Flow past two diamond-section cylinders in tandem arrangement at a low Reynolds number

Abstract

The unsteady flow surrounding two fixed diamond cylinders is analyzed at Reynolds number 100 over normalized center-to-center spacing ratios 2−15. By analyzing the contours of instantaneous vorticity, variations of recirculation length, surface pressure, and fluid forcing of cylinders, the value of normalized critical spacing is found to be 3.4. In the reattachment zone below critical spacing, vortex-shedding from the upstream (UC) and downstream (DC) cylinders is anti-phase. At the critical spacing, regular vortex-shedding commences also from the UC, and vortex-shedding from the cylinders becomes phase synchronized for the first time. The analysis of a vortex-shedding cycle at the critical spacing reveals that the cylinders shed vortices at the same frequency, but with a time delay. Impingement of vortices shed from the UC on the DC strengthens vorticity around the DC and shifts the instantaneous position of its forward stagnation point from the leading edge. The understanding that locations of stagnation points govern the direction and magnitude of lift force comes from the analysis of flow at the critical gap. When the surface bounded by stagnation points is occupied mostly with negative vorticity, the instantaneous lift is negative and vice versa. At critical spacing, mean streamlines show the emergence of an anti-wake at forward stagnation point of the DC for the first time. Over the entire range of cylinder separation, nine distinct patterns of separation topologies are identified. Below critical spacing, both pressure and viscous drag components, and hence, total drag of the DC are negative or upstream-acting.