A TRIBUTE TO M.M. (MICKY) ZDRAVKOVICH

Abstract

The flows around two tandem circular cylinders in the subcritical and supercritical flow regimes are studied through three-dimensional numerical simulations. Different spacing ratios L/D (where L is the center-to-center distance between the two cylinders with D being the diameter of the cylinders) from 2.0 to 5.0 is considered. The instantaneous flow structures, pressure distributions and hydrodynamic forces on two tandem cylinders are analyzed at subcritical (Re=2.2×104) and supercritical (Re=3.0×106) Reynolds numbers. The present numerical solutions demonstrated that at the two Re, for L/D<3.5, the shear layer from the upstream cylinder reattaches on the surface of the downstream cylinder and vortex street is only formed behind the downstream cylinder, while the shear layer from the upstream cylinder rolls up alternately for L/D≥3.5, and vortex shedding occurs from both upstream and downstream cylinders. Compared with the flow characteristics at Re=2.2×104, for Re=3.0×106, the flow separation positions on the upstream cylinder move backward and the width of the wake behind the upstream cylinder becomes narrower, which leads to forward movement of the reattachment position. At the supercritical Reynolds number, the mean drag and fluctuating lift coefficients of the upstream cylinder are nearly independent of L/D while the sharp increase of force coefficients of the downstream cylinder occurs for L/D=3.5. Comparing to the case at the subcritical Reynolds number, higher vortex-shedding frequencies from the upstream and downstream cylinders are identified. It is also revealed that the slope of the best fit line for φ (the phase lag of the fluctuating lift force between two cylinders) and L/D increases at the supercritical Reynolds number. In addition, for L/D=2.5, the mean drag coefficients of the upstream cylinder decrease sharply for Re>1.0×105, while those of the downstream cylinder rise slightly with the growing Re. Moreover, the fluctuating lift coefficients of the upstream cylinder are almost independent of Re, but those of downstream cylinder drop as Re increases.