Wake evolution and vortex structure characteristics of flow over two tandem semi-circular cylinders with flat surfaces facing each other

Abstract

This paper reports the results of a numerical investigation into the flow over two tandem semi-circular cylinders with flat surfaces facing each other and the associated wake flow characteristics. The effect of spacing ratio (L/D, L is the in-line spacing between two flat surfaces and D is the diameter of cylinders) ranging from 1 to 16 is examined in a low Reynolds number range of Re = 60–180. Five flow patterns are identified including the over-shoot, continuous reattachment, alternate reattachment, quasi-co-shedding, and co-shedding regimes. The difference between quasi-co-shedding and co-shedding regimes depends on the origin of the vortices shed from the downstream cylinder. Unlike the vortices generated due to the roll-up of shear layers detached from both upstream and downstream cylinders in the co-shedding regime, the vortices shed from the downstream cylinder come from upstream instead of the roll-up of shear layers for the quasi-co-shedding regime. The wake flow characteristics are discussed in terms of the vortex formation and shedding, wake structure and evolution, boundary layer separation and shear layer development, the occurrence of secondary vortex street, and the associated migrating vortex modes. The variations of hydrodynamic coefficients and Strouhal number are associated with the flow regime transition. When the alternate reattachment and quasi-co-shedding regimes emerge, a small pair of peaks of the root-mean-squared streamwise flow velocity (u*rms) fixedly occurs at the two corners of the downstream cylinder, illustrating the strong velocity fluctuation caused by vortices impingement and the secondary separation. Three types of vortex street are observed in the wake, where the secondary vortex street region is further divided into three parts in terms of the vortex structure, including S + P (a single vortex and a pair of vortices are formed per cycle in the secondary vortex street), P (a pair of vortices is formed per cycle in the secondary vortex street), and 2S (two vortices in opposite directions are formed per cycle in the secondary vortex street) modes. Two partitions in Re–L/D map (Re and L/D as the vertical and horizontal ordinates, respectively) are proposed in this work for the flow regime as well as the vortex street.