## 1 Introduction  
Flow separation is a common phenomenon in many industrial applications, including transportation vehicles and rotating machinery. Flow separation control has been an interesting topic in fluid dynamic study for many years, since flow separation leads to remarkable drag increase and/or lift changes with strong flow unsteadiness. As flow separation is a critical phenomenon for aircraft, flow separation control over airfoils is an important application. Among many compact devices that were recently developed, DBD plasma actuators are recently developed and have been shown to be very effective for flow separation control over airfoils [1; 2; 3; 4]. A DBD plasma actuator comprises two thin electrodes with a dielectric sandwiched between them (Figure 1) and is easily attached to an airfoil surface. The plasma actuator induces a weak jet-like flow (with a maximum speed of a few meters per second in general) in a small region near the airfoil surface as a result of ion motion in the plasma due to dielectric barrier discharge phenomenon induced by the high alternating current (AC) voltage applied on the electrodes. Both the experimental and computational analysis showed that this device is very effective for flow separation control at the Reynolds numbers less than 10\({}^{5}\)[5; 6; 7; 8; 9; 10; 11]. Figure 2 shows an example. \"DBD-PA OFF\" means that no voltage is applied to the DBD plasma actuator, and \"DBD-PA ON\" means that a high voltage is applied. The pictures in Figure 2 were taken in a low speed wind tunnel experiment with an NACA0015 airfoil with the chord length of 0.1 m in a freestream velocity of 10.0 m/s. The Reynolds number was 6.3 \(\times\) 10\({}^{4}\). The two pictures in Figure 2 show that the DBD plasma actuator changes fully separated flows at the leading edge of the airfoil to almost fully attached flows. There are several benefits of DBD plasma actuators compared to mechanical devices for flow control. DBD plasma actuators are simple and thin, can be added to the existing body, have a quick response, require a low input energy, and have sufficient flexibility to be used in different flow situations. One interesting features of DBD plasma actuators is the use of the so-called \"burst mode\". A time sequence of the input voltage for the burst mode is schematically presented in Figure 3. Here, the sinusoidal line plot corresponds to the base frequency of the high AC (alternating current) voltage in the continuous mode. \(f^{+}\) is the frequency of the duty cycle of the applied voltage and called burst frequency. \(T\) (s) is the period of one duty cycle and \(T_{on}\) (s) is the period during which the voltage is applied. The ratio, \(T_{on}\)/\(T\) is called the burst ratio denoted \(BR\). The base frequency signals are switched on and off by the base high-frequency signals. Thus, a high voltage is only applied during the limited period as a duty cycle. Previous studies showed that better control authority is achieved with less energy consumption in many of the flow and geometry conditions when the burst mode is used [10; 12; 13; 14]. The non-dimensional burst wave frequency. \(F^{+}\) (\(=f^{+}c/u_{\infty}\)) is used as a reference parameter in the literature, where \(f^{+}\) is the burst frequency, \(c\) is the chord length and \(u_{\infty}\) is the freestream velocity. Many previous studies showed that \(F^{+}\) = 1.0 is effective [12; 15], while some of the recent experimental and computational studies showed that \(F^{+}\) values between 2 and 20 are also effective [8; 13; 14; 16]. Figure 1: DBD (dielectric barrier discharge) plasma actuator. Figure 3: Schematic picture of frequencies for the burst mode. Figure 2: Flow control with the DBD plasma actuator (Experiment): (**a**) DBD-PA (dielectric barrier discharge plasma actuator) OFF; and (**b**) DBD-PA ON with burst mode.