# Numerical Study on Airfoil Aerodynamics in Proximity to
## 3 Results and Discussion
### Flow Field Analysis and Discussion
The former analysis implies that the upward movement of the particles on the water surface might directly impact on the pressure distribution on the airfoil besides the shape of the flow channel. This is instructive for the analysis of the lift change at different moments, especially the abrupt decline near \(t^{*}=0.8\). Therefore, we exhibit the vertical velocity of the particles on the water surface below the airfoil at different moments in \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]0 At \(t^{*}=0\), although the water surface under the airfoil starts to move downward according to Figure 16, the influence when the wave crest passes the lower surface of the airfoil on the airflow still exists. It is shown that the flow channel is compressed considerably in Figure 14a. Therefore, a large high velocity region appears and the pressure coefficients in this region are fairly low. At the same time, the peak of the wave locates at the trailing edge of the airfoil, and the particles on the water surface still move upward in this area (see Figure 16) and compress the air. Thus, there is a high pressure region near the trailing edge in \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]1 During the period from \(t^{*}=0\) to \(t^{*}=0.5\), the distance between the airfoil and the water surface increases, and the shrinkage of the flow channel at entry decreases. The wavy water surface under the airfoil mainly moves downward, and the interaction between it and the air weakens. Therefore, the change of the velocity and pressure is similar to the case of lower amplitude. In the period of \(t^{*}=0.5\)-\(0.8\), the crest of the wave moves towards the leading edge, and the distance between the wave and the airfoil decreases. Figure 16 shows that the particles on the water surface have a fairly high vertical velocity towards the airfoil. As the position of the stagnation point is close to the wave crest, the compression of the particles on the water surface leads to a high pressure peak at the leading edge of the lower surface. Therefore, in Figure 15, we can see the pressure coefficient of the leading edge at \(t^{*}=0.8\) is larger than 1. This sharp pressure increase enhances the shrinkage of the flow channel entry, and thus, the air flowing under the airfoil is blocked. Simultaneously, the air which have passed the leading edge accelerates towards the trailing edge because of the compression by the wavy water surface. A peak of negative pressure then comes into existence on the lower surface, and \(C_{t,Low}\) falls into the minimum value rapidly. Figure 17 shows the pressure contour around the airfoil at \(t^{*}=0.8\), where the high pressure region at the leading edge and the following low pressure region can be clearly observed. Additionally, the obstruction at the flow channel under the airfoil forces more air to flow above the airfoil. The velocity of the airflow above the upper surface increases consequently, causing the low pressure peak at the leading edge of the upper surface and the increase of \(C_{L,up}\). In the period of \(t^{*}=0.8\)-\(1\), the wave crest moves past the leading edge stagnation point. The blocking at the entry of the flow channel is relieved, and the airflow accelerates to flow into. The pressure coefficient on the lower surface returns to the normal value which is caused by the high  
\[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]2 Pressure coefficient distributions on the airfoil at different moments at \(a=0.1c\) and \(\alpha=0^{\circ}\). velocity. In addition, the suck peak on the upper surface disappears as the airflow over the upper surface decreases, and \(C_{Lup}\) decreases sharply.