44th Aerospace Sciences Meeting, January 9, 2006, Reno, Nevada

Plasma Flow Control Optimized Airfoil

Thomas C. Corke∗ Benjamin Mertz†

University of Notre Dame

Center for Flow Physics and Control

Aerospace and Mechanical Engineering Department

Notre Dame, IN 46556

Mehul P. Patel‡

Orbital Research Inc.

Aerodynamics Group

Cleveland, OH 44103

Single-dielectric barrier discharge (SDBD) plasma actuators have been shown to pro-duce changes in lift that are comparable to that of a moving plane flap. This opens theopportunity for flight control without moving surfaces, which has the advantages of simplic-ity, as well as lower form drag associated with flap hinge gaps. In our previous applicationof this, the plasma actuator was operated in a “steady” manner. This paper deals with adesign that allows the plasma actuator to operate in an unsteady manner. This has theadvantage of reducing the actuator power by 90 percent, as well as improving the actuatordurability. The concept involves the use of a laminar airfoil design that employs a separa-tion ramp at the trailing edge that can be manipulated by a plasma actuator to control lift.This is demonstrated through numerical simulations and experiments on a HSNLF(1)-0213airfoil. The numerical results are obtained using an unsteady, compressible Navier-Stokessimulation that includes a model for the plasma actuators. The experiments are performedon a 2-D airfoil section that is mounted on a lift-drag force balance. The results demon-strate lift enhancement produced by the plasma actuator that is comparable to a planeflap. They also reveal an optimum actuator unsteady frequency that scales with the lengthof the separated region and local velocity, and is associated with the generation of a trainof spanwise vortices. Other scaling paramters including the effect of Reynolds number ispresented.

I. Introduction

Recent advances in flow control research have demonstrated that plasma actuators could be efficientin different aerodynamic applications.1–4 Particularly, plasma actuators were proposed to provide aircraftmaneuverability as an alternative to conventional moving control surfaces. The goal of this work is to developthe area of applications of plasma actuators in this direction.

The SDBD plasma actuator consists of thin electrodes separated by a dielectric insulator. One of theelectrodes is typically exposed to the air. The other electrode is fully covered by the dielectric material. Aschematic illustration is shown in Figure 1. A high voltage a.c. potential is supplied to the electrodes. When

∗Clark Chair Professor, Associate Fellow AIAA†Ph.D.Candidate‡Senior Member, AIAACopyright c© 2006 by T. Corke and M. Patel. Published by the American Institute of Aeronautics and Astronautics, Inc.

with permission.

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44th AIAA Aerospace Sciences Meeting and Exhibit9 - 12 January 2006, Reno, Nevada

AIAA 2006-1208

Copyright © 2006 by T. Corke and M. Patel. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

����������������������������������������������������������������������������������

Kapton film

Airfoil

x/c = location

Actuator Electrode Arrangement

(air−side)

electrodes

Induced Flow

Figure 1. Schematic drawing of asymmetric electrode arrangement for plasma actuators used in experiments.

Figure 2. Photograph of plasma (blue) for asymmetric electrode arrangement shown in Figure 1. From Enloeet al. 5

the a.c. amplitude is large enough, the air ionizes in the region of the largest electric potential. This generallybegins at the edge of the electrode that is exposed to the air, and spreads out over the area projected bythe covered electrode. A photograph of the plasma for the electrode arrangement in Figure 1, is shown inFigure 2.

The process of ionizing the air in this configuration is classically known as a single dielectric barrierdischarge .5 The ionized air (plasma) in the presence of an electric field gradient produces a body force onthe ambient air ,6 inducing a virtual aerodynamic shape that causes a change in the pressure distributionover the surface on which the actuator is placed. The air near the electrodes is weakly ionized, and there islittle or no heating of the air.

The body force per volume of plasma is a vector, given as

FB =

(− ε0λ2D

φ

)~E 1

where ε0 is the permittivity of free space (8.854 × 10−12F/m), λD is the Debye length, φ is the electric

potential, and ~E is the electric field vector, where

~E = −~∇Φ. 2

The Debye length is the characteristic length for electrostatic shielding in a plasma. It varies with plasmadensity and temperature as

1

λ2D

=e2n0

ε0

(1

kTi+

1

kTe

)3

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where kTi and kTe are the ion and electron temperatures, n0 is the plasma density, and e is the elementarycharge.

This body force vector can be tailored through the design of the electrode arrangement and dielectricmaterial, which control the spatial electric field. The body force representation is also a convenient formto incorporate the effect of the actuators in Navier-Stokes (N-S) simulations of the flow field. Such N-S simulations have been used to design and optimize different plasma actuator arrangements .7–9 Otheractuator optimizations come from the choice of the a.c. time series shape, which controls the amount andduration of the plasma .5,6

The plasma actuators are low power devices, with typical power levels of approximately 2-40 Watts perlinear foot of actuator span. They can be operated either in a “steady” or unsteady manner. In the “steady”operation, the input driving a.c. frequency is well above the fluid response frequency and therefore the flowsenses a constant body force. In unsteady operation, the higher driving a.c. frequency is switched on andoff at lower frequencies down to a fraction of a Hertz. The latter can be used to excite fluid instabilities thatact to further amplify the actuator effect. In the unsteady operation, very short duty cycles are possible,which reduce the actuator power significantly. For example, in applications of separation control in whichunsteady forcing is the most effective, a 10% duty cycle is sufficient, which lowers the power requirement by90% compared to steady operation .10,11

The important property of the single dielectric barrier discharge is that it is self-limiting and thereforestable at atmospheric pressures .5,6 During the a.c. cycle, the electrons and ions move according to theelectric potential, in an attempt to cancel it. In one-half of the cycle, electrons move from the exposedelectrode to the surface of the dielectric. The buildup of charge on the dielectric eventually balances thea.c. potential so the plasma generation stops. This is the self-limiting aspect of the dielectric barrier thatprevents a cascade of charges that would cause an electric arc. In the other half of the a.c. cycle, theplasma reforms and electrons that were deposited on the dielectric travel back to the exposed electrode.The electrons do not leave the dielectric as readily as they do the exposed electrode, and the volume of theplasma is reduced. Because the body force on the external flow is proportional to the volume of plasma, itsspace-time characteristic is essential for quantitative prediction of the actuator effect.

The first demonstration of the use of SDBD plasma actuators for lift control on wing sections withoutflow separations, was presented by Corke et al.12 This involved placing actuators near the trailing edge ofa NACA 0015 airfoil that were operated at a constant a.c. frequency, referred to as “steady operation”.The actuators were found to produce a shift to negative angles in the zero-lift angle-of-attack, α0L, whilemaintaining the same lift versus angle of attack slope, dCl/dα. The effect was then equivalent to that of apositively deflected trailing edge flap. This has been verified a second time in a different facility by Corkeet al.11 These later results included drag polars that demonstrated a translation of the drag bucket that isassociated with the increased camber effect of plane flaps.

Numerical simulations of the “steady” plasma actuator effect on lift enhancement on airfoils has beendone by Hall13 and Hall et al.14 This involved an inviscid panel method model in which the plasma actuatorwas simulated as a doublet. The similarities in the flow effects of the plasma actuator and inviscid doubletwere first demonstrated by Orlov et al.7 The simulations investigated the effects of the number, placementand amplitude of actuators on the lift coefficient for a range of angles of attack within the linear dCl/dαrange. The simulations were found to capture all of the results of the previous experiments. This thenprovided an efficient “design tool” for determining the optimum placement of plasma actuators to obtain liftcontrol that could be used for flight control.

The advantages of using plasma actuators instead of traditional trailing edge flaps or ailerons for flightcontrol are their simplicity, without need of moving surfaces, lower wing weight, and lower drag due to theelimination of hinge gaps that can account for as much as a 10% drag increase on the wing.15 The hinge gapis also a source of radar reflection which is a factor in some designs. In the ultimate application of plasmaactuators on wings, a “virtual shape” could come about by their judicious placement on the surface of ageneric shape. The choice of the generic shape might come from the consideration of such factors as wingstrength-to-weight or internal volume. The aerodynamics of the wing would then be varied according to theflight plan, e.g., high lift at take-off and landing, and a virtual drag bucket at the design Cl for efficientcruise and endurance.

Although the “steady operation” of plasma actuators have proven to be effective for lift control, we havean interest in further reducing the power required by the actuator, as well as obtaining larger changes in

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the lift coefficient per actuator input amplitude. One of the areas of great success of the plasma actuatorshas been in separation control. For example when applied to the leading edge of an airfoil, the maximumlift coefficient and stall angle of attack can be significantly increased.11 With separating flows, it has beendemonstrated11 that an optimum frequency exists at which the flow can be forced to reattach. In all of thepast applications, this frequency is nominally an order of magnitude lower than the a.c. frequency that isused to ionize the air over the actuator. The input time series to the plasma actuator is then the higherfrequency a.c. that is switched on and off at the lower frequency that is optimal for separation control. Ithas been shown11 that the duty cycle of the lower frequency can be reduced to as little as 10%, therebyreducing the power requirement compared to “steady operation” by 90%.

The concept of the plasma flow control optimized airfoil is to

1. use a laminar airfoil design that maintains a favorable pressure gradient over as much of the uppersurface as possible, and

2. incorporate a separation ramp at the trailing edge that can be manipulated by a plasma actuator inorder to control lift.

The advantages of this concept are intrinsicly lower drag than conventional airfoils because of the laminarflow profile, and a separated flow at the trailing edge that can easily be controlled with an unsteady plasmaactuator at very low power levels.

As a test of this approach, an HSNLF(1)-0213 airfoil is used. With this, the effect of unsteady plasmaactuators for controlling the lift coefficient versus angle of attack was investigated through numerical simu-lations and experiments. The effects of actuator frequency and amplitude, and chord Reynolds number werealso investigated in order to determine design scaling relations.

II. Results

A. Numerical Simulations

The HSNLF(1)-0213 airfoil is well known as a low-speed natural laminar flow profile. The profile and CFDsolution grid are shown in Figure 3. Experimental results of this profile for a range of Mach numbers from0.14 to 0.77 and a range of Reynolds numbers from 3 to 11 million are available from Sewall et al.16

The numerical results are obtained using a time-dependent, viscous compressible Navier-Stokes simulationthat includes a model for the plasma actuators. In this study, the algorithm used to solve the Navier-Stokesequations was CFL3D, which is a NASA developed code. This code solves the time-dependent conservationlaw form of the Reynolds-averaged Navier-Stokes equations. The spatial discretization involved a semi-discrete finite volume approach. Upwind-biasing is used for the convective and pressure terms, while centraldifferencing is used for the shear stress and heat transfer terms. Time advancement is implicit with theability to solve steady or unsteady flows.

The computational grid was generated using GRID3D software. In order to simulate the plasma actuator,the body force given by Eq[1] was separately solved numerically.17 This involved solving for the electrostaticpotential, Φ, given in Eq[2] which gives upon substitution, the following one-equation form

∇(ε∇Φ) = s(x, y)c2

λ2D

φ 4

where s(x, y) is a rectangular subdomain in the air over the plasma actuator that is 1 at the intersection ofthe exposed and covered electrodes (see Figure 1) and decreases exponentially to 0 at the downstream edgeof the covered electrode; and 0 over the exposed electrode. This spatial distribution is consistent with time-dependent light emission measurements of the plasma over the covered electrode during the a.c. cycle ,5,6

and a lumped-electrical model for the plasma actuator.17,18

The solution of the spatial distribution for the voltage potential is substituted into Eq[1] to obtain the

spatial body force, ~FB(x, y). This added body force is applied to the computational grid points at thelocation of the actuator in the solution of the flow field. For the “steady” actuator effect, the body forceis constant at every time step. For the “unsteady” actuator effect, the unsteady period during which theactuator is on and off is discretized into the solution time steps.

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−0.6 −0.4 −0.2 0 0.2 0.4 0.6−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

The location of the actuator

Figure 3. HSNLF(1)-0213 wing section shape and computational grid used in numerical simulations.The location of plasma actuator is at the upstream edge of the separation ramp, at x/C = 0.6.

The pressure coefficient distributions obtained from the simulations are presented in Figure 4. Thiscorresponds to a free-stream Mach number of 0.69 which can be directly compared to the experimentalresults of Sewall et al.16 The solid curve corresponds to base flow. The simulation slightly over-predicts theCp values in the upstream portion of the suction-side separation ramp (0.45 ≤ x/C ≤ 0.65). Otherwise thegeneral features are consistent with the experimental results.

The sharp drop in the Cp values over the suction surface past x/C = 0.6 is indicative of a flow separation.This can be seen in the skin friction distributions shown in Figure 5. The plasma actuator design and locationused in the simulation was intended to affect the separated flow. Both the “steady” and “unsteady” actuatorsin the simulations moved the separation location, as well as the degree and extent of the separated flow. The“unsteady” actuator was operated at a dimensionless frequency, F+ = fLsep/U∞ = 1, where Lsep is thestreawmwise extent of the flow separation. It is evident from the simulation for the same actuator amplitude,that the “unsteady” actuator is more effective in reducing the separation zone.

The manipulation of the separated zone by the plasma actuator in the simulations results in a change inthe lift and drag on the wing. This is demonstrated in Figure 6 which shows the lift and drag coefficientsfor a range of angle of attacks for the base flow, with a “steady” plasma actuator, and with an “unsteady”plasma actuator with F+ = 1. The simulations indicate that the plasma actuator effect on the separationzone results in a shift in α0L and movement of the drag bucket that is equivalent to a positive increase inthe wing camber. For the same actuator amplitude, the “unsteady” actuator produces a larger change inthe lift coefficient than the “steady” actuator. This has an even better result because in practice the powerused by the “unsteady” operation is nominally 1/10th that of the “steady” operation.

Our past experiments11,19,20 have indicated that periodic forcing at F+ = 1 is optimum for separationcontrol. Therefore we examined this with regards to the lift enhancement in the simulation for the HSNLF(1)-0213 wing section. The result is shown for M = 0.69 and α = 0 in Figure 7. This indicates that there is anoptimum frequency for the lift enhancement, and that it occurs at F+ = 1.

We were interested in examining the flow structure on the suction side of the airfoil, especially over theseparation ramp. To view this, we first computed flow streamlines. These are shown at the top part ofFigure 8 when viewed in a relative frame of reference moving at 0.6U∞. The relative frame of reference forthe streamlines brings out a spanwise oriented vortex that is associated with the separated zone. A more

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Figure 4. Pressure coefficient distribution around HSNLF(1)-0213 wing section for base flow, steadyand unsteady plasma actuators. Symbols show the experimental results from Sewall et al.16 atM = 0.69.

Figure 5. Skin friction distribution on suction side of HSNLF(1)-0213 wing section for base flow,steady and unsteady plasma actuators. M = 0.69.

quantitative approach for viewing vortices is the λ2 criterion first proposed by Joeng and Hussain.21 Thebottom part of Figure 8 shows contours of −λ2. This clearly identifies the center of the spanwise vortexobserved in the streamlines in the top part of the figure. In addition, it indicates a small vortex near thetrailing edge, suggesting a small flow separation at the trailing edge. In fact, this had also been identified in

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Figure 6. Lift coefficient versus angle of attack (left) and drag polar (right) for the base flow, with a“steady” plasma actuator, and an “unsteady” plasma actuator with F+ = 1. M = 0.69.

Figure 7. Effect of “unsteady” actuator frequency on lift coefficient enhancement for the airfoil atzero angle of attack. M = 0.69.

the numerical simulations of the flow over the same airfoil by Shiokawa at al.22

Figure 9 compares the effect of the actuator on the vortex structure over the separation ramp as identifiedby the λ2 criterion. Specifically it shows −λ2 contours over the upper surface of the airfoil for cases with theplasma actuator off (a), and on at the optimum unsteady frequency (F+ = 1) for the actuator amplitudeused for Figurefig:lift (b) and at an amplitude 20% larger (c).

With the “unsteady” actuator operating at F+ = 1, the −λ2 contours identify two additional vorticesover the airfoil trailing-edge ramp. This is consistent with the optimum reduced frequency if we substitute

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Figure 8. Flow streamlines viewed in a relative frame of reference moving at 0.6U∞ (top) and λ2

contours for the same flowfield (bottom). M = 0.69.

for the wave length in terms of the frequency, λ = c/f into the reduced frequency, namely

F+ = fLsep/U∞ =cL

λUinfty= 1. 5

The nominal convection speed of a large-scale vortex in a boundary layer is c = 0.5U∞. Therefore uponsubstitution

λ = 0.5Lsep. 6

Based on this scaling, we expect two vortices in the separated region when excited by the unsteady actu-ator at F+ = 1. This has also been observed in flow visualization in experiments using unsteady plasmaactuators.19,20

Focusing on Figure 9, the λ2 contours indicate that the size of the base-flow vortex is reduced by theunsteady plasma actuator. This is consistent with the skin friction distribution that was shown in Figure 5,which indicated a substantial reduction in the separated flow region with the unsteady actuator. A furtherreduction in the size of the base-flow vortex is evident in the lower plot when the actuator amplitude in thesimulation is increased by 20%.

One of the issues with the plasma actuator is how its effect on the lift coefficient for this airfoil scaleswith the free-stream speed or equivalently with the chord Reynolds number. This is illustrated in Figure10 which shows the effect of the chord Reynolds number on the change in lift coefficient produced by theunsteady actuator at F+ = 1 for a zero angle of attack. Here the solid curve corresponds to amplitudeused in Figure 6, and the dashed curve corresponds to a 20% higher actuator amplitude. Focusing on thelower amplitude (solid curve), up to Rec ∼= 300K there is only a slight dependence of the lift coefficient onReynolds number. Above that Reynolds number, the change in lift produced by the actuator with a fixedamplitude, is proportional to Re−1

c . The effect of the 20% higher actuator amplitude (dashed curve) is toproduce a larger change in the lift coefficient and thereby shift the curve upward in Figure 10. At the higheramplitude the region of Reynolds number independence has increased slightly to approximately Rec ∼= 400K.Above that Reynolds number the lift enhancement decreases at a slightly lower rate compared to the loweramplitude. The Re−1

c dependence observed here above Rec ∼= 300K is significantly better than that foundfor the “plasma flap” approach of Corke et al.11,12 and Hall,13,14 which had ∆CL ∝ Re−2. Therefore such

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Figure 9. −λ2 contours over the upper surface of the airfoil for cases with the plasma actuator off (a),and on at the optimum unsteady frequency (F+ = 1) for the actuator amplitude used for Figure 6 (b)and at an amplitude 20% larger (c). M = 0.69.

an optimized airfoil which utilizes a separation ramp can require significantly less power to implement athigher speeds.

B. Experiments

The experiments were conducted in one of the subsonic wind tunnels in the Center for Flow Physics andControl (FlowPAC) in the Hessert Laboratory at the University of Notre Dame. The facility is an open-return blow-down wind tunnel with a 45.72 cm (18 in) wide by 30.48 cm (12 in) high by 91.44 cm (3 ft) longtest section. The test section is equipped with a clear Plexiglas side-walls that allow optical access to viewthe model for flow visualization.

The HSNLF(1)-0213 airfoil was mounted vertically on the support sting of a lift-drag force balance. Theforce balance was mounted on the top of the test section. A photograph of the force balance with the airfoilin the test section is shown in Figure 11. A stepper motor on the force balance drove the angular position ofthe support sting. Its motion was controlled by the data acquisition computer through software. With this,the angular position was repeatable to within 0.005 degrees. The force balance used a strain-gauge bridge toprovide voltage outputs proportional to the respective lift and drag forces. Calibration of the force balancewas done by applying known weights to a cable pulley system attached to the support sting.

The HSNLF(1)-0213 airfoil had a 15.24 cm (6 in) chord and a 30.48 cm (12 in) span. The size of the

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Figure 10. Effect of chord Reynolds number on the change in lift coefficient produced by the unsteadyactuator at F+ = 1 for a zero angle of attack. Solid curve corresponds to amplitude used in Figure 6.Dashed curve corresponds to a 20% higher actuator amplitude.

Figure 11. Photograph of HSNLF(1)-0213 model mounted on force balance in wind tunnel test section.

airfoil was a balance between minimizing blockage effects and maintaining a large enough chord Reynoldsnumber. At the largest angle of attack of 18◦, the blockage was 1.7%, which required a minimal correctionfor the blockage in the measured lift and drag coefficients.

The airfoil was cast using an epoxy-based polymer in a two-piece mold. The mold was precisely machinedfrom an Aluminum plate using a numerical-controlled milling machine. A photographs of the airfoil in thelower half of the mold is shown in Figure 12.

A free-stream speed of 21 m/s was used in the experiments. This gave a chord Reynolds number of 215K.

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Figure 12. Photograph of cast HSNLF(1)-0213 wing model lying in lower half of machined aluminummold. Plasma actuator is visible on upper surface past maximum thickness x/C location.

The plasma actuator consisted of two copper electrodes separated by two 0.1 mm (2-mil.) thick Kaptonfilm layers. The electrodes were made from 0.0254 mm thick copper foil tape. The electrodes were arrangedin the asymmetric arrangement illustrated in Figure 1. They were overlapped by a small amount (of theorder of 1 mm), in order to ensure a uniform plasma in the full spanwise direction.

The plasma actuator was bonded directly to the surface of the airfoil. The location of the downstreamedge of the exposed electrode was at x/C = 0.6.

The frequency of the a.c. voltage supplied to the electrodes was between 5-8 kHz. The actual frequencywas tuned to minimize the overall power in the actuator electronics. The a.c. voltage amplitude to theelectrodes ranged from 7 to 11 kVp−p. The unsteady operation consisted of cycling the a.c. voltage off andon with an unsteady period, T . The percentage of time (duty) within the period that the a.c. was on wascontrollable. A duty cycle of 10% was used. The power was approximately 2 Watts per foot span.

The results for the experiment are presented Figure 13. This shows the lift coefficients versus angleof attack (left) and drag polar (right) for the measured base flow, and for an “unsteady” plasma actuatorwith F+ = 1. For reference, measurements from Sewall et al.16 at M = 0.10, which is comparable to ourexperiment, are shown as the filled squares. The drag coefficients have been normalized by CD0

of the baseflow to account for the drag on the support sting.

The linear portion of the lift versus angle of attack agrees well with the measurements in the literature.16

For the drag, the location of the minimum drag lift coefficient agrees with that in the literature, but their isnot as well a defined drag bucket.

The effect of the “unsteady” actuator at F+ = 1 is comparable to that in the previous numericalsimulations. That is, there is a nearly constant increase in CL that is consistent with an increase in themagnitude of ∆α0L. This has an accompanying shift in CLminD towards higher CL that is characteristic ofan increase in the wing camber.

III. Summary

The concept of a plasma flow control optimized airfoil for lift control without moving surfaces wasinvestigated. The basic features of this approach was to use a laminar airfoil design that maintains afavorable pressure gradient over as much of the upper surface as possible, and incorporate a separation rampat the trailing edge that can be manipulated by a plasma actuator in order to control lift. The advantagesof this concept are intrinsicly lower drag than conventional airfoils because of the laminar flow profile, anda separated flow at the trailing edge that can easily be controlled with an unsteady plasma actuator at verylow power levels.

As a test of this approach, an HSNLF(1)-0213 airfoil is used. With this, the effect of unsteady plasmaactuators for controlling the lift coefficient versus angle of attack was investigated through numerical simu-lations and experiments. The effects of actuator frequency and amplitude, and chord Reynolds number werealso investigated in order to determine design scaling relations.

The numerical simulations indicated that the an optimum frequency existed for the unsteady plasmaactuator to produce the maximum change in lift. This occurred at F+ = fLsep/U∞ = 1, where Lsep is thestreamwise extent of the separated zone. Operating at F+ = 1 resulted in the formation of two spanwise

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Figure 13. Lift coefficients versus angle of attack (left) and drag polar (right) for the measured baseflow, and for an “unsteady” plasma actuator with F+ = 1. Filled squares correspond to measurementsby Sewall et al.16 at M = 0.10

vortices with a streamwise wave length of 0.5Lsep. This significantly reduced the size of the separated zone,and increased the lift.

A nearly constant change in the lift coefficient occurred for angles of attack up to stall. This wasaccompanied by a shift in the lift coefficient at minimum drag. The result is consistent with an increase incamber that is a characteristic of the positive deflection of a plane flap. Numerical simulations indicatedthat for a constant actuator amplitude, the change in lift was nearly constant to approximately Rec = 300K,and for higher Reynolds numbers decreased as Re−1

c . This is significantly better than the “plasma flaps”previously investigated11–14 which decreased as Re−2

c . Therefore such an optimized airfoil which utilizesa separation ramp can require significantly less power and therefore has the potential to be implement athigher speeds.

Acknowledgment

This work was supported by Orbital Research Inc. under a SBIR Phase II Contract from the USAF/AFRL,MN, under Contract Number FA8651-05-C-0105, monitored by the USAF Program Manager Mr. EdwardoFreeman. The U.S. Government is authorized to reproduce and distribute reprints for government purposesnot withstanding any copyright notation therein.

References

1Post, M. and T. Corke. 2003. Separation control on high angle of attack airfoil using plasma actuators. AIAA Paper2003-1024, also AIAA J., 42, 11, p. 2177.

2Post, M. and Corke, T. 2004. Separation control using plasma actuators - stationary and oscillating airfoils. AIAA Paper2004-0841. Also AIAA J.

3Huang, J., Corke, T. and Thomas, F. 2003. Plasma actuators for separation control of low pressure turbine blades. AIAAPaper 2003-1027. To appear AIAA J.

4Corke, T. C. and Post, M. L., 2005. Overview of plasma flow control: concepts, opimization, and applications. AIAAPaper 2005-0563.

5Enloe, L, T. McLaughlin, VanDyken, Kachner, E. Jumper, and T. Corke. 2004. Mechanisms and Response of a singledielectric barrier plasma actuator: Plasma morphology. AIAA J., 42, 3, p. 589. Also AIAA 2003-1021.

6Enloe, L, T. McLaughlin, VanDyken, Kachner, E. Jumper, T. Corke.. M. Post, O. Haddad. 2004. Mechanisms andResponse of a single dielectric barrier plasma actuator: Geometric effects. AIAA J., 42, 3, p 585.

7Orlov, D., E. Erturk, M. Post, and T. Corke. 2001. DNS Modeling of Plasma Array Flow Actuators. Bulletin of theAmerican Physical Society Fluid Dynamics Division, Annual Meeting.

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8Orlov, D., T. Corke, and M. Post, 2002. DNS Modeling of plasma array flow actuators. Bulletin of the American PhysicalSociety Fluid Dynamics Division, Annual Meeting.

9Orlov, D., T. Corke, and Haddad, O., 2003. DNS Modeling of plasma actuators. Bulletin of the American Physical SocietyFluid Dynamics Division, Annual Meeting.

10Post, M. 2004. Plasma actuators for separation control on stationary and oscillating wings. Ph.D Dissertation, Universityof Notre Dame.

11Corke, T., He, C. and Patel, M., 2004. Plasma flaps and slats: an application of weakly-ionized plasma actuators. AIAAPaper 2004-2127.

12Corke, T., E. Jumper, M. Post, D. Orlov, and T. McLaughlin. 2002. Application of weakly-ionized plasmas as wingflow-control devices. AIAA Paper 2002-0350.

13Hall, K. D. 2004. Potential flow model for plasma actuation as a lift enhancement device. M.S Thesis, University of NotreDame.

14Hall, K., Jumper, E., Corke, T. and McLaughlin, T. 2005. Potential flow model of a plasma actuator as a lift enhancementdevice. AIAA Paper 2005-0783.

15Corke, T., Design of Aircraft, Prentice-Hall Publishers, New York, 2002.16Sewall, W., McGhee, R., Viken, J., Waggoner, E. Walker, B., and Millard, B. 1985. Wind tunnel results for a high-speed,

natural laminar-flow airfoil designed for general aviation aircraft. NASA TM 87602.17Orlov, D. and Corke, T. 2005. Numerical simulation of aerodynamic plasma actuator effects. AIAA Paper 2005-1083.18Orlov, D., Corke, T. and Patel. M. 2005. Electric circuit model for aerodynamic plasma actuator. AIAA Paper 2006-1206.19Huang, J. 2005. Documentation and control of flow separation on a linear cascade of Pak-B blades using plasma actuators.

Ph.D., University of Notre Dame, Notre Dame, Indiana.20Huang, J., Corke, T. and Thomas, F., 2005. Unsteady Plasmpa actuators for separation control of low pressure turbine

blades. To appear AIAA J..21Jeong, J. and Hussain, F. 1995. On the identification of a vortex. J. Fluid Mech., 285, p. 69-94.22Shiokawa, M., Matsushima, K., and Nakahashi, K. 2005. Design and aerodynamics of lift enhancement control for a single

element airfoil. AIAA Paper 2005-0853.

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