A direct boundary integral equations method to subsonic flow with circulation past thin airfoils in ground effect Original Research Article

A direct method for solving the problem of subsonic flow past a lifting or non-lifting airfoil in ground effects is presented. The problem is formulated in terms of velocity and it does not make use of the potential or the stream function. The non-linear boundary condition is used. In this way, the solution is exact in the incompressible case for any shape of the airfoil (not necessarily thin). For the compressible case, we use linear equations of motion and the solution will be valid for thin airfoils. A set of Green functions that satisfies the boundary condition on the ground are deduced and an integral equation on the airfoil only is constructed. We solve the integral equation by means of a collocation method. The circulation is introduced as a parameter of the problem and it is related to the Kutta condition. The equal-pressure Kutta condition is used but the problem remains linear due to the formulation in velocities. In the incompressible case the solution for the circular body is compared with the exact solution, the coincidence being almost perfect. The other numerical experiments designed for the lifting profile NACA-4412, enlighten the compressibility and ground effects.