Subsonic airfoils with a given pressure distribution

An inverse design procedure for airfoils, based on hodograph techniques, has been developed. For subcritical flows the subsonic portion of the pressure distribution is prescribed; for supercritical flows the stream function on the sonic line is given instead of the supercritical portion of the pressure distribution. In the special variables we use, the equation for the stream function may be solved iteratively using a fast Poisson solver, for the subsonic portion of the flow; for supercritical flows, the supersonic portion is calculated using a characteristic calculation. The results are then mapped back to the physical plane to determine the airfoil shape. Both subcritical and supercritical results are presented. The show good agreement with the direct computation of the flow past the designed airfoil. (Author)