Evolution and fluid dynamic effects of pulsed column-shaped plasma

Accepted Manuscript Evolution and fluid dynamic effects of pulsed column-shaped plasma Irina Znamenskaya, Ekaterina Koroteeva, Igor Doroshchenko, Nikolay Sysoev PII: DOI: Article Number: Reference:

S0894-1777(18)31617-0 https://doi.org/10.1016/j.expthermflusci.2019.109868 109868 ETF 109868

To appear in:

Experimental Thermal and Fluid Science

Received Date: Revised Date: Accepted Date:

11 October 2018 21 June 2019 5 July 2019

Please cite this article as: I. Znamenskaya, E. Koroteeva, I. Doroshchenko, N. Sysoev, Evolution and fluid dynamic effects of pulsed column-shaped plasma, Experimental Thermal and Fluid Science (2019), doi: https://doi.org/ 10.1016/j.expthermflusci.2019.109868

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Evolution and fluid dynamic effects of pulsed column-shaped plasma Irina Znamenskaya, Ekaterina Koroteeva, Igor Doroshchenko, and Nikolay Sysoev Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

Abstract We study the development, as well as the thermal and fluid dynamic effects of a pulsed column-shaped plasma generated at low pressure using a volume discharge arrangement. The conditions are achieved when the volume discharge contraction leads to pulsed localized deposition of most of the electrical power into a straight plasma column, 24-mm in length. First, we investigate the effect of pressure on the discharge morphology and afterglow evolution using combined electrical measurements and time-resolved streak and image glow recordings. Then we conduct the high-speed shadow imaging and the PIV visualization of the induced post-discharge transient flow that includes a cylindrical shock wave, a rarefaction wave, and a contact surface. The shock wave front expands at a Mach number of 1.4–1.8, as measured on the shadow images. The contact surface, after interacting with the reflected rarefaction wave, stagnates at a radius around 4 mm separating the discharge-heated gas from the shock-heated gas. Finally, we perform 3D CFD simulations to complement the flow visualization experiments and show that, at the present experimental conditions, about 0.12–0.16 J of energy is thermalized on a sub-microsecond time scale within a cylindrical breakdown volume. Keywords: pulsed energy deposition, constricted plasma column, shock waves, CFD, time-resolved shadowgraphy, PIV PACS: 52.80.Fn, 47.40.-x, 47.80.Jk, 52.35.Tc, 47.11.-j

Preprint submitted to Experimental Thermal and Fluid Science

July 6, 2019

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1. Introduction In recent years, plasma-based devices operating in a pulsed (or pulsedperiodic) mode have demonstrated great potential in a variety of applications, the most important being high-speed flow control [1, 2] and plasma-assisted ignition and combustion [3, 4]. Commonly referred to as plasma actuators, plasma devices for pulsed energy deposition to the flow include nanosecond dielectric barrier discharges (ns–DBDs), sliding discharges, localized arc filament actuators [5, 6, 7, 8]. These discharges are typically powered by high-voltage pulses of short duration (less than a few hundreds of nanoseconds) that allow for efficient generation of excited species and relatively low power consumption [9]. The control authority of any plasma actuator depends largely on the spatial distribution of discharge energy. Increasing the interaction region between an external flow and discharge plasma is necessary for the application of discharge plasmas at full scale. Sliding surface discharges (“plasma sheets”) are capable of generating more extended plasma layers compared to traditional surface ns-DBDs [10]. A pulsed volume discharge that is initiated between two plasma sheets can produce large-scale plasma occupying full inter-electrode volume. Such a discharge is the subject of the present investigation. Compared to the well-studied DBDs, almost no research data is available regarding electrical and fluid dynamic properties of such volumetype discharge arrangements. The spatial distribution of energy deposition to the gas within the breakdown volume depends on the discharge filamentation. At certain operating conditions, the transition from a diffuse to a constricted, or filamentary, discharge mode is usually observed for pulsed discharges [11]. The conditions for discharge contraction require special attention since this effect may increase the electrical energy coupled to the plasma and lead to a more complex post-discharge flow. Gas pressure is likely to play a major role in discharge uniformity [12, 13]. Studies have shown that pressure decrease has a stabilizing and elongating effect on the surface DBDs [8, 14, 15]. The effect of pressure variation on a pulsed volume discharge is explored in the present paper. Another factor of interest is the energy transfer from the discharge plasma to the gas. Studies of pulsed discharge plasmas in air have shown two energy thermalization stages with different time scales, usually referred to as “rapid” and “slow” heating [2, 16, 17, 18]. The rapid heating of gas within the break2

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down volume on a sub-microsecond time scale generates pressure waves or stronger blast (shock) waves. These waves can manipulate an external flow in a desirable manner by interacting with bow and attached shock waves, changing lift and drag coefficients or controlling flow separation [19, 20, 21, 22, 23]. Moreover, a pulsed volume discharge initiated in the presence of a travelling shock wave provides experimental realization of the classical Riemann problem - the rapid energy increase changes the Rankine-Hugoniot relations at the initial shock [24]. Various flow visualization methods have been employed to capture the post-discharge flow including discharge-induced vortices, shock/compression waves, and contact discontinuities: laser shadowgraphy [25, 26, 27], interferometric [28, 29] and schlieren techniques [30, 31], particle image velocimetry (PIV) [32, 33], etc. The comparison between experimentally measured and numerically predicted temporal flow evolution has been successfully applied to determine the fraction of the total discharge energy that is rapidly converted into gas heating [28, 25, 34, 31, 27]. On the contrary, the “slow” gas heating, which may occur on time scales ranging from tens to hundreds of microseconds, does not produce shock/pressure waves but generates thermal perturbation and strong density/viscosity gradients in the flow near the breakdown region. This residual heating has received more attention only in the last few years and its effect on the flow has yet to be properly elucidated. Recent studies suggest, however, that it may be related to formation of large-scale coherent structures in the flow and even dominate the discharge control authority, especially in applications regarding boundary layer transition and flow separation [16, 35, 36]. This paper studies the development and the induced fluid dynamics of a volume discharge initiated in quiescent air at low pressure. In the diffuse discharge mode, the energy deposition from the volume discharge is quasiuniform and the discharge plasma occupies the entire inter-electrode volume of 100×30×24 mm3 (figure 1(a)). In the constricted mode, most of the electrical energy is deposited into a single, long (24 mm in length) and narrow (less than 2 mm in radius) vertical plasma column (figure 1(b)). To the best of our knowledge, the size of column-shaped plasma, generated using any other discharge arrangement, has never exceeded 10 mm [2, 29, 31]. While keeping the applied input power constant, we analyze the changes in discharge morphology with pressure. For the constricted discharge mode, we perform PIV and high-speed shadow imaging to capture the expansion of the generated cylindrical shock wave and the heated gas channel from 0 to 40 µs after the discharge pulse. We also conduct computational fluid dynamics 3

Figure 1: Photographs of a diffuse pulsed volume discharge at p = 70 Torr (a) and a constricted plasma column at p = 140 Torr (b).

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(CFD) simulations to gain more insight into the evolution of the transient post-discharge flow. The comparison between the measured and computed flow evolution is used to determine the amount of electrical energy transferred into rapid gas heating and, thus, to quantify the discharge performance.

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2. Experiments

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2.1. Experimental setup The experiments were conducted in a discharge test chamber installed into a rectangular tube having a cross-section of 48 mm (width) × 24 mm (height) [24]. The end view of the discharge arrangement and the electrical circuit are shown in figure 2. Two opposite (top and bottom) walls of the discharge chamber were made of two 1-mm thick fiberglass (dielectric) plates. A pair of 100-mm long parallel copper electrodes was etched on each of the dielectric plates and separated by 30 mm. The other two opposing sidewalls were quartz glass windows and provided optical access to the chamber. Low pressure ambient air (p = 20–250 Torr) was used as a working gas. A main capacitor, C1 , was charged to 25 kV and connected to each electrode pair via capacitors C2 . The discharge of the main capacitor generated two distributed sliding discharges (plasma sheets), each covering a surface area of 100×30 mm2 on the top and bottom surface of the test chamber. These plasma sheets preionized the gas facilitating the initiation of a volume discharge between them [37]. The total electrical energy stored in the main capacitor (charged to 25 kV) was about W ∼ 0.71 J. Typical voltage waveforms for a similar discharge arrangement, not mounted within a shock tube facility, can be found in [38]. 4

Figure 2: Discharge test chamber (end view) and electrical circuit: R1 = 1 MΩ, R2 = R3 = 1 kΩ, Rshunt = 0.18 Ω, C1 = 2270 pF, C2 = 470 pF.

Figure 3: Schematic of the discharge test chamber (a) with the setup for shadow imaging; (b) with the PIV setup: 1 – light source (flashlamp or laser); 2 – diaphragm; 3 - converging lens; 4 and 16 - rotating prisms; 5 – digital CCD camera; 6 - pulse generator for the highspeed camera, the discharge and the light source; 7 – discharge power supply; 8 – digital oscilloscope; 9 - high-speed video camera; 10 – camera lens; 11 - discharge chamber; 12 PC; 13 - constricted plasma column; 14 – cylindrical shock wave; 15 - discharge electrodes; 17 - vertical laser sheet; 18 - PIV camera (LaVision Systems); 19 – PIV laser. The top wall of the chamber with the second set of plasma electrodes is not shown. The green dashed lines mark the area imaged by both experimental techniques.

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As expected, at constant applied voltage, the discharge morphology strongly depended on the initial pressure in the test chamber. Figure 1 shows two photographs of the discharge glow taken using a digital single-lens reflex camera Canon EOS 550D. We conducted the experiments in a dark room (the discharge was the only light source) and set the exposure time of the camera to infinity. At low initial pressures (a few tens of Torr), the discharge plasma optical emission was mostly uniform in the breakdown volume (figure 1(a)). As the initial gas pressure in the test chamber increased, the plasma uniformity decreased until the diffuse volume discharge became filamentary and eventually shrank into a narrow, 24-mm in length, constricted plasma column (figure 1(b)). In all the experiments, the plasma contraction always occurred close to the edge of the electrodes approx. 10 mm from one of the chamber side walls (as illustrated in figure 3). The discharge current waveforms were obtained using a high-voltage shunt connected to a digital oscilloscope. Two high-speed cameras - a streak camera BIFO K008 and a nine-frame camera BIFO K011 - provided a time-resolved measure of the light intensity emitted from the discharge plasma in the nearinfrared and visible spectral range. The cameras were setup perpendicular to the chamber window (in place of “9” in figure 3). The discharge optical emission in the spectral range of 370–850 nm passed through a 100 µm horizontal slit oriented parallel to the surfaces of the plasma sheets. The mean light intensity was calculated over a span of several pixels in the middle of the plasma column. The duration of discharge plasma glow was derived from 0.2–20 µs streak recordings for different discharge morphologies: diffuse (figure 1(a)) or constricted (figure 1(b)). 2.2. Flow visualization Time-resolved visualization of the flow dynamics induced by the contraction of the volume discharge was performed using high-speed shadowgraphy. Figure 3(a) schematically shows the test chamber with the shadowgraph optical setup. A high-speed camera captured the shadow images either with 320×192 pixels resolution at a rate of 100000 frames/s or with 128×48 pixels resolution at an increased rate of 525000 frames/s. The setup included two possible light sources: a 532 nm laser or a flash lamp. The camera exposure time was set to 1 µs. The acquired shadow images were enhanced during the post-processing by subtracting a reference (background) image and adjusting the brightness and contrast.

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Together with the shadowgraphy, the instantaneous velocity fields of the discharge-induced flow were obtained using a PIV system (figure 3(b)). The pulsed light source was a double-pulse Nd:YAG laser providing an average output of 180 mJ per pulse (9 ns pulse width) at a wavelength of 532 nm. It created a vertical laser sheet that passed through the axis of the plasma column and was oriented perpendicular to the side windows of the chamber (in the y-z plane). Solid seeding particles of titanium dioxide (TiO2 ), having a mean diameter of 1 µm and a density of 915 kg/m3 , were inserted into the test chamber. A rotating prism directed the light scattered by the particles to a LaVision Imager Pro CCD camera of 1600×1200 pixels resolution. The time delay between two laser pulses was set to 3 µs. We followed the induced flow dynamics for the first few tens of microseconds after the discharge pulse, when the shock wave front was within the PIV camera’s field of view. Therefore, the maximum repetition frequency of the PIV laser (up to 40 Hz) allowed capturing only one double-frame image in each experiment, for various delays after the discharge pulse. The image pairs were post-processed using a crosscorrelation algorithm implemented in the DaVis 8.3 software package from LaVision. The interrogation window size was 16×16 pixels with a 50 % overlap for the final iteration. Erroneous vectors were eliminated using a Q < 1.5 threshold for the correlation peak ratio and a median filter. Since the experiments were performed at pressures lower than 250 Torr, that posed a particular challenge for the PIV imaging due to the fast sedimentation of the tracer particles on the walls of the discharge test chamber. For example, at pressures around 150 Torr in the absence of an external flow, a critical decrease in the concentration of the tracer particles was observed already 1 min after seeding. Therefore, to maintain sufficient particle concentration in each experiment, we employed a special seeding procedure [39]. The procedure involved introducing the solid tracers using a Laskin nozzle from one side of the tube, while pumping from its opposite side was creating a flow of the tracers towards the test chamber. Following such excessive seeding, we sealed the chamber and then pumped it to the working pressure. The PIV measurements were carried out immediately after pumping before the seeding density decreased.

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3. Results and Discussion 3.1. Electrical and optical characteristics of the discharge Ambient pressure is known to have a profound effect on characteristics of plasma discharges. From the perspective of flow control, which is assumed to be performed at high altitudes, the investigations of the pressure influence on discharge characteristics at pressures lower than atmospheric are of particular importance. Here, we analyze the influence of pressure variations on the electrical and optical characteristics of the pulsed volume discharge. The volume discharge breakdown is preceded by the development of two sliding surface discharges (plasma sheets) that lasts around 30 ns. This UV-preionization makes it possible for the electric current to flow through the volume. Figure 4 presents typical waveforms of the discharge current measured at different initial air pressures. The voltage pulse amplitude was 25 kV. The corresponding side views of discharge plasma for each pressure value are also given. They show that the plasma uniformity decreases with increasing the air pressure until the plasma contraction occurs and the volume discharge transitions into a single large-scale “filament” (plasma column). The current waveforms show that, when the initial pressure is less than 50 Torr, there are usually few cycles of decaying current oscillation (figures 4(a)-(b)). With increasing the pressure up to 100 Torr (but before the contraction) the current waveforms become aperiodic with an increase in the electrical resistance of the inter-electrode gap (figure 4(c)). At pressures higher than 120–130 Torr (after the contraction) the waveforms are again periodic since the conductivity of gas in the breakdown region is also higher (figure 4(d )). The amplitude of the first current peak decreases with pressure for a diffuse (volume) discharge and remains at a constant level (500–600 A) for a constricted plasma column. The pressure dependence of the discharge current duration, as measured at half of the peak amplitude, is shown in figure 5. This value is, on average, 200 ns and overall does not exceed 400 ns. In the diffuse (volume) discharge mode the current duration increases as the gas pressure increases. It is probably because the reduced electric field (E/N) decreases with pressure increase resulting in lower ionization rates and longer times to achieve the electron density required for the discharge breakdown. Figure 6 shows time-resolved images of the pulsed discharge recorded using the streak camera BIFO K008 under four levels of initial air pressure in the test chamber: 90 (diffuse mode), 130, 140 and 160 Torr (constricted 8

Figure 4: Discharge current waveforms at four values of initial air pressure together with corresponding images of discharge glow. The voltage pulse amplitude is 25 kV.

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Figure 5: Duration of discharge current and discharge afterglow as a function of gas pressure. The arrow indicates the approximate transition from the diffuse discharge plasma to the column-shaped plasma.

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mode). Figure 6 also includes the corresponding photographs of discharge glow with marked positions of the horizontal slit of the streak camera and the plasma electrodes. Note that multiple less intense column-type glowing in figures 6 (b-d ) is due to optical reflection. The plots of relative light intensity as a function of time show that the rising time and the average duration of the diffuse (volume) discharge afterglow are 120 ns and 390 ns, respectively. The afterglow of the column-shaped plasma has approximately twice higher intensity that decays exponentially after discharge initiation. The afterglow duration of the plasma column increases with pressure (up to 250 Torr) reaching 5–6 µs and is significantly longer than in the diffuse mode. Typically, at ambient pressures lower than 100 Torr the discharge is diffuse and the contraction is not observed. At pressures around 100–150 Torr the volume discharge localizes into a straight 24-mm long column, and the glow intensity increases to a maximum value, and then the intensity decreases with further pressure increase. At pressures higher than 250 Torr the volume discharge regime does not develop - there are only two surface discharges glowing on the top and bottom of the chamber. The observed effect of pressure variations on the volume discharge morphology is similar to that reported for a different but much better explored discharge configuration - a DBD discharge. When the ambient pressure decreases below a certain level, the surface DBD plasma also transitions from filamentary (constricted) to quasi-uniform (diffuse) [8, 11, 15].

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The time-resolved evolution of a single plasma column up to 5.7 µs is given in figure 7. The duration of each frame is 100 ns (the minimum value allowed by the BIFO K011 camera), and time between the frames is 600 ns. The column radius, as measured at half the peak emission intensity, is rc = 1.2–1.5 mm. The visible size of the column in this image, however, appears slightly larger due to overexposure. The nine-frame camera recordings confirm the decay of the column-shaped plasma afterglow within several microseconds after the discharge pulse. According to figure 5, the average duration of the diffuse (volume) discharge afterglow is of the same order as the current duration whereas the afterglow duration of the column-shaped plasma is an order of magnitude longer than the current duration (few thousands vs. few hundreds of nanoseconds). Thus, the afterglow of the constricted plasma column continues for several microseconds after the cessation of the breakdown current. The time scale for rapid localized heating of gas, however, appears to be shorter than this afterglow time and comparable to the width of the discharge current pulse. 3.2. Experimental and numerical flow visualization Here, the PIV and shadow imaging were conducted separately and provided instantaneous 2D cross-sections of the discharge test chamber: in the y-z and the x-y planes, respectively (see Figure 3). Both flow visualization techniques showed that each discharge contraction is followed by the formation of three shock waves: an expanding cylindrical shock wave from the column-shaped plasma and two weaker quasi-planar shock waves from the plasma sheets (surface discharges). Figure 8(a) shows the temporal evolution of the flow induced by a constricted plasma column (the initial air pressure is p = 157 Torr) captured by time-resolved shadow imaging. The images were recorded at the highest available frame rate of the high-speed camera (525000 frames/s) and limited spatial resolution (only a central part of the test chamber, 5-mm in height, was captured). The first frame shows the induced flow 3.8 µs after the discharge pulse, and the inter-frame time is 1.9 µs. The images clearly visualize the central bright region of the discharge-excited gas that is separated from the ambient air by a contact discontinuity (contact surface, (2)). Parts of a cylindrical shock front (1) expanding away from this column-shaped region and the contact surface are also captured and their motion can be tracked.

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Figure 6: Time-resolved images of discharge plasma afterglow at: (a) 90 Torr (diffuse mode); (b) 130 Torr; (c) 140 Torr; (d ) 160 Torr (constricted mode). Yellow dashed lines mark the electrode location, red boxes mark the positions of a 3-cm-long horizontal slit for streak imaging.

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Figure 7: Nine-frame image of a plasma column evolution, from 0.1 to 5.7 µs after the discharge initiation, p = 124 Torr.

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As compared to the shock wave front, the position of the contact discontinuity appears to remain almost unchanged over time. Due to limited spatial resolution, the fronts of two quasi-planar shock waves from the surface discharges (plasma sheets) are yet outside the camera’s field of view. However, these fronts are visible on the full-frame images (figure 8(b) both at 4 and 12 µs after the discharge pulse. These two images also visualize the full-size column of discharge-excited gas separated from the ambient air by the contact surface (2). We note here that the full-frame shadow images demonstrate remarkable stability of the contact surface shape during the entire observation period (up to 25 µs after the discharge pulse). Figure 9(a) shows two example PIV images of the induced flow taken at later time instants, 22 and 32 µs, after the discharge pulse. The initial air pressure was p = 140 Torr. The length of the velocity vectors and the background color on the images are scaled by the velocity magnitude, and the same color bar is applied. A white horizontal arrow indicates the direction of the cylindrical shock front. Two vertical arrows indicate two quasi-planar shock waves induced by the sliding surface discharges (plasma sheets) that travel away from the opposite chamber walls towards each other. Their intersection occurs approx. 25–30 µs after the discharge pulse. Figure 9(a) captures the flow velocity field before, and figure 9(b) - after the intersection. The comparison of the PIV images at different time instants after the discharge reveal that the strength and the propagation speed of the cylindri13

Figure 8: A sequence of five shadow images of the post-discharge flow captured at a frame rate of 525000 frames/s (a) and two shadow images captured at 100000 frames/s (b): 1 – shock wave front; 2 – contact discontinuity. Initial air pressure is p = 157 Torr.

Figure 9: PIV vector fields 22 and 32 µs after the discharge pulse, p = 140 Torr. White arrows mark the directions of the moving shock fronts. Purple rectangles indicate the initial location of the discharge plasma.

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cal shock wave slightly decrease as it expands outwards, as well as the flow velocity behind the front. It is worth noting that inertia of the seeding particles becomes very prominent around the shock wave fronts and, thus, hinders quantitative analysis of the PIV images. The non-ideal particle tracking results in broadening of the wave front width and lower values of maximum measured velocity behind it. This error, however, can be efficiently quantified using numerical particle tracking methodology that incorporates particle dynamics into CFD simulations [33]. Figure 10(a) illustrates the flow dynamics resulting from the discharge contraction on a space-time diagram. The discharge breakdown creates a

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narrow plasma column with the subsequent formation of a cylindrical shock wave, a contact discontinuity (contact surface) and a rarefaction wave. The rarefaction wave propagates inwards to the center of the column, then reflects at the center and propagates back outwards trailing the shock wave. As the contact surface interacts with the rarefaction wave, its velocity decreases to zero and its expansion ceases. Figure 10(b) shows variations of the positions of the shock front and the contact discontinuity with time as measured from the time-resolved shadow images (at the center of the discharge chamber). The average initial radius of the plasma channel is schematically marked at t = 0 µs. The contact surface is found to remain almost stationary (at x ∼ 4 mm away from the center of the plasma column) starting from 5–7 µs after the discharge pulse. The shock front velocity appears to depend weakly on the initial pressure over the range of p = 150±15 Torr. Its average value is 550 ± 70 m/s (which corresponds to a Mach number of 1.4–1.8) and agrees well with the PIV data [40]. The formation of shock waves confirms the rapid thermalization of the discharge energy. This means that a large fraction of electrical energy is converted to heat faster than the acoustic time scale, determined as the ratio of the characteristic size of the plasma to the local speed of sound, that is ∼ 3 µs in the present case. The possible slow gas heating should occur within the volume of the discharge-excited region that is separated from the shockheated ambient air by a contact discontinuity. The raw PIV images indicate that no tracer particles remained within the breakdown volume. This implies that the region behind the contact discontinuity can not be resolved by the PIV method; the expansion of this region, however, can be followed using the time-resolved shadow imaging (Figure 8). Thus, it is possible to locate the volume of the discharge-excited air, where stochastic flow perturbations on a sub-millisecond time scale may take place. To gain more insight into the complex induced fluid dynamics and estimate the discharge energy efficiency, we conducted CFD numerical simulations. We employed an in-house 3D CFD code based on the solution of the compressible unsteady Navier-Stokes equations [27]. The solver implements a Godunov-type finite-volume numerical scheme with the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver for computing the convective fluxes at the control volume interfaces. The scheme uses the MUSCL approach with a minmod limiter for interpolation of the primitive variables at the volume interfaces and an explicit second-order Runge-Kutta routine for the time integration. The solver can be also run in parallel using the do15

Figure 10: Space-time diagram of the discharge-induced flow evolution (a)) and the comparison between experimentally measured (p = 135-165 Torr) and numerically calculated (p = 150 Torr, τp = 0 µs, ∆W = 0.15 J) positions of the shock wave (SW) front and the contact discontinuity (CD) (b)).

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main decomposition approach in combination with the MPI (Message Passing Interface) library. The computational domain contained only a part of the discharge test chamber, 24×24×48 mm3 in size, to reduce the computational costs. After a grid convergence study, a final mesh size was set to 300×300×600 Cartesian cells. The working gas (air) was treated as calorically perfect, with a constant heat capacity ratio (γ = 1.4). The pulsed energy deposition was modelled adding a source term into the energy equation, so that the total energy rapidly transferred into gas heating within a cylinder of radius rc and length L = 24 mm was ∆W . In the numerical simulations, we varied the value of ∆W (6 W ) until numerical predictions fitted best the experimentally measured dynamics of the shock wave front and the contact discontinuity. We have also tested several pulse widths, τp , from 0 (instantaneous energy deposition) to 5 µs, for the same value of total deposited energy ∆W . The 3D simulations provided better insight into the entire dischargeinduced fluid dynamics. They revealed that the cylindrical shock wave reflects from the closest side wall approx. 15 µs after the discharge pulse and travels back towards the breakdown region. The planar shock waves generated by the surface discharges are of weaker intensity but also influence the resulting flow field, for instance, by slightly accelerating the cylindrical shock. Figure 10(b)) includes the comparison between the CFD-predicted and experimentally measured dynamics of the shock wave front and the con16

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tact discontinuity. As noted before, the position of the contact discontinuity remains unchanged on the shadow images from approx. 5–7 µs after the discharge pulse. Similar dynamics in the numerical simulations was achieved for pulse widths τp not exceeding 1–2 µs. For longer energy pulses, the expansion of the contact surface stops at much later time instants after the energy deposition. This observation confirms that the gas heating, responsible for the induced flow dynamics, occurs on a sub-microsecond time scale. Due to the stochastic character of the discharge development and the experimental error, the best agreement between numerical and experimental data was observed for a range of ∆W values, 0.12–0.16 J. This means that around 20 % of the total electrical energy stored in the main capacitor is transferred entirely into gas heating within the single plasma column on a sub-acoustic time scale.

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4. Conclusions

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We have presented an experimental and numerical study of a single-pulse plasma discharge and the fluid dynamics induced by the discharge in lowpressure air. First, we have conducted electrical and optical measurements to fully characterize the development of a pulsed volume discharge with UVpreionization from two plasma sheets. The results indicate that under the same applied voltage pulse (25 kV), discharge contraction is a threshold phenomenon and strongly depends on the initial air pressure. At pressures around 100–150 Torr, the diffuse volume discharge shrinks into a straight narrow plasma column, 24 mm in length. We have found that the afterglow time of the column-shaped plasma is relatively long (1–6 µs). However, the rapid thermalization of the electrical energy (and the shock wave formation) occurs on sub-microsecond time scales that are comparable with the duration of the discharge current. We have performed flow visualization experiments to capture and quantify the evolution of the complex transient fluid flow induced by the discharge. The time-resolved shadowgraphy has shown that fast localized gas heating generates two cylindrical flow discontinuities: a shock wave and a contact surface. The space-time diagram of their evolution during the first 25 µs after the discharge has been obtained. The contact discontinuity separating the discharge-heated medium from the shocked ambient air remains almost stationary starting from 5–7 µs. The shock wave with an average Mach number of 1.6 expands with a slowly decreasing speed, and the velocity behind 17

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its front agrees with the PIV measurements. Both the shock wave and the contact surface are found to exhibit remarkable stability during the entire observation period. Finally, we have complemented the experimental flow visualization with the CFD simulations. Comparing the experimentally measured dynamics of the shock front and the contact discontinuity with the numerical predictions, we have estimated that about 0.12–0.16 J of energy is transformed into heat on a sub-microsecond time scale within a single plasma column. This flow analysis has also shown that the contact discontinuity, after interacting with a rarefaction wave reflected from the symmetry axis of the plasma column, stops its outward motion and becomes almost stationary several millimeters away from the axis. Thus, it is possible to locate the region of slow heating that may cause thermal perturbations on a sub-millisecond time scale. The slow heating effects, together with the shock (blast) waves induced by localized rapid heating of gas, determine the flow control authority of the pulsed nanosecond discharge with cylindrical symmetry. This work has been supported by Russian Science Foundation (Grant number 18-19-00672). The authors would also like to thank Dr Irina Mursenkova, Dr Fyodor Glazyrin and Dr Tahir Kuli-Zade for their assistance in preparation of the experiments. [1] D. D. Knight, Survey of Aerodynamic Drag Reduction at High Speed by Energy Deposition, Journal of Propulsion and Power 24 (6) (2008) 1153– 1167, doi:10.2514/1.24595, URL https://doi.org/10.2514/1.24595. [2] A. Montello, D. Burnette, M. Nishihara, W. R. Lempert, I. V. Adamovich, Dynamics of Rapid Localized Heating in Nanosecond Pulse Discharges for High Speed Flow Control, Journal of Fluid Science and Technology 8 (2) (2013) 147–159, doi:10.1299/jfst.8.147, URL https://doi.org/10.1299/jfst.8.147. [3] A. Starikovskiy, N. Aleksandrov, Plasma-assisted ignition and combustion, Progress in Energy and Combustion Science 39 (1) (2013) 61–110, doi:10.1016/j.pecs.2012.05.003, URL https://doi.org/10.1016/j.pecs.2012.05.003. [4] Y. Ju, W. Sun, Plasma assisted combustion: Dynamics and chemistry, Progress in Energy and Combustion Science 48 (2015) 21–83, doi:10.1016/j.pecs.2014.12.002, URL https://doi.org/10.1016/j.pecs.2014.12.002. 18

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