SIMPLE DESIGN OF MULTIPLE AERODYNAMIC PLASMA ACTUATOR

A new simple design of multiple dielectric barrier discharge (DBD) actuator intended for gas §ow acceleration in thin boundary layer on lengthy aerodynamic surface is proposed. The operability of the considered multi-DBD-actuator is con¦rmed experimentally. Proposed method of measurements of the electric power consumed by the actuator permits to estimate this value simply and with acceptable accuracy. The thrust generated by DBD-actuator and thrust-to-power relation were estimated owing to pressure probe measurements of the induced §ow velocity.


INTRODUCTION
At present signi¦cant attention is given to study of possible applications of plasma actuators for gas §ow control on aerodynamic surfaces [14].For example, laminar-to-turbulent transition delay in boundary layer on airplane wing is one of the e¨ective methods of friction drag reduction and, consequently, fuel consumption and atmospheric pollution decrease.Electrogasdynamic method of laminar §ow control (EGD-LFC) on a swept wing proposed at TsAGI [5,6] implies volumetric force impact and, as a consequence, boundary layer §ow acceleration in small vicinity of a wing leading edge along the whole of the edge.Dielectric barrier discharge actuators in series [7] seem to be suitable for creation necessary force impact over a lengthy part of a wing surface.But it must be taken into account that the boundary layer thickness near the swept wing leading edge of typical civil airplane at cruise §ight conditions is very small (less than 0.5 mm) [8].This circumstance demands the use of diminutive enough actuators.At the same time, the cross-talk phenomenon between the adjacent electrodes of actuators in series reduces the advantage of the multiple DBDs concept if the successive actuators of usual two-electrode con¦guration are placed at a very short distance [9].
Several innovative designs of multiple DBD-actuators have been proposed to eliminate this damaging cross-talk phenomenon [10].In design [11], each single two-electrode DBD-actuator in series is replaced by a three-electrode actuator where the third buried electrode is electrically linked with the high-voltage exposed electrode and acts as a shield of one (for example, left) edge of each exposed electrode.Dielectric barrier discharge takes place near opposite (right) edges of the exposed electrodes thereby supporting the volumetric force impact and §ow acceleration only in one direction (from left to right) along a streamlined surface.Two dielectric layers separate successively the exposed, the shielding, and the buried grounded electrodes.Note that minimal spatial period of multi-DBDactuators studied experimentally in [11] is p = 20 mm.
Another multi-DBD-actuator consisting of combination of smooth highvoltage buried electrodes, saw-like exposed grounded electrodes, and saw-like exposed §oating interelectrodes has been proposed and studied in [12].Spatial period of the investigated multi-DBD-actuator in [12] is equal to p = 25 mm.More complex design of large-scale multi-DBD-actuator with spatial period of p = 40 mm has been considered in [13].Two main features distinguish this design from usual two-electrode one.First, the plane exposed electrodes are replaced by thin wires in order to enhance the volumetric force impact of each single DBD, according to [14].Second, the potential alteration of the successive both exposed and buried electrodes between high-voltage and ground is used in order to cancel their damaging interference.
The e¨ectiveness of all mentioned designs has been con¦rmed experimentally.But all of them do not take into account some features of practical application in EGD-LFC.First of all, signi¦cant miniaturization of the multi-DBD-actuators [1113] is necessary for their possible application in laminar §ow control on a swept wing because of very small boundary layer thickness, as it was mentioned above.Moreover, a precipitation of water on a wing surface in the case of a §ight in clouds can lead to uncontrolled gas breakdown in actuators [12,13] where high-voltage swing between adjacent air-exposed electrodes is present.Finally, every multiple DBD-actuator will be installed over a wing skin which must be electricity-conductive according to electrostatic safety requirements.It means that additional dielectric layer separating the wing skin and actuators is necessary in designs [1113].

PROPOSED DESIGN OF MULTIPLE DIELECTRIC BARRIER DISCHARGE ACTUATOR
First of all, note that the electric potential acquired by an airplane as a whole in §ight due to various electrization processes is determined below conventionally as zero or grounded.The idea of the shielding buried electrodes electrically linked with the exposed ones proposed in [11] has been adopted in numerical modeling [15] of slightly modi¦ed design of multi-DBD-actuator shown in Fig. 1.Distinctions from design [11] consist, ¦rst, in the presence of grounded wing skin A and, second, in the arrangement of the grounded accelerating electrodes B and the high-voltage shielding electrodes C under the same external dielectric layer 1 separating the buried electrodes B, C, and the high-voltage exposed electrodes D. Electric ¦eld strength in the vicinity of the left edges of the exposed electrodes is reduced due to the shielding electrodes and DBD attenuates in these regions.Resulting horizontal volumetric force F generated in DBD near the right edges is directed from left to right.The internal dielectric layer 2 separates electrodes B, C, and the wing skin A. Numerical modeling in [15] executed for geometric parameters p = 10 mm, h e = 2 mm, h s = 2 mm, h a = 5 mm, d 1 = 1 mm, and d 2 = 2 mm con¦rmed signi¦cant positive in §uence of the shielding electrodes.Next evident step in simpli¦cation and improvement of multi-DBD design made in [15] consists in the removal of buried accelerating electrodes B. In this case, the grounded wing skin acts as common accelerating electrode for all exposed electrodes in series.At the same time, the probability of electric breakdown in glue layer between the electrodes B and C at too small distance between them is removed.
Figure 2 demonstrates the dependencies of the ratios of the maximum values of the electric ¦eld strength on the active (right) E 1 and the passive (left) E 2 edges of the external electrodes on the width of the shielding electrode at two values of the external dielectric thickness d 1 .The right edge of the shielding electrode is located under the middle of the external one.Further displacement of this edge to the right noticeably weakens the ¦eld strength on the right active edge of the external electrode.This in §uence limits at some extent the possibility of a decrease of the exposed electrode width.The data in Fig. 2 are obtained in [15] by solving the electrostatics Figure 2 The ratio of the maximums of the electric ¦eld strength at the opposite edges of the external electrodes at d1 = 0.5 (1) and 0.25 mm (2) problem without accounting for the surface charge on the external dielectric layer at the following parameters: the spatial period p = 10 mm, the width of the external electrode h e = 2 mm, its height is 50 µm, the radius of rounding of its edges is 5 µm, thickness of the inner dielectric layer is d 2 = 1 mm, its relative permittivity is ε 2 = 2.1, and the permittivity of the external dielectric layer is ε 1 = 3.5.The presented data demonstrate that the shielding electrodes can be of a very narrow for e¨ective screening of passive edges of the external electrodes at a su©ciently thin external dielectric layer.As a consequence, the more lengthy parts of the grounded electrode A may be involved in generation of a volumetric force than in design with the buried accelerating electrodes B of ¦xed width.
The operability of the proposed simpli¦ed design of multi-DBD-actuator consisting of the common accelerating electrode A, the shielding electrodes C, and the exposed electrodes D as well as the possibility of its essential miniaturization have been con¦rmed in experiments described below.

EXPERIMENTAL EQUIPMENT AND METHODS
The ¦rst model of multiple DBD-actuator used in experiments was made of two glass ¦bre laminate plates, 145 × 150 mm in size.The thicknesses of the upper and lower plates were d 1 = 0.5 mm and d 2 = 1 mm, respectively.Nine parallel §at copper electrodes of 50-micron height and 115-millimeter length in span direction were arranged on both sides of the upper plate with spatial period p = 12 mm.The width of the air-exposed electrodes was h e = 2 mm, their height was 50 µm, and the width of the shielding electrodes was h s = 3 mm.Each shielding electrode was shifted under the nearest exposed one up to 1 mm.The second plate contained a continuous copper electrode on the whole lower surface.The plates were pasted together by special glue under low ambient pressure to avoid possible discharge ignition in air bubbles between the plates.The air §ow velocity induced by the actuator impact in initially quiescent air was measured over the model by Pitot probe made of ceramic pipe with the external and internal diameters of 1.2 and 0.7 mm, respectively.Di¨erence between total and static pressures was measured by special inclined alcohol pressure microsensor.When measuring the velocity pro¦les, the sensor was moved by a traversing microgear at steps of 0.1 mm normal to the model surface.The model and the traversing microgear were mounted on a common platform.The Pitot probe also could be moved along the center of the model, perpendicular to the external electrodes.
Continuous electrode on the lower plate was grounded and alternating high voltage was applied on air-exposed and shielding electrodes placed on the upper plate.Dielectric barrier discharge on the model was excited by high-voltage power supply generating alternating pulses with the amplitude V h = 1.56 kV and the duration t imp = 20 µs.The repetition rate of pulses, i. e., the discharge frequency, was controlled by variation of the pause duration t int between the pulses and could be varied in the range f ≡ 0.5/(t imp + t int ) = 2.512.5 kHz.
The power supply consisted of two main units ¡ the power module and the module of high-voltage pulses generation.The power module consisting of a supply-line ¦lter and thyristor recti¦er was, in essence, the controllable directcurrent source with output controlling voltage V c = 20250 V. Controlling direct current I c and voltage V c were measured by proper devices arranged in the power supply module.
The module of generation of high-voltage pulses consisted of two units ¡ the module of excitation and the module of pulses formation.The excitation module was intended for generation of two series of pulses and control of their parameters t imp and t int .A quartz oscillator with frequency 1 MHz was used as a source of initial pulses ensuring high stability of the prescribed parameters.The formation of proper high-voltage pulses supplied on the model of DBD-actuator was executed in the bridge transformer circuit containing power high-voltage ¦eldistors.Control of forms and values of the high voltage V h and current I h in the secondary circuit of the transformer was realized by digital oscilloscope of series RIGOL DS1062C.
Figure 3a demonstrates that the amplitude of the high voltage V h applied to the model depends linear on the controlling voltage V c supplied by the directcurrent source.The slope angle of the approximating line does not depend on the frequency f because this angle is determined by relation of turns in transformer coils.In the present case, V h /V c = 47.As an example, the oscillograms of high voltage V h and total (displacement plus conduction) current I h in the secondary circuit of the transformer are shown in Fig. 3b for t imp = 20 µs and t int = 60 µs, i. e., f = 6.25 kHz.

MEASUREMENTS OF THE INDUCED FLOW VELOCITY
The  First of all, note that the discharge glow was observed visually only on the right unshielded edges of all exposed electrodes.The dependences of the induced velocity on the streamwise coordinate x presented in Fig. 4 are nonmonotonic but this velocity always remains positive similar to measurements in [1113].It means that the force impact of the actuator is directed in one side (from left to right) over the whole model.
According to Fig. 4, it seems that induced §ow achieves the saturation state after the third-¦fth single actuator depending on the discharge frequency.To clarify this case, Fig. 5 presents the velocity distributions in the vertical direction measured after the ¦rst, second, third, and ninth exposed electrodes at 4 mm from their right edges (i.e., at x = 4, 16, 28, and 100 mm) at high-voltage amplitude V h = 4.2 kV and frequency f = 6.25 kHz.Indeed, the maximal induced velocity increases fast from 1.5 m/s after the ¦rst actuator up to 2.4 m/s after the third one and only to 3 m/s after the ninth actuator.
But the maximum of the induced velocity is not the essential characteristic of plasma actuators because it depends, for example, on external over §ow.The intrinsic characteristics of plasma actuators determinative their e¨ectiveness for §ow control are the time averaged and spatial integrated volumetric force created by actuator and the average consumed electric power.The velocity distributions presented in Fig. 5 permit to estimate the algebraic sum of the positive volumetric force generated by actuator and the negative skin friction force incipient due to §ow appearance.Simplest integral momentum method applicable for pressure probe measurements [14] was used for total force calculation.The results are presented in Fig. 6.One can see that the sum of volumetric and skin friction forces increases almost linear after the ¦rst three actuators but then its growth becomes much slower.It seems evident that the volumetric force generated by actu-  But the integral of the friction along the model surface increases modulo more rapidly than linear because of gradual increase in the vertical gradient of §ow velocity on the model surface and, hence, local skin friction.A very signi¦cant contribution of viscous drag in total thrust produced by single DBDactuator was emphasized in [16].Local skin friction can be measured by more complex and precise methods than used here, for example, by particle image velocimetry [17].Nevertheless, a crude estimate can be obtained using the data of Fig. 5.The average skin friction between the third and ninth electrodes is estimated as τ w ≈ µ-u/-y where µ ≈ 1.8 • 10 −5 kg/(m•s), -u ≈ 2 m/s, and -y ≈ 5 • 10 −4 m; hence, τ w ≈ 0.07 N/m 2 .Local skin friction is integrated along the part of the surface -x ≈ 0.07 m; hence, the integral friction force is estimated as F f = −τ w -x ≈ −5 • 10 −3 N/m and is modulo comparable with the values of the total force in Fig. 5, i. e., really contributes noticeably in this force.

SIMPLE METHOD OF THE CONSUMED ELECTRIC POWER MEASUREMENT
Two methods are usually used for computation of the electric power consumed by DBD-actuator [10].The ¦rst one consists in time-averaged integration of the product of current and voltage applied to actuator over several cycles of the discharge.The main problem of this method is related with the presence of high current peaks; therefore, high enough resolution in current measurements is necessary.Another method is based on placing a capacitor between grounded electrode and earth, plotting the voltagecharge curve (usually called ¤Lissajous loop¥) and calculation of the area of this curve corresponding to the energy dissipated by the discharge during one cycle.The features of the high-voltage power source used in the current experiments permit to estimate the electric power consumed by the discharge simply and with acceptable accuracy immediately during an experiment at variation of its parameters, for example, amplitude and frequency of the applied voltage, ambient pressure, etc. Controlling voltage V c and current I c at the output of the recti¦er module gives the value of the total electric power P tot = I c V c consumed, at ¦rst, by the module of generation of high-voltage pulses and, at second, by the discharge on the model of multi-DBD-actuator, i. e., P tot = P gen + P dis .If the model is cut o¨from power supply, the total power is consumed only by the module of pulses generation, i. e., P tot = P gen .Preliminary measurements of P gen with the model in the silent state at various controlling voltage V c permit henceforth to calculate the discharge power as P dis = P tot − P gen .
Figure 7 represents the dependences of the consumed power on controlling voltage at the discharge frequency f = 6.25 kHz corresponding to the results

Figure 7
Dependences of the consumed electric power on controlling voltage at f = 6.25 kHz: 1 ¡ Ptot; 2 ¡ Pgen; and 3 ¡ P dis shown in Figs. 5 and 6.Here, the power consumed by the discharge per unit length of the exposed electrodes P 1 is shown too.In particular, P 1 = 44 W/m at the controlling voltage V c = 90 V corresponding to the high-voltage amplitude V h = 4.2 kV.
The data of Figs. 6 and 7 permit to estimate the average energy e©ciency E of the considered multi-DBD-actuator de¦ned as the relation of average total force to consumed power per unit length of the exposed electrodes [18].The unit average force is evaluated here as one third of the force measured behind the third electrode F 1 = 12.9/3 = 4.3 mN/m.As P 1 = 44 W/m at V h = 4.2 kV and f = 6.25 kHz, then E ≈ 10 −4 s/m.This value is appreciably less than the best e¨ectiveness (E ≈ 6 • 10 −4 s/m) achieved in single DBD-actuator [10].Moreover, the average force density per unit of a streamlined surface obtained in the considered actuator is estimated as F ≡ F 1 /p = 4.3/12 = 0.36 N/m 2 .According to the numerical estimations [19], the EGD-LFC method demands the value of the average volumetric force density about F = (34) N/m 2 .It means that further improvement and optimization of the considered multi-DBDactuator is necessary.

LIMITATIONS OF MULTIPLE DIELECTRIC BARRIER DISCHARGE ACTUATOR MINIATURIZATION
The possibility of signi¦cant miniaturization of the proposed design of multi-DBD-actuator was veri¦ed.Figure 8a shows the model with two multiple actuators made of the same materials as above, i. e., the upper and lower dielectric plates thicknesses are d 1 = 0.5 mm and d 2 = 1 mm.The width of both external and shielding electrodes is h e = h s = 1 mm.The shielding electrodes is quite di¨erent.In this case, the discharge takes place even on the shielded edge of the lowermost electrode and is almost hidden on active edges of the ¦rst three lower electrodes.One can hope that the operable multiple actuator with the period less than 5 mm can be made by a decrease of the thicknesses of the dielectric layers.
Accounting for previous results, the model of multi-DBD-actuator containing 12 couples of the exposed and shielding electrodes with sizes indicated in Fig. 9 (p = 6 mm) has been made.The photo in Fig. 9b shows the discharge picture at the applied voltage of 8 kV and 10 kHz.It is evident that the discharge takes place only on all active (lower) edges of the exposed electrodes and generates the force impact and the induced §ow top-down.

CONCLUDING REMARKS
The preliminary experimental study revealed the potentiality of the proposed design of multi-DBD-actuator for application in electrogasdynamic laminar §ow control on a swept wing.

Figure 1
Figure 1 Design of multiple DBD-actuator: A ¡ grounded wing skin; B ¡ grounded accelerating electrodes; C ¡ high-voltage shielding electrodes; D ¡ high-voltage exposed electrodes; and 1 and 2 ¡ dielectric layers

Figure 3
Figure 3 Dependence of high-voltage amplitude on controlling voltage (a) and typical oscillograms of high voltage (1) and current (2 ) (b) component of the §ow velocity induced by multi-DBD-actuator in initially quiescent air directed along the model surface was measured by pressure probe placed on the surface and moving along it perpendicular to the exposed electrodes, i. e., approximately at the height y = 0.6 mm.The results of measurements at three values of the discharge frequency f = 4.16, 5, and 6.25 kHz are shown in Fig.4.The amplitude of high-voltage pulses was equal to V h = 4.2 kV at the controlling voltage V c = 90 V.Note that the current value in low-voltage circuit of power supply is proportional to the discharge frequency and is determined in this case by the relation I c /f ≈ 0.26 A/kHz.

Figure 6
Figure 6 Distribution of total induced force along the model

Figure 8 Figure 9
Figure 8 Photos of multi-DBD-actuators (a) and the discharge (b) at period p = 4 mm (top) and 5 mm (below)