A wake source model for bluff body potential flow

Abstract

A theory is presented for two-dimensional incompressible potential flow external to a symmetrical bluff body and its wake. The desired flow-separation points are made the critical points of a conformal transformation to a complex plane in which surface sources in the wake create stagnation conditions at the critical points. The stagnation streamlines then transform to tangential separation streamlines in the physical plane, with separation at the desired pressure. The position and strength of the sources are determined by the requirements of separation position and pressure coefficient. The flow inside the separation streamlines is ignored and base pressure is assumed constant at the separation value. Features of the theoretical model include a finite wake width, a pressure distribution on the separation streamlines decreasing asymptotically towards the free stream value at infinity and a simple analytic expression for the pressure distribution on the body. Comparisons of the theory with experimental data and with other theories are presented for the normal plate, the circular cylinder, the 90° wedge, and the elliptical cylinder. Although simpler to apply than the other theories, the present theory produces at least as good agreement with the experimental data.