Discrete vortex method simulation of the flow around a circular cylinder with and without rotation

Abstract

In this paper we simulate the two-dimensional, incompressible, unsteady flow around a circular cylinder. Two cylinder configurations are considered: with and without rotation. We use a lagrangian meshfree vortex method to calculate global as well as local quantities in a high Reynolds number flow. In our novel algorithm vortices with a Lamb core 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 the application of the circle theorem. The dynamics of the body wake is computed using the convection-diffusion splitting algorithm, where the convection process is carried out with a lagrangian firstorder time-marching scheme, and the diffusion process is simulated using the random walk method. The aerodynamic forces are calculated from the unsteady Blasius equation, and the pressure distribution is also computed. Our results for the lift and drag coefficients, Strouhal number and pressure coefficient are found to be in good agreement when compared to numerical and experimental results available in the literature.