EMENDATION OF THE BROWN-AND-MICHAEL EQUATION, WITH APPLICATION TO SOUND GENERATION BY VORTEX MOTION NEAR A HALF-PLANE

A reappraisal is made of the Brown & Michael (1954, 1955) equation tha t is widely used to model high-Reynolds-number vortex shedding in two dimensions by rectilinear vortices of time-dependent circulations. It is concluded that the equation introduces an unbalanced and unacceptab le surface force that can significantly influence predicted flow chara cteristics. A corrected equation is derived which removes this force, and is applied to determine the sound generated at low Mach numbers wh en a line vortex translates around the edge of a rigid half-plane. The solution of this problem in the absence of vortex shedding (Crighton 1972) is extended by permitting shedding to occur at the edge in accor dance with the unsteady Kutta condition. The shed vorticity is assumed to roll-up into a concentrated core whose motion is calculated by bot h the emended and original Brown & Michael equations. The two models e xhibit large qualitative differences in the predicted wake flow near t he edge; both predict significant reductions in the radiated sound, bu t the reduction is smaller by about 4 dB for the emended Brown & Micha el equation.