# Dynamic Stall Characteristics of the Bionic Airfoil with Different Waviness Ratios
## 4 Results and Analysis
### Dynamic stall control mechanism of the wavy leading Edge
The airfoil with R = 1.0 stalled at this moment, the primary separation vortex began to depart from the upper surface, and the low-velocity recirculation zone covered both the trough section and the second half of the crest section. Figure 15c shows the \(C_{p}\) curves and flow field for an angle of attack of 20\({}^{\circ}\). Due to the gradual movement of the separation vortex away from its low-pressure zone and the vortex-induced velocity loss, the \(C_{\rm I}\) of the baseline airfoil dropped sharply. Simultaneously, the counterclockwise vortex was rolled up by the separating vortex at the trailing edge, and a low-pressure zone formed, which resulting in a bow moment higher than the airfoil with R = 1.0. At this time, the trailing-edge vortex had fallen off the bionic airfoil. Even at the maximum angle of attack, a small part of the flow at the leading edge of the crest section still adhered to the airfoil surface, acting as a \"wing knife\" to limit the spread of the separation vortex along the spanwise direction. When the angle of attack started to decrease, the aerodynamic coefficients of the two airfoils showed different trends. From Figure 10, it can be seen that the \(C_{\rm I}\) of the baseline airfoil underwent small-amplitude oscillations, while that of the bionic airfoil with R = 1.0 changed steadily. Figure 15d shows the \(C_{p}\) curve and flow field when the angle of attack dropped to 17\({}^{\circ}\). It can be seen from Figure 11 that the \(C_{\rm I}\) of the baseline airfoil rose back to a high point because, as the secondary separation vortex moved downstream and  
Figure 15: Flow fields and pressure coefficients of different sections at different angles of attack. (a) 14\({}^{\circ}\)\(\uparrow\) (b) 18\({}^{\circ}\)\(\uparrow\) (c) 20\({}^{\circ}\)\(\uparrow\) (d) 17\({}^{\circ}\)\(\downarrow\). strengthened, as depicted in Figure 15d, the lift increased. As the angle of attack decreases further, secondary separation vortex shedding causes \(C_{\rm I}\) to fall. Figures 11 and 15 show that a sinusoidal bionic leading edge promotes the advanced generation of the separation vortex, but its strength decreases. Although the weaker separation vortex caused a loss in the lift peak, it significantly reduced the drag peak and suppressed the dynamic stall. Simultaneously, the bionic leading edge suppressed secondary separation vortex generation, thus the lift coefficient changed smoothly during the descent process. Figure 16 shows the profiles of the pressure coefficient \(C_{p}\) of the 3D suction surfaces of the baseline and bionic airfoils at different angles of attack. When the angle of attack was \(14^{\circ}\), regardless of the airfoil shape, the airflow was attached to all the airfoil surfaces and the pressure coefficient distribution was relatively uniform. Low \(C_{p}\) values were distributed near the leading edge and \(C_{p}\) increased along the chord direction. The distribution of \(C_{p}\) changed locally when a wavy leading edge was applied to the airfoil, with low and high pressures appearing in trough and peak areas, respectively. In addition, the pressure gradient behind the groove was more unfavorable than the pressure gradient after the crest because low \(C_{p}\) appeared in the groove. At the same time, the distance between the trailing edge and the crest was longer than the distance between the trailing edge and the groove. For the bionic airfoil (R = 0.2), the number of waviness was the lowest and therefore this wavy leading edge had little effect on the \(C_{p}\) distribution, with the overall distribution of \(C_{p}\) being similar to that of the baseline airfoil. Even when R = 0.4, the general \(C_{p}\) was not significantly different from that of the baseline and the case of R = 0.2 in the distribution (Figure 16a). This is consistent with the result that the \(C_{\rm I}\) and \(C_{d}\) for R = 0.2 and 0.4 are similar.