## 5 Results
### Use of Burst Waves: Observations in Our Early Study  
As described in Section 1, burst waves are effective for better control of flow separations. Figure 5 shows the experimental result showing the effect of burst frequencies over the lift coefficients \(CL\) (\(=L/\frac{1}{2}\rho u_{\infty}^{2}c\)) at the angle of attack of \(12^{\circ}\), which is just above the stall angle. Here, \(L\) is the lift of the airfoil and \(c\) is the chord length of the airfoil representing the length scale. \(BR\) is the percentage burst ratio and \(BR\) = 100% corresponds to the continuous mode of the applied voltage. Although not shown here, the \(CL\) value without the DBD plasma actuator was about 0.55. This indicates that continuous mode (BR = 100) did not increase \(CL\) value and was considered to not effectively change large-scale leading-edge separation. Burst mode actuation is in general more effective than continuous mode actuation. A frequency of \(f^{+}\) = 600 Hz (corresponding to the non-dimensional burst frequency, \(F^{+}\) = 6.0) with a burst ratio (\(BR\)) of 10% is very effective. In the literature, it had been shown that \(F^{+}\) =1.0 (\(f^{+}\) = 100 Hz in this experiment) was very effective for achieving a high \(CL\)[12; 16] although the effectiveness of a much higher \(F^{+}\) was not confirmed. For the future discussion in this manuscript, please note that the applied voltage in this experiment was 4.0 kV (\(Vpp\)), which is low compared to many other experiments for the DBD plasma actuator. This sensitive low voltage was intentionally chosen so that we could find the effect of the burst frequency and other plasma actuator parameters on the aerodynamic coefficients. With higher voltages being applied, the difference in _CL_ values between \(BR=50\%\) and \(BR=10\%\) became smaller and the effect of the burst frequencies decreased. At any rate, the experimental results posed two questions: Why did the burst mode show better flow control authority? Why did \(F^{+}=6.0\) realize higher _CL_ compared to \(F^{+}=1.0\) in this experiment? As the angle of attack is just above the stall angle and the applied voltage is very low for the case shown in Figure 5, the results in the experiment were very sensitive to a small change in the flow and environmental conditions. Therefore, \(14^{\circ}\), which is a few degrees above the stall angle, was selected for the main case for the discussion below. Experiments were also conducted at this angle of attack with higher voltages (5.0 kV-6.0 kV (_Vpp_)) [38]. Figure 6 shows plots of surface \(C_{p}\left(=(p-p_{\infty})/\frac{1}{2}\rho u_{\infty}^{2}\right)\) distributions over an NACA0015 airfoil under three different DBD plasma actuator conditions: (a) DBD-PA OFF (plasma actuator not used); (b) \(F^{+}=1.0\); and (c) \(F^{+}=6.0\). The burst ratio was set to be 10 (10% duty cycle) for all the cases. Flows are unsteady, so the plotted CFD data are based on the time and span-averaged values. The computational results were obtained through the present extensive study. The experimental result was taken from Ref. [39]. The simulation results in all the three plots show good agreement with the corresponding experiment. Without the DBD plasma actuator, there are flat \(C_{p}\) distributions over the upper surface of the airfoil (shown in Figure 6a), which indicates that flow separation occurs at very near the leading-edge. With the DBD plasma actuator on, negative pressure is produced over the upper surface of the airfoil and the lift coefficient is somewhat recovered. Better flow control with higher burst frequencies is also confirmed in this CFD analysis since the leading-edge suction peak is well recovered in Case (c) with \(F^{+}=6.0\). At angles of attack below the stall angle, laminar flow separation occurs near the leading edge of the airfoil when without the DBD plasma actuator. A turbulent transition makes the separated flow to attach to the airfoil surface at this Reynolds number.