# 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
(**a**) Oval; (**b**) GOE 464; (**c**) NACA 0012; (**d**) Rectangle. 2.2 Effects of Different Flapping Airfoil Layouts on the Aerodynamic Characteristics of Flapping Airfoils  
There are various airfoil layouts for fixed airfoil aircraft, including single airfoil, double airfoil, and three airfoils, and there are also different layout options for flapping airfoils. Some insects in nature have two pairs of wings, such as dragonflies and butterflies, and the aerodynamic characteristics are affected by distinct flapping wing layouts. The aerodynamic characteristics of conventional flapping airfoil layout, parallel flapping airfoil layout, and tandem flapping airfoil layout in the absence of longitudinal flow are researched in this section. As indicated in Figure 23, the horizontal arrangement of two flapping airfoils is called a parallel layout, and the vertical arrangement of two flapping airfoils is called a tandem layout. The distance between the two flapping airfoils is twice the chord length of the airfoil. The flapping airfoil is an elliptical shape with a chord length of h and a maximum thickness of 0.12 h. The flapping airfoil is carried out according to Formula (1), where \(\alpha_{0}=45^{\circ}J_{a}=\) h,\(\alpha_{a}=90^{\circ}\),\(\phi=90^{\circ}\), and \(f=100\) Hz. The lift and drag coefficient curves of different flapping airfoil configurations are shown in Figures 24 and 25, respectively. From Figure 24, it can be established that there are two peaks and two valleys in the lift coefficient curve of flapping airfoils within a stroke. This characteristic of the lift coefficient curve is caused by distinct lift mechanisms and stall mechanisms. From Table 7, it can be seen that under the simulation conditions of this paper, the periodic average lift coefficient of the tandem layout is about twice that of the conventional configuration, and the periodic average drag coefficient of the tandem layout is about 1.78 times that of the conventional arrangement. The periodic average lift coefficient of the parallel layout is 1.3 times that of the conventional arrangement, and the  
Figure 22: Vorticity cloud map of leading edge vortex capture mechanism. (**a**) Oval; (**b**) GOE 464; (**c**) NACA 0012; (**d**) Rectangle. The flow field cloud maps of the Trailing vortex capture mechanism and the leading edge vortex delay stall mechanism with different layouts are shown in Figures 26 and 27, respectively. It can be derived that although the flapping airfoil layouts are distinct, the flow field structure is comparable. During the flapping process, leading edge vortices are caused at the leading edge of the flapping airfoil, while trailing edge vortices are generated at the trailing edge. The upper airfoil surface of a flapping airfoil is a low-pressure area, while the lower airfoil surface is a high-pressure area. There is a pressure difference between the upper and lower airfoil surfaces. The differences in the flow fields are the distinct strengths of the leading edge vortices produced, the different strengths of the trailing vortices captured, and the differences in pressure differences between the upper and lower airfoils. From the flow field cloud map, it can be noted that there is a mutual influence between the airflow around the two flapping airfoils in a parallel or tandem layout, especially the airflow between the two flapping airfoils. The strength of the leading edge vortices formed by the two flapping airfoils is different, and the low-pressure area on the upper airfoil surface is different. The lift on the two flapping airfoils is greater and the drag is also the same. These phenomena may explain why the tandem and parallel layout lift and drag coefficients are not twice those of the conventional layout. The lift efficiencies of the three flapping airfoil layouts are demonstrated in Table 8. The conventional layout performs best with an efficiency of 34.41%, and its stable vortex structure avoids multiple airfoil interference.