Two-dimensional potential flow solutions with separation

Abstract

A procedure for constructing two-dimensional incompressible potential flowfield solutions with separation and a recirculation region is presented. It naturally makes use of complex variable theory and other analysis techniques such as conformal mapping and the generalized Poisson integral formula. Flowfield determination is reduced to solution of a boundary value problem in various simple domains. The entire velocity field is described analytically; stream function and velocity potential contour maps are readily constructed. Example solutions are presented. Solutions for sharp leading edge airfoils at arbitrary angle of attack are completely determined, including the limiting angle of attack for upper-surface flow re-attachment. For other configurations (e.g. circular cylinder, backward-facing step) the analytical solution contains one or more free parameters, whose values may be inferred from boundary layer theory or experiment.