Annu. Rev. Fluid Mech. 2010 Corke

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    Dielectric Barrier DischargePlasma Actuators forFlow Control

    Thomas C. Corke, 1 C. Lon Enloe,2and Stephen P. Wilkinson 31Center for Flow Physics and Control, Aerospace and Mechanical Engineering Department,University of Notre Dame, Notre Dame, Indiana 46556; email: [email protected] of Physics, U.S. Air Force Academy, Colorado Springs, Colorado 80840

    3Flow Physics and Control Branch, NASA Langley Research Center, Hampton, Virginia 23681-2199

    Annu. Rev. Fluid Mech. 2010. 42:50529

    First published online as a Review in Advance onSeptember 21, 2009

    The Annual Review of Fluid Mechanics is online at uid.annualreviews.org

    This articles doi:10.1146/annurev-uid-121108-145550

    Copyright c 2010 by Annual Reviews. All rights reserved

    0066-4189/10/0115-0505$20.00 The U.S. Government has the right to retain anonexclusive, royalty-free license in and to any copyright covering this paper.

    Key Wordsaerodynamic control, ionized gasses, body force

    Abstract The term plasma actuator has now been a part of the uid dynamics control vernacular for more than a decade. A particular type of plasma aator that has gained wide use is based on a singledielectric barrierdischa(SDBD) mechanism that has desirable features for use in air at atmosphpressures. For these actuators, the mechanism of ow control is througgenerated body-force vector eld that couples with the momentum in external ow. The body force can be derived from rst principles, andeffect of plasma actuators can be easily incorporated into ow solvethat their placement and operation can be optimized. They have been uin a wide range of internal and external ow applications. Althoughtially considered useful only at low speeds, plasma actuators are effecta number of applications at high subsonic, transonic, and supersonic Mnumbers, owing largely to more optimized actuator designs that were veloped through better understanding and modeling of the actuator physNew applications continue to appear through a growing number of pgrams in the United States, Germany, France, England, the NetherlanRussia, Australia, Japan, and China. This review provides an overviethe physics and modeling of SDBD plasma actuators. It highlights somthe capabilities of plasma actuators through examples from experimentssimulations.

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    1. BACKGROUND There has been increasing interest in dielectric barrier discharge (DBD) plasma actuators forcontrol in the past 10 years worldwide. The tremendous growth in research stems from tspecial features, including the fact that they are fully electronic with no moving parts; a fasresponse for unsteady applications; a very low mass, which is especially important in applic with high g-loads; the ability to apply the actuators onto surfaces without the addition of cavitieholes; theefcient conversion of the input power without parasitic losses when properly optim

    (Enloe et al. 2004b, Orlov 2006, Roth & Dai 2006, Thomas et al. 2009); and the ability to simuleasily their effect in numerical ow solvers (Corke et al. 2006, Orlov 2006). The specic DBD conguration used for plasma actuators consists of two electrodes

    uncoated and exposed to the air and the other encapsulated by a dielectric material; hencerefer to this conguration as single dielectric barrier discharge (SDBD). For plasma actuapplications, the electrodes are arranged in a highly asymmetric geometry as opposed toparallel-plate arrangement common in industrial DBD uses. An example conguration is shin Figure 1 . The electrodes are supplied with an AC voltage that, at high enough levels, cthe air over the covered electrode to weakly ionize (typically less than 1-ppm weakly ionizeIn the classic description, the ionized air is a plasma, which is why these are referred to as pactuators (Cavalieri 1995, Corke & Matlis 2000, Corke et al. 2001). The ionized air appears

    characteristic of the composition of the air as ionized components of the air recombine anexcite (Davidson & ONeil 1964). The emission intensity is extremely low, requiring a darkspace to view by eye.

    In the presence of the electric eld produced by the electrode geometry, the ionized air rein a body-force vector eld that acts on the ambient (nonionized, neutrally charged) air. The bforce is the mechanism for active aerodynamic control.

    Langmuir (1928) introduced the term plasma into the physics literature to denote a net elecally neutral region of gas discharge. This denition has been broadened since and now refersystem of particles whose collective behavior is characterizedby long-range Coulomb interact

    Voltagesource AC

    Induced owPlasma

    Dielectric layer

    Actuator location reference

    Exposed electrode edge

    Coveredelectrode

    a

    b

    Figure 1Schematic illustration of a singledielectric barrier discharge plasma actuator (a) and photograph of ionizair at 1-atm pressure that forms over an electrode covered by a dielectric layer (b).

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    (Kunhardt 2000). Although plasmas are often simply considered as interpenetrating uids con-sisting of electrons, positive ions, and neutral particles, the air discharges consist of a multiplicity of species in numerous charge states, including negative ions. Nonetheless, the quasi-neutral ap-proximation applies to these, as to almost all, plasmasthat is, the total density of negatively andpositively charged particles in any region of the plasma is approximately equal, with only smalldeviations possible locally. Highlighting another property of plasma discharges in air, they areoften described as collisional; i.e., the electron-neutral collision frequency is of the order of, orgreater than, the plasma frequency (the characteristic frequency of electrostatic oscillations in theplasma). This is a property of air at atmospheric pressures typical of ight, the relevant regime forDBD plasma actuators.

    A gas discharge is created when an electric eld of sufcient amplitude is applied to a volume of gas to generate electron-ion pairs through electron impact ionizationof the neutral gas (Kunhardt 1980, Kunhardt & Luessen1981, LLewellyn-Jones1966, Raizer1991).This requires thepresenceof an initiating number of free electrons, which can either be present from ambient conditions orintroduced purposely (Kunhardt 1980, Kunhardt & Luessen 1981).

    A traditional (industrial) arrangement for creating a self-sustained gas discharge at low pressuresof a few torr or less has involved separated facing electrodes. The electric eld established by thetwo electrodes can either be by direct current (DC) or alternating current (AC). The plasma isgenerated by increasing the amplitude of the electric eld above the breakdown electric eld, E b, which is the value needed to sustain electron-ion pairs in the gas in the absence of space-charge elds (Kunhardt 1980, Kunhardt & Luessen 1981, LLewellyn-Jones 1966, Raizer 1991). The minimum breakdown electric eld is a function of the driving frequency. At atmosphericpressure, E b is generally lower for an AC input. The optimum AC frequency depends on the staticpressure and the particular gas. Once created, the electric eld needed to sustain the plasma, E s , islower than E b. The difference between the breakdown and sustaining electric elds is a functionof the operating conditions (LLewellyn-Jones 1966, Meek & Craggs 1978, Nasser 1971, Raizer1991).

    As a consequence of the plasma conductivity, there is a current, I , that ows between theelectrodes. A region is formed between the plasma and the cathode electrode, whose role is toprovide current continuity at this interface. The current in the boundary region consists of twocomponents: the conduction current, I c , and the displacement current, I d . For DC elds, I d is zero,and the remaining conduction current consists of electron and ion components. For AC elds,the contribution of the displacement current to the total current increases with frequency and canbecome an important practical consideration in power-supply design.

    Whenthe operatingconditions (applied eld, electrode cross-sectional area, andstatic pressure)are such that the current density in the boundary region near the cathode is independent of thecurrent owingin thecircuit, thedischargeis calleda normalglow discharge(Kunhardt& Luessen1981, LLewellyn-Jones 1966, Meek & Craggs 1978, Nasser 1971, Raizer 1991, Roth 1995). Forconstant current, the current density in a normal glow discharge scales with the square of thestatic pressure. Therefore, the cross-sectional area of plasma decreases with increasing pressure at constant current. As the static pressure increases at constant current, the current density increasesuntil the threshold for the development of instabilities leading to a transition to an arc phase isreached. The threshold current for the development of the glow-to-arc transition depends on theoperating conditions of the discharge.

    Many aerodynamic ow-control applications would require plasma actuators to operate nearatmospheric pressure. This favors AC operation over DC because of the lower breakdown voltagerequirement andlack of real currents responsible forelectrode corrosioneffects. In addition,whenconsidering any gain an application might provide in system efciency, one needs to factor in the

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    power required to operate the actuators. Thus there is a need to consider the actuators mefcient operating conditions to maximize its effect with respect to input power.

    Barrier discharges can be operated in various modes (e.g., diffuse, patterned, lamentarycrodischarge), and the terminology can often become confusing. A good review of the vamodes and terms is presented by Kogelschatz (2002). All techniques, however, use a dielbarrier on the surface of one or both electrodes. Okazaki and coworkers were among the ruse this approach (Kanazawa et al. 1988, 1989, 1990; Kogoma & Okazaki 1994; Okazaki1993; Yokoyama et al. 1990). In this case, because of the dielectric layer, the electrodes menergized with an AC eld. Barrier discharges have been operated historically in the micrcharge mode (Eliasson & Kogelschatz 1991, Kogelschatz et al. 1997). In this mode, the discconsists of a number of parallel laments, each of which has a limited lifetime. The lamenessentially streamer discharges whose lifetimes are governed by the capacitance of the diebarrier (Eliasson & Kogelschatz 1991). The passage of the streamer across the discharglocally charges this capacitance, reversing the local eld and thus terminating the lament.

    In sinusoidally driven DBDs, the plasma forms in nonthermal equilibrium (not to be conf with nonequilibrium plasma due to excitation time dependency) in which the electrical encoupled into the gas is mainly used to produce energetic electrons while the gas remains apimately at ambient temperature, rising only slightly. This is because of the self-terminatiothe discharge, which prevents microdischarges from degenerating into thermal arcs (Falken& Coogan 1997). Self-termination results from the accumulation of electrons at the dielesurface facing the cathode. The internal electric eld caused by the accumulation of electronthe dielectric surface reduces the local eld strength, and the microdischarges choke themsas the extinction eld is reached (Falkenstein & Coogan 1997).

    For an SDBD, during one half of the AC cycle, electrons leave the metal electrode and toward the dielectric, where they accumulate locally. In the reverse half of the cycle, electrosuppliedbysurfacedischargesonthedielectricandmovetowardthemetalelectrode.Thetimesof the process depends on the gas composition, excitation frequency, and other parameters. Iat atmospheric pressure, it occurs within a few tens of nanoseconds (Falkenstein & Coogan 1

    Kline et al. (2001) have studied time-resolved images of spatiotemporal patterns in adimensional (1D) DBDsystem. They obtained images of plasma laments that revealed dischastages that lasted only approximately 100 ns. Several discharge stages could occur during acycle of the driving oscillation, each producing a distinct lament pattern. In some dischathere was a temporal structure but spatial disorder, and in others there was both temporalspatial disorder.

    The dielectric barrier conguration also supports a uniform diffuse discharge operationshown by Okazaki and coworkers (Kanazawa et al. 1988). The mechanisms that play a role are well understood (e.g., Decomps et al. 1994; Roth 1995; Massines et al. 1996, 1998; Tet al. 1998). The stability of the diffuse mode depends on the AC frequency, the gas typethe excitation power. The discharge is most stable in helium and mixtures that contain helalthough other gases have been used including air (Decomps et al. 1994; Kanzawa et al. Massines et al. 1996, 1998; Roth 1995; Trunec et al. 1998). The electrode separation is usmall, of the order of a few centimeters. The electron density of the plasma generatedby this mis of the order of 1010 cm 3. Although interesting from a scientic standpoint, the conditions support this mode of the discharge are specic enough that they are unlikely to be encounin a device designed for aerodynamic applications.

    Massines and coworkers (BenGadri et al. 1994, Massines et al. 1998, Rabehi et al. 199 veloped a 1D model for the DBD dynamics based on the numerical solution of the electronion continuity and momentum transfer equations coupled to Poissons equation. As is typic

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    Flow direction

    CoveredelectrodeExposedelectrode

    Plasma actuator(top view)

    Figure 2Photograph of smoke tube introduced at the edge of a boundary layer that is bent toward the wall by a plasmaactuator oriented so that the electrodes are parallel to the streamwise direction. Figure taken from Post 2001.

    high-pressure discharges, the electrons and ions were assumed to be in equilibrium with the elec-tric eld. Their model gave space and time variations in the electric eld, and the electron and iondensities. The authors accounted for the charge accumulation on the dielectric as the dischargedevelops and derived the voltage boundary conditions for dielectrics by considering an equivalent circuit of the gas gap in series with the equivalent capacitor of the dielectric.

    One of the earliest low-speed demonstrations of a plasma actuator was performed by Rothet al. (1998, 2000). They utilized an array of electrodes separated by a glass-epoxy printed-circuit board to manipulate the boundary-layer ow over a at plate at free-stream velocities from 4 to26 m s 1. They investigated a number of electrode geometries, one of which was similar to that shown in Figure 1 . With this electrode conguration, they observed that ambient air, marked by smoke, was drawn toward the covered electrode. A similar photograph recorded by Post (2001) isshown in Figure 2 . In this case, the electrodes are aligned parallel to the mean ow direction. Thisaccentuates the width of the stream tube that is drawn toward the wall by the actuator. Velocity surveys of the actuator-induced ow by Roth et al. (1998, 2000) documented a wall-normal mean velocity prole that is similar to what might be produced by a tangential wall jet. The deectionof the external ow toward the surface of the dielectric and the jetting of the ow in the directionof the exposed electrode toward the covered electrode are hallmarks of this actuator design. Any simulation models for these actuators need to produce this behavior.

    2. DIELECTRIC BARRIER DISCHARGE ACTUATOR PHYSICS

    2.1. Experimental Observations

    In classic DBD processes, the input waveform is sinusoidal. When the AC amplitude is largeenough so that the electric eld exceeds E b, the air ionizes. The ionized air is always observedto form over the electrode that is covered by the dielectric. To the unaided eye, the ionized airappears to be generally uniform in color and distribution, with some structure evident that oftenappears attached to a particular location on the exposed electrode. The photograph in Figure 1is a typical example. Time-resolved images of the ionization process, however, indicate it to bea highly dynamic, spatially evolving, nonequilibrium process with features that develop on thetimescale of the AC period (milliseconds) or less.

    Enloe et al. (2004a) studied the space-time evolution of the ionized-air light emission over asurface-mounted plasma actuator using a photomultiplier tube tted with a double-slit aperture

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    P M T o u t p u t

    n o r m a l i z e d b y m a x i m u m

    V o l t a g e

    Time (10 4 s) Time (10 4 s)

    1.0

    0.8

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    01 0 1 2 3 4 5 1 0 1 2 3 4 5

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    Figure 3 Time series of photomultiplier-tube (PMT) output ( a) that is viewing ionized-air light emission at one location over an electrodecovered by a dielectric and corresponding AC input (b) to a plasma actuator. Figure taken from Orlov 2006.

    to focus on a narrow 2D region of the plasma. The slit was parallel to the edge of the exelectrode and could be moved to different locations over the electrode covered by the dielectrsample time series from Orlov (2006) of the photomultiplier-tube output that was acquired plocked with the AC input to the actuator is shown in Figure 3 . The light emission is taken aindication of the plasma density, which is a good assumption based on the disparate timebetween the recombination time (order of 10 8 s) (Vidmar & Stalder 2003) and the dischtimescale (order of 10 3 s).

    There are several fundamental features of light-emission time series. First, the air is ioonly over part of the AC cycle. Second, when it does ionize, its character differs between thand second halves of the AC cycle. Finally, the light emission is made up of narrow spikemight indicate numerous microdischarges. Similar observations have been documented by Eet al. (2004a), Massines et al. (1998), Eliasson & Kogelschatz (1991), and Kogelschatz et al. (1 who generally characterize this process as a DBD.

    The explanation for the difference in the emission character in the two half-cycles is asso with the source of electrons. During the negative-going half-cycle, the electrons originate frombare electrode, which is essentially an innite source that readily gives them up. In the posgoing half-cycle, the electrons originate from the dielectric surface. These apparently docome off as readily, or when they do, they come in the form of fewer, larger microdischargesstructural difference ineach dischargemode isevident inhigh-speed imagesof themicrodischathat, in fact, make up the apparently uniform actuator discharge (Figure 4 ). This asymmetry beenmodeled by Boeuf et al. (2007)and plays an important role in the efciency of the momencoupling to the neutrals. It further suggests that some optimization can come in the selectiothe AC waveform to improve the performance of the plasma actuator.

    Figure 5 shows a composite of light-emission time series similar to the one in Figure 3 measured at differentpositionsoverthedielectricsurface. These areshownas contours of conslight-emission intensity for one period, T , of the AC cycle.

    The space-time character of the plasma light emission over the covered electrode has a numof interesting features. For example, there is a sharp amplitude peak near the edge of the expelectrode at the rst initiation of the plasma. As time increases, the plasma sweeps out fro junction to cover a portion of the encapsulated electrode. This was similarly noted by Gibal

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    a

    b

    Figure 4High-speed (5-ms exposure) photographs of individual microdischarges in the negative-going (a) andpositive-going (b) phases of plasma-actuator discharge, highlighting the structural asymmetry between thephases. Figure taken from Enloe et al. 2008.

    Pietsch (2000). As the plasma sweeps out away from the edge of the exposed electrode, its light emission appears to become less intense. Estimates (Enloe et al. 2004a, Orlov 2006, Orlov et al.2006) indicate that the intensity decreases exponentially from the junction. This led to the use of an exponential weighting to correct the spatial dependency of the plasma actuator body force inearlier electrostatic ow simulations (Orlov et al. 2003, Orlov & Corke 2005, Voikov et al. 2004). Two global features of the space-time evolution of the plasma formation are the velocity at whichthe plasma front moves across the dielectric and the maximum extent of the plasma during the AC cycle. The velocity is represented by the slope, dx / dt , of the front. In Figure 5 , the velocity of the fronts is approximately the same for the two halves of the AC cycle, but the plasma extent differs. We note that these measurements indicate the time development of the envelope of themultiple microdischarges that compose the DBD. Although Hoskinson et al. (2008) have beenable to make some estimates of thedevelopment rate of individual microdischarges through carefulexamination of fast (280 ns) gated images, no experimental apparatus exists that can implement frame rates in the hundreds of megahertz that would be necessary to image the development of an individual microdischarge event.

    Orlov (2006)investigated theeffectsofvoltage andACfrequencyon theextent andpropagation velocity of the discharge. He found that the maximum extent increased linearly with increasing AC voltage amplitude, and it was independent of the AC frequency. However, the velocity of theplasma front increased linearly with both AC amplitude and frequency. In Orlovs measurements,the velocity of the discharge front ranged from 70 to 190 m s 1.

    As mentioned above, plasma actuators with the asymmetric electrode design inFigure 1 inducea velocity eld similar to that of a tangential wall jet. Enloe et al. (2004b) correlated the reactionforce (thrust) generated by the induced ow with the actuator AC amplitude. A similar experi-ment was performed by Thomas et al. (2009) to investigate parameters in the actuator design.

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    0 10 200

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    Figure 5Space-time variation of the measured plasma light emission for a singledielectric barrier discharge plaactuator corresponding to one period, T , of the input AC cycle. The x axis is the distance over the coverelectrode measured from the edge of the bare electrode at the interface of the covered electrode. Figuretaken from Orlov 2006, Orlov et al. 2006.

    A schematic of their setup and sample results are shown in Figure 6 . At the lower voltages,induced thrust was proportional to V 3.5 AC . This was rst observed by Enloe et al. (2004b). Thoet al. (2009) veried the consistency between the reaction force and the uid momentum btegrating the velocity proles downstream of the actuator. Post (2004) found that the maximinduced velocity was proportional to V 3.5 AC , which is consistent with conserved momentum inself-similar velocity-prole region near the actuator.

    Post (2004) and Enloe et al. (2004b) showed that, with increasing AC amplitude, the maxi velocity induced by the plasma actuator was limited by the area (extent for a unit spanwise of the covered electrode. Thus the dielectric area needed to store charge can be too small tofull advantage of the applied voltage. This effect can be observed in the thrust measuremeFigure 6 at the highest voltages for the Teon dielectric, at which the thrust no longer increas V 3.5 AC and begins to asymptote.

    Enloeetal.(2004a)computedthepowerdissipationinthedischargebysamplingthevoltagecurrent waveformsacross theelectrodes andnumerically integrating the product of the wavefoover one period of the discharge to integrate out the reactive power and account exclusfor the power dissipated in the plasma. The dissipated power also followed V 3.5 AC , indicatindirect proportionality with the induced momentum. They considered a model for the air abthe dielectric material covering the electrode that consisted of a capacitor and resistor in sFigure 7 shows this model for the SDBD plasma actuator. Before the air ionizes, the capaC 1, corresponds to the value for air. When the air ionizes, this capacitor effectively bec

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    Dielectric

    Insulator

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    Spring scale Induced thrust

    Induced ow

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    T h r u s t ( g m )

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    12 188 10 14 16 20

    TeonGlassT = C 1V 3.5

    a b

    Figure 6Schematic of experimental setup for measuring induced thrust from a singledielectric barrier dischargeplasma actuator (a) and measured thrust versus applied AC voltage (b). Figure taken from Thomas et al.(2009).

    a short circuit. The remaining circuit elements, R1 and C 2, then form a voltage divider. Theimpedance, Z 2, of the capacitance, C 2, is given as Z 2 = i / C 2, where = 2/ f AC , and f AC isthe AC frequency. For a xed frequency, C 2 would be a constant. Then one might expect that theelectrical power dissipated by the plasma would be V 2 AC / R1 or generally be proportional to V 2 AC .However, experiments (Enloe et al. 2004a) indicate that this is not the case.

    There are several possible reasons why the power dissipated by the plasma is not proportionalto V 2ac . These include (a) that C 2 is not constant but increases with the applied AC voltage and/or(b) that R1 decreases with increasing applied AC voltage.

    Considering that the sweep-out velocity of the plasma front has been documented to increase with increasing voltage, the area over the dielectric that composes the capacitance, C 2, increasesfasterwith increasing voltage.Therefore, thevalue of C 2 isnotconstant but increases in proportion

    Plasma

    Exposed electrode

    Dielectric surface

    Insulated electrode

    V ac

    R p C 1 A C 1B

    C 2BC 2 AC 3

    Figure 7Lumped-element circuit model of a singledielectric barrier discharge plasma actuator. Figure taken fromEnloe et al. 2004a.

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    0.14

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    E ffi c i e n c y ( m N / W )

    Gas composition (% O 2)

    Figure 8Plasma-actuator net-force production as a function of the percentage of oxygen. Figure taken from Enloet al. 2006.

    to V AC . With regard to R1, numerical simulations of the circuit in Figure 7 intended to repduce the output waveforms observed in experiments indicated that the resistance needed toinversely with the applied voltage (Enloe et al. 2004a). Therefore, both effects are in play.

    The dependency of the dissipated power in the plasma and the induced momentum onapplied voltage is an important characteristic that any physical model needs to replicate. Tresults indicate that models must include the dynamics of the plasma initiation and sweepover the dielectric covered electrode that occurs twice during the AC period. Naude et al.s (electrical model for DBD addressed this with the addition of electrical elements (Zener dithat switchthecurrent path betweendifferentpassivecircuit elements to control thecharacterist with voltage and frequency.

    One nal attribute of DBD plasmas as aerodynamic actuators (as opposed to their dischcharacteristics alone) is the importance of the species composition of the plasma, specicaldramatic difference that the presence of oxygen in the air makes in the actuators force productiEnloe et al. (2006) showed, and other experimenters have subsequently conrmed, that remooxygen from the air surrounding the plasma actuator only modestly changes its discharge perties (20% in such parameters as discharge current for a given voltage). However, its remresults in a dramatic reduction in the net force produced (by up to 80%). This is illustrateFigure 8 . The propensity of oxygen to form negative ions (by electron attachment) adds a spto the composition of the plasma that is usually not accounted for in the typical analysis of plthat assumes that positive ions and negative electrons are formed in equal numbers.

    2.2. Dielectric Barrier Discharge Body-Force ModelsOne of the rst models for a DBD plasma actuator, developed by Massines et al. (1998), 1D model based on a simultaneous solution of the continuity equations for charged and exparticles and the Poisson equation.

    Paulus et al. (1999) developed a particle-in-cell simulation to study the time-dependent lution of the potential and the electrical eld surrounding 2D objects during a high-volpulse. The numerical procedure was based on the solution of the Poisson equation on a grid

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    domain containing an L-shaped electrode to determine the movement of the particles through thegrid. The simulation showed that the charged particles move toward the regions of high electricpotential, creating a high-electric-eld strength near the electrodes edges. In addition, it showedthat the plasma builds up on a very short, microsecond, timescale.

    A model for the body force produced by the plasma on the neutral air was presented by Rothand colleagues (Roth et al. 2000, Roth & Dai 2006). This model was based on a derivation of theforces in gaseous dielectrics given by Landau & Lifshitz (1984). The body force is proportionalto the gradient of the squared electric eld, namely

    f b = d d x

    12

    0 E 2 . (1)

    This model can be problematic as it is based on a static formulation and does not account for thepresence of the charged particles, both of which have been shown to be important in experiments.Boeuf & Pitchford (2005) raised the same warning in their derivation of Equation 1. Enloe et al.(2004b) further showed that the body force given by Equation 1 is only correct in the special caseof a 1D condition where E = E x i , E y = E z = 0, and / y = / z = 0. This special case is not relevant to physical applications that are at least 2D.

    Shyy et al. (2002) presented a model for the body force that is widely used in the literaturebecause of its simplicity. A basic assumption of this model is that the electric-eld strength, E ,decreases linearly from theedge of thebare electrode towardthedielectric-covered electrode.Thisassumption is not consistent with experiments (Enloe et al. 2004b, Orlov 2006, Orlov et al. 2006), which show an exponential spatial decay. As a result, the model overpredicts the actuator effect.Furthermore, it produces body-force vectors that point away from the dielectric surface, whichis again inconsistent with experiments. Finally, the body-force magnitude in the model is a linearfunction of the AC voltage rather than being proportional to V 3.5 AC , as observed in experiments.

    Singh&Roy(2008)usedtheresultsofthebodyforcesobtainedfromarst-principlesimulationalong with empirical observations of actuator behavior to develop an approximation for the 2Dbody-force components. This approach makes the calculation of the body force a curve-ttingproblem that is only valid for a single-actuator conguration. Similar to Shyy et al.s model, it does not include temporal characteristics of the body force, and the net body force does not scaleproperly with voltage.

    Suzen and colleagues (Suzen et al. 2005, Suzen & Huang 2006) utilized the electrostatic model with an imposed Gaussian distribution for the spatial charge distribution to compute the plasmabody force using Enloe et al.s (2004a,b) formulation. They proposed to split the electrostaticequations into two parts: the rst part due to the external electric eld and the second part due tothe electric eld created by the charged particles. Qualitatively, the net body-force vectors appearto be physical. However, the scaling with AC voltage is incorrect, being proportional to V 2 AC . Suchscaling is a closed-form solution of the electrostatic model (Orlov 2006), from which Suzen et al.smodel originated.

    Boeuf & Pitchford (2005) considered a collisional discharge in a numerical estimation of theforce acting on gas molecules in a 2D asymmetric surface DBD. For this, they considered nitrogenat atmospheric pressure. They concluded that the asymmetry in the electrode conguration in-duces an asymmetry in the ow, comparable with a DC force in surface corona discharges. Boeuf et al. (2007) subsequently extended their simulation to encompass multiple microdischarge eventsand not only were able to simulate the qualitative difference between positive- and negative-goingdischarges that experimentershave observed, they also concluded that it is the electric-eld effectson the charged particles left after these microdischarges terminate that are the predominate causeof force production by the actuator.

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    There have been numerous models developed for DBDs in air that include complicated chistry. These models usually include 2030 reaction equations, each with different reaction tand energy outputs. These equations account for electron, ion-neutral, and neutral-neutral actions in different gases that are present in the air (Gibalov & Pietsch 2000, Golubovskii 2002, Kozlov et al. 2001, Madani et al. 2003, Pai et al. 1996). For the most part, these models wdeveloped for simple 1D geometries consisting of axisymmetric facing electrodes. To simplichemistry, Font and coworkers (Font 2004, Font & Morgan 2005) recently considered the pladischarge in a 2D asymmetric plasma actuator that included only nitrogen and oxygen react With this model, they were able to simulate the propagation of a single streamer from theelectrode to the dielectric surface and back.

    Likhanskii et al. (2006) modeled the weakly ionized-air plasma as a four-component mixtneutral molecules, electrons, and positive and negative ions that included ionization and rebination processes. Their simulations indicated the importance of the presence of negative in the air. They also suggest that the charging of the dielectric surface by electrons in the catphase is critical, during which they believe it acts as a harpoon pulling positive ions forwaaccelerating the gas in the anode phase.

    Generally speaking, the charged-particle models can precisely describe all the differentcesses involved in the plasma actuator. However, they are computationally time-consumingrequire signicant computer resources. This is especially true if they are applied to air at atmospheric pressures. Such simulations are not suitable to be a part of a design tool that wbe used in the iterative optimization of the plasma actuators and the design of ow-control acations based on plasma actuators.

    Orlov and colleagues (Orlov 2006, Orlov et al. 2006) addressed the need for anefcient metto predict the body-force eld of SDBD plasma actuators by developing a space-time lumelement circuit model that is a variation of the one proposed by Enloe et al. (2004a) showFigure 7 .

    A schematic of Orlov and colleagues (Orlov 2006, Orlov et al. 2006) model is shoFigure 9 . The unique aspect of this model is the division of the domain over the covered electrinto N parallel networks. The properties of each parallel network depend on its distance fromexposed electrode. These were designated parallel network 1, which is closest to the expelectrode, to parallel network N , which extends the furthest distance over the covered electr

    Each parallel network consists of an air capacitor, a dielectric capacitor, and a plasma-reselement, as in the earlier model (Enloe et al. 2004a, Orlov 2006). Zener diodes were added a threshold voltage level at which the plasma initiates and to switch into the circuit the difplasma-resistance values based on the current direction, which experiments had shown important. The N -circuit arrangement is illustrated in Figure 9 .

    The values of the air capacitor and resistor in the n-th subcircuit are based on their distafrom the edge of the exposed electrode. The value of the dielectric capacitor for each subcis a property of the dielectric material. Assuming that the paths are parallel to each other, anlength of path, I n, is proportional to its position number, n, it then follows that the air capacitaof the n-th subcircuit, C an, is proportional to 1/ n, and the air resistance of the n-th subcircuiproportional to n. Based on this, subcircuits that are furthest from the edge of the electrodes the lowest air capacitance and the largest air resistance.

    For a time-varying (AC) applied voltage, the voltage on the surface of the dielectric at th nparallel network is given as

    d V n(t )dt

    = d V app(t )dt

    C anC an + C dn

    + kn I pn(t )

    C an + C dn,

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    Parallel subcircuits

    l n

    NN4321

    Covered electrode

    Covered electrode

    Dielectric layer

    Exposed electrode

    Exposed electrode

    AC voltage source

    Dielectric surface

    V app

    C 1d C 2d C nd

    C 1a C 2a C na

    D1f

    R1f

    D1b

    R1b

    D2f

    R2f

    Dnf

    Rnf

    D2b

    R2b

    Dnb

    Rnb

    a

    b

    Figure 9Space-time lumped-element circuit model for a singledielectric barrier discharge plasma actuator that divides the region over a covered electrode into N subregions (a) that each represents a parallel arrangement of circuit elements (b). Figure taken from Orlov 2006, Orlov et al. 2006.

    where I pn(t ) is the time-varyingcurrent through theplasmaresistor, and thediodes are representedby thevariablekn. When the thresholdvoltageis exceeded,kn = 1. Otherwise,kn = 0.Thecurrent through the n-th plasma resistance is given by

    I pn (t ) = 1 Rn

    V app(t ) V n(t ) , (3)

    where Rn = Rnf or Rn = Rnb, basedon thecurrent direction.The ratioof thetwoplasmaresistancesused by Orlov and colleagues (Orlov 2006, Orlov et al. 2006) was Rnf / Rnb = 5, which was basedon the difference in the currents measured in experiments (Orlov 2006).

    The solution of the model equations gives the voltage on the surface of the dielectric, V n(t ),and the current, I pn (t ), for each parallel circuit element. The space-time variation in the rectiedcurrent agreed well with the experimental observations of the plasma light emission (Figures 3and 5) for a large range of AC voltages and frequencies (Orlov 2006, Orlov et al. 2006).

    The space-time dependent voltage, V n(t ), from the lumped-element model serves as the time-dependentboundaryconditionfor theelectric potential, ,foundinthesolutionoftheelectrostaticPoisson equation:

    ( ) = 1 2D. (4)

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    x (t )

    Bare electrodeBC:V app (t )

    DielectricBC:V n(t )

    DielectricBC:V = 0

    Figure 10Computational domain for calculation of unsteady plasma body force. BC refers to boundary conditionsused in solving Equation 4.

    The time-dependent extent of the plasma on the surface of the dielectric, x(t ), species the reg where charged particles are present above the covered electrode. This denes a moving bounas shown in Figure 10 . The boundary value of the electric potential on the bare electrode is

    applied voltage V app(t ). At the outer boundaries at innity, the boundary conditions are = 0 The electric potential, (t ), is determined at small time steps of the AC cycle. It is then

    to calculate the time-dependent body force produced by the plasma, given by

    f b (t ) = c E (t ) = 0 2D

    (t ) E (t ),

    where it is necessary to keep track of the direction of the current, which signies the sign ocharge, , on the dielectric, and therefore the sign convention for the body force.

    This model certainly has the benet of being computationally efcient. The question is,correct? Or, more accurately, do the assumptions of the model made in the interest of efcistill allow it to replicate the behavior of the actuator, or is too much of the essential physic

    Orlov and colleagues model allows the plasma boundary conditions to evolve over a timthat is short compared with that of the AC waveform that is driving the actuator. As a dconsequence, the net (AC cycle-averaged) body force from this model scales as V 3.5 AC , which agr with experiments (Orlov 2006). It also predicts an asymptote in the body force at higher voltagthe covered electrode is too small.The model also indicates that for a givenplasmaactuatordesthere is an optimum AC frequency that maximizes the net body force. These are considerathat relate directly to how an actuator might be elded in a practical system.

    Nonetheless, the model, by necessity, cannot describe the evolution of the microdischathemselves, during which time the local nonuniformities in charge density are the most extr This may not be as signicant a drawback as one might think. The results of the moddone by Boeuf et al. (2007) indicate that although the forces on the plasma are greatesting these short (tens of nanoseconds) periods, in fact the largest contribution to the total fis a result of the electric elds interaction with the charged particles remaining after thecrodischarges have terminated because these particles outlive the microdischarges by ordemagnitude (microseconds).

    Orlov and colleagues model does not explicitly address the effect of oxygen and its propto form negative as well as positive ions, but in fact it does encompass this phenomenon impEquation 5 effectively states that the force on the neutrals is the same as the force on the plOn one hand, this is an excellent assumption: The ionized particles represent such a small fra

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    of the air that the probability of an ion or electron crossing the gap between the electrode andthe dielectric surface (or back) without interacting with a neutral molecule is vanishingly small.On the other hand, the momentum-transfer cross section for electrons on neutrals is substantially smaller than that for ions on neutrals, so the assumption that one can simply track the net chargedensity, c , to compute the force on the neutrals by the plasma is incorrect. If, conversely, enoughelectrons attach themselves to the oxygen molecules to form large, heavy negative oxygen ions,the electric force on the ions is the same as on the original electrons, but the momentum-transfercross section is increased, so that, in fact, the implicit assumption of Equation 5 is satised.

    A frequently discussed topic is the vector direction of the plasma body force during the ACcycle. The formulation given in Equation 5 indicates that throughout the AC cycle, the body force is always oriented in the direction from the bare electrode toward the covered electrode. This could be the result of the assumptions made in the formulation of the model, in particularthe quasi-steady assumption that the timescale of the electron and ion movement is much smallerthan the AC period.

    This is certainly true for the electrons. The question is whether it is true for the ions. Thecharged-particle simulations of Font and colleagues (Font 2004, Font & Morgan 2005) that in-cluded nitrogen and oxygen reactions followed the propagation of a single streamer from the bareelectrode to the dielectric surface and back. They suggested that during the forward discharge(when the electrons are pushed away from the bare electrode and the positive ions are pulledback toward the bare electrode), the net momentum is not zero, but favors the ions so that thereis a net momentum toward the bare electrode. In the back discharge (when the electric eld isreversed), their simulations have a resultant force that is away from the bare electrode, toward thedielectric [as in Orlov and colleagues (Orlov 2006, Orlov et al. 2006) model]. The magnitude of body force in the back discharge was signicantly larger than in the forward discharge so that thecycle-averaged vector from the simulation was overwhelmingly toward the dielectric, as observedin the time-averaged experiments (Thomas et al. 2009).

    Font and colleagues scenario might be categorized as PUSH-pull, in which the upper- or low-ercase words signify the relative magnitude. Orlov and colleagues model would indicate PUSH-push. What is the experimental evidence?

    Forte et al. (2006) performed time-resolved laser-Doppler-velocimetry measurements of theow induced by anSDBDplasmaactuator similar to that shown inFigure 1 , ina quiescent neutralow. They were able to capture the streamwise and wall-normal velocity components within aperiod of the AC input. The laser-Doppler-velocimetry measurements indicated that during the AC cycle, theu component oscillatedbetween a large positiveu and a small but positiveu, and wasnever negative. This result supports a PUSH-push scenario. Kim et al. (2007) arrived at the sameconclusion by observing ows with time-resolvedparticle-image velocimetry. Recent experimentsby Enloe and colleagues (Enloe et al. 2009, Porter et al. 2007) indicate (using an entirely different experimental method) a PUSH-push scenario when the net effect of the actuator is concerned, with the magnitude of the effect of the plasma alone being comparable on both the negative- andpositive-going half-cycles, bringing these experimental results into closer agreement with thosepredicted by Orlov and colleagues (Orlov et al. 2006, Orlov 2006) model. Given that the sameeffect is shown by drastically different means, it seems well established that both half-cycles of thedischarge add momentum to the ow in the same direction.

    2.3. Optimization The insight that comes from developing a better understanding of the physics behind the SDBDplasma actuator can suggest approaches to optimize its performance. The following sections pro- vide some examples.

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    2.3.1. AC waveform. The observations that the ionization occurs as long as the differencetween the instantaneous AC potential and the charge buildup on the dielectric exceeds a thresh value suggest that there are AC waveforms that are optimal. For example, a square wave optimum, a sine wave is better, and a triangle wave is better yet. (These are waveforms meaat the actuator input. In practice, low-level signal inputs to high-voltage ampliers can expersignicant ltering and shape alteration.) This can be extended further by considering a wavefothat emphasizes the time givento the PUSH and minimizes the time of the push. Such a wavefo would be a sawtooth with the greatest duty cycle possible allocated to the polarity of the dVsuch that electrons are emitted from the exposed electrode and deposited on the dielectric surfaEnloe et al. (2004a) veried this experimentally.

    An alternate waveform receiving some attention is very narrow (nanosecond) pulses. Tare sometimes used in combination with sinusoidal waveforms or small DC components (Oet al. 2009). The addition of a DC generally leads to a so-called sliding discharge. A new pactuator based on that effect is discussed in Section 4.1.

    2.3.2. Geometry. Forte et al. (2006) experimentally examined the effect of the amount of ovebetween the bare and covered electrodes in an asymmetric arrangement similar to that showFigure1 . Theydened the gap spacing, g , to be positive when there wasa nonoverlappingdista

    between the edges. Interpreting their results, and normalizing the gap by the width of the covelectrode Lce, which must be a factor, they found that there was little effect on the maximinduced velocities for 0 g / Lc e 2. For larger (positive) gaps or overlap, the effectiveness oplasma actuator dropped off rapidly.

    Because the effect of the plasma actuator on the neutral ow is through a body force, we ethat the effect of multiple actuators is linearly additive. This was rst conrmed by Post (2and later by Forte et al. (2006) and Thomas et al. (2009).

    2.3.3. Thickdielectrics. There aretwoimportantpropertiesof thedielectricmaterial: thebreadown voltage per thickness (volts per millimeter) and the dielectric coefcient, . The minimuthickness of the dielectric needs to be sufcient to not break down at the applied voltage, althfor some materials, this can be accomplished with only a fraction of a millimeter of thicknessmm typical for Kapton). Recent evidence (Thomas et al. 2009) shows a benet in using thdielectric layers made of materials that have lower dielectric coefcients. The general objis to lower the capacitance of the actuator. The capacitance is proportional to / h, where hthe thickness of the dielectric. The power loss through the dielectric is proportional to f AC Therefore, lowering the capacitance ( / h) lowers the power loss through the dielectric, whiotherwise manifest in heating, and allows higher voltages to be reached. Because the bodyis proportional to V 3.5 AC , the motivation is to be able to operate at higher voltages.

    2.3.4. AC frequency. Orlov and colleagues (Orlov 2006, Orlov et al. 2006) model indithat there is an optimum AC frequency to maximize the body force that depends on the actucapacitance. Thomaset al. (2009) investigated this using a 6.35-mm-thick glass dielectric actu The results are shown in Figure 11 . For this actuator design, the 8-kHz AC frequency haslowest maximum thrust, and the 1-kHz frequency has the highest thrust. Again at xed p( I V ), if the current ( I ) is too large, the applied voltage (V ) will decrease and the body f(thrust) will decrease. The visible indication of the increased current is the appearance obright laments in the plasma. The voltage at which these rst occur varies linearly with f ACexpected based on the relation for power loss through the dielectric.

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    3.0

    2.5

    2.0

    1.5

    1.0

    0.5

    0

    5 10 15 20 25 30

    8 kHz4 kHz2 kHz1 kHz

    T h r u s t ( g m )

    VAC (kVrms)

    1 kHz

    2 kHz

    4 kHz

    8 kHz

    a b

    Figure 11(a) Induced thrust from a singledielectric barrier discharge plasma actuator for a 6.35-mm-thick glassdielectric for different AC frequencies of the applied voltage. (b) Corresponding images of plasma for eachfrequency at maximum thrust, showing the ionized air produced by the actuator. The lowest imagerepresents the uniform ionization that occurs within the voltage range at which the thrust is proportional to voltage to the 3.5 power. The other four images correspond to the maximum thrust point at the respective AC frequencies shown in the left panel. Figure taken from Thomas et al. 2009.

    3. EXAMPLE APPLICATION: EXPERIMENT AND SIMULATION

    A visual experimental demonstration of SDBD plasma actuators was the suppression of the vonK arm an vortex street behind a circular cylinder given by Thomas et al. (2008a,b). As an exam-ple, Figure 12 shows two particle-image-velocimetry images taken with the plasma actuatorsoff and on at ReD = 33,000. Four plasma actuators were located on the downstream half of the cylinder at the 90 , 135 , 225 , and 270 positions, as measured in the clockwise directionfrom the stagnation line on the upstream side of the cylinder. The actuators were the asymmetricelectrode design shown in Figure 1 . The dielectric was the 6.4-mm-thick glass wall of the cylin-der. The plasma actuators kept the ow attached on the lee side of the cylinder, resulting in amerged jet of uid on the wake centerline that modied the mean ow and suppressed the vortexshedding.

    Mertz & Corke (2009) performed a simulation of Thomas et al.s experiment and modeled the

    plasma actuator in the manner of Orlov (2006), as described in Section 2.2. Figure 13 a

    showsthe AC cycle-averaged body-force vector eld computed for the simulation. This illustrates theactuatordesign,which, onaverage,oriented themean body-force vector in themean owdirectionand toward the wall of the cylinder. The effect of the body force on the ow around the cylinder was simulated using FLUENT with the body-force vector array supplied through a user-denedinput. Streamlines from the simulation with the plasma actuator effect off and on are shown inFigure 13 b . These corroborate well with the experiment.

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    a b

    Figure 12Particle-image-velocimetry images of the ow behind a circular cylinder at ReD = 33,000 with plasmaactuators on the lee side of the cylinder off (a) and on (b). Figure taken from Thomas et al. 2008.

    4. FUTURE EXPECTATIONS

    4.1. Sliding Discharge

    A relatively new design for plasma actuators is based on a sliding discharge. This concerst developed for laser-pumping applications (Arad et al. 1987). A number of researchersadapted it to atmospheric-pressure plasmas (e.g., Louste et al. 2005, Thomas et al. 2008a, Zoet al. 2007). The concept is to utilize the AC DBD to weakly ionize the air, and then to superposDC potential that establishes a corona discharge between spatially separated electrodes. Thecomponent induces the sliding discharge. The advantages of this concept are that large plsheets can be produced and the plasma is stable with no glow-to-arc transition, except wheDC component is above the DC breakdown limit for the air.

    a b

    Y ( m )

    Y ( m )

    0.2

    0

    0.2

    0.3

    0.2

    0.1

    0

    0.10.20.3

    0.4 0.2 0 0.2 0.4 0.6 0.8 X (m)

    0.2 0 0.2 0.4 0.6 0.8 X (m)

    Figure 13Body-force vectors for a plasma actuator (a) and ow streamlines (b) from ow simulations that include the plasma actuator body fooff and on. Figure taken from Mertz & Corke 2009.

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    a Plasma

    Catode

    DC voltage

    Induced air ow

    Anode

    AC voltage

    Additionalinsulator

    Dielectric

    Excitationelectrode

    Ground Ground

    0 kV DC 50 kV DC

    SDBD discharge(DC off)

    SlidingDBD discharge(DC on)

    7 . 6

    c m

    b

    Figure 14(a) Schematic of triode plasma actuator and (b) photographs of plasma for dielectric barrier discharge (DBD) operation and with slidischarge operation. Figure taken from Thomas et al. 2008a.

    Thomas et al.s approach is unique from the others cited above. It is referred to as a triodeplasma actuator because the electrode arrangement and the use of the dielectric material are

    similar to that of a discrete triode amplier. A schematic of the triode plasma actuator is shownin Figure 14 a . When the triode actuator is operating only with the AC input on, it functions asan SDBD device. Figure 14 b shows that the plasma generated in this case is only visible near theedges of the two exposed electrodes. However, the addition of the DC caused the visible plasmato completely ll the space between the electrodes.

    Figure 15 shows a comparison between the thrust generated by the triode plasma actuator when operated in DBD and sliding discharge modes. The thrust measurement was performedin an identical manner to that shown in Figure 6 . When the DC was off, the thrust followedthe power-law growth that is characteristic of SDBD plasma actuators. There was also a clearthreshold voltage below which thrust was too low to be measured. When the DC was on, there was a thrust produced even at zero AC level. The thrust in this case then varied approximately

    linearly with the AC level. Obviously, the thrust was signicantly larger with the sliding discharge.Further optimization is forthcoming, but these results suggest great potential for this approach.

    4.2. Plasma Sensor In addition to ow control, a new AC plasma sensor for velocity measurements has recently beendeveloped by Matlis & Corke (2005). Although it was originally intended for highMach number,high-enthalpy ows, it is quite well suited for low-speed ows, or applications in which harshconditions make more conventional ow sensors unusable. A recent example of its use includesthe detection of traveling stall cells in a transonic compressor stage (Matlis et al. 2008). Thistechnology offers the unique opportunity for combined plasma actuators and sensors that could

    be benecial for closed-loop feedback control in a single element.

    5. SUMMARY There is an ever growing number of applications of SDBD plasma actuators that have appeared inthe literature. A partial list of these includes exciting boundary-layer instabilities on a sharp coneat Mach 3.5 (Corke et al. 2001, Kosinov et al. 1990, Matlis 2004), lift augmentation on a wing

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    DC off DC on (48 kV)

    0.35

    0.30

    0.25

    0.20

    0.15

    0.10

    0.05

    0

    0 20 40 60VAC (pp kV)

    T h r u s t ( N / m )

    Figure 15Comparison between thrust generated by a triode plasma actuator for dielectric barrier discharge and sliddischarge operation. Figure taken from Thomas et al. 2008a.

    section (Corke et al. 2002, 2006; Goeksel & Rechenberg 2004; Goeksel et al. 2006; Nelson2006; Patel et al. 2006), low-pressure turbine blade separation control (Huang 2005; Huang e2006a, 2006b; List et al. 2003; Rizzetta & Visbal 2007; Suzen et al. 2007; Wall et al. 2007), ttip-clearance ow control (Douville et al. 2006, Morris et al. 2005, Van Ness et al. 2006), body ow control (Asghar et al. 2006, Do et al. 2007, Thomas et al. 2006), turbulent boundlayer control (Balcer et al. 2006, Hultgren & Ashpis 2003, Porter et al. 2007, Wilkinson 2unsteady vortex generation and control (Nelson et al. 2007, Visbal & Gaitonde 2006), andfoil leading-edge separation control (Corke et al. 2004; Post 2004; Post & Corke 2003, 2New applications continue to appear as more investigators gain experience in using theseactuators.

    Our understanding of the SDBD physics inherent to the plasma actuators has led todevelopment of quantitative models that have shown remarkable agreement with experim which point to improved designs and operation. The recent optimization of the actuators producby better choices of thick dielectric materials and AC input frequencies and waveforms has order-of-magnitude improvements in their performance compared with earlier designs. Sliddischargeapproaches offer thepotential for further signicant improvement.All these areopen

    the scope of application conditions for these ow-control devices.

    DISCLOSURE STATEMENT T.C.C. is a partial holder and C.L.E is a co-inventor of U.S. Patent No. 7,380,756, Sidielectric barrier aerodynamic plasma actuator, and S.P.W. is a co-inventor of U.S. PaNo. 6,200,539, Paraelectric gas ow accelerator.

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    Enloe C,FontG, McLaughlin T,OrlovD.2008.Surfacepotentialand longitudinalelectriceldmeasurementsin the aerodynamic plasma actuator. AIAA J. 46:273040

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    Annual Review of

    Fluid Mechanics

    Volume 42, 201Contents

    Singular Perturbation Theory: A Viscous Flow out of G ottingen Robert E. OMalley Jr. 1

    Dynamics of Winds and Currents Coupled to Surface Waves Peter P. Sullivan and James C. McWilliams 19

    Fluvial Sedimentary Patterns

    G. Seminara 43Shear Bands in Matter with Granularity

    Peter Schall and Martin van Hecke 67

    Slip on Superhydrophobic Surfaces Jonathan P. Rothstein 89

    Turbulent Dispersed Multiphase Flow S. Balachandar and John K. Eaton 111

    Turbidity Currents and Their Deposits

    Eckart Meiburg and Ben Kneller

    135 Measurement of the Velocity Gradient Tensor in Turbulent Flows

    James M. Wallace and Petar V. Vukoslav cevi c 157

    Friction Drag Reduction of External Flows with Bubble andGas InjectionSteven L. Ceccio 183

    WaveVortex Interactions in Fluids and SuperuidsOliver B uhler 205

    Laminar, Transitional, and Turbulent Flows in Rotor-Stator CavitiesBrian Launder, S ebastien Poncet, and Eric Serre 229

    Scale-Dependent Models for Atmospheric Flows Rupert Klein 249

    Spike-Type Compressor Stall Inception, Detection, and ControlC.S. Tan, I. Day, S. Morris, and A. Wadia 275

    vii

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    Airow and Particle Transport in the Human Respiratory SystemC. Kleinstreuer and Z. Zhang

    Small-Scale Properties of Turbulent Rayleigh-B enard ConvectionDetlef Lohse and Ke-Qing Xia

    Fluid Dynamics of Urban Atmospheres in Complex Terrain H.J.S. Fernando

    Turbulent Plumes in Nature Andrew W. Woods

    Fluid Mechanics of Microrheology Todd M. Squires and Thomas G. Mason

    Lattice-Boltzmann Method for Complex FlowsCyrus K. Aidun and Jonathan R. Clausen

    Wavelet Methods in Computational Fluid Dynamics

    Kai Schneider and Oleg V. Vasilyev Dielectric Barrier Discharge Plasma Actuators for Flow Control

    Thomas C. Corke, C. Lon Enloe, and Stephen P. Wilkinson

    Applications of Holography in Fluid Mechanics and Particle Dynamics Joseph Katz and Jian Sheng

    Recent Advances in Micro-Particle Image Velocimetry Steven T. Wereley and Carl D. Meinhart

    Indexes

    Cumulative Index of Contributing Authors, Volumes 142

    Cumulative Index of Chapter Titles, Volumes 142

    Errata

    An online log of corrections to Annual Review of Fluid Mechanics articles may be at http://uid.annualreviews.org/errata.shtml

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