# Optimization of a dielectric barrier discharge actuator by stationary and non-stationary measurements of the induced flow velocity: application to airflow control

Maxime Forte, Jérôme Jolibois, Jérôme Pons, Éric Moreau, Gérard Touchard,

Michel Cazalens

► To cite this version:

Maxime Forte, Jérôme Jolibois, Jérôme Pons, Éric Moreau, Gérard Touchard, et al. Optimization of a dielectric barrier discharge actuator by stationary and non-stationary measurements of the induced flow velocity: application to airflow control. Experiments in Fluids, 2007, 43 (6), pp.917-928. 10.1007/s00348-007-0362-7. hal-05077757

HAL Id: hal-05077757

https://hal.science/hal-05077757v1

Submitted on 21 May 2025

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# Optimization of a Dielectric Barrier Discharge Actuator by Stationary and Non-stationary Measurements of the Induced Flow Velocity - Application to Airflow Control

M. Forte<fnref n="1" />, J. Jolibois<fnref n="1" />, J. Pons<fnref n="1" />, E. Moreau<fnref n="1" />, G. Touchard<fnref n="1" /> and M. Cazalens<fnref n="2" />

E. Moreau (Corresponding author)

Email: eric.moreau@lea.univ-poitiers.fr

Tel: +33 549496940

Fax: +33 549496968

**Abstract.** Several studies have shown that a surface Dielectric Barrier Discharge (DBD) may be used as an ElectroHydroDynamic (EHD) actuator in order to control airflows. In this paper, a parametric study has been performed in order to increase the velocity of the ionic wind induced by such actuators. The results show that an optimization of geometrical and electrical parameters allows us to obtain a time-averaged ionic wind velocity up to 8 m/s at 0.5 mm from the wall. Moreover, non-stationary measurements of the induced wind have been performed with synchronized records of current and voltage signals. These experiments show that the DBD actuator seems to generate a pulsed velocity at the same frequency than the applied high voltage.

## 1 Introduction

Several studies have shown that discharges in air at atmospheric pressure may be used as ElectroHydroDynamic (EHD) actuators for airflow control along profiles (Moreau, 2007). Applications like drag reduction, flow reattachment or detachment and instability control are particularly concerned. Up to now, two kinds of discharges have mainly succeeded in modifying actively flow characteristics: DC corona discharges and AC dielectric barrier discharges (DBD). Both actuators generate a cold plasma on the surface of the profile and work by creating ionic wind and by injecting kinetic energy inside the boundary layer of the airflow. The abilities of the DC corona discharge to modify boundary layer profiles have been shown by Moreau et al. (2006), Leger et al. (2002) or Artana et al. (2002) for instance.

<footnote n="1">¹ LEA (Laboratoire d'Etudes Aérodynamiques), CNRS/ENSMA/University of Poitiers, BP30179, 86962 Futuroscope Cedex, France</footnote>

<footnote n="2">² SNECMA (SAFRAN Group), 77550 Moissy Cramayel, France</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1 DBD actuator setup (side view)</figcaption></figure>

The study related to the present paper has focused on the single DBD actuator which is presented in Fig. 1. This actuator consists of two metallic electrodes asymmetrically mounted on both sides of a dielectric plate. The active electrode is supplied with AC high voltage which is needed to maintain the discharge and to evacuate charge build-up on the dielectric surface. The other electrode is grounded. Roth et al. (1998, 2000) have shown the ability of this actuator to modify the properties of a boundary layer over a flat plate. The authors show that the discharge induces an airflow of several m/s tangentially and very close to the wall. Recently, Grundmann et al. (2006) studied the linear stability of a boundary layer modified by a single DBD actuator. They showed that the influence of the actuator on the velocity profile remains long enough to damp the growth of disturbances and to delay transition. Rivir et al. (2003) or List et al. (2003) have both shown that the use of such actuators on low pressure turbine blades enables the control of the laminar separation. More recently, some works performed by Post et al. (2004) and Corke et al. (2005) with NACA airfoils have shown lift improvement in stall configurations. Moreover, Gaitonde et al. (2006) studied this configuration with the help of numerical simulations.

In order to improve the abilities of this device, several studies have focused on the discharge without free airflow. These works are mainly observation and parametric studies. For example, optical measurements carried out by Enloe et al. (2004) have revealed that the structure of the plasma is not the same between the positive half period and the negative half period of the applied voltage. It has also been pointed out by Pons et al. (2005) in our lab. In this study, we measured velocity profiles above the actuator without free airflow. More, we modified several geometrical and electrical parameters. Among other results, this study has shown that the mechanical energy increases gradually up to the limit of plasma extension. Recently, Roth and Dai (2006) have tried to quantify the part of the electrical power which is dissipated by heating the dielectric. They showed that the losses depend highly on the dielectric material.
On another hand, several authors tried to understand how the actuator adds momentum to the air by means of numerical simulations, taking into account the chemistry of various species. Recently, Boeuf et al. (2005, 2007) have performed simulations in a nitrogen-like gas (with positive ions only) and they showed that for a ramp or a sine voltage, the discharge current consists of large amplitude short pulses during which a filamentary plasma spreads along the surface, separated in time by long low-current discharge phases of corona type. Moreover, they assumed that the contribution of the low current phases to the total force may be predominant in comparison with the pulses contribution because the force induced during the corona phases acts over a much larger volume and for a longer time. Likhanskii et al. (2006) have conducted the same kind of simulation taking into account the chemistry of positive and negative ions (because air is also an electronegative gas). Even if the main flow induced by the actuator has been shown to be directed downstream, the authors assumed that some upstream flows (induced by ion motion back towards the exposed electrode during both half cycles of the sine applied voltage) may be a major source of inefficiency. Therefore, they suggested an optimal voltage waveform which could improve the actuator properties. For more details about airflow control by plasma actuators, see the review of Moreau (2007).

In this paper, the discharge-induced ionic wind is studied as a function of several parameters for a single actuator in absence of free airflow. First, a parametric study has been conducted with the purpose of increasing the induced velocity. The influence of materials, electrical parameters and the geometry of the actuator (electrode size, thickness, electrode gap, etc) have been studied over a large range. Secondly, non-stationary measurements of the induced velocity have been performed by Laser Doppler Velocimetry (LDV) with synchronized records of electrical current and voltage.

# 2 Experimental arrangements

## 2.1 The DBD actuator

The discharge setup consists of two flat 20 cm-long (span wise) rectangular electrodes, made of aluminium tape which is about 0.1mm thick. The actuator is mounted on a dielectric flat plate having a thickness of a few millimeters. The active electrode is connected to a power amplifier TREK +/- 30 kV (40 mA peak, 600 W) delivering a sine high voltage in a range of 10-30 kV in amplitude with a frequency of about 500-2000 Hz. The other electrode is grounded. Plasma appears on both sides from one electrode towards the direction of the
opposite electrode, with declining luminosity. Fig. 2 presents a top view photograph of the actuator turned on. As the exposure time is equal to several seconds, the plasma looks like a quite uniform glow in the transverse direction. In fact, the plasma is constituted of microdischarges distributed uniformly in time and space along the electrode length.

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Photograph of the DBD actuator in action (top view)</figcaption></figure>

Typical voltage and current waveforms are presented in Fig. 3 for a discharge on a glass plate (2mm-thick) for a frequency of 1 kHz and amplitude of 10 kV. The current is deduced from the voltage across a resistor connected in series between the “grounded” electrode and the ground. The $\frac{\pi z}{2}$ phase-shifted capacitive current has been subtracted on this graph.

<figure><img src="image_4.png" /><figcaption>**Fig. 3** Typical discharge current and voltage waveforms versus time</figcaption></figure>

We can see that series of short and intense pulses appear during the first half of each semi-period. Each pulse corresponds to one or several simultaneous microdischarges, appearing as soon as the voltage across the interelectrode space exceeds a given threshold.
Typical velocity profiles above a DBD actuator are shown in Fig. 4 when high voltage is applied (V = 20 kV, f = 1 kHz), for different x values (see the x,y axis on Fig. 1). The maximum velocity $U_{max}$ is reached at the end of the plasma area (x ~ 10 mm in this case) and at y = 0.5 mm from the wall. Downstream, the different profiles clearly show the diffusion phenomenon of the momentum transferred from the plasma to the air: The value of the maximum velocity decreases and the height of the profiles increases with increasing x values. Although the plasma seems to be quite uniform, we had previously shown that the DBD actuator seems to induce a pulsed airflow at the same frequency as the applied high voltage (Forte et al. 2005). Moreover, recent studies have shown that the discharge behaves quite differently during the negative and the positive half cycles of the sine voltage (Enloe et al. 2004, Boeuf et al. 2005, Pons et al. 2005, Likhanskii et al. 2006).

<figure><img src="image_5.png" /><figcaption>Fig. 4 Typical velocity profiles above the DBD</figcaption></figure>

## 2.2 Ionic wind velocity measurements

Firstly, the parametric study has been led with measurements of the induced velocity above the actuator with a total pressure probe made in glass connected to a Furness micromanometer FC014 (0-10 mm H₂O, 0-12 m/s). This kind of Pitot arrangement is very simple, fast and therefore perfectly suited to a parametric study. The probe can be moved precisely along 3 axes above the actuator with three Isel linear driving units monitored by a computer. The analogic output of the manometer is connected to a Keithley USB data acquisition module (16 bit, 50 kS/s). For each measurement, a record of 3000 samples at 1 kHz is made to ensure the convergence of the time-averaged velocity value.

Secondly, non-stationary measurements have been performed with a LDV system (Dantec Dynamics, BSA Model F80) which allows the acquisition of analog channels synchronized
with the velocity samples. Therefore, this device enables synchronized records of electric current, voltage and velocity. The whole system can be moved along 3 axes with the same devices as for the parametric study. LDV provides quantitative information about stationary and non-stationary velocity due to its large bandwidth (about 10 kHz).

## 2.3 Electrical measurements

For the parametric study, the voltage applied to the active electrode is measured by using the power amplifier internal probe. The current is deduced from the voltage across a resistor connected in series between the “grounded” electrode and the ground. Both waveforms are recorded using a fast Tektronix digital oscilloscope (100 MHz, 1.25 GS/s).

<figure><img src="image_6.png" /><figcaption>**Fig. 5** Cubic evolution of the electric power consumption versus voltage amplitude for different frequencies</figcaption></figure>

For the LDV measurements, both voltage and current waveforms are recorded by using the power amplifier internal probes. The amplifier current probe has a much lower bandwidth (10 kHz) than the resistor; therefore the pulses are not well resolved.

For example, electric power evolutions with the voltage amplitude and the frequency are given in Fig. 5 and Fig.6 for a 2 mm thick actuator made of glass (electrodes were 20 cm span wise). Note that power is a cubic function of the voltage but is a linear function of the frequency in the considered range of values.
<figure><img src="image_7.png" /><figcaption>**Fig. 6** Linear evolution of the electric power versus frequency for different voltage amplitudes</figcaption></figure>

**3 Parametric study**

Each of the following parameters has been modified one by one and the discharge has been characterized mechanically for each case:

* Electrode gap (-5 mm < d < 15 mm, see Fig. 7)

* Grounded electrode width (1 mm < L < 50 mm)

* Frequency (100 Hz < f < 2 kHz)

* Voltage amplitude (8 kV < V < 30 kV)

* Material permittivity (3 < $ε_r$*<10)*

* Dielectric layer thickness (1 mm < a < 3 mm)

Multiple actuators have also been studied in this first part; they consist in several actuators mounted in series, one behind the other.

<figure><img src="image_8.png" /><figcaption>**Fig. 7** Geometrical parameters studied</figcaption></figure>

**3.1 Electrode Gap**

First, the electrode gap *d* is modified from this geometrical and electrical base case: a 2 mm-thick flat plate made in PMMA is used with two 5mm-wide electrodes (f = 700 Hz, V = 20 kV). A parabola-like evolution of the maximum velocity with the electrode gap is
shown in Fig. 8. This maximum is extracted from several velocity profiles and is generally
found at y = 0.5 mm above the plane and at the end of the plasma area (10 < x < 12 mm).

In the first part of the graph, the maximum velocity increases with the gap up to an optimum
value for d = 5 mm. Increasing the gap may strongly modify the electric field distribution and
allow the ions to be accelerated for a longer distance. With a bigger gap, the electric field may
fall down because the effective dielectric thickness between the electrodes increases. When
the electrodes are one above the other (d = -5 mm) the symmetric distribution of the electric
field does not allow the ions to be accelerated as much as with a positive gap. One possible
explanation is that two ionic winds with opposite directions are generated by this
configuration: one is directed upstream while the other one is directed downstream with the
same velocity. The dissymmetry of the actuator is needed to induce ionic wind in one single
direction. This experiment proves the importance of the grounded electrode position.

<figure><img src="image_9.png" /><figcaption>**Fig. 8** Evolution of the maximum induced velocity with the electrode gap</figcaption></figure>

**3.2 Grounded electrode width**

For the next experiment, the same actuator and excitation are used (with electrode gap
d = 0 mm, f = 700 Hz and V = 20 kV) but we modify the grounded electrode width. The
maximum induced velocity versus the gap is presented in Fig. 9. This graph shows that an
asymptotic curve can fit with the observed evolution. In the first part of the graph, the
velocity increases with the electrode width and reaches a plateau. The wider the electrode is,
the further the plasma can expand. Injected ions are accelerated for a longer distance as in the
previous section (3.1), and therefore the velocity increases. The ions drift on the surface as
long as the voltage across the plasma is high enough. Moreover, the phenomena which made
the plasma self-sustaining (secondary emission) are dissipative, so when this voltage drops the
plasma cannot expand farther on the surface even with a wider electrode. That is probably
why the velocity reaches a plateau which means it is a waste of space and power to use a
wider grounded electrode. In our case, the optimum grounded electrode width is 20 mm (for
the geometric and electric parameters chosen here). More, we noticed that the same results
could be shown for an actuator with a 5mm-wide gap and a 15mm-wide grounded electrode.
This phenomenon may be explained by the fact that the plasma extension is never larger than
2 cm, for both geometrical configurations. Indeed, the maximum velocity depends usually on
the plasma extension limit.

<figure><img src="image_10.png" /><figcaption>**Fig. 9** Asymptotic evolution of the maximum induced velocity with the grounded electrode width</figcaption></figure>

**3.3 Frequency**

The same actuator is used for the next experiment, with the optimum electrode width (L = 20 mm, d = 0 mm, V = 20 kV). The graph in Fig. 10 shows the evolution of the maximum velocity above the actuator with the frequency. Electric power measurements have been performed during velocity records and this enables to plot the maximum velocity versus the power (Fig. 11). We can observe the same asymptotic evolution on both plots. In the first part of the graphs, the velocity increases with the frequency. Two phenomena may have an important part in this. First, when the frequency increases, the applied voltage slope also increases which probably enhances the ionisation. Secondly, the mean transferred charge increases with the frequency inducing more collisions between ions and gas. For high frequencies the maximum velocity reaches a plateau above an optimum value which is about
1200 Hz in the case studied here. During one half cycle of the sine voltage, the surface of the dielectric is charged and then relaxed during the following half cycle. It is probable that the charged surface does not have the time to fully relax for frequencies higher than a threshold value. Moreover, for those high frequencies ($1.5 \text{ kHz} < f < 2 \text{ kHz}$) the discharge has shown some instabilities and big energetic filaments at the surface of the dielectric.

<figure><img src="image_11.png" /><figcaption>**Fig. 10** Asymptotic evolution of the maximum induced velocity with frequency</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 11** Asymptotic evolution of the maximum induced velocity with electric power (the modified parameter is the frequency)</figcaption></figure>

## 3.4 Voltage

The graphs in the Fig. 12 shows the evolutions of the maximum velocity above the same actuator with the applied voltage amplitude ($L = 20 \text{ mm}, d = 0 \text{ mm}, f = 1 \text{ kHz}$). This time the evolution is not really asymptotic because the maximum velocity does not reach a plateau.
The velocity increases with the voltage because the electric field also increases and ions undergo higher Coulombian forces. Moreover, note that the fluctuations of the velocity increase with the applied voltage (the RMS values are plotted with error bars in Fig. 12). Once more, electric power measurements have been performed during velocity records and this enables to plot the maximum velocity versus the power (Fig. 13). This graph shows once more an asymptotic evolution as the one in Fig. 11. Note that after a threshold power value (about 35W), the actuator has huge electric power consumption for very little gain on the maximum velocity. Yet, according to the graphs in Fig. 12, higher velocities may be reached with supplies which could deliver higher voltage amplitude but, in this case, huge electric power consumption has to be expected.

<figure><img src="image_13.png" /><figcaption>**Fig. 12** Evolution of the maximum induced velocity with voltage amplitude</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 13** Asymptotic evolution of the maximum induced velocity with electric power (the modified parameter is the voltage amplitude)</figcaption></figure>

**3.5 Materials**

Fig. 14 presents the same plot than in Fig. 12 but for two different actuators: one is set up on a glass flat plate ($\sigma_g \sim 10$) while the other is set up on a PMMA flat plate ($\sim 3$). Although both actuators behave quite similarly, some differences have to be noticed. The first difference is that the velocity is higher on the glass for low voltages and then smaller than PMMA actuator for high voltages. This phenomenon was expected because the electric glass permittivity is higher than PMMA, so the electric field is higher and thus, the velocity is higher.

<figure><img src="image_15.png" /><figcaption>**Fig. 14** Evolution of the maximum induced velocity with the voltage for an actuator made with PMMA and for another actuator made in glass</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Fig. 15** Asymptotic evolution of the maximum induced velocity with the electric power for an actuator made with PMMA and for another actuator made in glass</figcaption></figure>

But for high voltages the electric field on the glass is too important and the discharge becomes filamentary and unstable. This phenomenon limits drastically the mechanical effect of the actuator and the velocity reaches a plateau. If the maximum velocity is plotted versus electric power for both actuators (Fig. 15), those graphs clearly show that for a given velocity value, the power consumption for the glass actuator is always higher than for the PMMA actuator (even twice higher for a maximum velocity of 5m/s). In fact, as explained theoretically by Roth and Dai (2006), the losses inside the dielectric increase linearly with its permittivity. More, they performed some experiments to show this but only in the case of high frequency DBD (5-7 kHz). According to our experiment, we assume that the dielectric material plays a major role on the efficiency of the actuator, even in the case of low frequency DBD.

**3.6 Dielectric layer thickness**

Fig. 16 presents the maximum velocity versus the applied voltage amplitude for three different actuators.
<figure><img src="image_17.png" /><figcaption>**Fig. 16** Evolution of the maximum induced velocity with the voltage for three actuators with different dielectric thickness</figcaption></figure>

The material, the electrode size and position are the same for each actuator ($L = 20$ mm, $d = 0$ mm, $f = 1$ kHz, PMMA) but the thickness of the dielectric flat plate changes: $a=1$, $a=2$ and $a=3$ mm. For a given voltage amplitude, the thinnest actuator induces the highest velocity. Obviously, decreasing the thickness leads to the same results than increasing the permittivity or the voltage amplitude: the electric field is stronger and thus, the velocity is higher. But with the thinnest actuator, the discharge becomes more easily filamentary and unstable at a relatively low voltage ($V = 17$ kV). The plasma is concentrated on several injection points with big energetic filaments which damage the material due to strong local heating. Moreover, the mechanical efficiency drastically decreases in this case.

The thickest actuator enables the use of higher voltage amplitudes, without filamentation. It explains why higher velocity is measured on this actuator for high voltage amplitudes. The maximum available voltage was here 30 kV, but it would be interesting to go on with these measurements with higher amplitudes and thicker dielectric plates.
<figure><img src="image_18.png" /><figcaption>**Fig. 17** Evolution of the maximum induced velocity with the electric power for three actuators with different dielectric thicknesses</figcaption></figure>

The graph in Fig. 17 presents the maximum velocity versus the electric power for two different actuators: one is 2 mm thick while the other is 3 mm thick. Note that both curves are nearly superimposed which means both actuators have the same efficiency but the thickest one induces a more stable discharge for a given power.

## 3.7 Multiple actuators

### 3.7.1 Velocity measurements

Previous works have shown that the use of a second actuator placed downstream the other one could enhance the induced velocity (Enloe et al. 2004). We try to investigate this phenomenon and to measure the velocity generated by these multiple actuators. In the first time, a double actuator has been set up on a PVC flat plate (3 mm thick) as presented in Fig. 18. The space between both single actuators is 1 cm.

<figure><img src="image_19.png" /><figcaption>**Fig. 18** Schematic side view of the multiple actuators</figcaption></figure>
The black curve presented in Fig. 19 (-▲-▲-), shows a velocity recording with a horizontal scan above the multiple actuators (at y = 0.5 mm) when discharge is ignited (V=20 kV, f = 1 kHz). The same sine high voltage is applied to the upper electrodes without phase shift. The positions of the electrodes are represented below the graph.

<figure><img src="image_20.png" /><figcaption>**Fig. 19** Horizontal velocity profiles with and without parasitic ionization</figcaption></figure>

As expected, the velocity increases up to the plasma extension limit and decreases downstream. However, it decreases faster than in the case of a single actuator. This is due to unwanted ionic wind directed upstream, generated by parasitic plasma as illustrated in Fig. 20. Thus, the second actuator induces the same velocity as the first one because the starting velocity is equal to zero. The pink curve in the Fig. 19 (-■-■-) shows the same velocity measurements as the black curve, but the active electrode of the second actuator is covered with PTFE tape in order to avoid parasitic ionization. The velocity increases up to the same value as the black curve but does not cancel downstream. Thus, the second actuator adds more momentum and the velocity reaches a higher value because the starting velocity is not equal to zero. The difference between both maximum velocities is about 1 m/s.

<figure><img src="image_21.png" /><figcaption>**Fig. 20** Problem of parasitic ionisation which creates unwanted ionic wind</figcaption></figure>
### 3.7.2 Effect of the space between each actuator

With regards to this problem of parasitic ionization, we investigated the role of the space between consecutive actuators (PTFE tape is set up in these experiments). Similar recordings have been made above three different actuators which have the same electrode configuration ($L = 20$ mm, $d = 0$) but with different values of inter-actuator space: 1, 2 and 3 cm. Horizontal velocity profiles above the three double actuators are presented in Fig. 21 when the discharge is ignited ($V = 20$ kV, $f = 1$ kHz).

<figure><img src="image_22.png" /><figcaption>Fig. 21 Horizontal velocity profiles with different spaces between the actuators</figcaption></figure>

The results show very little differences between the three double actuators, nevertheless we can notice some interesting points. When the velocity decreases (downstream the plasma area) the slopes are not the same for the three actuators. Above the 1-cm-spaced-actuators the velocity decreases more rapidly than above the 3-cm-spaced-actuators. In spite of the PTFE tape, it is probable that the unwanted wind has not totally disappeared, and this wind is faster when the actuators are closer which explains the slope differences. Moreover, the 2-cm-spaced-actuators seem to be an optimum configuration because they generate the fastest velocity.

### 3.7.3 Effect of the voltage amplitude

As the 2-cm-spaced-actuators seem to be an optimum configuration, they were used to study the influence of the voltage amplitude. Three horizontal profiles above the multiple actuators are shown in Fig. 22 for different voltage amplitudes: 20 kV, 25 kV and 30 kV ($f = 1$ kHz for each case).
<figure><img src="image_23.png" /><figcaption>**Fig. 22** Horizontal velocity profiles above multiple actuators for three different voltage amplitudes</figcaption></figure>

On the three curves, we can notice that the maximum velocity above the first actuator reaches usual values for each voltage amplitude (see the graph of Fig. 16 for a thickness of 3 mm). If we focus on the decreasing part of the velocity (downstream the plasma extension), we can see that the slopes are the same for $V = 20$ kV and $V = 25$ kV, but for 30 kV the velocity decreases strongly upstream the active electrode of the second actuator. It means that the PTFE tape is not enough efficient at this very high voltage and that it does not succeed in avoiding the parasitic ionization. In all the cases, the second actuator increases the maximum velocity of the first actuator of about 1 m/s. In fact, the second actuator behaves as if there were a free airflow but this starting velocity is provided by the first actuator. With the voltage amplitude $V = 30$ kV, the frequency has been increased up to $f = 2$ kHz on this multiple actuator and the velocity reaches 8 m/s. Those experiments also reveal an interesting phenomenon: the position of the maximum velocity seems to slide downstream (towards the right on Fig. 22) when the voltage amplitude is increased. This result is connected to the extension of the plasma area. The higher the voltage is, the further the plasma area extends and some previous works have shown that the maximum velocity position is at the end of the plasma area (Pons et al. 2005).

### 3.7.4 Effect of the number of actuators

To conclude on this parametric study, we tried to investigate the influence of the number of actuators. Four actuators have been placed one behind the other with a space of 2 cm between each one. The electrode configuration is still the same ($L = 20$ mm, $d = 0$). One horizontal velocity profile above the multiple actuators (at $y = 0.5$ mm) is presented in Fig. 23 when the
voltage is applied (V = 20 kV, f = 1 kHz). Additional acceleration occurs for each actuator and the velocity progressively increases. Each actuator adds about 1 m/s to the maximum velocity of the upstream actuator. It looks like the amount of additional momentum per actuator is likely to decrease with more actuators. It will be the subject of further investigations. Finally, note that the convergence of the measurements worsens when we move towards the last actuator which probably means that turbulence of the flow increases. More, a time-averaged ionic wind of 8 m/s has been measured for the same configuration with a voltage amplitude V=25kV. But experiments with higher voltage amplitudes could not be performed because the power limit of the supply was reached.

<figure><img src="image_24.png" /><figcaption>**Fig. 23** Horizontal velocity profile above four actuators places one behind the other.</figcaption></figure>

**4 Time-resolved LDV measurements of the induced velocity**

In a previous study (Forte et al. 2005), we found that the DBD actuator seems to induce pulsed airflow at the same frequency that the applied high voltage. In order to measure the phase-shift between the electric waveforms and the velocity, time-resolved measurements above the actuator have been performed by means of LDV. To operate such technique, seeding particles are needed in the air. For this reason, the actuator has been placed in a wind tunnel which generates a very slow airflow ($U_0 = 2$ m/s) to carry the smoke away and improve the LDV data rate.
## 4.1 Time-averaged velocity fields

At first, 2D time-averaged velocity fields above the actuator have been measured with the actuator turned on, (V = 15 kV, f = 700 Hz, Pel = 25 W) in order to characterize the topology of the induced ionic wind. The horizontal component of the velocity is shown in Fig. 25 while Fig. 26 presents the vertical component. Both fields are the results of 300 measurement points in a plane above the actuator as shown by the hatched area in Fig. 24.

<figure><img src="image_25.png" /><figcaption>Fig. 24 LDV measurement plane above the actuator</figcaption></figure>

We can notice in Fig. 25 that the fluid in the boundary layer is accelerated from 1 m/s to 3 m/s (at y = 1mm). The actuator effect is still perceived largely downstream the plasma area (which ends at x = 10 mm). The vertical velocity field (Fig. 26) underscores a zone of suction above the actuator where the airflow is deflected towards the wall (velocity is negative in the blue zone).

<figure><img src="image_26.png" /><figcaption>Fig. 25 Horizontal time-averaged velocity field above the actuator</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>Fig. 26 Vertical time-averaged velocity field above the actuator</figcaption></figure>

**4.2 Non-stationary measurements**

In the previous results, each measurement point corresponds to the recording of 20000 seeding particles velocities. Focusing on the instantaneous evolution of the velocity at a given point, we have access to the non-stationary information. Instantaneous evolutions of both velocity components (horizontal component u, vertical component v) are presented in Fig. 27, Fig. 28 and Fig. 29 with voltage and current signals for three different points:

* P1 (x=2mm, y=1mm)

* P2 (x=5mm, y=1mm)

* P3 (x=10mm, y=1mm)

The discharge characteristics are the same (V = 15 kV, f = 700 Hz). Note that if no microdischarge pulses are observed on current waveforms it is because the bandwidth of the sensor used here is very low (10 kHz). The capacitive current has been subtracted on this graph. Instantaneous evolutions at P1 are shown in Fig. 27. Each point of the velocity curves represents the record of one particle and that is why they are not regularly spaced. The actuator seems to generate a pulsed induced flow at the same frequency as the high voltage. This measurement is in accordance with our previous works (Forte et al. 2005). At this height in the free boundary layer (at y = 1 mm without any discharge), the horizontal velocity is 1.2 m/s. Thus, both half cycles of the discharge generate horizontal velocity (u component). But the discharge does not behave similarly during the negative and the positive half cycles. The red square-dotted curve shows that the negative half cycle induces more velocity (3.6 m/s) than the positive one (2.4 m/s).
<figure><img src="image_28.png" /><figcaption>**Fig. 27** Time evolution of horizontal and vertical velocity (respectively u and v) above the actuator synchronized with voltage and current recordings</figcaption></figure>

Finally, the positive half cycle seems to generate negative vertical velocity (blue triangle-dotted curve) while the negative half cycle does not affect this component. This phenomenon which happens only for the positive-going portion could explain the zone of negative velocity above the actuator (see the blue area in Fig. 26).

<figure><img src="image_29.png" /><figcaption>**Fig. 28** Time evolution of discharge current and voltage when the grounded electrode is encapsulated</figcaption></figure>

Previous works based on electrical (Pons et al. 2005) and optical (Enloe et al. 2004) measurements, have shown that two different discharge regimes occur during both half cycles. The negative-going portion has been found to produce a more uniform discharge than the positive-going one. A time evolution of the discharge current is presented in Fig. 28 when the grounded electrode is encapsulated. The difference between both half cycles is obvious: the positive discharge is more filamentary than the negative. It is probably why the induced
velocity is lower. The nature of the discharge regime seems to play an important role in the momentum transfer to the neutral fluid. Recent numerical works by Boeuf et al. (2005, 2007) or Likhanskii et al. (2006) show that the averaged force is not the same from one half-cycle to the other.

<figure><img src="image_30.png" /><figcaption>**Fig. 29** Time evolution of horizontal and vertical velocity (respectively $u$ and $v$) above the actuator synchronized with voltage and current recordings</figcaption></figure>

Instantaneous evolutions at P2 are presented in Fig. 29. Note once more that negative-going cycle induces more horizontal velocity than the positive one. But the mean velocity is higher (3.5 m/s) than the value at P1 (3m/s) just because P2 is in the area where the flow is accelerated. Moreover, fluctuations of the vertical velocity seem to have disappeared. This is in accordance with the vertical time-average velocity field (Fig. 26) where the area of negative values (blue area) stops towards higher $x$ values.

Instantaneous evolutions at P3 (downstream the plasma area) are shown in Fig. 30. This time, velocity fluctuations of both components seem to have disappeared and the horizontal velocity stabilizes around a mean value of about 3.5 m/s which is the same value as the mean velocity at the previous point P2. This attenuation of velocity fluctuations is probably due to diffusion phenomenon.

We have to be careful with our results, because the seeding particles, despite their small size, may be charged in the high electric field and be deflected by Coulombian forces. Yet, if we look the time evolution of the velocity downstream the plasma area, the fluctuations have disappeared and the horizontal velocity is exactly the mean of the extreme values of the fluctuations above the actuator ($2.4 + 3.6)/2 = 3$ m/s. Moreover, the same velocity has been measured with a Pitot probe at the same point and for the same discharge. Therefore, we assume that the error induced by the charge of particles is negligible.
**5 Conclusion**

This study has shown that the geometric parameters of the DBD actuator may affect drastically the discharge aspect and thus the induced ionic wind velocity. The results show that the maximum velocity increases, in an asymptotic way, with the frequency and the grounded electrode width but not with the applied voltage amplitude which means that higher velocities could be reached with higher voltage amplitudes. More, when the gap between both electrodes is modified, the maximum velocity is reached for an optimum value.

<figure><img src="image_31.png" /><figcaption>**Fig. 29** Time evolution of horizontal and vertical velocity (respectively *u* and *v*) above the actuator synchronized with voltage and current recordings</figcaption></figure>

Finally, it has to be noticed that the discharge does not behave similarly for different dielectric materials. The actuator seems to lose its mechanical efficiency if the electric field is too high because the discharge becomes filamentary. With regards to this phenomenon, the modification of the electric field distribution, by changing the dielectric layer thickness, induces a major effect on the induced velocity. An optimization of all the parameters enabled us to obtain an ionic wind velocity up to 7 m/s at 0.5 mm of the wall, for a single actuator and 8 m/s for multiple actuators.

Concerning the time-resolved LDV measurements, the results show that the DBD actuator generates a pulsed velocity at the same frequency as the applied high voltage and that the negative half period induces more velocity than the positive one. These measurements prove that the DBD does not act similarly during the negative and the positive half cycles.
**Acknowledgments** The authors gratefully acknowledge the technical and financial support of SNECMA (SAFRAN Group) (Contract N°920 430961). This work has been performed in the frame of a working group including researchers from two CNRS laboratory, LAPLACE (LAboratoire PLAsma et Conversion d'Energie) and LEA (Laboratoire d'Etudes Aérodynamiques) and also from ONERA (Office National d'Etudes et de Recherches Aérospatiales). The authors would like to thank members of this group for sharing their results and for fruitful discussions.

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