POWER CONSUMPTION BY AN SDBD PLASMA ACTUATOR AT VARIOUS PRESSURES

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1 AME60637: Ionization and Ion Transport Final Project Paper May 5, 2010 Notre Dame, IN USA POWER CONSUMPTION BY AN SDBD PLASMA ACTUATOR AT VARIOUS PRESSURES John A. Cooney, Jr. University of Notre Dame Notre Dame, Indiana, USA ABSTRACT Power measurements have been taken for an SDBD plasma actuator across a range of applied voltages, spanning 5 kv to 13 kv, and pressures, spanning 0.3 atm to 1.0 atm. This study has been motivated by recent investigations, including high speed, low pressure projectile applications as well as for use on utility-size wind turbines, where the exact power required to operate the actuators was of critical importance. The geometry of the actuator was a flat plate consisting of Teflon for the dielectric material and copper tape for the electrode material. The power was estimated from phase-averaging voltage and current measurements over many cycles. While the current could not be fully resolved, the expected trends for the dependence of power on applied voltage were exhibited lending confidence to the general accuracy of the experimental method. For a fixed potential, power was found to be inversely proportional to pressure over the range of pressures tested. Plotting voltage versus charge did not result in the assumed shape of a parallelogram. This was attributed to too little power dissipated to adopt the traditional shape and the practice of powering both electrodes, rather than grounding one. NOMENCLATURE C Capacitance I Current P Power Q Charge R Resistance T Period of Applied Waveform U Applied Potential c Empirical constant f Frequency of Applied Waveform p Pressure t Time β Ratio of capacitances Subscripts/Superscripts D Dielectric G Min RMS (Air) Gap Minimum Root Mean Square INTRODUCTION Background Dielectric barrier discharges (DBDs) have been studied for a variety of industrial applications for well over a century. In the last decade, DBDs have generated significant interest in the aerospace community as a potential means of flow control primarily beginning with the early work of Roth et al [1] and expanded by Enloe et al, [2], [3]. In applications of flow control, these devices are often referred to as plasma actuators. More precisely, because the typical geometry only utilizes a single dielectric, the phrase single dielectric barrier discharge (SDBD) plasma actuator is commonly used. The canonical geometry of a SDBD plasma actuator is given in Figure 1, where a dielectric material, in this case Kapton, separates two electrodes. One of the electrodes is covered up or insulated while the other is exposed to the freestream. Applying a strong voltage drop, typically on the order of kv, across the two electrodes results in plasma formation from the exposed electrode in the direction of the insulated electrode. Through the ionic wind phenomenon, additional velocity is imparted to the freestream, adding momentum to the flow. Figure 1. Typical SDBD Geometry Plasma actuators offer a number of benefits over traditionally mechanical means of flow control including 1.1

2 the ability to be integrally machined into surfaces, very quick time response, and lack of any moving parts. Compared to other types of plasma discharges for applications of flow control, DBDs offer the advantages of stability across a wide range of pressures, including atmospheric pressure, and relative ease of scaling. In order to operate these actuators, power is required, one difference from most mechanical means of flow control, in order to sustain a potential difference across the electrodes. The most successful applications have typically involved boundary layer manipulation and separation control. However, a number of groups are currently working on diverse aerospace applications. The reviews of Corke et al [4] and Kogelschatz [5] are suggested for further reading on the current state of research and typical applications. The exact power consumption of these actuators, though, has not always been a primary concern in many studies. In some cases, it was assumed that the gains offered by plasma actuators, such as the prevention of stall, outweighed power considerations. Alternatively, in other applications these devices would only be used rarely, such as alleviation of very strong gusts, and power consumption once again was considered negligible. Coupled with inherent difficulties in obtaining accurate power estimates, power measurements were not always made in experimental investigations and rules of thumb, such as the published estimate of 20 W / linear ft [6], were sometimes offered in lieu. However, two areas of personal research have involved applications where determining the exact power required held a much greater priority. The first application involved the feasibility of plasma actuators for steering supersonic projectiles by asymmetric shock generation. Here, power was a critical concern because there was very little room for a power supply in the projectile. This was further compounded by the operational regime of high speed and low pressure. Here, plasma actuators struggle to achieve sufficient control authority resulting in large power consumption in attempts to generate any significant effect. Another area of interest has been the application of plasma actuators on full-size, commercial wind turbines. In this case, power consumption was significant because the sole purpose of a wind turbine is to generate power. If the power required to run the actuators was greater than the increase in power generated by the turbine with their use, then there is little chance of these actuators being seriously considered. As a result, the purpose of the following investigation was to determine and implement an accurate way of measuring the power required for the operation of an SDBD plasma actuator. The experimental results will be compared to published, verified trends in order to assess the accuracy of the method. Finally, the influence of pressure on power consumption will be specifically examined, because while plasma actuators operate throughout a wide range of operational pressures, there has been little done in the way of parameter studies involving pressure. Previous Power Analyses In terms of past investigations into power consumption, Manley [7] presented the foundational power analysis for general DBDs. Qualitatively, he noted that power was only dissipated during periods of sustained discharge and that the sustained discharges visibly distorted the current waveforms. Moving onto his quantitative analysis, he first cast the discharge in terms of an equivalent circuit with a capacitance associated with the gap, c G, and a capacitance for the dielectric material, c D. The total capacitance of the actuator during sustained discharge as well as a new variable, β, for simplicity were then defined by: 1 = 1 + 1, C Total C G C D (1) β = C G /C D. (2) The total capacitance and the capacitance of the dielectric material were determined by creating a voltage versus charge plot. It was found that in this phase space, the resulting curve took on the shape of a well-defined parallelogram with sharp corners and sides. One set of parallel sides corresponded to active discharge while there was no discharge present when on the other pair. During periods without discharge, the only relevant capacitance was that of the dielectric. During sustained discharge, the effective capacitance was the total capacitance defined above. These two capacitances were given by the slope of each pair of sides with and without a discharge present, respectively. After determining these factors, the power was then estimated to be: P = 4 fc D ( 1+ β) 1 U Min ( U U Min ) (3), where U Min was the minimum applied potential for a sustained discharge [7]. A critical observation from this formulation was that once a geometry was selected, the only variables that impact power were the frequency of the applied waveform and the applied potential. 1.2

3 In publications pertaining to aerospace applications of dielectric-barrier discharges today, there are two popular methods for obtaining power estimates for plasma actuators. The first method as typified by Pons et al [8] recalled some of critical elements of Manley s analysis. First, a voltage versus charge plot was generated. This was achieved by measuring voltage with a high-voltage probe and a capacitor to measure charge. The average power in this case was given by: P = f T UdQ. (4) 0 This effectively amounts to determining the enclosed area and multiplying by the frequency. This method offered the benefits of greatest accuracy as the capacitor captures the full effects of the numerous microdischarges, despite their short time scales. In addition, the voltage versus charge plot can yield additional information about the actuator such as minimum required voltage for a sustained discharge and the effective capacitances before and during plasma generation. One critical restriction of this method was that unless expensive capacitors were used, one electrode must be grounded. An alternative method exemplified by Gregory et al [9] involved obtaining power estimates from voltage and current measurements using a highvoltage probe and some sort of current monitor. The drawback of this method was that the current often cannot be fully resolved. Microdischarges are primarily responsible for power dissipation and these occur on the order of ns resulting in very sharp spikes in current. Typical maximum sampling rates are limited to the MHz and GHz ranges which can be 1 to 2 orders of magnitudes slower than the lifetime of individual microdischarges. The individual microdischarges however randomly fluctuate in terms of exact location and magnitude. Thus, sampling over many periods and phase-averaging them together can still yield good estimates for the average current waveform even if the effects of each individual microdischarge were not captured. Assuming sufficient information can be obtained by sampling as quickly as possible over many periods, the power calculation was very simple. Here, as given by Becker et al [10], the average power was given by: P = 1 T T U ( t )I( t)dt. (5) 0 An important relationship in terms of power consumption of SDBD plasma actuators was derived by Enloe et al [3] where by casting the actuator geometry in terms of equivalent circuits, he was able to derive an analytical formulation for the dependence of power on applied potential. The relationship followed a power law of the form: P "U 7 / 2. (6) Using the power measurement method detailed directly above, Enloe et al then measured the power consumed by two different actuators and experimentally computed exponents of 3.35 and These were below but near the theoretical value of Finally, the only paper found that examined the influence of widely varying pressures on the performance of the plasma actuator was that of Gregory et al [9]. The influence of pressure was analyzed on a wide variety of characteristics including force, efficiency, ion generation, and required applied potential. A number of useful trends can be found here although a mathematical relation was not provided between pressure and power consumption. Also, all measurements were based off of supplying fixed powers whereas it would be preferred to simply apply a potential and then compute the required power. In these areas, it is hoped that this exploration will supplement the work already done by Gregory et al [9]. EXPERIMENTAL SETUP AND METHOD Model The experimental model consisted of a flat plate single dielectric barrier discharge (SDBD) plasma actuator utilizing Teflon as the dielectric and electrodes made of copper foil tape. This geometry was selected for ease of construction and the size requirements of the available pressure vessel. The flat plate of Teflon measured 6 in. by 6 in. having a thickness of in. Each electrode consisted of a strip of copper tape 1 in. wide and 4.5 in. long. The two electrodes were placed on opposite sides of the plate were centered along the width and length of the plate, but offset such that they overlapped just slightly by approximately 0.05 in. Sharp corners were rounded with scissors to limit strong buildups of localized plasma. This geometry is given in Figure 2 with the dimmer electrode being the covered electrode on the lower surface. Upon application of the electrodes to the flat plate, a soft material was placed over the electrodes and manual pressure was used to smooth the copper tape as much as possible. Other than this, no special treatment was taken with regard to the electrode surfaces. The covered electrode needed to be insulated, as it did not rest on a solid surface. This was achieved by applying Kapton tape followed by Teflon tape. Highvoltage insulating tape was then used to cover the insulated electrode as well the leads to each electrode. 1.3

4 Figure 2. Top View of Model, Dim. of in. Data Acquisition Due to readily available probes as well as the practice of powering both electrodes, the method used by Gregory et al [9] was used for this investigation. Thus, in order to estimate the power consumed by the actuator, voltage and current readings were collected for varying applied potentials and pressures. For consistency, the same nominal voltages were tested at each pressure even though a uniform, sustained discharge was not always present depending upon the exact pressure and voltage combination. The amplitudes of the applied potentials tested ranged from 5 kv to 13 kv in steps of 1 kv. Voltages greater than 13 kv were not tested due to the possibility of arcing through the dielectric at high pressures and around the dielectric at low pressures. The tested pressures included 0.3 atm through 1.0 atm in steps of 0.1 atm. The waveform of the applied potential was sinusoidal with a frequency of 2 khz. This was selected on a function generator and the resulting output voltages were then stepped from the order of volts to the required kilovolts through the use of transformers. The signal was fed into two transformers that operated 180 outof-phase relative to each other, but were otherwise identical. This allowed testing of peak-to-peak voltages up to twice the maximum rating of the wires and individual transformers. It would have been interesting to test the effects of different waveform shapes throughout this study but the properties of the transformers were such that the output signals were sinusoidal regardless of input waveform. Waverunner oscilloscope that sampled at 1 GHz throughout experimental testing. For each pressure and voltage tested, the voltage and current signals were phaseaveraged over 2000 cycles on the oscilloscope yielding averaged voltage and current waveforms over a single period. While 2000 consecutive cycles translated to 1 sec. of operation, the oscilloscope could not perform the averaging of waveforms on consecutive periods due to a time lag resulting from the computation. For each trial, the oscilloscope took approximately 30 sec. to sample and average 2000 total cycles. Tests were conducted in a small pressure vessel with an empty volume of approximately 2000 in 3. The operational gas was untreated atmospheric air. Sub-atmospheric pressures were tested with the aid of a JB Platinum model vacuum pump with the corresponding test pressures in the chamber read off a Wika pressure gauge. During testing, the desired pressure was set and a sweep through the test voltages was conducted. Upon conclusion of each sweep, the chamber was returned to atmospheric pressure and any new byproducts, in particular ozone, were allowed to dissipate. During this experimental investigation, the effects of changing chemical makeup inside the pressure vessel were assumed negligible due to the short duration, less than 15 min., of active testing. In addition, the effects of electrode and dielectric degradation were assumed small over the entire course of experimental testing. EXPERIMENTAL RESULTS Before estimating the average power consumed by the actuator, the voltage and current signals were analyzed for significant trends. Figure 3 depicts typical measurements over a single period. The first important note observed was that the voltage and current signals were 90 out-of-phase with each other. This was important because if both signals were uniform sinusoids, the power consumed would be zero regardless of the amplitude of each. Since this was not the case, one or both of the signals must be distorted as noted by Manley [7]. The sharp spikes in current are representative of the influence of microdischarges resulting in power dissipation. The current and voltage during operation of the actuator were measured using a Pearson current monitor and a LeCroy high voltage probe. The output from each probe was fed into a LeCroy 1.4

5 )).821 "& "! &!!&!"! 9:;;-/ !"&!!<!$ )! " # $ *+,-)).+/),01 % & ' ()"!!% Figure 3. Measurements over 1 Period For the same voltage and pressure, an example set of phase-averaged waveforms is given in Figure 4 along with sinusoidal fits. Since the sharp spikes are no longer present, there must be some mean distortion to one or both of the periodic signals. Plotting a general sine wave on top of the voltage signal yielded very good agreement. On the other hand, a general sine wave cannot be made to fit the current signal without discrepancies demonstrating power consumption. The majority of power dissipation was observed to occur on the positive half-period of the current signal. This agreed with the measurements over a single period as the number and magnitude of fluctuations in the current signal was greater for this half-cycle. $# 89:: )!<!=!<!'!<!&!<!%!<!$!<!#!<!"!!!<!"!!<!# 9:;;-/5)).>1,!"!$# The power for each test was computed according to Eq. 5 using the phase-averaged voltage and current waveforms. Figure 5 depicts the family of power curves obtained for the various pressures tested. Before plasma forms, the power measurements for a given applied potential remain constant throughout the pressures tested and increased slowly with applied potential. In this region, the power was nonzero due to dissipation by the resistances of the wires and potentially some weak ionization around wiring outside the pressure vessel. Despite the wires being rated above the voltages tested, plasma was audibly and visibly detected outside the pressure vessel during the first trial as well as some later trials. This was largely eliminated with high-voltage insulating tape and the trials were conducted again. Nevertheless, there may still have been some weak ionization occurring. Once a discharge was formed, each particular power curve began increasing rapidly with voltage and the curves no longer fall on a common line. Once this sustained discharge was created, some sort of power relationship was clearly visible between power and applied voltage. No appreciable difference was observed between the measurements at 0.9 atm and 1.0 atm perhaps indicating that there may not have been a sufficient change in gas properties to significantly impact power consumed by the actuator. As the pressure was decreased, a sustained discharge was created at progressively smaller voltages. This was due to electrons having an easier time reaching ionization kinetic energies for a fixed electric field as the gas number density had decreased. As a result, the power required at a fixed voltage increased as pressure decreased because the power law relationship initiated at earlier voltages. At lower pressures, the plasma covered a larger area and appeared less intense. However, further measurements, such as optical or probe measurements, would be needed to determine how the total amount of ions and other particles created changed with pressure. This would allow the relation between power consumed and generation of charged species to be computed which could be used as a measure of efficiency ,,-710 $! #!!#!$!!"!$!"!!#!!!"!!# 89::+.4,,-;0 Power (W) atm 0.9 atm 0.8 atm 0.7 atm 0.6 atm 0.5 atm 0.4 atm 0.3 atm!$#,!!"!#!"$!"$#!"%!"%#!"&!"&#!"'!"'#!"#!!"!$ ()*+,,-).,*/0 Figure 4. Phase-averaged waveforms Applied Voltage (kv) Figure 5. Power Consumed for Various Pressures Power and voltage were then plotted on logarithmic scales, given in Figure 6, thereby transforming the powervoltage relationship to a linear one. The logarithmic scales more clearly differentiated between regimes with and without a sustained discharge present. Data points for 1.5

6 which no plasma was present trended at a fixed slope before going through a transition region marked by a sharp increase in power. After this, a visibly uniform discharge was sustained and the curves once again displayed a linear dependence, but with a different slope. The transition between no discharge and a visibly uniform discharge was approximately 2 kv for this particular geometry. Applying a linear fit over the intervals of visibly uniform plasma for each pressure yielded experimental values for the exponent in the assumed power law relation. Table 1 gives the computed values for all pressures tested. It was first observed that all values fell below the analytical value of 3.50 as the experimental values ranged from 2.98 to 3.32 with an average value of For the small number of points available, these values appear to be on the order of the given experimental constants by Enloe et al [3] of 3.35 to Visibly, the slopes appear approximately constant once a uniform discharge was sustained and for pressures of 0.6 atm and greater, there was no discernible trend between the experimental values. However, decreasing the pressure beyond this point corresponded to progressively smaller values for the exponent. This indicated that the equivalent circuit analysis conducted by Enloe et al [3] at atmospheric pressure may not hold for pressures of 0.5 atm and below. Table 1. Calculated Exponent in Power Law p (atm) Experimental Value ,4(5**062!"!!" "!"!!!"!# *!7"*.-8 "79*.-8 "7:*.-8 "7;*.-8 "7<*.-8 "7=*.-8 "7>*.-8 "7?*.-8 $%%&'()*+,&-./(**01+2 Figure 6. Power using Logarithmic Scales!"! * While not a true indication of the average power consumed by the actuator, the rms of power was also calculated and plotted against the rms of the applied potential. This was conducted in order to confirm that the sampling speed was sufficiently fast to reasonably characterize the current signal. Assuming the plasma actuator can be modeled as a simple RC circuit, the rms power should depend on voltage according to the standard formula: P RMS = U 2 RMS R. (7) Once again, plotting on logarithmic scales in Figure 7 yielded a visibly linear relationship. While plotting the average power versus applied voltage on logarithmic scales heightened the contrast between regions before and after initial plasma formation, plotting the rms values completely obscured the presence of plasma. Applying a linear fit over the tested intervals from the previous analysis yielded exponents of between 2.01 and 2.06 except in the case of 0.90 atm for which the value was The discrepancy in the value indicated that an outside source may have negatively influenced this trial. Power RMS (W) atm 0.9 atm 0.8 atm 0.7 atm 0.6 atm 0.5 atm 0.4 atm 0.3 atm Voltage RMS (kv) Figure 7. RMS Characterizations Uniform plasma was generated for all pressures tested in the cases of nominally applied voltages of 11 kv, 12 kv, and 13 kv. The mean experimental applied potentials for each of these cases were: kv, kv, and kv. The data sets were linearly interpolated about these values for each pressure so that power could be plotted versus pressure for a fixed applied potential. In terms of appropriately fitting the data, it was first noted that the gap between curves increased as pressure decreased when average power was plotted versus applied voltage. Second, plotting the logarithm of both values indicated that the slopes remained roughly constant. 1.6

7 Thus, pressure acted by shifting the curves corresponding to the diminishing of the minimum applied potential for a sustained discharge. Based upon these two observations, a power law was assumed between power and pressure for a fixed applied potential: P p c. (8) Linearly fitting the data resulted in the following computed values for the constant c of , , and for the applied potentials of kv, kv, and kv respectively. Thus, for a fixed voltage over these pressures tested, the power consumed by the actuator was proportional to the inverse of pressure as the constant was almost exactly -1. The power measurements used and the resulting linear fits are given in Figure 8. charging cycle and maintained throughout the discharge. However, the scale of the discrepancy here appears too large to be solely due to this effect. Throughout all measurements, three of the four phases of the diagram almost perfectly collapsed with the fourth separating further and further out with increasing power consumption. In general, the power dissipated by this plasma actuator may have been too small to assume the canonical parallelogram relation. Applying the same voltages to larger actuators would stretch the graph out laterally as the charge would increase, while voltage would remain constant. Whether this would produce a characteristic parallelogram or merely widen the ellipses produced so far is unknown at this time. Another possibility was that actively powering both electrodes out-of-phase with each other somehow distorted the plot as most studies of this nature were done with a grounded electrode. U = kv U = kv U = kv (* (% Power (W) ,-./01''23+4 * %!*!(% Pressure (atm) Figure 8. Influence of Pressure for Fixed Voltage At this point, the intention was to compare the experimental results with the traditional power estimate derived by Manley [7] for dielectric-barrier discharges in atmospheric air. Plotting the experimentally measured voltage versus charge did not result in the assumed shape of a parallelogram, however. Instead, the curve appeared to be a sharp ellipse. Figure 9 gives a typical result at atmospheric pressure. The shapes may be that of a compressed parallelogram, but four sides were indistinguishable. As a result, estimates of the slopes and thus the capacitances of the electrodes and dielectric could not be made. At greater power consumptions, the ellipse appeared to become more, not less, rounded. In addition, the curves did not form closed loops presenting an additional discrepancy that grew with increasing power consumption. This indicated a net charge for the actuator. Font et al [11] found in experimental tests with an electrostatic probe that a positive DC offset was created within the first 10 0!(*!!!"!#!$ % $ # "! 56/701''254 &'(%!) Figure 6. Voltage-Charge Figure for Nominal Applied Voltage of 12 kv at 1.0 atm CONCLUSIONS This investigation demonstrated that accurate calculations can be made of the power consumed by an SDBD plasma actuator through measurements of the voltage and current. While the current cannot be perfectly resolved even sampling at the GHz scales, the spikes averaged out to a mean distorted current waveform from which the power could still be computed. The reliability of the method was demonstrated by the favorable comparison to published trends despite the rather small amount of data available at this time. The easiest way to increase the accuracy would be to test larger actuators that consume more power. This would limit the influence of geometric effects as well as increase the signal-to-noise ratio. However, a larger pressure vessel would need to be obtained to test the influence of pressure for larger actuators. The critical result obtained from this investigation has been the inverse dependence of power 1.7

8 upon pressure for fixed voltages. This simple relationship allows estimates to be made of the power consumed by a plasma actuator across a wide range of operational pressures without resorting to testing in a pressure vessel. The approximate power consumption at other pressures could be simply estimated from the power consumed at atmospheric pressure. Another useful result was the confirmation that the estimate of 20 W / linear ft was indeed a conservative estimate as the maximum power consumed in this study at atmospheric pressure was 3.2 W / linear ft, while the greatest power consumption overall was 9.6 W / linear ft. Thus, in cases where exact power consumption was not particularly important, this estimate proved to be a valid one. The discrepancy between the voltage versus charge plots obtained here and those published in literature was attributed to the relatively small amount of power dissipated by this model and the fact that neither electrode was grounded during operation. Testing larger actuators, potentially with the restriction of grounding one electrode, may produce the expected shapes or should provide further insight into this discrepancy at a minimum. ACKNOWLEDGEMENTS The author would like to thank Dr. David Go for guidance and support throughout the course of this investigation as well as Joseph Valerioti for permitting the use of his experimental setup and Christopher Porter for aid in developing the experimental method used here. REFERENCES [1] Roth, J.R., Dai, X., Rahel, J., Shermann, D.M., The Physics and Phenomenology of Paraelectric One Atmosphere Glow Discharge Plasma (OAUGDP TM ) Actuators for Aerodynamic Flow Control, 43 rd AIAA Aerospace Science Meeting and Exhibit, [2] Enloe, C.L., McLaughlin, T.E., VanDyken, R.D., Kachner, K.D., Jumper, E.J., Corke, T.C., Post, M., Haddad, O., Mechanisms and Responses of a Single Dielectric Barrier Plasma Actuator: Plasma Morphology, AIAA Journal, Vol. 42, No. 3, 2004, pp [3] Enloe, C.L., McLaughlin, T.E., VanDyken, R.D., Kachner, K.D., Jumper, E.J., Corke, T.C., Post, M., Haddad, O., Mechanisms and Responses of a Single Dielectric Barrier Plasma Actuator: Geometric Effects, AIAA Journal, Vol. 42, No. 3, 2004, pp [4] Corke, T.C., Post, M.L., Orlov, D.M., Single Dielectric Barrier Discharge Plasma Enhanced Aerodynamics: Physics, Modeling, and Applications, Experiments in Fluids, Vol. 46, No. 1, 2009, pp [5] Kogelschatz, U., Dielectric-barrier Discharges: Their History, Discharge Physics, and Industrial Applications, Plasma Chemistry and Plasma Processing, Vol. 23, No. 1, 2003, pp [6] Patel, M.P., Ng, T.T., Vasudevan, S., Corke, T.C., Post, M.L., McLaughlin, T.E., Suchomel, C.F., Scaling Effects of an Aerodynamic Plasma Actuator, 45 th AIAA Aerospace Sciences Meeting and Exhibit, [7] Manley, T.C., The electric characteristics of the ozonator discharge, Trans. Eectrochem. Soc., 84, 83-96, [8] Pons, J., Moreau, E., Touchard, G., Asymmetric surface dielectric barrier discharge in air at atmospheric pressure: electrical properties and induced airflow characteristics, J. Phys. D: Apply. Phys, 38, 2005, pp [9] Gregory, J.W., Enloe, C.L., Font, G.I., McLaughlin, T.E., Force Production Mechanisms of a Dielectric- Barrier Discharge Plasma Actuator, 45 th AIAA Aerospace Sciences Meeting and Exhibit, [10] Becker, K. H., Kogelschatz, U., Schoenbach, K. H., Barker, R. J., Non-Equilibrium Air Plasmas at Atmospheric Pressure, Philadelphia: Taylor and Francis, Inc., [11] Font, G.I., Enloe, C.L., McLaughlin, T.E., Orlov, D., Plasma Discharge Characteristics and Experimentally Determined Boundary Conditions for a Plasma Actuator, 45 th AIAA Aerospace Sciences Meeting and Exhibit,