IOP PUBLISHING PLASMA SOURCES SCIENCE AND TECHNOLOGY

Plasma Sources Sci. Technol. 20 (2011) 055009 (10pp) doi:10.1088/0963-0252/20/5/055009

Characterization of a surface dielectricbarrier discharge plasma sustained byrepetitive nanosecond pulsesKeisuke Takashima (Udagawa), Yvette Zuzeek, Walter R Lempert andIgor V Adamovich

Nonequilibrium Thermodynamics Laboratories, Department of Mechanical and Aerospace Engineering,The Ohio State University, Columbus, OH 43210, USA

E-mail: adamovich.1@osu.edu

Received 6 April 2011, in final form 2 August 2011Published 6 September 2011Online at stacks.iop.org/PSST/20/055009

AbstractThe paper discusses experimental characterization of a surface dielectric barrier dischargeplasma sustained by repetitive, high-voltage, nanosecond duration pulses. The discharge pulseenergy is controlled primarily by the pulse peak voltage and scales approximately linearly withthe length of the electrodes. Images of the plasma generated during the discharge pulse, takenby a nanosecond gate ICCD camera, show that the plasma remains fairly uniform in the initialphase of the discharge and becomes filamentary at a later stage. The temperature rise in thedischarge, operated in both continuous mode and in burst mode, is inferred from UV/visibleemission spectra. Phase-locked schlieren images are used to measure the speed of thecompression waves generated by the nanosecond pulse discharge and the density gradient inthe wave. The density gradient is inferred from the schlieren images using absolute calibrationby a pair of wedged windows. The results demonstrate that discharge filaments generatecompression waves with higher amplitude and higher speed compared with waves produced ina diffuse discharge. The density gradient in the compression waves is compared withnumerical modeling of propagating compression waves produced by short-pulse localizedheating, and shows satisfactory agreement between the model and the experimental results.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Plasmas generated in surface dielectric barrier discharge(DBD) flow actuators have been extensively studied over thelast decade (see [1, 2] and references therein). Typically, DBDplasma actuators are driven by high-voltage, sine wave acwaveforms, with frequencies ranging from a few kHz to a fewtens of kHz. In some cases, a dc bias or a series of short(nanosecond duration) pulses are added to the ac waveformto improve the actuator performance [3]. The dominantmechanism of neutral species flow acceleration by a surfaceDBD plasma, i.e. flow entrainment by ions accelerated in aspace charge region of the plasma (electrohydrodynamic, orEHD flow acceleration), appears to be well understood [1, 2].Compared with the Coulomb force interaction, the effect ofJoule heating in surface DBD actuators driven by ac voltagewaveforms appears insignificant.

One of the most critical issues for surface DBDplasma flow control technology is maintaining the actuatorperformance and achieving flow control authority at high flowvelocities. The main limitation on the use of EHD accelerationfor high-speed flow control is sustaining a high ion density,ni, in the space charge region of the electric discharge. Forthe EHD effect to be significant, the ratio of the Coulombforce work to the flow kinetic energy (the EHD interactionparameter) should be of the order of unity [4]. For electron/ionnumber densities achieved in atmospheric pressure surfacedischarges, ni ∼ 1010–1012 cm−3, significant EHD effect onthe flow can be achieved at free stream flow velocities ofu∞ ∼ 1–10 m s−1. Further ion density increase in the glowdischarge plasma is severely limited by ionization instabilitydevelopment. As a result, the use of EHD acceleration for high-speed flow control, at flow velocities of a few hundred m s−1,is problematic. However, recent experiments on high-speed

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 1. Schematic of a nanosecond pulse DBD plasma actuator, with a photograph showing a floating tip electrode.

airfoil flow control using DBD plasma actuators poweredby a series of high-voltage, nanosecond duration pulsesdemonstrate flow reattachment at much higher velocities, upto M = 0.85 [5]. In [5], it was suggested that in this case thedominant effect of the plasma on the flow is caused by rapidlocalized heat generation in the actuator. Indeed, shock wavesgenerated in quiescent air by localized heating in the dischargewere detected in [5].

If confirmed, this mechanism would be consistent with thehigh-speed flow control mechanism used in repetitively pulsedlocalized arc filament plasma actuators (LAFPAs) [6–11].The main idea of this approach is to force the flow with ahigh-amplitude, high-bandwidth perturbation, at a frequencyapproaching one of the flow instability frequencies, therebytriggering their subsequent growth in the flow. Previousstudies of flow control using LAFPAs in atmospheric pressurejet flows (M = 0.9–2.0) [6–11] demonstrated significantlocalized heating and repetitive shock wave formation bythe plasma, large-scale coherent structure generation, andmixing enhancement. This effect was achieved at a lowactuator power, of the order of ∼10 W per actuator, at forcingfrequencies near the jet column (preferred mode) instabilityfrequency. Also, our recent studies of high-speed flow controlover an airfoil, using DBD plasma actuators powered bynanosecond duration pulses [12], demonstrated generationof large-scale structures (spanwise vortices) similar to thosedetected in experiments using LAFPAs [11]. Finally, shockwaves generated by nanosecond pulse DBD plasma actuatorshave been detected in our recent experiments in a Mach 5flow [13]. This suggests that the mechanisms of flow controlfor both types of actuators may be fairly similar.

The objective of this work is to characterize the plasmaof a surface DBD plasma actuator driven by repetitive, high-voltage, nanosecond duration pulses and operating in quiescentair. In particular, measurements of temperature rise in theplasma, detecting compression waves generated in ambientair by localized heat release, and quantifying the compression

wave strength, are the critical technical issues. This workis closely related to a recent study of airfoil flow separationcontrol using surface DBD actuators powered by repetitivenanosecond pulses [12]. In particular, the same custom-designed nanosecond pulse plasma generator was used in bothseries of experiments.

2. Experimental setup and diagnostics

A schematic of the DBD plasma actuator used in this workis shown in figure 1. The actuator consists of an exposedhigh-voltage electrode 6.35 mm wide and a buried groundedelectrode 12.7 mm wide, separated by three layers of 25.4 mmwide Kapton tape, each layer 0.1 mm thick. Both electrodesare made of adhesive copper tape 0.1 mm thick. There is nooverlap between the two electrodes, as shown in figure 1.The actuator is mounted on a 50 mm outer diameter, 30 cmlong Nylon cylinder or on a 5 cm × 5 cm rectangular crosssection, 150 cm long channel made of glass fiber reinforcedplastic (GFRP). The actuator geometry is essentially the sameas in [12]. The GFRP channel was used to mount variablelength surface DBD actuators (up to 150 cm long) to measureenergy coupled to the plasma versus actuator length. For ICCDplasma imaging, schlieren imaging, and plasma temperaturemeasurements by emission spectroscopy, the actuator wasmounted on the Nylon cylinder and its length was fixedat 30 cm. The cylinder model was chosen to simplify theschlieren diagnostics alignment and to resolve the region nearthe actuator surface. During some of the present experiments,a floating electrode with a sharp point, also made of anadhesive copper tape, was placed on the top of the Kaptontape with the point located 2 mm away from the high-voltageelectrode, as shown in figure 1. This was done to stabilizea discharge filament in which the temperature was measuredby emission spectroscopy. For emission spectroscopy andcalibrated schlieren measurement, an additional Kapton layer

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 2. Schematic of a phase-locked schlieren system.

was added, bringing the total thickness of the dielectric barrierin the actuator to approximately 0.4 mm.

The repetitive nanosecond pulse voltage waveform ofa surface DBD discharge was generated by a high-voltagepulsed power supply, custom designed and built at Ohio StateUniversity. The power supply generates high-voltage pulses(peak voltage up to 20 kV, pulse duration 50–100 ns FWHM),at a pulse repetition rate of up to 10 kHz (in burst mode) or upto 2 kHz (in continuous mode). Both the peak voltage and thepulse energy coupled to the load are strongly load-dependent.Pulse voltage and pulse current are measured at the load usinga Tektronix P6015 high-voltage probe, a custom-made currentshunt probe, and Tektronix TDS2024 oscilloscope, as shownin figure 1. The current probe consists of five radially arranged1 � resistors connected in parallel, with a total resistance of0.2 �. The current probe impedance is set at 50 � by addinga 49.8 � resistor. The stray phase shift between the high-voltage probe signal and the current probe signal is determinedby reducing to zero the integral of the product of voltageand current, under the conditions when the pulse voltage is afew hundred volts and does not cause breakdown between theactuator electrodes. The estimated upper bound uncertainty inthe measured coupled pulse energy is 2%.

To detect compression waves (shock waves) generatedby the nanosecond pulse discharge in the DBD actuator, acustom-built phase-locked schlieren system was used, shownschematically in figure 2. The light source used was a5 W green light-emitting diode (LED). The schlieren imageswere acquired by a Thorlab DCC1545 CMOS camera. Todiscriminate stray UV/visible emission from the plasma, agreen dichroic filter was placed in front of the camera, asshown in figure 2. The LED pulse duration was set at 300 ns,and it was operated at the same pulse repetition rate as thatof the nanosecond pulse discharge in the DBD actuator. The

Figure 3. Schematic of schlieren light source refraction by a pair ofwedged windows.

LED drive circuit was synchronized with the pulsed plasmagenerator with a certain delay time, and phase-locked schlierenimages were accumulated over several hundred dischargepulses. The pulsed plasma generator jitter was approximately50–100 ns, with the overall timing uncertainty of ±200 ns(shock front position uncertainty of 0.07 mm).

The schlieren signal, ISch, is proportional to the relativedensity gradient integrated over the depth of field, as follows:

ISch ∝∫ a/2

−a/2

1

(n0 − 1)

∂(nair − 1)

∂xdz =

∫ a/2

−a/2

1

ρ0

∂ρair

∂xdz

= a1

ρ0

∂ρair

∂x(1)

where n0 and ρ0 are the index of refraction and the densityof air at 273 K and 1 atm, nair is the index of refraction in theregion of interest, a ≈ 4 cm is the depth of field, and ∂ρair/∂x

is the density gradient averaged over the depth of field. To inferthe average density gradient from the schlieren signal intensity,the schlieren system is calibrated using a pair of wedged BK-7glass windows, as shown in figure 3. The wedged surfaces ofthe windows are set parallel to each other, such that for thebaseline window orientation the transmitted schlieren beamis parallel to the incident beam. The distance between thenon-wedged surfaces is set to be equal to the depth of field,a = 4 cm. When window W2 is rotated, the transmittedbeam is refracted, and the beam focal point at the plane of theknife edge follows a circle with a diameter of approximately120 mm (i.e. much greater than the diameter of the focusedbeam, <1 mm). Therefore, if the rotation angle, ω, is small, itcan be assumed that the focal point moves across the knife edgein a straight line, along the x-axis for the window orientationshown in figure 3. Thus, the wedged window rotation changesthe schlieren signal intensity. It can be shown that the relativedensity gradient, averaged along the field of view, is related tothe window rotation angle as follows:

f = 1

ρ0

∂ρair

∂x= (nglass − n0)

n0 − 1

tan θ

asin ω, (2)

where nglass is the index of refraction of the window, θ = 2◦ isthe wedge angle, and ω is the rotation angle.

To obtain the density gradient across the shock wave, thevalue of f inferred from the schlieren signal intensity was

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 4. Time-resolved pulse voltage and current (top),instantaneous power and coupled energy (bottom) in a 148 cm longDBD plasma actuator. The pulse repetition rate is 10 Hz.

multiplied by the ratio of the depth of field, a, and the opticalpath along the shock, s

∂ρshock

∂x= f

a

s≈ f

a

(8Rδ)1/2, (3)

where R is the radius of a cylindrical shock wave and δ ≈0.1 mm is the apparent shock thickness in the phase-lockedschlieren image.

Images of the nanosecond pulse plasma during thehigh-voltage pulse and after the pulse were taken using anAndor ICCD camera with a UV lens. The time-averagedtemperature in the plasma was inferred from the nitrogensecond positive system spectra N2(C

3� → B 3�), (0,0) and(0,2) bands, taken using an OMA system with an Acton SP-300i spectrometer, 2400 lines mm−1 grating, and a PrincetonInstruments PI-MAX gated ICCD camera.

3. Results and discussion

Figure 4 shows time traces of pulse voltage, current,instantaneous power and time integral of the instantaneouspower (i.e. energy coupled to the actuator) measured in aDBD actuator 148 cm long. The pulse repetition rate wasfixed at 10 Hz. Increasing the actuator length resulted in apeak voltage reduction, from 16 kV for a 30 cm long actuator to11 kV for a 148 cm long actuator. This is caused by the actuatorcapacitance increasing as its length is increased, Cload ∼ 102–103 pF m−1. Note that varying the actuator length also changesthe voltage pulse rise time, controlled by the inductance andthe capacitance of the plasma generator, the actuator, and thecables. In this work, the shortest voltage pulse rise/fall time isapproximately 40 ns, which corresponds to a knee frequencyof ∼12 MHz and the wavelength of ∼24 m. Therefore, underthe present conditions, the nanosecond pulse DBD load can beconsidered as a lumped parameter circuit, because the actuatorlength is much shorter than a quarter of the wavelength.

Figure 5 plots coupled pulse energy per unit length,in mJ cm−1, defined as the integral of the instantaneous

Figure 5. Coupled pulse energy per unit length versus pulse peakvoltage for different actuator lengths. The pulse repetition rate is10 Hz.

Figure 6. Coupled pulse energy under steady-state operatingconditions of the plasma generator versus pulse repetition rate. Theactuator length is 44 cm.

power 300 ns after the beginning of the discharge pulse,for different actuator lengths and peak voltages. Duringthese measurements, the actuator length, initially 148 cm, wasgradually reduced to 15 cm, to exclude the effect of smalldifferences in geometry between different actuators. It canbe seen that the coupled energy per unit length is basicallycontrolled by the peak voltage and is nearly independent ofthe actuator length and the voltage rise time, which varied inthe range from 40 to 100 ns for the conditions of figure 5.Figure 5 also plots coupled pulse energy for negative polaritypulses, produced by a different pulsed plasma generator of thesame design. Note that coupled pulse energies for the samepeak voltage and different polarities are noticeably different.This effect may be attributed to the difference in charge build-up characteristics for different pulse polarities [3], but it maywell be due to difference in the residual inductance of the twoplasma generators. Figure 6 plots coupled pulse energy in a44 cm long actuator under steady-state conditions (measuredafter approximately 10 min of continuous operation of the

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 7. Photographs of repetitive nanosecond pulse discharges. (a) 150 cm long actuator, positive polarity pulses, 1 kHz pulse repetitionrate; (b) 30 cm long actuator, positive polarity pulses, 100 Hz and 4 kHz pulse repetition rates; (c) 30 cm long actuator, negative polaritypulses, 100 Hz and 4 kHz pulse repetition rates.

Figure 8. ICCD images of a positive polarity pulse discharge in a DBD actuator, shown together with the current pulse waveform. TheICCD camera gate time is 2 ns, the pulse repetition rate is 1 Hz.

plasma generator) versus pulse repetition rate. It can be seenthat increasing the pulse repetition rate from 10 Hz to 1 kHzresults in a coupled pulse energy increase by more than 50%,from 8.9 mJ to 14.8 mJ.

Figure 7(a) shows a photograph of a repetitive nanosecondpulse discharge in a DBD actuator 148 cm long, taken witha digital camera with a 0.8 s exposure. Figures 7(b) and(c) illustrate the effect of pulse repetition rate on dischargeuniformity. The camera exposure time was varied with pulserepetition rate to keep the number of discharge pulses duringthe exposure approximately the same. It can be seen that

the discharge becomes filamentary as the pulse repetitionrate is increased. This effect becomes even more apparentfor negative polarity pulses, shown in figure 7(c). At apulse repetition rate of 100 Hz, the negative polarity dischargeappears diffuse and nearly uniform. However, as the repetitionrate is increased above 1 kHz, multiple large-scale filamentsbegin to form.

Figure 8 shows a series of ICCD images of a positivepolarity nanosecond pulse discharge in the DBD actuatormounted on a cylinder model, at the pulse repetition rateof 1 Hz. In the images shown in figure 8, the camera gate

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 9. ICCD images of a negative polarity pulse discharge in a DBD actuator, shown together with the current pulse waveform. TheICCD camera gate time is 2 ns, the pulse repetition rate is 1 Hz.

is 2 ns. In the present experiments, the jitter between thedischarge pulse and the camera gate is within 1 ns. In figure 8,the discharge images are shown together with the currentwaveform, indicating the moment in time when they are taken.The discharge emission, initially observed near the high-voltage electrode (at the top of the ICCD images), propagatesalong the dielectric surface toward the grounded electrode(at the bottom of the images). The propagating emissionfront corresponds to the positive polarity current (i.e. currentdirected from the high-voltage to the grounded electrode). Theemission wave appears to have two distinct ‘fronts’. In thisphase, the discharge appears rather uniform, although somestructure can still be identified. Since the current in this phaseremains positive, positive charge builds up on the dielectricsurface.

After the current switches direction (approximately att = 70 ns in figure 8), the luminous wave propagating from thehigh-voltage electrode is observed again (at t = 80–130 ns).Since the current now has negative polarity, the positive chargebuild-up on the dielectric is reduced. The discharge filamentsnear the high-voltage electrode are constricted and becomediffuse on the dielectric side. The filamentary structure of thedischarge is also apparent from photographs (e.g. see figure 7)and visual observations.

Figure 9 shows ICCD images of the negative polaritydischarge, under the same conditions as in figure 8.Qualitatively, the discharge emission behavior is similar tothat of the positive polarity pulse. Initially, the emissionpropagates from the high-voltage electrode over the dielectriccovering the grounded electrode. During this phase, negativecharge accumulates on the dielectric surface. When the currentpolarity changes to positive (approximately at t = 70 ns infigure 9), the charge stored on the dielectric surface flowsback to the high-voltage electrode, and the emission wave

propagates over the dielectric surface again. Although thenegative polarity discharge appears somewhat more uniformthan the positive polarity discharge shown in figure 8,constricting filaments near the high-voltage electrode are stillapparent (see figure 9). Basically, plasma filamentationis observed when the electric charge accumulated on thedielectric surface is removed, independent of the pulse polarity.Further ICCD images demonstrate that location, shape andintensity of individual filaments are fairly random, althoughsome of the filaments have a tendency to form at nearly thesame locations. However, even these relatively reproduciblefilaments shift pulse-to-pulse considerably, over distancesexceeding their thickness (∼0.1 mm).

Rotational temperature in the discharge was inferredfrom the nitrogen second positive band system N2(C

3�u →B 3�g), using a synthetic spectrum code [14]. For this, theICCD camera exposure time was set to 1 µs to capture emissionfrom a single discharge pulse. During these measurements, thedischarge was operated in burst mode, with 50 pulses in a burstat 10 kHz pulse repetition rate and 10 Hz burst repetition rate.To take emission spectra from a filament stabilized by a sharptip floating electrode (see section 2), the filament emissionwas selected using collimation optics and a slit. Figure 10compares experimental emission spectra (vibrational band(0,0)) with best fit synthetic spectra. The experimental spectrain figure 10(a) were obtained from relatively diffuse plasma,without the floating tip electrode. The synthetic spectraproviding the best fit to the experimental spectra from pulses #1and #50 in the burst give rotational temperatures of T = 380±50 K and T = 450 ± 50 K, respectively. The experimentalspectra in figure 10(b) were obtained from a filament stabilizedusing a sharp tip floating electrode. In this case, temperaturesinferred from the synthetic spectra are significantly higher,T = 550 ± 70 K for pulse #1 and T = 650 ± 90 K for pulse

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 10. Nitrogen second positive emission spectra (vibrationalband (0,0)) from a DBD actuator, (a) without a sharp tip floatingelectrode, (b) with a sharp tip electrode. Spectra were taken with thepulser operating in burst mode, at a pulse repetition rate of 10 kHz,burst repetition rate of 10 Hz, with 50 pulses in the burst.

#50 in the burst, although the fit to experimental spectra is notas good as in diffuse plasma. Since the discharge emissionis observed only during the current pulse (e.g. see figures 8and 9), temperature rise during a pulse occurs over a periodof less than ∼200 ns. Kinetic mechanisms of rapid energythermalization (∼1 µs time scale at atmospheric pressure) inpulsed discharges in air at high reduced electric field (E/N ∼102–103 Td, 1 Td = 10−17 V cm2) are discussed in [15–18]. Kinetic modeling calculations suggest that the dominantprocesses contributing to rapid energy thermalization includequenching of excited electronic states of N2 molecules andO atoms (at E/N < 400 Td) [15, 17, 18], as well as ion–molecule reactions, electron–ion and ion–ion recombination(at E/N ∼ 103 Td) [16, 17].

Figure 11 shows phase-locked schlieren images of aMach wave generated by a nanosecond pulse DBD actuatorin quiescent air, for three different time delays between thedischarge pulse and the schlieren light source (LED) pulse.Both the discharge pulse and the schlieren light pulse repetitionrates are 1 kHz. These images are taken using a DBD actuatormounted on a cylinder model, looking in the direction parallelto the cylinder axis (z-axis in figure 11). The surface ofthe DBD actuator, mounted on the model, is curved in theimages. In figure 11, the image intensity is proportional to

the density gradient in the positive y-direction (i.e. up) andto the second derivative of the density along the horizontal(x) axis, because a pinhole light source is used instead of aslit source. Since the wave generated by the discharge pulseis propagating upward, lower intensity indicates compressionand higher intensity indicates expansion. It can be seenthat the wave in figure 11 consists of a compression waveand an expansion wave following it. To monitor the wavepropagation, a series of schlieren images have been taken fordelay times after the pulse ranging from 1 µs to 50 µs, with1 µs intervals. Figure 11 shows just three of these images, with10 µs intervals.

Figure 12 shows phase-locked schlieren images takenunder the same conditions but from a different direction,perpendicular to the cylinder model axis (x-axis in figure 11).In figure 12, the model is on the bottom of the images. Phase-locked schlieren images in figure 12 show a nearly planewave front propagating along the vertical axis, as well asmultiple circular waves. In figure 12, higher signal intensityindicates compression and lower intensity indicates expansion.It can be seen that the wave front near the actuator surfaceappears to have multiple ‘ripples’ created by individual circularwaves, coalescing into a superposition wave with an apparentlyplane front. It is likely that the line-of-sight averaging ofthese individual waves creates a ‘circular’ wave front apparentin the schlieren images of figure 11. It was observed thatthe individual circular wave pattern correlates well with thedischarge emission intensity pattern. As discussed above,heating in the discharge filaments occurs on the time scaleof ∼200 ns. This is comparable to the acoustic time scale,τacoustic ∼ d/a ∼ 300 ns, where d ∼ 0.1 mm is theapparent filament diameter in the ICCD camera images anda ∼ 300 m s−1 is the speed of sound. Therefore, suchrapid localized heating is likely to produce strong compressionwaves.

Figure 13(a) shows a phase-locked schlieren image takenusing a sharp point floating tip electrode in a positive polaritydischarge, again looking in the direction perpendicular to thecylinder model axis (x-axis in figure 11). The electrode tipis located near the center of the image. It can be seen thata circular compression wave is generated near the electrodetip. This wave propagates more rapidly than the plane wavegenerated by diffuse plasma, and its intensity on the schlierenimage is higher. In figure 13(b), showing a schlieren imagefrom the negative polarity discharge, both bright plasmaemission from a strong filament (compare with figure 7) anda circular compression wave originated from the filamentcan be detected. Again, the localized compression wavepropagates significantly more rapidly compared with the planecompression wave, and its intensity is higher.

Figure 14(a) plots the compression wave front positionabove the cylinder model surface versus time delay betweenthe nanosecond discharge pulse and the schlieren light sourcepulse. The two data sets shown are for the positive polaritydischarge, with and without the floating tip electrode. Thedata in figure 14(a) are obtained from phase-locked schlierenimages such as shown in figures 12 and 13. Symbol size infigure 14(a) indicates the uncertainty in the shock front location

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 11. Phase-locked schlieren images of a compression wave generated by a nanosecond pulse discharge for several time delays afterthe discharge pulse, 5 µs to 25 µs. Positive polarity pulses, discharge pulse repetition rate 1 kHz, camera exposure time 156 ms (images areaveraged over 156 discharge pulses). Images taken from a direction parallel to the cylinder axis.

Figure 12. Phase-locked schlieren images of a compression wave generated by a nanosecond pulse discharge for several time delays afterthe discharge pulse, 5 to 25 µs. Positive polarity pulse, pulse repetition rate 2 kHz, camera exposure time 214 ms (images are averaged over428 discharge pulses). Images taken from a direction perpendicular to the cylinder axis.

Figure 13. Close-up view of compression waves produced by adischarge filament stabilized by a sharp floating tip electrode. (a)Positive polarity pulses; (b) negative polarity pulses. Pulserepetition rate 2 kHz. Camera exposure time 214 ms (images areaveraged over 428 discharge pulses). Images taken from a directionperpendicular to the cylinder axis.

and schlieren light source timing, discussed in section 2.Figure 14(b) shows the wave Mach number calculated fromthese data. The wave front position is defined as the pointwhere the schlieren signal intensity reaches a local maximum.

Figure 14 also plots a M = 1 sound wave trajectory atT = 285 K (u = 338 m s−1) as a straight line. One can see thatseveral millimeters away from the actuator surface, the speedof compression waves generated by the pulsed discharge (i.e.the trajectory slope) becomes close to Mach 1. However, thecompression wave trajectories near the actuator surface areshifted up (especially the one with the floating tip electrode),indicating propagation at a speed higher than the speed ofsound.

The density gradient in the compression waves producedby the nanosecond pulse discharge was inferred from theschlieren signal intensity using wedged window calibration,as discussed in section 2. Figure 15 plots the density gradientin the wave, normalized by the ambient air density, versustime delay after the discharge pulse for two different sets ofconditions, positive polarity pulses with and without a floatingtip electrode. From figure 15, it is clear that the compressionwave amplitude is considerably enhanced using the sharp tipelectrode. However, the density gradient in the compressionwave generated in a discharge with a strong filament, stabilizedby a floating tip electrode, decays rapidly with the distancefrom the actuator surface. In the discharge without a floatingtip, the density gradient, although significantly lower near theorigin, decays more slowly with distance.

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

Figure 14. Time-resolved compression wave front location inferredfrom the phase-locked schlieren images. Symbol size represents theuncertainty in the shock front location and schlieren light sourcetiming. The straight line indicates the trajectory of a sound wave atT = 285 K.

Figure 15. Normalized density gradient in compression wavesgenerated by the nanosecond pulse discharge versus delay time afterthe pulse, compared with modeling calculations.

The compression wave density gradient inferred from thecalibrated schlieren images was compared with the densitygradient predicted by numerical modeling of propagatingcompression waves produced by short-pulse localized heating.For this, we used a one-dimensional compressible Navier–Stokes flow model developed in our previous work [7].Using this model, density gradient across a compression wavegenerated in atmospheric pressure air by an isolated filament0.1 mm in diameter, heated over a 100 ns period to a centerlinetemperature of T = 650 K (T ≈ 350 K) and T = 380 K(T ≈ 80 K), was modeled in cylindrical and sphericalgeometries. These filament temperatures were chosen basedon the emission spectroscopy temperature measurements (seefigure 10).

The results, plotted in figure 15, show that the densitygradient predicted in a spherical geometry compression wavewith the initial filament temperature of T = 650 K agrees

well with the measurements in a discharge with a floating tipelectrode. On the other hand, density gradient predicted in acylindrical geometry wave with the initial filament temperatureof T = 380 K is in satisfactory agreement with the dataobtained in a discharge without a floating tip electrode.Qualitatively, this result is expected. Indeed, since the size ofthe filament stabilized by a floating tip electrode is ∼1 mm× ∼0.1 mm (based on ICCD camera images), the compressionwave produced by the filament becomes a nearly sphericalwave at distances exceeding ∼1 mm from the actuator surface.On the other hand, the wave generated by a more diffusedischarge without a floating tip electrode propagates as anearly cylindrical wave, as shown in figure 11, and decayssignificantly more slowly.

4. Summary

This work discusses experimental characterization of a surfacedielectric barrier discharge (DBD) plasma sustained byrepetitive, high-voltage, nanosecond duration pulses. Current,voltage, instantaneous power, and coupled pulse energy in thesurface DBD actuator powered by high-voltage nanosecondpulses have been measured for different pulse peak voltages,pulse repetition rates, and actuator lengths. The resultsdemonstrate that pulse energy per unit length is controlledprimarily by the pulse peak voltage and is not affected by theactuator length. The results also show that the actuator canbe scaled to a length of at least 1.5 m. Images of the plasmagenerated during the nanosecond pulse discharge developmentwere taken by a nanosecond gate ICCD camera. The resultsshow that the plasma remains fairly uniform in the initialphase of discharge development and becomes filamentary ata later stage. Although the negative polarity nanosecond pulsedischarge generates a uniform plasma at low pulse repetitionrates (∼100 Hz), it becomes strongly filamentary as the pulserepetition rate is increased beyond ∼1 kHz.

The temperature rise in the discharge with a floatingtip electrode, inferred from UV/visible emission spectra, isT = 250 ± 70 K after the first pulse in a 50-pulse burst ata 10 kHz pulse repetition rate, and T = 350 ± 90 K afterpulse #50 in the burst. The temperature rise in more diffuseplasma without a floating tip under the same conditions isT = 80 ± 50 K after the first pulse and T = 150 ± 50 Kafter pulse #50 in the burst. Based on the ICCD images of theplasma, the estimated time scale for temperature rise duringthe pulse does not exceed ∼300 ns.

Phase-locked schlieren images were used to measure thespeed of compression waves generated by the nanosecondpulse discharge and the density gradient in the wave. Thedensity gradient was inferred from the phased-locked schlierenimages using absolute calibration by a pair of wedged mirrors.The results demonstrate that discharge filaments generatecompression waves with higher amplitude and higher speedcompared with those produced in a diffuse discharge. Thedensity gradients in these compression waves were comparedwith numerical modeling of propagating compression wavesproduced by short-pulse localized heating. The resultsof the calculations are in satisfactory agreement with the

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Plasma Sources Sci. Technol. 20 (2011) 055009 K Takashima et al

experimental data. Strong compression wave generation insurface DBD actuators powered by nanosecond dischargepulses at high repetition rates may be used for excitinginstabilities in air flow, and potentially for high-speed flowcontrol.

Acknowledgments

This work was supported by the Boeing Company, and bya US Air Force Office of Scientific Research STTR grant‘High Fidelity Simulation of Dynamic Weakly Ionized PlasmaPhenomena’.

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