"×22" unsteady transonic tunnel [13]...... 26
Figure 13: Airfoil oscillation assembly [13]...... 27
Figure 14: Mach number oscillation mechanism [13]...... 28
Figure 15: Empty tunnel Mach number variation with reduced frequency [20]...... 29 x
Figure 16: SSC−A09 airfoil with spanwise VGJs and surface pressure taps...... 32
Figure 17: Tunnel pressure measurement locations...... 34
Figure 18: Schlieren imagery of VGJ shock diamonds and spanwise flow uniformity. ... 39
Figure 19: Typical BOS setup with pertinent variables [42]...... 42
Figure 20: BOS tunnel setup diagram...... 43
6 Figure 21: CL vs. angle of attack comparison at M=0.2, Re=1.5×10 ...... 49
6 Figure 22: Airfoil CP distribution comparison at M=0.2, α=10°, Re=1.5×10 ...... 50
6 Figure 23: CM vs. angle of attack comparison at M=0.2, Re=1.5×10 ...... 51
Figure 24: CL and CM vs. angle of attack comparison with circular disturbance generators at M=0.16, Re=1.8×106 [46]...... 52
6 Figure 25: CL vs. angle of attack comparison at M=0.4, Re=3.0×10 ...... 53
6 Figure 26: Airfoil CP distribution comparison at M=0.4, α=10°, Re=3.0×10 ...... 54
6 Figure 27: CM vs. angle of attack comparison at M=0.4, Re=3.0×10 ...... 55
6 Figure 28: CL vs. angle of attack comparison at M=0.3, Re=1.15×10 [34]...... 57
6 Figure 29: Airfoil CP distribution comparison at M=0.3, Re=1.15×10 , α=12° [34]...... 58
6 Figure 30: CL vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.026...... 61
6 Figure 31: CM vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.026...... 62
Figure 32: CP of non-blowing (left) vs. blowing at Cq=0.0032 (right) at M=0.2,
Re=1.5×106, k=0.026...... 63
6 Figure 33: CL vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.050...... 64
6 Figure 34: CM vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.050...... 65
Figure 35: Flow modification vs. mass flux ratio for M=0.2, Re=1.5×106 (Part 1)...... 67
xi
Figure 36: Flow modification vs. mass flux ratio for M=0.2, Re=1.5×106 (Part 2)...... 68
6 Figure 37: CL vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.026...... 71
6 Figure 38: CM vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.026...... 72
Figure 39: CP of non-blowing (left) vs. blowing at Cq=0.0051 (right) at M=0.4,
Re=3.0×106, k=0.026...... 75
6 Figure 40: CL vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.050...... 76
6 Figure 41: CM vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.050...... 77
Figure 42: CP of non-blowing (left) vs. blowing at Cq=0.0051 (right) at M=0.4,
Re=3.0×106, k=0.050...... 79
Figure 43: Flow modification vs. mass flux ratio for M=0.4, Re=3.0×106 (Part 1)...... 82
Figure 44: Flow modification vs. mass flux ratio for M=0.4, Re=3.0×106 (Part 2)...... 83
Figure 45: CL and CM comparison with moderate to high pressure blowing at M=0.4,
Re=1.5×106, k=0.08, α=12−7°cos(ωt) [34]...... 85
6 Figure 46: CL vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.026...... 88
6 Figure 47: CM vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.026...... 89
Figure 48: CP of non-blowing (left) vs. blowing at Cq=0.0052 (right) at
M=0.4+0.07cos(ωt), Re=3.0×106, k=0.026...... 91
6 Figure 49: CL vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.050 ...... 92
xii
6 Figure 50: CM vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.050...... 95
Figure 51: CP of non-blowing (left) vs. blowing at Cq=0.0051 (right) at
M=0.4+0.07cos(ωt), Re=3.0×106, k=0.050...... 97
Figure 52: Flow modification vs. mass flux ratio for M=0.4+0.07cos(ωt), Re=3.0×106
(Part 1)...... 98
Figure 53: Flow modification vs. mass flux ratio for M=0.4+0.07cos(ωt), Re=3.0×106
(Part 2)...... 99
Figure 54: Flow modification vs. mass flux ratio for steady and time-varying freestream.
...... 101
Figure 55: Processed BOS image with reliable, unreliable, and no-data regions...... 104
Figure 56: Raw BOS image with reliable and unreliable regions...... 105
Figure 57: Far-field structure identification comparison of a pitching airfoil in a compressible freestream at M=0.4, k=0.05, using PDI (left) [50] and BOS (right)...... 106
Figure 58: Structure identification comparison of a pitching airfoil in a compressible freestream at M=0.4, k=0.05, using PDI (images a, b) [50] and BOS (images c, d)...... 107
Figure 59: Leading edge shock on a non-blowing case at M=0.4, k=0.050, Re=3.0×106.
...... 108
Figure 60: Leading edge shock when blowing at Cq=0.0051, at M=0.4, k=0.050,
Re=3.0×106...... 109
xiii
Figure 61: Shear layer angle amplitude of non-blowing (high-angle (a), low-angle (c)) and blowing at Cq=0.0052 (high-angle (b), low-angle (d)), M=0.4+0.07cos(ωt), k=0.026,
Re=3.0×106...... 111
Figure 62: Shear layer angle vs. phase for non-blowing and blowing at Cq = 0.0052,
M=0.4+0.07cos(ωt), k=0.026, Re=3.0×106...... 112
Figure 63: Airfoil load oscillation amplitude with moderate to high pressure blowing at
M=0.4, Re=1.5×106, k=0.08, α=12−7°cos(ωt) [34]...... 114
Figure 64: Vortical structures at CM stall of non-blowing (left) and blowing at Cq=0.0052
(right) at, M=0.4+0.07cos(ωt), k=0.026, Re=3.0×106...... 116
Figure 65: Flow separation of non-blowing (a) vs. blowing at Cq=0.0052 (b), and shear layer reattachment of non-blowing (c) vs. blowing at Cq=0.0052 (d),
M=0.4+0.07cos(ωt), k=0.026, Re=3.0×106...... 118
Figure 66: Bergh – Tijdeman bench top test...... 129
Figure 67: Power Spectral density of airfoil pressure tubing...... 130
Figure 68: Amplification Ratio of airfoil pressure tubing...... 131
Figure 69: Phase delay of airfoil pressure tubing...... 131
Figure 70: Corrected signal of an airfoil pressure tap...... 132
6 Figure 71: Combined CL and CM curves vs. Cq variation for M=0.2, Re=1.5×10 , k=0.026.
...... 134
6 Figure 72: Combined CL and CM curves vs. Cq variation for M=0.2, Re=1.5×10 , k=0.050.
...... 134
xiv
6 Figure 73: Combined CL and CM curves vs. Cq variation for M=0.4, Re=3.0×10 , k=0.026.
...... 135
6 Figure 74: Combined CL and CM curves vs. Cq variation for M=0.4, Re=3.0×10 , k=0.050.
...... 135
Figure 75: Combined CL and CM curves vs. Cq variation for M=0.4+0.07cos(ωt),
Re=3.0×106, k=0.026...... 136
Figure 76: Combined CL and CM curves vs. Cq variation for M=0.4+0.07cos(ωt),
Re=3.0×106, k=0.050...... 136
xv
Nomenclature
A = Test section area
A* = Throat area
AR = Airfoil aspect ratio b = Airfoil span
BOS = Background Oriented Schlieren c = Airfoil chord length
CM = Moment coefficient about the quarter chord
CL = Lift coefficient
CP = Coefficient of pressure
CPcrit = Critical CP
Cq = Mass flux ratio
Cμ = Momentum flux ratio
D = Mach disc diameter
+ F = Non-dimensional oscillating frequency (foscc/U∞) f = Camera focal length fosc = Physical oscillating frequency
K = Gladstone-Dale constant k = Reduced frequency (ωc/2U∞)
L = Mach disc spacing xvi
Lact = Span of actuation
M = Mach number
ṁ = Mass flow rate n = Index of refraction
P = Pressure
PR = Pressure ratio (Pj/P∞)
Re = Reynolds number based on airfoil chord
T = Temperature t = Time
U = Velocity
VGJ = Vortex Generator Jets x = Chordwise position y = Vertical displacement
Z = Distance from speckle pattern
α = Angle of attack
γ = Specific heat ratio
ε = Light angle of incidence
ρ = Density
ϕ = Phase angle
ω = Angular pitching frequency
Ψ = Rotor azimuth
xvii
Subscripts j = Jet max = Maximum min = Minimum
T = Total
∞ = Freestream
xviii
Chapter 1: Introduction
Helicopter dynamic stall is a well-researched performance limiting occurrence observed on the retreating blade of rotorcraft at high advanced ratios and during acrobatic maneuvers. The stall sequence is characterized by large torsional loading and unstable high amplitude aeroelastic flutter associated with high pitch link loads and potential loss of aircraft control. The postponement or alleviation of negative effects from dynamic stall through active flow control can increase rotor blade performance and expand the operational envelope of helicopters. Specifically, control of dynamic stall on rotorcraft could increase operational range, reduce noise and vibration, decrease thrust specific fuel consumption, reduce logistic footprints, and expand mission envelopes.
The objective of this thesis is to appraise the effectiveness of steady blowing through discrete portholes on a dynamically pitching airfoil at wind tunnel conditions representative of a helicopter rotor system in high speed forward flight. Blowing compressed air through an array of vortex generator jets (VGJ) near the leading edge causes local flow acceleration which thins the boundary layer and creates vortical structures which resist separation and encourage shear layer reattachment [1]. While the use of VGJ flow control is not a novel approach, the facilities and diagnostic equipment used in this investigation permit a unique exploration of VGJ flow control in a compressible, phase-locked, time-varying freestream. The conditions include unsteady compressible flow at high Reynolds numbers analogous to rotorcraft flight conditions. 1
To the knowledge of this author, the use of jets as active flow control in typical helicopter flight conditions has yet to be experimentally analyzed.
Section 1.1: Rotorcraft Mechanics and Dynamic Stall
Dynamic stall occurs on helicopter rotor systems at high advance ratios through shock-induced separation due to compressibility effects or surpassing the blade’s critical stall angle due to asymmetry of lift. As rotorcraft engage in forward flight, the rotor systems are geometrically divided into advancing and retreating halves. The advancing half has a rotational velocity concurrent with the direction of flight and the retreating half rotates opposite to the direction of flight. The effective freestream velocity disparity is depicted in Figure 1 where location 'A' represents the advancing blade at the Ψ=90° azimuth, and location 'C' is the retreating blade at the Ψ=270° azimuth. The aircraft induced speed enters the diagram from the Ψ=180° azimuth. As the lift generated by an individual blade is proportional to the square of the blade’s relative velocity, the resultant freestream velocity disparity creates a corresponding asymmetry of lift that grows with increasing airspeeds. Additionally, no-lift regions develop on the retreating blade near the rotor hub because the combined effect of the blade’s rotational velocity and oncoming relative wind are too low to generate meaningful lift. Thus, the lift producing blade span section on the retreating blade becomes smaller, further contributing to the asymmetry of lift. The total of these regions are depicted in Figure 2.
2
Ψ=180°
Ψ=270° Ψ=90°
Ψ=0°
Figure 1: Schematic of rotorblade relative velocity in forward flight [2].
Figure 2: Diagram of rotor disc lift regions in forward flight [2].
To compensate for the asymmetry of lift between the retreating and advancing blades, the relative pitch angle of the retreating blade increases to amplify the coefficient
3 of lift while simultaneously, the pitch angle of the advancing blade is decreased. In order to achieve the necessary angle of attack at each phase location of the rotor system, the blades pitch up and down in a sinusoidal pattern known as cyclic pitching. The maximum angle of attack corresponds to the lowest relative velocity (retreating blade) and the minimum angle of attack corresponds to the greatest relative velocity (advancing blade). Figure 3 represents a hypothetical rotor system pitch schedule with a corresponding phase relationship to Figure 1 where the greatest relative velocity is at the
Ψ=90° azimuth, minimum velocity is at the Ψ=270° azimuth, and the airspeed generated flow enters from the Ψ=180° azimuth.
Ψ=180°
Ψ=270°
Ψ=90°
Ψ=0°
Figure 3: Hypothetical rotorcraft pitch angle in high speed forward flight [2]. 4
As the helicopter airspeed increases, the amplitude of the cyclic pitch motion increases as depicted in Figure 4. At high advance ratios, in an effort to achieve the necessary angle of attack, the retreating blade exceeds a critical stall angle at the blade tip and the flow separates. Flow separation contributes to high drag and further reduces the lift producing region as depicted in Figure 5, which is a comprehensive diagram of lift and no-lift regions with associated angles of attack and resultant total aerodynamic forces. The dynamic stall region examined in this study is denoted as Part E.
The resultant complex aerodynamic phenomenon associated with high angles of attack is well known as dynamic stall and is accompanied by high lift coefficients and strong negative pitch moments. The state of airfoil flow attachment at specific phases of a pitch cycle with corresponding normal and moment coefficient orbits is depicted in
Figure 6. The dynamic stall process on a pitching rotor blade is caused by an unsteady boundary layer separation near the airfoil’s leading edge [3]. During high frequency cyclic pitching, circulation production is greatly enhanced by the presence of a favorable pressure gradient at the leading edge which leads to an increase in CLmax (lift overshoot) beyond static stall conditions [4]. An amplified circulation beyond that of static conditions accumulates locally as a result of the vortex advection downstream.
Eventually, the enhanced circulation exceeds its ability to remain attached and the accumulated vorticity is ejected into the outer flow. The vortex advection is due to an adverse pressure gradient and a local boundary layer flow reversal downstream. If the maximum angle of attack exceeds the static stall angle, the resulting increase in lift and associated rapid negative pitching moment is more intense than that of static stall [5].
5
Figure 4: Hypothetical pitch amplitude difference between advancing and retreating blades at various phases of flight [2].
Figure 5: Retreating blade stall and lift producing regions [2]. 6
Figure 6: Stall sequence of a pitching airfoil vs. stall sequence of a static airfoil [4].
Subsequently induced stages of aeroelastic instabilities and large amplitude vibrations move inboard from the blade tip [6]. Flight tests using tufts mounted to rotor blades at high speed flight show that the inboard movement of the stalled region can
7 encompass over 50% of the outer retreating blade radius (see Figure 7). As the severity of the stall increases, the large amplitude vibrations and instabilities associated with regions of negative damping cause substantial torsional loads on the rotor pitch links [7].
Through gyroscopic procession, the sudden loss of lift and violent negative moment on the retreating blades causes the rotor disk to pitch up over the nose. In extreme cases, the ensuing procession exacerbates stall on the retreating blade and the aircraft abruptly rolls towards the retreating side in a potentially unrecoverable condition [2].
Figure 7: Helicopter flight test results depicting stall regions on the retreating blade as seen from above [8].
8
The complexity and rapid sequence of local viscous/inviscid boundary layer interactions and vortex shedding associated with dynamic stall has been the subject of study for over seven decades. Early studies conducted in 2D tunnels on a pitching airfoil in steady, incompressible flow focused on characterizing the dynamic stall process to include the influence of reduced frequency and maximum angle of attack on vortex convection and are thoroughly documented [3] [5] [7]. At a high reduced pitching frequency, the boundary layer will thin and stall will be postponed to greater angles of attack. The maximum angle of attack categorizes the event as either light or deep dynamic stall. Light dynamic stall is characterized by low levels of hysteresis and an immediate flow reattachment. The degree of stall in this regime is very sensitive to Mach number, reduced frequency, and Reynolds number [7]. In the deep stall regime, the dynamic stall vortex is strongly developed with substantial peak lift and moment fluctuations. The loading fluctuates severely through the pitching cycle with strong hysteresis resulting in negative damping. Airfoil loading in this regime is insensitive to
Reynolds number, airfoil geometry, and reduced frequency [5] [4].
Through airfoil surface pressure measurements and laser interferometry, Carr and
Chandrasekhara determined that local compressibility effects are present in low-speed, incompressible flows and are a product of high angle stall penetration [9]. The occurrence of locally compressible flow is due to the continuation of attached flow at the high angles of attack reached prior to separation and is related to pitch rate.
Compressibility reduces dynamic lift overshoot and suction peak strength, and causes flow separation at lower angles of attack when compared to dynamic stall in an
9 incompressible freestream [6]. While the flow separation angle is dependent on compressibility, the degree of stall penetration beyond the static stall angle is primarily related to the reduced pitching frequency [10]. Compressibility effects are seen as leading edge stall and result in the formation of a dynamic stall vortex at much lower angles of attack than observed for an incompressible trailing edge stall [6]. Lorber and
Carta investigated large pitch oscillations at rotorcraft relevant Mach and Reynolds numbers and detected the presence of shocks near the leading edge, which strengthened at high pitch amplitudes even in a mildly compressible freestream [11]. They observed that the SSC−A09 airfoil is shock free during pitch oscillations at freestream M=0.2, but at M=0.4, local supersonic regions develop at x/c=0.005 and extend over the leading 8% chord [11]. As the airfoil pitches up, high frequency pressure oscillations appear at the shock, creating local instabilities. A distinct stall vortex is released at x/c=0.060, just downstream of the shock, and moves towards the trailing edge at about 14% of the freestream velocity. The vortex release point is forward of that for the M=0.2 case
(x/c=0.1) and the vortex speed is about 10% less than the M=0.2 condition [11]. As the convection speed for the compressible freestream is less than the incompressible freestream, shock-induced separation causes the stall to be more gradual and results in a more diffuse stall vortex in comparison to pressure gradient initiated separation [12].
The majority of helicopter rotor dynamic stall studies reported in the literature have been conducted in a constant velocity wind tunnel with a 2D airfoil pitching (or plunging) at the appropriate reduced frequency. Since dynamic stall on rotorcraft occurs during the retreating blade motion at advance ratios approaching 0.3 to 0.4, the relative
10 flow velocity “seen” by the retreating airfoil also varies during the dynamic stall event.
This time-varying relative velocity has a direct influence on the severity of the local pressure gradient. The physical interactions between time-varying velocity, airfoil geometry, compressibility, and flow control mechanisms on dynamic stall are not fully understood. The challenges of high speed [13] and low speed wind tunnel [14] design with the desired pitch and velocity oscillation amplitude has limited the widespread accessibility to such facilities. Thus, large amplitude time-varying velocity studies are primarily numerical and unfortunately lack the experimental studies necessary to validate the computations [15] [16]. A few researchers have experimentally investigated the combination of airfoil pitching and relative velocity oscillations, in incompressible conditions, including Furman et al., [17] and Favier et al. [18]. These studies concluded that a strong coupling exists between the two modes of oscillation, with unsteady freestream velocity having a strong impact on dynamic stall development. Observation of a pitching airfoil in an unsteady freestream by Pierce et al. [19] showed that a time- varying freestream significantly influences the degree of negative pitching moment as well as introduces unsteady moment oscillations at high angles of attack. Hird et al. [20]
[21] experimentally investigated the effects of compressibility in coupled Mach number and pitch oscillations at compressible Mach numbers where minimum Mach number occurred at the same phase angle as the maximum angle of attack. Through surface pressure integration and particle image velocimetry measurements on a pitching airfoil in a sinusoidal variation in Mach number, Hird et al. found that flow deceleration amplified vorticity which strengthened the dynamic stall vortex [20]. Mach number oscillations
11 showed accelerated flow around the airfoil leading edge beyond that of the steady freestream case at maximum angle of attack. The peak CL increased well beyond the peak value observed in steady freestream conditions (see Figure 8). Along with this higher peak CL, there was a more abrupt lift stall without a significant change in the stall angle. When flow hysteresis effects are present in large amplitude pitch oscillations, the principle non-dimensional parameter for dynamic stall vortex intensity and convection speed is reduced frequency [22]. Therefore, as reduced frequency locally varies as a function of freestream velocity, freestream velocity variation and dynamic stall progression are intrinsically paired and must be studied in tandem.
Figure 8: CL orbit of steady and unsteady freestream at k=0.05 [20].
12
Section 1.2: Flow Control of Dynamic Stall
As the understanding of dynamic stall increases, more recent research has focused on the development of control methods. As dynamic stall is a substantial aerodynamic performance limitation for modern rotorcraft, there is significant interest in delaying, reducing the severity, or eliminating the negative effects of stall altogether. Explorations into dynamic stall flow control have included approaches based on boundary layer suction, combustion-powered actuation, dielectric barrier discharge plasma actuation, zero-net-mass-flux blowing, steady and pulsed slot blowing, and tangential vortex generator jets. The referenced literature indicate that effective flow control is sensitive to chordwise location, forcing magnitude, airfoil geometry, and the presence of compressibility effects. However, while these studies inherently vary in flow condition and control apparatus, they have commonality in that flow control is achieved through various methods of boundary layer manipulation.
Published in 1957, Hinton [8] evaluated the effects of phase locked boundary layer suction in a wind tunnel as well as in full scale flight testing. Boundary layer suction was achieved by pumping 1000 ft3/min through 3.0 in slots installed at 27.5% chord over 50-94% blade radius. An activation valve opened at a blade azimuth of 234° and closed at 326°. When open, the valve created a vacuum in the blade spar which effectively sucked the boundary layer into the blade spar. Qualitative results from blade tufts and pilot observations combined with quantitative data from aircraft power and airspeed instruments indicated the absence of dynamic stall at an airspeed 13% above the
13 normal blade-stall limited airspeed [8]. This early flow control experiment evaluated multiple methods of flow control but ultimately determined suction was the most effective. The study suggested that the active flow control used to disrupt the normal boundary layer development provided substantial benefits to an aircraft in flight.
Chandrasekhara et al. [23] developed a dynamically deforming airfoil leading edge to modify the flow gradients by suitably shaping the airfoil geometry. The deformation reduced the local Mach number and adversity of the local pressure gradient at the point of leading edge vortex separation. Through smart materials and minimal leading edge displacement, two shapes were identified which prevented convection of the leading edge vortex at Mach numbers 0.3 and 0.4. Thus, vorticity generation was effectively managed. The flow in both cases remained attached over the leading quarter chord for the duration of the cycle with only light trailing edge separation at high angles of attack. As dynamic stall vortex generation and separation can be caused by either shock interaction near the leading edge or from rapid flow acceleration around the leading edge meeting a strong adverse pressure gradient, the degree of local flow acceleration and corresponding pressure gradient are substantial indicators in the development of flow control strategies [23].
Matalanis et al. [24] explored combustion-powered pulsed actuation on a tabbed
VR−12 airfoil through tangentially oriented slots, both numerically and experimentally.
Computational results at Mach numbers of 0.3 and 0.4 suggested that combustion powered actuation increased lift throughout the downstroke, improved negative moment peak, and reduced cycle averaged drag. Experimental investigations in incompressible
14 flow at Reynolds numbers up to 875,000, when pulsing at varying forcing frequency values near 1.0 validated the computational predictions and showed that actuation duty cycle governs the degree of flow control. Furthermore, this study demonstrated that complex active flow control mechanisms can be accurately modeled using computational techniques. As helicopter manufacturers lean heavily on computational modeling in rotorcraft design, this latter point is an important aspect of flow control relevance to the rotorcraft industry.
Plasma actuation flow control in both constant on and pulsed application are popular mechanisms due to their simplistic incorporation to current helicopter rotor systems. Investigations by Post and Corke [25] and Frankhouser et al. [26] demonstrated the potential of plasma actuation in deep dynamic stall in incompressible flow. Pulsed plasma actuation resulted in reduced lift hysteresis and delayed pitch moment stall by adding energy to the flow through thermal compression waves. However, the suitability of plasma actuation in a compressible freestream has not yet been fully explored due to shock formation from surface discontinuities at the mechanism application site.
Greenblatt and Wygnanski [27] conducted a comparison study on thin and thick leading edge symmetric airfoils using zero-net-mass-flux blowing. Actuation at Cµ values between 0.001 and 0.004 in incompressible flow near the leading edge resulted in substantial lift enhancement as well as negative pitching moment reduction. The thin leading edge NACA 0012 exhibited periods of post stall attachment unsteadiness which required an increase in actuation strength to overcome. In contrast, the thick leading edge airfoil, susceptible to trailing edge stall, demanded only minimal actuation to produce
15 meaningful flow enhancements with minimal shear layer instability. This study emphasized the significance of airfoil geometry and implied that certain flow control mechanisms are better suited for specific leading edge geometry.
Recently, Müller-Vahl et al. [28] used steady slot blowing at both the leading edge and mid-chord of a NACA 0018 airfoil to achieve dynamic stall control at Reynolds numbers ranging from 1.25×105 to 3.75×105. While leading edge blowing proved very effective at controlling stall, blowing from the mid-chord position did not alleviate leading edge stall, but did assist in substantial suppression of trailing edge separation.
With low blowing, at Cµ=0.6%, earlier shedding of the dynamic stall vortex was achieved, resulting in lower load fluctuations, but at the cost of decreasing stall penetration. At higher momentum flux, Cµ=7.2 %, blowing was able to fully attach the flow and prevent release of the dynamic stall vortex at stall penetration of 8 degrees beyond the uncontrolled stall angle of attack. Observed flow improvements or deteriorations based on the quantity of control application suggest that dynamic stall flow control authority is dependent upon actuation magnitude.
Beahan et al. [29] investigated a NACA 0015 airfoil subjected to periodic pitching motion fitted with multiple microjets normal to the surface in the first 12% chord. The microjets produced streamwise vortices and increased the mixing of high momentum outer flow with the less energetic boundary layer flow, thus thickening and energizing the boundary layer. With Cµ = 0.023 at Mach number 0.3, the microjet array alleviated the flow separation associated with dynamic stall in mild compressible flow.
When compressibility was increased to support the formation of lambda shocks near the
16 leading edge at Mach 0.4, steady blowing through the staggered microjet array effectively disrupted the negative effects of compressibility, showing that streamwise vorticity can eliminate shock-induced separation at the leading edge.
Larger VGJs oriented tangential to the surface of an airfoil have been used to produce streamwise vortices as a means of dynamic stall control. Singh et al. [30] employed inclined and skewed VGJs machined at two chord locations (leading edge and mid-chord) on a RAE9645 airfoil showing positive results with Cµ less than 0.01 in incompressible flow at a Reynolds number of 1.5×106. They determined that leading edge VGJs suppressed separation, reduced normal forces hysteresis, and condensed the section of the CM loop contributing to negative damping. The mid-chord inclined VGJs, when operated independently of the leading VGJs, were incapable of fully suppressing separation at the same momentum ratio. The comparative improvements based on jet location suggests that judicious chordwise location of flow control mechanisms can optimize their effect.
Section 1.3: Normal Oriented Vortex Generator Jets Flow Control
Normal oriented VGJ blowing interacts with the bulk flow differently than tangentially oriented jet blowing. Whereas a tangentially oriented jet adds momentum to the boundary layer, normally oriented jets influence boundary layer development through local flow acceleration and convection of vortical structures without adding streamwise momentum to the bulk flow. The physics supporting active blowing through VGJ
17 aligned normal to the surface is based on the vortex structure interaction of a jet in a perpendicular crossflow. When compressed air is blown through discrete ports on an airfoil surface, the high density and pressure of the jet penetrates the shear layer creating a locally constricted area for the bulk flow to negotiate. To satisfy the law of conservation of mass, the flow must accelerate locally to transit the induced constriction.
In an incompressible crossflow, the local velocity increase is directly proportional to the constriction, translating to a locally favorable pressure gradient and boundary layer thinning. Due to the nature of the incompressible flow, the presence of the jets elongates the streamlines far upstream such that the flow arrives at the constriction at the appropriate velocity, resulting in a reduced boundary layer thickness upstream of the jets.
When applied to an airfoil, the increased boundary layer edge velocity results in a spanwise CP decrease on the suction surface upstream of the jets. The increased suction in the vicinity of the jets increases CL and improves CM (if jets are near the leading edge).
As the angle of attack increases, the favorable pressure gradient in the vicinity of the jets anchors the boundary layer and suppresses separation. The interaction between the oncoming boundary layer and the conical structure of a discrete jet will generate horseshoe vortices similar to that of a cylinder in a crossflow. The size of these horseshoe vortices is dependent upon the oncoming boundary layer thickness. These vortices add structure to the flow over the surface and further oppose flow separation.
In a compressible flow, the basic physics are comparable but with the additional effects of varying density, potential for shocks, and the Prandtl-Glauert effect.
Investigations by Fric and Roshko showed the viscous interaction between the jet and
18 freestream entrains a portion of the freestream into the jet, creating counter-rotating vortices [31]. Simultaneously, the freestream momentum turns the vortex structure downstream as depicted in Figure 9. The height above the surface at which the flow bends is a function of the jet to freestream momentum ratio. These secondary impacts have relevant bearing on the overall efficacy of VGJ blowing in compressible flow.
Counter-rotating Vortex Pair
Figure 9: Normal jet vortex generation [31].
Dickmann and Lu [32] conducted a numerical study of normal jets in both subsonic and supersonic crossflow over a flat plate. In subsonic conditions at a jet to freestream pressure ratio of PR=5, the jet obstruction influenced the CP upstream of the jet by as much as 2.5 jet diameters and laterally by 1.2 jet diameters. The CP directly upstream of the jet exit experienced an increased CP due to the highly adverse pressure gradient created by the jet obstruction. However, downstream and at lateral distances, the horseshoe vortices created by the jet to leading edge boundary layer interaction created a
19 favorable pressure gradient [32]. The favorable pressure gradient decreased CP and thinned the boundary layer locally. Immediately downstream of the jet exit there is a substantial decrease in CP that extends further downstream with increased pressure ratio and freestream Mach number. In a supersonic crossflow, it was observed that a bow shock forms around the jet, leading to the formation of additional vortical structures [32].
A numerical study by Muppidi and Mahesh [33] showed that a high momentum jet emitted into a cross-flow entrains fluid from the freestream on the downstream side of the jet. The study also showed that the counter-rotating vortex pairs are created from the bending of the jets by the crossflow and that the jet would remain a conical structure until fully turned by the freestream. Once formed, the counter-rotating vortex pairs may entrain high momentum fluid from the freestream towards the near wall region [33].
Gardner et al. studied normal VGJs employed at 10% chord to control dynamic stall in compressible flow, both numerically [1] and experimentally [34] [35] [36].
Figure 10 is an adaptation of a pressure sensitive paint interrogation of an airfoil section with and without steady blowing at increasing angles of attack. The jets are indicated as white dots and pressure taps are denoted as black dots. The upper half of the figure, denoted with (i), is the uncontrolled case and the bottom, denoted with (ii), is the controlled condition. Gardner et al. observed spanwise uniform suction adjacent to the
VGJs as well as regions of low pressure propagating downstream from the jets, as was observed by Dickmann and Lu [36]. In agreement with Muppidi and Mahesh, Gardner et al. surmised that the jets have similar properties to that of an ejector and entrain a portion
20 of the low momentum surface flow, amplifying the intensity of the low pressure region adjacent to the jets [36] [1].
(i)
(ii)
6 Figure 10: PSP CP distribution of 3D flow around VGJs at M=0.3; Re=0.53×10 ; k=0.05, α=13±7° during stall. a) α=14.2° b) α=15.5° c) α=16.7° d) α=17.7° (i) No blowing (ii) Blowing at Cμ=0.12 [36].
Gardner et al. ascertained commendable airfoil performance improvements utilizing normally oriented VGJs fitted at 10% chord when blowing at Cµ values spanning 0.007 to 0.068 in both steady and pulsed blowing. These momentum flux ratios equate to approximate mass flux ratios (Cq) from 0.002 to 0.01 at M=0.4. They showed promising dynamic stall control on a pitching OA209 transonic rotorcraft blade at steady 21 compressible freestream conditions at Mach numbers of 0.3-0.5 and Reynolds numbers up to 1.9×106 [35]. As indicated in Figure 10, VGJs sustained a suction peak upstream of the jets and functioned to anchor the flow against separation.
Additional results amplified stall penetration, reduced negative moment peak, and improved hysteresis over a wide range of pitch oscillation amplitudes. They evaluated several Cq and VGJ spacing combinations at varied maximum angle of attack in order to determine an optimal condition [35]. With this breadth of data, it was determined that the effectiveness of steady blowing progressively declines as maximum angle of attack is increased. Low Cq resulted in amplified airfoil load oscillations in post stall, but as Cq increased to the maximum system capability, the load oscillations decreased [34]. While
Gardner et al.’s investigation is very comprehensive and has similarities to the present study, VGJs effectiveness was not evaluated in a time-varying, compressible freestream at rotorcraft relevant Reynolds numbers.
Herein lies the objective and uniqueness of this study; to evaluate normally oriented VGJs as an active flow control mechanism to alleviate the detrimental impact of dynamic stall in a steady and time-varying freestream at rotorcraft conditions. The interrogation techniques used permit surface pressure measurements for comparison with
Gardner et al. but also include flow visualization to analyze off-surface flow features.
Additionally, the uniqueness of the test facility enables flow control evaluation at
Reynolds numbers twice as large as Gardner et al.’s study for the same Mach number.
Thus, the test conditions evaluated are more representative of a realistic helicopter rotor system in forward flight conditions.
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Chapter 2: Experimental Methodology
This experimental investigation was conducted in The Ohio State University unsteady transonic dynamic stall facility which is capable of examining pitching and static airfoils in both time-varying and steady freestream. All quantitative data presented were generated from surface and tunnel pressure measurements. Qualitative Background
Oriented Schlieren supplemented pressure measurements for off-surface flow characteristics. A Sikorsky SSC−A09 airfoil modified with VGJs oriented normal to the surface at 10% chord served as the vehicle for this investigation. A stepdown regulator from 2200 psi to 300 psi controlled the pressure supplied to the airfoil VGJ plenum.
Each component employed in this setup as well as how each device is implemented into the system is described in detail. This chapter includes the intricate orchestration necessary to achieve highly time-accurate, synchronized data.
Section 2.1: Experimental Facility
Data collection was conducted in the 6"×22" unsteady transonic wind tunnel at
The Ohio State University, the design and capability of which are detailed by Gompertz et al. [13]. The tunnel has electrically operated rotating mechanisms to oscillate the airfoil pitch and the freestream Mach number, either independently or synchronously, with an adjustable phase difference between the two. Figure 11 is a schematic of the 23 tunnel and Figure 12 shows the range of possible operating conditions for the tunnel as well as the conditions for this investigation (marked in red). The freestream flow is supplied to the test section through a 20 cm (8 in.) diameter high pressure supply line from two 42.5 m3 (1500 ft3) air storage tanks pressurized up to 17 MPa (2500 psi) with inline air dryers to maintain air purity. The high pressure air flow is controlled by two valves. The first is a positioning globe valve which opens to a predetermined area to establish the air mass flow and total pressure. The positioning globe valve is controlled through LabVIEW software and is used to regulate the test section pressure below the maximum operating pressure of 350kPa (50 psia) and set the test section Reynolds number. The flow density is established by the total pressure when combined with the estimated flow temperature. Through Sutherland’s formula, the flow viscosity is predicted which establishes the final variable necessary to estimate Reynolds number.
The second valve is a pneumatically controlled fast acting valve used to start and stop the flow of high pressure air. The pneumatic solenoid valve opening and closing the fast acting valve is electrically signaled through LabVIEW software.
The settling chamber is equipped with a perforated plate, a honeycomb section, and eight screens (60 mesh) to condition the flow and lower the test section turbulence intensity to less than 0.5% at steady flow conditions. A subsonic nozzle with a contraction ratio of 15:1 further establishes flow uniformity in the 1.1 m long,
15.2 cm×55.9 cm test section. The solid sidewalls have high tensile fittings for fixed or rotating clear and opaque windows to hold the airfoil, while the spanwise floor and ceiling are perforated with 3.2 mm straight holes yielding an effective porosity of 6%.
24
Ceiling and floor isolation cavities are open to the flow downstream of the test section and aid in producing a high quality flow in the test section by reducing wave reflections.
The tunnel is always operated in a choked flow condition, with the throat downstream of the test section. The Mach number based on throat area is calculated using the isentropic area ratio equation provided below.
1 1 2 2( 1) 1 (1 M ) A 1 ( ) 2( 1) 2 A* 2 M
The throat area can be easily modified for both static and dynamic Mach number with variation of evenly spaced blockage bars in the throat area. Since the test section Mach number is uniquely established by the ratio of choke area and test section area, Reynolds number can be set freely of the Mach number by controlling stagnation pressure [13].
Elliptical Choke Vanes
Figure 11: Schematic of OSU 6"×22" unsteady transonic tunnel [13].
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Figure 12: Operating limits of OSU 6"×22" unsteady transonic tunnel [13].
Recent modifications to the 6"×22" transonic tunnel enable operation in several dynamic modes: pitching airfoil in steady freestream, phase-locked pitch and freestream oscillations, and a static airfoil in an unsteady freestream. This wide range of conditions allows the flow to simulate several compressible dynamic conditions, but only the first two modes were utilized in this investigation. The first dynamic mode, pitch oscillations in a steady freestream, allows for the airfoil to pitch in a sinusoidal pattern throughout the run. An oscillation mechanism is powered by a 5-hp motor which drives a face cam and linkage arm connected to the airfoil mounting window. The mechanism can be operated at frequencies up to 21 Hz with typical oscillation amplitudes of 5° and 10°. Figure 13 illustrates the pitch oscillation assembly.
26
Flow
Connection Bar 5-hp A/C Motor Movement
Lever Arm V-Belt Fly Wheel
Eccentric Disk
Pulley diameter ratio sets frequency range
Figure 13: Airfoil oscillation assembly [13].
The second dynamic operating mode utilized in this investigation is phase locked pitch and Mach oscillations. Mach oscillations were produced by rotation of four elliptical choke vanes in the choke area, driven by a stepper motor slaved to the pitch oscillation motor. The choke vane stepper motor is slaved such that the Mach oscillation frequency is synchronized to the pitch oscillation frequency at a desired phase delay through a predetermined phase offset. The target phase offset for the entirety of this investigation was such that maximum angle of attack occurred with minimum Mach number. As the blowdown tunnel is operated at a sufficiently high pressure ratio to choke the flow at the downstream throat, the throat area produced by the choke vanes uniquely modulates the test section Mach number. Gompertz et al. [13] characterized these details of the wind tunnel and calculated pressure wave propagation through the
27 tunnel. The Mach number as measured in an empty tunnel at various reduced frequencies is plotted for one complete choke vane revolution in Figure 15. At low reduced frequencies, the variation in Mach number matches the predicted sinusoid value of
M=0.4+0.07cos(ωt) well, but at the highest reduced frequencies, there is some distortion of the waveform as well as a phase lag. For all three dynamic tunnel operations and an airfoil of 0.1524 m chord, the Mach number operation ranges from Mach number 0.2 to
1.0 and Reynolds number can range from 2 to 16 million/foot. These ranges allow for experimental studies with relevant reduced frequencies for rotorcraft dynamics.
Figure 14: Mach number oscillation mechanism [13].
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Figure 15: Empty tunnel Mach number variation with reduced frequency [20].
Section 2.2: Data Acquisition
Data acquisition of time-dependent information during these dynamic transonic wind tunnel tests is critical to obtain accurate results. A series of three computers are utilized to control, synchronize, and record analog signals (temperature, angle of attack, etc.) and pressure data in the 6"×22" unsteady transonic facility.
The first computer is the main control system that operates the positioning valve.
The position of the valve is set by supplying an analog signal from a terminal Data
29
Acquisition Board (DAQ Board) to the electronic positioner that opens the valve to the correct setting to obtain the user defined pressure and Reynolds number throughout the run. After the positioner valve is set, the computer also sends a digital signal to the fast acting pneumatic valve to open a path to the high pressure storage tanks. In addition, this computer monitors the stagnation chamber pressure in real time to allow for an emergency shutoff if a tunnel abnormality is detected. Once the tunnel has passed through the transient of pressurization, this computer signals a DAQ Board to output a trigger signal that is used by the remaining data acquisition computers to begin the recording process.
The second computer is purely a data acquisition computer that records the analog signals from the various devices installed on the tunnel. Two DAQ Boards are used to record signals; a National Instruments BNC-2120 with PCI-6251 card, and a National
Instruments BNC-2121 Quadrature board with a PCI-6602 card that records the optical encoders. Both boards record data at 100 kHz. The BNC-2120, after receiving the trigger signal from the control computer records various instruments including wake position, pressure transducers, trigger signals, encoder once-per-rev signals, and can also output digital and analog signals for triggering and timing of various other pieces of equipment. The BNC-2121 Quadrature board records three different optical encoders that are used during the different dynamic tunnel configurations. One encoder is used to measure the angle of attack of the airfoil during dynamic pitching, and is connected directly to the airfoil. The second encoder measures the phase position of the airfoil and is connected to the motor shaft of the pitching mechanism. The third encoder measures
30 the angular position of the elliptical rotating choke vanes when operating in an unsteady freestream Mach number configuration.
The third computer is part of a stand-alone system that operates the ESP Pressure
Scanner System. The ESP system allows for multiplexed sampling of 64 pressure signals at a rate of 1000 Hz. This is used to record airfoil surface pressures as well as total and static tunnel pressures from various locations within the tunnel.
Both the data acquisition computer system and ESP Pressure system computers are connected to a Quantum Composer Model 9514 Pulse Delay Generator that is used as an external clock. This ensures that both systems record data at a known and highly accurate rate of 100 kHz. Use of an external clock is crucial to obtaining the time-critical information during dynamic experiments to allow for proper alignment of all recorded signals.
Section 2.3: Test Article
The airfoil used for this study was a milled aluminum SSC−A09 model with span b and chord c of 15.2 cm (6 in.) resulting in an aspect ratio AR = 1 (Figure 16). The airfoil was not designed with through-pass optical access in mind and features a 3.5 cm
(1.38 in) diameter boss for rotation about the quarter chord. The model is fitted with 30 pressure taps on the suction surface and 23 taps on the pressure surface. The pressure taps are connected to two ESP 32HD pressure scanners via flexible tubing of 1.4 mm
(0.06 in) diameter and approximately 20 cm (9 in) long.
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Figure 16: SSC−A09 airfoil with spanwise VGJs and surface pressure taps.
Airfoil surface pressure signals are recorded with pressure scanners and then integrated in post processing to obtain accurate lift, moment, and pressure drag measurements. The pressure scanners used for this experiment are well suited for the dynamic flow features that will be present on the airfoil and are capable of multiplexing at high rates and can be triggered externally. Individual pressure sensors have thermal compensation to minimize measurement shifts with temperature. The surface pressure taps are connected to the ESP Pressure Scanner System to obtain surface static pressure measurements. The pressure coefficient is calculated at each tap location by means of the following equation.
P 1 P C P 1 M 2 2
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Integration of the upper and lower surface CP chordwise distribution was used to calculate sectional lift (CL) and sectional moment coefficient (CM) about the quarter chord as per equations found in the literature [37]. It is important to note that these equations do not include any skin friction forces. The drag coefficient (CD) was calculated but is not included in this report because it was based on surface pressure measurements which do not account for viscous losses, making the calculations incomplete.
Two ESP 32HD Pressure Scanners are mounted outside of the test section, in-line with the mid-chord of the airfoil. The test article pressure taps are connected to the pressure scanner ports via plastic tubing of 1.4 mm diameter (0.06 in). The ESP 32HD scanners are miniature electronic differential pressure units consisting of an array of 32 silicon piezoresistive pressure sensors with a differential of ±210 kPa per scanner port.
The electrical outputs from the pressure sensors are multiplexed through a single onboard instrumentation amplifier. The multiplexed amplified output signal is connected to a
DTC Initium scanner interface and passed to the dedicated computer via Ethernet cable.
A Quantum Composer Pulse Delay Generator which is triggered by the DAQ control computer is used as an external TTL pulse train to ensure a stable sample interval. By means of TTL triggering, a maximum pressure scanning rate of 1,200 Hz is capable. In this experiment, however, a scanning rate of 1000 Hz was used to ensure a consistent time interval. In addition to a stable sample interval, triggering assures accurate temporal correlation with the various analog signals which are recorded by the DAQ computer.
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Section 2.4: Tunnel Instrumentation
The tunnel is outfitted with pressure ports that are recorded by the ESP Pressure
Scanners via varied length tubing of 1.4 mm diameter (0.06 in). These pressure ports are located at various tunnel locations and record either total or static pressure. The total pressure measurements include one pitot located in front of the subsonic nozzle, another total pressure from a pitot-static probe located 0.46 m (18 in) forward and 0.20 m (8 in) down from the airfoil centerline, and another pitot probe located on a wake rake that is
0.46 m (18 in) downstream of the airfoil. The static pressures are measured at the pitot static probe located 0.46 m (18 in) forward and 0.20 m (8 in) down from the airfoil’s quarter-chord, two static pressure taps are located at the airfoil’s quarter-chord and are mounted in the upper and lower plenum of the test section. Locations are depicted in
Figure 17. Pneumatic corrections based on tube geometry were applied to compensate for amplitude attenuation and phase lag; the details of which are provided in Section 2.5.
Elliptical Choke Vanes
Pitot Probe Pitot Probe Wake Probe Plenum Static Ports Figure 17: Tunnel pressure measurement locations. 34
The freestream Mach number was calculated by using the average of the upper and lower static plenum pressures and the wake probe total pressure (when wake is not in use) or settling chamber pitot probe. The equation used was the isentropic relationship of
Mach number to static-total pressure ratio. Both methods of calculating the freestream
Mach number result in identical Mach number values.
1 2 P M 1 1 P T
Over the course of a run, the flow temperature decreases at a rate of approximately 0.5 K/s (1°F/s) depending on Mach number and Reynolds number as the air is discharged from the constant-volume high pressure storage tanks. As a consequence, the speed of sound can decay by as much as 9 m/s during a 30 second run.
An Omega J-Type thermocouple is used to measure the stagnation chamber temperature.
The total temperature is recorded at 10 Hz and saved to the Data Acquisition computer.
After the tunnel start-up transient, the rate of temperature decay is relatively linear. A numerical interpolation was applied between each sample to generate sufficient data density for necessary calculations. The static temperature in the test section was calculated via isentropic temperature relationships with freestream Mach number.
1 T 1 2 1 M TT 2
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Section 2.5: Dynamic Compensation
Pneumatic distortion of the signal was taken into consideration for these experiments. Plastic tubing was used to connect the airfoil to the ESP pressure scanners, and transmit the surface pressure. The tubing length and diameter combined with the small sensor volume of the internal transducers of the ESP scanner and the high natural frequencies associated with the tunnel, can result in pneumatic distortion. To minimize the distortion of the pressure signals, tubing of minimum length was utilized.
During the collection of dynamic pressure measurements, specific steps were carried out to address the attenuation of the measured pressure signals due to the viscous effects with the tubing and sensors of the ESP pressure scanners. In 1965 Bergh and
Tijdeman developed an analytic model which corrects for the attenuation and phase lag associated with pneumatic tubing [38]. The model that was developed implements the tubing geometry (diameter and length), transducer volume, and the ambient conditions to develop a transfer function to characterize the dynamic response for each tube segment and sensor. The Bergh Tijdeman model (B-T model) is a transfer function of the corrected pressure amplification ratio and phase shift from the values measured by the sensor of the surface pressure tap in the frequency domain. The transfer function has the capability to include discontinuities in tubing length and radius to account for the difference in internal pressure ports within the airfoil and the tubing that connects the ports to the ESP pressure scanners. Appendix A contains more information about the
Bergh – Tijdeman dynamic compensation.
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Section 2.6: Vortex Generator Jets
The airfoil was fabricated with a row of spanwise vortex generator jets near the leading edge. The VGJ diameter and spacing are 1% and 11.2% of airfoil chord, respectively, and spread over the center 10 cm of span, as depicted in Figure 16. Lorber and Carta identified the stall vortex release point on the SSC−A09 airfoil to be at 10% chord during constant pitch rate and 6% chord during sinusoidal oscillations at comparable Mach and Reynolds numbers [39]. While not necessarily ideal, the VGJs are located at 10% chord as this was close to the release point for the dynamic stall vortex on the SSC−A09 airfoil during sinusoidal pitching, but also at a thick enough chord section to support the blowing apparatus. The VGJs are oriented normal to the surface, which is similar to the configuration determined by Gardner et al. [35] to be optimal for dynamic stall control at higher maximum angles of attack. An internal uniform cavity with a diameter of 3 mm (0.125 in) at 10% chord serves as a VGJ manifold and connects the airfoil to the high pressure air source through a threaded steel tube.
High pressure air was stepped down from greater than 10.3 MPa (1500 psi) to a maximum of 2 MPa (300 psi) through a high pressure regulator. High pressure air was delivered to the test section via a flexible high strength rubber hose with a 6.4 mm (0.25 in) barbed disconnect. A 400 psi dial pressure gauge and Omega J-type, fast-response thermocouple are installed on the piping upstream of the flexible tubing. The instrumental uncertainty for the pressure gauge and thermocouple is Pj, 5 psi and
Tj, 0.1K, respectively. The applied mass flux ratio was calibrated with an Alicat MCR
37
Series 3000 SLPM mass flow controller with a maximum pressure difference of 1.1 MPa
(160 psi). A mass flow rate correlation established a relationship between the mass flow controller and downstream density, which was calculated using the ideal gas law and measurements from the pressure gauge and thermocouple. A strong relationship was evident and a curve-fit was used to extrapolate mass flow rates at tube pressure measurements above 1.1 MPa (160 psi).
The VGJ exit Mach number was estimated by measuring the total pressure at the jet exit plane with a 0.7 mm external diameter pitot tube. Due to the small exit diameter and jet diffusion, a jet static pressure measurement was unobtainable. However, the averaged total pressure to ambient pressure ratio (PR=Pj/P∞) across the jets suggested a supersonic flow condition. Schlieren imagery was used to verify and further characterize the VGJ structure. The resultant schlieren image, shown in Figure 18, not only verified the supersonic nature of the jet flow but also enabled the flow to be classified as an underexpanded nozzle with shock diamonds clearly visible. The jet PR approximation was corroborated through the Prandtl-Pack relationship of Mach disc spacing and diameter.
2.4퐿 2 푀 = √( ) + 1 푗 휋퐷
Experimental measurements have shown this ratio to include up to 20% error, depending on PR. Assuming jet static pressure is slightly greater than P∞, the VGJ is estimated to be Mj≈1.4±0.25 for a predicted mass flux ratio at Cq=0.0040 for a M=0.4 case.
38
Flow uniformity across the VGJs is shown in Figure 18 to be relatively consistent through the center four VGJs. However, the first (far left) VGJ has a slightly lower pressure ratio and the last (far right) VGJ has a slightly higher pressure ratio. As the pressure taps are located between jets 3 and 4, the inequality between jets 1 and 6 should be inconsequential.
Figure 18: Schlieren imagery of VGJ shock diamonds and spanwise flow uniformity.
A non-dimensional ratio used in the literature to quantify the blowing rate is the mass flux ratio (Cq). The advantage of this ratio is that the jet exit velocity measurement is not necessary. The calculation for Cq is defined below where the values in the numerator relate to the VGJ exit mass flow rate and the denominator is associated with
39 freestream mass flow rate. For all calculations, the gas constants for air were set at γ=1.4 and R=287 J/kg-K. For the below equation, ṁj is the mass flow rate of the jets, ρ∞ is the freestream density, and U∞ is the freestream velocity. The chord length is c, and the effective span with VGJs fitted is Lact.
푚̇푗 퐶푞 = 휌∞푈∞푐퐿푎푐푡
Section 2.7: Background Oriented Schlieren
Pressure taps are ideal to obtain valuable information about the lift and moment coefficients. However, the pressure taps only provide information about the flow along the airfoil surface in the vicinity of the tap. Flow features that are present outside of the boundary layer or spanwise non-uniformities typically remain undetected.
Vortex generator jets are effective in part because of the streamwise vorticies, which occurs well away from the airfoil surface. To analyze the flow around the airfoil and capture the off-surface structures and jet interaction, Background Oriented Schlieren
(BOS) was implemented. BOS is an optical, quantitative measurement technique based on the principles of schlieren, which detects minute changes in the flow refractive index, n, due to density variations [40]. However, unlike traditional schlieren, precision mounted collimation mirrors are unnecessary. BOS is still an emerging measurement technique, but has gained substantial traction when studying large flow fields [41]. BOS has been used to quantitatively characterize shock structures in nozzles and around aerodynamic objects, as well as to detect wing tip vorticies on helicopter rotors in flight 40
[42] [41]. A BOS study on flow around a cylinder proved that vortical structures are also detectable by their radially oriented refractive gradient [41]. Shocks are depicted as gradients in the refractive index [42].
Background Oriented Schlieren was selected for this investigation due to the 2D nature of the VGJ, bulk flow interaction. Other quantitative flow measurement techniques, such as Particle Image Velocimetry, would be challenged to characterize the
VGJ structures due the lack of tracer particle density. As the VGJs were sourced with compressed air, the VGJ flow is clearly detectable with BOS [43]. Thus, BOS is a suitable technique because of its ability to capture spanwise average vortical structures,
VGJ blowing, and spanwise density gradients produced by the shear layer and shocks.
The simplistic setup consists of a backlit randomized speckle pattern, a camera, and a flowfield of interest. A camera was focused on the backlit speckle pattern with the flowfield established in between. Variations in the flowfield refractive index change the incidence angle of light rays through the flowfield, resulting in an apparent image distortion in the camera image as depicted in Figure 19 [42]. In this diagram, ε represents the light ray incidence angle change and Δy represents the apparent image deformation in pixels for the change in refractive index. The Z indexes represent various measurement distances which, when combined with the lens focal length, account for frame magnification and sensitivity. Based on the magnification factor, the virtual image distortion at the background plane, Δy′, can be calculated [42].
41
Figure 19: Typical BOS setup with pertinent variables [42].
The detected refractive index variations are related to density through the
Gladstone-Dale equation provided below where K is a material constant; for air in this case.
푛 − 1 = 퐾휌
The distortion of the speckle pattern from the light refraction is processed using
Partical Image Velocimetry software (DaVis®) to determine the displacement. A 12×12 interrogation window with 75% overlap was applied to determine cross-correlation of pixel displacement. Pixel displacement magnitude is proportional to refractive index, and ultimately the spatial gradients of density field [40].
The experimental setup is depicted in Figure 20. The camera used was an ultra- high speed Phantom 1210 CMOS camera set at an image resolution of 1024×800 pixels.
42
A 200 mm focal length Nikon lens with an aperature setting of 32 f/# was used to image the background pattern at a sufficient distance to apply the small angle theorem and still maintain an optimal field of view. The camera was placed 1.03 m from the center of the test section and 1.4 m from the speckle pattern. Frames were captured at approximately
3000 fps, with a maximum exposure time of 398 μs. The camera was synchronized to the pitch motor phase to ensure airfoil images were captured at identical phase and angle of attack. The speckle pattern was created by generating a pattern of 57,000 randomly positioned 0.57 mm diameter dots. At the selected viewing distance, this resulted in 5.2 pixels/mm and 3.37 pixels/dot. The speckle pattern was lit by a constant illumination,
14000 lumen DC LED array.
0.38 m
1.03 m
Figure 20: BOS tunnel setup diagram.
43
Section 2.8: Measurement Uncertainties
As this is a transient tunnel, the tunnel conditions are constant for a period of 5.9 seconds, during which surface and tunnel pressure data were acquired at 1000 Hz. The data were analyzed and truncated as necessary to eliminate tunnel acceleration or deceleration transients. The resultant sample for steady data was time-averaged over approximately 4.5 seconds. The unsteady data were phase-averaged over 14 to 56 cycles, depending on the pitching frequency, with higher frequencies associated with more averaged cycles. Fewer phase-averaged cycles is manifested as apparent high frequency oscillations in the lift and moment loops with increased uncertainty. Calculations for lift and moment coefficients were obtained by trapezoidal integration of the measured pressure distributions. Temperature, angle of attack, and pitch phase revolutions were acquired at 100 kHz for 10 seconds such that temperature and phase data overlapped the duration of pressure acquisition. Lift and moment coefficient calculations were synchronized with the corresponding angle of attack to generate lift and moment loops.
The accuracy of the measured quantities depends on the individual accuracy of the various instruments used to measure the flow parameters as well as the number of cycles used in the data set. These uncertainty estimates are used to measure the confidence of the results obtained in this study. An analysis was conducted in the manner outlined by Coleman and Steele [44] to estimate the relevant calibration uncertainties with the wind tunnel. The tunnel-relevant, dominant uncertainty estimates based on
44 pressure, DaVis® pixel displacement (outside of shear layer), and analog instrumentation of a low frequency pitching airfoil in an incompressible, steady freestream are:
M, ±0.005; Re, 5,000; α, 0.05°; T∞, 0.05 K; k, ±0.0007;
CP, 0.05; CL, 0.05; CM, 0.02; Cq, ±0.00005
Uncertainty for Background Oriented Schlieren: Δx, ±0.07; Δy, ±0.09 pixels;
45
Chapter 3: Results and Discussion
Blowing flow control was evaluated over a range of conditions including: static pre and post stall in a steady freestream, dynamic stall with sinusoidal pitch oscillations in steady freestream, and dynamic stall with coupled pitch and freestream oscillations.
To eliminate the influence of a boundary layer trip, the baseline condition for this study is the SSC−A09 with VGJs present but without blowing applied, hereafter referred to as
“non-blowing”. Steady state data will be presented first, followed by pitch oscillation results, and closed by a discussion on dynamic stall under coupled conditions. The key contribution of this thesis focuses on the impact of steady blowing under coupled pitch and time-varying freestream conditions. Each section will highlight the pre-stall and post-stall events and the impact of VGJs. At the end of each section there will be a side- by-side comparison with historical results of vortex generators (jets or otherwise) at similar conditions. The chapter is concluded with qualitative BOS insight into off- surface flow features that supplement pressure measurements.
The judgment criteria as to the optimization and comparison of blowing at various mass flux ratios is based on modification of stall penetration, peak and cycle average loading, and reduction in negative damping. The significance of each metric is mission and application dependent; however, for the purposes of this study, the weighting criteria for optimization is based on alleviation of the negative aspects of dynamic stall. As minimum negative moment peak and negative damping are most detrimental to high 46 speed rotorcraft flight, improvement in these two features is most important. Stall penetration enables the retreating blade to operate at greater angle of attack without the consequences of dynamic stall; therefore, separation delay is next in importance.
Improvements in cycle average CL and CM balance are naturally of great interest and next in terms of weighted criteria. Modification of CL,max and apparent angle of lift stall are of lesser importance. Peak CL and associated stall angle of attack depicted in lift coefficient curves are often a manifestation of the dynamic stall vortex convection as shown in
Figure 6 and are thus difficult to independently control. In some cases, as will be shown, an optimal value was unobtainable due to system pressure limitations.
Due to conservation of momentum, the compressed air exhausted through the
VGJs applies a point load on the airfoil at 10% chord, which was not included in the moment coefficient data presented throughout this chapter. As the jets are located 15% chord forward of the aerodynamic center, the jets create a steady negative moment ranging from -0.0010>CM,j>-0.0034 over the range of mass flux ratios evaluated in this study, which decrease minimum CM by 1.5% to 2.6% and cycle average CM by 5.3% to
8.5%, depending on the condition. The change in minimum CM is within the uncertainty calculations and can be neglected. The change to cycle average CM is substantially greater, but because the jets are constantly on, a simple application of a trim tab can correct for the additional negative moment. Therefore, changes to cycle average CM due entirely to the force of the jets should be considered for real world application, but are neglected throughout this study.
47
Section 3.1: Static Airfoil in a Steady Freestream
This section examines the results of VGJ blowing at fixed angles of attack under steady freestream at Mach numbers of 0.2 and 0.4 at corresponding Reynolds numbers
1.5×106 and 3.0×106, respectively. Steady data at M=0.2 and M=0.4 were evaluated in the non-blowing configuration and compared with blowing data at Cq=0.0029 and
Cq=0.0040, respectively. Only one mass flux ratio was tested at each static condition to serve as a proof of concept rather than an exercise in optimization,
Figure 21 represents the change in lift when blowing was applied at static conditions in an incompressible freestream. It is apparent that in the pre-stall region, at
α<15.0°, VGJ blowing resulted in a slight increase in CL. Figure 22 represents the measured pressure distribution over both the upper and lower surfaces of the airfoil for the non-blowing case as well as with VGJ application. The observed lift increase is due to the low pressure spike starting at 10% chord coinciding with the lateral and downstream vicinity of the VGJs. The sharp low pressure area adjacent to the VGJ is most likely due to jet entrainment of the bulk flow. The downstream suction is linked to the boundary layer jet interaction. These low pressure regions are a product of a jet in crossflow [32] and were also observed by Gardner et al. with steady blowing [35] and will be discussed again later. It is also interesting to note that, in Figure 22, there is an adverse pressure gradient immediately upstream of the VGJ suggesting a small stagnation region. However, the suction peak around the leading edge is maintained and does not appear to be affected by the pressure gradient. It will be shown later that this latter
48 feature is not maintained at higher mass flux ratios or in a compressible freestream.
When separation occurs in the non-blowing case, the stall is very sharp; this behavior is indicative of a leading edge stall [45] which was observed by Lorber and Carta [11] at similar conditions (not shown). With VGJ blowing applied, the static lift stall is delayed by Δα=1.0° and the stall shape changes from a sharp to a more gradual decrease in lift.
The stall delay suggests the locally favorable pressure gradient at the VGJ resists sudden, leading edge separation and modifies the stall process from a leading edge stall to that of a trailing edge stall. As the stall shifts to a trailing edge stall, lift in the post-stall region is increased by 20-25% over the non-blowing case.
6 Figure 21: CL vs. angle of attack comparison at M=0.2, Re=1.5×10 .
49
6 Figure 22: Airfoil CP distribution comparison at M=0.2, α=10°, Re=1.5×10 .
The amplified suction distribution associated with steady blowing is not entirely upstream of the quarter chord location at all angles of attack. Figure 23 represents the impact of VGJ blowing at Cq=0.0029 compared to the non-blowing case on the moment coefficient about the quarter chord under steady conditions. It shows a positive moment shift at low angles of attack where the flow is mostly attached. Due to the transition to a trailing edge stall profile, airfoil loading immediately prior to stall suggests a slight nose down distribution. However, as the separated region extends forward, VGJ application resists the immediate negative moment spike at the point of stall observed in the non- blowing case. Furthermore, steady blowing resulted in an improved CM by up to 50% in the immediate post stall region as evident by the CM gradient. At α=20°, the blowing CM and non-blowing CM appear to converge, suggesting that steady blowing has limited effect in incompressible flow in deep static stall.
50
6 Figure 23: CM vs. angle of attack comparison at M=0.2, Re=1.5×10 .
A study by Heine et al. in 2013 used passive circular disturbance generators fixed near the leading edge of an OA209 airfoil at M=0.16, Re=1.8×106 [46]. The disturbance generators had dimensions of: diameter = 2% chord, protrusion = 0.18% chord, and spacing = 10% chord [46]. While the flow control mechanism is not a jet, the cylindrical shape of the disturbance generators create vortical structures in agreement with those created by the conical shape of VGJs. As the generator configuration and flow conditions are similar to the present study, the study by Heine et al. provides a comparable benchmark for VGJ flow control at static incompressible conditions. Lift and moment coefficients with and without disturbance generators installed, as shown in
51
Figure 24, exhibit separation delay and post stall CL and CM improvements in qualitative agreement with VGJ application displayed in Figure 21 and Figure 23.
Figure 24: CL and CM vs. angle of attack comparison with circular disturbance generators at M=0.16, Re=1.8×106 [46].
In the pre-stall regime, the disturbance generators used by Heine et al. reduced peak lift by ΔCL,max≈4%, but increased post stall CL by more than 50% at α=18° with no clear inflection point in lift up to α=20° [46]. In agreement with the current study, the disturbance generators modify the stall behavior from that of a sharp leading edge stall to that of a gentle stall characteristic of a trailing edge stall. Furthermore, Heine et al. observed substantial improvements in CM in post stall at 15°<α<19°, at similar levels to those achieved using VGJs in the present study [46]. Therefore, aside from a change in peak CL, flow alterations from VGJ application at static conditions in a steady freestream concur with results obtained using passive vortex generators such as those presented by
Heine et al.
52
6 Steady data at M=0.4 were evaluated at Cq=0.0040 and Re=3.0×10 . As indicated in Figure 25, the separation in the non-blowing case occurs at a lower angle of attack than that observed in the incompressible flow. This feature is expected based on compressibility effects and associated adverse pressure gradient with increased compressibility [45] [47]. Also due to compressibility effects, the stall behavior of the non-blowing airfoil at M=0.4 is not as severe as in the incompressible case, indicating that the flow physics near stall have changed slightly.
6 Figure 25: CL vs. angle of attack comparison at M=0.4, Re=3.0×10 .
53
In contrast to the incompressible flow case, when blowing is applied, the integrated airfoil loading is unaffected at α<10°. This is explained in the pressure distribution at α=10° provided in Figure 26, namely that the suction peak is reduced slightly and the additional suction in the vicinity of the VGJ does not extend downstream beyond 20% chord. In further contrast to the incompressible case, as the airfoil angle of attack approaches stall, due to the decreased suction peak, blowing appears to decrease
CL and indeed the peak CL is reduced by 2.5%. Due to the CL plateau at peak CL, it is difficult to pinpoint the angle of attack at which separation occurs in Figure 25 and quantify the stall delay. However, it is evident that blowing postpones stall and sustains lift in the post-stall regime. At α>12°, blowing generated an increase in CL by an average of 8.2% above that of the non-blowing airfoil.
6 Figure 26: Airfoil CP distribution comparison at M=0.4, α=10°, Re=3.0×10 .
54
In agreement with the lift forces depicted in Figure 25, the moment coefficient illustrated in Figure 27 shows that blowing has little impact in the pre-stall regime. This is in contrast to the incompressible case where the CM showed slightly detrimental effects just prior to stall. However, in concurrence with the incompressible condition, the VGJ effect is quite evident in the post-stall regime. Whereas the non-blowing airfoil undergoes an immediate and sharp CM drop at separation, the blowing case delays moment stall for an additional Δα=2°. In the post-stall, at α>16°, steady blowing improved the CM by an average of 12.8%. At α>19°, the two CM curves begin to converge, suggesting blowing effect is reduced at high angles of attack.
6 Figure 27: CM vs. angle of attack comparison at M=0.4, Re=3.0×10 .
55
The static test cases in both a compressible and incompressible freestream provided great insight into the effectiveness of VGJ blowing. It is apparent that steady blowing provides slight lift improvement at lower angles of attack only in an incompressible freestream yet consistently improves the flow in the post stall regime.
Steady blowing delayed separation in both cases and improved CL and CM in the immediate post-stall with diminishing effectiveness in deep stall. Furthermore, airfoil surface pressure measurements suggest a low pressure region and locally favorable pressure gradient in the vicinity of the VGJ during actuation. The downstream and upstream reach of the VGJ appears to be dictated by freestream compressibility.
Assuming these features are span-wise uniform, the investigation at static conditions demonstrates successful flow control using steady VGJ application at the two Cq values evaluated. This is especially true for a partially or fully separated airfoil.
Gardner et al. published results of blowing through VGJs at 10% chord, at M=0.3,
Re=1.15×106 on a static OA209 rotorcraft airfoil at mass flux ratios 2.5 times greater than those evaluated in this study. For comparison purposes, a CL curve extracted from
Gardner et al is provided in Figure 28 and shows similar results with the present study at
M=0.4, Re=3.0×106 in Figure 25 [34]. In comparison with the current research, Gardner et al. observed negligible flow change at pre-stall angles of attack, suppressed separation to a greater angle of attack, and witnessed lift improvement in the post-stall regime [34].
Specifically, when blowing was applied at Pj=6 bar (Cq=0.01), the peak CL was increased by 12.8% and stall was delayed by Δα=2.5°. Lift in the post stall was increased by up to
40%. However, in contrast to data from the current investigation provided in Figure 25,
56 the stall profile does not appear to transition to that of a trailing edge stall when blowing was applied. This latter point may be airfoil specific or attributed to the slight variation in flow conditions. Interestingly, as pressure was increased, Gardner et al. identified a blowing saturation point at Pj=7 bar (Cq=0.012) where Pj>7 bar blowing did not show significant variation from the Pj=10 bar (Cq=0.017) results depicted in Figure 28 [34].
A further comparison between Gardner et al. and the study herein shows that the airfoil Cp distribution data, as observed in Figure 26, depict similar characteristics.
Specifically, airfoil pressure distribution extracted from Gardner et al. (Figure 29) when blowing at Pj=6 bar (Cq=0.01) and Pj=10 bar (Cq=0.017) demonstrate an increased CP just upstream of the jets, a local CP reduction in the vicinity of the VGJs, and increased suction in the wake of the jets [34]. All three of these characteristics observed by
Gardner et al. are clearly evident in this study, as seen in Figure 26.
6 Figure 28: CL vs. angle of attack comparison at M=0.3, Re=1.15×10 [34].
57
6 Figure 29: Airfoil CP distribution comparison at M=0.3, Re=1.15×10 , α=12° [34].
VGJ application in a similar configuration, conditions, and mass flux ratio provided in Gardner et al. [34] are in good agreement with results of the current study.
Gardner et al. did not present CM data for this case, but observations of VGJ application on CL under static conditions demonstrate consistency in stall delay, post stall benefits, and local CP alterations in the vicinity of the VGJs.
Section 3.2: Airfoil Pitch Oscillations in a Steady Freestream
As VGJs have proven successful at influencing stall under static conditions in a manner consistent with published results, this section considers the effects of steady blowing on an airfoil undergoing sinusoidal pitch oscillations in a steady freestream. To make comparisons to the static case, the mean tunnel conditions were maintained at a
Mach number and Reynolds number similar to that evaluated in Section 3.1. Data were acquired at reduced frequencies of k=0.026 and k=0.050 at a pitch schedule of 58
α=9.5°−10.5°cos(ωt). Based on the static airfoil results in Section 3.1, VGJ flow control is expected to be most apparent in the post stall regime. To provide a more comprehensive evaluation, the mass flux ratio was varied for each of the flow conditions evaluated. In the interest of brevity, only the optimal Cq will be discussed in detail for each Mach number and reduced frequency case. Results for non-optimal cases are provided in Appendix B. The criteria for optimal Cq is as described in the Chapter 3 introduction. A quantitative comparison of the effects of blowing based on Cq in both the incompressible and compressible freestream will be presented at the end of the section as well as comparison with historical data of blowing application with similar configuration and test conditions.
Section 3.2.1: Airfoil Pitch Oscillations in an Incompressible Freestream
Flow control was evaluated on a pitching airfoil in an incompressible freestream at M=0.2, Re=1.5×106, and k=0.026. While blowing at other mass flux ratios resulted in varied degrees of flow control, the optimal mass flux ratio for this condition was determined to be Cq=0.0032. The black orbit in Figure 30 represents the lift of the non- blowing airfoil at the aforementioned conditions and the red line represents the lift orbit when blowing is applied; this will be consistent throughout this chapter. The CL stall point in Figure 30 penetrates beyond the static case due to airfoil pitching. The dynamic stall sequence is quite abrupt with a rapid decrease in lift and onset of hysteresis and is consistent with historical data presented in Figure 6 [4] as well as previous studies at
59 these experimental conditions shown in Figure 8 [20] [21] [39]. Variation in pressure data between The Ohio State University studies on the SSC−A09 and historical data is due to pressure tap location and concentration, and tunnel effects – a detailed explanation of which is provided by Hird et al [20].
Unlike blowing in the static, incompressible case, no variation in lift occurs during the upstroke when blowing is applied to a pitching airfoil in an incompressible freestream. Recall that blowing increased pre-stall lift in the static, incompressible case but did not demonstrate an apparent lift increase in the static compressible case. It is well known that the process of pitching may introduce local compressibility near the leading edge of an airfoil in an otherwise incompressible freestream [6]. This may factor into the lack of pre-stall CL increase observed. Though blowing has no effect during pre-stall, it is quite apparent that blowing increases airfoil performance at high angles of attack. The
VGJs delay separation by Δα=1.2°, increase CL,max by 3.2% and cycle average CL by
5.9%. In the non-blowing case, at α=19°, oscillatory loading appears in the lift curve indicating accumulation of additional vorticity and brief reemergence of the separation bubble. This temporary episode of flow reattachment results in high loading instability when stall occurs sufficiently prior to αmax and is documented in the literature [39].
Through stall delay, blowing suspends the onset of load oscillation and reduces its duration. During the downstroke, blowing accelerates flow reattachment and increases
CL substantially at 19°>α>10°.
60
6 Figure 30: CL vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.026.
From Figure 31, it is clear that there is little variation in moment between the blowing and non-blowing cases prior to stall. Moment stall occurs at α≈17° for the non- blowing case and is accompanied by a sharp negative moment spike to CM,min=−0.21.
This is attributed to the loading shift as the stall vortex transits the airfoil upper surface.
Blowing delays moment stall by Δα=1.6° and improves the cycle average moment by
16.7%. Blowing at Cq=0.0032 shows little effect on the dynamic stall vortex strength as there is negligible change in CM,min. Negative damping, which contributes heavily to blade flutter, is identified in the literature by clockwise rotation in the moment orbit [48].
During the downstroke, the non-blowing case demonstrates an interval of negative
61 damping as represented by the shaded area bounded at 17.5°>α>12.5°. The gray shading is for the non-blowing case and the red shaded region fills the region of negative damping for the blowing case. This designation will be consistent throughout this chapter. VGJ blowing reduces the area contributing to negative damping by 64.7% and causes the flow reattachment to shift Δα=3.7° earlier in the cycle, as indicated during the downstroke at
α=16.7° when CM is greater than the pre-stall value.
Negative Damping
6 Figure 31: CM vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.026.
One of the challenges with flow reattachment under dynamic conditions is shear layer breakdown and overcoming a strongly adverse pressure gradient near the leading
62
CP
Vortex CP Traces Vortex CP Traces
Figure 32: CP of non-blowing (left) vs. blowing at Cq=0.0032 (right) at M=0.2, Re=1.5×106, k=0.026.
edge [49]. The VGJ structures are thought to organize the separated shear layer and pull it closer to the surface [35]. The region of locally favorable pressure gradient in the vicinity of the VGJs assists in overcoming the adverse pressure gradient. Reemergence of the separation bubble as suggested in the CM orbit is confirmed by the suction peak at
ϕ≈210°. The reattachment process, beginning at the leading edge, is in agreement with the dynamic reattachment process outlined by Ahmed and Chandrasekhara [49].
It is well known that as reduced frequency increases, the degree of stall penetration correspondingly increases [39]. When reduced frequency is increased from 63 k=0.026 to k=0.050, stall is delayed and occurs at α=19.2° for the non-blowing case as indicated in Figure 33. Therefore, stall is naturally occurring less than 1.0° from αmax in the non-blowing case, but enhancement with blowing is still evident. Blowing at the optimal mass flux ratio of Cq=0.0030 yielded insignificant stall delay and peak lift improvement. However, a dramatic lift amplification is observed during the reattachment process on the downstroke from 20°>α>12°, which led to a cycle average CL increase of
3.8%. Thus, on an airfoil pitching at k=0.050, blowing showed marginal stall penetration improvement or increase in lift likely due to the baseline stall onset occurring near αmax.
6 Figure 33: CL vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.050.
64
Negative Damping
6 Figure 34: CM vs. angle of attack comparison at M=0.2, Re=1.5×10 , k=0.050.
While the blowing modification to the lift orbit is subtle, the moment loop enhancements are much more distinguishable. Examination of the moment curve in
Figure 34 shows that moment stall occurs close to αmax (18.0° specifically) for the non- blowing case. The increased vorticity generated with greater reduced frequency results in a strong and sudden negative moment plunge to CM,min=−0.23. VGJ application delays separation by Δα=0.7° and improves the negative moment spike by 21.7%. It is evident that the reattachment process is indeed accelerated by blowing and the flow is fully attached 4.3° earlier in the downstroke. The accelerated flow reattachment leads to a
65
46.4% reduction in the region of negative damping and a cycle average moment improvement of 11.3%.
Figure 35 and Figure 36 compare the effect of blowing at varied mass flux ratio over reduced frequencies, k=0.026 and k=0.050 in an incompressible freestream. The flow improvement are represented as a blue line for steady blowing at k=0.026 and a green line at k=0.050. The figures represent a variation from the non-blowing reference condition as either a percentage or a physical change in angle of attack. With the exception of negative damping (last plot in Figure 36), a positive value indicates flow improvement. The trend of flow alteration with varied mass flux ratio is generally consistent across the metrics at both reduced frequencies, but less deviation from the non- blowing case is observed at the greater reduced frequency. Even though VGJ employment at the same mass flux ratio does not result in the same quantifiable transformation with varied reduced frequency, the optimal mass flux ratio for both reduced frequencies is approximately Cq≈0.003. However, due to the sparseness of data points, the precise identification of the optimal mass flux ratio cannot be confirmed.
Blowing at Cq=0.003 resulted in the best balance of improvement in the negative moment spike (ΔCM,min) and cycle average ΔCM with the most reduction in negative damping.
While blowing at Cq=0.004 yields greater improvements in cycle average values and stall delay, these gains are marginalized by the aggravated CM,min and attenuation of the reattachment angle and negative damping gains. Additionally, it is possible that delay in separation at k=0.050 is confined by the angle of attack amplitude limit, suggesting that if
αmax were greater, flow separation could be further postponed. Other criteria such as
66 negative damping reduction and cycle average moment improvement seem less susceptible to angle of attack amplitude and are clearly sensitive to reduced frequency.
Figure 35: Flow modification vs. mass flux ratio for M=0.2, Re=1.5×106 (Part 1).
67
Figure 36: Flow modification vs. mass flux ratio for M=0.2, Re=1.5×106 (Part 2).
As the applied VGJ mass flux ratio is increased, the cycle average CL and CL,max also increase. Separation is further deferred to later in the cycle with increased blowing.
However, the delay in flow separation and apparent increase in lift has the consequence of a potentially strengthened dynamic stall vortex as evident by the detrimental cycle
68 average CM and amplified CM,min spike at Cq=0.005 in both cases. At both reduced frequencies, there appears to be a mass flux ratio between Cq=0.003 and Cq=0.004 at which flow reattachment and attenuation of the area of negative damping show the greatest improvement. Furthermore, even low mass flow blowing can improve these last two conditions. As strong negative moment transients and negative damping lead to severe torsional helicopter blade pitch link loads, alleviation of this condition is highly desirable. Depending on application, benefits in CM and negative damping at lower Cq potentially outweigh the improved stall penetration achieved at greater Cq.
Section 3.2.2: Airfoil Pitch Oscillations in a Compressible Freestream
As rotorcraft dynamic stall typically occurs in compressible conditions, the evolution of this investigation naturally progresses to evaluate the efficacy of VGJ flow control of dynamic stall in a compressible freestream. Blowing was applied to an airfoil pitching at two reduced frequencies, k=0.026 and k=0.050, in a steady M=0.4 freestream
6 at Re=3.0×10 . Data were acquired at four mass flux ratios ranging from Cq≈0.002 to
Cq≈0.005 for each reduced frequency. Employing the same criteria for VGJ optimization as discussed in the chapter introduction, the optimal mass flux ratio for flow control in a compressible freestream was determined to be the maximum mass flux achievable,
Cq≈0.005. It is important to note that increased compressibility reduces the angle of attack at which the dynamic stall vortex sheds and introduces the potential for locally supersonic flow which can result in shock-induced separation [6]. As VGJ flow control
69 has been demonstrated in a pitching airfoil in incompressible flow, the purpose of this section is to examine steady blowing with the introduction of compressibility.
Consistent with the literature, the stall angle of attack for the non-blowing case in
Figure 37 is indeed less than that of the M=0.2 at k=0.026 case and the measured stall penetration beyond the static condition is approximately the same as that observed for
M=0.2 at k=0.026 [10]. The effects of compressibility are quite evident in that the stall is less abrupt. Indeed the suppressed CL overshoot observed could be the result of a decreased vortex convection speed related to shock-induced separation as observed in the literature [11]. At slower convection speeds, the vortex is less concentrated, which diminishes the suction surface area covered by the stall vortex, thus decreasing its intensity. Steady blowing at Cq=0.0051 on a pitching airfoil in a compressible freestream yielded similar results as those observed in the static case. Specifically, no CL variation occurs in pre-stall and blowing reduces CLmax by 1.6%; both of which were observed in
Figure 25. In contrast to the static condition, blowing at Cq=0.0051 decreases the apparent lift stall by Δα=0.6°, which may suggest that blowing causes additional flow acceleration, resulting in earlier onset of shock formation. However, the lack of lift increase with vortex advection may not be a sign of early separation at all, but an indication that the VGJs are preventing the vortex from traversing the airfoil surface.
70
6 Figure 37: CL vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.026.
In the post stall regime, the lift orbit of the controlled case includes lift oscillations which allude to intermittent shear layer reattachment as observed in the literature and are consistent with deep dynamic stall [39] [27]. The load oscillations are at a non-dimensional forcing frequency of F+≈0.123. This propensity of blowing to encourage flow reattachment and associated lift oscillations continues beyond maximum angle of attack and is apparent during the downstroke at α>12°. Indeed during the downstroke, VGJ driven reattachment cycles augment lift during the downstroke through full flow reattachment and increase cycle average CL by 6.0%. In agreement with flow control application in the incompressible cases, VGJ blowing has greater flow 71 enhancement in the post stall regime through accelerating reattachment and reducing hysteresis.
Negative Damping
6 Figure 38: CM vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.026.
The moment orbit comparison of blowing at Cq=0.0051 and the non-blowing case at M=0.4 when pitching at k=0.026 is presented in Figure 38. The moment stall slope is gradual, which is indicative of a slower, diffused stall vortex which supports the possibility of shock interaction, based on observations by Lorber [12]. Notice that blowing delays moment stall by Δα=0.8°, which is contrary to that observed in the lift curve discussed previously and suggests that if indeed shock-induced separation is 72 occurring, the VGJs minimize this effect. Furthermore, the negative moment plunge from the first shear layer separation at α≈15.0° is arrested, suggesting that vortex advection over the surface is interrupted by the VGJs, which accounts for the absence of a lift overshoot. The CM briefly increases at α≈17°, which agrees with the angle of attack at which lift oscillations occur, further supporting temporary reattachment of the shear layer and suction peak return.
While moment oscillations are most likely undesirable, one cannot ignore that blowing improves cycle average CM and minimum CM by 25.0% and 14.5%, respectively.
The VGJs accelerate flow reattachment throughout the post stall regime and achieve full reattachment Δα=3.0° earlier in the cycle than in the non-blowing case and hysteresis effects are reduced. Most importantly for rotorcraft stability, the improved moment orbit is further characterized by an elimination of the region associated with negative damping.
Comparison of the cycle average upper surface CP distribution between the non- blowing and blowing at Cq=0.0051 cases is presented in Figure 39. It provides potential insight into the physics supporting the observed flow characteristics and enhancements.
It should be noted that the continuous low pressure region at 10% chord marks the clear presence of the VGJs in the blowing case. The critical CP for locally sonic conditions is indicated in the plots by a white contour line at ϕ≈110° on the upstroke. In both the blowing and non-blowing cases, the initial vortex convection occurs just after
CP,min 73 115°<ϕ<140° in the non-blowing case implies a diffused vortex consistent with shock- induced separation. Contrastingly, in the blowing case, the low pressure trace from the first vortex is quite narrow and a low pressure region remains upstream of the jets, suggesting that the boundary layer does not fully separate. Low pressure regions resulting from convection of subsequent vortices are similarly narrow, denoting that VGJ blowing interrupts shock-induced separation. Additionally, the absence of a strong vortex convection suggests the VGJs delay full separation, justifying the corresponding lift decrease at α=14.9° in the lift curve and arrested initial negative moment spike in the moment curve. It is further observed in Figure 39, that blowing sustains twice the suction than non-blowing upstream of 10% chord, with cycles of flow attachment and subsequent shedding indicated by the periodic low pressure traces. Blowing appears to promote flow reattachment throughout post stall phases at 125°<ϕ<225° as indicated by the leading edge low pressure region present in the blowing case and absent in the non-blowing case. The reattachment intervals suggest that the combination of VGJ structures and a locally favorable pressure gradient are effective at organizing the shear layer and overcoming the adverse pressure gradient observed in the non-blowing case. The return to pre-stall conditions occurs at ϕ=230° which corresponds to α=15.5° on the downstroke of the moment orbit. It is interesting to note that with blowing engaged, CP,min exceeds CP,crit at ϕ≈250°, inferring that VGJ blowing is capable of establishing amenable conditions for reattachment in the presence of shocks. 74 CP,crit CP Vortex CP Trace Vortex CP Traces CP,crit CP,crit Figure 39: CP of non-blowing (left) vs. blowing at Cq=0.0051 (right) at M=0.4, Re=3.0×106, k=0.026. Given the suitability of blowing to control dynamic stall at k=0.026, VGJ flow control was further investigated at k=0.050, representing a greater level of airfoil unsteadiness and realistic rotorcraft conditions. As in the k=0.026 case, the optimal mass flux ratio for the k=0.050 case is determined to be Cq=0.0051, which was the maximum value tested. Figure 40 is the portrayal of the CL versus angle of attack orbit at M=0.4, 6 k=0.050, Re=3.0×10 for both the non-blowing case and the blowing case at Cq=0.0051. Due to elastic deformation of the mechanical pitch mechanism at high frequency oscillation, the pitch amplitude increases, resulting in a pitch schedule of 75 6 Figure 40: CL vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.050. α=9.5°−11.5°cos(ωt). The lift stall at α=17.1° for the non-blowing case exhibits a soft rounded lift curve representative of a diffused dynamic stall vortex and shock development. The controlled case displays the same soft stall behavior as the non- blowing case but lift stall is delayed by Δα=0.3° and CL,max is increased by 1.4%. Both of these alterations are inverse to the k=0.026 case at the same mass flux ratio, suggesting that the jet to shear layer interaction is different at varied reduced frequencies. However, one commonality in the blowing case is the appearance of a flow reattachment transient in the post stall regime, resulting in lift oscillation at an F+≈0.231, which is roughly twice that of the k=0.026 case. However, during the downstroke, these load oscillations 76 disappear and a steady lift enhancement is observed, suggesting an accelerated gradual flow reattachment. This rapid flow reattachment and lift augmentation during the downstroke reduces orbit hysteresis and improves cycle average CL by 7.2%. Negative Damping 6 Figure 41: CM vs. angle of attack comparison at M=0.4, Re=3.0×10 , k=0.050. Analysis of the moment orbit in Figure 41 shows features which correspond to that of the lift curve. During the upstroke through stall, marginal CM diversions are observed between the blowing and non-blowing cases. Blowing at Cq=0.0051 delays vortex advection and moment stall by Δα=0.7°. During vortex convection at 14°<α<18°, the moment slope is noticeably steeper in the blowing case; decreasing from 77 dCM/dα=−0.028 (non-blowing) to dCM/dα=−0.042 (blowing), which could imply that the dynamic stall vortex is more concentrated in the blowing case. At α≈18°, blowing interrupts the nose down moment trend corresponding to transient shear layer reattachment. The temporary reattachment observed in the blowing case leads to an improvement in CM,min by 5.3%. Immediately upon cresting αmax, the moment slope exhibits a steep positive slope. The positive CM slope is evidence of an accelerated shear layer reattachment which coincides with the CL increase observed during the downstroke in Figure 40. The CM data marks a return to pre-stall conditions at Δα=3.8° earlier in the cycle with blowing, which eliminates negative damping and improves cycle average CM by 17.7%. The CP distribution comparison between the non-blowing case and the blowing case, at Cq=0.0051 at M=0.4, k=0.050, is provided in Figure 42. The first observation is that the white regions denoting CP,crit observed in Figure 39 are non-existent in the non- blowing case and are quite minor in the blowing case. This is symptomatic of a shock free cycle in the non-blowing case and mostly shock free cycle in the blowing case. However, the broad diffusion of the low pressure streak marking the slowed dynamic stall vortex convection in the non-blowing case is consistent with shock-related separation outlined in Section 1.2 and suggests the presence of shocks [12]. Indeed the calculated CP,crit=−3.54 and the minimum phase average CP=−3.51, further indicating that shocks are most likely present, but either due to pressure tap resolution or pressure phase averaging, are not detected with pressure measurements. 78 CP Vortex CP Trace Vortex CP Traces CP,crit Figure 42: CP of non-blowing (left) vs. blowing at Cq=0.0051 (right) at M=0.4, Re=3.0×106, k=0.050. The local low pressure region due to the VGJs is clearly evident at 10% chord in the blowing case of Figure 42. The vortex convection streak of the blowing case at ϕ≈135° is substantially narrower in comparison with the diffused streak in the non- blowing case. This accounts for the steep moment gradient at separation. The suction generated by the vortex shedding supports the lift increase from the non-blowing case at peak CL. Furthermore, blowing appears to anchor the shear layer beyond the initial vortex convection as revealed by the low pressure region upstream of 10% chord extending from separation to αmax (135°<ϕ<180°). The lift enhancement observed in 79 Figure 40 at α>17° is the result of the unstable shear layer reattachment and separation cycle. During the downstroke, the favorable pressure gradient upstream of the jets promotes flow reattachment along the leading edge almost immediately as evidenced by the low pressure region at the leading edge at ϕ≈190° and corresponding CL increase in Figure 40. Full flow reattachment, beginning from the leading edge, is significantly earlier in the cycle in the blowing case. It is unclear if the lift oscillations, so clearly defined in the k=0.026 data set of Figure 39, are absent at k=0.050 or phase averaged into a dilute low pressure distribution at 135°<ϕ<180°. It is possible that reattachment transients are less periodic at higher reduced frequency due to a temporal interruption by VGJ blowing. Observations in the literature show that reattachment progresses on an absolute timescale and, thus, the process spans a greater portion of the cycle at high frequency [49] and the CL curve supports the periodic nature of the oscillations. Furthermore, it has been shown that blowing conditions the shear layer to reattach during the downstroke. The incoherent appearance of attachment intervals in the post stall regime at k=0.050 could be that the temporal relationship between reattachment and pitch rate is such that reattachment is inconsistently halted, resulting in cycle to cycle inconsistent vortex convection. While the underlying physics behind the non-distinct vortex traces may not be clear, it is quite clear that blowing delays separation and enhances reattachment. Figure 43 and Figure 44 comprise the key quantitative effects of varying mass flux ratio in a compressible steady freestream at M=0.4 and Re=3.0×106 for the two reduced frequencies considered. As noted in the incompressible cases, the general trend 80 of each metric is consistent between the two reduced frequencies. However, the enhancements due to VGJ application are more pronounced at k=0.026 with the one exception being lift stall delay in Figure 44, which shows a divergence between the two reduced frequencies. The delay in moment stall, however, is in good agreement between the two reduced frequencies. When considered in concert, the change in peak CL and minimum CM suggest that blowing at k=0.026 is weakening the stall vortex more substantially than blowing at the same mass flux at k=0.050. Also, trend line inflections such as those observed in peak CL and minimum CM in Figure 43, occur at greater Cq values for the k=0.050 investigation. Specifically, at k=0.026, blowing at Cq=0.002 increases peak CL, but at Cq>0.002, blowing reduces peak CL. Considering the same metric at k=0.050, blowing at Cq<0.004 (inflection point) increases peak CL, but blowing at Cq>0.004 shows a negative slope. If greater mass flux ratios were achievable, the k=0.050 trend may match the k=0.026 trend. This suggests that an increased mass flux is required to obtain the same degree of flow control at amplified reduced frequencies. The principle metrics of cycle average CL, cycle average CM, and negative damping clearly show the substantial flow improvements achieved via VGJ application at even low Cq=0.002. In both cases evaluated, blowing delays moment stall, improves cycle average coefficients, and accelerates flow reattachment. VGJ blowing, even at low mass flux ratios, in a compressible freestream resists flow separation in the presence of locally sonic flow, appears to disrupt the negative consequences associated with vortex convection, and reduces hysteresis. Based on the flow enhancement trends with Cq, the optimal mass flux ratio may not have been achieved and greater benefits are possible. 81 Figure 43: Flow modification vs. mass flux ratio for M=0.4, Re=3.0×106 (Part 1). 82 Figure 44: Flow modification vs. mass flux ratio for M=0.4, Re=3.0×106 (Part 2). Thorough studies by Gardner et al. on compressible dynamic stall flow control employing steady blowing through leading edge VGJs, yielded cycle average CM and CL improvements and a reduction in negative damping [34]. Their evaluation of a pitching 6 airfoil in a steady freestream at M=0.4, k=0.08, Re =1.5×10 at Pj=6 bar (Cq=0.006), and 83 Pj=10 bar (Cq=0.01), as shown in Figure 45, are at similar conditions and VGJ configuration to this study, enabling direct comparison. In Figure 45, as mass flux ratio is increased, CL,max decreases, ultimately decreasing by 7% at Cq=0.01. From Figure 37, the results of this study indicate that blowing in a k=0.026 cycle reduces peak CL, which is in good agreement with Gardner et al data in Figure 45. Low Cq application on a pitching airfoil at k=0.050 in this study, amplified peak CL as evident in Figure 43. However, at maximum Cq=0.005, ΔCL,max is almost negligible, suggesting that if Cq levels as high as those evaluated in the Gardner et al. study were applied to this condition, CL,max would most likely decrease. Additionally, the change in cycle average CL was increased by 4% at maximum Cq, with the majority of the lift recovery occurring during the reattachment process of the downstroke, as is observed throughout this study and illustrated in Figure 43 [34]. However, moderate blowing pressures (Cq=0.006) in the Gardner et al. study amplified secondary lift oscillations in the post stall (see Figure 45), which is consistent with Cq=0.0051 at M=0.4, k=0.026 in this study (see Figure 37). Interestingly, in Figure 45, load oscillation amplitudes decrease as Cq is increased from 0.006 to 0.01. Load oscillation damping was not achieved in this study, most likely due to system pressure limitations. Therefore, it is noted that amplified blowing can damp airfoil load oscillations in the post stall while maintaining an overall average CL increase. 84 j P =0 bar → Cq=0 j P =6 bar → Cq=0.0060 j P =10 bar → Cq=0.0100 Figure 45: CL and CM comparison with moderate to high pressure blowing at M=0.4, Re=1.5×106, k=0.08, α=12−7°cos(ωt) [34]. In the Gardner et al. study, the moment stall was delayed by Δα=0.5° when blowing at both Cq=0.006 and Cq=0.010 as evident in Figure 45 [34]. The CM,min from the initial vortex convection is improved by 60% and minimum CM from secondary oscillations are improved by 59% at Pj=10 bar (Cq=0.010) and the initial region of negative damping present in the non-blowing case was eliminated [34]. Flow reattachment was greatly accelerated in both cases, improving by Δα≈3.5° and 4.5°, respectively. However, due to the increased load oscillations in the post stall region when blowing at Pj=6 bar (Cq=0.006), additional regions of negative damping were generated. When blowing was increased to Pj=10 bar (Cq=0.01), the cycle is free of regions of negative damping. Quantitative flow control results from the present study are on the same order of magnitude with Gardner et al. and the qualitative CM stall behavior outlined in Figure 45 is in excellent agreement with Figure 38 of this study. 85 Section 3.3: Airfoil Pitch Oscillation in a Time-Varying Compressible Freestream As blowing has demonstrated the capability to alleviate the negative effects of dynamic stall in a steady compressible freestream, the progression of this study leads to test conditions more representative of rotorcraft flight conditions. This section presents results for steady blowing on an airfoil subjected to sinusoidal pitch oscillations and phase-locked time-varying compressible freestream. Data were acquired at reduced frequencies of k=0.026 and k=0.050, M=0.4+0.07cos(ωt), at a mean Reynolds number of 6 Re=3.0×10 . Data were acquired at mass flux ratios from Cq=0.002 to Cq=0.005. The mean optimal mass flux ratio for both pitching frequencies is determined to be Cq=0.005 and will be discussed in detail. All further data acquired in the time-varying freestream is available in Appendix B. The phase difference between pitch oscillation and freestream oscillation was such that the minimum Mach number occurred at αmax. Similar to a helicopter rotor relative wind, the freestream velocity was decelerating during the upstroke and accelerating during the downstroke. As Reynolds number, reduced frequency, and mass flux ratio are functions of freestream velocity, these parameters vary locally in a sinusoidal pattern. The time-varying mean to peak amplitudes of Reynolds number, reduced frequency, and mass flux ratio are ±0.4×106, ±0.007, and ±0.0004, respectively. The unsteadiness of these parameters is important to note and take into consideration when comparing flow control effectiveness on a pitching airfoil between a steady and time-varying freestream at the same mean values. For the purposes of this section, blowing is compared to a non-blowing case subjected to the same freestream and 86 non-dimensional parameters. Therefore, all further annotation of non-dimensional parameters will represent their mean value. Blowing at Cq=0.0052 was determined to be the optimal mass flux ratio while pitching at k=0.026 in a time-varying freestream. Figure 46 presents lift orbit modifications due to VGJ activation. Initial observations indicate that blowing yields very similar results in an unsteady freestream as determined in the steady freestream condition. The non-blowing case in the time-varying freestream depicts flow separation at α=16.0°, which is a Δα=0.5° greater than that of the steady freestream case and is consistent with the literature [20] [22] depicted in Figure 8. Steady blowing induces an earlier, apparent lift stall by Δα=−0.6° and reduces peak CL by 2.4%. The non-blowing airfoil exhibits a period of flow reattachment and subsequent separation at α≈18.0°, indicating that the pressure gradient of the decelerated flow near αmax is disposed to reattachment. Thus, it is no surprise that VGJ activation exploits this condition to a great degree, resulting in amplified intervals of flow reattachment. The strength of the lift increase is within 3.5% of the CL,max calculated at lift stall. Additionally, the oscillation non-dimensional frequency is estimated at F+≈0.126, which is within 2% of the F+ estimated in the steady compressible freestream case. The load oscillations carry over to the downstroke and flow acceleration. Steady blowing appears to achieve full reattachment at a substantially greater angle of attack than the non-blowing case, with an average lift increase of 25.6% during the downstroke at 20°>α>11°. The large lift augmentation during the reattachment process leads to a cycle average CL increase of 9.5% and a significant overall reduction in hysteresis. 87 6 Figure 46: CL vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.026. The effect of blowing at Cq=0.0052 on moment about the quarter chord in an unsteady compressible freestream pitching at k=0.026 is displayed in Figure 47. Consistent with all previously presented conditions, steady blowing has marginal impact in the pre-stall and post reattachment regimes at α<12°. Also consistent with the previous sections, the VGJs appear to delay separation by Δα=1.0°. The initial moment stall was arrested in the blowing case due to the temporary shear layer reattachment. The strong positive moment gain observed at α≈18.0° is attributed to the longer period of reattachment, suggesting substantial circulation gain and return of the separation bubble. 88 As this occurs at a high angle of attack with a decreasing dα/dt, VGJs are unable to maintain flow attachment and the accumulated vorticity convects downstream with a negative moment plunge. However, as this secondary vortex is weaker than the primary vortex of the non-blowing case, blowing improves the minimum CM by 15.0%. As discussed in previous sections, the VGJs appear to generate a favorable pressure gradient locally and the jet vortical structures encourage the shear layer to attach to the surface downstream of the VGJs. Blowing achieves full reattachment Δα=3.2° earlier than the non-blowing case, which results in a cycle average CM improvement of 27.3%. Negative Damping 6 Figure 47: CM vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.026. 89 Because the period of the reattachment intervals carry through αmax, the peak of the first oscillation occurs at the same angle of attack (α≈18°) as the trough of the third cycle. A minute region of clockwise moment rotation is thus created, meaning that negative damping is not fully eliminated, but rather reduced by 97.0% and shifted to an alternative portion of the cycle. The moment improvements include reduction in hysteresis and earlier flow reattachment, but also reveal potentially detrimental unsteady load oscillations, which can generate additional negative damping. The CP comparison of the non-blowing and blowing cases evaluated in the unsteady freestream at k=0.026 are presented in Figure 48, which closely resembles Figure 39 from the steady compressible freestream at the same reduced frequency. One distinction, however, is that the blowing case retains a lower suction peak following initial boundary layer separation until the second flow separation at ϕ≈145°. This implies that the VGJs prevent full boundary layer separation at α=16° and preserve vorticity. Consistent with shock-induced separation, the pressure trace of the initial vortex convection in the non-blowing case is slower and diffuse [12]. The controlled case, however, has narrow bands of low pressure from vortex convection, suggesting that the VGJs lessen the effects of shocks. The iterations of flow reattachment and separation are clearly defined by the evenly spaced vortex pressure traces due to boundary layer separation. Additionally, the pressure trace of the initial vortex is faint in comparison to the pressure trace of the non-blowing vortex, possibly denoting that the vortex convection was substantially high off the surface of the trailing edge, attenuating the negative effects of vortex convection. It is conceivable that the viscous effects of the VGJ shear layer 90 entrain the dynamic stall vortex and propel it into the bulk flow. However, the surface pressure measurements alone do not sufficiently explore this hypothesis. CP Vortex CP Trace Vortex CP Traces CP,crit CP,crit Figure 48: CP of non-blowing (left) vs. blowing at Cq=0.0052 (right) at M=0.4+0.07cos(ωt), Re=3.0×106, k=0.026. While the physical mechanisms of how the VGJs attenuate the suction generated by vortex convection are unknown, it is clear that blowing alleviates much of the negative effects of dynamic stall on a pitching airfoil in a time-varying freestream. Results from steady blowing at Cq=0.0052 in a compressible, time-varying freestream at k=0.026 are in good agreement with the results of blowing in a steady freestream at the 91 same mean Mach number. Therefore, the influence of freestream unsteadiness on VGJ flow control effectiveness is slight. Thus, VGJ flow control data acquired in a steady compressible freestream at a reduced frequency of k=0.026 provide a reasonable prediction of quantitative flow improvements from VGJ flow control data acquired in an unsteady freestream environment. 6 Figure 49: CL vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.050 Flow control data were acquired when blowing at 0.002 92 Due to pitch mechanism link deformation, the sinusoidal angle of attack amplitude increased to 11.5°, as observed in Section 3.2.2 at k=0.050. Figure 49 presents the lift orbit of the optimal mass flux ratio overlaying the baseline non-blowing case. The influence of the unsteady freestream is much more pronounced at k=0.050 than was observed in k=0.026. Consistent with previous studies, due to the waning compressibility effects and increased local reduced frequency, the CL gradient increases at α>10°, resulting in a greater peak CL than observed in the steady freestream case [20] [22]. Also, flow separation in the non-blowing case in the unsteady freestream is later in the cycle than observed in the steady freestream case. The CL trend between the blowing and non- blowing cases in Figure 49 are in excellent agreement indicating that active blowing does not interrupt the global flow features of coupled pitch and freestream oscillations. The quantitative flow alterations from blowing in this case are similar to those observed in the steady case of the same mean parameters (Figure 40). During pitch upstroke at α<12°, VGJ activation demonstrated negligible modification to airfoil loading. However, at α>12° through separation, blowing decreases CL, resulting in a peak CL reduction by −1.4%. The apparent angle of attack for flow separation of the blowing case is suppressed by Δα=0.3° beyond that of the non-blowing case. A simultaneous reduction in peak CL and delay of separation is not observed in the steady freestream case. This signals a possible subtle change in physical interaction between the VGJs and time-varying freestream. As the controlled airfoil approaches αmax, the VGJs establish a favorable pressure gradient, which triggers a temporary reformation of the separation bubble, resulting in the single lift oscillation observed in Figure 49. 93 Consistent with the previous sections, steady blowing initiates an earlier shear layer reattachment during the downstroke, leading to a cycle average CL increase of 5.2%. Examination of the moment orbit over the cycle, as presented in Figure 50, reveals similar results to those obtained on a blowing airfoil in a steady compressible freestream. The effects of the decreasing compressibility are evident from the deep moment plunge well beyond that of the steady compressible case. The negative moment trend is indicative of a strong vortex convection due to amplified vorticity accumulation associated with greater stall penetration. VGJ blowing delays the onset of flow separation by Δα=1.0°. As the flow remains attached to a greater angle of attack, vorticity accumulation is also greater, which should lead to an exacerbated minimum moment transient. However, in the blowing case, this does not occur as the VGJs mitigate the negative moment plunge by 4.6%. Furthermore, the CM gradient immediately following separation in the blowing case is steeper than that of the non- blowing case. The steep gradient exhibited in the blowing case is consistent with a concentrated vortex convection. The gradient of the non-blowing case is suggestive of shock instabilities which lead to a diffused vortex convection. Both of these latter observations were present in the steady freestream case at k=0.050 in Section 3.2.2. The interval of reattachment as the airfoil reaches αmax creates a small loop in the CM orbit as well as a secondary vortex. Flow separation was possibly induced by the sudden flow changes due to abrupt gradient changes in both airfoil pitch and freestream compressibility. The propensity for VGJs to accelerate free shear layer reattachment has been shown throughout this study and is further evident in this case on the downstroke. 94 The shear layer reattachment of the blowing case occurs Δα=3.2° earlier in the cycle when compared to the non-blowing case. The positive moment gradient improves the cycle average moment by 15.1%, and significantly reduces negative damping. However, due to the small moment loop at αmax, negative damping is not fully eliminated. Negative Damping 6 Figure 50: CM vs. angle of attack comparison at M=0.4+0.07cos(ωt), Re=3.0×10 , k=0.050. The CP distribution for both the blowing and non-blowing cases corroborate observations made during evaluation of the moment and lift orbits and is provided in Figure 51. As was detected in previous sections, the VGJs are marked by the persistent 95 low pressure line at 10% chord. There are two low pressure traces in the blowing case associated with a primary and secondary vortex convection at ϕ≈135° and ϕ≈180°, which correspond to Figure 49 as the peak lift location and load oscillation at maximum angle of attack. While the pressure traces of the shed vortices appear blurred in the cycle- averaged data in Figure 51, instantaneous data reveals a consistent shedding angle of two distinct vortices. The favorable pressure gradient upstream of the VGJs fosters and sustains a suction peak at 80°<ϕ<300° (α>7.5°). The postulation based on CM gradient of a diffused vortex convection in the non-blowing airfoil due to leading edge shock formation is substantiated by the vortex pressure trace and the white contour at ϕ≈120°, indicating CP is less than CP,crit. The slope of the vortex pressure trace (dϕ/dx) in the non- blowing case is greater than that of the blowing case. A greater slope indicates a slower convection speed, as ϕ is related to time, which means that the non-blowing vortex convects slower over the surface in comparison to the blowing case. Typically, a rapid vortex convection speed would entail a rapid nose down moment to a substantially detrimental CM. However, in the blowing case, this does not occur because the low pressure region associated with the vortex convection is weaker than the diffused vortex of the non-blowing case. Additionally, the VGJs maintain a semblance of a suction peak near the leading edge to balance the vortex induced suction at the trailing edge. The weak suction associated with the vortex convection in the blowing case suggests that the VGJs disrupt the normal convection of the dynamic stall vortex and mitigate shock- induced instabilities. The start of leading edge flow reattachment is evident by the low pressure in the blowing case at ϕ=200°. In contrast, a similar CP value does not emerge 96 in the non-blowing case until ϕ>225°. A final observation for the blowing case is the absence of distinct vortex pressure traces for the deep stall load oscillation. The traces are quite prevalent in Figure 48 for the k=0.026 case and align with the reattachment cycles. While inconclusive, their absence may signal a highly unstable shear layer with cycles of flow reattachment and separation caused by the VGJ shear layer interaction. CP Vortex CP Trace Vortex CP Traces CP,crit CP,crit Figure 51: CP of non-blowing (left) vs. blowing at Cq=0.0051 (right) at M=0.4+0.07cos(ωt), Re=3.0×106, k=0.050. 97 Figure 52: Flow modification vs. mass flux ratio for M=0.4+0.07cos(ωt), Re=3.0×106 (Part 1). The resulting quantified flow deviation from a non-blowing reference due to VGJ blowing at varying mass flux ratios are provided in Figure 52 and Figure 53. It is clear that flow characteristics generally improve with increased mass flux ratio and the figure trends suggest that a greater mass flux ratio is required at k=0.050 to achieve the same 98 Figure 53: Flow modification vs. mass flux ratio for M=0.4+0.07cos(ωt), Re=3.0×106 (Part 2). quantitative improvements obtained at k=0.026. There is also evidence that the VGJs can have detrimental effects, such as indicated for the aggravated minimum CM at Cq<0.005 in the k=0.050 case depicted in Figure 52. However, even slight blowing, while detrimental in minimum CM, improves the cycle averaged lift and moment, and 99 drastically reduces negative damping. At the other end of the Cq spectrum, based on the trends, it appears that the optimal mass flux ratio was not attained due to system pressure limitations. Another key observation is the similarities in both performance trends and flow modification values between the time-varying freestream investigation (Figure 52 and Figure 53) and the compressible steady freestream section (Figure 43 and Figure 44). This provides further evidence that VGJ performance measurements acquired in a steady compressible freestream are a good prediction of the anticipated VGJ performance on a pitching airfoil in a low amplitude freestream oscillation. The change in CM stall angle, cycle average CM, negative damping, and reattachment angle for both the steady and time-varying freestream cases are overlaid in Figure 54. These measurements are not exceptional, but rather were selected as a balance between indicators of flow control and report brevity. The change in CM stall angle has consistent results when blowing at all mass flux ratios at k=0.050, but is only consistent at Cq=0.002 and Cq=0.005 for the k=0.026 cases. This suggests some variation in flow control at intermediate mass flux ratios, but convergence occurs at the highest mass flux ratio. However, the improvement in cycle average CM is in excellent agreement between the cases. The reduction in negative damping demonstrates that the predicted elimination of negative damping at k=0.05 in the steady freestream case represents the negative damping value for the time- varying freestream case at k=0.05. However, negative damping reduction from VGJ blowing at Cq=0.002 in the steady freestream at k=0.026 over predicts the effectiveness of VGJ blowing at the same Cq and frequency in a time-varying freestream. The change 100 in reattachment angle, indicating the VGJ ability to reattach the shear layer in different flow conditions, is quite consistent between the four cases with a slight variation at intermediate mass flux values. It is not surprising that flow reattachment improvement is relatively consistent as it progresses on an absolute time-scale [49]. Figure 54: Flow modification vs. mass flux ratio for steady and time-varying freestream. 101 Though the flow conditions in a time-varying freestream clearly add a degree of unsteadiness on airfoil loading, limited differences are observed due to the VGJ and unsteady flow interaction. These similarities in comprehensive results for the steady and unsteady flow conditions strongly suggest that the effects of time-varying freestream on VGJ performance can be considered quasi-steady. Thus, VGJ studies conducted on a pitching airfoil in a steady compressible freestream provide a reasonable prediction of the anticipated VGJ application results over a pitching airfoil in an unsteady freestream. This last statement is not to suggest that a time-varying freestream can always be considered quasi-steady. The low amplitude of the freestream oscillation conducted in this investigation is minor in comparison to the effects due to pitch oscillation amplitude. Therefore, within the conditions of this investigation, time-varying freestream compressibility and velocity can be considered quasi-steady, as was also noted in previous research [22], However, this may not always be the case as a comparison between the data presented in Section 3.2.1 and Section 3.2.2 clearly demonstrate the significance of varied compressibility on VGJ performance. Section 3.4: Time-Resolved Background Oriented Schlieren Instantaneous, qualitative Background Oriented Schlieren imagery was used to corroborate airfoil surface pressure measurements and provide insight into the behavior of off-surface flow structures. Additionally, since BOS integrates the effects of density gradients across the span, the technique may capture additional disturbances not in the 102 vicinity of the pressure taps. BOS data were acquired at each freestream condition and mass flux ratio evaluated. BOS data provide evidence of weak shocks in the first 5% chord during the upstroke in both the blowing and non-blowing cases in a compressible freestream. Strong blowing triggers leading edge shear layer reattachment which coincides with airfoil load oscillations in the post stall regime. BOS imagery of blowing cases at Cq=0.005 reveal an absence of coherent stall structures in the far field which may indicate that the high momentum jets both distort and entrain the structures, altering their trajectory further from the airfoil trailing edge. Interestingly, the BOS data reveal that cycle-to-cycle flow features mentioned above remained consistent regardless of freestream environment and mass flux ratio. Therefore, to prevent redundancy, this section will primarily focus on blowing at Cq=0.0052 on an airfoil pitching at k=0.026 in a time-varying freestream, unless otherwise stated. The one deviation from this is the confirmation of shocks in the non-blowing case, at k=0.050 in a steady freestream at M=0.4 from Section 3.2.2, which showed characteristics of shocks but peak CP did not exceed CP,crit in the pressure data. The BOS data presented herein is of instantaneous images and is qualitative in nature, which falls short of the full potential of the technique. Figure 55 is a typical post- processed BOS image showing pixel displacement magnitude with minor displacement represented in blue and greater displacement represented in red. White regions indicate a pixel displacement magnitude greater than four pixels while regions of limited data are covered in black. The no-data regions as marked in Figure 55 are where light passage was blocked such as where the airfoil pressure tubing exits the tunnel (lower right 103 VGJ Shear Layer Vortical Airfoil Structure Window distortion VGJ plumbing hose clamp Non-uniform light intensity/ Pressure tap and VGJ Tunnel Window plumbing Vibrations distortion Figure 55: Processed BOS image with reliable, unreliable, and no-data regions. quadrant), high pressure hose clamps (lower side of leading edge), and the airfoil rotation boss (center circle). Additionally, due to tunnel movement, local window refraction index variations, and light intensity variations; erroneous pixel displacements emanate radially from the rotating boss and are present along the airfoil upper surface near the trailing edge as marked in Figure 55. Due to these distortions and no-data regions, quantitative results were unreliable. Figure 56 shows a raw image with the airfoil and background dot pattern, which illustrates these challenges. A correlation between Figure 55 and Figure 56 identifies and labels the areas where flow structures are believed to exist. The areas without interference capture the sharp density gradients associated with flow structures, shear layer edges, and shocks. These features are depicted as pixel 104 displacements, providing time-resolved, qualitative interpretation sufficient for the purposes of this investigation. Non-uniform VGJ light intensity Airfoil boss VGJ plumbing hose clamp Pressure tap and VGJ Scratch plumbing Figure 56: Raw BOS image with reliable and unreliable regions. The mechanics of BOS are very similar to Point Diffraction Interferometry (PDI) in that both use the principle of variations in light refractive index to identify local changes in density and quantitatively solve for density using the Gladstone-Dale equation discussed in Section 2.7 [9]. Whereas BOS processing is based on perceived pixel displacement of the background pattern, PDI produces interference fringes representing contours of optical path differences caused by density variations [9]. Sharp gradients in the local refractive index are expressed as tightly packed fringes in PDI imagery and 105 large pixel displacements in BOS imagery. Therefore, flow features observable in PDI imagery can be used to qualitatively validate the presence of flow structures in BOS imagery. Far field structures appear after flow separation and have small local changes to the index of refraction. Figure 57 shows a comparison between PDI (left) of a pitching RC(6)−08 airfoil at k=0.05, in a steady M=0.4 freestream and BOS (right) of the SSC−A09 airfoil at the same conditions. A vortical structure extending from the shear layer to the far-field, as indicated by PDI fringes, corresponds to pixel displacements extending from a shear layer in the BOS image. Furthermore, PDI imagery of both an attached and separated RC(6)−08 airfoil, shown in Figure 58, illustrate the contours’ orientation associated with a suction peak (a) and the separated shear layer (b). These flow features coincide with corresponding pixel displacements in the BOS imagery, shown in Figure 58 (c) and (d), and validate the qualitative identification of specific flow structures associated with dynamic stall using BOS. Fringes vs. Pixel Vortical Displacements Structure α=16.5° α=14.5° ϕ=131.8° Figure 57: Far-field structure identification comparison of a pitching airfoil in a compressible freestream at M=0.4, k=0.05, using PDI (left) [50] and BOS (right). 106 a α=10.0° b α=14.5° α=11.0° α=16.5° Shear ϕ=98.2° Suction ϕ=131.8° Layer Peak c d Figure 58: Structure identification comparison of a pitching airfoil in a compressible freestream at M=0.4, k=0.05, using PDI (images a, b) [50] and BOS (images c, d). Lorber and Carta reported that the SSC−A09 airfoil is prone to leading edge shock formation and subsequent shock-induced separation which results in a more gradual stall and is characterized by a more diffuse stall vortex [39] [12]. Recall that the phase averaged CP distribution provided in Figure 42 in Section 3.2.2 showed evidence of a diffuse stall vortex for the non-blowing case but a concentrated vortex streak in the blowing case, suggesting that the non-blowing case suffered from shock-induced separation and the blowing case did not. However, the CP distribution for the non- blowing case did not exceed CP,crit, but did show evidence of shock-induced separation. 107 In contrast, the blowing case CP did exceed CP,crit, yet did not exhibit the stall characteristics of shock-induced separation. α=13.6° ϕ=112.8° Shock Figure 59: Leading edge shock on a non-blowing case at M=0.4, k=0.050, Re=3.0×106. Shocks are easily identified in Background Oriented Schlieren imagery due to their sharp index of refraction gradient (e.g., see Venkatakrishnan and Meier [42]). A shock oriented normal to the airfoil surface is represented by a change in pixel displacement in the stream-wise direction. Pixel displacements in opposite directions over a very small distance indicate a shock. This is akin to traditional schlieren with a vertical knife-edge, and thus measuring only the density gradient in the stream-wise direction. Figure 59 is a BOS image showing horizontal pixel displacement at the leading edge of the airfoil at M=0.4, k=0.050, at α=13.6°, ϕ=112.6°. White indicates 108 pixel displacement to the right and black indicates a pixel displacement to the left. The interface between the contrasting colors as marked in Figure 59 supports the claim of shocks forming within the leading 5% chord. The pictorial representation of a shock was confirmed with BOS imagery of flow condition with a known shock (Figure 60). The presence of shocks, the diffuse dynamic stall vortex captured in the CP distribution of Figure 42, and the stall sequence observed in BOS confirms that the non-blowing airfoil is indeed characterized by shock-induced separation. It is important to note, that if this study was reliant on pressure measurements alone, the presence of shocks would not have been confirmed. α=13.6° ϕ=112.8° Shock VGJ Figure 60: Leading edge shock when blowing at Cq=0.0051, at M=0.4, k=0.050, Re=3.0×106. 109 BOS imagery confirmed the presence of shocks in the blowing case at M=0.4, k=0.050 Figure 60. However, the corresponding diffuse dynamic stall vortex does not appear in the CP distribution of the blowing configuration of Figure 42, suggesting that even though shocks are present, the stall behavior is not that of shock-induced separation. This further substantiates the claim that VGJs are an effective mechanism to resist shock- induced separation as put forth by Gardner et al. [35]. As observed in all blowing cases throughout Chapter 3, a positive effect of VGJ blowing is earlier shear layer reattachment, which results in a reduced region of negative damping and reduction in hysteresis. However, this significant contribution to flow control also aggravates periodic load fluctuations in the post stall regime. When strong blowing is applied, the airfoil loading oscillates substantially in comparison to the non- blowing case. The most egregious observed example of airfoil load oscillations in comparison to the non-blowing case is VGJ application at Cq=0.0052 in a compressible, time-varying freestream at k=0.026. These instabilities are manifested in the CP distribution for these conditions (Figure 48, Section 3.3) as re-establishment of a separation bubble and a subsequent series of four low-pressure, downstream-convecting streaks between 120°<ϕ<224°. Load oscillations are suggested to be caused purely by temporal shear layer reattachment and subsequent ejection. Figure 61 is BOS imagery of the airfoil pitching at k=0.026 in a time-varying freestream as discussed in Section 3.3. The images on the left are of the non-blowing condition and the images on the right are of blowing at Cq=0.0052. The shear layer is depicted as a streak emanating up from the leading edge of the airfoil as reported in Figure 58. In these particular figures, the shear 110 α=19.2° α=19.2° ϕ=156.7° ϕ=156.7° VGJ normal Max shear Max shear layer angle layer angle VGJ a b α=19.9° α=19.9° ϕ=172.2° ϕ=172.2° Min shear VGJ streamwise Min shear layer angle alignment layer angle VGJ c d Figure 61: Shear layer angle amplitude of non-blowing (high-angle (a), low-angle (c)) and blowing at Cq=0.0052 (high-angle (b), low-angle (d)), M=0.4+0.07cos(ωt), k=0.026, Re=3.0×106. layers are near their maximum (top) and minimum (bottom) trajectory during the upstroke with relation to the airfoil leading edge. Notice that the blowing case has a greater shear layer oscillation amplitude in comparison to the non-blowing case, 111 confirming the VGJ induced shear layer instability and relative stability of the non- blowing case. This side-by-side view of the shear layer amplitude angles confirms that the shear layer is highly unstable, especially with blowing applied. Figure 62: Shear layer angle vs. phase for non-blowing and blowing at Cq = 0.0052, M=0.4+0.07cos(ωt), k=0.026, Re=3.0×106. Once the flow has separated and ejected the dynamic stall vortex, the shear layer lifts off the entire airfoil surface resulting in a fully separated flow. The periodic unsteady nature of the shear layer results in the continuous shedding of smaller vortical structures from the leading edge. The high momentum from the jets amplifies this unsteady behavior and generates larger amplitude oscillations, or flapping of the shear layer. At times, the oscillations temporarily reattach the shear layer to the leading edge surface. The calculated periodicity of this movement is at F+=0.121, and coincides with the CP distribution of Figure 48 and CL oscillations in Figure 46. To appreciate the large 112 amplitude flapping of the shear layer with VGJ's applied compared to the unsteady oscillations of the non-blowing case, the separated shear layer angle relative to the chord line is plotted versus phase in Figure 62. At pre-separation angles of attack and when the shear layer is close to the surface, the VGJ's are bent with the bulk flow (Figure 61 (d)) characteristic of a typical jet in a crossflow as discussed in Section 1.3. However, as the flow begins to separate and the shear layer lifts off the airfoil surface, the portion of the jet within the separated region becomes normal to the surface, and the portion of the jet penetrating the separated shear layer bends in alignment with the shear layer trajectory as shown Figure 61 (b). It is important to note that a phase lag exists between the jet orientation oscillation and the shear layer trajectory oscillation. As the shear layer reaches a maximum distance from the airfoil surface, the jet has a slight lag but eventually completely penetrates the shear layer and is fully normal to the surface as shown in Figure 61 (b). Recall from Section 1.3 that the jet’s alignment with the crossflow generates the counter-rotating vortex pairs as discussed by Muppidi and Mahesh [33]. Thus, only the portion of the jet penetrating the shear layer and interacting with the freestream is capable of and expected to produce counter-rotating vortex pairs. A conjecture on the physical explanation of the VGJ amplified shear layer oscillation is that the jets act as a forcing mechanism (through viscous entrainment) when the shear layer begins to flap away from the surface, pushing the shear layer further away from the surface to a greater angle than if blowing was not applied. At this high trajectory, the shear layer angle is over-extended and, much like a stretched spring 113 seeking equilibrium, the bulk flow accelerates the shear layer back towards the airfoil surface. The temporal lag between the shear and jet angles causes the jet to penetrate the shear layer, forming counter-rotating vortex pairs outside of the shear layer as the shear layer begins to flap down. The added mass and structure outside of the separated shear layer, in this case, act to force the shear layer back towards the airfoil surface, ultimately causing temporary reattachment. This conjecture supports the observation that blowing at a sufficiently high mass flux ratio could stabilize the shear layer and damp post stall load oscillations. j P =0 bar → Cq=0 j P =6 bar → Cq=0.0060 j P =10 bar → Cq=0.0100 Figure 63: Airfoil load oscillation amplitude with moderate to high pressure blowing at M=0.4, Re=1.5×106, k=0.08, α=12−7°cos(ωt) [34]. At moderate mass flux ratios, such as those applied in this study, this is obviously not the case as load oscillations are amplified. Load oscillations were also observed by Gardner et al. as depicted by the red CL curve of blowing at Cq=0.0060 in Figure 63 [34]. However, blowing at Cq=0.0100 such as that attained by Gardner et al., demonstrated that 114 post stall load oscillations can be damped as shown in Figure 63 [34]. In this figure, Gardner et al. stabilized the shear layer in the post stall region without compromising the other benefits of VGJ flow control such as CM improvement, accelerated reattachment, CL increase on the downstroke, and reduced negative damping. The moment stall and subsequent negative moment plunge are mitigated at α=17.0° when VGJs are applied at Cq=0.0052 for the time-varying freestream at k=0.026 as depicted in Figure 47 of Section 3.3. This is shown in the CP distribution in Figure 48 and described in Section 3.3 as a weak initial vortex shed and low suction amplitude. The instantaneous BOS images displayed in Figure 64 correspond to the respective phase and angle of attack of minimum moment from the initial vortex convection for the blowing and non-blowing cases. When evaluating the BOS stall sequence of the blowing case in Figure 64 (right), there is no evidence of coherent vortical structures in the far field at the blowing cases’ respective separation angles. This is in contrast to the non- blowing case, which depicts a clear roll-up of the shear layer and corresponding separated structure. The physical reason for this phenomenon is unclear and undeterminable with the present BOS and pressure data. However, it is possible that the conical structure of the high-pressure VGJs diminish the span-wise uniformity of the dynamic stall vortex through warping and stretching. This effectively decreases the refractive index gradient associated with the edges of the vortex structure, making it less evident in BOS imagery. As it is well known that a jet in cross-flow entrains a portion of the freestream into the jet structure [1] [33], a related hypothesis based on flow entrainment is that, through viscosity, the high momentum VGJ entrains portions of the dynamic stall vortex 115 and ejects it into the far field. As the structure is substantially distant from the pressure taps, it remains undetected. This would explain the weak low pressure region near the trailing edge (Figure 48) and would mitigate the negative moment spike so distinct in Figure 47, at the respective ϕ and α. α=16.5° α=17.0° ϕ=131.8° ϕ=136.1° VGJ Distinct Vortical Incoherent Structure Vortical Structure Figure 64: Vortical structures at CM stall of non-blowing (left) and blowing at Cq=0.0052 (right) at, M=0.4+0.07cos(ωt), k=0.026, Re=3.0×106. The CM and CP data (Figure 47 and Figure 48) for blowing versus non-blowing in the time-varying freestream case when pitching at k=0.026 show that steady blowing at Cq=0.0052 delays flow separation by Δα=1.0° and accelerates reattachment by Δα=3.2° over the non-blowing case, which are two primary flow enhancements achieved with steady VGJs. BOS imagery captures the flow separation progression beginning from the trailing edge during moment stall at α=15.8°, ϕ=126.6° for the non-blowing case, which corresponds with the inflection point consistent with the onset of moment stall in Figure 47. The light blue region outlined in Figure 65 designates the shear layer near the trailing 116 edge is still attached in the blowing case (b), but is not present in the blowing case, indicating the shear layer is separating. To reaffirm the separation progression for the blowing case, BOS reveals trailing edge separation at α=16.8°, ϕ=134.5° (not shown), which also coincides with CM stall for the blowing case. The shear layer separation sequence is much clearer in time resolved images versus the snapshots displayed in Figure 65. During the downstroke, at α=15.0° and ϕ=238.6°, the reattachment process observed in the BOS data progresses from leading to trailing edge as described by Ahmed and Chandrasakehra [49]. The light blue region near the trailing edge of Figure 65 represents the shear layer extending from the leading edge to the trailing edge. BOS images show the light blue region lift from the surface at the onset of stall. Figure 65 (d) shows that the shear layer in the blowing case is reattached to the airfoil trailing edge, which coincides with CM values above pre-separation levels at α=15.0° in Figure 47. The shear layer of the non-blowing case (c) remains detached at the same angle of attack and does not reattach until α=12.8° (not shown). The reattachment process in both cases corresponds to the return of the suction peak annotated in the CP distribution (Figure 48) at the associated phase locations and is much easier to discern in a time-resolved image series. Observations of the separation and reattachment process at the trailing edge and their collaboration with the CM and CP figures is consistent across all conditions tested in this study. The insight into the reattachment process and sequence validates the flow physics inferred by the pressure measurements. The BOS data also confirms that steady 117 VGJ activation accelerates flow reattachment. As the progression was identical in both a steady freestream and time-varying freestream, the BOS data indicates that the separation and reattachment procession in a low amplitude, time-varying freestream can be modeled by a pitching airfoil in a steady freestream at matched mean conditions. Unfortunately however, the underlying physics supporting accelerated reattachment is not revealed. α=15.6° Separating α=15.6° Attached Flow ϕ=126.6° Flow at ϕ=126.6° at Trailing Trailing Edge Edge a b Reattaching α=15.0° α=15.0° Fully Reattached Flow at ϕ=238.6° ϕ=238.6° Flow at Trailing Trailing Edge Edge c d Figure 65: Flow separation of non-blowing (a) vs. blowing at Cq=0.0052 (b), and shear layer reattachment of non-blowing (c) vs. blowing at Cq=0.0052 (d), M=0.4+0.07cos(ωt), k=0.026, Re=3.0×106. 118 Chapter 4: Conclusion VGJ flow control on a SSC−A09 airfoil was investigated on a static and dynamically pitching airfoil in both compressible and incompressible freestreams, as well as dynamic pitching with phase-locked freestream oscillations. The mean Mach numbers for the steady conditions were M=0.2 and M=0.4 and the Mach number for freestream oscillation was M=0.4+0.07cos(ωt). The mean Reynolds numbers for the experiments were Re=1.5×106 and Re=3.0×106, for incompressible and compressible cases, respectively. Four mean mass flux ratios ranging from 0.002 VGJs proved to be effective flow control mechanisms in all conditions evaluated. Specifically, VGJs postponed boundary layer separation and softened the stall profile to that of a trailing edge stall and resisted shock-induced separation. BOS confirmed the presence of shocks in both the blowing and non-blowing cases of compressible dynamic stall. VGJ blowing demonstrated the greatest benefit in the post separation regime primarily due to the favorable local pressure gradient and interaction of the separated shear layer with VGJ structures. Blowing consistently improved cycle average moment and increased cycle average lift, especially during the downstroke. BOS established that VGJs triggered an earlier flow reattachment which reduced hysteresis and circuits of 119 clockwise rotation on the CM curve related to negative damping. However, too aggressive of VGJ application amplified shear layer instabilities, resulting in potentially detrimental load oscillations. BOS indicated that VGJs amplify shear layer instabilities, initiating cycles of temporary reattachment and vortex shedding at a relatively consistent F+ based on reduced pitching frequency. There was no mass flux ratio identified which prevented separation under any condition evaluated in this study, but an optimal Cq range, with maximum benefits was found. Optimal mass flux ratio is approximated at Cq≈0.003 for a pitching airfoil in an incompressible freestream. The optimal mass flux ratio for a pitching airfoil in a compressible freestream was not determined due to system pressure limitations, but is estimated to be at Cq>0.005. Blowing at mass flux ratios outside of this range caused deteriorating returns and an aggravated negative moment spike. The effectiveness of VGJ flow control is suggested to be primarily a function of maximum angle of attack, pitching frequency, and mean freestream compressibility. As these three parameters increase, the mass flux ratio necessary to attain similar degrees of flow control is also increased. VGJ flow control evaluated on a pitching airfoil in steady compressible freestream at M=0.4 and time-varying compressible freestream at M=0.4+0.07cos(ωt) experience similar quantitative and qualitative trends with varied mass flux ratio, regardless of reduced frequency. Therefore, at low freestream oscillations, airfoil pitching frequency is the dominant factor in VGJ effectiveness and, as such, a low amplitude time-varying freestream can be considered quasi-steady. Performance 120 enhancements obtained from an airfoil with active VGJs from that of a non-blowing airfoil in a steady compressible freestream provide a good prediction of the expected performance measurements when blowing is applied to an airfoil in a low amplitude unsteady compressible freestream. As steady VGJ employment demonstrated little benefit at low angles of attack, but clearly aids in reattachment, a recommendation for further study is to conduct phase- locked VGJ blowing such that the VGJs are only active as necessary. Phase-locked VGJs applied during the reattachment process would reduce mass flux requirements by limiting the VGJ duty cycle. This study indicated that even low mass flux blowing in a compressible freestream aided in the reattachment process and eliminated negative damping. Therefore, low mass flux, phase-locked blowing could be an economical solution to achieve targeted flow control on a pitching airfoil. The freestream oscillation amplitude evaluated in the time-varying freestream portion of this study remained of secondary importance to the effects of pitch amplitude. High speed flight, where dynamic stall is of greatest concern for rotorcraft, has much greater freestream Mach number oscillation amplitudes. While this degree of freestream oscillation may be excessive, focusing a study on higher amplitude freestream oscillations with a decreased amplitude angle of attack schedule may be warranted. Lastly, the optimal mass flux ratio to overcome the unsteady load oscillations in the separated region was not achieved. A thorough investigation with greater pressures and mass flux ratios may identify a break point at which VGJs fully suppress dynamic stall on a pitching airfoil without post stall oscillations. 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O., "Dynamic Stall in Pitching Airfoils: Aerodynamic Damping and Compressibility Effects ," Annual Review of Fluid Mechanics, vol. 47, pp. 479-505, 2015, doi: 10.1146/annurev-fluid-010814-013632. [49] Ahmed, S. and Chandrasekhara, M. S., "Reattachment Studies of an Oscillating Airfoil Dynamic Stall Flowfield," AIAA Journal, vol. 32, no. 5, pp. 1006-1012, May 1994, doi: 10.2514/3.12087. [50] Carr, L. W., Chandrasekhara, M. S., Wilder, M. C., and Noonan, K. W., "Effect of Compressibility on Suppression of Dynamic Stall Using a Slotted Airfoil," Journal of Aircraft, vol. 38, no. 2, pp. 296-309, April 2001, doi: 10.2514/2.2762. 127 Appendix A: Dynamic Compensation Modeling The Bergh – Tijdeman (B-T) analytical model was applied to correct for viscous effects in the tubing-sensor system of the airfoil pressure signals. This was done to correct for the pneumatic distortion of the signal to obtain accurate pressure amplitude and phase alignment during dynamic pitch oscillation. The parameters required for pneumatic correction with the Bergh – Tijdeman model are pressure tubing geometry (inner diameter and length) and transducer volume. These values are provided in the table below. Table 1: Bergh-Tijeman tubing and sensor geometry. Pressure Tubing Inner Diameter (in) Length (in) 0.057 12 Transducer Volume (in3) 0.000809 A bench top experiment was conducted to show the validity of the B-T model on various tube lengths. The results are shown in Figure 66. For tube lengths less than 22 inches, the amplification ratio (AR) is in good agreement with the B-T model up to 80 Hz, and the phase delay is approximately zero up to 100 Hz. This demonstrates that the airfoil pressure signal does not require correction at low frequencies. Due to the pressure perturbations from airfoil pitching and dynamic effects of freestream oscillations, tunnel pressure measurements also experience time sensitive measurements. As the tube lengths 128 for most tunnel measurements exceed 22 inches, dynamic compensation was applied as necessary. Figure 66: Bergh – Tijdeman bench top test. The B-T analytical model was then applied to pressure signals of the SSC-A09 airfoil with pitch oscillations at 14 Hz. During the data reduction process, frequencies above 300 Hz are filtered out of the pressure signal using a low pass band filter. The power-spectral density (Figure 67) shows that there is a peak frequency at 14 Hz which naturally corresponds to the pitching frequency. This spike is subsequently followed by additional minor spikes at subharmonic frequencies until the cutoff frequency at 300 Hz, at which point the filter flattens the signal. When applying the B-T analytical correction, it is not until frequencies above the third subharmonic that compensation may be required (see Figure 68 and Figure 69). The amplification ratio and phase delay at these 129 subharmonics are tabulated in Table 2. Considering the B-T application in this case for this particulate model, at 100 Hz, the amplification ratio is 1.846 dB and the phase delay is −.22°. This demonstrates that out to three times the pitching frequency of the airfoil, the phase delay is −0.05° or less and the amplification ratio is increased by approximately 10% (1.103 dB). A sample of the corrected pressure is provided in Figure 70. Figure 67: Power Spectral density of airfoil pressure tubing. 130 Figure 68: Amplification Ratio of airfoil pressure tubing. Figure 69: Phase delay of airfoil pressure tubing. 131 Figure 70: Corrected signal of an airfoil pressure tap. Table 2: Amplification and phase delay of airfoil model. Frequency Phase Delay AR (dB) (Hz) (°) 14 -0.01417 1.011 28 -0.03023 1.044 42 -0.05034 1.103 56 -0.07555 1.191 70 -0.1085 1.321 85 -0.1554 1.522 98 -0.2126 1.794 132 Appendix B: Non-Optimal Results Appendix B of this report provides combined lift and moment orbits at each test condition evaluated. The intent of this appendix is to provide the reader additional reference data that was not otherwise discussed in the body of the report. In the interest of conciseness, the figure sizes are reduced and lift and moment orbits are paired. The first figures are of lift and moment orbits for blowing at four mass flux ratios on a pitching airfoil in an incompressible freestream at k=0.026 and k=0.050. The second set of figures provide lift and moment orbits for VGJ flow control in a steady compressible freestream at k=0.026 and k=0.050. The final contribution of this appendix are figures representing VGJ application at all mass flux ratios evaluated on a pitching airfoil in a time-varying freestream at k=0.026 and k=0.050. 133 6 Figure 71: Combined CL and CM curves vs. Cq variation for M=0.2, Re=1.5×10 , k=0.026. 6 Figure 72: Combined CL and CM curves vs. Cq variation for M=0.2, Re=1.5×10 , k=0.050. 134 6 Figure 73: Combined CL and CM curves vs. Cq variation for M=0.4, Re=3.0×10 , k=0.026. 6 Figure 74: Combined CL and CM curves vs. Cq variation for M=0.4, Re=3.0×10 , k=0.050. 135 Figure 75: Combined CL and CM curves vs. Cq variation for M=0.4+0.07cos(ωt), Re=3.0×106, k=0.026. Figure 76: Combined CL and CM curves vs. Cq variation for M=0.4+0.07cos(ωt), Re=3.0×106, k=0.050. 136