## 5 Results
### Three Important Flow Features and the Guidelines from the Observations
Figure 11a,b shows two image shots of the computed flow fields obtained with the ensemble and moving average [27; 40]. A sequence of vortices is observed, and the number of these vortices corresponds to the burst frequency \(F^{+}\). These vortices are important because they promote large-scale momentum exchange, which contributes to better control of separated flows and increase the authority of the plasma actuator. Figure 9: Aerodynamic performance versus Burst frequency: \(\alpha=12^{\circ}\), \(BR=10\%\), \(Re=6.3\times 10^{4}\). A small disturbance related to the unstable mode of the shear layer would effectively work when the shear layer stays sufficiently close to the airfoil surface. This occurs for the thick airfoil at an angle of attack just above the stall angle because thick airfoils have large radius of curvature at the leading edge. When the airfoil is thin, a separated shear layer is located far away from the surface as the radius of curvature at the leading edge is small. Small flow disturbances may not be sufficient to induce a separated shear layer coming closer to the airfoil surface. Basically, a smaller \(F^{+}\) creates stronger and larger vortices. Therefore, actuation with \(F^{+}=1.0\) creates larger and stronger two-dimensional vortices. These strong vortices might be capable of inducing the separated shear layer to move closer to the airfoil surface. This might be why \(F^{+}=1.0\) work better for the NACA0006 airfoil, and \(F^{+}=6.0\) works better for the NACA0015 airfoil. Similarly, when the angles of attack are much higher than the stall angle, the shear layer separated from the leading edge stays further away from the airfoil surface. Therefore, \(F^{+}=1.0\) also works well. In summary, these vortices would work efficiently especially when a separated shear layer stays away from an airfoil surface. The two flow features above depend on the parameters of the burst mode. On the other hand, the actuator-induced streamwise momentum always exists. It depends on the input voltage, base frequency and others. Thus, jet-like flows introduced by the plasma actuator near the airfoil surface are another important flow feature. The induced momentum becomes largest in the continuous mode and becomes smaller for lower burst ratios. All three of the flow features described above always exist in the flow field induced by a DBD plasma actuator. By a proper choice of the actuator parameters such as the voltage, base frequency, burst frequency, and burst ratio, some of the flow features can be enhanced and become dominant in the flows. By optimizing the parameters for the flow and geometry conditions to be applied,  
Figure 11: Ensemble-averaged flow fields. Black contour lines are second invariant of the velocity gradient tensors Q-criterion [27]: NACA0015, \(\alpha=12^{\circ}\), \(BR=10\%\), \(D_{c}=1.0\), \(Re=6.3\times 10^{4}\). Figure 10: Instantaneous PIV particle images [39] (Experiment). NACA0015, \(\alpha=\)12\({}^{\circ}\), \(BR=10\%\), \(Re=6.3\times 10^{4}\). good control of flow separation can be achieved. Therefore, a plasma actuator works more efficiently than other flow control devices. The strategy for choosing the good parameters for the DBD plasma actuator can now be determined based on the discussion above. It is more effective to use a high frequency considering the instability of the separation shear layer when the separation is weak, or the shear layer stays near the airfoil surface. We can control the flow separation with a low input voltage. It is more effective to use a frequency that is low enough to create strong and large two-dimensional spanwise vortices. Needless to say, it is always more effective to increase the input voltage which induces stronger jet-like flows. The DBD plasma actuator works better than other flow control systems since all the three flow features work together.