## 4 Results and Discussion
### Comparison with Controlled Flow at Post-Stall Angle of Attack  
This section discusses the differences between the controlled flows at the pre- and post-stall angles of attack. Figure 19 shows \(C_{\text{P}}\) and \(C_{\text{f}}\) distributions at the post-stall angle of attack (\(\alpha=12\)). In the PA-OFF case, a massive separation occurs from the leading edge of the airfoil, and thus, the \(C_{\text{P}}\) shows a flat distribution on the suction side, and the \(C_{\text{f}}\) value takes a negative value on most of the airfoil surface. Because of the massive separation, the \(C_{\text{L}}\) of the PA-OFF case is significantly lower compared to the pre-stall angles (Figure 7a). The burst drive with \(F^{+}\) can suppress the massive flow separation and create flow reattachment, while the continuous drive cannot. The flow reattachment in the Burst case increases the \(C_{\text{L}}\) and decreases the \(C_{\text{D}}\) significantly. Both the \(C_{\text{L}}\) increase and \(C_{\text{D}}\) decrease contribute to \(L/D\) improvement, as shown in Figures 6 and 7. The detailed discussion may be found in [15]. On the other hand, at the pre-stall angles of attack, in the PA-OFF case, a separation bubble, which does not exist at the post-stall angle of attack, is formed on the airfoil's upper surface, and its position and size affect the aerodynamic coefficients, as discussed in Section 4.3. The change in the separation bubble by PA control does not contribute much to the \(C_{\text{L}}\) increase but mainly reduces the \(C_{\text{D}}\) and contributes to the increase in \(L/D\) (Figures 6 and 7). At \(\alpha=4\) and \(8\), the \(C_{\text{L}}\) decreases due to the shrink of the separation bubble, but the \(C_{\text{D}}\) reduction is larger than the \(C_{\text{L}}\) decrease, so the \(L/D\) increases. The difference in the flows in the Burst case at each angle of attack becomes more apparent when the discussion includes the instantaneous flow at \(\alpha=12\). Figure 20 shows the instantaneous flow of the Burst case at \(\alpha=12\). This flow resembles that at \(\alpha=10\) shown in Figure 16c. The two-dimensional vortex structures induced by PA rapidly break down into fine vortices. Figures 21 and 22 show the TKE distributions and the PSDs of the chordwise velocity fluctuations for the Burst case at \(\alpha=12\). The PSD shows the value at the position where the TKE is the largest (indicated by the black cross symbol in Figure 21) at each cord length position. The region where TKE is locally high is seen at \(0.1\lesssim x\lesssim 0.4\), and a PSD decay of the \(-5/3\) slope is seen at all stations in Figure 22 because the turbulent transition rapidly occurs. The turbulence growth shown by these TKE and PSDs also resembles those at \(\alpha=10\). The rapid turbulent transition draws the shear layer and reduces the separation region. On the other hand, as discussed in Section 4.4, at the lower angles of  
Figure 19: Pressure coefficient (\(C_{\text{P}}\)) and skin friction coefficient (\(C_{\text{f}}\)) distributions on the airfoil’s upper surface at \(\alpha=12\). attack (\(\alpha=4\), \(6\), and \(8\)), the burst actuation induces the two-dimensional vortices, which maintain their spanwise shape (Figure 16). The transport of the two-dimensional vortices draws the shear layer to the airfoil surface and shrinks the separation bubble. Additionally, those two-dimensional vortices suppress the turbulent transition. The suppression of turbulence transition can be confirmed by the spectrum in Figure 18.  
As discussed above, the control mechanism is different between near the stall angle of attack (\(\alpha=10\) and \(12\)) and at lower angles of attack (\(\alpha=4\), \(6\), and \(8\)). This may be because the pressure gradient on the airfoil surface increases as the angle of attack increases. The pressure gradient may promote the collapse of the two-dimensional vortices induced by PA near the stall angle of attack.