# 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  
For fixed airfoil aircraft, the aerodynamic characteristics of airfoils are associated with the flight quality of the aircraft. The aerodynamic characteristics of low-speed airfoils are closely connected to the thickness, curvature, and angle of attack of the airfoil. Excited by this, the aerodynamic characteristics of flapping airfoils with different characteristics are explored in this section, where the parameters in the flutter motion function are as follows: \(\alpha_{0}=45^{\circ}\), \(h_{a}=\) h, \(\alpha_{a}=90^{\circ}\), \(\phi=90^{\circ}\), and \(f=100\) Hz. Four typical airfoils with various thicknesses and curvature were selected for research. The four airfoils are rectangular airfoils with simple geometric shapes, elliptical airfoils with sharp corners at both ends and smooth curves, classic fixed airfoil aircraft airfoil NACA0012, and bird like airfoil GOE 464. The specific characteristics of each airfoil are described in Table 4.  
Figure 18: Vorticity cloud map of leading edge vortex delayed stall mechanism. (**a**) Horizontal straight trajectory t = 0.85 T; (**b**) elliptical trajectory t = 0.86 T; (**c**) “\(\infty\)” shaped trajectory t = 0.8 T; (**d**) 45\({}^{\circ}\) tilt trajectory t = 1.3 T. \begin{table}
\begin{tabular}{c c} \hline \hline
**Trajectory Type** & **Lifting Efficiency** \\ \hline elliptical trajectory & 40.29\% \\ “\(\infty\)” shaped trajectory & 47.82\% \\
45\({}^{\circ}\) tilt trajectory & 31.55\% \\ horizontal straight trajectory & 34.41\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Lifting efficiencies of flapping airfoils with different motion trajectories. The initial position of the airfoil is at the origin, and the moment when the airfoil is at the rightmost end is chosen as the starting time, and two periodic data are selected for research. The lift coefficient curves of the four airfoils are unveiled in Figure 19, and the drag coefficient curves are indicated in Figure 20. Because their kinematic parameters are the same, and the flapping airfoil lift mechanism is the same, the trend of the lift and drag coefficient curves of the four airfoils is similar: the absolute values of the lift coefficient and drag coefficient increase when the lift mechanism is in effect. When the lift mechanism ends, the lift coefficient curve and the absolute value of the drag coefficient decrease. The peaks and valleys of the lift coefficient curves and drag coefficient curves of different airfoils are different in size, and the values of the lift coefficient and drag coefficient of the four airfoils are obviously various. The aerodynamic characteristics of flapping airfoils are influenced by the thickness of the airfoil. Comparing the lift and drag coefficient curves of rectangular airfoils and elliptical airfoils, it can be discovered that the peak lift and drag coefficients of rectangular airfoils are larger than those of elliptical airfoils. The difference in thickness distribution between rectangular airfoils and elliptical airfoils is that the thickness distribution of rectangular airfoils is uniform, and the front and rear edges are relatively tight. The elliptical airfoil is thick in the middle, with small thickness on both sides and sharp corners at the front and rear edges. The differences in their lift and drag characteristics indicate that the aerodynamic characteristics of flapping airfoils are influenced by the thickness of the airfoil. Comparing the lift and drag of NACA0012 and elliptical airfoils, the influence of thickness on the aerodynamic characteristics of flapping airfoils can also be seen.