1 © 2014 IOP Publishing Ltd Printed in the UK

1. Introduction

Plasmas generated in surface dielectric barrier discharge (SDBD) flow actuators have been extensively studied over the last decade, see Moreau (2007), Corke et al (2010), Leonov et al (2010), Kriegseis et al (2013), Adamovich et al (2012),

Kotsonis et al (2014), Wang et al (2013) and references therein. DBD plasma actuators are typically driven by ac waveforms or by repetitive nanosecond duration pulses, with frequencies/pulse repetition rates ranging from a few tens of Hz to a few tens of kHz. In some cases, a series of short (nanosecond dura-tion) pulses and/or a dc bias are added to the ac waveform to

Journal of Physics D: Applied Physics

Dynamics of energy coupling and thermalization in barrier discharges over dielectric and weakly conducting surfaces on µs to ms time scales

Sergey B Leonov, Vitaly Petrishchev and Igor V Adamovich

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

E-mail: leonov.2@osu.edu

Received 2 August 2014, revised 15 September 2014Accepted for publication 23 September 2014Published 27 October 2014

AbstractThe paper presents experiments characterizing discharge development and energy coupling in a surface dielectric barrier discharge (SDBD), atmospheric air plasmas over dielectric and weakly conducting surfaces, over a wide range of time scales and electrical conductivities. The experiments are done using nanosecond pulse (NS) both single polarity and alternating polarity) and ac voltage waveforms. Discharge development and mechanisms of coupling with quiescent air are analysed using nanosecond gate camera imaging, schlieren imaging, and laser differential interferometry. It is shown that NS SDBD plasmas generate stochastic, localized, near-surface perturbations on a long time scale (>100 μs) after the discharge pulse. These perturbations, entirely different from compression waves generated on a short time scale (~1–10 μs), are caused by discharge contraction and originate from the ends of the filaments. Surface conductivity has almost no effect on discharge behaviour if RC time of the conducting surface layer is much longer compared to the characteristic time of NS or ac voltage waveforms. In the opposite limit of short RC time, the conducting layer acts as an extension of the high-voltage electrode. Discharge contraction significantly increases energy stored on the dielectric surface, which in this case exceeds energy dissipated as Joule heat. The stored energy is dissipated if the discharge pulse is followed by an opposite polarity pulse. In a single polarity discharge, on the other hand, surface charge accumulation limits energy coupled to the plasma by subsequent pulses. The results demonstrate that surface plasma actuator control authority may be significantly increased by using an alternating polarity pulse waveform, which is more effective than the removal of surface charge between the pulses using a weakly conducting surface.

Keywords: dielectric barrier discharge, charge transfer, flow control

(Some figures may appear in colour only in the online journal)

S B Leonov et al

Printed in the UK

465201

JPD

© 2014 IOP Publishing Ltd

2014

47

J. Phys. D: Appl. Phys.

JPD

0022-3727

10.1088/0022-3727/47/46/465201

Papers

46

Journal of Physics D: Applied Physics

IOP

0022-3727/14/465201+18$33.00

doi:10.1088/0022-3727/47/46/465201J. Phys. D: Appl. Phys. 47 (2014) 465201 (18pp)

S B Leonov et al

2

improve the actuator performance, see Opaits et al (2008a), Opaits et al (2008b), Likhanskii et al (2008).

The dominant mechanism of ac DBD actuator effect on low-speed flows, near-wall flow entrainment by ions accel-erated in a space charge region of the plasma (electrohy-drodynamic (EHD) flow acceleration), appears to be well understood, Moreau (2007), Corke et al (2010). The magni-tude of this effect is controlled by peak electric field and space charge density in the discharge (primarily in near-electrode and/or streamer head regions). Thus, maintaining actuator performance and flow control authority at high flow velocities requires increasing the field and the electron/ion density. This increase, however, is limited by (i) surface charge accumula-tion, which reduces the electric field in the plasma, and (ii) ionization instability development, discharge constriction, and formation of filaments in the near-surface plasma, potentially making localized Joule heating a more significant effect. As a result, the use of EHD acceleration for high-speed flow con-trol, at flow velocities of a few hundred m s−1, remains chal-lenging. Recently, flow separation control by ac DBD plasma actuators has also been demonstrated in high-speed flows (M  =  0.1–0.4), achieved by increasing peak ac voltage and dielectric thickness, Kelley et al (2012). Determining whether the actuator effect on the flow at these conditions is caused by EHD body force or by localized Joule heating remains an open question.

In SDBD actuators powered by high-voltage nanosecond pulse waveforms, on the other hand, EHD acceleration appears to be insignificant, Little et al (2012). The use of these actua-tors in flows over airfoils at a non-zero angle of attack dem-onstrates significant control authority, resulting in boundary layer flow reattachment at high flow velocities, M = 0.17–0.85, and over a wide range of pulse repetition rates, Roupassov et al (2009), Rethmel et al (2011), Correale et al (2011), Little et al (2012). Roupassov et al (2009) suggested that in this case the dominant effect of the plasma on the flow is caused by rapid localized heat generation in the actuator, rather than by EHD flow acceleration. Indeed, they detected compres-sion waves in quiescent air generated by localized heating in the nanosecond pulse discharge in the DBD actuator, on sub-acoustic time scale. Over the last few years, dynamics of com-pression waves generated in nanosecond pulse DBD plasma actuators in quiescent air has been studied in detail, and they were traced to wavelets generated by individual discharge filaments, Starikovskii et al (2009), Takashima et al (2011a), Peschke et al (2011), Benard et al (2012), Dawson and Little (2013), Zhao et al (2014). Also, recent plasma flow control experiments in Mach 0.12–0.26 flows over an airfoil, Little et al (2012), demonstrated that repetitive flow perturbations by nanosecond pulse DBD (NS-DBD) actuators produced boundary layer tripping at low angles of attack and generated coherent flow structures (spanwise vortices) at large angles of attack. Both effects resulted in boundary layer reattachment of the top (suction side) surface of the airfoil.

In spite of these detailed studies, there appears to be no direct evidence that compression waves generated by heating on sub-acoustic time scale are indeed the dominant factor in boundary layer tripping or generation of coherent flow

structures. In fact, the mechanism by which highly transient perturbations created by compression waves moving rap-idly away from the wall affect the relatively slow flow in the boundary layer is not understood. The ratio of the char-acteristic time scales for these two processes is of the order of τ τ ∼∞a c u/ ~ / 10 ,fflow wave

2 where a is the speed of sound, u∞ is the free stream flow velocity, and cf is the skin friction coefficient. One of the main difficulties in identi-fying the mechanism causing the flow perturbations is that most experimental methods used for flow visualization in repetitively pulsed NS-DBD plasmas, such as phase-locked schlieren, Takashima et al (2011a), or phase-locked particle image velocity (PIV), Zhao et al (2014), are sensitive only to flow structures that are reproducible pulse-to-pulse, and treat stochastic perturbations as noise. Although rapid (i.e. sub-acoustic time scale) heating in the discharge may well be a significant factor affecting the flow, recent time-resolved measurements of temperature in a nanosecond pulse discharge filament in air, Montello et al (2013a), Montello et al (2013b), have shown that dynamics of gas heating in these plasmas after the discharge pulse is more complicated. Specifically, these experiments demonstrated ‘rapid’ heating (occurring on the time scale τrapid ~ 0.1–1 µs·atm and resulting in compression wave formation), followed by ‘slow’ heating (on the time scale τslow ~ 10–100 µs·atm). Since the acoustic time scale, τacoustic ~ d/a, where d ~ 0.1–1 mm is the filament diameter and a ~ 0.3 mm µs−1 is the speed of sound, is τacoustic ~ 0.3–3 µs, ‘slow’ heating, caused primarily by N2 vibrational relaxation by O atoms, Montello et al (2013a), Montello et al (2013b), does not generate compression waves. On the other hand, ‘slow’ heating in near-surface filamentary discharges may well result in formation of transient low-density regions in the boundary layer and contribute to flow instability development. If the dis-charge filaments are stochastic, identification and quantifying this effect becomes challenging. Basically, the use of phase-locked methods would result in strong underestimation of sto-chastic flow perturbations caused by this effect.

The other key process that may strongly influence energy coupling in near-surface discharges and consequently their effect on the flow is charge accumulation on dielectric sur-face and its subsequent removal, dynamics of which is not well understood. Currently, the prevailing view appears to be that surface charge accumulation has a detrimental effect on energy coupled in the surface discharge, as well as EHD flow entrainment (net thrust), Soloviev (2012), Starikovskiy et al (2014). Various approaches to reduce charge accumulation, to prevent ‘reverse breakdown’, and to enhance surface charge removal between the discharge pulses are being explored, Petrishchev et al (2014), Starikovskiy et al (2014). However, it remained not clear whether surface charge neutralization or removal (‘bleeding’) would indeed enhance energy coupling and flow control authority.

In the present work, dynamics of energy coupling and thermalization in surface plasma actuators, powered both by nanosecond pulses and by ac waveforms, is studied using nano-second gate intensified charge-coupled device (ICCD) camera plasma imaging, short time resolution schlieren imaging, and laser differential interferometry (LDI) over a wide range

AQ2

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

3

of time scales. Dynamics of surface charge accumulation is monitored by surface capacitive probe. To study the effect of surface charge removal between the discharge pulses, the dis-charge is sustained over partially conducting liquid surfaces, over a wide range of electrical conductivities, such that the ratio of the discharge pulse duration (ac waveform period) over the characteristic time of surface charge removal (RC time of the actuator, where R is the plasma resistance and C is the actuator capacitance) is varied over several orders of mag-nitude. The main objectives of this work are (i) to identify the dominant effects of surface charge accumulation and ‘slow’ heating (compared to the acoustic time scale) in surface DBD discharge plasmas on energy coupling and flow perturbations, and (ii) to analyse surface DBD and charge transfer dynamics on weakly conducting surfaces. The results have direct impli-cations for enhancing the effect of surface plasma actuators on boundary layer flows.

2. Experimental apparatus, diagnostics, and data reduction

The present experiments have been performed in quiescent room air at atmospheric pressure, using a small-scale SDBD setup shown schematically in figure 1(a). Following common practice, the discharge electrodes are made of adhesive copper tape 36 µm thick, placed on the top of a Teflon dielectric base-plate 20 mm thick, with the overlap between the electrodes varied from 0 to 40 mm, and separated by Kapton dielectric film (50 µm thick, three layers), used as a dielectric barrier, as shown in figure 1(a). In some of the experiments, the Kapton surface was covered by a layer of liquid (distilled water, saline solution, or various alcohols). The bottom electrode was grounded, and the top electrode was powered by a nanosecond pulse power supply or an ac power supply (both are described in greater detail below). Figure 1 also illustrates the coordi-nate system and the notations used in the present work, with the x axis directed parallel to the surface and perpendicular to the high-voltage electrode edge, y axis parallel both to the surface and the high voltage electrode edge, and z axis perpen-dicular to the surface. The origin of the coordinate system is at the edge of the high-voltage electrode.

The discharge and the induced flow diagnostics include a high voltage probe (Tektronix P6015A), a current probe (Pearson model 2877), an ICCD camera (Andor iStar, min-imum gate 10 ns), a surface charge sensor (CS), and a custom-built high resolution schlieren system, using a high-power pulsed diode laser (pulse duration 100 ns) and a framing camera (frame rate up to 2000 frames per second, Basler acA2000-340).

The effect of the discharge on density fluctuation spectra in quiescent air was studied using a LDI diagnostics described in greater detail by Salyer et al (2000), and used in our pre-vious work, Nishihara et al (2005). Briefly, an unpolarized He–Ne laser beam (Coherent He–Ne laser, model # 31–2025) is split into two linearly polarized beams using a Wollaston prism and sent parallel to the surface, through two different regions. Both the reference and the probe beams are directed in the y-direction, parallel to the high-voltage electrode edge, at a distance z = 2–3 mm above the surface and at different positions from the electrode, x = −50 mm (i.e. outside of the plasma, reference beam) and x = 5–30 mm (probe beam). The location of the probe beam can be controlled by rotating the prism. The resultant phase shift between the two beams is pro-portional to the average density difference along the two beam paths. Therefore, Fourier transform of the resultant interfer-ence signal, taken with a LeCroy Model WAVEPRO 7100 A oscilloscope, yields the gas density fluctuation spectrum (rela-tive to the reference laser beam). The reference and the probe laser beam diameters, which limit the spatial resolution of the LDI signal, are approximately 0.5 mm each. Two types of LDI signal time series are acquired by the oscilloscope, one at a sampling rate of 1 Gs s−1 over a time interval of 1 ms, and the other at a sampling rate of 100 Ms s−1 over a time interval of 10 ms, with the discharge operating over 10 s. The spectra are obtained by applying the Fourier transform to the time series. Note that, contrary to acoustic perturbations, thermal pertur-bations in nanosecond pulse DBD plasmas in ambient air are nearly stagnant, and may be detected more efficiently when they are convected by a flow and cross the probe beam path. In ac surface DBD discharges, which generate a near-surface jet flow due to ion wind, Moreau (2007), Corke et al (2010), detection of thermal perturbation by LDI is more effective.

Figure 1. (a) Schematic of SDBD electrodes/dielectric assembly used in the present experiments (see details in the text); (b) equivalent electrical circuit used for estimating the discharge parameters.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

4

The surface CS is a small rectangular shape copper strip with the dimensions x × y = 8  ×  12 mm, placed on the top of the first Kapton dielectric tape layer and covered by two addi-tional Kapton layers, as shown in figure 1. It may be placed at different distances from the top (high voltage) electrode; usually the distance between the edge of the high-voltage electrode and the nearest edge of the sensor is x = 3–12 mm. During the discharge operation, the time-dependent potential of the sensor is measured by the high-voltage probe. The sur-face area of the sensor is ACS ≈ 1 cm2, such that these meas-urements yield surface charge per unit area (charge surface density). The RC time constant of the sensor/voltage probe circuit is τ = RC =  6 ms. At low discharge pulse repetition rates, taking into account slow charge removal from the sensor via the high-voltage probe between the discharge pulses is quite straightforward. Based on voltage and current waveform measurements and ICCD plasma images, it may be concluded that the presence of surface CS has a negligible effect on DBD plasma parameters.

Figure 1(b) shows a schematic of the equivalent electrical circuit used for estimating the discharge parameters. Here Lps is an effective inductance of the high-voltage power supply and the leads connecting it to the discharge electrodes (internal resistance of the power supply is not shown); Cfix represents the capacitance of the electrodes/dielectric assembly without the plasma, which varies depending on the electrodes overlap in the range of Cfix  =  8–55 pF; Rpl is the resistance of the plasma, which varies strongly during the run and run-to-run, depending on peak applied voltage and pulse duration; and Cpl is an additional capacitance caused by charge accumulation on the dielectric surface during the discharge, which varies depending on the surface area covered by plasma.

Two high-voltage power supplies have been used in the present experiments. The first is a nanosecond pulse gener-ator, Takashima et al (2011a), Takashima et al (2012), which generates alternating polarity pulses with peak voltage up to Ups  =  16 kV, pulse repetition rates up to f  =  50 kHz, and pulse duration of τpulse ≈  80 ns full width at half maximum

(FWHM). Briefly, the pulses are formed from input dc voltage (500–800 V) using high-current IGBT transistor switches and magnetic pulse compression circuits. The alternating polarity pulse train generated by the pulser can be converted to a series of only positive or only negative polarity pulses, using sev-eral ultra-fast high-voltage diodes (UF1007-T, rated for 1 kV peak voltage) connected in series between the high-voltage terminal of the pulse generator and the high-voltage discharge electrode, as well as between the high-voltage electrode and ground. Typical positive polarity pulse voltage and current waveforms generated by the pulser connected to the surface DBD assembly shown in figure 1(a), as well as a signal from the surface CS placed x = 5 mm from the high-voltage elec-trode, are plotted in figure 2. In the present experiments, the nanosecond pulse generator operated at pulse repetition rates ranging from f = 200 Hz to 5 kHz.

The second power supply consists of a high-voltage ac amplifier Trek 20/20, driven by a function generator pro-ducing a low-voltage sine wave signal. Typically, the func-tion generator/amplifier operates at a frequency of f = 1–2 kHz and generated sine wave voltage amplitude of Ups = 10–16 kV. The operation of both power supplies is synchronized with the diagnostics used (ICCD camera and schlieren system).

The discharge parameters are estimated based on the data of the following electrical measurements: voltage pulse wave-form, Ups(t), total discharge current, IΣ(t), and local surface charge, Qcs(t), on the surface CS. The procedure used to deter-mine the discharge parameters from these data includes sev-eral steps shown in table 1. Typical waveforms of discharge parameters inferred from these measurements are plotted in figure 2(b).

Analysis of the oscillograms shown in figure  2(b) leads to the following statements, important for further discus-sion: (1) discharge pulse results in considerable accumula-tion of net charge on the dielectric surface; (2) the surface charge is slowly removed from the surface after the pulse; (3) significant fraction of the charge accumulated during the pulse may remain on the surface until the next pulse (see the

Figure 2. Typical oscillograms of SDBD operated with electrodes powered by nanosecond pulses of alternating polarity at a pulse repetition rate of 200 Hz, for a positive polarity pulse: (a) measured parameters: electrode voltage, Ups; current in the external circuit, IΣ; voltage on surface CS, Ucs. (b) Calculated parameters: conduction current, Ipl; total surface charge, QΣ; local surface charge at position of CS, Qcs; coupled pulse energy, Epl.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

5

residual negative charge remaining from the previous pulse in figure 2(b)); and (4) during alternating pulse polarity opera-tion, charge accumulated on the surface has the sign opposite to the charge deposited by the previous pulse. The results for the negative polarity pulse are similar. Note that voltage and current waveforms alone do not supply sufficient information on surface charge accumulation in the nanosecond pulse dis-charge, and providing such information is the main purpose of the surface CS. As will be discussed in section 3, the results of the present work suggest existence of a significant effect of surface charge deposition processes on the overall discharge energy balance.

3. Surface DBD powered by nanosecond pulses over solid dielectric surfaces

3.1. Plasma morphology

In the available literature, most studies of the morphology of surface DBD plasmas sustained by nanosecond pulse and ac waveforms report streamer-like structures formed in positive polarity discharges and more diffuse appearance of negative polarity discharges, Gibalov and Pietsch (2000), Leonov et al (2010), Corke et al (2010). Several studies, such as Joussot et al (2011) and Akishev et al (2013), report that increasing driving voltage above a certain threshold, or increasing the pulse duration to microsecond range results in formation of leaders, or ‘negative surface spark’ structures in the negative polarity discharge. In nanosecond duration, negative polarity pulses (τpulse  << 100 ns), generation of ‘negative sparks’ appears unlikely.

In the present experiments, dynamics of SDBD plasmas sustained by alternating polarity, high-voltage nanosecond pulses has been monitored by a fast ICCD camera (Andor iStar), synchronized with trigger input pulses controlling operation of the high-voltage pulse generator. Figure 3 shows two series of images taken in positive polarity (a) and negative

polarity (b,c) pulses, for time delays after the beginning of the voltage pulse of t < 100 ns (pulse peak voltage is achieved at t ≈ 80 ns, see figure 2(a)). As can be seen in figure 3(a), during the positive polarity pulse, at t = 10–20 ns, a surface ioniza-tion wave propagates from the high-voltage electrode, with the velocity of V  ≥ 1 mm ns−1. Next, formation of streamer-like plasma filaments is detected at t = 40–70 ns, before the pulse voltage reaches maximum at t = 80 ns. During the pulse voltage reduction, weak emission is detected from the region occupied by the decaying plasma. Note that the initial ioniza-tion wave could not be detected in long camera gate images, due to its low luminosity compared to the filaments.

A similar surface ionization wave propagates from the high-voltage electrode during the negative polarity pulse (see figure 3(b), t = 10, 30, 70, and 90 ns). However, its velocity is much lower compared to that for the positive polarity wave, V  ≈  0.2 mm ns−1. The other significant difference is that in most cases the negative polarity ionization wave looks quite uniform. Images of the decaying plasma, taken after the voltage peaks and starts to decrease, appear similar to those taken during positive polarity pulses of the same amplitude.

A major change in the negative polarity discharge struc-ture is observed during the late stage of the voltage rise, if pulse peak voltage is increased above a certain threshold. In this case, sudden contraction, Raizer (1991), of the surface discharge is detected, as seen in figure  3(c). The effect can be described as rapid transformation of near-uniform surface plasma to multiple constricted filaments, which results in sig-nificant increase of energy coupled during the negative polarity pulses. Surface discharge contraction occurs at the following conditions: (1) high pulse peak voltage, Umax > 13 kV at the present conditions; (2) sufficiently long voltage rise time, t > 50 ns at the present conditions; and (3) low internal resist-ance and inductance of the pulse generator, such that peak conduction current is not strictly limited. Note that this effect is not observed in same polarity pulse sequences, either posi-tive or negative.

Table 1. Discharge parameters inference/estimate based on the following measured values: Ups(t), voltage waveform on high-voltage electrode; IΣ(t), total discharge current; and Ucs(t), voltage on surface CS.

Capacitive current, calculated from applied voltage waveform and capacitance of electrode/dielectric assembly, Cfix (without plasma)

= = ×I Q t C U td / d d / dcap fix ps

Conduction current (total current minus capacitive current) Ipl = I∑ − Icap

Total charge deposited on dielectric surfaceQΣ

∫= ×I td

t

0pl

Local charge deposited on surface CS Qcs = Ccs × Ucs

Estimated effective capacitance of surface plasma Cpl ≈ Csc × QΣ / 3Qcs

Estimated voltage across the plasma Upl ≈ Ups − Qcs / Ccs

Total energy dissipated in the plasma and stored on dielectric surfaceEΣ

∫= × ×I U td

t

0pl ps

Energy dissipated in the plasma

∫= × ×E I U td

t

pl0

pl pl

Electrostatic energy stored on dielectric surface after the pulse Est = EΣ – Epl

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

6

3.2. Surface charge accumulation and decay

A series of measurements has been performed to obtain insight into the role of surface charge transfer and discharge contrac-tion on dynamics of energy release in SDBD plasmas. For both discharge pulse polarities, a typical value of surface charge den-sity right after the pulse is σ ≥ 0.1 µC cm−2, with residual sur-face charge density on the time scale ~100 µs after the pulse of σ = 0.02–0.04 µC cm−2. As shown in figure 4(a), surface charge decay occurs on three significantly different time scales: ~1 µs, ~100 µs, and ~1–102 s. The last time scale is approximate and strongly depends on the ambient conditions, such that residual charge can be detected on the surface after several hours and even days. The time scale for the most rapid process of surface charge decay, ~1 µs, depends strongly on the distance from the electrode, as illustrated in figures 4(b) and (c). Basically, sur-face charge is removed more rapidly from the region close to the high-voltage electrode, and the asymptotic (~100 µs after the pulse) surface charge density is typically lower compared to regions further away from the electrode.

Positive and negative polarity discharge pulses do not exhibit substantial differences during surface charge decay dynamics on ~1 µs time scale. This process is likely to be controlled by near-surface charge drift in the plasma, in the ‘reverse’ electric field sustained during the voltage reduction on the electrode. The slower surface charge removal process, on the time scale of ~100 µs (see figure 4(a)) is likely caused by the drift of surface-trapped (bound) charges, Golubovskii et al (2002). Both these processes result in additional energy release near and at the dielectric surface. The fraction of this ‘secondary’ energy release, compared to the total energy coupled by the discharge pulse, varies from a negligibly small value in diffuse surface discharges up to ~70% in con-stricted (filamentary) surface discharges, as discussed in the

subsequent sections. This energy fraction can be estimated as Est = EΣ − Epl (see table 1). Most of the charge accumu-lated on the dielectric surface near the high-voltage electrode during the discharge pulse is rapidly returned to the external circuit when the voltage is reduced (see figures 4(b) and (c)). However, charge deposited on the dielectric surface further away from the electrode stays there for a longer time, and a significant fraction of it, approximately σ ≈ 0.03 µC cm−2, remains there until arrival of the next, opposite polarity, pulse, as shown in figures 4(b) and (c).

The most apparent difference between surface charge density dynamics in alternating polarity mode and single polarity mode discharges is significantly higher charge transfer to the surface in the alternating polarity discharge, as shown in figures 4(d) and (e), 0.18–0.20 µC cm−2 (alternating polarity) versus  ≈0.08 µC cm−2 (single polarity, positive) and  ≈0.09 µC cm−2 (single polarity, negative). At the same time, the residual surface charge density after the pulse (on the time scale of ~10–100 µs) is similar for both modes. The dynamics of surface charge decay after the pulse for these two modes appears somewhat different, demonstrating stepwise reduction after negative single polarity pulses, due to ‘reverse breakdown’ (see the kinks in figure 4(e)).

The next series of measurements was done to quantify the effect of discharge contraction and pulse waveform polarity on charge transfer and energy coupled by the discharge pulse. During these measurements, the alternating polarity nanosecond pulse plasma generator was operated at the same pulse repetition rate, f = 200 Hz, and same input dc voltage. Peak output pulse voltage varied somewhat, because of the change in the DBD load parameters (particularly the electrode capacitance). The width of the discharge electrodes was the same, y = 25 mm, and the overlap between the grounded and the high-voltage electrode was varied between 0 and 40 mm, to vary the electrode capacitance between

Figure 3. ICCD camera images of nanosecond pulse surface DBD plasma sustained by an alternating polarity pulse train. High-voltage electrode, 25 mm wide, is visible on the left, camera gate 12 ns; time delay after the voltage rise is indicated in each frame. (a) Positive polarity pulse, peak voltage Umax = 13 kV; (b) negative polarity pulse, Umax = 13 kV, no contraction; (c) negative polarity pulse, Umax = 14.5 kV, contraction occurs.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

7

Cfix = 12 pF (baseline, no electrode overlap), Cfix = 35 pF (small overlap), and Cfix = 55 pF (significant overlap), see figures 1(a) and (b). Note that increasing the electrode capacitance using this approach somewhat increases the voltage pulse duration comparing to the baseline, by 10–20%. The main reason for var-ying the electrode overlap was to induce discharge contraction, which readily occurs when the load capacitance is increased. A simple estimate shows that, for plasma resistance of Rpl ~ 103 Ω (estimated from peak current and voltage, see figure 2(a)),

the estimated internal inductance of the high-voltage pulse gen-erator of Lps ~ 10–5 H prevents discharge instability development on time scales shorter than τ ≤ Rpl / Lps ≈ 10–8 s. Increasing the capacitance of the electrodes to Cfix ≈ 10−10 F induces a current instability developing on the time scale of τ < Rpl· Cfix ≈ 10–7 s. In fact, contraction of the negative polarity surface discharge has been observed at Cfix = 55 pF and was not detected at base-line conditions (Cfix = 12 pF). Some non-uniformity of the sur-face plasma, indicating instability onset, was apparent already

Figure 4. Typical traces of surface charge density, measured by the surface CS in the SDBD discharge powered by nanosecond pulses of alternating polarity (a–e) and same polarity (positive and negative, (d–e)), at a pulse repetition rate of f = 5 kHz and voltage amplitude of Ups = 14.5 kV. (a) Surface charge density taken over a time interval of 1 ms, CS location x = 3 mm; (b, c) surface charge waveforms in the alternating polarity mode for positive polarity (b) and negative polarity (c) pulses, shown at higher time resolution for sensor location at x = 3, 6, and 12 mm. (d, e) Comparison of surface charge waveform in the single polarity mode comparing to the alternating polarity mode at the same conditions: (d) positive polarity; (e) negative polarity.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

8

at Cfix = 30–35 pF. Finally, measurement results for these three electrode configurations were compared with an additional set of data, taken when the electrodes were powered by a train of same polarity pulses, with high voltage diodes placed between the pulse generator and the discharge electrodes. The result of these measurements are summarized in table 2 and shown in figure 5.

As seen from table 2, constricted surface discharge plasma (generated at Cfix = 55 pF) couples higher total energy per pulse compared to diffuse plasma (generated at Cfix = 12 pF), by about a factor of two, for both positive and negative polarity pulses. Also, at the conditions when contraction occurs (at Cfix = 55 pF), a substantial fraction of coupled energy, up to 70%, is stored on the dielectric surface, as surface charge. From figure 5(a), it is apparent that constricted surface plasma transfers more charge to the dielectric surface, relatively far away from the high-voltage electrode (increase of surface charge transfer shown in figure 5(a) is mainly due to a larger surface area covered by the discharge). As discussed above, the surface charge decays by a two-stage process, with characteristic times τ1 ~ 1 µs and τ2 ~ 100 µs (see figure 4). Note that conversion of energy coupled to the plasma (or to the dielectric surface) during surface charge removal to heat may take longer time (see discussion in section 3.4).

From figure 5(b), it can be seen that surface charge transfer during the pulse, for the discharge operating in the alternating polarity mode, is much higher compared to the single (posi-tive or negative) polarity mode, by about a factor of 5. Peak

conduction current in the alternating polarity mode is also sig-nificantly higher compared to same polarity pulse sequences at the same peak voltage, as seen from table 2. This is con-sistent with figures 4(d) and (e), showing that for the alter-nating polarity pulse sequence the residual charge (before the pulse) has the opposite sign compared to the charge accumu-lated during the pulse, which significantly enhances net charge transfer. Finally, for the alternating polarity pulse sequence, electric field due to residual surface charge accumulation, directed along the dielectric surface, is likely to enhance ioni-zation wave/streamer propagation along the surface during the next, opposite polarity, discharge pulse. Similarly, for single polarity pulse sequences, residual electric field formed after the previous pulse is likely to counter discharge propagation during the next pulse, which may create a strong saturation effect, Thomas et al (2009). This effect is the primary reason for higher total energy coupled by every discharge pulse in the alternating polarity mode, compared to the single polarity mode (by approximately an order of magnitude, see table 2).

3.3. Effect of discharge on quiescent air: two types of perturbations

Dynamics of quiescent ambient air perturbations by the SDBD has been studied using schlieren visualization based on the Toepler technique, Settles (2001). All schlieren images

Table 2. Measured and calculated discharge parameters for four operation modes: baseline configuration with no electrode overlap, two configurations with different overlaps, and same polarity pulse sequences. Run-to-run variation of parameters does not exceed 20%. ‘ + ’ and ‘ − ’ indicate’ the pulse polarity.

ParameterNon overlapped,

Cfix = 12 pFOverlapped, Cfix = 35 pF

Overlapped, Cfix = 55 pF

Single polarity pulses

Pulse polarity + ‒ + ‒ + ‒ + ‒

Surface charge transferred, µC 0.2 0.22 0.35 0.36 0.75 0.8 0.08 0.07Total energy coupled, mJ 3.0 2.6 3.8 4.0 6.2 7.0 0.6 0.55Energy stored after pulse, mJ 0.2 0.25 0.78 0.8 4.6 5.3 0.2 0.25Peak conduction current, A 6.5 5.5 7 7 18 17 4.1 3.4Peak pulse voltage, kV 14.3 14.5 12.8 12.7 10.9 11 14.5 14.5Peak voltage slope, kV ns−1 0.26 0.29 0.21 0.21 0.18 0.14 0.28 0.29

Figure 5. Comparison of surface charge accumulation, QΣ, measured for different electrode overlaps (capacitance values) and different pulse polarities: (a) alternating polarity pulse trains (contraction detected at Cfix = 55 pF); (b) alternating polarity versus same polarity pulse trains (peak voltage is the same in both cases). t = 0 corresponds to the beginning of pulse voltage rise.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

9

obtained in the present work are single-shot images taken at different time delays after the discharge pulse, such that no phase-locked accumulation over multiple discharge pulses has been used. Note that using this approach to characterize the effect of surface discharges on quiescent air and on airflow is quite critical. Although phase-locked imaging makes possible identification of repeatable weak perturbations in repetitively pulsed experiments, Takashima et al (2011b), Nishihara et al (2011), Benard et al (2012), it ‘averages out’ stochastic per-turbations, essentially treating them as noise. Due to this limi-tation, phase-locked images do not provide sufficient insight into dynamics of perturbations induced by the discharge.

A typical sequence of schlieren images for an alternating polarity of pulses is shown in figure 6. These images have been taken with the electrodes powered by an alternating polarity high-voltage nanosecond pulse waveform, at pulse peak voltage of Ups = 14 kV and pulse repetition rate of 200 Hz. As can be seen from figure 6, two different types of perturbations have been observed: (i) weak shock waves generated within a few µs after the discharge pulse, which disappear from the field of view within 25 µs (see figures 6(a)–(d)) and are reproduced extremely well pulse-to-pulse; and (ii) localized ‘spots’, which

become visible at delay times exceeding ~25 µs and appear randomly distributed pulse-to-pulse. The shock waves, also detected in several previous studies, Roupassov et al (2009), Takashima et al (2011b), Nishihara et al (2011), Benard et al (2012), appear nearly identical for positive and negative polarity pulses. On the other hand, localized stochastic ‘spots’ produced after positive and negative polarity pulses appear quite different, and are more pronounced for negative pulses (compare images in figures 6(e) and (f) and figures 6(g) and (h)). The near-surface ‘spots’ produced at long time delays by the positive polarity pulses (labelled ‘pos.’ in figure 6) appear on a smaller spatial scale. These stochastic perturbations can be identified in the schlieren images for quite long delay times after the discharge pulse, up to t ~ 1 ms.

At low pulse peak voltages, when discharge contrac-tion is not observed, the shock wave appears nearly plane and fairly weak, based on the contrast of the schlieren images (see figure  7(a)). When peak voltage is increased and contraction occurs, the wave amplitude also increases, and contributions from individual cylindrical compression ‘wavelets’ can be identified, as can be seen from figures 7(b) and (c). At Ups max = 8 kV (figure 7(a)), contraction does not

Figure 6. Schlieren images of quiescent air perturbations caused by a nanosecond pulse surface DBD plasma, for different delay times after the discharge pulse. Pulse peak voltage 14 kV, pulse repetition rate 200 Hz, ‘side view’ (high voltage electrode is on the left), approximate image size x × z = 25  ×  11 mm, discharge is in a constricted mode. Delay time and polarity are shown on images; for delay time t < 25 µs schlieren images look very similar for both polarities.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

10

occur, while at Ups max = 14 kV (figure 7(c)), contraction is well pronounced and significantly affects the compression wave amplitude and structure. After contractions occurs, the detectable length of the shock wave in the x-direction (per-pendicular to the high voltage electrode edge, see figure 1) increases from x < 10 mm to x > 20 mm, and wave amplitude appears higher for negative polarity pulses. The apparent wave amplitude correlates directly with the coupled dis-charge pulse energy. Note that when the electrodes are powered by single polarity pulse trains (i.e. only positive or only negative), the shock waves appear much weaker com-pared to the ones generated by the alternating polarity pulse trains, at the same pulse peak voltage. This is illustrated by figure 8, where direct correlation between the discharge pattern (filamentary versus diffuse) and the resultant shock wave amplitude is readily apparent.

The locations of stochastic ‘spot’ perturbations, detected at long delay times after the discharge pulse (see figures 6(e)–(h)) also correlate directly with the ICCD camera images of constricted discharge plasmas, taken at the same condi-tions as schlieren images. To illustrate this important point, figure  9 shows schlieren images and ICCD camera images of the same discharge pulses: (a, b) negative polarity pulse, ‘side view’ (high-voltage electrode on the left); (c, d) positive polarity pulse, ‘front view’ (high-voltage electrode straight ahead). For illustrative purposes, the locations of plasma fila-ments (filament origin and end regions in the side view) and perturbation ‘spots’ in figure  9 are identified with arrows. Qualitatively, two energy release zones can be identified in the negative polarity constricted surface discharge, one near the high-voltage electrode, near the origin of the filaments, and the other near the end ‘nodes’ of the plasma (identified as regions 1 and 2 in figure 9(b)). It appears that in this case,

energy release along the rest of the filament is not as signifi-cant. This may be due to high conductivity of the filament (with the estimated peak current I ~ 1 A in each filament and current density of > 103 A cm−2), and thus low electric field along the filament. On the other hand, in the positive polarity constricted surface discharge, energy appears to be released along the entire filament of a nearly cylindrical shape.

3.4. Time scales of thermal perturbations in NS DBD

Two different types of perturbations generated by the nanosecond pulse surface DBD discharge, detected in the schlieren images (see section  3.3) suggests existence of two mechanisms of energy thermalization in the discharge, occurring on two different time scales. Recent time-resolved measurements of rotational/translational temperature and N2 vibrational populations in nanosecond pulse filament dis-charges in air, by picosecond coherent anti-Stokes Raman scattering (CARS), Montello et al (2013a), Montello et al (2013b), and by spontaneous Raman spectroscopy, Lo et al (2012), Lo et al (2014a), Lo et al (2014b), provide insight into kinetics of energy thermalization. Specifically, ps CARS temperature measurements in a nanosecond pulse discharge in air at P  =  100 Torr, Montello et al (2013a), demonstrate very rapid heating of the gas in the discharge filament, up to ΔT ~ 200 K on the time scale of t ~ 0.1 µs, which is much shorter compared to the acoustic time scale, tacoustic ~ d/a ~ 5 µs, where d ~ 2 mm is the filament diameter and a ~ 0.4 mm µs−1 is the speed of sound. This suggests that rapid heating, caused primarily by quenching of N2 excited electronic states by oxygen, N2

* + O2 → N2 + O2, Montello et al (2013b), would result in significant pressure overshoot in the filament. This pressure overshoot, with subsequent gasdynamic expansion of the filament, would be equivalent to a high-amplitude pressure perturbation generated by the discharge in a flow, at the frequency equal to the discharge pulse repetition rate. Qualitative evidence of this expansion was detected in phase-locked schlieren images, which show compression waves originating in the discharge filament and propagating in the radial direction after the discharge pulse, on the time scale of several µs, Montello et al (2013b). Significant pressure overshoot in a nanosecond pulse dis-charge filament in atmospheric pressure air, up to P = 3 atm on the time scale of ~1 μs after the pulse, was also inferred from spontaneous Raman measurements, Lo et al (2014b).

The subsequent ‘slow’ heating, up to T ~ 850 K on the time scale of t ~ 50–500 μs after the discharge pulse at P = 100 Torr, detected in air but missing in nitrogen, occurs on the same time scale as N2 vibrational temperature reduction, Montello et al (2013a), and is caused by V–T relaxation of nitrogen by O atoms, N2(v) + O → N2(v − 1) + O, Montello et al (2013b). These data are consistent with spontaneous Raman measure-ments in a nanosecond pulse discharge filament in atmospheric pressure air, which demonstrate N2 vibrational relaxation and significant temperature rise on the time scale of t ~ 10–100 μs after the discharge pulse, Lo et al (2014b). Summarizing, these results demonstrate that energy thermalization and temperature rise in nanosecond pulse air plasmas occur in two stages, (i)

Figure 7. Schlieren images of the shock wave generated by nanosecond pulse surface DBD plasma, taken 4 µs after the discharge pulse, for different pulse peak voltages. Pulse repetition rate 200 Hz, ‘front view’ (high voltage electrode is straight ahead). Image width is approximately y = 22 mm. (a) Ups max = 8 kV, no discharge contraction observed; (b) Ups max = 11 kV, weak contraction; (c) Ups max = 14 kV, strong contraction observed.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

11

‘rapid’ heating on the time scale τrapid ~ 0.01 μs·atm, caused by collisional quenching of excited electronic states of N2 mole-cules by O2, and (ii) ‘slow’ heating on the time scale τslow ~ 10–100 μs·atm, caused by N2 vibrational relaxation by O atoms.

There appears to be little doubt that shock waves gener-ated by surface nanosecond pulse discharges, detected in pre-vious and present work (e.g. see figures 6(a)–(d)), are due to rapid heating in the discharge on sub-acoustic time scale. It is also tempting to attribute late localized ‘spot’ perturbations (see figures  6(e)–(h)) to slow heating caused by vibrational

relaxation of nitrogen, since they appear first on the same time scale as τslow ~ 100 μs after the discharge pulse. However, this conclusion may be somewhat premature since it is pos-sible that the late energy thermalization near the wall may be caused by localized heating, and subsequent cooling, of the dielectric wall near the origin and the ends of the discharge filaments (e.g. figures 9(a) and (b)). Additional studies, com-paring temperature rise and late perturbations in near-surface nanosecond pulse discharge in air versus nitrogen, are neces-sary to resolve this issue.

Figure 8. Direct correlation between negative polarity discharge images taken 60 ns after the pulse voltage rise, and schlieren images of the shock wave taken 7.5 µs after the discharge pulse: (a, c) alternating polarity pulse train, (b, d) single (negative) polarity pulse train. ‘Side view’ (high voltage electrode is on the left), Ups max = 14 kV. Spatial scale is indicated in the figures.

Figure 9. Schlieren images (a, c) and ICCD camera images (b, d) of the plasma and discharge-induced perturbations, taken from two directions: ‘side view’, negative polarity (a, b); and ‘front view’; positive polarity (c, d). Voltage amplitude Ups = 14 kV, frequency 200 Hz. For schlieren images, time delay is 100 µs after the discharge pulse; for ICCD images, time delay of camera gate is 50 ns after the beginning of voltage rise, camera gate 20 ns. Perturbations due to delayed energy thermalization, appearing as localized ‘spots’, are readily apparent.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

12

4. Surface DBD over weakly conducting surfaces

4.1. Basic criteria for a weakly conducting surface

One of the objectives of the present work is analysis of the effect of surface conductivity on dynamics of SDBDs. Most previous studies, Opaits et al (2008b), Soloviev (2012), Starikovskiy et al (2014), suggested that the use of a weakly conducting sur-face may prevent the effect of saturation of ion wind sustained by these discharges, by reducing residual surface charge accu-mulated during a previous discharge pulse (or previous half-period for ac DBD discharges). In the present work, a thin, weakly conducting liquid layer on the top of Kapton dielectric is used to introduce surface conductivity, which can be varied over a fairly wide range by using different liquids.

To estimate the effect of a weakly conducting liquid layer on the discharge dynamics, consider a plane geometry arrangement with a solid dielectric layer with the thickness d1 and permittivity ε1, and a liquid layer on top of it, with the thickness d2, conductivity σ, and permittivity ε2, as shown in figure 10. The gradient of potential along the surface, due to the finite conductivity of the liquid layer is expressed as follows,

σ∂∂

= − ⋅ ⋅⋅

U

xI x

d Y( )

1 1,

2(1)

where I(x) is the conduction current through the liquid layer and Y is its width. The gradient of the current, due to charge accumulation on the dielectric is given as

ε ε∂

∂= −∂

∂⋅ ⋅I

x

U

t

Y

d.0 1

1(2)

From these two equations, the equation  for the time-dependent potential distribution along the surface is obtained in the form of diffusion/heat conduction equation  in a 1D semi-infinite medium,

∂

∂= ∂

∂U x t

tD

U x t

x

( , ) ( , ),

2

2(3)

where the effective diffusion coefficient is σ ε ε=D d d /1 2 0 1 By solving this equation, electric potential and current distri-bution along the surface can be obtained for a given voltage pulse shape on the high-voltage electrode (assuming the asymptotic boundary condition U(x,t)→0 at x→∞), using Duhamel’s integral or a numerical solution. In a number of cases, a self-similar solution, U(ξ), can be obtained, with the self-similar variable

ξτ

= x

D4,

2

liq(4)

where τliq is the characteristic time for the dielectric surface charging at a distance x from the high-voltage electrode, esti-mated at the conditions when ξ ~ 1. The conductivity of the liquid layer can be neglected if the voltage pulse duration, τpulse, is much shorter compared to τliq, i.e.

τ τ ε εσ

≪ x

d d~

4.pulse liq

20 1

1 2(5)

At the conditions of the present experiments (the extent of the liquid layer along the surface x ~ 3  ×  10–2 m, ε1 = 3.5, d1 ~ 10–4 m, d2 ~ 10–3 m), this gives

τσ

≪×

−

− −s[ ]10

  [Ohm m ].pulse

8

1 1 (6)

Table 3 lists electrical conductivities for several liquids tested in the present work, both tabulated values and results of direct measurements, for actual liquid samples used in the experiments. Note that tabulated conductivities of these liquids vary significantly since they are strongly dependent on temperature and level of impurity. In addition, electrical conductivity of liquids also depends on the electric field, which is important for high peak electric field conditions of the present experiments. For this reason, two separate sets of measurements have been performed: (1) at low electric fields, using a standard ohm-meter, and (2) at high electric fields, using a saw-tooth voltage waveform with peak electric field of Emax = 10 kV cm−1 (for high-conductivity saline solution, Emax = 50 V cm−1 was used) and frequency of 1 kHz. A sig-nificant difference has been detected between low electric field and high electric field measurement results. For further analysis, the results of high electric field measurements were used. Based on the data of table 3 and the criterion of equa-tion (6), distilled water and alcohols tested may be considered as dielectrics on the time scale of nanosecond pulse surface DBD discharges (τpulse ~ 0.1 μs). On the other hand, in typical ac surface DBD discharges, as well as between nanosecond discharge pulses (at frequencies or pulse repetition rates of f ~ 1 kHz, τ ~ 103 μs), these liquids should be considered con-ductors. Most ionic solutions, such as saline (0.9% NaCl in water, σ ≈  1 Ohm−1 m−1), behave as conductors even during nanosecond pulse discharges. Note that the measurement results in table 3 should be considered as approximate, since conductivity of liquids increases with peak electric field and rate of electric field variation, which may be important in nanosecond pulse discharges, Ushakov et al (2007).

4.2. Discharge properties and surface charge transfer

Figure 11 shows ICCD camera and schlieren images of a nanosecond pulse discharge on the Kapton surface par-tially covered with a relatively high electrical conductivity saline solution (0.9% NaCl in water), with the thickness of d2 ≈ 1 mm and length of x ≈ 30 mm. From the images, it is apparent that the saline layer acts simply as an extension of the high-voltage electrode. Indeed, the plasma initiates near

Figure 10. Schematic of SDBD assembly with a layer of liquid on top of dielectric surface, used to control surface conductivity (not to scale).

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

13

the right edge of the liquid layer, away from the electrode (see figures 11(a) and (b)), and the shock wave also originates at the same location (see figure 11(c)). Since a significant frac-tion of the discharge pulse energy is dissipated as Joule heat in the liquid layer (estimated to be ~20% per cm from dis-charge observations at different liquid layer lengths), and due to residual surface charge removal through the liquid layer, the shock wave is significantly attenuated. At these condi-tions, discharge contraction was observed at somewhat higher pulse peak voltage compared to dry Kapton surface, both for positive and negative pulse polarities. Note that in this case the conducting liquid layer results in a significant overlap between the electrodes, which may affect the voltage at which contraction occurs (see section 3.2).

When the Kapton surface is covered by a layer of a low electrical conductivity liquid, distilled water or alcohol (such as butanol), the discharge behaviour changes dramatically. In this case, the plasma originates right at the edge of the high-voltage electrode and propagates over the liquid surface, as illustrated in figure 12. Note that at these conditions the dis-charge behaviour may well be affected by the fact that the plasma is generated in near saturated vapour/air mixture,

rather than in dry air, Petrishchev et al (2014). A weak shock wave is also detected in the schlieren images, extending from the high-voltage electrode edge. In this case, no perturbations, such as ‘spots’ (see section 3.3), are observed near the liquid surface at time delays longer than ~ 1 μs.

Dynamics of surface charge accumulation and dissipa-tion on the surface of weakly conducting liquids covering the Kapton dielectric layer was measured by the surface CS. The results for distilled water, propanol, and butanol, as well as for dry Kapton surface (baseline), are shown in figure 13, for a nanosecond pulse discharge with alternating polarity pulses, at pulse repetition rate of 5 kHz. It is apparent that peak charge accumulated on the surface is about the same for all cases, see figure 13(b). Some difference in dynamics of surface charge dissipation between positive and negative polarity pulses is detected, especially for water (see figure  13(a)). Surface charge dissipation rates on the time scale t ~ 1 µs are close to each other (figure 13(b)), but vary significantly at longer time delays, t = 10–100 µs, as is apparent from figure 13(a). The part of the surface charge decaying on the time scale of t ~ 1 µs is likely removed due to a rapid volumetric process, which appears to be similar for solid and liquid surfaces.

Table 3. Electrical conductivities of selected liquids and estimates of characteristic time of dielectric charging, τliq, indicating whether the liquid layer behaves as a dielectric or a conductor.

Type of liquid σ (Ohm−1 m−1) tabulatedaσ (Ohm−1 m−1) measuredb (E < 10 V cm−1)

σ (Ohm−1 m−1) measuredb (E > 1 kV cm−1)

τliq, μs estimated (E > 1 kV cm−1)

Distilled water 5  ×  10−6 to 1  ×  10–4 1  ×  10–4 5  ×  10–4 20Saline (0.9%) 1.76 0.5 1.2 0.01Methanol 1.6  ×  10–7 to 3  ×  10–7 2  ×  10–4 1.5  ×  10–3 6Ethanol 1  ×  10–7 to 10  ×  10–7 3  ×  10–4 9  ×  10–4 102-propanol 1  ×  10–6 to 5  ×  10–6 5  ×  10–6 6  ×  10–5 1601-butanol 1  ×  10–6 to 5  ×  10–6 1  ×  10–5 8  ×  10–5 120

a Tabulated data (measured at low electric fields) taken from the available literature.b Measured using liquid samples used in the experiments, at constant or slowly varying field.

Figure 11. Nanosecond pulse surface DBD plasma over Kapton dielectric covered by a layer of saline solution (0.9% NaCl in water). Alternating polarity pulse train, Ups max = 14.5 kV. (a) ICCD camera image, positive polarity pulse, time delay after voltage rise 70 ns; (b) ICCD camera image, negative polarity pulse, time delay after voltage rise 70 ns; (c) schlieren image of the shock wave, time delay after positive polarity discharge pulse 10 µs.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

14

The dynamics of charge that remains trapped on the surface may be considered in the following way. This process occurs in two stages: (1) rapid removal of the charge from the liquid surface in the transverse direction, toward the Kapton surface, due to high transverse conductivity (note that this process cannot be detected by the present CS); and (2) slow charge transport in the axial direction, toward the electrode, which has near zero potential after the discharge pulse. The charac-teristic time of the first process is controlled by the transverse resistance, Rtr, and the capacitance of the liquid layer, Cliq, τ ε ε σ= × =R C / ,tr tr liq 0 and is in a range of τtr = 10−7–10–5 s, while the time scale for the second process is τliq = 10−5–10–4 sec (see section 4.1). Since the capacitance of the liquid layer and the solid dielectric (Kapton) layer are comparable, elec-trostatic energy stored on the surface after the discharge pulse also dissipates in two stages, resulting in Joule heating of the liquid layer.

Estimates of characteristic time for charge dissipation from liquid surfaces, inferred from experimental traces of sur-face charge decay, plotted in figure 13, are listed in table 4. Reasonably good agreement is obtained with the estimates based on the measured conductivity of the liquids (see table 3 for comparison). Table  4 also lists surface charge transfer magnitude and energy deposition at these conditions.

For surface DBD discharges sustained by ac voltage wave-forms, with frequencies in the range of a few kHz, the charac-teristic time for voltage rise can be defined as follows,

τ =∂ ∂

≈ −⎜ ⎟⎛⎝

⎞⎠

U

U t/10 s,AC

max

4 (7)

which is 3 orders of magnitude longer compared to a typical nanosecond pulse duration, τpulse ~ 10–7 s. This implies that some polar liquids, such as distilled water, will behave as con-ductors in ac discharges, quite contrary to their dielectric-like

Table 4. Comparison of surface nanosecond pulse discharge parameters for several weakly conducted liquids. Data taken for the same pulse generator operation parameters (alternating pulse polarity sequence, pulse peak voltage 14 kV, pulse repetition rate 500 Hz).

Parameter Dry Kapton 1-butanol 2-propanol Distilled water

Polarity + ‒ + ‒ + ‒ + ‒

Charge deposited, µC 0.28 0.26 0.22 0.21 0.15 0.17 0.12 0.10Energy deposited, mJ 3.6 3.5 3.3 3.4 3.0 3.2 2.0 1.8Surface charge decay time, μs 2000 2000 180 140 110 105 6.4 5.0

Figure 12. ICCD camera images of nanosecond pulse surface DBD plasma over Kapton dielectric partially covered by a weakly conducting liquid: (a) distilled water, positive polarity pulse; (b) distilled water, negative polarity pulse; (c) butanol, positive polarity pulse; (d) butanol, negative polarity pulse. Alternating polarity pulse train, Ups max = 14.5 kV, time delay after voltage rise 70 ns. High-voltage electrode shape and the extent of liquid layer are indicated in image (a) and are the same for all images shown.

Figure 13. Dynamics of surface charge density over dry Kapton surface (baseline) and over Kapton surface covered by a weakly conducting liquid, measured by the surface CS placed x = 5 mm from the high-voltage electrode. Discharge sustained by nanosecond pulses of alternating polarity, pulse repetition rate f = 5 kHz, peak voltage Ups max = 14 kV (no negative pulse contraction is detected). (a) Long time scale; (b) short time scale, positive pulse polarity.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

15

behaviour in nanosecond pulse discharges. This has been verified by a simple test, during which ICCD camera and schlieren images of two different types of surface discharges over liquid layers (ac and nanosecond pulse) have been taken. ICCD images of ac surface DBD discharge over two repre-sentative liquids, distilled water and butanol, are shown in figure 14. It can be seen that the plasma originates near the part of the liquid pool perimeter which not in contact with the high-voltage electrode, such that the liquid serves as the elec-trode extension. Qualitatively, this behaviour is essentially the same as has been observed in a nanosecond pulse discharge over saline solution (see figure 11) and entirely opposite to a nanosecond discharge over distilled water (see figure 12), demonstrating clearly that distilled water acts as a dielectric in nanosecond pulse surface DBD discharges and as a con-ductor in ac surface DBD discharges. For distilled water, the effect of electrode extension was observed for water pools up to 75 mm long. Other polar liquids, with conductivities exceeding σ > 10–6 Ohm−1·m−1, exhibit similar behaviour. In

the ac discharge over butanol, at frequencies above 30 kHz, when τAC ~ 10–5 s <<  τliq ~ 10–4 s (see table 2), the plasma begins to extend from the high-voltage electrode over the liquid butanol surface, as expected.

In ac surface DBD discharges, the liquid layer often becomes unstable due to the ion wind generated by the dis-charge over the surface, such that the liquid is affected by the induced airflow. To maintain stability of the liquid layer and to keep its thickness about the same, in some experiments it was replaced by a sheet of porous filter paper ~0.5 mm thick, soaked in the liquid. The high-voltage electrode was installed with a ~1 mm gap above the Kapton dielectric sur-face, as can be seen in figure 15. In schlieren images of ac DBD plasmas, shown in figure 15, a near-surface jet of air, with the velocity of several meters per second, is detected. Since the flow in the near-wall jet is heated slightly by the surface DBD plasma, providing an optical density gradient in the z-direction (perpendicular to the wall), it is visualized by schlieren. A dark wedge-like area, visible near the surface in

Figure 14. ICCD camera images of ac discharge over a layer of distilled water (a) and butanol (b). Frequency f = 1 kHz, voltage Ups

max = 11 kV, camera gate 1 ms, liquid layer thickness approximately 1 mm, high voltage electrode width y = 25 mm.

Figure 15. Schlieren images of ac discharge over dry Kapton surface, butanol and distilled water liquid layers. AC frequency f = 2 kHz, peak voltage Ups max = 11 kV, liquid layer thickness d2 = 1 mm. Dark wedge-like areas near the surface indicate regions of ion wind. (a) Dry Kapton surface; (b) sheet of filter paper soaked in butanol; (c) sheet of filter paper soaked in distilled water.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

16

figure 15, indicates the region of ion wind where the flow tem-perature is somewhat higher. Schlieren images taken over the dry Kapton surface and over the liquid butanol layer appear similar (see figures 15(a) and (b)), indicating the presence of ion wind over the liquid layer, even though plasma emission over butanol is detected predominantly near the perimeter the liquid pool (such as shown in figure 14(b)). It is likely that the ion wind is generated at both interfaces, (i) between the high-voltage electrode and the liquid, and (ii) between the liquid and Kapton dielectric. In the ac surface discharge over a water layer (distilled water in figure  15(c)), the plasma originates at the edge of the liquid layer far from the high-voltage elec-trode, such that the ion wind region is detected only over the dry Kapton dielectric surface (see figure 15(c)).

4.3. Discharge-induced density perturbation spectra

LDI spectra of perturbations induced by ac surface DBD plasma over dry Kapton surface, for different locations of the probe beam (see section 2) and different peak voltages are shown in figure 16. In the spectra, baseline was measured

with the discharge operating but with the probe beam placed z  >  50 mm above the surface. When the probe beam is located near the high-voltage electrode (x  =  5 mm), peaks corresponding to ac driving frequency, as well as higher harmonics, can be detected in the spectra (see figures 16(a) and (b)). It is easy to see that baseline is free from electro-magnetic interference. When the probe beam is moved fur-ther away from the electrode, these peaks nearly disappear (x = 10 mm), and high-frequency perturbations are damped as well (x  =  30 mm). Increasing peak ac voltage demon-strates a dramatic rise in the intensity of perturbations, as shown in figure 16(b), by up to an order of magnitude within a moderate frequency range (~1–10 kHz). At the same time, discharge contraction and plasma filamentation are detected. It is important to note that the rise of perturbation inten-sity in the high-frequency range, ~10–300 kHz, is detected only when contraction occurs, at Umax  ≥  14 kV at present conditions (see figure  16(c)). This demonstrates that high-frequency perturbations are produced only when the plasma is filamentary, which may have significant implications for flow control by surface DBD plasmas.

Figure 16. LDI spectra of perturbations produced by ac surface DBD plasmas; semilog scale. (a) f = 2 kHz, Umax = 12 kV, distance between high-voltage electrode and probe beam x = 5–30 mm; (b) f = 1 kHz, x = 5 mm, peak voltage Umax = 12–18 kV; (c) same as (b) but showing an extended frequency range, with 12 and 18 kV spectra shown at low spectral resolution for illustration purposes. A spike at 40 kHz is caused by modulation of the laser beam.

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

17

5. Summary

The results of the present work demonstrate several effects, the significance of which appears to have not been fully real-ized previously.

First, it is shown that NS SDBD plasmas generate high-amplitude, broadband, stochastic, point-wise, near-surface perturbations on a long time scale (>100 μs) after the dis-charge pulse. It is demonstrated that these ‘slow’ perturba-tions, entirely different from previously observed compression waves generated on a short time scale (~1–10 μs) after the pulse, are caused by discharge contraction and originate from the ends of individual streamers where they attach to the sur-face. The ‘slow’ perturbations occur approximately on the same time scale as vibrational relaxation of nitrogen in nano-second filament discharges away from the surface, Montello et al (2013a), Montello et al (2013b), Lo et al (2012), Lo et al (2014a), Lo et al (2014b), although the effect of local-ized heating, and subsequent cooling, of the dielectric wall near the ends of the discharge filaments also cannot be dis-counted. Compression waves generated in nanosecond pulse surface discharges on microsecond time scale may be one of possible mechanisms of flow forcing and generation of large-scale coherent structures, Little et al (2012). Thermal pertur-bations of the boundary layer on sub-millisecond time scale may play significant role in boundary layer transition and sep-aration control at low and moderate instability frequencies. Generation of the latter type of perturbations has been demon-strated in the present work, especially at the conditions when discharge contraction significantly enhances coupled energy and surface charge deposition. These perturbations may well be dominant in nanosecond pulse discharges with alternating pulse polarity, as well as in ac discharges at high peak volt-ages. However, detailed mechanism of surface DBD effect on boundary layer flow parameters is not fully understood, and identifying it remains a challenge. Additional work is neces-sary to verify these hypotheses, and to compare/quantify the effect of ‘rapid’ compression waves and ‘slow’ perturbations on the flow. Preliminary measurements of airflow density fluc-tuation spectra generated by diffuse and constricted (filamen-tary) surface discharges suggest that high-frequency airflow perturbations, in the frequency range of ~10–500 kHz, are produced primarily by filamentary discharges, indicating their significant potential for flow control applications.

It is also demonstrated that discharge contraction results in significant increase of energy stored on the dielectric surface during and after the NS discharge pulse, which in this case greatly exceeds energy dissipated as Joule heat (up to a factor of 3–4). The stored energy is released and dissipated as heat if the discharge pulse is followed by an opposite polarity pulse, even at relatively low pulse repetition rates (below 1 kHz). In a single polarity pulse discharge, on the other hand, sub-stantial surface charge accumulation severely limits the amount of energy coupled to the plasma by subsequent pulses. This is readily apparent from coupled/stored energy measure-ments, as well as from qualitative comparison of amplitudes of compression waves generated by alternating polarity and single-polarity NS-DBD discharges, which exhibit dramatic

difference. This effect has a major impact on the effective-ness of NS-DBD surface plasma actuators used for high-speed flow control. The present results strongly suggest that actuator control authority may be significantly increased by using an alternating polarity pulse voltage waveform, which is more effective than ‘bleeding’ the surface charge between the pulses, if a single polarity voltage waveform is used.

Finally, it is shown that surface conductivity has almost no effect on the discharge behaviour as long as RC time of the conducting surface layer/dielectric layer is much longer com-pared to the characteristic time of NS or ac voltage waveforms (i.e. pulse duration or sine wave half-period). In the opposite limit of a very short RC time, the conducting surface layer acts as an extension of the high-voltage electrode. This effect is of considerable significance for development of surface plasma actuators for flow control. Basically, it suggests that opera-tion of nanosecond pulse surface DBD actuators, at the condi-tions of extensive water condensation on the actuator surface, would not be affected significantly. On the other hand, water condensation on the surface of ac DBD actuators would con-siderably reduce control authority, due to a major energy dissipation in the conducting liquid layer. A simple physics-based criterion estimating the effect of surface conductivity on discharge propagation is obtained.

Acknowledgments

This work has been supported by AFOSR project ‘Nonequilib-rium molecular energy coupling and conversion mechanisms for efficient control of high-speed flow fields’. The authors would like to thank Dr Munetake Nishihara for his help with LDI measurements.

References

Adamovich I V, Little J, Nishihara M, Takashima K and Samimy M 2012 Nanosecond pulse surface discharges for high-speed flow control 6th AIAA Flow Control Conf. (New Orleans, LA, 25–28 June 2012) pp 2012–3137

Akishev Yu, Aponin G, Balakirev A, Grushin M, Petryakov A, Karal’nik V and Trushkin N 2013 Stepwise expansion of a surface dielectric barrier discharge as a result of alternation in formation of streamers and leaders J. Phys. D: Appl. Phys. 46 1352041

Benard N, Zouzou N, Claverie A, Sotton J and Moreau E 2012 Optical visualization and electrical characterization of fast-rising pulsed dielectric barrier discharge for airflow control applications J. Appl. Phys. 111 033303

Corke T C, Enloe C L and Wilkinson S P 2010 Dielectric barrier discharge plasma actuators for flow control Annu. Rev. Fluid Mech. 42 505–29

Correale G, Popov I, Rakitin A, Starikovskii A, Hulshoff S and Veldhuis L 2011 Flow separation control on airfoil with pulsed nanosecond discharge actuator 49th AIAA Aerospace Sciences Meeting (Orlando, FL, 4–7 January 2011) pp 2011-1079

Dawson R and Little J 2013 Characterization of nanosecond pulse driven dielectric barrier discharge plasma actuators for aerodynamic flow control J. Appl. Phys. 113 103302

Gibalov V I and Pietsch G J 2000 The development of dielectric barrier discharges in gas gaps and on surfaces J. Phys. D: Appl. Phys. 33 2618–36

J. Phys. D: Appl. Phys. 47 (2014) 465201

S B Leonov et al

18

Golubovskii Yu B, Maiorov V A, Behnke J and Behnke J F 2002 Influence of interaction between charged particles and dielectric surface over a homogeneous barrier discharge in nitrogen J. Phys. D: Appl. Phys. 35 751–61

Joussot R, Boucinha V, Weber R and Hong D 2011 Negative spark leaders on a surface DBD plasma actuator IEEE Trans. Plasma Sci. 39 2194–5

Kelley C L, Bowles P, Cooney J, He C and Corke T C 2012 High mach number leading-edge flow separation control using ac DBD plasma actuators 50th AIAA Aerospace Sciences Meeting (Nashville, Tennessee, 9 − 12 January 2012) pp 2012-0906

Kotsonis M, Correale G, Michelis T, Ragni D and Scarano F 2014 Nanosecond-pulsed plasma actuation in quiescent air and laminar boundary layer J. Phys. D: Appl. Phys. 47 105201

Kriegseis J, Duchmann A, Tropea C and Grundmann S 2013 On the classification of dielectric barrier discharge plasma actuators: a comprehensive performance evaluation study J. Appl. Phys. 114 053301

Leonov S, Opaits D, Miles R and Soloviev V 2010 Time-resolved measurements of plasma-induced momentum in air and nitrogen under DBD actuation Phys. Plasmas 17 113505

Likhanskii A, Shneider M, Macheret S and Miles R 2008 Modeling of dielectric barrier discharge plasma actuator in air J. Appl. Phys. 103 053305

Little J, Takashima K, Nishihara M, Adamovich I and Samimy M 2012 Separation control with nanosecond pulse driven dielectric barrier discharge plasma actuators AIAA J. 50 350–65

Lo A, Cessou A, Boubert P and Vervisch P 2014a Space and time analysis of the nanosecond scale discharges in atmospheric pressure air: part I. Gas temperature and vibrational distribution function of N2 and O2 J. Phys. D: Appl. Phys. 47 115201

Lo A, Cessou A and Vervisch P 2014b Space and time analysis of the nanosecond scale discharges in atmospheric pressure air: II. Energy transfers during the post-discharge J. Phys. D: Appl. Phys. 47 115202

Lo A, Cléon G, Vervisch P and Cessou A 2012 Spontaneous Raman scattering: a useful tool for investigating the afterglow of nanosecond scale discharges in air Appl. Phys. B 107 229–42

Montello A, Burnette D, Nishihara M, Lempert W R and Adamovich I V 2013a Dynamics of rapid localized heating in nanosecond pulse discharges for high speed flow control J. Fluid Sci. Technol. 8 147–59

Montello A, Yin Z, Burnette D, Adamovich I V and Lempert W R 2013b Picosecond CARS measurements of nitrogen vibrational loading and rotational/translational temperature in nonequilibrium discharges J. Phys. D: Appl. Phys. 46 464002

Moreau E 2007 Airflow control by non-thermal plasma actuators J. Phys. D: Appl. Phys. 40 605–36

Nishihara M, Jiang N, Rich J W, Lempert W R, Adamovich I V and Gogineni S 2005 Low-temperature supersonic boundary layer control using repetitively pulsed MHD forcing Phys. Fluids 17 106102

Nishihara M, Takashima K, Rich J W and Adamovich I V 2011 Mach 5 bow shock control by a nanosecond pulse surface dielectric barrier discharge Phys. Fluids 23 066101

Opaits D F, Shneider M N, Miles R B, Likhanskii A V and Macheret SO 2008a Experimental investigation of dielectric barrier discharge plasma actuators driven by repetitive high-voltage nanosecond pulses with dc or low frequency sinusoidal bias J. Appl. Phys. 104 043304

Opaits D F, Shneider M N, Miles R B, Likhanskii A V and Macheret S O 2008b Surface charge in dielectric barrier discharge plasma actuators Phys. Plasmas 15 073505

Peschke P, Goekce S, Hollenstein C, Leyland P and Ott P 2011 Interaction between nanosecond pulse DBD actuators and transonic flow 42nd AIAA Plasmadynamics and Lasers Conf. (Honolulu, Hawaii, 27–30 June 2011) pp 2011–3734

Petrishchev V, Leonov S and Adamovich IV 2014 Studies of nanosecond pulse surface ionization wave discharges over solid and liquid dielectric surfaces 52nd AIAA Aerospace Sciences Meeting (SciTech 2014) (National Harbor, MD, 13–17 January 2014) pp 2014-0667

Raizer Yu P 1991 Gas Discharge Physics (Berlin: Springer) pp 1–449

Rethmel C, Little J, Takashima K, Sinha A, Adamovich I and Samimy M 2011 Flow separation control using nanosecond pulse driven DBD plasma actuators Int. J. Flow Control 3 213–32

Roupassov D V, Nikipelov A A, Nudnova M M and Starikovskii A Yu 2009 Flow separation control by plasma actuator with nanosecond pulsed-periodic discharge AIAA J. 47 168–85

Salyer T R, Collicott S H and Schneider S P 2000 Feedback stabilized laser differential interferometry for supersonic blunt body receptivity experiments 38th Aerospace Sciences Meeting & Exhibit (Reno, NW, 10–13 January 2000) pp 2000-0416

Settles G S 2001 Schlieren and Shadowgraph Techniques (Berlin: Springer) pp 1–370

Soloviev V R 2012 Analytical estimation of the thrust generated by a surface dielectric barrier discharge J. Phys. D: Appl. Phys. 45 025205

Starikovskii A Yu, Nikipelov A A, Nudnova M M and Roupassov D V 2009 SDBD plasma actuator with nanosecond pulse-periodic discharge Plasma Sources Sci. Technol. 18 034015

Starikovskiy A, Tkach N, Post M and Miles R 2014 Dielectric barrier discharge control and thrust enhancement by diode surface 52nd AIAA Aerospace Sciences Meeting (SciTech 2014) (National Harbor, MD, 13–17 January 2014) pp 2014-0144

Takashima K, Adamovich I V, Czarnetzki U and Luggenhölscher D 2012 Development of fast ionization wave discharges at high pulse repetition rates Plasma Chem. Plasma Process. 32 471–93

Takashima K, Zuzeek Y, Lempert W R and Adamovich I V 2011a Characterization of surface dielectric barrier discharge plasma sustained by repetitive nanosecond pulses Plasma Sources Sci. Technol. 20 055009

Takashima K, Adamovich I V, Xiong Z, Kushner M J, Starikovskaia S, Czarnetzki U and Luggenhölscher D 2011b Experimental and modeling analysis of fast ionization wave discharge propagation in a rectangular geometry Phys. Plasmas 18 083505

Thomas F O, Corke T C, Iqbal M, Kozlov A and Schatzman D 2009 Optimization of dielectric barrier discharge plasma actuators for active aerodynamic flow control AIAA J. 47 2169–78

Ushakov V, Klimkin V F and Korobeynikov S M 2007 Impulse Breakdown of Liquids ed V Ushakov (Berlin: Springer)

Wang J-J, Choi K-S, Feng L-H, Jukes T N and Whalley RD 2013 Recent developments in DBD plasma fow control Prog. Aerosp. Sci. 62 52–78

Zhao Z, Li J-M, Zheng J, Cui Y D and Khoo B C 2014 Study of shock and induced flow dynamics by pulsed nanosecond DBD plasma actuators 52nd AIAA Aerospace Sciences Meeting (National Harbor, MD, 13–17 January 2014) pp 2014-0402

J. Phys. D: Appl. Phys. 47 (2014) 465201