Numerical simulation of the viscous flow around bluff bodies via the random Vortex method

The viscous, incompressible and laminar flow around bluff bodies is analysed via a random vortex method using a hybrid (Eulerian-Lagrangian) scheme. The Navier-Stokes equations, written in the form of vorticity equations, are split into nonlinear convection and linear diffusion parts according to a fractional step method. Vorticity is modelled by discrete point vortices. Vortices are created on the surface to satisfy the zero tangential velocity boundary condition. Random walks are applied to the vortices to simulate the diffusion equation. Vortices are then convected in an inviscid calculation in the Lagrangian scheme to simulate the convection equation. The velocity of each vortex is calculated using the Clould-in-Cell method.The random vortex method is developed to simulate the flow around a circular cylinder with a splitter plate. A conformal transformation is used to map the cylinder with a splitter plate to a unit circular cylinder. The force coefficients and Strouhal number are presented for various lengths of the splitter plate and are in good agreement with experiments.The random vortex method has also been developed for the flow around a circular cylinder vibrating transverse to the flow in a channel. The results are presented for various values of Reynolds number, forcing frequency and vibration amplitudes. The effect of blockage on the drag coefficient is presented. The drag coefficient and vortex shedding frequency are shown to compare favourably with experimental results. The flow around a vibrating cylinder with a splitter plate is also simulated. The results are presented for various values of forcing frequency and lengths of the splitter plate.The flow around multiple stationary cylinders is also simulated. Also, results are presented for the flow around two cylinders, one of which is forced to oscillate in a transverse direction. The numerical results of Strouhal number are in reasonable agreement with experiments