NUMERICAL SIMULATION OF THE FLOW AROUND A SQUARE CYLINDER USING THE VORTEX METHOD

Abstract

The study of external incompressible flows around bluff bodies finds extensive applicability to real-life problems. Such flows are characterized by unsteady flow separation for high values of the Reynolds number, where a Von Karman-type periodic wake is formed. The prediction of these flows is very difficult, and one has usually to rely on specific experimental data to calculate the aerodynamic forces on the body. In order to numerically simulate this flow, this paper uses a new mesh-free two-dimensional Discrete Vortex Method associated with a Panel Method to calculate the lift and drag coefficients, as well as the pressure coefficient on a square cylinder, for a high Reynolds number flow. Lamb vortices are generated along the cylinder surface, whose strengths are determined to ensure that the no-slip condition is satisfied and that circulation is conserved. The impermeability condition is imposed through a source panel method, so that mass conservation is explicitly enforced. The dynamics of the body wake is computed using the convection-diffusion splitting algorithm, where the diffusion process is simulated using the random walk method, and the convection process is carried out with a lagrangian second-order time-marching scheme. Results for the aerodynamic forces and pressure distribution are presented.