# Elongating the area of plasma/fluid interaction of surface nanosecond pulsed discharges

Kossi Djidula Bayoda, Nicolas Bénard, Éric Moreau

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Kossi Djidula Bayoda, Nicolas Bénard, Éric Moreau. Elongating the area of plasma/fluid interaction of surface nanosecond pulsed discharges. Journal of Electrostatics, 2015, 74, pp.79-84. 10.1016/j.elstat.2014.12.004. hal-03629668

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# Elongating the area of plasma/fluid interaction of surface nanosecond pulsed discharges

K.D. Bayoda, N. Benard and E. Moreau.

Institut PPRIME (CNRS UPR 3346, Université de Poitiers, ENSMA)

Dpt Fluide, Thermique et Combustion

Bld Marie et Pierre Curie

Téléport 2, BP 30179, 86962 Futuroscope, France

## Abstract

Plasma-assisted flow control is of high industrial interest, but practical applications at full scale often requires a large surface of interaction between the weakly ionized non-thermal plasma propagating at the surface of the dielectric material and the boundary flow developing at the dielectric wall. Nanosecond pulsed Dielectric Barrier Discharge (DBD) have demonstrated promising results of flow control even at high-speed, but their interacting region is limited to a small surface covering only a few cm². In this paper, the conditions to extend a surface nanosecond pulsed discharge *via* longer ion drift region are documented. In particular, it is shown that a sliding discharge regime can develop and fully fill an inter-electrode distance of 40 mm. This sliding discharge is obtained by applying a potential difference larger than 26 kV between both upper air-exposed electrodes stuck on the dielectric surface and separated by 40 mm. This particular discharge mode results in a large increase of the total consumed energy (+120%) while the plasma/fluid surface is increased by 300% in comparison with a single nanosecond DBD actuator that only propagates over 10 mm. Schlieren visualizations confirm that the sliding regime modifies the topology of the induced pressure wave. This discharge regime promotes the formation of two hemispheric pressure waves originating from both air-exposed electrodes in regard while an horizontal region of high pressure gradient, caused by the increase in plasma extension, is observed. It is also shown that an increase in the negative dc component does not enhance the mechanical effects observed with the Schlieren setup.
Introduction

A part of the gas in contact with aerodynamic objects can be easily ionized by exciting the air
molecules using an electric field exceeding the breakdown voltage of the air at atmospheric
conditions. This localized ionization finds several applications in aerodynamic. Among the
numerous investigations related to the flow manipulation by surface electrical discharge, the
reduction of flow separation over curved or inclined surfaces, the drag reduction in view of
fuel consumption improvement or the manipulation of laminar-to-turbulent transition are
some of the practical applications where non-thermal plasma discharges demonstrated a good
effectiveness at least for in-lab conditions. At the beginning, surface corona discharges were
investigated to modify a laminar boundary layer [1] or to mitigate flow separation [2]. In
parallel, surface Dielectric Barrier Discharges (DBD) were also developed as flow control
actuators [3, 4, 5, 6]. These two types of non-thermal plasma discharges take advantages of
the momentum transfer induced by the collision of charged and neutral particles in order to
dynamically affect the flow conditions at the surface of an aerodynamic object. More recently,
it has been demonstrated that repetitive nanosecond pulses can replace the usual ac waveform
high-voltage (HV) usually applied to ionize the gas. The use of fast-rising HV pulse is clearly
effective for flow separation control over a wide range of Reynolds number as it is shown in
[7, 8, 9, 10] but the flow control mechanism is no more based on the momentum addition as
for ac DBD. For such discharge the flow control mechanism has still to be fully elucidated but
some scenarios have emerged, all of them being related to the fast and localized deposition of
heat at the dielectric surface, this heat release resulting in a pressure gradient (pressure wave)
propagating above the dielectric wall [11, 12]. Good effectiveness has been demonstrated
more specifically when the outer flow velocity is high [7, 13]. As for DBD supplied by ac
voltage, optimization of the electrode geometry or of the applied signal is expected to be a
way to improve the performance of the nanosecond pulsed discharge [14, 15]. Among these
optimizations, the need for a large surface of plasma/fluid interaction is even more essential
for plasma-assisted flow control implemented on aerodynamic model having realistic scale
factor.

The present experimental investigation aims at demonstrating that the surface
discharge produced at the edge of the high voltage electrode supplied by nanosecond pulses
can be extended over a longer distance using a third counter-electrode. This configuration is
similar to the three-electrode configuration known as *sliding discharge* for ac voltage source
where a third electrode with a negative DC component can force the drift of ionized species in
the inter-electrode region leading to the formation of a large scale plasma layer [16, 17, 18].
Similar configuration is used in [19], but using microsecond pulses as voltage source in place
of an ac one. Again, the longer plasma extension caused by the sliding effect is observed. In
2012, Song *et al.* [20] changed the microsecond pulses source for series of nanosecond pulses
as it is conducted in the present investigation. They confirm the capability of three-electrode
configuration for promoting longer plasma extension but several essential information, such
as the inter-electrode distance, the deposited energy or conditions to ignite a sliding regime,
are not documented in [20].

Here, the primary objective is the definition of the electrical conditions required to
transform a usual nanosecond pulsed discharge to a sliding one. A particular attention is paid
to the measurement of the electrical consumption of the actuator because this consumption is
partially related to the energy deposited on the dielectric surface and surrounding gas. It was
already demonstrated that the local heat release is fully corroborated with the electrical
deposited energy, a heat production mainly caused by the vibrational excitation [21]. This
heat release is responsible for a sudden pressure gradient that causes a pressure wave
propagating normally to the dielectric wall surface, the strength of this pressure wave linearly
increasing with the consumed energy as it was numerically and experimentally shown in [21]
and [11, 12, 22], respectively. In a second part of the paper, qualitative optical visualizations
of the induced pressure wave and heat release signature are proposed by using a Schlieren test
bench. These experiments are designed to reveal the modifications on the induced pressure
wave when a sliding discharge forms.

Experimental setup

In all tested configurations, the dielectric is made of a 2-mm thick flat plate
(Polymethyl methacrylate, εr=3.3). The electrodes are made of aluminum foil with thickness
of 75 µm. The reference single DBD (S-DBD) consists of two electrodes placed in regard and
separated by the dielectric barrier. In this case, as in all following designs, the active electrode
(electrode 1 in Figure 1) has a width of 10 mm. The grounded electrode (electrode 2 in Figure
1a) is 40 mm wide as in [17]. The third electrode (electrode 3 in Figure 1b) can be connected
to the ground (configuration called G-DBD later in the paper), let floating (F-DBD) or can be
supplied by a negative DC component to establish a so-called sliding discharge as it will be
shown later in this letter (SL-DBD). For all the actuators, the spanwise length is maintained at
120 mm (i.e., maximal plasma covered surface of 4800 mm²).
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>Figure 1: (Color online) Sketches of the electrode arrangement for the reference S-DBD (a) and the configuration used for a floating, grounded or negatively biased third electrode (b).</figcaption></figure>

The voltage on the electrode (3) is provided by a negative dc power supply (SPELLMAN, -40 kVmax, 150 W). The choice of a negatively biased voltage on electrode (3) refers to the literature data where sliding regime can be produced only for negative dc component on electrode (3) [17]. In all the tests, the electrode (1) is connected to a fast-rising pulse generator (FID FPG 40-30NK, 30 kVmax, 35 mJ), producing HV pulses at a repetition rate of 1 kHz. The total currents flowing through electrodes (1) and (3) are measured using current transformers (Bergoz CT-D5.0 and CT-D1.0) connected to a WaveRuner oscilloscope (Lecroy, 204 mxi, 2 GHz bandwidth), these two currents being considered in the computation of the electrical energy consumption.

In complement to the electrical measurements, an optical characterization of the discharge is performed by using an intensified CCD camera (Princeton, PI-MAX4 1024EM)
coupled with an UV lens (100F/2.8). The camera opening gate width is synchronized with the
electrical system. The iCCD camera is placed above the plasma sheet and directed toward the
dielectric (top-view with field of view of 36x40 mm²). The exposure time is fixed at 60 ns in
order to observe the full extension of the plasma layer over the dielectric surface. In a final
experiment, the pressure wave caused by the surface heat deposition is characterized by using
a Schlieren optical bench. The light source (nanolite twin flash) is focused on a 1 mm pinhole
by a condenser lens (see Figure 2). The pinhole is positioned at the focal distance of the
concave mirror 1 (a cylindrical flat mirror is used to compact the optical bench). Parallel light
beams are produced between mirrors 1 and 2 while the actuator is located at the center of
these two concave mirrors. The light from the source point is then focused on an horizontal
knife edge in order to visualize vertical pressure gradients. The images are collected by an
ICCD camera (PIMAX4) equipped with a 180 mm objective (Nikkor), this equipment leading
to a spatial resolution of 5.4 pixels per mm. A delay generator (SRS DG 645) is used to
trigger the light source, the applied voltage and the ICCD camera. The light source produces a
20 ns flash at a repetition rate of 5 Hz. The applied voltage is at 1000 Hz and measurements
concern the 100th HV pulse. Images are recorded 60 µs after the voltage pulse applied to
electrode (1). Only side views have been performed in this study. The camera operates in
accumulation mode in order to average the produced pressure wave over 100 images and then
reinforce the visual trace of the pressure wave. Background subtraction (based on a 100
images average) is also used to reduce the image noise and to emphasize the changes in gas
density due to the discharge. In the present investigation, the light source is unfortunately not
regular in intensity due to small displacements of the arc location in the flash-lamp. Then, no
indirect quantitative comparison between the configurations (as done in [22] for instance) can
be provided with this Schlieren setup.
<figure><img src="image_4.png" /><figcaption>Figure 2: (Color online) Sketch of the Schlieren setup for the produced pressure wave characterization.</figcaption></figure>

## Results

### a) Time evolution of voltage and discharge current

Illustrations of the voltage for nanosecond pulses with amplitude of 16 kV applied to electrode 1 are shown in Figure 3. In all of the cases, the rising and falling times of the voltage signal are about 15 ns, without any noticeable voltage plateau between the rising and falling periods. The total current evolution (composed of a capacitive component in addition to the discharge current) presents two main peaks. The first one (at t=13 ns) is positive and it is caused by the discharge propagating on the dielectric surface. For the reference case, the maximal positive current peak reaches amplitude of about 1.7 A/cm (per cm of electrode spanwise), this peak occurring when the applied voltage attains its peak value. The addition of a floating or grounded electrode does not modify the amplitude of this current peak. Figure 3d showing the current evolution for the SL-DBD configuration with electrode 3 connected to - 16 kV clearly exhibits a higher positive current peak amplitude, reaching about 2.4 A/cm (increase of 41% by comparison with the reference configuration).
For the negative part of the current (from time t=18 ns to t=40 ns), no major change can be observed for the configurations where no negative dc component is applied to electrode (3). In all of these configurations, the maximal negative current peak has similar time evolution and peak amplitude (of about -1.4 A/cm). However with the SL-DBD configuration, the amplitude of this negative current peak is slightly reduced in amplitude by comparison with the three other configurations (maximal negative current amplitude of -1.3 A/cm).

The time evolution of the total current $i_3$ is measured simultaneously to $i_1$, the objective being to characterize a possible collection by electrode (3) of the charges deposited on the dielectric barrier during the HV pulse (Figure 4). As it is shown in this figure, positive current peaks are observed at time t=55 and t=100 ns for negative dc component ($V_{DC}$, with $V_{DC}<0$) of -16 kV and -12 kV, respectively. These collected currents present peak values of 0.55 and 0.13 A/cm for $V_{DC}=-16$ kV and $V_{DC}=-12$ kV, respectively. The presence of these currents confirms that some positive charges produced at electrode (1) are collected due to their drift under the influence of the electric field between electrodes (1) and (3). With this three-electrode arrangement, the nanosecond pulse discharge serves as an ionizer while the third electrode attracts a part of the charged species, as it was observed with an ac voltage source connected to electrode (1) [17, 18, 23]. Another interesting point deduced from Figure 4 is that the sliding regime occurs earlier for high $|V_{DC}|$. Indeed, the current $i_3$ increases at t= 55 ns in Figure 4 when -16 kV is applied to electrode (3) whereas it needs 100 ns to ignite the collection of charges for $V_{DC}=-12$ kV. This suggests a faster propagation of the ionized front when the electric field between electrodes (1) and (3) is increased. For $V_{DC}=-16$ kV, the delay of 55 ns is in agreement with the results shown in Figure 3. After 55 ns, a part of the charges are collected, this justifying the reduced amplitude of the negative current at this time for the SL-DBD configuration.
<figure><img src="image_5.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(c)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(d)</figcaption></figure>

Figure 3: Voltage and total current i₁ measurements on electrode 1 for the reference single DBD (a), and DBD with a floating electrode 3 (b), a grounded electrode 3 (c) and electrode 3 supplied by -16 kV dc component (d).
<figure><img src="image_9.png" /><figcaption>Figure 4: Total electrical current $i_3$ collected at electrode (3) when negative dc component is applied.</figcaption></figure>

b) Optical characterization of the plasma morphology

Top-views of the plasma discharge propagating along the dielectric surface are proposed in Figure 5. These images are integrated over a pulse period (from t=0 to 60 ns), and then the plasma formed during the rising and falling parts of the pulse are superimposed. The discharge is mainly composed of many streamers distributed along the exposed electrode. Each of these filaments presents several branching during their propagation. These long filaments extend up to 10 mm for the S-DBD, the F-DBD and the G-DBD configurations. The similar plasma extension in these three cases demonstrates that the addition of a third electrode without a bias voltage has almost no interest regarding the propagation of the streamer channels. However, when $V_{DC}$=-16 kV is applied to electrode (3) (Figure 5d), the ionized channels cross over the inter-electrode distance. The connection with the electrode (3) occurs by bright spots, and one streamer formed at electrode (1) can connect to electrode (3) by several spots. In this configuration, $|V_{DC}|$ is high enough to ignite the drift of the positive
ions formed at electrode (1) and to reduce the screening effect of the charges deposited on the dielectric surface that are partially collected by electrode (3).

These images by fast opening gate show how a sliding discharge can form with a nanosecond pulsed DBD source. It confirms that the discharge can be largely extended, from a propagation length of 10 mm, the sliding discharge mode produces an extension up to 40 mm (extension increase of about 300%). The present paper is limited to the case of an inter-electrode distance of 40 mm, but there is no doubt that longer extension can be obtained by using appropriated voltage source.

<figure><img src="image_10.png" /><figcaption>Figure 5: Top-views of the plasma sheet propagating in the inter-electrode gap for S-DBD, F-DBD, G-DBD and SL-DBD ($V_p=16$ kV and $V_{DC}=-16$ kV for SL-DBD configuration).</figcaption></figure>

### c) Electrical energy consumption of the actuator

In this section, the electrical energy consumption of the actuator is computed and compiled in Figure 6, this for nanosecond pulse voltage amplitude ranging from 2 up to 22 kV. This energy includes the contribution of the discharge formed at electrode (1) as well as the electrical consumption caused by the electric potential applied to electrode (3). The energy consumption evolves in a similar manner for S-DBD, F-DBD, and G-DBD. The increase in the applied voltage amplitude $V_p$ promotes higher consumed energy reaching a maximal value of 0.5 mJ/cm, a value in agreement with the one reported in [7, 10, 11, 21, 22, 24, 25].
for the three V<sub>DC</sub> applied to electrode (3) are also proposed in Figure 6. In all of the investigated cases, the energy consumption is not modified by comparison with the S-DBD configuration, this up to a threshold V<sub>DC</sub> value. A sudden increase in the energy consumption is observed when the potential difference between electrodes (1) and (3) is larger than 26 kV corresponding to a reduced electric field of 26 kV divided by 4 cm, i.e. 6.5 kV/cm. In the case of ac source voltage, the same threshold value of reduced electric field has been found [18]. This increase in energy consumption corresponds to the formation of a sliding discharge regime. In Figure 6 it is shown that this discharge regime can increase the consumed energy up to 1.1 mJ/cm (with V<sub>p</sub>= 20 kV and V<sub>DC</sub>= -16 kV). The sliding regime increases the consumed energy by about 120% by comparison with a S-DBD. The figure also demonstrates that the sliding discharge can form at lower V<sub>p</sub> by increasing |V<sub>DC</sub>| (sliding regime ignited for V<sub>p</sub>=20 kV and V<sub>DC</sub>=-8 kV or for V<sub>p</sub>=12 kV and V<sub>DC</sub>=-16 kV). This reduction in the V<sub>p</sub> potential applied to electrode (1) is caused by a modified charge distribution over the inter-electrode space (negative charges are produced in the electrode (3) region). On one hand, the present results indicate that the consumed energy is increased by 120% with the sliding regime.

The consumed energy is often used in literature as an approximation of the deposited energy, the deposited energy being mostly converted into gas heating [11, 14, 15, 22]. In the previous paragraph, it was considered that the current collected on electrode (3) corresponds to a part of the energy consumed by the actuator. This is correct from an electrical point of view, but in sliding discharge the non-stationary high-voltage V<sub>p</sub> is the source for gas ionization. Then, one can think that a good approximation of the deposited energy in nanosecond sliding discharge consists of considering the energy consumed from the voltage source (i.e., by integration of the absolute value of the product of current i<sub>1</sub> and voltage V<sub>p</sub> over the pulse) minored by the energy consumed at electrode (3). By this approach, the
current (and the corresponding energy) collected at electrode (3) is not integrated in the energy deposited on the dielectric wall.

If we consider the deposited energy as the difference between the energy consumed at electrode (1) minus the energy consumed at electrode (3), the amount of energy deposited on the wall in case of SL-DBD is reduced by 25% on average (Figure 7). However, the total energy consumed at electrode (1) corresponds to an energy flowing through the entire inter-electrode distance. This energy is not fully deposited on the dielectric barrier, but could contribute to a reinforcement of the actuator effects on the gas when its main part travels between the two air-exposed electrodes. It is clear from this figure that the consumed energy caused by $i_1$ is increased for a SL-DBD by comparison with S-DBD (0.5 and 0.7 mJ/cm at $V_p=20$ kV for S-DBD and SL-DBD, respectively). This figure also demonstrates that a significant part of the total energy consumed by the actuator is due to the collected current $i_3$.

<figure><img src="image_11.png" /><figcaption>Figure 6: Electrical energy consumption at different nanosecond pulsed voltages for the electrode arrangements of Figure 1.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 7: Electrical energy consumption for SL-DBD by considering $(i_1+i_3)$, $i_1$ or $(i_1-i_3)$ currents and energy consumption for S-DBD. Here $V_{DC}$=-16 kV</figcaption></figure>

### d) Optical characterization of the produced pressure wave and near-wall region

Side views of the pressure wave signature caused by the heat release at the dielectric surface are plotted in Figure 8. In absence of a $V_{DC}$ component (i.e., for S-DBD, F-DBD and G-DBD), all measurements indicate a similar pressure gradient topology. This topology is composed of a straight region at the top of an hemispheric region, this latter region being centered at the edge of the active electrode. This is typical of the pressure wave produced by a nanosecond DBD as already described in literature [7, 11, 15, 22, 24]. All of these publications suggest that the semi-spherical part of the wave is caused by the contribution of the fast energy released at the tip of the active electrode whereas the linear signature is directly correlated with the plasma propagation along the dielectric surface. The addition of a third electrode supplied by a negative dc component clearly modifies the gas region above the discharge. As it is shown in Figure 8d, the linear region of the compression wave is significantly extended, it finally covers all the inter-electrode distance (i.e. 40 mm). Another clear modification is the addition of a second semi-spherical signature originating from the edge of electrode (3). This second hemispheric region is at a same vertical position than the
semi-spherical region initiated at electrode (1). Thus, both hemispherical regions propagate at
a same speed estimated here about 360 m/s. It is also clear from Figure 8d that the second
semi-spherical region presents a weaker pressure gradient. The reduced pressure gradient
formed at electrode (3) is certainly due to a smaller change in local temperature at this
position. Indeed, it can be considered that the plasma at electrode (1) is the only source for a
rapid gas heating process. Energy dissipation should occur during the drift of ionized species
across the inter-electrode gap. The heat released at electrode (3) is then subsequently reduced
by comparison with the region at the edge of electrode (1). A similar topology has been
previously reported in Roupassov et al. [7] using a symmetrical electrode arrangement where
positive and negative pulses are applied to electrode (1) and (3). The authors concluded that
this special electrode arrangement provides a more homogeneous energy distribution in the
inter-electrode gap, but they also reported a decrease of the energy released densities with this
configuration. A last observation concerns the density variations above the dielectric layer. In
the present measurements, large changes in the gas density are caused by the high repetition
rate (1000 Hz) by comparison with other studies where the pulse frequency is lowered by
several orders of magnitude (in [22] for instance). However, the addition of the negative VDC
component on electrode (3) clearly extends the region of heat deposition. As it is shown in
Correale *et al.* [12], one possible flow control mechanism relates to the amplification of the
natural instabilities of the boundary layer due to the local heat released at the tip of the air-
exposed electrode. An extended heat deposition as the one illustrated in Figure 8d should have
a strong influence on the actuator effectiveness on bounded flows.
<figure><img src="image_13.png" /><figcaption>Figure 8: Side views of the pressure wave produced by a S-DBD (a), a F-DBD (b), a G-DBD (c) and the SL-DBD configuration (d). The applied $V_p$ is 16 kV and $V_{DC}$=-16 kV for (d).</figcaption></figure>

Some additional measurements have been conducted to illustrate the effects of an increase in the consumed electrical energy on the electro-mechanical conversion. For that purpose, Schlieren measurements have been performed for increasing values of the applied pulse voltage amplitude $V_p$ applied on the S-DBD configuration (Figure 9). The results indicate that the position of the hemispheric pressure wave contribution is not affected by the applied voltage, but three major changes can be observed. Firstly, the linear part increases in length when the applied voltage $V_p$ is increased (10, 13 and 16 mm for $V_p$=10, 14 and 18 kV, respectively). Secondly, the pressure gradient is reinforced for increasing voltage amplitude $V_p$. Thirdly, the light diffraction is higher close to electrode (1) and along the discharge propagation line due to higher local temperature. Because of the heat dissipation of the previous pulses, the light diffraction is also visible upstream and downstream of electrode (1). As it was already demonstrated in [11, 12] or [22, 24, 25], in the present study the mechanical and thermal effects are intimately linked to the consumed energy (that can be considered as deposited energy for the S-DBD case) with a noticeable reinforcement of the pressure wave and thermal signature with the consumed energy increases.
<figure><img src="image_14.png" /><figcaption>Figure 9: Side views of the pressure wave produced by a S-DBD for different $V_p$ values.</figcaption></figure>

It was shown in Figure 8 that the SL-DBD can produce two intersecting pressure waves connected by a linear top. Here, Schlieren images for $|V_{DC}|$ from 12 to 16 kV are shown in Figure 10. Despite the increase in consumed energy at higher $|V_{DC}|$ (see Figure 6 or Figure 11), the strength of the induced pressure waves propagating in the surrounding air is not modified when the dc component is increased. By increasing $|V_{DC}|$, only the gas density above the dielectric barrier is altered with a thickening of the region of high temperature. The limited influence of $|V_{DC}|$ suggests that the total consumed energy is not completely converted into thermal energy. Figure 11 summarizes the energy consumption by considering the different currents measured for a SL-DBD with $V_p=16$ kV while $|V_{DC}|$ is varied. This figure demonstrates that the energy consumption due to the HV signal at electrode (1) increases with $|V_{DC}|$, while the deposited energy (as it has been defined earlier in this paper) reduces with increasing $|V_{DC}|$. The reduction in the deposited energy between $V_{DC}=-10$ kV and $V_{DC}=-16$ kV is about -0.04 mJ/cm$^2$. This reduction is small and it could explain why the pressure wave
signature is nearly not sensitive to the $|V_{DC}|$ value. However, the energy consumption due to electrode (1) is increased by +0.08 mJ/cm between $V_{DC}=-10$ kV and $V_{DC}=-16$ kV. This small increase could be responsible for the increase in temperature observed all along the propagation path of the discharge. Figure 11 also indicates that a significant part of the increasing total consumed energy is caused by $i_3$, but the present investigation suggests that this ‘additional’ energy consumption has only a minor influence on the heat transfer and pressure wave formation. However, the increase in the current collected at electrode (3) is related to a rise in the density of the drifting species. The authors suspect that a significant part of the energy consumed at electrode (3) could be transformed into an EHD body force due to the ions drifting under the influence of the electrical potential at electrode (3). This will be elucidated by a coming experimental campaign.

In the context of flow control, the sliding regime is certainly of interest as the interacting plasma/fluid surface is largely increased. However, the present Schlieren images suggest that there is no need for using a high $|V_{DC}|$ value if the control mechanism is based on thermal deposition, a potential difference larger than 26 kV is sufficient.
<figure><img src="image_15.png" /><figcaption>Figure 10: Side views of the pressure wave produced by a SL-DBD for $V_p=16$ kV and different $V_{DC}$ values.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 11: Electrical energy consumption for SL-DBD with $V_p=16$ kV by considering ($i_1+i_3$), 'i₁', i₃, or ($i_1-i_3$) currents.</figcaption></figure>
Conclusions

The present paper proposes an overview of the conditions necessary to reach a sliding
regime over an inter-electrode distance of 40 mm while the main electrode is excited by
pulses with nanosecond rise time at constant Vp. It is demonstrated that the addition of a third
electrode let as a floating electrode or connected to the ground has only few effect on the
discharge regime and in no way it can promotes a sliding discharge. A sliding discharge forms
only when the electrode is supplied by a high enough |VDC| (with VDC<0). In the present
configuration, it is shown that a potential difference (also referred as onset voltage in [18])
higher than 26 kV (6.5 kV/cm of gap distance) between electrode (1) and (3) is necessary to
extend the discharge and to fill all the inter-electrode distance. The sliding regime increase the
peak current value (as it was observed in [18] with an ac HV on electrode (1)) and it affects
the consumed energy (value up to 1.1 mJ/cm has been observed). It is demonstrated that the
longer plasma extension caused by the sliding regime extends the linear part of the pressure
wave produced by nanosecond pulsed DBD. Furthermore, two hemispheric pressure waves
are observed with a SL-DBD configuration. However, the Schlieren images suggest that a rise
in |VDC| does not improve the performance of the actuator in terms of heat release or pressure
wave production. When the sliding regime is initiated, no additional changes in gas density
has been observed can be expected by increasing the dc component |VDC|. However, the larger
region of interaction between an external flow and the discharge region should improve the
capability of nanosecond DBD for plasma-assisted flow control. These mechanical
considerations are currently under investigations as well as the characterization of the
discharge by optical emission spectroscopy.

Acknowledgment
The equipment used in this work was funded by the French Government program "Investissements d'Avenir" (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01) and Région Poitou-Charentes. This work is conducted under DGA supervision and partially funded by ANR (INOPLAS, ANR-13-ASTR-0015-01).

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