## 4 Results and Discussion
### Averaged Flow Feature  
In this section, we discuss what flow changes with the PA control cause an aerodynamic characteristic change. In the following discussion, the results at \(\alpha=4\) are omitted because their overall tendency is similar to that at \(\alpha=6\), and arguments will be made with the results at \(\alpha=6\), \(8\), and \(10\). Figure 9 shows the pressure coefficient (\(C_{\text{p}}\)) distribution around the airfoil obtained in each case. The shape of the NACA0015 airfoil is drawn in gray on the background. The black up- and down-pointing triangle symbols indicate the highest and lowest airfoil surface positions at each angle of attack, respectively. The characteristic changes in the \(C_{\text{p}}\) distribution with the PA control are mainly observed on the airfoil's upper surface. In the Continuous cases, the \(C_{\text{p}}\) value at the suction peak near the leading edge lowered, and the plateau region moved toward the trailing edge and slightly shrunk. In the Burst cases, the \(C_{\text{p}}\) plateau region was significantly reduced, and the \(C_{\text{p}}\) value at the suction peak became low at \(\alpha=6\) and \(10\). The local variation of \(C_{\text{p}}\) seen at \(0.2\lesssim x/c\lesssim 0.5\) in the Burst cases at \(\alpha=6\) and \(8\) was due to the merging of the two-dimensional vortex structures. The details are discussed in Section 4.4. Additionally, at \(\alpha=8\), the pressure on the underside of the airfoil was slightly lower than that of the PA-OFF and Continuous cases. Figure 8: Pressure drag coefficient (\(C_{\text{D}_{\text{p}}}\)) versus angle of attack (\(\alpha\)). Figure 7: Lift coefficient (\(C_{\text{L}}\)) and drag coefficient (\(C_{\text{D}}\)) versus angle of attack (\(\alpha\)). We discuss the \(C_{\text{p}}\) distribution in more detail from the perspective of reducing \(C_{\text{D}_{\text{p}}}\). Since the force due to the surface pressure acts perpendicularly to the airfoil surface, the force contribution direction (thrust or drag) depends on the orientation of the airfoil surface. When there is no inflection point on the suction side, such as the NACA0015 airfoil, the surface pressure at the front half region from the highest point of the airfoil contributes to thrust, while the surface pressure at the back half part from the highest point contributes to drag increase. In Figure 9, since the suction peak exists upstream from the highest point in each case, the lower the pressure at the peak position, the more significant the contribution to thrust and the lower \(C_{\text{D}_{\text{p}}}\). On the contrary, in the PA-OFF case shown in Figure 9, most of the plateau region caused by the separation bubbles exists downstream from the highest point; thus, the negative pressure contributes to the drag. Figure 10 shows the distribution of the skin-friction coefficient (\(C_{\text{f}}\)) on the airfoil's upper surface in each case. In the PA-OFF case at \(\alpha=6\), \(C_{\text{f}}\) is negative in the range of \(0.1\lesssim x/c\lesssim 0.5\), indicating that the flow is separated and forms separation bubbles. The negative \(C_{\text{f}}\) region coincides with the plateau region in Figure 9a. In the Continuous cases in Figure 9, the pressure of the suction peak is reduced at any angle of attack. On the other hand, as shown in Figure 10, the plateau region in Figure 9 is moved to the trailing edge side due to the movement of the separation bubble position (the area where \(C_{\text{f}}\) is negative) to the downstream. The movement of this plateau region to the downstream contributes to the \(C_{\text{D}_{\text{p}}}\) increase. However, since the contribution of the \(C_{\text{D}_{\text{p}}}\) decrease because the pressure decrease in the suction peak is larger and \(C_{\text{D}_{\text{p}}}\) slightly decreases at any angle of attack, as shown in Figure 8. In the Burst cases, the suction peak value of \(C_{\text{p}}\) near the leading edge is lower than the other cases at \(\alpha=6\) and 10 (Figure 9a,c).