# Numerical Study on Airfoil Aerodynamics in Proximity to
## 3 Results and Discussion
### Flow Field Analysis and Discussion
To clarify the difference between the low and high amplitudes for the wavy water surface, the velocity of the particles on the water surface in a larger region at \(t^{*}=0.8\) is given in \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]3 For different wave amplitudes, the magnitude of the velocity component in the horizontal direction is similar, while that in the vertical direction is in approximate proportion to the wave amplitude. Consequently, the influence of the high amplitude wave on the air under the airfoil enhances markedly when the wave moves upward. Besides, the airfoil locates between the dashed lines in \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]4 For the case where the amplitude is \(a=0.05c\), the wave is scarcely affected by the pressure distribution beneath the airfoil. Whereas for the high amplitude wave, it shows that the velocity distributions below the airfoil are different from those at a wavelength ahead of the airfoil. At the leading edge of the airfoil, the high pressure region on the lower surface is so powerful that it puts off the upward movement of the wave and accelerates the wave in the horizontal direction. Hence, there exists strong interaction between the airfoil and the wavy water surface when the wave amplitude is higher, and it is the main reason for the unusual change of lift coefficient. \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]5 Vertical velocity of the particles on the water surface below the airfoil at different moments. \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]6 Pressure contour around the airfoil at \(t^{*}=0.8\). It can be concluded that the flow mechanism of the airfoil moving over the wavy water surface with a higher amplitude is different from that with a lower amplitude. For the high amplitude wave where the wave peak is close enough to the airfoil, the vertical movement of the water surface directly affects the pressure distributions on the airfoil apart from the compression effect on the flow channel. When the wave crest moves below the leading edge stagnation, the compression by the wave creates a high pressure region and prevents air from flowing under the lower surface. Thus a large low pressure region with low speed occurs at the lower surface and leads to lift loss. The velocity contour and pressure coefficient distribution of \(\alpha=1^{\circ}\) with the same wave amplitude are shown in Figures 19 and 20. Similar phenomena can be found at \(\alpha=1^{\circ}\), except that the peak magnitude of the high pressure at the leading edge and the following low pressure declines. This is because that the leading edge at \(\alpha=1^{\circ}\) is higher than that at \(\alpha=0^{\circ}\), and the larger distance weakens the blocking effect. \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]7 Velocity contour of \(\alpha=1^{\circ}\) at \(a=0.1c\) and \(t^{*}=0.8\). \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]8 Velocity of particles on the water surface: (**a**) horizontal velocity; (**b**) vertical velocity. \(V_{x}=\) velocity component in the horizontal direction; and \(V_{z}=\) velocity component in the vertical direction. After clarifying the unusual lift loss at \(\alpha=0^{\circ}\) and \(1^{\circ}\) under the case of high amplitudes, the flow mechanism of higher angles of attack is explained briefly. Taking the result of \(\alpha=2^{\circ}\) and \(a=0.1c\) as an example, the velocity contour at \(t^{\star}=0.8\) is shown in Figure 21, the pressure coefficient distributions of different moments are shown in Figure 22 and the change of lift coefficients is shown in \[C_{p}=\frac{p-p_{\infty}}{1/2\rho V_{\infty}^{2}} \tag{7}\]9 Figure 21 shows that the distance between the airfoil leading edge and the wave crest is larger than that at \(\alpha=0^{\circ}\) and \(1^{\circ}\). Compared with Figure 14d or Figure 19, the blocking effect disappears. Thus, the low velocity area expands to nearly the whole lower surface of the airfoil instead of assembling at the leading edge.