An Investigation into the Sensory Application of DBD Plasma Actuators for Pressure Measurement

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1 An Investigation into the Sensory Application of DBD Plasma Actuators for Pressure Measurement Monique M. Hollick 1, Maziar Arjomandi 2, Benjamin S. Cazzolato 3 The University of Adelaide, Adelaide, South Australia, 5005, Australia This paper investigates the effect of air pressure on the current used by Dielectric Barrier Discharge (DBD) plasma actuators and the voltage limits for plasma production in these actuators. The purpose of this research was to determine whether DBD plasma actuators have potential for application as a pressure sensor at sub-atmospheric pressure conditions. It was found that these actuators were sensitive to air pressure and possessed a distinct, non-linear relationship between the electrical current consumed by them and ambient pressure. It was also found that lower and upper voltage limits for plasma production increased approximately linearly with pressure. p = Air pressure d = Electrode gap d m = Molecular diameter N A = Avagadro s number T = Temperature R = Universal gas constant λ = Mean free path length E = Electric field α = Ionisation constant Nomenclature 1. Introduction Dielectric Barrier Discharge plasma actuators have recently attracted much attention for their potential for flow control applications. They are able to generate small propulsive forces due to collisions of neutral air molecules with accelerating plasma ions and have the ability to actively alter the flow of air in nearby areas via an ionic wind. It has been observed that plasma actuators are sensitive to a variety of atmospheric conditions, including air velocity, humidity and air pressure, which exposes them to many potential practical applications. The advantages of the employment of DBD plasma actuators as pressure sensors are numerous. Being a purely electrical device, these actuators do not present the disadvantages regarding weight, reliability, wear, bandwidth limitations and complicated heat transfer relationships inherent in most mechanical devices. Furthermore, if they are to be used as pressure sensors they can easily be embedded into the structure of the body to which they are applied, and they do not have damageable parts found in common dynamic pressure sensors such as hot wires or pitot tubes. Due to the short timescale of plasma formation, DBD actuators have relatively fast response times, particularly with respect to flow-based and other mechanical sensors. They are also capable of making comparatively high bandwidth pressure measurements and are operable in a range of atmospheric conditions, inferring that they 1

2 would be particularly reliable and effective as sensors for aerospace and commercial airflight applications. There have recently been a number of investigations into the effect of pressure on the body force and velocity profiles produced by DBD plasma actuators. Matlis et al [7] investigated the feasibility and advantages of using plasma actuators as a hypersonic anemometer based on the actuator s sensitivity to flow velocity. They found that the plasma actuator was sensitive to the mean and fluctuating components of mass flux up to Mach 5, with high frequency response without compensation and improved signal to noise ratio relative to typical hot-wire sensors. It was also determined that the plasma actuator was operable at low static pressures. Abe et al [1] considered the effect of pressures from 0.2 atm to 1 atm on the induced actuator thrust, resulting from ion momentum transfer to neutral particles, for various gases. This study found that the maximum thrust in air was produced at around 0.7 atm, indicating that the mechanism for momentum transfer was dependent on air pressure. They explained this in terms of a sum of effects caused by pressure reduction shorter pulse lengths and a wider region covered by the pulses, in conjunction with an increase in mean path length and an increase in electrical power. Benard et al [2] explored the effect of flow velocity and mass flow rate for pressures between 0.2atm and 1atm and demonstrated similar findings to Abe et al [1]. They found that flow velocity and mass flow rate initially increased with pressure before exhibiting maximum values at 0.6 atm and dropped off significantly thereafter. They proposed that this phenomenon resulted from a compromise between the higher ionisation level and more extended plasma region at lower air pressures with the greater number of momentum transfers by collision at higher air pressures. Versailles [13] studied the effects of higher than atmospheric pressures on velocity profiles and the induced body forces and revealed nonlinear reductions in both parameters with increasing pressure, which agrees with the trends presented by Benard et al [2] and Abe et al [1] of decreasing values beyond sub-atmospheric pressures of approximately 0.6 atm and 0.7 atm respectively. Whilst there has previously been significant research undertaken with respect to the flow control and force production capabilities of these actuators at different pressure conditions, there has been relatively little investigation into the effects of air pressure on the current and power consumption in DBD plasma actuators and their subsequent feasibility as pressure sensors for aerospace and commercial airflight applications. Abe et al [1] and Benard et al [2] revealed that the time-averaged electrical power consumption decreased with increasing air pressure from 0.2atm to 1atm, however, the precise relationship of physical model for this trend is yet to be fully formed. Chartier et al [4] explored the sensitivity of DBD plasma actuators to air pressure by investigating the influence of pressure on the current waveform and RMS values. They found that the amplitude of the current spikes in the time series data increased with decreasing pressure, shown in Figure 1 (a). The study also revealed high sensitivity of the actuator s current waveform to pressure in the frequency range of 3x10 5 to 3x10 6 Hz after spectral analysis of the filtered signal. In particular, it was determined that there is a reduction in the RMS current with air pressure which follows a near quadratic relationship, as shown in Figure 1 (b). 2

3 (a) (b) Figure 1 (a) Current waveforms at different pressures showing larger and more frequent current spikes at decreasing pressures and (b) Filtered current waveform RMS with respect to absolute pressure [4]. The objective of this study was to further investigate, both theoretically and experimentally, the effect of air pressure on the current and power consumption of the DBD plasma actuator and to explore the limits of plasma production with respect to applied voltage, at various air pressures in order to examine the suitability of these actuators for pressure sensor applications at sub-atmospheric pressure conditions. For this purpose, a theoretical model, based on the Townsend mechanism and the disparity between the plasma production mechanisms in each AC half cycle, was constructed. A simple experimental set up using a DBD actuator in a pressure dome is implemented to investigate the sensitivity of the power consumed and the current used by plasma actuators to pressure. 2. Theoretical Models 2.1 Pressure Current Relationship The electrical power consumed by a DBD plasma actuator can be attributed to the energy required to cause the electron avalanche phenomena associated with dielectric barrier discharge, as well as to accelerate the ions. Heating of the plasma due to increased velocities 3

4 and light emission due to electron-ion recombination are bi-products of these two effects and therefore the energy associated with them need not be explicitly considered. Electrical power, which can be expressed as P elec = VI, is proportional to the RMS current if the RMS voltage is constant. The RMS current is dependent on the number of electrons which reach the anode per second, the vast majority of which result from secondary ionisation due to the Townsend mechanism [12]. It is well-known that the mechanisms of plasma production vary in two AC half cycles. During the positive half cycle, when the electrons are accelerated towards the exposed electrode, no electric field shielding occurs. Orlov et al [10] describes the mode of discharge to be streamer-type. The negative half cycle involves electrons accelerating towards and arriving on the dielectric surface, causing electric field shielding and resulting in a glow-type discharge. In the work of Boeuf et al [3], the current pulses in the positive half cycle are observed to be approximately one hundred times larger in amplitude and twenty to thirty times less frequent than those associated with the negative half cycle. In addition, the time integrated electrohydrodynamic (EHD) force, which depends on the number of ions and therefore the number of electrons, is determined by Boeuf et al [3] to be approximately five times greater in the positive half cycle. These two findings suggest that the positive, streamertype discharge half cycle contributes roughly five times more towards the RMS current than the negative glow-type discharge half cycle. The Townsend mechanism is the process by which a very small number of electrons are accelerated by an electric field and cause further ionisations through collisions with neutral molecules, initiating an avalanche effect. The ionisation constant, α, describes the number of electrons produced per avalanche per unit length in the Townsend mechanism, and is known to be a function of the applied electric field and the pressure. The total number of electrons produced per avalanche is found by the exponent of the product of the ionisation constant with the distance to the anode. For a streamer-type discharge, Meek [8] described the relationship between α with the electric field, E (kv/cm), electrode gap, d and air pressure, p (torr), as αd + ln α = ln p (E ln (pd) ) (1) p 2 For a constant electric field of E = 45kV/cm and electrode gap of d = 1mm, the number of electrons per avalanche and air pressure is found to possess a power law relationship when Equation (1) is solved for α for different air pressures and the exponential relationship between the ionisation constant and the number of electrons per avalanche, n = e αx, is employed (Meek [8]). The best fit to the number of electrons per avalanche with pressure is found to be a power law with a power constant determined by Matlab to be The fit relationship for the determined number of electrons is given by Equation (2) and plotted in Figure (2), n = 11240p (2) 4

5 Al h E Figure 2 Power law determined for the number of electrons per avalanche determined by Equations (1) and (2) for an electric field of 45kV/cm and electrode gap of 1mm. The relationship between the ionisation constant and the pressure in the glow discharge regime is often expressed as (Kind et al. [5]) α = Ape Bp E (3) where p is in bar and E is in kv/mm; A and B are empirical constants. The ionisation constant in this half cycle has a much more rapid decrease with pressure due to the exponential decay component in the relationship. Although this half cycle only makes a minor contribution to the RMS current, it is expected to cause the value of the power in the relationship for the RMS current given by Equation (2) to become more negative. In addition, Paschen s Law [11] indicates that the breakdown electric field increases with increasing air pressure between 0.2 and 1 atm. This effect would result in less time per half cycle for micro-discharges and therefore cause a more rapid reduction in current with pressure and subsequently lower the power constant as well. A qualitative expectation is that RMS current decreases non-linearly, approximately with the inverse square root of the air pressure, following a relationship of general form I rms = f( 1 p ) (4) 2.2 Voltage Limits for DBD Plasma Production The breakdown voltage in air is dependent on the pressure and gap distance, described by Paschen s Law [11]. The relationship between the breakdown voltage and product of pressure and gap distance is given as V b = B(pd) ln ( Apd (5) ln 1 ) ϒ 5

6 where A, B and ϒ are constants dependant on air conditions. At a constant gap distance, for pressures between 0.2 atm and 1atm, the breakdown voltage increases with increasing pressure. It is well known that for gaps of the order of a millimetre, this relationship has a linear approximation: V b = 30pd kV [6]. It is expected, therefore, that the minimum voltage for plasma generation in the DBD actuator increases approximately linearly with increasing pressure. As the voltage to gap ratio increases, the plasma discharge regime changes. For current densities greater than several mam -1, Moreau [9] suggests that the plasma discharge regime changes from glow to filamentary. As the pressure increases, the mean free path between particles decreases, therefore a higher voltage must be applied in order to accelerate the ionised electrons by a sufficient amount to achieve high enough kinetic energies to initiate the filamentary discharge regime. The applied electric field required, equal to the voltage to gap ratio, is proportional to the air pressure in a simple collisional model where the acceleration of charged particles is due to the electric field and all momentum is transferred to the neutral particles in collisions such that v 2 f = 2qE λ (6) m where v f is the average final velocity of the charged particle, q is the elementary charge, m is mass of the particle and E is the applied electric field. The mean free path length, λ, of these particles is given by the following equation, as expressed by Chartier et al [4] RT λ = (7) πd 2 m N A p 2 where R is the universal gas constant, T is the temperature, d m is the diameter of the molecules and N A is Avagadro s number. The square of the average final velocity of charged particles, and therefore their kinetic energy, is proportional to E/p, therefore it is expected that the upper limit of the voltage for DBD plasma production increases approximately linearly with pressure assuming that the required kinetic energy for the filamentary regime remains uniform at all pressures. As such, it is expected that both the lower and upper limits of voltage for DBD plasma production increase approximately linearly with pressure. 3. Experimental Setup A single Dielectric Barrier Discharge plasma actuator consisting of two aluminium electrodes of 140mm length, 12.7mm width and 50µm thickness was employed for plasma production as shown in Figure 3a). The electrodes were placed, without gap, on either side of a 2mm plexiglass dielectric plate and the lower electrode covered with insulating Kapton tape. The actuator was placed in a pressure dome, with a type-k thermocouple for temperature monitoring, connected to a vacuum pump capable of reducing the air pressure inside the dome from 1 atm down to 0.1 atm. The pressure was measured using the analogue gauge on the vacuum pump (Figure 3b). The exposed electrode was driven by an AC voltage produced by a Minipuls2 plasma generator designed for voltages up to 24kV p-p (8.5kV rms ) and frequencies of 5 30kHz. The voltage and current measurements were made using a PicoScope 5402 PC oscilloscope with a sample rate of 1GS/s, 250MHz bandwidth and 8 bit resolution. Throughout this experiment, 6

7 the RMS output voltage on the oscilloscope was kept constant at 4.5V, corresponding to the peak-to-peak input voltage of 12.73kV due to the nominal 1:1000 output voltage division ratio of the plasma generator. A sinusoidal wave with a frequency of 13 khz was employed, whilst the chamber pressure was varied, the applied voltage was held constant and the current produced was measured. Kapton tape encapsulated electrode Aluminium tape (140mm overlap) Figure 3a) Top view of plasma actuator Plasma generator Plasma actuator Vacuum pump Pressure gauge Figure 3 b) Experimental set up including the vacuum pump attached to the pressure dome containing the plasma actuator, thermocouple and the attached plasma generation equipment. 4. Experimental Results 4.1 Pressure Current The voltage and current waveforms produced by the PicoScope at 1atm are presented in Figure 4, showing the sinusoidal voltage (blue) and the current waveforms (red). The current consumed is related to the PicoScope voltage reading by the ratio 10V/A. It can be seen in this figure that during the positive half cycle, larger and less frequent current pulses are present, generally around the peak current values. These large pulses are not present during the negative half cycle, where smaller pulses are produced and few at maximum amplitude currents. This current waveform supports the aforementioned assumption that the positive 7

8 half cycle contribution to the RMS current produced is significantly greater than that of the negative half cycle. The phase difference between the waveforms, due to the capacitively coupled nature of the plasma production, indicates that it is not feasible to calculate the consumed power from the product of the RMS voltage and current. Figure 4 The voltage (blue) and current (red) waveforms produced at 1atm, showing the dominant current pulses during the positive half cycle. The RMS current was recorded from the PicoScope readout as the pressure was reduced from 1atm down to 0.2atm in 0.2atm increments. Three measurements were made at each pressure and the mean values were plotted in Figure 5 along with a curve fitted to the data, the form of which is chosen to produce the minimum sum of squared errors. The fit, shown in Figure 5 is a power law with the index of , which is within the scope of the prediction made in the theoretical model as given by Equation (4). 8

9 C Figure 5 Power law curve fitted to the experimental data for the mean current RMS (ma) versus absolute pressure (atm). This fit has a sum of squared errors of and an R-squared value of which indicates that this fit is a high fidelity prediction of the experimental results. In Chartier et al s [4] work, Fourier Transforms were performed on the current waveforms and a spectral analysis was carried out after passing the raw signal through a high pass filter. The RMS current values were then calculated from the frequency spectrum in the highly sensitive range of 3x10 5 to 3x10 6 Hz at each pressure. However, in the work presented in this article, spectral analysis was not performed on the signals and the RMS current was determined through reading the average RMS value displayed on the PicoScope. This method of current measurement is sufficiently accurate for the accuracy permitted by the analogue pressure measurements, and reduces calculation time through simplicity. The results above are in partial agreement with the work of Chartier et al [4], who shows a decreasing current at a decreasing rate with respect to increasing pressure, but propose a quadratic fit to the data. Therefore, these results support the theoretical hypothesis developed in this paper that plasma actuators are sensitive to air pressure and that the RMS current produced decreases nonlinearly with a declining rate as the pressure increases. Further work needs to be done in order to reconcile experimental observations with a theoretical model based of the physical behaviour of the plasma production at varying air pressures. 4.2 Voltage Limits for Plasma Production The limits of plasma production with respect to the applied voltage were considered at each pressure interval. The minimum and maximum voltages were determined, for the same actuators employed in the previous section, by examining the average RMS voltage reading on the PicoScope as the power source voltage was adjusted at 13kHz. The minimum voltage was determined by noting the average RMS voltage on the PicoScope when plasma production ceased. The estimation of maximum voltages was difficult due to the possibility of arcing at high voltages and the limits of the plasma generator. Therefore, the maximum 9

10 voltage measurements displayed here are slightly lower than what is actually possible for the production of DBD plasma discharge. Figure 5 shows the lower and upper limits of the plasma production at varying pressures, where the shaded region indicates the range for plasma production. In the bottom region, no plasma is produced, and in the top region, the filamentary regime is entered and sparks initiated. Both limits increase with increasing pressure, in addition to a slight increase in the voltage range with pressure. The lower voltage limit increases approximately linearly with increasing pressure, in agreement with the theoretical hypothesis that Paschen s Law for the breakdown voltage in air increases approximately linearly with pressure at electrode gaps of the order of millimetres. The upper limit of the voltage, which corresponds to the threshold for production in the filamentary regime, was predicted to increase in a roughly linear fashion in the collisional model of the plasma discussed in this paper. Since the kinetic energy required is independent of pressure and proportional to the squared final velocity of charged particles, and subsequently the ratio E/p, the voltage required is directly proportional to the air pressure. This hypothesis is also reflected in the experimental results shown in Figure 5. Figure 5 The lower and upper limits of the RMS voltage for ranging pressures at 13 khz. The shaded region indicates the range for plasma production, the bottom region represents no plasma production and the top region is where the filamentary regime is entered and sparks initiated. 5. Conclusions In this work the sensitivity of plasma actuators are sensitive to pressure with the purpose of application as a pressure sensor was investigated. This study suggests that there is a distinct relationship between the current production of a DBD plasma actuator and the air pressure. As the pressure is increased from sub-atmospheric 0.2atm up to 1 atm, the current decreases, and it appears to follow a power law relationship with a power index of , indicating that the current is close to being inversely proportional to the square root of the air 10

11 pressure. This result is within the scope of the predicted theoretical outcomes, which assumes that the RMS current is dominated by the positive half cycle, streamer-type micro-discharges. The lower and upper voltage limits for plasma production both increase with increasing pressure in an approximately linear fashion, as theoretically predicted. The lower limit trend can be explained Paschen s Law, whilst the upper limit trend can be attributed to the reduction in mean free path at increased pressures which requires higher voltages to produce sufficient charged particle kinetic energies. In order for plasma actuators to be implemented as pressure sensors, it is necessary to establish a more accurate and quantitative theoretical model for current production with pressure variation which correlates closely with experimental results. This will likely require more extensive numerical techniques and computer modelling. The lower and upper limits of DBD plasma production should also be investigated more closely in order to determine the voltage requirements for employment as a pressure sensor. Acknowledgements The authors would like to acknowledge the support and financial assistance from The Sir Ross and Sir Keith Smith Fund. Thanks is also extended to Mei Cheong and Stephan Wolf, of the University of Adelaide, for their assistance in the experimental work featured in this report. Acknowledgements must also be given to the Electrical and Mechanical Engineering Workshops at the University of Adelaide for their expertise and support. Disclaimer Research undertaken for this report has been assisted with a grant from the Smith Fund ( The support is acknowledged and greatly appreciated. The Smith Fund, by providing for this project, does not verify the accuracy of any findings or representations contained in it. Any reliance in any written report or information provided to you should be based solely on your own assessment and conclusions. The Smith Fund does not accept any responsibility of liability from any persons, company or entity that may have relied on any written report or representations contained in this report if that person, company or entity suffers any loss (financial or otherwise) as a result. References 1 Abe T., Takizawa Y. and Sato S., A parametric experimental study for momentum transfer by plasma actuator, AIAA Journal, , Benard N., Balcon N. and Moreau E., Electric wind produced by a surface dielectric barrier discharge operating in air at different pressures: Aeronautical control insights, Journal of Physics D: Applied Physics, 41, (5 pp), Boeuf J,. Lagmich Y., Unfer T., Callegari T. and Pitchford L., Electrohydrodynamic force in dielectric barrier discharge plasma actuators, Journal of Physics D: Applied Physics, 40, , Chartier B., Arjomandi M and Cazzolato B, An investigation on the application of DBD plasma actuators as pressure sensors, AIAA Proceedings, , Kind D., Feser K., High-Voltage Test Techniques, second ed., Newnes, Oxford,

12 6 Lux J., High Voltage Experimenter s Handbook Paschen s Law, 2004, Available at < Accessed 29 th January Matlis E., Corke T. and Gogineni S., A.C. plasma anemometer for hypersonic mach number experiments, AIAA Paper , Meek M., A theory of spark discharge, Physical Review, 57, (1940) 9 Moreau E., Air-flow control by non-thermal plasma actuators, Journal of Physics D: Applied Physics, 40, pp , Orlov D., Font G. and Edelstein D., Characterisation of discharge modes of plasma actuators, AIAA Journal, 46, pp , Paschen F., Wied. Ann., 37, 69, Townsend J., The conductivity produced in gases by the motion of negativelycharged ions, Nature, 62, pp , Versailles P., Gingras-Gosselin V. and V. Duc, Impact of pressure and temperature on the performance of plasma actuators, AIAA Journal, 48, 4, pp ,