## 4 Results and Discussion
### Averaged Flow Feature
In addition, the plateau region is reduced at all angles of attack, and therefore, \(C_{\text{D}_{\text{p}}}\) value becomes lower than the Continuous cases. Figure 9: Pressure coefficient (\(C_{\text{p}}\)) distributions around the airfoil. The relationship between the flow field and the pressure distribution on the airfoil surface is discussed in more detail. Figure 11 shows time- and spanwise-averaged flows colored with the chordwise velocity normalized by the freestream velocity (\(u/U_{\infty}\)) for each case, and Figure 12 shows the displacement thickness (\(\delta^{*}\)) on the airfoil's upper surface. Figures 11 and 12 are helpful in understanding the separation bubble size in the wall-normal direction of the airfoil. The displacement thickness is nondimensionalized by the chord length. The NACA0015 airfoil is shown in the background to the same scale as the displacement thickness. In all cases, the flow separates from around \(x/c\simeq 0.1\), forming a separation bubble, although it is difficult to see in the Burst cases. The flow on the airfoil's upper surface (suction side) generally accelerates due to the flow bending at the leading edge of the airfoil (the red region in Figure 11), creating the suction peak, as seen in Figure 9. In the present flow fields, the shape of the separation bubble existing in this acceleration region changes due to the PA control; thus, the value of the suction peak also changes in each case. The pressure distribution in the presence of the separated region on the airfoil surface can be predicted by assuming that the airfoil thickness increases as much as the thickness of the separated region. The smaller the displacement thickness, the lower the effect of the boundary layer and separated area, and the flow becomes closer to the potential flow of the NACA0015 airfoil. In Figure 12, the displacement thicknesses of the Continuous and Burst cases are smaller than that of the PA-OFF case in the region of \(0.1\lesssim x/c\lesssim 0.4\) at any angle of attack. When the flow bends, the pressure inner side of the curved flow becomes lower as the radius of curvature becomes smaller. Therefore, in the Continuous and Burst cases with the thin displacement thickness, the radius of curvature of the flow near the leading edge of the airfoil is smaller than in the PA-OFF case, and the pressure is lower. However, in Figure 9, the suction peak value of the burst case at \(\alpha=8\) is almost the same as that of the PA-OFF case. The exceptional suction value of the burst case at \(\alpha=8\) may be caused by the flow separation near the trailing edge on the suction side. At \(x/c\simeq 0.9\) in Figure 10, \(C_{\text{f}}\) is almost zero, and in Figure 11, the low-speed region is larger near the trailing edge than in the other cases. Due to this trailing edge separation, in Figure 10, the displacement thickness of the Burst case near the trailing edge (\(0.8\lesssim x/c\lesssim 1\)) becomes the thickest, and the radius of curvature on the airfoil's upper surface increases, resulting in weakening the acceleration of the flow near the leading edge and affecting the value of the suction peak.