Thermal characterisation of dielectric barrier discharge plasma actuation driven by radio frequency voltage at low pressure

In this study, the thermal characterisation of dielectric barrier discharge plasma actuation driven by radio frequency (RF) voltage waveform at low pressure is studied. The RF discharge images and voltage–current waveforms are quite different under 3 and 40 kPa. The thermographic method has been proposed for the spatial–temporal temperature field on the actuator surface. At 3 kPa, the high-temperature region is mainly concentrated on the surface of the high-voltage electrode. Along the spanwise direction, the surface temperature gradually increases until it reaches the maximum at the edge of the electrode and then decreases. Similarly, in the chordwise direction, there also exists the maximum value on the surface of the electrode. After discharge starts, the surface temperature rises rapidly, and subsequently, the increasing slope of temperature curves gradually decreases until thermal equilibrium has been reached at about 100 s. The effects of the pressure, duty cycle, and operating power on the thermal characterisation are also investigated experimentally. At low pressure, the discharge mode is diffuse glow discharge, and the high-temperature region covers the whole electrode. As the pressure increases the surface temperature ascends non-linearly, while the surface temperature is linearly dependent on the duty cycle and operating power.


Introduction
As a new active control technology, plasma flow control technology has become the research frontier of airflow control [1][2][3].
One promising plasma actuation type is radio frequency (RF) discharge plasma actuation, in which the applied voltage oscillates at frequencies of up to MHz to sustain the discharge primarily through electron diffusion, as investigated in [4,5].Apart from high heating efficiency, the RF discharge has the advantages of high stability in the high-speed airflow and convenient power regulation, which has wide application prospect in flow control [6][7][8].Klimov et al. conducted the plasma flow control experiment using a surface RF plasma actuator at Mach number 0.4.It is revealed that the surface pressure is increased up to 10-30% and stagnation pressure is decreased up to 15-30% at plasma on [9].
Moralev et al. applied RF dielectric barrier discharge plasma actuation on a NACA 23012 airfoil model and found that at 13°a ttack angle drag coefficient is reduced by 40% with increasing frequency modulation [10].
Kazansky et al. carried on the airfoil flow control experiments of RF discharge under the frequency of 0.35 MHz.Due to the RF discharge plasma actuation, the separation bubble size is reduced and the separation point is shifted downstream by 25% chord length [11].
Compared with dielectric barrier discharge driven by a sine high voltage with the frequency of several kHz [12], the maximum induced velocity caused by the RF dielectric barrier discharge is too little to have the capability of flow actuation [13].Therefore, the flow control mechanism of RF plasma aerodynamic actuation may not be based on the velocity of the induced flow.However, the RF discharge has a significant heating effect that may affect the shock wave and improve the performance of the supersonic aircrafts [14,15].
Leonov et al. used a 27 MHz RF power supply to study the high-frequency filamentary discharge actuation characteristics.The experimental results showed that the rotational temperature of the high-frequency plasma can reach 4000 K under the stationary condition of operating pressure 120 Torr [16].
Wang et al. experimentally investigated the thermal and induced flow velocity characterisation powered by RF.It is revealed that the maximum dielectric surface temperature is higher than an alternating current power supply in dozens of kHz [17].
Low pressure is regarded as the typical working environment of aircraft, at which the plasma actuation characterisation is quite different from that at atmospheric pressure [18,19].Liu et al. found that a transition between the striated and non-striated modes for capacitively coupled RF CF4 plasmas can be observed by changing the pressure [20].Tian et al. studied the characteristics of surface dielectric barrier discharge by using nanosecond pulse power under different pressure and the result showed that the discharge length, brightness, and discharge power increase with the pressure decreasing under 3650 Pa [21].
However, up to the moment, there is a dearth of research on the thermal characterisation of RF discharge at low pressure.With this motivation, the spatial-temporal temperature field distribution of dielectric barrier discharge plasma actuation driven by RF voltage under low pressure has been studied, and the effects of the pressure, duty cycle and operating power on the thermal characterisation are also investigated experimentally.

Experimental setup
The experimental setup is reported in Fig. 1.For uniform and stable plasma generation, the actuator is powered by a RF power amplifier (Model AG1017L).The operation frequency can be adjusted from 10 kHz to 10 MHz continuously, and the maximum output power is 500 W. In addition, the impedance matching circuit is connected between the discharge actuator and RF generator, which can not only decrease the power loss but also increase the operating power of the actuator.
DBD discharge temperature has been evaluated by using a FLIR infrared camera (SC7300M) in the 3.7-4.8μm spectral range.Its temperature range lies between −20 and 1500°C with an accuracy of ±1%, and the distance between the infrared camera and plasma actuator is about 40 cm.
The plasma actuator consists of two tungsten electrodes mounted on either side of the dielectric.The high-voltage electrode and grounded electrode are both 2 mm wide and 26 mm long, and the electrode gap is 1 mm.ceramics (boron nitride) characterised by high melting point, high hardness and good insulation.During the experiment, the actuator is installed inside a vacuum chamber for the desired air pressure by pumping up air from the chamber.

RF discharge under 3 and 40 kPa
Fig. 2 shows the discharge images and voltage-current waveforms of RF discharge under 3 and 40 kPa.The experiment conditions are as follows: the discharge frequency is 0.56 MHz, the operating power is 95 W, and the duty cycle is 10%.It can be observed from Fig. 2a that the discharge is diffuse glow discharge, while many small discharge channels appear in Fig. 2b, which results from diffuse-to-filament discharge transition [22].The voltage waveforms are both symmetrically distributed in the positive and negative half-cycles because the size and the shape of two electrodes on the actuator is exactly the same, resulting in self-bias on the electrodes approximately negligible.However, the peak to peak voltage at 3 kPa is less than that of 40 kPa.In fact, based on the basic principle of gas discharge, the plasma generation process is determined by the reduced electric field E/N [23].Obviously, the particle concentration at 40 kPa is higher than that at 3 kPa, which makes it more difficult to discharge at a higher pressure where higher discharge voltage is required.What's more, at 3 kPa the current waveform has two peaks per cycle, whereas many burrs appear at 40 kPa due to the filamentous discharge mode.In addition, phase displacement can be observed between the voltage and current waveform because the actuator is the capacitive load.

Spatial-temporal temperature field distribution on the actuator surface
In this experiment, the surface temperature of the actuator is measured by using an infrared thermal imager.However, the emissivity of the actuator surface is not strictly equal to one, resulting in the experimental error in the measured value.To get the exact surface temperature, the relationship between the actuator surface temperature and the measured temperature is mentioned as follows [24]: where ε is the actuator surface emissivity, T measure is the measured temperature by the infrared thermal imager, T surface is the actuator surface temperature, T gas is the atmospheric temperature of the experiment.Then the actuator surface temperature formula can be deduced ( The experimental room temperature is 25°C, the actuator surface emissivity equals to about 0.8 by experimental calibration. Based on this method, the thermogram of the temperature field distribution on the actuator surface is obtained in the experimental case of the duty cycle of 5%, the operating power of 85 W, the discharge frequency of 1.41 MHz, the pressure of 3 kPa and run time of 100 s.As shown in Fig. 3a, to make the discharge area clearer, the high-voltage electrode is represented by a rectangle.Also, the unit of the temperature value is degree centigrade (°C).Obviously, the higher dielectric surface temperature is mainly distributed on the electrode surface corresponding to the discharge plasma distribution in Fig. 2. Fig. 3b represents the temperature variation along the spanwise direction (X-direction) under different ordinates (Y = 6.2, 6.8, 7.5, 8.1, 8.8 mm).For each curve, the surface temperature gradually increases until it reaches the maximum at X = 13 mm and then decreases.The surface temperature curve of Y = 6.8 mm is higher than any other curve.Fig. 3c shows the temperature variation along the chordwise direction (Y-direction) with X = 13 mm.The variation along the chordwise direction is similar to that of the spanwise direction, and there also exists the maximum value on the surface of the electrode.It can be found that at low pressure the temperature field distribution is quite similar to that previously observed in the RF surface barrier discharge at atmospheric pressure [17].
The temporal distribution of the actuator surface temperature is analysed combined with the curves of the surface temperature versus time at different pressures (0.6-100 kPa) shown in Fig. 4. As discharge begins, the actuator surface temperature gradually increases until saturation, which occurs when thermal equilibrium has been reached at 100 s.It can be observed that there still exist burrs on the temperature curves, which are much smaller than those at atmospheric pressure [17].From the previous research at low pressure, glow discharge plasma is evenly covered on the electrode gaps and the discharge heating is nearly uniform [22].In this case, without large temperature fluctuation, the burrs on the temperature curves become smaller.
It has been confirmed that the surface temperature of the actuator is closely related to the electrical parameters and the actuator geometrical parameters [25,26] (3) where t is the discharge run time, T plasma is the temperature of the discharge plasma which is equal to T surface when the thermal equilibrium has been reached, T o is the atmospheric temperature at the initial time of discharge, h is the heat transfer coefficient, α is the thermal diffusivity of the actuator dielectric, λ is the thermal conductivity of the actuator dielectric.Obviously, the variation of the actuator surface temperature can be predicted from this formula, and electrical parameters and actuator geometrical parameters mainly determine the value of T plasma and τ.
To verify the applicability of the formula the data fitting is needed.From Fig. 5a it can be found that the experimental data and theoretical values fit well at 60 kPa with τ = 0.03609 and T plasma = 116.08.To predict the temporal distribution of the actuator surface temperature under any pressure, the variation of T surface and τ is calculated and shown in Fig. 5b.In each case, the determination coefficient r 2 is approximately equal to one, which means the fitting degree is very high.Therefore based on these curves, the temporal distribution curve under different pressures can be roughly estimated when other conditions remain unchanged.

Temperature measurements under different pressures
Keeping duty ratio at 5%, operating power at 131 W, and discharge frequency at 1.41 MHz, the thermograms of the RF discharge under different pressures are shown in Fig. 6.As seen from the images, the high temperature is located at the high-voltage electrode edge, and the temperature of the plasma discharge region gradually increases with the pressure rising.The maximum surface temperature (153°C in Fig. 6j) is higher than that generated by a sine high voltage with a peak-to-peak voltage of 33 kV and frequency of 1 kHz [25].
It is obvious that the actuator surface temperature is proportional to the energy of a single cycle, and the variation of energy of the single cycle with pressure has been obtained by analysing the Lissajous figures [22].With the increase of the pressure, the area of the Lissajous figure and energy of the single cycle gradually ascend.Note that the total capacitance also changes significantly with the pressure, which is affected by the coverage area of the plasma on the actuator surface.Under higher pressure, the gas density in the vacuum chamber is higher and the diffuse-tofilament discharge transition occurs [22], therefore the coverage area of the plasma on the actuator surface is reduced as well as the total capacitance.As a result, the resistance value of the actuator is affected, which leads the increase of energy of the single cycle.The evolution of maximum surface temperature with the pressure in Fig. 7 also agrees with the above analysis.

Temperature measurements under different duty cycles at 3 kPa
Fig. 8 shows the thermograms of the RF discharge under different duty cycles.The experimental conditions are as follows: the pressure is 3 kPa, the operating power is 131 W, and the discharge frequency is 1.41 MHz.The overall temperature of the RF discharge is lower than discharge under atmospheric pressure [17].With the increase of the duty cycle, the high temperature region becomes larger, and its spatial temperature field distribution is different from that of nanosecond-pulse discharge [28].
According to the definition, the duty cycle only represents the length of the pulse in the pulse period, which has nothing to do with the discharge characteristics [22].The relationship between the energy required to heat and the duty cycle can be approached as follows: where Energy heat is the energy required to heat, T pulse /T period is the duty cycle, Δt is the time that the system reaches the heat equilibrium, η is the energy exchange efficiency, Power is the operating power of the RF power.Keeping other conditions fixed, with the duty cycle increasing, the energy required to heat also increases, which leads to a linear increase of the surface temperature.As shown in Fig. 9, when the gas pressure is 3 kPa, the maximum surface temperature evolves with the duty cycle as where a = 21.47 ± 1.10 and b = 938.49± 24.62 are best-fit values with the determination coefficient r 2 = 0.9959 which confirms the above analysis.

Temperature measurements under different operating powers at 3 kPa
In this subsection, the spatial evolution of the surface temperature with the operating power varying from 51 to 148 W is studied, and the experimental conditions are as follows: the discharge frequency is 1.41 MHz, the duty cycle is 5%, and the pressure is 3 kPa.As shown in Fig. 10, the maximum value of discharge temperature is 47°C with the operating power of 51 W. As the operating power increases to 148 W, the maximum value reaches 79°C, and the high-temperature region almost covers the entire electrode.
From (5) it can be inferred that when operating power is higher, the peak-to-peak voltage and discharge energy per cycle rises, thus the surface temperature also ascends linearly similarly to the variation affected by the duty cycle.As shown in Fig. 11, at 3 kPa the maximum surface temperature evolves with the load power as where a = 28.64 ± 0.79 and b = 0.32 ± 0.01 are best-fit values with the determination coefficient r 2 = 0.9992.Due to the determination coefficient is close to one the experimental variation of the surface temperature shows good agreement with the theoretical trend.

Conclusion
In this study, the thermal characterisation of dielectric barrier discharge plasma actuation driven by RF voltage waveform at low pressure is studied and the conclusions are as follows: At 3 kPa pressure, the high-surface temperature is located on the surface of the high-voltage electrode.In the spanwise direction, the surface temperature gradually increases until it reaches the maximum at X = 13 mm and then decreases.Also, in the chordwise direction, there also exists the maximum value on the surface of the electrode.As discharge begins the dielectric surface temperature gradually increases until saturation, which occurs when thermal equilibrium has been reached at 100 s.Due to the uniform heating of the glow discharge at low pressure, the burrs on the temperature curves significantly are smaller than that of atmospheric pressure.
With the increase of the pressure, the surface temperature ascends non-linearly, and the high-temperature region becomes more and more concentrated.The maximum surface temperature (153°C) is higher than that generated by a sine high voltage with a peak-to-peak voltage of 33 kV and frequency of 1 kHz.
The surface temperature increases linearly whether the duty cycle or operating power increases.As the duty cycle increases, the high-temperature region becomes larger.When the operating power is high, the high-temperature region almost covers the entire electrode.
Due to the significant thermal characterisation, it is quite possible that the heating effect of the RF discharge may lead to the shock/boundary layer interaction.Enhancing the intensity of RF discharge at low pressure and further investigating the shock wave control in supersonic flow should be focused on later.

Acknowledgments
This work is supported mainly by the National Natural Science Foundation under grant nos.11472306, 51407197 and 51507187.

Fig. 1 Fig. 2
Fig. 1 Schematic of the experimental setup , and Jukes et al. have proposed the temporal distribution of the surface temperature expression shown as follows [27]: T surface (t) = T plasma − T o 1 − e −τt erfc τt + T o .

Fig. 3 Fig. 4
Fig. 3 Temperature field distribution of RF discharge at 3 kPa (a) Thermogram recorded by the infrared camera of RF discharge at 3 kPa (b) Evolution of surface temperature along the spanwise direction (c) Evolution of surface temperature along the chordwise direction (X = 13 mm)

Fig. 5 Fig. 6 Fig. 7 Fig. 8
Fig. 5 Evolution of the surface temperature with time (a) Experimental and theoretical variation of the surface temperature at 60 kPa (b) Variation of T surface and τ with pressure (0.6-100 kPa)

Fig. 9 Fig. 10 Fig. 11
Fig. 9 Evolution of the maximum surface temperature with a duty cycle The 1 mm thick dielectric is made of High Volt., 2018, Vol. 3 Iss.2, pp.154-160 This is an open access article published by the IET and CEPRI under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)