Study of an atmospheric surface barrier discharge actuator using a
nanosecond rising high-voltage power supply
Rabat H.1, Pons J.2, Hong D.1, Weber R.3, Leroy A.3
1
GREMI, UMR6606, CNRS/Université d’Orléans, 14 rue d’Issoudun, BP 6744, 45067 Orléans cedex 2, France
2
3
EPEE FR776 CNRS, c/o GREMI, 14 rue d’Issoudun, BP 6744, 45067 Orléans cedex 2, France
PRISME, UPRES 4229, Université d’Orléans, 8 rue Léonard de Vinci, 45072 Orléans cedex 2, France
Abstract: In the field of flow control by plasma actuator, an original high-voltage
power supply has been developed to provide a nanosecond rising followed by
millisecond decay. With this device, a 15 kV discharge on a polymer dielectric
barrier can be obtained with a rise time of about 30 nanoseconds. A slow decay
in the millisecond range is controlled by resistor/capacitor loads connected to the
actuator. This particular discharge was characterized by the electrical
measurements (current and voltage) as well as by fast imaging using an
intensified camera. Studies on the action of such discharge in ambient air have
also been carried out by Laser Doppler Velocimetry, by differential pressure
measurement (Pitot tube) and by Mach-Zehnder interferometry. In particular,
velocity measurements confirmed a higher production of ionic wind in the first
half part of negative phase compared to the positive one of a “sinusoidal” signal.
In the same way, the study of the nanosecond part has revealed differences
between negative and positive pulses. Moreover, the interferometric diagnostic
shows a supersonic propagation of shock wave and allows estimation of pressure
variations induced by this one.
Keywords: plasma
interferometry
actuator,
nanosecond
1. Introduction
A plasma actuator consists in using a discharge on a
profile to interact with the boundary layer of an
airflow to modify its properties. Since the early
works of Roth’s group [1], many researches have
been made to optimize the process from its design to
its power supply. Most studies have concerned
sinus-driven dielectric barrier discharges with
voltage rise times in the millisecond (ms) range, for
which the generation of ionic wind is believed to be
the main process in plasma/flow interaction. In
recent years a broadening interest has aroused for
fast rise pulses in the nanosecond (ns) range,
following the publication of Starikovskii et al. [2]
who demonstrated that plasma interacts with the
ambient medium by the generation of a shock wave.
The present paper focuses on a DBD actuator where
the effects of ns and ms ramps are combined in a
pulse,
imaging,
velocimetry,
single pulse allowing for the generation of both a
shock wave and ionic wind. For this, an original
power supply has been built and different
diagnostics have been used to both characterize the
shock wave pressure front and the ionic wind
velocity field. A specific interest has been carried on
the influence of the voltage pulse polarity.
2. Experimental set-up
2.1. The actuator and its power supply
Our plasma actuator is a multilayer of
polyester/polyimide strips and copper tape. A side
view of the actuator can be seen on Figure 1 (see [3]
for more information). The configuration used has 3
mm gap between the electrodes and a useful length
of L=70 mm. Plasma formation on one side is
prevented with a dielectric strip stuck onto the
surface facing the edge of the corresponding
electrode.
0.5 mm
U1
R2
6 mm
3 mm
6 mm
actuator
R1
U2
I1
C1
power
supply
2.2. The interferometric method
To determine the shock wave velocity and to
estimate the pressure disturbance from this one, a
Mach-Zehnder interferometer was built and is
presented in Figure 3.
laser He Ne
632.8 nm
thyratron
beam
expander
Figure 1. Schematic of power supply and actuator
configuration.
actuator
To run the discharge, an original power supply was
built (see Figure 1). A typical voltage pulse applied
between the electrodes is presented in Figure 2, with
a zoom on the ns part. It consists of a 30-ns rise
ramp, followed by a plateau of approximately 1 µ s
(not visible on the graphs due to the chosen scales)
and finally an exponential decay with a
characteristic time around 0.5 ms. According to the
plugging a positive or negative pulse is applied to
the actuator, and the ns (resp. ms) ramp becomes
positive (resp. negative) or negative (resp. positive).
Voltage (kV)
16
Voltage (kV)
15
14
10
12
5
0
-10 0
10
Time (ns)
10 20 30 40 50
8
6
4
30 Current (A)
- positive
25
20
15
10
5
0
-5
-10
-15
- negative
-20
-25
Time (ns)
-30
0
100
200
mirror
beam
splitter
mirror
beam
splitter
screen
i CCD
camera
Figure 3. Schematic of the Mach-Zehnder interferometer.
A HeNe laser beam (632.8 nm) was expanded with
two lenses to obtain a beam two times larger than the
plasma width. The expanded beam was divided into
a probe beam passing through the studied medium
and a reference beam. When these two beams are
combined on a frosted screen, an interferogram (see
Figure 4) with parallel fringes appears due to the two
optical path differences. The image on the screen is
collected using an iCCD camera (Andor iStar 734).
Interferogram
FFT
Inverse FFT
Phase
2
0
-2
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time (ms)
Figure 2. Voltage and current pulses versus time.
The obtained current for each polarity is shown in
the upper frame in Figure 2. A single strong pulse is
generated during the ns part, with a magnitude in the
range of 15-30 A. Under the observed conditions,
the absolute value of the current has been found
lower in negative polarity than in positive polarity.
Figure 4. The four steps in the digital processing of
interferograms.
Knowing the scale, interferograms acquired at
different times allow to determine the propagation
velocity value of the shock wave. Moreover, the
digital processing of the interferogram presented in
Figure 4 allows to calculate the phase shift variation
(method describe in [4]) above the actuator.
From the phase angle , the refractive index can
be deduced by the equation (1):
n − n = φ × , (1)
where n is the refractive index of the ambient air at
room temperature, λ the laser wavelength, and L the
actuator length (L = 70 mm). The refractive index
can also be determined from equation (2), which
derives from the Gladstone-Dale law:
∆P = "
)
#$%
'( )*
b)
, (2)
where P is the pressure, T the temperature, R the gas
constant, and < > the Gladstone-Dale constant
function of the laser wavelength and of the gas
composition [5]. Then, from (1) and (2), a relation
between the phase and the pressure variation shift
can be found, as:
×(
a)
× P . (3)
Equation (3) allows estimating the pressure shift
map around the shock wave from the interferogram,
assuming that temperature is uniform and that the
perturbation is homogeneous over the total electrode
length.
3. Results
Figure 5 presents iCCD images of a 15kV-1kHz
discharge for both polarities. Streamers can be seen
during the positive ramp and a more diffuse shape
during the negative ramp, both in nanosecond or in
millisecond part. The difference is about the length
of the discharge between the two polarities: 9 mm
for positive pulse versus 6 mm for the negative
pulse.
The ionic wind velocity has been measured, using a
2-component Laser Doppler Velocimetry system
(Dantec Dynamics BSA 51N) using the 488 and
514.5 nm beams of an Ar-Kr laser. The velocity
components have been deduced from phase
averaging operation over a 120 s acquisition with a
0.5 to 1 kHz acquisition rate. Figure 6 shows the
c)
d)
10mm
Figure 5. iCCD images of the discharge: (a) ns part of positive
pulse, (b) ms part of positive pulse, (c) ns part of negative
pulse, (d) ms part of negative pulse.
3.2
2.8
2.4
Velocity modulus (m/s)
n=1+
time evolution of the velocity at the place where the
average velocity has been found to be maximal: in
this case, we found about 1.5 m/s at x = 5 mm and y
= 0.7 mm with a positive pulse and about 3 m/s at x
= 9 mm and y = 0.5 mm with a negative pulse. The
values of x correspond very well with the plasma
extension length of the ms discharge deduced from
the images shown above.
2.0
1.6
1.2
0.8
Negative-going
Positive-going
0.4
0.0
-0.4
-0.2
0.0
Time (ms)
0.2
0.4
Figure 6. Velocity modulus versus time for the two polarities at
the maximal average velocity place.
These curves show that ns discharge does not
contribute to velocity generation. It tends to brutally
slow down and divert the previously generated flow.
Only both positive and negative going ms discharges
are able to generate ionic wind with the best
production in negative ramp. The new fact here is
the confirmation that positive streamers indeed
contribute to ionic wind creation. In general, the fact
that the acceleration zone length agrees well with the
plasma extension length confirms the non-negligible
role of streamers in flow acceleration.
a)
Pa
4. Conclusion
It is the first separate observation of the effects of
positive and negative ns and ms fronts on DBD
actuator interaction with the ambient air, and the
first experimental estimation of overpressure
associated with shock waves generated by ns fronts.
References
[1] D. M. Sherman, J. R. Roth, and S. P. Wilkinson,
Influencing an Aerodynamic Boundary Layer using
a Surface Layer of One Atmosphere Uniform Glow
Discharge (Plasma American Physical Society,
Division of Plasma Physics Meeting, 1996)
b)
Pa
[2] A. Y. Starikovskii, A. A. Nikipelov, M. M.
Nudnova, and D. V. Roupassov, SDBD plasma
actuator with nanosecond pulse-periodic discharge
(Plasma Sources Sci. Technol. 18 034015, 2009)
[3] Joussot R., V. Boucinha, R. Weber, H. Rabat, A.
Leroy-Chesneau, and D. Hong
(Thermal
Characterization of a DBD Plasma Actuator:
Dielectric Temperature Measurements Using
Infrared Thermography, AIAA-102, 2010)
Figure 7. Pressure map deduced from interferogram at 20 µs for
(a) positive pulse and (b) negative pulse.
From interferometer measurements, propagation
velocities have been found in the range 400-500 m/s
confirming the supersonic nature of the wave [2].
Figure 7 shows pressure map variation at 20 µs after
the ns discharge. According to Starikovskii et al. [2],
the cylindrical part of the observed perturbation is
assumed to be emitted by corona discharges at the
tip of the electrode, whereas the plane part would
correspond to the streamers extending at the surface.
Moreover, we found that the shock wave is more
intense in positive polarity with a maximum
overpressure value around 1200 Pa, against 1000 Pa,
in negative polarity. It is consistent with the fact that
a stronger current pulse is achieved. Heating may
therefore be more intense and the process is more
efficient for energy transfer to the shock wave.
These results confirm the calculations already
performed in similar conditions from simulations [2,
6].
[4] H. Rabat, and C. de Izarra (Check of OH
rotational temperature using an interferometric
method, J. Phys. D: Appl. Phys. 37 2371, 2004)
[5] W. C. Gardiner, Y. Hidaka, and T. Tanaka
(Refractivity of combustion gases, Combustion and
Flame 40 213-219, 1981)
[6] T. Unfer and J. P. Bœuf (Modelling of a
nanosecond surface discharge actuator J. Phys. D:
Appl. Phys. 42 194017, 2009)