A Numerical Solution for Potential Flows Including the Effects of Vortex Shedding

This paper reports on an attempt to include vortex shedding effects into potential flow calculations using the boundary element method. Significant computational advantages result because of the relatively simple approach to handling separation at the sharp edges while working only with the boundary values. A discrete vortex method was incorporated into a time domain boundary element algorithm for the numerical simulation of oscillating flow past a normal flat plate. Separation from a sharp edge results in the formation of a vortex sheet issuing from the edge. This vortex sheet is modeled by a series of discrete vortices introduced one at a time into the flow field at regular intervals. The motion of each vortex is traced over time using its convection velocity. As long as the Keulegan-Carpenter number is small enough, vortex shedding takes place close to the edge. The discrete vortex method can, in such cases, be looked upon as the inner region solution to the problem of normal oscillating flow past the flat plate. This inner region solution has to be matched with the outer potential flow solution. The combination of boundary element and discrete vortex methods provides this matching and at the same time does not require calculations inside the domain.