Quantitative numerical analysis of flow past a circular cylinder at Reynolds number between 50 and 200

Results of numerical simulations are presented for flow past a stationary circular cylinder at low Reynolds numbers (Re=50–200). The simulations were carried out using a finite-volume code employing a fractional step method with second-order accuracy in both space and time. A sensitivity study on numerical parameters concerning the domain size, grid independence and time step resolution was carried out in detail for Re=100. Global time-averaged results on force coefficients, non-dimensional velocities and pressures, including their corresponding r.m.s. values, as well as various quantities related to the separation and vortex shedding characteristics are presented. A non-monotonous streamwise velocity recovery in the intermediate wake is observed for Re > 50 , a phenomenon that has been grossly overlooked in the past. There are two plateaus along the wake centerline, in particular for Re=200. The first, which is the most distinct, ranges from about x=9 to x=16 at a wake deficit velocity of 0.38, x being counted in diameters behind the cylinder axis; the second one appears from x=25 to x=28 at a wake deficit velocity of 0.54. This phenomenon seems to be related to an associated change-over in the orientation of the von Kármán vortices and the merging trends, especially for Re=200 beyond x=25, as observed from instantaneous vorticity fields. Three-dimensional simulations using spanwise lengths of 10 and 12 (diameters) were carried out at Re=200. After a long initial phase with regular three-dimensional mode A flow features increasing very slowly in amplitude, the flow went into a state with distinct pulsating forces acting on the cylinder, the pulsations being seemingly randomly localized across the cylinder span. In this second, much more chaotic, flow state, the time-averaged results were in agreement with previous experiments and with parts of previous numerical studies.