Wall interference in a subsonic windtunnel with slotted walls

Abstract

A method for the calculation of wall interference in a subsonic windtunnel was developed. A rectangular windtunnel with slotted and solid wall elements was used. A lifting model, represented by horse shoe vortices, was place symmetrically about the center inside windtunnel. The total velocity potential for the flow inside the windtunnel is expressed as the summation of perturbation potential and the velocity potential at free stream velocity. The perturbation potential is the contribution from the model and the boundaries of the windtunnel. The model potential is assumed known and the interference potential, which is due to the walls of the tunnel, is calculated. A non-dimensional Laplace equation for the interference potential is fourier transformed and solved. The particular solution is a Bessel function. This solution is used to obtain an expression for the interference potential due to any slotted or solid wall element. The expression is multiplied by the influences coefficient of each element. The influence coefficients are obtained by satisfying the boundary conditions. The total interference potential due to each element is calculated. The sum of the contribution due to all elements gives us the interference potential due to the wall. The interference potential is used to obtain the upwash and the streamline curvature in the transformed plane. This is inverted to obtain the upwash and the streamline curvature in the physical plane.