THE APPLICATION OF THE BOUNDARY INTEGRAL-EQUATIONS METHOD TO SUBSONIC FLOW WITH CIRCULATION PAST THIN AIRFOILS IN A WIND-TUNNEL

In this paper we apply the direct boundary integral equations method to subsonic flow with circulation past a thin airfoil in a wind tunnel. A set of Green's functions for the equations of the velocity perturbation is deduced. These functions together with the non-linear limit condition imposed just on the surface profile lead to a Fredholm integral equation of the second kind over the profile only. The integral formulation has the advantage not to truncate the flow domain and to save computing effort when numerical solving is performed, due to the lack of the tunnel walls discretisation. In the case of the incompressible fluid we use the exact equations of motion, which implies a valid solution for any shape of the profile, being not necessarily thin. In the case of the compressible fluid we use the linearized motion equations, which implies a valid solution only for thin airfoils. The integral equation obtained on the surface, together with the circulation integral formula are solved via a collocation method. The numerical tests made for the circular obstacle show a very good agreement with the theory. The numerical experiments on the NACA-4412 profile were made in order to determine the tunnel and the compressibility effects being compared to the unbounded flow.