Stall control at high angle of attack with plasma sheet actuators

Transcription

1 Exp Fluids (27) 42: DOI 1.17/s RESEARCH ARTICLE Stall control at high angle of attack with plasma sheet actuators Roberto Sosa Æ Guillermo Artana Æ Eric Moreau Æ Gérard Touchard Received: 15 June 26 / Revised: 14 August 26 / Accepted: 11 October 26 / Published online: 1 November 26 Ó Springer-Verlag 26 Abstract We analyzed the modifications of the airflow around an NACA 15 airfoil when the flow was perturbed with electrohydrodynamic forces. The actuation was produced with a plasma sheet device (PSD) consisting in two bare electrodes flush mounted on the surface of the wing profile operated to obtain a discharge contouring the body in the interelectrode space. We analyze the influence of different parameters of the actuation (frequency, input power, electrodes position) on the aerodynamic performance of the airfoil, basing our study on measurements of the surface pressure distribution and of the flow fields with particle image velocimetry technique. The experiments indicated that at moderate Reynolds numbers (15, < Re < 333,) and at high angles of attack, steady or periodic actuations enabled large improvement of the lift and drag/lift aerodynamic coefficients by reattaching the flow along the extrados. However, to attain the same results steady actuations required larger power consumption. When exciting the flow with a moderate value of nondimensional power coefficient (ratio of electric power flow with the kinetic power flow), a frequency of R. Sosa G. Artana (&) Laboratorio de Fluidodinámica, Universidad de Buenos Aires, Buenos Aires 146, Argentina gartana@fi.uba.ar E. Moreau G. Touchard Laboratoire d Etudes Aerodynamiques (UMR 669 CNRS), Université of Poitiers, Poitiers 8622, France excitation produced a peak on the coefficients that evaluate the airfoil performance. This peak in terms of a non-dimensional frequency was close to.4 and can be associated to an optimal frequency of excitation. However, our work indicates that this peak is not constant for all stalled flow conditions and should be analyzed considering scale factors that take into account the ratio of the length where the forcing acts and the cord length. List of symbols b electrode length in the span direction c cord length f exc frequency of excitation of the actuator l curvilinear coordinate in the tangential direction of the surface x axis coincident with the airfoil cord (being x = the leading edge position) C l momentum addition coefficient C W power addition coefficient surface pressure coefficient P C i P P qu 2 2 C Dp C l F + L ele P i P Re U W ele a pressure drag coefficient lift coefficient reduced frequency of excitation length of the interelectrode space in the streamwise direction surface pressure at position i pressure of the free air stream Reynolds number¼ U c t free stream velocity electric power of the discharge angle of attack

2 144 Exp Fluids (27) 42: d q t plasma sheet thickness air density kinematic coefficient of viscosity of the air 1 Introduction The separation of boundary layers in the case of aerodynamic bodies produces energy and lift losses. Consequently flow control strategies have focused on the alteration of the location of the boundary layer separation and the mitigation of the effects produced by this phenomenon. In the flow around airfoils, the main objectives of the research efforts with actuators have been to prevent or to postpone the stall using either steady or unsteady actuations. When using a steady actuation in the flow, the purpose of the actuation is to impart additional momentum to the retarded fluid within the boundary layer and thus delay separation. When dynamic actuations are proposed, a periodic momentum addition is imposed to fluid layers close to the airfoil surface. The flow receptivity to excitations related to the fluid inherent instabilities (Huerre and Monkewitz 199), especially those associated to the separated shear layer of the Kelvin Helmholtz type, is taken into account when performing the cyclic actuation. The purpose is to profit the natural amplification of small periodic perturbations and by this mean promoting the entrainment of high-speed fluid of the free stream into regions with low velocities of the separated flow. Since the end of the last decade, a large number of researchers have been interested in the use of electrohydrodynamic (EHD) actuators mainly for aeronautic applications. The EHD devices produce an ionization of the flowing air close to the surface of the body and add localized momentum to the flow through collisions process of the migrating charged particles with the neutral species of the gas. The EHD devices distinguish from other electromagnetic devices, by the fact that currents involved are so low that the intensities of the magnetic forces are negligible compared to the electric ones. The main advantages of these actuators are that they have no moving part, a very short response time (delays in the establishment of a discharge are theoretically of the order of nanoseconds). The efficiency to transform electrical to mechanical energy has been analyzed in a previous work based on particle image velocimetry (PIV) measurements of actuated and nonactuated flows, (D Adamo et al. 22). The EHD actuators may be ordered in three large groups based on the different electrical characteristics of the discharge in which the actuation on the flow is based: Coronas-based devices (CD) Dielectric barrier discharge devices (DBD) Plasma sheet devices (PSD) Coronas-based devices use a self-sustaining discharge (corona discharge) produced by electrodes that establish in the air an electric field configuration with strong inhomogeneities. They comprise the use of at least one electrode having a very low radius of curvature that generally is a needle or a very thin wire. As a consequence of the electric field configuration the ionization process is confined to regions close to the highfield electrodes. Thus, in this phenomenon there are active electrodes, surrounded by ionization regions where free charges are created and low-field regions where charged particles drift and react in their movement towards the passive electrodes. An important number of reports detail the changes observed in different flows with this kind of actuation (Bushnell 1983; Malik et al. 1983; Noger et al. 1997; Colver and El-Khabiry 1999). The devices with dielectric barrier (DBD) use periodically excited electrodes, one exposed to the air, whereas the other is encapsulated by a dielectric material (Roth et al. 1998; Roth and Sherman 2; Wilkinson 23). The dielectric barrier interposed between both electrodes serves to stabilize the discharge avoiding the impact of the ions on the cathode and thus preventing the heating of it and the formation of new avalanches or breakdown from the electron secondary emission. Usual configurations consist of planar electrodes separated by a thin dielectric film disposed in an arrangement parallel in the spanwise direction of an aerodynamic surface. In order to achieve a self-sustaining discharge, the DBD devices are obliged to be periodically excited. Frequencies of excitations are in the range of some kilohertz, and the discharge shows a diffuse light indicating that ionization process occurs at close vicinity of the air-exposed electrode. Plasma sheet devices, like the one used in this work, produce the gas discharge with two air-exposed electrodes. They are disposed flush mounted on the surface of a dielectric body with an inter-electrode distance of some centimeters. The electrodes excitation may be undertaken with a DC or with a periodic potential difference that is adjusted to produce an ionization process that occupies the whole interelectrode space.

3 Exp Fluids (27) 42: Plasma Sheet Leading Edge Airfoil Upper Surface Fig. 1 Plasma sheet formation by mean of a PSD actuator In this region the surface looks contoured by a thin film of ionized air or plasma sheet (see Fig. 1) of small thickness (some tenths of micrometers). The currents of plasma sheets exhibit a DC component and a large number of peaks with frequencies of the order of some kilohertz. In a previous work (Moreau et al. 24) we explained some characteristics of the current behavior and more detailed studies of the physics of this discharge are now being undertaken. The PSD require a careful finishing of electrodes to impede the formation of spurious electric field concentration. Further, the electrode dispositions that may curve the electric field lines avoiding the direct facing of electrodes (like on curved surfaces or inside slots) enable easier operation of the device without arcing. Significant airflow velocities (larger than some meters per second) on the PSD also inhibit the thermal instabilities of the discharge that may lead to filamentation or arcs (Kunhardt 2) and different reports show that plasma sheets regimes are promoted by the presence of airflow blowing in the region where electrodes are placed (Leger et al. 22). a b V 1 V 1 V 2 V 1 V 2 V 2 Fig. 2 Different EHD actuator devices: a DBD, b PSD and c three electrode system of the SD c V 2 Recently, a new subgroup of PSD named sliding devices (SD) has been developed. They may also produce stable plasma sheets with less restrictive conditions (Louste et al. 25) by using two air-exposed electrodes and a third one separated by a dielectric barrier (see Fig. 2). One of the electrodes is excited with an AC potential and the others are connected either to a DC potential or grounded. The aerodynamic performance of these devices is under study now. The first researches reported proposing stall control with dielectric barrier devices (Scherbakov et al. 2; Johnson and Scott 21; Corke et al. 22; Post and Corke 23; Roth 23) or with plasma sheet actuators (Vilela Mendes and Dente 1998; Sosa 22; Sosa and Artana 22, 26) have been mainly concerned with steady excitations of the flow. More recent reports have described experiments with dielectric barrier devices considering unsteady excitations on airfoils (Post and Corke 24; Corke and Chuan He 24). A distinctive characteristic of PSD is that as a consequence of the ionization process that takes place, the actuation is distributed in a large region rather than confined around one active electrode (as occurs with DBD). In consequence steady or cyclic actuations by PSD do not produce necessarily the same effects on the flow than with other EHD actuators. The objective in this work is to analyze the effect produced by the different PSD actuation parameters (frequency, input power, electrodes position, etc.) on the aerodynamic performance of the airfoil. Our study is based on the analysis of flow fields obtained by particle image velocimetry technique and on surface pressure distributions. In order to facilitate the comparisons of the aerodynamic performance achieved with the EHD actuation with other kind of actuations we have selected the NACA 15 airfoil model that has been extensively studied by other researchers using dynamic excitations (Seifert et al. 1996; Greenblatt and Wygnanski 2; Post and Corke 24). 2 Experimental setup 2.1 Wind tunnel and models The measurements have been done in a wind tunnel loop of rectangular cross-section (.5 m.5 m) and enabled the test of models at flow velocities up to 3 m/s. The airfoil model of our study (Fig. 3) was an NACA 15 section shape (chord dimension 2 mm, spanwise dimension 45 mm) of polymethyl

4 146 Exp Fluids (27) 42: Fig. 3 Scheme of the NACA 15 Airfoil Model (units are in mm) metacrylate (PMMA). The airfoil has been fabricated in two separate parts (male and female) enabling to obtain a hollowed body. The fixation of the airfoil was performed on both ends through pieces of electrical insulating material (Nylon). In the test section, the angle of attack was manually varied and recorded in digital photographs to establish its value with accuracy up to.1. More detailed descriptions of the wind tunnel characteristics and of the models may be found in a previous report (Artana et al. 23). Experiments have been undertaken in a velocity range of 1 25 m/s with an associated Reynolds number (Re = U c/m) comprised within the interval < Re < The airfoil was disposed in the test section with different angles of attack corresponding to the post-stall regimes. At the flow conditions of our experiments, separation with no reattachment and without hysteresis was observed for angles higher than 15. The blockage ratio in the wind tunnel loop reached in the worst condition 8.6 at the highest angle of attack (21.7 ). No correction for blockage effects has been applied to the data obtained. 2.2 EHD excitation Two plane parallel electrodes, consisting of strips of 3.5 mm width of thin aluminum foil (5 lm thick), were flush mounted on the surface of the airfoil in the spanwise direction covering 85% of the span. In the general cases, one of them was located at the leading edge position (x/c = ), whereas the second one was placed at x/c =.18 on the extrados of the airfoil. The ends of both electrodes were rounded to avoid a large field concentration in this region Periodic excitation For this case a high voltage power amplifier ( to ±2 kv, ±2 ma, 2 khz bandwidth) and a signal generator were used to impose a positive square wave high voltage (HV) at the leading edge electrode while the potential of the downstream electrode was fixed by a negative DC high voltage power supply ( 4 kv, 3.75 ma). An HV probe enables the monitoring of the signal delivered by the sources. The discharge current was measured with the help of an AC current transformer (2 ma, precision lower than 3 la, bandwidth of 1 khz) connected to an oscilloscope. The current transformer is of the inductive type and consists of a toroidal sensor with inner diameter of 28 mm placed around the AC HV cable Steady excitation For this kind of excitation two DC high voltage (HV) power supplies (±4 kv, 3.75 ma) with different polarities were considered. The positive one was connected to the electrode placed on the leading edge meanwhile the negative one imposed the voltage to the electrode placed downstream. The potential difference and the mean value of the discharge current were indicated by the HV power supplies with a precision of.1 kv and 1 la, respectively.

5 Exp Fluids (27) 42: Velocity field measurements The velocity field has been measured using a PIV technique. The tracers were produced by a smoke generator producing droplets of pure cosmetic grade oil with a mean size of about.3 lm. The system was illuminated with a laser sheet of a Yag laser of 2 mj placed vertically in the middle of the span of the airfoil. Each pulse had duration of.1 ls and the time between a pair of pulses was, depending on the experiment, in the range of 2 5 ls. A progressive scan interline camera capable of producing images of 1,28 pixels 1,24 pixels was used. without introducing a significant error, as concluded in our previous report (Artana et al. 22) Uncertainty of flow field measurements The system resolution for distances can be estimated as the product of the pixel resolution (a very conservative value is 1/4 pixel) and the pixel size. In that way, the resolution of the velocity field can be estimated dividing the latter value by the time between the pair of pulses. In our case the pixel size (ps) varied from about.9 to.2 (1 3 m/pixel) leading to a very conservative value of uncertainty for the velocity of PIV data processing Dv 1 4 ðpixelþpsðm=pixelþ 1 ffi 1:125 m/s DtðsÞ ð1þ To obtain the vector fields a treatment of the recorded images was undertaken with commercial PIV software using an adaptive correlation technique. In this treatment we have considered two refinement steps, and the final interrogation area size was of 16 pixels 16 pixels with an overlap of 5%. Each velocity field was filtered with both, a peakvalidation and a range validation, filters. Peak validation filter based on a detectability criterion (Keane and Adrian 1992) validated vectors with a ratio of the highest peak to the second highest peak in the correlation plane larger than a fixed value (1.2 in our case). The range validation filter enabled the establishment of the range admitted for the modulus of the velocity vectors. In our case, we have considered a value of three times of the free stream flow velocity U as the upper limit. Six hundreds pairs of digital images taken at pairs every.1 s were examined in each experiment. The mean velocity field of the airflow was obtained by averaging the 6 instantaneous flow fields. Convergence of the time averaged values towards the mean value has been tested adopting lower intervals and is largely assured with our experimental conditions Particle tracking In PIV experiments the velocity of the tracers and that of the fluid particles surrounding them should be coincident. The occurrence of slipping causes the seeding particles to swim in the moving media and then the information obtained must be carefully examined. In our experimental design, the smoke generator created a cloud with a mean particle diameter of.3 lm. The influence of coulombian forces on the tracer s trajectories can then be disregarded 2.4 Pressure measurements For the surface pressure distribution experiments, 3 pressure ports drilled at the half of the span location of the airfoil were considered. The pressure holes diameters were 1.5 mm and their centers were streamwise spaced. Electrical insulating tubes of Tygon (internal diameter =.5 mm) carried the pressure from the ports to a set of 3 independent solid-state sensors (ion-implanted piezoresistive strain gage) with their output connected to a data acquisition system. The tubes were inserted into the holes, passed through the hollow of the airfoil and brought out through the support of one end of the model. The free stream velocity U was measured using a micromanometer connected to a Pitot tube positioned at the entrance of the test section The lift and of drag pressure coefficients The coefficients of lift and drag pressure are estimated by integration of the pressure coefficient (C P ) distribution around the airfoil. C l ðt; aþ ¼ 1 c I C Dp ðt; aþ ¼ 1 c I C p ðs; t; aþ ~ U U d ~ l C p ðs; t; aþ ~ U U d ~ l ð2þ ð3þ where l is the curvilinear coordinate in the tangential direction of the surface and a is the angle of attack of the airfoil and c is the airfoil cord length. When separation takes place, the surface pressure at different ports may exhibit a time dependent behavior.

6 148 Exp Fluids (27) 42: The pressure detected by the sensor is not the real surface pressure as this magnitude is dampened by the system of pressure transmission (Bergh and Tijdeman 1965). Therefore, to obtain the effective instantaneous value of the pressure a reconstruction of the signal is required. A way of achieving this is to establish the gain for the different frequencies of the tube-transducer system. However, the mean value of the pressure may be easily obtained without any reconstruction by an adequate time integration of the direct measurement of the fluctuating surface pressure. In order to assume the convergence to the mean value, the interval T of measurement must be much longer than the characteristic time of the flow fluctuations. In our case, the characteristic time may be roughly estimated (Roshko 1954) considering a Strouhal number about a value of.2. Our experiments have been performed by acquiring the surface pressure at times larger than several seconds. Such intervals, even in the more adverse situations exceeded in more than one order of magnitude those characterizing the dynamics of vortex shedding. The estimations of the time averaged value of C P has also been carried out under the same considerations about the time of integration T than those for surface pressure C p ðs; aþ ¼ 1 T Z T Cpðs; t; aþdt ð4þ In next sections we also make use of the coefficients C l (a) and C Dp (a) defined by C Dp ðaþ ¼ 1 T Z T C Dp ðt; aþdt ð8þ are assured only when a concordance of phase between the pressures values at the different measurement points is verified. Such concordance (temporal problem) was not tested in the present report. Furthermore, as a consequence of the geometry of the model, in a region towards the trailing edge (x/c >.78) was not possible to dispose pressure probes and the pressure distribution there remained undetermined. Owing to this spatial problem, the coefficients C l (a) and C Dp (a) could be calculated only with an integration over those coordinates that ignore the fluid dynamics of regions quite close to the trailing edges. Based on these two reasons (spatial and temporal problems) it is not exact to directly extrapolate values of the mean lift force and drag pressure force experienced by the airfoil from the parameters C l (a) and C Dp (a) of our tests. However, these coefficients give a fruitful data and we will take them as a useful tool to compare the aerodynamic performance of the airfoil in the presence or absence of the discharge. 2.5 Actuator s controlling factors The EHD actuator behavior is governed by independent variables named controlling factors. We consider here two non-dimensional coefficients as controlling factors: the power coefficient C W and the reduced frequency F +. C l ðaþ ¼ 1 c I C Dp ðaþ ¼ 1 I c C p ðs; aþ ~ U U d ~ l C p ðs; aþ ~ U U d ~ l ð5þ ð6þ Uncertainty analysis The equivalence between the coefficient C l (a) and C l ðaþ the time averaged values of C l (t, a) C l ðaþ ¼ 1 T Z T C l ðt; aþdt or between C Dp (a) and C Dp ðaþ ð7þ Fig. 4 Discharge current and anode voltage potential waveform at f exc = 4 Hz. A driving voltage, B HV signal (5 kv/div), C discharge current (.1 ma/div). Zero is at one division down the central crosshair

7 Exp Fluids (27) 42: The power coefficient C W The power added to the flow as a consequence of actuation may be expressed by means of a nondimensional power coefficient C W defined as C W ¼ W ele L ele :5qU 3bd ð9þ c where d is the thickness of the ion drift region in our case considered constant in all experiments and equal to 5 lm, the order of the thickness of the plasma sheet; b is the electrode length (span direction), c the airfoil cord and L ele is the electrode separation. W ele is the electric power of the discharge and may be easily calculated by means of W ele ¼ 1 T Z T VðtÞIðtÞdt ð1þ where V(t) is the electrode difference potential, I(t) is the current discharge. The integral in Eq. (1) is performed on the interval T, and this time must coincide with the period of the excitation when the actuator is AC operated. The coefficient C W represents the ratio of two powers (the power associated to the flow of kinetic energy density and the electric power) multiplied by a factor that takes into account a non-dimensional length in the streamwise direction where actuation is produced. A controlling factor that considers the momentum added by the EHD actuator instead of C W could also be used. This momentum coefficient has been defined as the ratio of the momentum added, to that in the freestream (Greenblatt and Wygnanski 2). When excitation is achieved by a mechanical or electrical means, the mean momentum coefficient is defined by hc l i¼ 1 :5q 1 U 2 1 L q 1 Z 1 hu 2 idy ð11þ where: L is usually taken as the length of the body under consideration (in our case the airfoil chord c is employed), and Æu 2 æ represent the square velocity averaged in time adjacent to, and downstream the actuator. Although for EHD actuation ÆC l æ measurements have been previously considered (D Adamo 22) (a typical value of ÆC l æ is about.15) within this work, we utilize the power coefficient C W as an alternative of ÆC l æ. This choice is based on the fact that the evaluation of C W allows us to compare different EHD actuators without requiring to dispose the velocity profile u(y,t). On the other hand, the ÆC l æ coefficient considers the momentum transfer as the only mechanism by which the discharge interacts with the neutral fluid. It does not take into account any contribution of other coupling mechanism between the discharge and airflow, such as alterations of fluid properties by ionization of the gas, which have been suggested by different researchers (Scherbakov et al. 2). The coefficient C W, on the contrary, is able to compute all the energy added to the flow independently of how this energy is coupled with the baseline flow Reduced frequency F + The effect of the frequency of actuation (f exc ) on the flow has been studied in terms of a reduced frequency F + F þ ¼ f excc U ð12þ This reduced frequency compares the frequency of excitation to the inverse of the convective time of transit through a distance equal to the cord length that is in strong relationship to the natural frequency of vortex shedding. The value of the reduced frequency is zero when steady actuation is considered and when cyclic actuation Current(mA/m) 2,8 2,6 2,4 2,2 2, 1,8 1,6 1,4 1,2 1, Voltage difference (kv) Fig. 5 Mean current (per unit length of electrode) as a function of the voltage difference for the steady excitation. The angle of attack was 2.7 and free airstream velocity 25. m/s

8 15 Exp Fluids (27) 42: was considered with excitation frequencies spanning from 1 to 1, Hz the reduced frequencies lied in the range.8 < F + < 17. The PSD produce a forcing in fluid layers at close vicinity of the surface. It has not yet been demonstrated that the frequency of the electric excitation of the actuator is replicated exactly as a frequency of forcing of the flow for PSD. This has not been studied in this report but is subject of present research (Moreau et al. 24; Forte et al. 26). 3 Experimental results 3.1 Discharge characteristics Periodic excitation Typical examples of the signal generator driving voltage, the anode HV and the current flowing in the circuit are shown in Fig. 4. Similar curves were observed along the whole range of the frequencies tested (1 1, Hz). The analysis of these curves indicates that as expected the current was in phase with the excitation voltage. In the upper stage of the step, the anode attained positive HV values and the voltage difference between the electrodes was high enough to enable the plasma sheet formation. The current flowing in the system exhibited a first peak of several milliamperes, as consequence of the large displacement current (capacitive effect). This is followed by a relaxation process towards a quasi-steady current value (about.2 ma in Fig. 4) with small current peaks. In a second phase, when the driving voltage is switched off even though the cathode remains at high negative voltage, the plasma sheet disappears and the current only exhibited a negative peak associated to a displacement current (capacitive effect) followed by a relaxation process. At high frequencies a slight distortion of the HV step was observed as a consequence of limitations of the power supplies used in our study Steady excitation The discharge of our experiments was produced with two steady HV simultaneously connected to the electrodes. The current flowing was similar to that observed during the upper stage of the step in the preceding case showing a quasi-steady value with small current peaks. The current was in consequence a superposition of pulsating discharge with pulses in a broad spectrum but with a dominant frequency of some kilohertz and a DC component. Recent experimental results have given further insight into this aspect (Moreau et al. 24) and more studies are now being in course to better understand the complex nature of these phenomena. The visual inspection of the discharge gave almost coincident aspects, such as luminosity, noise emission and sheet thickness (about the electrode thickness), for both excitation modes (steady and periodic). The skimming, grazing, or sliding discharge that was obtained with pulsed voltages has shown similar characteristics to the one we have observed. Main aspects of this kind of discharges have been described under the theory of planar ionization waves (Lagarkov and Rutkevich 1993). The mean value of the current flowing in the circuit is determined by the voltage difference applied to the electrodes but the current for a fixed voltage difference increased with the velocity of the flow on the electrode region. Figure 5 represents the i(v) curve for an angle of attack of 2.7 and a velocity of the free airstream of 25. m/s Power of the actuation When AC excitation was studied, we have considered that experiments with the same driving voltage and presenting the same quasi-steady current (the one that can be easily monitored during experiments) have had the same coefficient C W. Strictly this introduces a minor error, as for high frequencies at the beginning of the cycle the signal of Cp º 1 m/s Actuator off F + =.2 F + =.2 F + =1 F + =2 F + =4 F + =1 Inviscid baseline 2,,2,4,6,8 1, x/c Fig. 6 Near post-stall regime surface pressure distribution. Angle of attack 15.8, Re = 133,333, C W = 52.95

9 Exp Fluids (27) 42: Fig. 7 Near post-stall regime time averaged flow fields. Angle of attack 15.8, Re = 133,333. a Actuator off, C W =.; b actuator on, C W = 52.95, F + =1 the anode voltage is deformed as the power amplifier fails to produce at high voltage the square signal of the driving voltage. So, it cannot be assured that experiments undertaken at very high frequencies will have the same C W than those corresponding to experiments undertaken at low frequencies even though we consider the same driving voltage and the same quasisteady current. On the other hand the cyclic actuation has associated a reactive power (Roth and Xin Dai 26) that is not included in this coefficient but that implies a requirement for the power supply considered. The electric power for excitation with the PSD of our experiments was limited in terms of power per unit length of actuator in the spanwise direction to maximum values of about 8 W/m. This limit of operation is

10 152 Exp Fluids (27) 42: Cp m/s 2,,2,4,6,8 1, x/c fixed by the destabilization of the discharge from a plasma sheet configuration towards a filamentary discharge or arcing. The maximum values on this range depended on the velocity of the free air stream and the angle of attack. It has been observed that the higher the velocity on the region of the discharge was, the larger attainable power with PSD was. 3.2 Surface pressure distributions and time averaged flow fields Actuator off (Baseline) F + =.4 F + =.8 F + =.2 F + =.28 F + =.4 Inviscid Theory Fig. 8 Near post-stall regime surface pressure distribution. Angle of attack 19.8, Re = 333,333, C W = 3.35 We show in this section the results of mean pressure distributions and the time averaged flow fields in the absence and in the presence of the actuation for different values of the controlling factors C W and F +. For the sake of clarity, the analysis of aerodynamic coefficients is postponed to the next section. The pressure distribution results are shown accompanied by the reference distributions of theoretical inviscid flows obtained from the formulation of Theodersen (1934). The time averaged velocity fields are illustrated with the corresponding streamlines to have better insight into flow field characteristics. As the airfoil angle of attack is increased the actuation produced different flow configurations. We distinguish between the non-stalled conditions and those when actuation takes place with a separated flow. For the non-stalled conditions the effect of the actuator on the flow was almost negligible and produced only slight accelerations in the region of the inter-electrode space. On the contrary on the stalled conditions large effects were produced by the forcing. In a previous article (Sosa et al. 24) we have proposed to gather the stalled conditions in three groups or regimes: near, middle and deep post-stall regimes Near post-stall regime This regime is characterized by the possibility to obtain a complete flow reattachment by suitable actuation of the flow either adjusting C W or F +. It takes place when the airfoil is disposed with moderate angles of attack (15 < a <2 ). Periodic excitation In Fig. 6 the pressure distributions for a = 15.8 and C W = are represented. The unforced flow exhibited an almost constant value on the airfoil suction side (upper surface or extrados); such kind of distribution is characteristic of a fully separated flow. The PSD actuation eliminated this plateau and the pressure distribution showed a strong low-pressure region near the leading edge followed by a rapid pressure recovery towards the trailing edge. These distributions agreed with those of fully attached flows. The adjustment of the frequency of excitation to different values altered the pressure distributions near the leading edge but the pressure recovery towards the trailing edge was similar for all the frequencies considered. On the lower surface (intrados) the actuation increased the value of the surface pressure, indicating a retardation of the flow on this side. This effect requires some explanation. The passage from a nonstalled condition to a stalled condition (or vice versa) produces an important rearrangement of the mass flow distribution in the wind tunnel section. As the free airstream velocity is kept constant independently of the airfoil condition, the retardation of the flow produced by a wake is accompanied by an increase of the velocity of other regions of the same section. This induces changes in upstream also. If actuation fully (or partially) reattaches the flow, the region of retarded flow of the wake disappears (or diminishes its wideness) and the regions of irrotational flow are no longer (or less) forced to compensate the deficit of mass flow. A reduction of velocity of the intrados, as we observed when actuation is on, is in consequence consistent with a reattachment phenomenon. For the level of actuation considered, the intrados pressure showed no clear sensitivity to the frequency of excitation (in agreement with the extrados behavior) and whatever the frequency was the full attachment occurred. The time averaged flow fields with their streamlines (Fig. 7) are a useful tool to better illustrate our analysis. When actuation is absent it can be observed in Fig. 7a the existence of a clear recirculation zone

11 Exp Fluids (27) 42: Fig. 9 Near post-stall regime time averaged flow fields with associated streamlines. Angle of attack 19.8, Re = 333,333. a Actuator off, C W =.; b actuator on, C W = 3.35, F + =.28 associated to the separated flow. When actuator is operated (Fig. 7b) the reattachment of the flow takes place and this zone disappears. The streamlines then contoured the model indicating a full reattachment of the flow. At regions close to the downstream electrode, there is a slight deformation of the streamlines. We associate this effect to PIV results contamination produced by a reflex of the laser sheet on the electrode that modifies the correct treatment of images by the PIV software. In Fig. 8 we represent pressure distributions of the near stall regime for a higher angle of attack (a=19.8 ) and for C W coefficients about one order of magnitude lesser than those of Figs. 6 and 7. The curves with actuation of this figure again showed a low-pressure region near the leading edge on the

12 154 Exp Fluids (27) 42: Fig. 1 Near post-stall regime time averaged flow fields with associated streamlines. Angle of attack 19.8, Re = 333,333. a Actuator on, C W = 3.35, F + =.4; b actuator on, C W = 6.37, F + =.28 suction side of the airflow followed by a small pressure recovery towards the trailing edge. The bubble of separation of the actuated flow, indicated by the presence of a plateau of pressure, occupied a position close to the trailing edge but did not cover the whole upper surface as it did in the absence of discharge. In concordance with results obtained with other actuators (Weier and Gerbeth 24), the size of the recirculating bubble may be reduced or almost disappear by adjusting either the frequency or the power supplied to the flow. It can be observed in Fig. 8 that the curve corresponding to F +.4 outstands from the rest. For this frequency the pressure recovery towards the trailing edge is more important and in consequence the bubble suffers a much important reduction of its size.

13 Exp Fluids (27) 42: Cp ,8 1 m/s DC Leading Edge Excitation 2,,2,4,6,8 1, x/c Actuator off (Baseline) C W = C W = C W = Inviscid Theory Fig. 11 Near post-stall regime surface pressure distribution. Angle of attack 15.8, Re = 133,333 In the intrados, the curves approached to those corresponding with the inviscid pressure distribution. This occurred regardless of the frequency of excitation as the bubble of the actuated flow, of slight size in all cases, only produced reduced velocity deficits. The corresponding time averaged flow field velocities and the associated streamlines are represented in Figs. 9 and 1. The flow without actuation (Fig. 9a) exhibited a large bubble of recirculation. As a consequence of actuation with a moderate C W (Fig. 9b) a partial reattachment can be obtained meanwhile the large bubble transformed to one with a smaller size located in a position quite close to the trailing edge. For the same C W, and adjusting the frequency of excitation (Fig. 1a) the reattachment process could be enhanced. Effectively, this figure demonstrates that the recirculation bubbles may fully or almost fully disappear producing a reattachment of the flow, with no longer clear recirculation bubble present. On the other hand by increasing C W the size of the recirculation bubble could also be largely diminished (Fig. 1b). A comparison of Fig. 1a and 1b indicates, however. that the attachment was better with frequencies adjustment (almost full reattachment) than by power increasing (partial reattachment with a small bubble in the trailing edge). Steady excitation We show in Fig. 11 results concerning pressure distributions of the near stall regime for steady actuation at different values of C W. On the intrados the actuation increased the value of the surface pressure and decreased the velocity on this side. On the extrados, we observe a region of constant pressure corresponding to a fully separated flow when actuation was absent. This region changed drastically when actuation was activated and distributions with an important suction towards the leading edge were observed. These results occurred for the three C W considered and were a sign that separation was eliminated. The time averaged flow fields and the streamlines of this averaged field are represented in Fig. 12. These figures clearly demonstrate that the actuator operation produced the reattachment of the flow, as when it was activated the streamlines gently contour the model. Figure 13 shows the effect of increasing the power coefficient on this regime. We can observe that the flow can be either fully attached to the airfoil (Fig. 13a) or that a flow with separation may take place (Fig. 13b). The full or almost full attachment is achieved by exciting the flow with a level of power that is high enough. If the power is lesser the position of the separation line in this last case is a function of the input, being closer to the trailing edge for the higher values of the C W. This is evidenced by the suction side of the airflow, where the actuation generated a lowpressure region near the leading edge followed by a small pressure recovery towards the trailing edge. The bubble of separation, indicated by the plateau of pressure, occupied positions close to the trailing edge but did not cover the whole upper surface as it did in the absence of discharge. On the intrados, the actuation increased the pressure and the curves approached to the distribution of the inviscid case as in cyclic excitations. For higher angles of attack (a =19.7 ) the pressure distributions showed different behavior than the one observed for cyclic excitation (Fig. 14) and for this case, even the power levels were much larger, a partial flow reattachment was observed Middle post-stall regime In this regime the flow could not be forced to a fully reattached configuration neither by increasing C W nor by modifying the frequencies of excitation of the actuator. The actuator produces, however, a large displacement of the line of separation downstream the leading edge. Periodic excitation Figure 15 brings out the difference of behavior with the preceding regime (near post-stall). The figure reveals that frequencies for the lower range produced higher values of pressure in the intrados where curves showed a more marked trend to the inviscid behavior. The cyclic excitations induced attachment of the flow as the pressure recovery on the extrados indicates.

14 156 Exp Fluids (27) 42: Fig. 12 Near post-stall regime time averaged flow fields with associated streamlines. Angle of attack 15.8, Re = 133,333. a Actuator off, C W =; b actuator on, C W = However, for the high frequencies range, the actuator resulted less effective. The time averaged flow fields and their associated streamlines are shown in Fig. 16. The recirculation bubble of the case without actuation (Fig. 16a) disappeared when the actuator was applied (Fig. 16b). In regions close to the downstream electrode, the actuation produced a perturbed zone with some similarities with a separation bubble followed by a reattachment. We have associated the existence of this perturbed zone to the existence of a 3D effect by the forcing in these regions. Steady excitation Pressure distributions for steady excitations at differents C W are showed in Fig. 17. On the intrados the actuation increased the value of the pressure and decreased the velocity. The

15 A Inviscid Exp Fluids (27) 42: a Cp Cp b Re= Actuator off DC Excitation C W = Inviscid Theory 2,,2,4,6,8 1, x/c Re= Actuator off DC Excitation C W = Re= Actuator off DC Excitation C W = Inviscid Theory,,2,4,6,8 1, Fig. 13 Near post-stall regime surface pressure distribution. Angle of attack a Actuated flow fully attached to the airfoil, b actuated flow partially attached to the airfoil Cp ,,2,4,6,8 1, x/c x/c Actuator off (Baseline) DC Excitation C W =15.94 AC Excitation C W =6.37, F + =.28 Inviscid Theory 19,7 25 m/s Leading edge Excitation Fig. 14 Near post-stall regime surface pressure distribution. Angle of attack 19.7 ; Re = 333,333 Cp m/s ,,2,4,6,8 1, x/c distributions resulted quite coincident when values of C W were of the same order and differences occurred only for C W values much higher. If we analyze the extrados, we observe that when actuation was absent the flow was fully separated and that the actuation postponed separation as the suction towards the leading edge indicate. As the coefficient C W was increased, these peaks were observed higher and for the highest values of C W the separation line was displaced towards the trailing edge and the flow resulted almost fully attached. The time averaged flow fields and their associated streamlines are shown in Fig. 18 (the base line flow is the same as in Fig. 16a). We can observe in presence of actuation that the separation line displaced downstream in correspondence with the observed suction peaks in the pressure distributions. For low levels of actuation, the flow contoured the airfoil at the vecinity of the leading edge and then separates without posterior reattachment (Fig 18a). As the reduced power was increased, the separation line moved further downstream. The perturbed zone observed for periodic excitation is still observed but its size was much lesser in these cases (Fig. 18b). The reduction of size of this zone, however, was observed with values of C W much higher than the one considered for periodic excitation experiments Deep post-stall regime Actuator off (Baseline) F + =.8 F + =.4 F + =.8 F + =1.6 Theory Fig. 15 Middle post-stall regime surface pressure distribution. Angle of attack 2.7 ; Re = 333,333; C W = 6.6 For higher values of the angle of attack a deep stall regime is observed. In this regime a full reattachment of the flow cannot be observed neither adjusting the value of C W nor the value of F +. The actuated flow in this case can remain attached only for a small cord length.

16 158 Exp Fluids (27) 42: Fig. 16 Middle post-stall regime time averaged flow fields with associated streamlines. Angle of attack 2.7 ; Re = 333,333. a Actuator off, C W =.; b actuator on, C W = 6.6, F + =.28 Periodic excitation Figure 19 illustrates the fact that even using higher values of C W than in the preceding regime a full reattachment could not be achieved for any tested frequency. The extrados pressure distributions exhibited regardless of the frequency considered the low-pressure region followed by a large plateau that can be associated to a flow separation without reattachment. On the contrary the maximum suction peak, the pressure value of the plateau and the position of initial point of the plateau could be modified upon a frequency variation. Then, even though the PSD forcing did not enable to impede the separation, a control of the separation line in this regime may still be achieved by adjusting the value of the frequency of excitation.

17 Exp Fluids (27) 42: Cp D.C. Excitation Actuator Off Cw=12.75; Re=333, Cw=19.12; Re=333, Cw=25.5; Re=333, Cw=31.87; Re=333, Cw=317; Re=233, Inviscid Theory,,2,4,6,8 1, X/C Fig. 17 Middle post-stall regime surface pressure distribution. Angle of attack Lift and drag pressure coefficients The preceding sections enabled us to demonstrate that for the different angles of attack there is an influence of F + and C W on the reattachment process. The analysis with the lift and drag pressure coefficients that we propose in this section would enable, in some extent, to better highlight this dependence. Figure 23 presents the lift coefficient differences DC l (periodic actuation on minus actuation off) and the difference of the ratio D(C l /C Dp ) (periodic actuation on minus actuation off) as a function of F +. The values of the C l and C Dp coefficients for the non-actuated case for different angles of attack are detailed in the caption of the figure. The DC l and D(C l /C Dp ) values corresponding to DC excitations are summarized in Table 1 as a function of C W. 3.4 Near post-stall regime The time averaged flow fields and their associated streamlines are shown in Fig. 2 to gain in clarity. The figures reveal that the large bubble when actuation was off, reduced its size and displaced towards the trailing edge when the actuation was on. The PIV tests for this regime also revealed in agreement with pressure distribution results, that the size of the recirculation bubble and its position depended on the frequency of excitation. Our observations corroborate that the larger regions were produced for the higher values of F +. Steady excitation Further with steady excitations, in this regime the flow could not be forced to a fully reattached configuration. Figure 21 illustrates the fact that even using higher values that triplicate the C W used with the preceding periodic cases a full reattachment could not be achieved. Regardless to the type of actuation considered, bubbles of separation at positions close to the leading edge always persisted as the extrados pressure distributions that have always exhibited a low-pressure region followed by a large plateau evidences. The time averaged flow fields and their associated streamlines for steady excitation are shown in Fig. 22. The large bubble when actuation was off (see Fig. 2a) can be reduced and displaced towards the trailing edge as the steady actuation was applied. The size of this bubble, however, was smaller than the one observed for the higher F +. For this regime the influence of the frequencies of excitation on the aerodynamic coefficients is evidenced by the analysis of curves for a = 15.8 and a = 19.8 in Fig. 23. The actuation produces an important increase of the aerodynamic coefficients C l and of the ratio C l /C Dp. These enhancements were associated, as previously detailed, to the passage from a separated flow configuration (actuator off) to a fully attached flow (actuator on). For an angle of attack a = 15.8 a relatively large value of C W (C W = 52.95) has been considered. In these experiments, a better performance of the lift coefficient C l was achieved with the lower range of frequencies F +, where the largest values of suctions in the inter-electrode region were observed. However, the lack of a clear effect of the frequency of excitation on the ratio C l /C Dp indicated that a compensation of the lift coefficient increase with a simultaneous drag pressure increase occurs for the low range of frequencies. The study of the same experiment but with steady excitation experiments indicated that similar airfoil performances may be achieved by adjusting the power of the DC actuator (see Table 1). However, the DC actuation required supplying a larger power to the flow. At higher angles of this regime and for much lesser values of power (curves for a = 19.8 C W = 3.35) a peak in the actuated airfoil performance coefficient occurred in correspondence with F +.4. For this

18 16 Exp Fluids (27) 42: Fig. 18 Middle post-stall regime time averaged flow fields with associated streamlines. Angle of attack 2.7. a Actuator on, C W = 25.5, Re = 333,333; b actuator on, C W = 317, Re = 233,333 value a full (or almost full) reattachment has been observed. With other frequencies the flow exhibited a bubble of recirculation that depending on its size degradates more or less the airfoil performance. For this angle of attack, a comparison of the steady and periodic excitation (Table 1) indicates that DC excitation may achieve similar effects than those of periodic but it again requires larger power consumption Middle post-stall regime The behavior in this regime, for periodic excitation, is illustrated in Fig. 23 with curves for an angle of attack a = 2.7. Furthermore, a relatively reduced value of power was considered in these experiments (C W = 6.6). In this case, however, no peak of the aerodynamic performance was detected and in conse-

19 Exp Fluids (27) 42: Cp m/s 2,,2,4,6,8 1, x/c quence no clear preferential frequency could be observed. When the flow is steadily actuated with small values of non-dimensional power, the actuated flow contours the airfoil at the vicinity of the leading edge and then separates without posterior reattachment. For the higher values of C W tested, the performance of periodic excitation could not be achieved by a steady one even supplying values of power one order of magnitude larger Deep post-stall regime Actuator off (Baseline) F + =.8 F + =.2 F + =.28 F + =.6 F + =2 Inviscid Theory Fig. 19 Deep post-stall regime surface pressure distribution. Angle of attack 21.6, Re = 333,333, C W = 8. At these regimes the flow is partially reattached and a degradation of the airfoil performance can be observed as higher values of frequencies are used. This is ascribed to the influence of the frequency of excitation on the size and position of the recirculation bubble. As the lower frequencies better postpone the separation than the higher frequencies, the airfoil performance enhances for these frequencies. The comparison with steady excitation indicates that in this regime similar effects may be achieved by the DC actuator by suitably adjusting the power of it, but also occurs that this actuation as in the near stall regime requires large power supply to reattach the flow. 3.5 Some considerations related to the optimal reduced frequency F + The analysis of the receptivity of separated flows to different frequencies of forcing is quite a complicated problem. Different authors (Mittal et al. 25; Wu et al. 1998) signal that the characteristic frequency which may dominate the dynamics of the flow (f flow ) depends on the non-linear interacting phenomena with different characteristics frequencies such as the wake vortex shedding frequency (f wake ), the free shear layer frequency (f sl ) and a frequency associated to instabilities in the bubble of separation (f sep ) if it exists. As a result, the experimental results obtained by different authors have found values of effective F + varying over a wide range depending on the kind of actuations and the flow configurations considered. In general, when reducing the intensity of actuation with different actuators, an optimal value of the frequency of the forcing may be detected that in many cases has been close to 1. (Greenblatt and Wygnanski 2; Seifert and Pack 1999; Amitay et al. 21). In our study when low values of C W were considered (curves for a = 19.8, C W = 3.35, power consumption per unit of electrode length W ele /b ~ 5.5 W/m) a peak in the actuated airfoil performance occurred in correspondence with F +.4. With higher values of C W,we have observed a broad range of effective forcing frequencies instead of a definite F + opt. The same value for the optimal frequency (F + opt.5 for a =19 ) anda similar broadening in the effective excitation frequency as the power level increased had been also observed in similar studies with EMHD (electro-magneto-hydrodynamic) actuators (Weier et al. 23). The nature of the forcing of this study was of magnetohydrodynamic nature with forces acting in a region of similar relative length (d/c.1) than our inter-electrode space. Recent studies with DBD actuators operated at different frequencies have been undertaken (Corke and Chuan He 24; Corke and Post 25). These results have shown a large sensitivity of the flow to the frequency of excitation and for electric power levels relatively small (W ele /b ~ 6.5W/m) a peak of aerodynamic performance indicated that for a =16 the optimal frequency occurred at F + opt 1.. As we compare our results of similar input of power of those of DBD, we observe that the optimal frequencies F + opt are quite different. We associate these differences to the different characteristics of the forcing introduced by both actuators. The large ionization regions of PSD where the forcing takes place (L ele / c.15) cannot be considered punctual as it is the case for a DBD. In consequence when cyclic actuations are proposed even though similar reduced frequencies could be considered, they should not necessarily excite the flow with the same wavelengths. In consequence, as we observe, the frequencies producing higher performances should not be coincident for the different EHD actuators. Our argument is reinforced by the

20 162 Exp Fluids (27) 42: Fig. 2 Deep post-stall regime time averaged flow fields and associated streamlines. Angle of attack 21.6, Re = 333,333. a Actuator off, C W =.; b actuator on, C W = 8, F + =.8 agreement of PSD results with those of Weier et al., where the forcing regions were similar in both experiments and the optimal frequencies resulted quite coincident. For the higher values of the power we observe a shift of frequencies towards the lower range. The curves are in fact curves obtained for the same quasi-steady current and with the same driving voltage. Strictly these curves do not correspond to curves with the same electric power as a consequence of deformation of the voltage signal with the frequency of excitation that we have mentioned in previous section. This effect should be higher for the larger frequencies and so we cannot conclude from our experiments that for the case with important C W the lower range of frequencies are better than other one.

21 Exp Fluids (27) 42: Cp Actuator off (Baseline) DC Excitation C W =23.9 AC Excitation C W =8, F + =.2 Inviscid Theory m/s Leading Edge Excitation a C L,55,5,45,4,35 α=15.8 -C W = α=19.8 -C W = 3.35 α=2.7 -C W = 6.6 α=21.6 -C W = 8.,3,25 1,2 2,,1,2,3,4,5,6,7,8,9 1, x/c Fig. 21 Deep post-stall regime surface pressure distribution. Angle of attack 21.6, Re = 333,333 b,15,,2,4,6,8 1, 1,2 1,4 1,6 1,8 2, 3, F + (Cl/C DP ) 2,5 2, 1,5 α=15.8 -C W = α=19.8 -C W = 3.35 α=2.7 -C W = 6.6 α=21.6 -C W = 8. 1,,5,,2,4,6,8 1, 1,2 1,4 1,6 1,8 2, F + Fig. 23 Difference on coefficients of aerodynamic performance as a consequence of actuation at different frequency of excitation. a Difference of the coefficients C l ; b difference of the ratio C l /C Dp. For the cases actuator off the values of the coefficients (C l ;C l /C Dp ) are for a = 15.8 : (.56; 3.1), a = 18.8 (.56; 2.47), for a = 19.8 :(.59; 2.34), for a = 2.7 : (.62; 2.29), and for a = 21.7 : (.67; 2.25) Fig. 22 Deep post-stall regime: time averaged flow fields and associated streamlines. Angle of attack 21.6, Re = 333,333; actuator on, C W = Actuator s location Previous research efforts have shown that with different kind of actuators the forcing of the flow was more effective when actuators were placed at, or close to, the separation line (point) (Greenblatt and Wygnanski 2). Particularly, for the PSD it has been shown that flow control at low Re numbers (Re 1 4 ) the efficiency of actuation depends among other parameters on the distance between the position of the actuator and the laminar separation point (Sosa and Artana 26). This work has shown that for steady EHD actuation the higher this distance the higher the intensity level required to produce similar effects of reattachment. Subsequent works have also analyzed at higher Reynolds number the effect of electrode placement for the same kind of airfoil but constructed with a larger chord and will be communicated soon (Jolibois et al. 26). In the present work, considering higher Re number (Re 1 5 ) and also periodic excitation we could corroborate the previous results related to the actuator location influence. The time averaged flow fields and their associated streamlines, corresponding to a = 15.8 and

22 164 Exp Fluids (27) 42: Table 1 Difference on coefficients of aerodynamic performance as a consequence of actuation with a DC excitation A (degree) C W DCl D(Cl/C Dp ) For the cases actuator off the coefficients C l and the ratio C l /C Dp are the same as the caption of Fig. 23 Re = 133,333, are represented in Fig. 24. In absence of actuation it can be observed in Fig. 7a the existence of a clear recirculation zone associated to the separated flow. When actuation occurs close to the leading edge and for C W = and F + = 1 (Fig. 24a) the flow reattachment takes place and this zone disappears. However, for the same flow conditions when the actuator was located close to the trailing edge (anode at x/c =.55, cathode at x/c =.79) the separated flow was not modified whatever the F + and C W considered, and the time averaged flow fields and their associated streamlines (Fig. 24b) almost correspond to the baseline flow. Let us consider a flow regime corresponding to the linear part of the curve, C L vs. a (non-stalled flow), to visualize how the actuation forces the flow. We analyze the streamlines of the vector field obtained by making the difference of the time averaged velocity field for the actuator on and off cases. ( ~ U dif ¼ ~ U on ~ U off, where: ~ U on is the actuated flow velocity field and ~ U off is the baseline velocity field). On Fig. 25 (Re = 1, and a =13 ) we can observe that the actuations force the flow tangentially downstream the actuator but does not tangentially pull the flow from upstream. On the contrary the actuation induces a fluid movement of suction in the direction normal to the wall that continues downstream the actuator with a tangential acceleration. This agrees with other related works where it has been observed similar effects (Moreau et al. 25; Jolibois 26). In consequence these results signal that for the range of Reynolds number considered the electrode placement, and in consequence the forcing, has to be in proximity to the separation line if reattachment is the required use for the actuator. 4 Conclusions We have analyzed the influence on the aerodynamic performance of an airfoil, of different relevant nondimensional parameters (power addition, reduced frequency) characteristic of actuation with PSD. The significant modifications were observed when the flows were actuated in post-stall conditions meanwhile actuation in naturally attached flows did not produce important changes in the flow structure. In flow regimes considered (Re 1 5 with associated velocities of some tenths of meters per second) a periodic or steady actuation enables to prevent or postpone separation for angles of attack overcoming the steady stall angle up to 6. According to the angle of incidence and to the receptivity of the flow to the actuation, three different behaviors could be identified: near, middle and deep post-stall regime. In the first regime a full or almost full reattachment of the flow may be achieved either by a suitable adjustment of the frequency of excitation or of the power supplied to the actuator. In the middle poststall regime, the separation line could be postponed to positions close to the trailing edge but could not be eliminated. For the third group only a partial reattachment could be observed and the separation occurred always at moderate values of x/c. In the first group and for small values of the nondimensional power coefficient C W, we could observe a peak of the aerodynamic performance in correspondence with a frequency F +.4. As we increased power, a broadening of the receptivity of the flow to different frequencies was observed and the aerodynamic performance of the actuated airfoil resulted much less sensitive to the frequency of actuation. The comparison of flows with reduced levels of actuations of PSD and other EHD devices, like the DBD, reveals a difference of the optimal frequency of excitation. We have associated this difference to the fact that the PSD acts in a larger length in the streamwise direction (inter-electrode space). Even though our results signal the importance of the ratio between the inter-electrode distance and the cord length, a detailed study on the influence of this parameter on the optimal frequency of forcing should be undertaken in future. A comparison of the steady excitations with periodic ones indicates that similar effects could be

23 Exp Fluids (27) 42: Fig. 24 Near post-stall regime time averaged flow fields. Angle of attack 15.8, Re = 133,333. a Leading edge actuator on, C W = 52.95, F + =1;b trailing edge actuator on, C W = 52.95, F + =1 achieved with both kinds of forcing. The steady excitation required, in general, a larger input power and this was more marked for the middle post-stall regime. However, it should be signaled that the excitation with DC sources does not have an associated reactive power due to capacitive effects as the periodic excitation. The efficiency of the forcing with the PSD depends, such as with other actuators, on the relative distance between the position of the actuator and the separation point (line). This is a consequence that the actuation of the flow produces suction mainly in the direction normal to the wall rather than tangentially upstream. Our research indicates that the optimal actuator

24 166 Exp Fluids (27) 42: Fig. 25 Time averaged velocity field difference (actuator on actuator off) and associated streamlines with the actuator placed at the vicinity of the trailing edge (x/c =.55 x/c =.79, C W = , angle of attack 13, Re = 1,) location seems to be in the proximity of the separation line and if the PSD is placed too far downstream no effect should then be observed. Acknowledgments This research has been done with grants UBACYT I3 and PICT of the Argentine government. References Amitay M, Smith D, Kibens V, Rarekh D, Glezer A (21) Aerodynamics flow control over an unconventional airfoil using synthetic jet actuator. AIAA J 39(3): Artana G, D Adamo J, Leger L, Moreau E, Touchard G (22) Flow control with electrohydrodynamic actuators. AIAA J 4(9): Artana G, Sosa R, Moreau E, Touchard G (23) Control of the near wake flow around a circular cylinder with electrohydrodynamic actuators. Exp Fluids 36(6): Bergh H, Tijdeman H (1965) Theoretical and experimental results for the dynamic response of pressure measuring systems. National Aero and Astronautical Research Institute, Amsterdam, NLR report F.238 Bushnell D (1983) Turbulent drag reduction for external flows. AIAA paper no Colver G, El-Khabiry S (1999) Modeling of DC corona discharge along an electrically conductive flat plate with gas flow. IEEE Trans Ind Appl 35(2): Corke T, Chuan He (24) Plasma flaps and slats: an application of weakly-ionized plasma actuators. AIAA paper no Corke T, Post M (25) Overview of plasma flow control: concepts, optimization, and applications. AIAA paper no , Reno, Nevada Corke T, Jumper E, Post M, Orlov D, McLaughlin T (22) Applications weakly ionized plasmas as wing flow control devices. AIAA paper no D Adamo J, Artana G, Moreau E, and Touchard G (22) Control of the airflow close to a flat plate with electrohydrodynamic actuators. ASME paper no Forte M, Jolibois J, Moreau E, Touchard G, Cazalens M (26) Optimization of a dielectric barrier discharge actuator by stationary and non stationary measurements of the induced flow velocity-application to airflow control. In: 3rd AIAA flow control conference 5 8 June 26, San Francisco, California Greenblatt D, Wygnanski I (2) The control of flow separation by periodic excitation. Progr Aerosp Sci 36: Huerre P, Monkewitz P (199) Local and global instabilities in spatially developing flows. Annu Rev Fluid Mech 22: Johnson J, Scott S (21) Plasma aerodynamic boundary layer interaction studies. AIAA paper no Jolibois J, Forte M, Moreau E (26) Separation control along a Naca 15 airfoil using dielectric barrier discharge actuators. IUTAM, London, September Keane R, Adrian R (1992) Theory of cross correlation analysis of PIV images. Appl Sci Res 49: Kunhardt E (2) Generation of large volume atmospheric pressure non-equilibrium plasmas. IEEE Trans Instrum Meas 28(1):189 2 Lagarkov A, Rutkevich I (1993) Ionization waves in electrical breakdown of gases. Springer, Berlin Heidelberg New York, pp Leger L, Moreau E, Touchard G (22) Electrohydrodynamic airflow control along a flat plate by a DC surface corona discharge velocity profile and wall pressure measurements. AIAA paper no Louste C, Artana G, Moreau E, Touchard G (25) Sliding discharge in air at atmospheric pressure: electrical properties. J Electrostatics 63: Malik M, Weinstein L, Hussaini M (1983) Ion wind drag reduction. AIAA paper no Mittal R, Kotapati B, Cattafesta L (25) Numerical study of resonant interactions and flow control in canonical separated flow. AIAA paper , Reno, Nevada Moreau E, Artana G, Touchard G (24) Surface corona discharge along an insulating flat plate in air applied to electrohydrodynamically airflow control: electrical properties. Electrostatics 23, vol 178, IOP Publishing Ltd, Bristol-Philadelphia, Moreau E, Labergue A, Touchard G (25) DC and pulsed surface corona discharge along a PMMA flat plate in air: electrical properties and discharge-induced ionic wind. J Adv Oxidation 8(2): Moreau E, Leger L, Touchard G (26) Effect of a DC surface non thermal plasma on a flat plate boundary layer for airflow velocity up to 25 m/s. J Electrostatics 69: Noger C, Chang JS, Touchard G (1997) Active controls of electrohydrodynamically induced secondary flow in corona discharge reactor. In: Proceedings of the 2nd International Symposium Plasma Technology Pollution Control, Bahia, pp Post M, Corke T (23) Separation control on high angle of attack airfoil using plasma actuators. AIAA paper no Post M, Corke T (24) Separation control using plasma actuators stationary and oscillating airfoils. AIAA paper no Roshko A (1954) On the drag and shedding frequencies of two dimensional bluff bodies. NACA TM 3169, 61, 118 Roth JR (23) Aerodynamic flow acceleration using paraelectric and peristaltic electrohydrodynamic (EHD) effects of a one atmosphere uniform glow discharge plasma. OAUGD, Physics of Plasmas 1(5):