Effect of opposite phase AC voltage application using dual power supplies on thrust and induced flow of plasma actuator

This study proposes a new driving method using dual power supplies to address a trade-off between power supply miniaturization and the high voltage output driving of a dielectric barrier discharge plasma actuator by simultaneously applying two AC voltages with opposite phases to the exposed and encapsulated electrodes. The performance of the proposed method was compared with that of two conventional driving methods that use a single power supply. The maximum peak-to-peak voltage with the single power supply was 23 kV, whereas that with the dual power supplies using a transformer with a lower output capability was 30 kV. At the same peak-to-peak voltage, the method using dual power supplies had intermediate time-averaged thrust and induced flow velocity among the three methods. This is attributed to the different discharge distributions at the edge of the exposed electrode, which are caused by the different electric field strengths for each method.


Introduction
Recently, dielectric barrier discharge plasma actuators (DBD-PAs) have been developed as advanced active flow-control devices without moving parts.After a basic structure of DBD-PA was proposed by Roth et al. 1) in 1998, Corke et al. 2,3) demonstrated in 2002 that DBD-PA can potentially control flow separation from the airfoil.Figure 1 shows a typical DBD-PA comprising a dielectric material and a pair of asymmetrically located thin electrodes.When an AC voltage with a peak-to-peak voltage (V p-p ) of several kV to several tens of kV at a frequency of several hundreds of Hz to several tens of kHz is applied between the electrodes, ambient air near the edge of the exposed electrode is weakly ionized, forming DBD plasma. 4)Then, charged particles in the DBD plasma are accelerated by Coulomb force due to the electric field, and a one-way tangential flow is induced along the dielectric surface because of momentum transport through collisions between charged and neutral particles.
In addition to fundamental studies on the plasma morphology and the jet acceleration mechanism of DBD-PAs, [5][6][7][8] application research on DBD-PAs for fluid machinery (e.g. wd turbines, 9) automobiles 10,11) ) has been conducted both experimentally and numerically.The maximum flow velocity induced by a single DBD-PA has remained below approximately 10 m s −1 , as shown in previous studies.12,13) Because the Reynolds number (Re) in practical fluid machinery is often greater than 10 5 , it is necessary to improve technologies that can generate the larger thrust and induced flow velocity to enhance the aerodynamic control effect of DBD-PAs at high Re.For example, in terms of the components of DBD-PAs, studies related to dielectric materials, 14,15) serrated 16,17) and wire exposed electrodes, [18][19][20][21] tri-electrodes PAs (TED-PAs), 22,23) and DBD-PAs with discretized encapsulated electrode 24) have been conducted.][27] However, these technologies relating to power supply miniaturization alone do not improve the performance of DBD-PAs considering the generated thrust increases in proportion to V p-p 3 -V p-p 5 .28,29) However, increasing the output voltage of a single compact power supply can lead to technical issues, such as an increase in the transformer size owing to an increase in the number of the coils and the occurrence of discharge inside the transformer under the high voltage.Therefore, there is a trade-off between power supply miniaturization and the high output voltage driving of DBD-PAs.
To eliminate this trade-off, this study proposes a new method for driving DBD-PAs with dual power supplies that apply opposite-phase AC voltages separately to the exposed and encapsulated electrodes.Figure 2(a) shows a schematic of the circuit and the applied voltage waveforms to drive a DBD-PA with dual power supplies.By using dual power supplies, substantial V p-p per cycle of voltage is doubled compared to a single power supply.Additionally, a dual power supply reduces the weight and installation space of each power supply.Furthermore, by combining distributed compact power sources that control the flow around various fluid machinery (e.g.automobiles and aircraft), the voltage applied to DBD-PAs can be increased to enhance the aerodynamic control effect.If the thrust and induced flow velocity using the dual power supplies are comparable to those using a single supply, it can be a valuable method when a significantly large thrust generation is required.
In this study, three connections, as shown in Fig. 2, are tested to evaluate the performance of a DBD-PA: "Aconnection" driven by dual power supplies, and "B-connection" and "C-connection" by a single one.In the "Bconnection" and "C-connection," the electrodes to be grounded are reversed, and in B-connection [Fig.2(b)], the encapsulated electrode is grounded similar to most previous studies.Conversely, C-connection [Fig.2(c)] is a practical connection method [30][31][32] wherein the exposed electrode is grounded to prevent electric shocks and short circuits occurring on the dielectric surface. Te changes in the DBD-PA performance owing to these different connections were quantitatively evaluated by analyzing the power consumption, thrust, and spatial velocity distribution of the induced flow under DBD-PA driving.

Experimental method and setup
The DBD-PA used in this study comprised a 3 mm thick dielectric made of polycarbonate (PCTA-110-50-3; Misumi Group Inc., Tokyo, Japan) and exposed and encapsulated electrodes made of a 0.074 mm thick conductive copper foil tape (CCH-36-101-0050; Parker Chomerics, Woburn, MA, USA).The encapsulated electrode was electrically insulated by coating it with moisture-curable, low-viscosity silicone rubber (KE-3494; Shin-Etsu Chemical Co., Ltd., Tokyo, Japan).A 2.0 mm thick bakelite (BLBA-110-50-2; Misumi Group Inc., Tokyo, Japan) was attached to the rear side of the dielectric as a jig for fixing the test piece to the pedestal for thrust measurement.
Figure 3(a) shows a schematic of the measurement system for the thrust and power consumption in the A-connection, and Fig. 3(b) depicts the experimental sequence.The voltage signal output by the function generator (WF1974; NF Holdings Corp., Kanagawa, Japan) was amplified by the power supply system.The DBD-PA was driven with a duty ratio of 100% by a sinusoidal voltage output by the power supply unit (PSI-PA 1050 N, PSI-PW0500; PSI Co., Ltd., Saitama, Japan) with a transformer that is interchanged according to the maximum applied V p-p .In this study, the driving frequency of the DBD-PA ( f base ) was fixed at f base = 4 kHz.One transformer (PSI-TR20; PSI Co., Ltd., Saitama, Japan) was used for the B-and C-connections, whereas two transformers (PSI-TR15 × 2 units; PSI Co., Ltd., Saitama, Japan) were employed for the A-connection to apply the opposite-phase voltage.The current through the circuit (I PA ) was calculated using Ohm's law based on the measured voltage across a resistor (B-551, 250 Ω; Graphtec Co., Ltd., Kanagawa, Japan) using a voltage probe (Tek P6139A; Tektronix).For the A-connection, the AC voltages between the two electrodes and ground (V PA = V PA1 − V PA2 ) were measured using two high-voltage probes (P6015A; Tektronix).An electronic balance (IUZ-101; ASONE Co., Hamamatsu, Japan) was used to evaluate the thrust.The reaction force caused by the induced flow of the DBD-PA was measured as load data with an electronic balance and converted to thrust.The load data measured by the electronic balance were acquired for 60 s for each condition, as shown in Fig. 3(b).The DBD-PA was driven from 5 to 35 s, and   116002-2 © 2023 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd V PA1 , V PA2 , and I PA were recorded five times using an oscilloscope (DPO4104B; Tektronix).The same experimental procedure was adopted for the B-and C-connections; however, the measured applied voltage was only V PA1 (=V PA ).As shown by Eq. ( 1), the power consumption per unit electrode length P [W/m] is given as: where l (=0.09 m) is the length of the exposed electrode of the DBD-PA and T is one period of the AC voltage.The averaged power consumption P ave is defined as five times the average value of P.
The spatial velocity distribution of the induced flow was analyzed using particle image velocimetry (PIV).To visualize the two-dimensional cross-section (x-y) of the induced flow, dioctyl sebacate (DOS) droplets atomized by the Laskin nozzle were introduced into the test chamber as seeding particles and laser sheet lights with a wavelength of 532 nm were irradiated onto the midspan of the exposed electrode by a double-pulse Nd:YAG laser (Nano S 30-15PIV, 15 mJ per pulse; Litron Lasers Ltd., Rugby, UK).A series of experiments for PIV analysis were conducted simultaneously for 80 s with 10 times the V PA1 , V PA2 , and I PA measurements for estimating P ave .A pair of flow images were acquired at 3.75 Hz using a cross-correlation camera (PIV CAM 13-8; TSI, Inc., Shoreview, MN, USA) with a resolution of 1280 × 1024 pixels.Therefore, the instantaneous flow velocity distributions analyzed by PIV using 300 pairs of images were obtained in approximately 80 s.Velocity vectors (u, v) of each 16 × 16 pixels interrogation window were analyzed with a 50% overlap to satisfy the Nyquist criterion using PIV software (Insight ver.3.53; TSI Inc.).The laser irradiation interval to acquire a pair of flow images (Δt) was determined such that the maximum displacement of the seeding particles within the interrogation window was less than 4 pixels.Δt was varied from 16-50 μs depending on the maximum velocity of the induced flow, which changed depending on the driving conditions of the DBD-PA.

Thrust characteristics
Figure 4 shows the time series of thrust variations measured by the electronic balance in the case of A-connection, where V p-p was varied from 14-25 kV in 1 kV increments.The thrust immediately increased at 5 s when the AC voltage was applied and became roughly constant after 15 s, regardless of V p-p .Then, it dropped after 35 s because the DBD-PA driving was stopped.This confirmed that the trend of thrust change over time was similar for the B-and C-connections.To quantitatively compare the difference in the thrust during DBD-PA driving by the three connection methods, the averaged value of the temporal thrusts between the dashed lines from t = 15-30 s in Fig. 4 (for 15 s) was defined as the time-averaged thrust (F ave ). Figure 5 shows the F ave as a function of V p-p .The error was estimated as the standard deviation of F ave for 15 s.The data were plotted and fitted in the range 14-23 kV to compare the performance of the three connections over the same voltage range.All measurement results are also shown at the top left of Fig. 5.Under the same V p-p condition, F ave was maximized in the B-connection and followed in order by the A-and C-connections.In terms of thrust for the A-connection newly proposed in this study and for the B-connection showing the maximum thrust value, F ave for the B-connection was approximately 20% larger than that of the A-connection.However, the A-connection can output a voltage of up to 30 kV, although the A-connection uses transformers with a lower output capability than those used in the B-and C-connections.Additionally, F ave constantly increased, which indicated that multiple small power supplies succeeded in increasing the thrust.Meanwhile, fitting F ave as a function of V p-p in the range 14-23 kV, indicates that F ave is proportional to V p-p 5.8 (A-connection), V p-p 5.0 (B-connection), and V p-p 5.6 (C-connection), respectively.For the B-connection, Ashpis et al. 28) and Nakano et al. 29) also reported that F ave is proportional to V p-p 4.8 for V p-p ⩽ 25 kV, which is close to the condition used in this study.Therefore, considering the B-connection adopted in most previous studies, the thrust measured in this study is approximately reasonable.
Figure 6 shows P ave as a function of V p-p .Similar to the thrust, the results for the range 14-23 kV are shown; however all measurement results are included at the top left.P ave is proportional to V p-p 3.3 (A-connection), V p-p 2.9 (B-connection), and V p-p 2.9 (C-connection).Regarding the B-connection, Corke et al. 3) Enloe et al. 4) and Murphy et al. 12) reported that P ave is proportional to V p-p 3.5 .Although there is no quantitative agreement owing to the different thicknesses of 116002-3 © 2023 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd the dielectric, our results are close to those of previous studies. 3,4,12)Compared with the same V p-p , the B-connection has the largest value of P ave among the three connections.
The A-and C-connections, where a high voltage is applied to the encapsulated electrode, consumed less power than the Bconnection at the same V p-p .Accordingly, the A-and Cconnections exhibited lower thrust values than the B-connection.
As for the driving efficiency of the DBD-PA, we discuss the difference in the thrust-power ratio for the three connections.Figure 7 shows the relationship between P ave and F ave with the fitting lines given by the least-squares method.All measurement results are shown at the top left in Fig. 7.The slope of the fitting line (m) denotes the thrust generated per unit power consumption; therefore, the thrust-power ratio is an indicator of the driving efficiency of the DBD-PA.Although the least-squares approximation cannot reproduce the experimental results in the low power consumption region, this method was adopted to provide a quantitative comparison of the thrust-power ratio.The slopes of the fitting lines calculated from the measuring points of V p-p = 14-23 kV were evaluated as m = 0.21 mN W −1 (A-connection), 0.28 (B-connection), and 0.19 (C-connection), respectively.Thus, the driving efficiency of the DBD-PA was in the order of the B-, A-, and C-connections as well as the thrust order.

Velocity distributions of induced flow
The averaged velocity distributions of the induced flows were analyzed by PIV, and the differences in the velocity profiles of the three connections were compared.Figure 8 shows the averaged velocity distributions in the x-y cross-section of the induced flow for V p-p = 20 kV for the (a) A-connection, (b) B-connection, and (c) C-connection.The velocity vector (u, v) was using 300 instantaneous data points in each interrogation window analyzed by PIV, while the erroneous vectors were excluded as data for averaging.In all the three connections, it was observed that the tangential flow was induced from the exposed electrode edge along the dielectric surface.A slight suction flow was also seen towards the exposed electrode.
Figure 9(a) shows the y-directional distribution of the averaged x-component velocity (u ave ) at x = 15 mm away from the edge of the exposed electrode at V p-p = 20 kV.The position taken at the maximum value of u ave was almost the same for all three connections.Additionally, the width of the induced flow was the same among these connections.For further investigation, Fig. 9(b) shows the non-dimensional velocity distributions at the same location as in Fig. 9(a).y is non-dimensional by half-width b 1/2 taking half value of the maximum value of u ave (u max ), where u ave is non-dimensional by u max .The non-dimensional velocity distribution is almost the same for the three connections, and there is no difference in the qualitative jet characteristics.Figure 10 shows u max as a function of V p-p which can be fitted by a linear function.The variable u max is enlarged in the order of the B-, A-, and C-connections at the same V p-p .The thrust F [N/m] induced by the DBD-PA is expressed as: where ρ is the air density and δ is the width of the induced flow.The order of the F at the same V p-p is the B-, A-, and C-connections, which is the same as the order of u max because δ is almost the same for the three connections.The order of the thrust considered in this way is consistent with the results shown in Fig. 5.

Discussion
We evaluate why B-connection exhibits the highest P ave and u max among the three connections at the same V p-p .Figure 11 shows the images of (a) no discharge and DBD plasma at  encapsulated electrode overlapped below is called the "UE side," and the bottom edge side of the exposed electrode is called the "BE side."Similar levels of DBD emissions from the UE side were observed for all three connections.In contrast, the DBD emission distributions around the BE side can be distinguished among the three connections.For the Bconnection, DBD emissions from the BE side can be seen over the entire area.Meanwhile, weak discharge occurs at the cable connection part sufficiently far from the encapsulated electrode.Therefore, it is possible that corona discharge occurs when a high voltage is applied to the exposed electrode.Conversely, the area of light emission at the BE side decreased in the order of the A-and C-connections.Changes in the DBD-PA performance due to differences in the three connections were discussed based on a numerical analysis of the electric potential using the Galerkin finite element method.The electric potential and electric field vectors are formulated as where ε 0 and ε r are the electric permittivity in vacuum and the relative permittivity of the dielectric, respectively; f is the electric potential; ρ c is the charge density; and E is the electric field vector.ε r is equal to 2.9, assuming the presence of polycarbonate. Figure 12 shows the computational domain and numerical conditions.In this analysis, ρ c was set to 0 C m −3 over the entire area.The electric potential difference between the electrodes was set to 10 kV, assuming a maximum voltage in the AC with V p-p = 20 kV.Dirichlet boundary conditions, with f equal to 0 kV, were applied to the left, right, top, and bottom side of the computational domain.Figure 13 shows the distributions of the electric field intensities E abs and E for the three connections.The value of E abs at the UE side for the B-connection is 10% larger than that for the C-connection, and the A-connection is intermediate among the three connections.
To consider the effect of the different E abs values at the UE side on the performance of DBD-PAs, we focus on the electrohydrodynamic force acting on a gas mixture containing electrons, single positive, negative ions, and neutral particles (f EHD ).The physical quantity f EHD can be considered as the momentum transfer per unit volume by collisions between charged and neutral particles.As main contribution to the current is the drift component; diffusive current can be neglected, and f EHD is given as: where, for arbitrary chemical species sp (= e: electrons, p: positive ions, n: negative ions), μ sp is the mobility, n sp is the number density, and j sp is the conductive current, respectively.Reference 33 shows that positive ions mainly contribute to f EHD when the potential difference between the electrodes is positive, whereas negative ions mainly contribute to f EHD when the potential difference between the electrodes is negative.In any case, the larger E abs is, the larger is the value of f EHD in the positive direction of x-axis, i.e. in the main flow direction of the induced flow.Reduced electric field, where E abs is divided by the number density of ambient air, also increases as E abs increases.As the reduced electric field increases, the electron energy received per mean free path increases.Therefore, the ionization reaction occurs more actively and the number density on the right-hand side of Eq. ( 5) increases, leading to the highest f EHD for the Bconnection, where E abs at the UE side was the largest.Therefore, the B-connection shows the highest thrust, power consumption, and induced flow velocity among the three connections.
Subsequently, E abs at the BE side were compared for the three connections.Figure 14 shows y-directional distributions  116002-6 © 2023 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd of E abs at the BE side.The maximum values of E abs for the three connections in this line were calculated as 5.4 × 10 3 kV m −1 (A-connection), 7.9 × 10 3 (B-connection), and 3.0 × 10 3 (C-connection).This order is consistent with the order of the area of light emission from the BE side shown in Fig. 11.For the A-and B-connections, E on the BE side was generated from two contributions: the potential difference between the exposed and encapsulated electrodes and the difference between the far boundary and the exposed electrode.Conversely, the C-connection has no potential difference between the far boundary and the exposed electrode because it is grounded.Therefore, E of the Cconnection at the BE side is generated only by the potential difference between the exposed and encapsulated electrodes.These differences in E at the BE side cause different discharge patterns for the three connections.All devices in this study were installed in a sealed acrylic container fixed to an aluminum frame placed on a concrete floor.Therefore, the sides of the acrylic sealed containers play the role of a grounded boundary that causes the difference of E abs distribution among the three connections.When DBD-PAs are applied to fluid machinery such as automobiles, aircraft, and wind turbines, the surface of the fluid machinery could act as an electrical grounded boundary.Therefore, the grounded boundary in such practical environments has a greater impact on the performance of DBD-PA compared to the experimental conditions of this study.
The above results indicate that although the advantage of driving the DBD-PA with dual power supplies appears to be limited, this connection can substantially increase V p-p compared with driving it using a single power supply.In practice, the maximum sinusoidal voltage of up to V p-p = 23 kV was applied with a single power supply; however, when employing dual power supplies, it increased up to V p-p = 30 kV, as shown in the wide range views of Figs. 5 and 6.It is noteworthy that a thrust larger than 30 mN m −1 can be generated by driving the DBD-PA with dual power supplies outputting 15 kV.In our previous studies, relatively inexpensive and readily available power supplies that can output up to V p-p = 20 kV were used; however, a prototype that outputs V p-p = 30 kV had many technical problems, such as the breakdown inside the transformer.In the case of the Bconnection, which is most common and safe to operate, the maximum potential difference between the exposed and ground electrodes is approximately 15 kV, and hence, further care must be taken with the creeping discharge and wiring methods in the higher voltage range.However, compared to the B-connection with a single power supply, the A-connection with dual power supplies has half the potential on the DBD-PA surface, even under the same V p-p .Therefore, the A-connection can potentially reduce these risks.
In terms of engineering applications, the advantages and disadvantages of the A-connection are explained.To apply the same maximum V p-p with the A-and B-connections, the A-connection requires additional space for installing dual power supply units compared to the B-connection.Conversely, the weight or size of the A-connection is not necessarily doubled.Because the V p-p per unit is halved, the number of turns in the step-up transformer as well as the size of the ferrite core can be reduced.Additionally, because only one control unit is required for driving the DBD-PA in the opposite phase, the size and weight of the power supply can be reduced with the A-connection rather than the B-connection.
Toward the practical use of DBD-PAs, we aim to develop a fuel-efficiency improvement technology that reduces aerodynamic drags by installing DBD-PAs in automobiles.In this case, it is necessary to drive DBD-PAs that are independently installed at multiple locations by using compact distributed power supplies.The A-connection can increase the applied V p-p by combining two adjacent power supplies.Therefore, the usefulness of the A-connection becomes more pronounced in fluid machinery equipped with compact distributed power supplies.

Conclusions
This study proposed a new method for driving DBD-PAs with dual power supplies that apply opposite-phase AC voltages separately to the exposed and encapsulated electrodes named "A-connection" in contrast to conventional methods driving a single power supply named "B-connection" (grounded encapsulated electrode) and "C-connection" (grounded exposed electrode).Performance tests using a DBD-PA consisting of a 3 mm thick dielectric made of polycarbonate, and exposed and encapsulated electrodes made of a 0.074 mm thick conductive copper foil tape were conducted using the three connections for evaluating thrust measured by an electric balance and analyzing velocity distributions by the PIV.The results showed that the Bconnection demonstrated the highest time-averaged thrust, thrust-power ratio, and averaged velocity, followed by the Aand C-connections, respectively at the same V p-p .This order of the three connections was the same as that of the maximum voltage applied to the exposed electrode.For instance, when the DBD-PA was driven at V p-p = 20 kV, the maximum voltage at the exposed electrode was 5 kV (Aconnection), 10 kV (B-connection), and 0 V (C-connection) for the three connections.The electric field analysis at V p-p = 20 kV using the Galerkin finite element method revealed that the electric field intensities at the upper and bottom edge sides of the exposed electrode were in the order of the B-, A-, and C-connections.Additionally, the strength and area of the DBD plasma discharge near the exposed electrode increased in the order of electric field strength, which caused a difference in the performance of the three connections.This indicates that the A-connection had an intermediate performance in the same voltage range among the three connections.However, the ability to use dual power supplies can increase the output voltage range.The maximum output voltage for the B-and C-connections was 23 kV, whereas the A-connection successfully output 30 kV using a transformer with a lower output capability.Therefore, the A-connection can enhance the performance of DBD-PAs with an inexpensive and compact power supply.

Fig. 3 .
Fig. 3. (a) Schematic of the thrust measurement system of the A-connection and (b) sequence of thrust measurement.

Fig. 4 .
Fig.4.Time series of the thrust variations measured by the electronic balance for the A-connection.Fig.5.F ave as a function of V p-p for the three connections.

Fig. 6 .Fig. 7 .
Fig.6.P ave as a function of V p-p for the three connections.

Fig. 8 .
Fig. 8. Averaged velocity distributions of induced flow analyzed by PIV for (a) A-connection, (b) B-connection, and (c) C-connection for V p-p = 20 kV.

Fig. 9 .Fig. 10 .
Fig. 9. (a) y-directional distribution of u ave at x = 15 mm away from the edge of the exposed electrode, and (b) non-dimensional flow velocity distributions when u ave is divided by u max and y is divided by the half width b 1/2 at V p-p = 20 kV for the three connections.

Fig. 11 .
Fig. 11.Images of (a) no discharge and DBD discharge at V p-p = 20 kV for (b) A-connection, (c) B-connection, and (d) C-connection.

Fig. 12 .
Fig. 12. Computational domain and numerical conditions for electric field analysis.

Fig. 14 .
Fig.14.y-directional distribution of E abs at the BE side for the three connections.