# Numerical Simulation of Flapping Airfoil Aerodynamic Characteristics
## 3 Results and Analysis
### Effects of Structural Parameters on the Aerodynamic Characteristics of Flapping Airfoils
#### 3.2.1 Effects of Different Airfoils on the Aerodynamic Characteristics of Flapping Airfoils
The data of the periodic average lift coefficient and drag coefficient for different airfoils are displayed in Table 5. From this data, it is observed that the cycle-averaged lift coefficient of the elliptical airfoil is the smallest, and the cycle-averaged lift coefficient of the GOE464 airfoil type is the larger one. The periodic average lift coefficient of the GOE464 airfoil is about 1.6 times that of an ellipse, which suggests that flapping airfoils using the GOE464 airfoil are more conducive to the aircraft climbing upwards. The periodic average drag coefficient of the elliptical airfoil is the largest, while that of NACA0012 is the smallest. The periodic average drag coefficient of the elliptical airfoil is about 1.58 times that of NACA0012. Furthermore, the cycle-averaged drag coefficients of the four airfoil types are all positive, indicating that rightward thrust can be generated by all four airfoil cycle flutters and the vehicle flies to the right. This implies that the direction of flight is not affected by the difference in airfoil type. The flow field cloud maps of different flapping airfoils at t = 0.46 T are illustrated in Figure 21, and the flow field cloud maps of different flapping airfoils at t = 0.85 T are shown in Figure 22. At t = 0.46 T, there is a leading edge vortex delay stall lift mechanism in the flapping motion process of all four airfoils. At t = 0.85 T, there is a Trailing vortex capture lift mechanism in the flow field of all four airfoils. The same lift mechanism is included in the flapping motion process of these four different airfoils, and why their lift and drag coefficient curves tend to be similar can be explained. Due to the different geometric characteristics of airfoils, the intensity of leading edge vortices in the flow field, the size and intensity of the low-pressure region on the upper airfoil surface, and the pressure difference between the upper and lower airfoil surfaces. \begin{table}
\begin{tabular}{c c c c} \hline
**Airfoil** & \begin{tabular}{c} **Periodic Average** \\ **Lift Coefficient** \\ \end{tabular} & \
\begin{tabular}{c} **Periodic Average** \\ **Drag Coefficient** \\ \end{tabular} &
\begin{tabular}{c} **Periodic Average** \\ **Lift-Drag Ratio** \\ \end{tabular} \\ \hline Oval & 0.569565441 & 0.123594957 & 4.608322664 \\ GOE 464 & 0.905649405 & 0.098208462 & 9.221704406 \\ NACA 0012 & 0.772951404 & 0.07794027 & 9.917227724 \\ Rectangle & 0.725099956 & 0.093237428 & 7.776919315 \\ \hline \end{tabular}
\end{table} 
Table 5: Cycle average values of lift and drag coefficients. Figure 20: Drag coefficients of different airfoils. As shown in Table 6, the lifting efficiencies of the different airfoils present large differences. The bionic airfoil GOE464 has the best performance with an efficiency value of 56.18%, the NACA0012 airfoil and rectangular airfoil have similar efficiencies of 43.21% and 43.10%, respectively, while the basic elliptical airfoil has the lowest efficiency of 34.41%. This difference in efficiency is mainly due to the difference in hydrodynamic characteristics of the airfoils. The GOE464 airfoil, with leading edge curvature and nonlinear thickness distribution, is more effective in maintaining leading edge vortex attachment, and its efficiency is improved by 63.2% compared to the standard elliptical airfoil. It is worth noting that the rectangular airfoil outperforms the elliptical airfoil by 43.10% efficiency despite its simple geometry. In engineering applications, the GOE464 airfoil should be preferred when maximum efficiency is sought. While the rectangular airfoil should be considered when a simplified manufacturing process is required, which still maintains efficiency levels above 43%. \begin{table}
\begin{tabular}{c c} \hline
**Airfoil** & **Lifting Efficiency** \\ \hline oval & 34.41\% \\ GOE 464 & 56.18\% \\ NACA 0012 & 43.21\% \\ rectangle & 43.10\% \\ \hline \end{tabular}
\end{table} 
Table 6: Lifting efficiencies of flapping airfoils with different airfoils. Figure 21: Vorticity cloud map of leading edge vortex delayed stall mechanism.