Numerical predictions of flows past two tandem cylinders of different diameters under unconfined and confined flows

Flows past two tandem cylinders of different diameters placed in a free-stream velocity and between two parallel walls are numerically studied via a lattice Boltzmann method. In both the big-small arrangement (BSA) and the small-big arrangement (SBA), the diameter of the big cylinder is adopted as the characteristic length and the diameter ratios of two cylinders are 0.5, 0.625, 0.75 and 0.875, respectively. The effects of the Reynolds number, diameter ratio, arrangement pattern, cylinder spacing and plane boundaries on the flows are systematically investigated. In the binary-vortex regime, the results show that for both the unconfined and confined cases, vortices are shed from both cylinders in a coupled frequency which is mainly dependent on the front cylinder in contrast with the case of an isolated cylinder. The vortex structures in BSA are more regular than those observed in SBA and the plane boundaries have a modulation effect on the flow. In SBA, the flow structure becomes more irregular as the diameter ratio is decreased and as the Reynolds number is increased and the mechanism of such a phenomenon is also discussed. In both BSA and SBA, when the cylinder spacing is increased to a threshold, the wake structure translates from the reattachment regime to the co-shedding regime and the critical spacing in BSA is smaller than that in SBA. As the cylinders are placed in proximity to each other, the negative and positive drag coefficients of the downstream cylinder are observed in BSA and SBA, respectively. The positive drag coefficient in SBA decreases as the diameter ratio is increased.