Slender Body Theory for Three-Dimensional Boundary-Layer Induced Potential Flows

Abstract

Abstract : The application of slender body theory for the evaluation of three- dimensional boundary layer induced surface crossflow and streamwise velocities is considered. The method is applicable to sub- and supersonic flows when small perturbation theory applies, and when the Reynolds number is large so that the thin boundary layer approximation is valid. The resulting potential problem is, in general, reduced to a two-dimensional consideration of the flow over an expanding cylinder with porous boundary conditions. As a model problem, the induced surface velocities are determined for the constant density flow over a body with constant elliptical cross-section. The limiting solutions for a flat plate of finite span and a near circular cross-section are obtained in a simple analytic form. In the former case, within the limitations of slender body theory, the results are in exact agreement with the complete three-dimensional solution for this geometry.