# Dynamic Stall Characteristics of the Bionic Airfoil with Different Waviness Ratios
## 5 Conclusions  
The flow around bionic airfoils with different spanwise waviness ratios under dynamic stall conditions has been studied numerically. A NACA 0015 airfoil with an aspect ratio of 1.5 was modified with a tubercle leading edge, with a wavelength of 0.2 \(C\) and amplitude of 0.025 \(C\). Different waviness ratios including R = 0.2, 0.4, 0.6, 0.8, and 1.0 were investigated. The main conclusions from this study are as follows:  
1. As revealed by numerical simulations, a skew-induced mechanism can explain the generation of streamwise vorticity. From another standpoint, the spanwise vorticity rippled along the span of the airfoil caused by the tubercle leading edge, which leads to the generation of streamwise vorticity. 2. The greater adverse pressure gradient of the trough section at the wavy leading edge promotes advanced separation. The flow on the surface of the crest weakens the effect of the separating vortex on the trough and restricts its spanwise propagation. Figure 16: Pressure coefficients for different airfoils. (**a**) Baseline, R = 0.2, R = 0.4; (**b**) R = 0.6, R = 0.8, R = 1.0. Simultaneously, the wavy leading edge suppresses dynamic stall and prevents a delay in separation. 3. The application of a wavy leading edge significantly reduces the peak drag coefficient. The peak lift coefficient is also reduced but to a much smaller degree than the peak drag coefficient. For example, the peak drag coefficient of a bionic airfoil with R = 0.8 is reduced by 16.67% and the peak lift coefficient is reduced by 9.27%. 4. It has been demonstrated that the dynamic hysteresis effect is gradually improved as the waviness ratio increases. Thus, the area of the hysteresis loop is the smallest for the bionic airfoil with R = 1.0. [PERSON] conducted the study and analysis. [PERSON] supervised all activities. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Key R&D Program of China (number 2019 YFB1504601) and National Natural Science Foundation of China (number 51676152). Not applicable. The authors declare no conflict of interest. The application of a wavy leading edge significantly reduces the peak drag coefficient. The peak lift coefficient is also reduced but to a much smaller degree than the peak drag coefficient. For example, the peak drag coefficient of a bionic airfoil with R = 0.8 is reduced by 16.67% and the peak lift coefficient is reduced by 9.27%. It has been demonstrated that the dynamic hysteresis effect is gradually improved as the waviness ratio increases. Thus, the area of the hysteresis loop is the smallest for the bionic airfoil with R = 1.0. [PERSON] conducted the study and analysis. [PERSON] supervised all activities. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Key R&D Program of China (number 2019 YFB1504601) and National Natural Science Foundation of China (number 51676152). Not applicable. The authors declare no conflict of interest. The application of a wavy leading edge significantly reduces the peak drag coefficient. The peak lift coefficient is also reduced but to a much smaller degree than the peak drag coefficient. For example, the peak drag coefficient of a bionic airfoil with R = 0.8 is reduced by 16.67% and the peak lift coefficient is reduced by 9.27%. It has been demonstrated that the dynamic hysteresis effect is gradually improved as the waviness ratio increases. Thus, the area of the hysteresis loop is the smallest for the bionic airfoil with R = 1.0. [PERSON] conducted the study and analysis. [PERSON] supervised all activities. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Key R&D Program of China (number 2019 YFB1504601)  
[PERSON]; [PERSON]; [PERSON]; [PERSON] Review on bio-inspired flight systems and bionic aerodynamics. _[PERSON]_**2020**, _34_, 170-186. [CrossRef]
* _[PERSON] et al.