Vortex shedding from edges including viscous effects

Abstract

This paper describes results obtained by using the inviscid Cloud-in-Cell vortex method to model the vortex sheet which is shed and rolls up from a single sharp edge. There is good agreement between these results and previous (Pullin 1978) computations of the development of the sheet in impulsively started incompressible inviscid flow. The Cloud-in-Cell method has been modified to include viscous diffusion calculated by finite differences on the mesh to give a mixed Eulerian-Lagrangian Navier-Stokes solver. This method has been shown to model the diffusing free vortex and the Stokes boundary layer quite accurately. It is used to compute impulsively started flow past sharp right-angled edges and edges with small rounding. The effect of viscous diffusion on the development of the shed vortex is discussed.The method is also used to study the effect of rounding on the vortex shedding from a right-angled edge in oscillatory flow. This problem is particularly important in determining the roll damping and hence response of certain types of ship hull in waves. It is shown that the strength and effect of the shed vortices rapidly decrease as the ratio of the edge radius to the oscillation amplitude increases, and that at larger values of this ratio the mode of shedding changes from two vortices per cycle from one edge to a more complicated mode. The computed results are compared with flow visualisation using dye and neutrally buoyant particles in water flow around an oscillating edge.