# Numerical Simulation of Flapping Airfoil Aerodynamic Characteristics
## 4 Summary  
In this paper, the effects of flap motion parameters and structural parameters on the aerodynamic characteristics of the flap are analyzed by using a two-dimensional model, the mechanisms affecting the lift and drag of the flap are revealed, the characteristics of the flow field during the motion of the flap are visualized by means of cloud diagrams, and the trailing-vortex capture mechanism and the leading edge vortex delayed stall mechanism are explained. The following conclusions are drawn:  
1. When the flapping airfoil flaps, the shedding of leading edge vortices can cause a decrease in the lift of the aircraft. The lift of the vehicle can be effectively enhanced by the trailing vortex capture mechanism and the delayed stalling mechanism of the leading edge vortex, leading edge vortex strengthening is achieved by the trailing vortex capture mechanism by absorbing the kinetic energy of the trailing vortex, and the leading edge vortex delayed stall mechanism by elevated the residence time of the leading edge vortex on the airfoil, and thus the lift is increased. It can be seen that the increase and decrease in vehicle lift is greatly influenced by the leading edge vortex. 2. Increasing the flapping frequency can improve the lift and drag characteristics of flapping airfoils. As the flapping frequency increases, the low-pressure area on the upper airfoil surface strengthens, resulting in greater lift for the airfoil. During flapping motion, lift is generated most of the time, and when the direction of travel is changed, it is affected by short-term negative lift, which is very small and can be ignored. The horizontal thrust on the airfoil grows with the rise in flapping frequency, and the drag coefficient on the flapping airfoil during one cycle is positive, indicating a trend for the aircraft to fly to the right. 3. The aerodynamic characteristics of flapping airfoils with distinct trajectories are observed, and it is identified that the flapping frequency, amplitude, and phase difference are identical. The lift characteristics of flapping airfoils with elliptical trajectories, horizontal straight trajectories, and \"co\" shaped trajectories are not substantially different, while the drag coefficients are significantly distinct. When the maximum flapping stroke is the same, and the rate and phase difference are also the same, the lift characteristics are affected differently due to the different symmetry axes of the motion trajectory. 4. The aerodynamic characteristics of the flapping airfoil with different thickness ratios are researched, and it is found that there is a law of influence on the aerodynamic characteristics of the flapping airfoil, and in the case of no incoming flow in the longitudinal direction, the lift coefficient of the flapping airfoil is decreasing with increase in the thickness ratio of the airfoil. The aerodynamic characteristics of the flapping airfoil cannot be improved exponentially by the tandem and parallel layouts, and the tandem layout is more conducive to the advancement of the aerodynamic characteristics of the flapping airfoil compared with the parallel layout. Associated with the fact that most of the insects with multiple pairs of wings in nature are in \begin{table}
\begin{tabular}{c c} \hline \hline
**Layout Type** & **Lifting Efficiency** \\ \hline General layout & 34.41\% \\ Tandem layout & 25.31\% \\ Parallel layout & 29.15\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Lifting efficiencies of flapping airfoils with different layout types. tandem layout, this phenomenon of insects may be explained to some extent by the above findings. * The study of lifting efficiency shows that the flutter motion parameters and structural parameters have a significant effect on the efficiency. From the perspective of motion parameters, the flutter frequency shows an inverse relationship with lifting efficiency. The efficiency at 25 Hz is 102.3% higher than that at 150 Hz, indicating that low-frequency motion is more conducive to energy conversion.