## 5 Results
### Use of Burst Waves: Observation from the Later Stage of Study (2011-2017)  
From the results thus far, the two questions raised earlier have not yet been answered. The first was why the use of burst waves improved flow control authority, while the second was why \(F^{+}\) = 6.0 showed a better flow control than \(F^{+}\) = 1.0 in both our experiments and simulations. Numbers of iLES simulations were conducted under the project of application software development of the K supercomputer in Japan [40; 41; 42; 43; 44]. Simulations with different parameters (airfoil geometry, angle of attack, Reynolds number, \(D_{c}\), \(F^{+}\), etc.) identified the solutions to these questions. Other extensive studies have been conducted in the experiments similarly [39]. Much information was obtained by this activity. Some of the results are presented here among them. More results can be found in the references above. Figure 7 shows the effect of the actuator position [45]. Thick vertical dotted lines are the separation points when without the DBD plasma actuator. As has been pointed out in the past, a DBD plasma actuator achieves the best \(L\)/\(D\) when it is located near the separation points. This is also true for other angles of attack, other airfoils and other DBD plasma actuator parameters.  
Next, we discuss the answers to the two questions above. Figure 8 illustrates how aerodynamic performance (_L/D_) is influenced by the chordwise growth of the turbulent energy. Each symbol in this figure corresponds to one simulation. We first drew the TKE (turbulent kinetic energy) contour map over the entire flow field over the airfoil. At each chorwise station from the leading edge, the maximum value of TKE is searched in the lateral direction. Thus, we obtain the chordwise distribution of the maximum value of TKE for each chordwise location (TKE_max). The chordwise distribution of TKE_max has a peak and Gaussian-like profile near the peak. The half-width of the first peak of TKE_max profile is computed as a reference value of the rapidity of the TKE growth (or turbulent energy promotion) as it is considered to have strong relation with the smoothness of the turbulent transition. Each point in this figure corresponds to the _L/D_ versus the rapidity of the TKE growth thus computed for each case. Details on the method used for computing the rapidity of the TKE growth have been discussed [40]. There are obviously three groups in this figure. One group at the bottom right shows a slow growth of turbulence, resulting in a low \(C_{L}/C_{D}\) (same as _L/D_). They fail to achieve good flow separation control. The other group at the top left has a rapid growth of turbulence, resulting in a high _L/D_. They are successful in flow separation control. These results indicate that the promotion of the TKE energy, namely, the promotion of laminar-turbulent transition is one important mechanism for the separated flow control by the DBD plasma actuator. There is an interesting third group located in the top left region. They are successful for flow separation control and achieve high _L/D_ even though the growth of turbulence is slow. This suggests that another mechanism may exist for the flow separation control authority of the DBD plasma actuator. Note that analysis of the instantaneous flow for this group shows a two-dimensional spanwise vortex remaining near the airfoil surface up to the middle-to-rear part of the airfoil, where a transition occurs. This phenomenon ensures a high _L/D_.