# Dynamic Stall Characteristics of the Bionic Airfoil with Different Waviness Ratios
## 4 Results and Analysis
### Dynamic stall control mechanism of the wavy leading Edge  
In the preceding subsections, we have qualitatively analyzed the influence of a wavy leading edge on the dynamic stall characteristics of the NACA 0015 airfoil. We now take R = 1.0 as an example to quantitatively analyze the control mechanism of dynamic stall compared with the baseline airfoil. Figure 13 shows the location of the airfoil section for this analysis. When the angle of attack increased to 5.8\({}^{\circ}\), 8.5\({}^{\circ}\), and 11.2\({}^{\circ}\), \(C_{\text{l}}\) maintained linear growth (Figure 12) and the flow adhered to the airfoil surface. A comparison of the pressure coefficients of each section is given in Figure 14, where \"Baseline\" represents the cross-section of the baseline airfoil, \"Peak\" represents the cross-section of the crest, and \"Trough\" represents the trough section. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Airfoil** & **Clmax** & **Cdmax** & **\(\Delta\)Clmax** & **\(\Delta\)Cdmax** \\ \hline Baseline & 1.51 & 0.48 & & \\ R = 0.2 & 1.50 & 0.43 & \(-\)0.67\% & \(-\)10.42\% \\ R = 0.4 & 1.49 & 0.42 & \(-\)1.32\% & \(-\)12.5\% \\ R = 0.6 & 1.41 & 0.41 & \(-\)6.62\% & \(-\)14.58\% \\ R = 0.8 & 1.37 & 0.40 & \(-\)9.27\% & \(-\)16.67\% \\ R = 1.0 & 1.34 & 0.39 & \(-\)11.26\% & \(-\)18.75\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of results for different airfoils. Figure 12: Lift coefficients for different airfoils. (**a**) \(C_{1}\) for R = 0.2; (**b**) \(C_{d}\) for R = 0.2; (**c**) \(C_{1}\) for R = 0.4; (**d**) \(C_{d}\) for R = 0.4; (**e**) \(C_{1}\) for R = 0.6; (**f**) \(C_{d}\) for R = 0.6; (**g**) \(C_{1}\) for R = 0.8; (**h**) \(C_{d}\) for R = 0.8; (**i**) \(C_{1}\) for R = 1.0; (**j**) \(C_{d}\) for R = 1.0. With the angle of attack increased, the suction peak force on the baseline airfoil increased, while the peak suction force on the trough section increased significantly. At an angle of attack of 14.0\({}^{\circ}\), \(C_{p}\) exceeded \(-5\). This is because part of the airflow converges from the crest to the trough and the velocity increases. The zone of high negative pressure for the trough section increased in size and the adverse pressure gradient became stronger. Conversely, part of the airflow that was about to reach the crest was drawn by the negative pressure at the front edge of the trough, thus the acceleration effect of the flow around the front edge of the crest was weakened. As a result, the peak value of \(C_{p}\) on the crest section was always small. As the angle of attack increased, the peak suction force on the airfoil increased. When the angle of attack was 16\({}^{\circ}\) (Figure 15a), the growth rate of \(C_{1}\) for the bionic airfoil changed, whereas that of the baseline airfoil was still linear. The airflow in the trough section was boosted to the average level in a shorter time. The strong reverse pressure gradient makes separating the airflow in the trough section easier and a separation vortex appeared in advance. The accompanying low-pressure effect caused a small plateau in the \(C_{p}\) of the trough cross-section. This further increased the lift on the airfoil in the trough section, thereby changing the \(C_{1}\) ratio. Figure 14: Comparison of pressure coefficients for different angles of attack. (**a**) 5.8\({}^{\circ}\); (**b**) 8.5\({}^{\circ}\); (**c**) 11.2\({}^{\circ}\); (**d**) 14.0\({}^{\circ}\). Figure 13: Location of the airfoil section. Figure 15b shows the \(C_{p}\) curves and flow fields when the angle of attack was increased to 18\({}^{\circ}\). The \(C_{\rm I}\) of the baseline airfoil was close to its peak value (the lift coefficient reached its peak value at an angle of attack of 17\({}^{\circ}\)) and the separation vortex almost covered the upper surface. As the vortex moved downstream, the low-pressure area moved backward and the \(C_{p}\) peak value decreased.