A vortex method for viscous unsteady flows

Abstract: A simple method is presented for the creation of vorticity from a solid boundary in the form of discrete vortex blobs. These vortices have uniform-vorticity cores and are released from a number of points distributed around the body surface at a small distance away from the surface. Their strengths are obtained by satisfying the no-slip condition at the midpoints of the corresponding vortex sheets. The dynamics of these vortices is then considered by including the effect of viscous diffusion by random walk approach. The method is applied to the starting flow past a circular cylinder. A detailed parametric study shows that viscosity has the most significant effect on the computed results and, in order to obtain meaningful results, it must be reduced suitably to compensate for the artificial viscosity arising from numerical integration of equations of motion of the discrete vortices. Results are obtained for three typical Reynolds numbers of 9500, 3000 and 550, and are found to be in very good agreement with experimental measurements for the center-line velocity distribution. In particular, the case of Re=&5Q illustrates the usefulness of the present model even at low Reynolds numbers. The vortex patterns, velocity vectors and particle path lines also conform to the experimental flow visualization pictures. Though the method is developed for a simple configuration like a circular cylinder, it can be easily extended to any general body shape. 1