Laminar steady and unsteady flow around a convex-shape grooved cylinders

This paper provides the impact of roughness on the hydrodynamic behavior of the fluid over a convex-shape grooved cylinder by examining the shape and amplitude of the groove influence on the average flow rate. Direct numerical investigations of two-dimensional flow around a convex-shape grooved cylinder are performed at Reynolds number up to 100. A Reynolds number up to 40 corresponds to laminar flow in a stable state presenting the creeping and symmetry regimes and Re of 100 corresponds to laminar unstable flow presenting pure Karman vortex street flow regime. The number of grooves is set at 10, 20 and 30, uniformly spread around the periphery of the cylinder, with three different wave amplitudes of 1/50, 1/25 and 1/12.5, for each geometry. The numerical algorithm applied in this investigation is based on the finite volume method. The obtained results are compared with the smooth cylinder at the same Reynolds number, that latter shows excellent agreement with the available data in the literature. The forces acting on the cylinder are seen to be reduced by the presence of the grooves; this reduction is more significant with increasing groove amplitude, especially at a high Reynolds number. At Reynolds number equal 100, when the groove number and wave amplitude are set to 10, 1/12.5, respectively, the drag coefficient is lowered by about 10%, while the lift coefficient is reduced by around 25%.