Surface vorticity modeling of flow around airfoils

A surface vorticity method based on the new Kutta condition has been developed for solving the steady flow around an airfoil and unsteady separated flow past airfoil with a spoiler. In a discussion of the Kutta condition, it is argued that the appropriate Kutta condition is required to obtain a satisfactory solution. In this paper, two new methods of satisfying the Kutta condition incorporated in the surface vorticity method are described. The first method, which is based on results from flow visualization, is to introduce an additional control point at a short distance downstream of the trailing edge. In order to account for the fact that the velocity above the trailing edge is different from that below as in the real flow, the second method is to add a finite segment of vortex sheet downstream of the trailing edge. The present Kutta conditions are incorporated into the surface vorticity method and extend to solve unsteady flow around an airfoil with a spoiler. The computational results are in reasonable agreement with other computation as well as experiments.