# Streamer inhibition for improving force and electric wind produced by DBD actuators

Antoine Debien, Nicolas Bénard, Éric Moreau

► To cite this version:

Antoine Debien, Nicolas Bénard, Éric Moreau. Streamer inhibition for improving force and electric wind produced by DBD actuators. Journal of Physics D: Applied Physics, 2012, 45 (21), pp.215201. 10.1088/0022-3727/45/21/215201 . hal-05077712

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Submitted on 21 May 2025

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# Streamer inhibition for improving force and electric wind produced by DBD actuators

Antoine DEBIEN¹, Nicolas BENARD¹, Eric MOREAU¹

¹Pprime Institute, CNRS, University of Poitiers, ENSMA UPR 3346, BP 30179 F86962, Futuroscope Chasseneuil Cedex, France

E-mail: antoine.debien@univ-poitiers.fr

**Abstract.** The use of thin wires from 13 to 300 µm in diameter as exposed electrode of a surface dielectric barrier discharge plasma actuator is experimentally investigated by electrical and optical diagnostics, electrohydrodynamic force measurements and produced electric wind characterization from time-averaged and time-resolved measurements. The streamers inhibition and the glow discharge enhancement due to the use of a thin wire active electrode fully modify the topology and the temporal behaviour of the thrust and of the electric wind production. With a typical plate-to-plate DBD, the electric wind velocity increases during the negative going cycle. With a wire-to-plate design, both positive and negative going-cycle discharges result in an electric wind velocity increase. Four main quantitative results are as follows: (1) for a power consumption of 1 W/cm, the force is increased from 65 to 95 mN/m when a 13 µm wire is used (2) this corresponds to a 15 % electric wind velocity enhancement (3) electromechanical efficiency can be increased from 0.1 to 0.25 % (4) these improvements have been applied for definition of a new multi-DBD design plasma actuator that allows us to produce a mean velocity of 10.5 m/s.

## 1. Introduction

By ability to create a wall jet, surface dielectric barrier discharges (SDBD) are used as actuators in flow control applications. Used to manipulate airflow [1,2], SDBD actuators can modify the laminar-to-turbulent transition, reattach airflow and affect the dynamic of large-scale flow by actuation close to the wall. The main advantage of SDBD is its very short response time, its low power consumption and its low flow profile (no drag penalty) and its ability to conform on any surface. This actuator is usually composed of two plate electrodes asymmetrically flush mounted on both sides of a dielectric plate supplied by an ac voltage. As a sufficient ac high voltage is applied, a discharge occurs on the air-exposed surface. An electrohydrodynamic force is created and momentum transfer occurs from charged particles to neutral particles, leading to an electric wind with maximum velocity up to about 7 m/s [3]. The discharge induced during the positive and the negative going-cycles of one ac sine period present two different plasma regimes [3, 4-6]. These discharge differences between both going-cycles are due to the asymmetry of SDBD. The positive going-cycle results in a corona-like discharge with high pulses traducing the presence of streamers. During the positive going-cycle, electrons move toward the air-exposed electrode and cause further ionization before to be collected by the air-exposed electrode. The negative going-cycle induces a glow discharge with small pulses, corresponding to a period of dense small current peaks. In this going-cycle, electrons liberated by the active electrode remains on the dielectric, which self-limits the electric field, inducing a glow discharge [6]. Modeling and numerical simulations used to describe weakly ionized air plasma are generally made with a four-fluid mixture (neutral molecules, electrons, positive and negative ions) [6-11]. They show that high current breakdown (streamers) are interrupted periodically by low current phases corresponding to positive ion cloud formation during the positive going-cycle [7-9] when negative ion cloud continually
expanding through high frequency pulses from small amplitude corresponds to electron attachment [9]
during the negative going-cycle, as experimentally highlighted in [5] for instance.

Both discharges produced during both half-cycles results in an unsteady electric wind with velocity
fluctuations at the same frequency than the sine high voltage frequency [3, 12, 13]. In 2007 [3], non-
stationary measurements of the electric wind have shown that a greater velocity is produced during the
negative going-cycle than during the positive one. The force produced by streamer is recognized as
being locally great, but the weak number of positive current pulses and their short duration results in a
low averaged momentum production [14, 15]. In [3, 14, 15], a better electro-mechanical conversion is
reported during the negative-going cycle (where negative ion cloud is continually growing up) than
during the positive one. As a result, one can expect that large changes in the discharge regime should
influence the temporal body force production.

Moreover, the impact of the active electrode shape on thrust production has been studied by different groups. It appears that the active electrode shape affects the time-averaged force produced by the SDBD actuator and that the force efficiency (force/power consumption) increases when the thickness of the exposed electrode is reduced [16]. For instance, the use of a cylindrical active electrode having a diameter smaller than approximately 0.3 mm leads to a force that increases exponentially when the diameter is further reduced [17]. In 2010, Hoskinson and Hershkowitz [18] confirmed the influence of a cylindrical active electrode shape. In this study, the discharge was driven by a symmetric triangular voltage. Cylindrical (from 0.025 to 1 mm in diameter) and rectangular (15 mm of length and thickness from 0.036 to 1.1 mm) active electrodes with several materials (copper, tungsten and steel) were investigated. Measurements of the global force produced by a SDBD actuator have been conducted with an electronic balance; they showed that the produced force could be further improved by using a thin cylindrical active electrode. They also revealed a change in the discharge regime when thin wires were used. Filament-free plasma discharge was observed instead of a streamer discharge.

The aim of the present study is to go further in the comparison between plate-to-plate and
wire-to-plate surface dielectric barrier discharges and to detail the impact of the wire diameter on the
discharge characteristics. In a first part, the discharge regime is observed using both current
measurements and plasma visualizations by an iCCD camera. To characterize the mechanical DBD
properties, two methods are usually used. The first one consists in measuring the time-averaged thrust
induced by the discharge. It is postulated that the thrust corresponds to the EHD force (reduced by the
skin friction at the wall) without consideration for temporal and spatial evaluation of the force field
[16-19]. The second method relates to spatially and temporally resolved velocity measurements by
optical diagnostics (particle image velocimetry or laser Doppler velocimetry) [1]. In a second part, the
paper proposes a complete experimental analysis and contrasts with previous studies because
geometry, dielectric permittivity, dielectric thickness and applied high voltage waveforms differ. The
mean thrust production, the time-averaged electric wind velocity and its time resolved behaviour are
measured. In a last part, optimizations derived from the first sections are used to define a new
arrangement to achieve a very effective multi-DBD design. The combination of an optimized electrode
shape and original electrical connections between electrodes increases the produced electric wind at an
unseen level.

## 2. Experimental setup and facilities

The DBD actuator is made of two electrodes asymmetrically flush mounted on each side of a dielectric plate (3 mm-thick PMMA, figure 1). The grounded electrode (span wise 90 mm, width 20 mm) is insulated with an epoxy resin. A small gap of 2 mm separates the active electrode and the grounded one. The High Voltage (HV) active electrode is rectangular (aluminum foil, 10 mm-wide, 80 µm-thick, figure 1a) or cylindrical (tungsten wire with diameter of 300, 100, 50, 25 and 13 µm, figure 1b). The active electrode is connected to a power amplifier (Trek, ± 30 kV, 20 mA) driven by a waveform generator (Hameg HM8310). The voltage waveform is sinusoidal with high voltage amplitudes from 14 to 22 kV (frequency of 1 and 1.5 kHz). The discharge current is measured through a shunt resistor (100 Ω) placed in series between the lower electrode and the ground. The current signal is digitalized via an oscilloscope (Lecroy Wave Surfer 424, 8 bits, ± 2 %). The electrical power consumed by the plasma discharge is computed by integration of the charge/voltage curves, the charge being determined in measuring the voltage at a 47 nF capacitor placed between the lower electrode and ground (4.4 % standard deviation). To further investigate the discharge current, 60 periodic cycles are
measured at a 500 MS/s sampling rate. The capacitive component due to the presence of the dielectric is removed before current analysis.

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Sketch (not to scale) of a plate-to-plate DBD (a) and a wire-to-plate DBD (b).</figcaption></figure>

Fast-imaging of the ionization process is also provided. Images of the plasma are collected by a fast gateable iCCD camera (Princeton, Pi-max2 Gen2) with 1024x1024 pixels² matrix. The camera is placed in front (top view) of the plasma discharge. The field of view (26x26 mm², with a resolution of about 25 µm/pixel) is obtained by using a 105 mm macro lens that captures visible and UV wavelengths (Nikkor).

A balance (Denver instrument, SI-603, ± 0.02 mN, 48 – 60 Hz) is used to measure thrust produced by the surface discharge. The SDBD actuator is fixed vertically on the balance to measure the longitudinal force. The balance is placed in a Faraday box to prevent RF interferences. Time-averaged force is estimated from 1500 samples recorded at a rate of 50 Hz by the balance, via a Labview interface. The mean standard deviation of the mean force measurements is equal to 0.7 %.

A glass home-made pressure probe (internal diameter equal to 0.6 mm) is used to measure the pressure resulting from the produced electric wind. Pressure is measured by an analogical manometer (Furness FC014, 0-12 m/s, 0.01 % precision, 10 Hz) and the time-averaged horizontal component of the electric wind velocity is determined with Bernoulli equation from 500 samples at 100 Hz by an A/D convertor (Keithley 16 bit, 50 kS/s). Standard deviation of the electric wind measurements is equal to 0.08 m/s.

Velocity fields of the electric wind are obtained by Particle Image Velocimetry (P.I.V.). It is performed using a JAI 12-bit camera (Pulnix, RM-4200CL, 2048*2048 pixels²). A 105 mm lens (Nikkon, AF micro Nikkor, f/ 1:2.8 D) allows us a velocity field of 60*60 mm². The laser sheet is produced by an Nd-YAG multipulse (Quantel, Big Sky Laser Twins Ultra 300 mJ) synchronized with the camera using an IDT MotionPro Trigger. Instants of acquisition are piloted via a signal generator (Tektronik, AFG 3022B). Velocity fields are computed from images using a Dantec software. A multipass algorithm using a first pass of 32*32 pixels² and a final one of 16*16 pixels² with an overlap of 50% results in a vector velocity every 240 µm. In a first time, time-averaged velocity fields are computed with 300 instantaneous velocity fields acquired at an interval of 200.005 ms, chosen to correspond to a non-harmonic frequency of the HV actuation frequency. In a second time, twenty phase-averaged velocity fields per ac voltage cycle (time resolution of 50 µs) are computed from 260 instantaneous velocity fields acquired via a high-resolution PIV system (flow field of 26x26 mm² with a spatial resolution of 100 µm) by adding a teleconverter (Kenko, MC7 AF 2.0 DGX) on the camera. This allows us to reproduce the time-resolved velocity of the produced electric wind, with a time resolution of 50 µs.
### 3. Electrical properties

#### 3.1 Current measurements

<figure><img src="image_3.png" /></figure>

**Figure 2:** Current versus time for a plate-to-plate DBD and several wire-to-plate DBD for 22kV and 1.5 kHz: (a) wide view in the range between -40 and + 360 mA (instantaneous snapshot of one ac cycle in black and envelope of 60 ac cycles in blue); (b) zoomed view (between -3.5 mA and +2 mA).
The discharge current is observed during one ac cycle (figure 2a, black curves). In addition, the current envelope has been recorded. It results from the superposition of the maximal and minimal values of the current during 60 periods (figure 2a, blue curves). Notice that the time is non-dimensional as $t* = t \times f$ with t the time and f the high voltage frequency. Then the non-dimensional duration of one ac cycle is $t* = 1$.

For a plate-to-plate DBD (figure 2a), the current is characterized by two distinct periods of pulses, corresponding to the discharges occurring during both going-cycles. The positive going-cycle, where streamers occur, is characterized by high current pulses up to 200 mA. The glow regime occurring during the negative going-cycle results in small pulses up to 10 mA. This composes a well-known result [5]. For the wire-to-plate DBD, the discharge regime is fully different (figure 2a). During the positive going-cycle, high current pulses period (due to streamer occurrence) decreases with the wire diameter, resulting in a filament-free regime as initially called in [18]. During the negative going-cycle, the glow discharge is composed with a few pulses (typically around $t* \approx 0.4$, see figure 2a) followed by smaller pulses with reduced amplitude. Figure 2b shows a zoomed view (between -3.5 mA and +2 mA) of the discharge current versus time when the active electrode is a plate and a 13-µm wire. On one hand, it highlights that the streamers occurring during the positive going-cycle are partially removed when the 13-µm wire is used instead of a plate active electrode. On the other hand, the glow component is significantly enhanced. During the negative going-cycle, the number of current peaks increases when the glow current slightly decreases.

## 3.2 Plasma visualizations

The modifications in the discharge regime when the HV active plate electrode is replaced by a wire have been observed by iCCD plasma visualizations. As it is expected that high current pulses phase corresponds to a filamentary discharge mode while low current pulse phase results from a diffuse discharge mode, four time windows of 166 µs gate width are acquired, as resumed in figure 3. Time windows 1 and 2 are recorded during the positive going-cycle when time windows 3 and 4 correspond to the negative going-one (Figure 4).

<figure><img src="image_4.png" /><figcaption>**Figure 3:** Instants of iCCD time windows acquisition over an actuation period.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 4:** Top view of the plasma discharges (166 µs exposure time, see figure 3, iCCD pictures) from plate-to-plate (80 µm-thick), 100 µm and 13 µm wires (from the top to the lower) corresponding to the four time windows over one actuation period. Grounded electrode is toward the up. Discharge is driven at 22 kV and 1 kHz.</figcaption></figure>

For the plate-to-plate DBD (first line in figure 4), the positive going-cycle is characterized by propagation of streamers that extend from the active electrode up to 20 mm (time windows 1 and 2). During the negative going-cycle (time windows 3 and 4), diffuse micro discharges occur, as observed in 2008 by Hoskinson *et al.* [20]. They extend up to about 12 mm. Moreover, the discharge does not ignite homogeneously along the high voltage electrode but it starts from individual spots.

With the 100 µm wire diameter active electrode, the positive going-cycle presents two phases. During the first phase (time window 1), streamers occur downstream and upstream the active wire electrode up to about 6 mm. This corresponds to the current peaks observed for t* between -0.1 and 0 in figure 2a. During the second phase (time window 2), there is no streamer as shown in the current curve (figure 2a). The light emitted from the wire shows the presence of an ionization zone around the HV electrode, as observed in low-pressure glow corona discharge. The negative going-cycle (time windows 3 and 4) highlights a diffuse discharge (extending up to 8.5 mm). With the 13 µm diameter wire, a filament-free corona discharge occurs during both going-cycles. The diffuse discharge extends up to about 8 mm during the negative going-cycle (time windows 3 and 4). The discharge modifications may be explained by two reasons: the absence of irregularities at the wire HV electrode cancels the streamer ignition and the more intense electric field at the HV electrode vicinity results in a more uniform glow in the ionization region.
### 3.3 Electrical Power Consumption

Electrical power consumption is due to glow and streamer discharge occurrence. In fact, streamers occur over a very short time (a few nanoseconds) while their number is considerably smaller than the occurrence of negative current pulse. As a result, the main contributor to the electrical power consumption relates to the glow discharge. However, the scale factor between the glow and the streamer components of the current does not allow us to characterize both components simultaneously (see Figure 2a and 2b). This is a drawback to compute the electrical power consumption by integrating the product $v(t) \times i(t)$. Thus the electrical power consumption is computed here by integrating a charge/voltage curve [21] with a 47 nF capacitor as explained in the experimental setup section. This method makes the computation more accurate than using the product $v(t) \times i(t)$.

Figure 5 presents the electrical power consumption versus applied voltage for all the DBD configurations. For a fixed voltage, the power consumption is greater when a wire HV electrode is used, because the glow discharge during the positive going-cycle is fully enhanced when the number streamers is decreased (see figure 2b).

<figure><img src="image_6.png" /><figcaption>**Figure 5:** power consumption versus applied voltage at 1.5 kHz for plate-to-plate (80 µm-thick) and wire-to-plate DBD.</figcaption></figure>

## 4. Mechanical properties

As explained in the introduction, the mechanical effects of the DBD are characterized by time-averaged thrust measurements, determination of the electric wind velocity and induced flow topology versus time.

### 4.1 Discharge Thrust

Force is shown as a function of the electrical power consumption (figure 6). The frequency is set to 1.5 kHz and the electrical power is modified by adjusting the applied voltage from 12 to 22 kV. As previously observed [16], force is a linear function of electrical power consumption. For a plate-to-plate DBD, a thrust of about 60 mN/m is measured when the consumed electric power is equal to 1 W/cm. The use of a thin wire HV electrode instead of a plate results in higher thrust for a same electrical power consumption. More especially, force is larger as the wire diameter decreases (for fixed electrical power consumption) such as in [18]. The actuator effectiveness (in mN/W), that corresponds to the mean produced force divided by the electrical power consumption is shown in Figure 7 as a function of the wire diameter. With a usual plate-to-plate DBD, the force is equal to
0.65 mN per consumed electrical Watt. By using a thin wire, the actuator effectiveness is increased by 12 % for a 300 µm wire and by 46 % for a 13 µm wire with a maximum value of 0.97 mN/W, the effectiveness increases in a - 0.086 power law.

<figure><img src="image_7.png" /><figcaption>**Figure 6:** Thrust versus electrical power (frequency = 1.5 kHz, voltages from 12 to 22 kV).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 7:** Force effectiveness versus wire diameter at 1.5 kHz.</figcaption></figure>

Figure 8 shows force production versus electrical power consumption for a fixed frequency (set to 1500 Hz, voltage is increased from 12 to 22 kV) and a fixed amplitude voltage (set to 20 kV, frequency is adjusted from 500 to 2000 Hz). Three configurations are presented: plate-to-plate, 100 µm and 13 µm wire diameters. For all the configurations and whatever the parameter modified to
adjust power consumption, force production increases with electrical power consumption. Moreover, for a fixed power, it appears that the maximum force is obtained with the power signal with the highest voltage amplitude. In the case of plate-to-plate configuration (figure 8) and a fixed power of 0.36 W/cm, the force produced for a frequency of 1500 Hz ($V \approx 16$ kV) is 23.6 mN/m while at a half frequency (750 Hz, $V = 20$ kV), the measured force is 27.2 mN/m. Thus, for the same power consumption, the force was improved by 15 %. To obtain a 15 % increase of force with a supply frequency of 1500 Hz, the electrical power consumption must be increased by 12 % representing 0.40 W/cm. This demonstrates that increasing the voltage has a better consequence on force production (i.e.; larger force) than increasing the driving frequency. When the plate electrode is replaced by a wire, this later remarks is further verified. Regardless the diameter of the wire, force is enhanced by 32 % at constant consumed power (0.40 W/cm) and high voltage supply.

<figure><img src="image_9.png" /><figcaption>**Figure 8:** Thrust versus electrical power for an amplitude voltage variation (frequency set to 1500 Hz) or a frequency driving signal variation (amplitude voltage set to 20 kV).</figcaption></figure>

## 4.2 *Time-averaged electric wind velocity*

Modifications in the global thrust are due to the changes in the local velocity and in the topology of the electric wind velocity. First, time-averaged horizontal velocity profiles are measured with a pressure probe. Figure 9 shows horizontal velocity profiles at 0.9 mm above the wall. For the plate-to-plate DBD, the electric wind velocity reaches 6 m/s at $x \approx 10$ mm and then it decreases slowly downstream the discharge region because there is no EHD force anymore and its effects dissipate. When the plate active electrode is replaced by a wire electrode, the behavior is quite similar. However, the maximum velocity (measured for $7 \le x \le 9$ mm) increases when the wire diameter is decreased.
For wire diameter smaller than 100 µm, it is higher than the one measured with the plate-to-plate DBD, contrary to the electric wind produced with a wire having thickness larger than 100 µm.

Vertical velocity profiles are shown in figure 10. Again, the maximum electric wind velocity is smaller with the 300 and 100 µm diameter wires than with the plate active electrode. However, the upper part of the velocity profile is thicker (velocity gain of 37% at y = 5 mm). In [18], the authors observed that the body force linearly increases when reducing the diameter of the wire electrode. The present complementary measurements indicate that for wire thicker than 100 µm, the body force increase is not only due to an increase in the produced electric wind velocity but it relates to a wall jet thickening.

<figure><img src="image_10.png" /><figcaption>**Figure 9:** Electric wind for 22 kV and 1.5 kHz measured at y = 0.9 mm, where velocity is maximal.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 10:** Electric wind for 22 kV and 1.5 kHz measured 15 mm downstream the active electrode.</figcaption></figure>

Finally, maximum measured velocity versus the wire diameter is shown in figure 11. The dot lines indicate the maximum velocity obtained with the plate-to-plate DBD. It appears that the larger gain in velocity is observed for low voltages. At 14 kV, all the wires smaller than 300 µm improve the
electric wind velocity. For instance, the gain attains 75 % for 13 and 25 µm but this gain is reduced to 13 % when voltage is increased to 24 kV.

<figure><img src="image_12.png" /><figcaption>Figure 11: Maximal velocity versus wire active electrode diameter for three different voltages (frequency 1.5 kHz).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 12: Efficiency as a function of wire active electrode diameter.</figcaption></figure>

Vertical velocity profiles can be used to compute the produced mechanical power, in using the following equation [1, 22]:

$$P_{mec} = \int_{y} \frac{1}{2} \rho lV(y)^3 dy \quad (1)$$

where ρ is the air density, l the electrode length and v(y) the electric wind velocity versus y. Knowing the power consumed by the actuator, we can estimate the electromechanical efficiency, as shown in figure 12.
Firstly, we can remark that efficiency is small, in the order of a few 0.1 % as commonly observed for surface DBD [1]. The smaller wire is, the more the efficiency is large. On one hand, for wire diameters greater or equal than 100 µm, the mechanical power increases slightly more than the electrical power consumption (see figure 5). In this diameter range, efficiency increases when the diameter is decreased. On the other hand, for wires smaller than 100 µm, the mechanical power increases and the electrical power decreases, resulting in an increase of the efficiency slope. Compared to plate-to-plate DBD, the effect of the wire electrode is more significant for low voltages. At 14 kV, efficiency is multiplied by 3.3 while at 22 kV, it is increased by 43 % (see 13 µm wire-to-plate, figure 12).

### 4.3 Time-averaged electric wind topology

Time-averaged velocity fields obtained from PIV experiments are shown in figure 13 for three configurations (plate-to-plate DBD and wire-to-plate DBD with 13 and 100 µm). The aim of these velocity fields is to observe the topology of the produced electric wind. For all the cases, a wall jet is created from the active electrode edge to downstream. The velocity measured here with the PIV system is similar to the one previously determined with the pressure probe. The PIV acquisitions bring more details on the fluid suction developing above the discharge (-10 ≤ x ≤ 10 mm). For the plate-to-plate DBD, the suction induces a vertical velocity which achieved - 0.9 m/s. Furthermore, a recirculating region forms at x = 20 mm and y = 10 mm. Contrary to the plate-to-plate DBD, no recirculation is created downstream the active wire electrode. In this case, fluid suction is enhanced with a maximum vertical velocity achieving - 1.2 and - 1.3 m/s for 100 and 13 µm, respectively. For the wire-to-plate DBD, a backward flow originates from the electrode backside. The coexistence of this backward flow and suction zone is responsible for a recirculation zone upstream the wire active electrode, its size decreasing with the wire diameter.

<figure><img src="image_14.png" /><figcaption>**Figure 13:** mean longitudinal (left) and transversal (right) flow field for plate, 100 and 13 µm wire active electrode with norm (left) and streamline (right) at 22 kV and 1.5 kHz (scale in millimeter).</figcaption></figure>
4.4 Time-resolved velocity

Another manner to characterize the produced flow is to investigate its time-resolved behavior. Time-
evolution of the horizontal velocity at four discrete points located at 1 mm above the wall is shown in
figure 14, for a high voltage of 24 kV at 1 kHz. With a plate HV active electrode, plasma discharge
induces a horizontal velocity at the same frequency that the high voltage frequency, as we had already
shown in [3, 11]. Horizontal velocity fluctuations at x = 5 and 10 mm are characterized by a velocity
increase at the ignition of the negative discharge (t* ≈ 0.4, see figure 2a) and a decrease when it
switches off (t* ≈ 0.8). At x = 5 mm, velocity oscillates between 2.5 (at t* ≈ 0.1-0.2) and 3.8 m/s (at
t* ≈ 0.5-0.7), resulting in fluctuations equal to 1.3 m/s in amplitude. For x = 15 and 20 mm, we can see
that velocity fluctuations rapidly decrease to about 0.4 m/s, due to viscosity effect. One can notice that
the mean velocity increases from x = 5 to 15 mm (respectively 3.1 to 4.2 m/s) because the flow
accelerates up to the discharge extension (about 10 mm, see figure 9).

<figure><img src="image_15.png" /><figcaption>**Figure 14:** Temporal evolution on horizontal electric wind above plasma sheet (24 kV, 1 kHz).</figcaption></figure>

For the wire-to-plate DBD, velocity fluctuations drastically change. Contrary to plate-to-plate DBD where the maximum velocity was just achieved during the negative going-cycle, we observe that both going-cycles contribute to velocity production. Indeed, there is a velocity acceleration at t* ≈ 0.4 and t* ≈ 0.8, exactly when the negative and the positive discharges ignite, respectively (see figure 2a). Moreover, contrary to the plate-to-plate DBD, the maximum instantaneous velocity is achieved during the positive discharge, showing that it is more effective than the negative discharge with this electrode design. As observed for plate-to-plate arrangement, the reduction of the discharge extension is here responsible for a fast diminution of fluctuations. At x = 5 mm and y = 1 mm, fluctuations are equal to
2.2 m/s. They fall down to 0.6 m/s at x = 10 mm. Fluctuations evolution are quasi-similar for 13 and 100 µm wire-to-plate DBDs.

<figure><img src="image_16.png" /><figcaption>**Figure 15:** Velocity fields (0 – 6 m/s) of the electric wind produced by a plate-to-plate DBD (80 µm-thick, 24 kV, 1 kHz) at different times (scale in millimeter).</figcaption></figure>

Figure 15 shows the vectors of the velocity produced by a plate-to-plate DBD at several times of one ac cycle. As in figure 14, it highlights that for t* < 0.3, the produced velocity is low and it is mainly parallel to the wall in the discharge region. From t* ≈ 0.3 to 0.45, the velocity increases to finally reach a maximum value at t* ≈ 0.55 (5.5 m/s). At t* ≈ 0.55, the electric wind wall jet is thicker and the vectors are deviated toward the wall, showing a more intense suction effect above the discharge. From t* ≈ 0.65 to 0.9, the velocity decreases. This is especially verified in the region for which 0 < x < 5 mm.
<figure><img src="image_17.png" /><figcaption>**Figure 16:** Velocity fields (0 – 8 m/s) of the electric wind produced by the 13 µm wire configuration (24 kV, 1 kHz) at different times (scale in millimeter).</figcaption></figure>

Figure 16 presents the vector fields and the velocity norm in the case of the wire-to-plate DBD, this at height different times (notice that the velocity ranges from 0 (in blue) to 8 m/s (in white)). At $t^* \approx 0.05$, during the positive discharge, the produced velocity and the suction are maximum. An instantaneous velocity of 7.5 m/s is achieved, corresponding to an improvement of 37 % by comparison with a typical plate-to-plate DBD arrangement. At $t^* \approx 0.35$, velocity is produced tangentially to the wall in the particle colliding region, resulting in thinner velocity profiles ($0 < x < 5$ mm). The velocity and suction have greatly decreased. The velocity profile is thinner. At $x \approx 5$ mm and $y \le 2$ mm, the vertical component of the velocity is positive, showing that the electric wind wall jet separates from the wall. Then the velocity increases until $t^* = 0.5$, and it decreases until $t^* = 0.85$.
From $t^* \approx 0.85$ to 0.95, we can observe a strong acceleration of the fluid due to the positive-going cycle discharge.

## 4.5 Multi-DBD actuator

The goal of this last part is to use the wire-to-plate design for a multi-DBD actuator. There are two objectives for multi-DBD designs. The first one concerns an increase in the maximal velocity produced by plasma actuator. Indeed, velocity accumulation has already been observed for such arrangements of DBD in series [3, 23-27]. The second objective is to develop an actuator providing a tangential wall jet over an extended surface in case of large-scale applications.

<figure><img src="image_18.png" /><figcaption>**Figure 17:** Sketch of the inversed multi-DBD.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 18:** Horizontal velocity profiles measured 0.6 mm above an inversed multi-DBD actuator.</figcaption></figure>

To take advantages of the cumulative effect, the DBDs have to be close to each other, but in this case mutual interactions between electrodes can limit the accumulation of electric wind velocity. This result from a counter-wind in opposite direction from each air-exposed HV electrode toward the grounded electrode located at its left [3, 25]. A solution consists of using a shield electrode embedded in the dielectric with a suitable arrangement of the HV and grounded electrodes [25]. Here a new multi-DBD design is proposed with four DBD actuators in series, with better results than in [25]. First, the plate active electrodes are replaced by thin wires (diameter of 25 µm) according to the results
presented previously in this paper in order to enhance the electric wind produced by each single DBD. Secondly, interaction between successive DBD has been cancelled by alternating the HV electrode and the grounded one, from one DBD to the successive one (figure 17). In such conditions, velocity measurements have been conducted. For instance, figure 18 presents an horizontal velocity profile measured 0.6 mm above the wall (with a pressure probe), from x = 0 (position of the first wire HV electrode, on left in figure 17) to x = 150 mm (25 mm downstream the right edge of the last grounded electrode, on right in figure 17). From x = 0 to about 20 mm, the velocity drops from zero to 6 m/s and then decreases because there is no EHD force downstream the plasma extension. Then each successive single DBD add velocity that cumulates up to 10.5 m/s downstream the last single DBD. This is significantly larger than usual observed maximum velocity. Such arrangement may provide a new way to improve control authority of DBD plasma actuator in flow control scenari.

**5. Conclusion**

The present works compared the surface discharges produced by both wire-to-plate and plate-to-plate designs. This investigation includes current analysis, iCCD plasma visualisations, measurements of the thrust induced by both discharges and characterization of the time-averaged and time-resolved electric wind created by the plasma actuators.

Main results are followings:

(1) Current measurements and iCCD visualisations highlight that the use of a thin wire instead of a plate high voltage electrode results in the cancellation of streamers, inducing an increase of the maximum electric wind velocity.

(2) The mean force efficiency is equal to 0.65 and 0.95 N per consumed electrical Watt for the plate-to-plate and the wire-to-plate DBD, respectively.

(3) With a wire active electrode, the topology of the produced electric wind is fully modified and the suction effect is enhanced.

(4) The evolution of the electric wind versus time depends strongly on the high voltage electrode shape. In the case of a typical plate-to-plate DBD, there is a velocity increase at the ignition of the negative going-cycle discharge and a velocity decrease during the positive going-cycle, showing that the negative discharge is more efficient than the positive one. On the contrary, with a wire-to-plate DBD, the velocity increases during both half cycles, with a velocity increase when the discharge occurs and a decrease when there is no discharge. Moreover, the maximum velocity is produced during the positive discharge.

(5) Finally, the use of four successive wire-to-plate DBD for a multi-DBD actuator allows us to reach an electric wind velocity of 10.5 m/s. An optimization of electrical and geometrical parameters should produce a velocity up to about 12 m/s.

**Acknowledgment**

This work was supported by the 7th Framework Program FP7/2007-2013, PLASMAERO (grant agreement n° 234201). We acknowledge R. BELLANGER, P. BRAUD and A. CLAVERIE for their help during the measurements.

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