Numerical simulation of steady incompressible slip flow around a circular cylinder at low Reynolds numbers

Abstract

Steady viscous flow past a circular cylinder with velocity slip boundary condition is numerically solved. The Navier–Stokes equations are solved using the vorticity-stream function formulation for two-dimensional incompressible flows. A time-accurate solver is developed which can be used for accurate solution of time-dependent flows. However, only steady results for Reynolds numbers up to 40 are presented in this paper. Most of the emphasis is dedicated to the validation of the solver and the results, something which is more or less missing in previous studies of slip flows. There has been a controversy regarding the computation of the drag coefficient and its various contributions in the past. As reviewed in the text, some papers did not present the formulation of the drag coefficient and only presented the results, some papers used the no-slip formulae and some papers presented formulae for the slip case but did not validate them. Due to this controversy, we derived formulae for the various contributions to the drag coefficient and validated them by comparison to existing data, especially using an analytical solution of Oseen’s equation for creeping flow around a cylinder with slip condition. At the end, some results are presneted including wall vorticity and slip velocity distribution, streamlines, vorticity contours and various contributions to the drag coefficient.