Simulation of unsteady flow past tapered circular cylinders using an immersed boundary method

Abstract

Three-dimensional numerical calculations of laminar vortex shedding behind a linearly tapered circular cylinder with taper ratio 75:1 have been carried out at a Reynolds number 131 (based on the large diameter and the uniform inflow velocity) using a Finite Volume code. Computations were performed on a staggered-Cartesian grid and a direct forcing Immersed Boundary Method (IBM) was used to transform the boundary condition at the solid surface into internal boundary conditions at the nodes of the Cartesian grid. Results showed a pattern of discrete oblique shedding cells, which included both vortex dislocation and vortex splitting. The local Strouhal number versus local Reynolds number curve showed excellent qualitative agreement with the experimental results reported by Piccirillo and Van Atta in 1993. However, quantitative deviations exist between the two techniques. Numerical noise (oscillations) was observed along the span in the steady flow calculation with Reynolds number 40, the reason for which has to be further investigated. The overall computational performance of the IBM proved to be very promising when compared to the boundary fitted or unstructured grid solvers