Low-Re flow past an isolated cylinder with rounded corners

Abstract

Direct numerical simulation is performed for flow past an isolated cylinder at Re=1,000. The corners of the cylinder are rounded at different radii, with the non-dimensional radius of curvature varying from R+=R/D=0.000 (square cylinder with sharp corners) to 0.500 (circular cylinder), in which R is the corner radius and D is the cylinder diameter. Our objective is to investigate the effect of the rounded corners on the development of the separated and transitional flow past the cylinder in terms of time-averaged statistics, time-dependent behavior, turbulent statistics and three-dimensional flow patterns. Numerical results reveal that the rounding of the corners significantly reduces the time-averaged drag and the force fluctuations. The wake flow downstream of the square cylinder recovers the slowest and has the largest wake width. However, the statistical quantities do not monotonically vary with the corner radius, but exhibit drastic variations between the cases of square cylinder and partially rounded cylinders, and between the latter and the circular cylinder. The free shear layer separated from the R+=0.125 cylinder is the most stable in which the first roll up of the wake vortex occurs furthest from the cylinder and results in the largest recirculation bubble, whose size reduces as R+ further increases. The coherent and incoherent Reynolds stresses are most pronounced in the near-wake close to the reattachment point, while also being noticeable in the shear layer for the square and R+=0.125 cylinders. The wake vortices translate in the streamwise direction with a convection velocity that is almost constant at approximately 80% of the incoming flow velocity. These vortices exhibit nearly the same trajectory for the rounded cylinders and are furthest away from the wake centerline for the square one. The flow past the square cylinder is strongly three-dimensional as indicated by the significant primary and secondary enstrophy, while it is dominated by the primary enstrophy (ωz2) for the rounded cylinders.