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.