Integral Equation Method for Subsonic Flow Past Airfoils in Ventilated Wind Tunnels

The method of contour distribution of sources and vortices, used to calculate potential flows about twodimensional airfoils in free air, is extended to flows around airfoils under the constraint of ventilated wind tunnel walls. Based on the concept of fundamental solutions, the source and vortex singularities are modified to satisfy the boundary conditions at the walls. The application of the airfoil boundary condition reduces the problem to a Fredholm integral equation of the second kind for the source density function. The numerical solutions obtained by a finite element technique are in good agreement with experimental results. I. Introduction A LARGE part of established wall interference theory is based on the simplifying assumption that the wall effects can be evaluated from an estimated far flowfield of the model, considering only the wind tunnel wall boundary condition. The result is interpreted in terms of modifications to the freestream. If the model is small enough, these can be expressed as corrections to the direction and speed of the stream, constant over the model (the angle of attack and Mach number corrections). If the model has appreciable length, a more refined interpretation, involving the streamline curvature and buoyancy (pressure gradient) effects, is required. The model boundary condition enters the problem only in the final stage, if there is a need to evaluate the wall effects in terms of model quantities, such as the surface pressure distribution, aerodynamic forces, moments, etc. A comprehensive account of this approach, its applicability and limitations is given in Ref. 1. It is perhaps worth emphasizing that the above concept