Transition of wake flows past two circular or square cylinders in tandem

Abstract

This paper presents the dependence of flow transitions and flow regimes on Reynolds number Re (≤ 105) and scaled cylinder center-to-center spacing S* (≤ 10) for two tandem cylinders. Both circular and square cross-sectional geometries are considered, and a comparison of results is made between the two geometries. To do so, data available from the literature are collected, and supplementary numerical simulations are done to complement the literature data so as to provide clear-cut flow maps in the Re-S* domain. We identified the borders of Re- and S*-dependent flows, including steady, unsteady, transition, slender/extended body, alternating reattachment, bistable, and co-shedding flows. The flow interference between two tandem cylinders with S* < S*cr is susceptible to stabilize the flow that requires a higher Re for the onset of vortex shedding than the isolated cylinder counterpart, where S*cr is the critical spacing for the onset of co-shedding flow. Besides, the flow interference generally postpones and advances the onset of secondary vortex shedding associated with the transition from two- to three-dimensional vortex shedding for S* < S*cr and S* > S*cr, respectively. Two flow maps are made for the two geometries, both yielding fundamental contributions toward a better understanding of the flow interference effect on various flow transitions. The flow maps determine the regions of a dearth of knowledge, which future studies may pay attention to. Finally, the drag inversion, hysteresis, and flow patterns in the proximity of the onset of vortex shedding for tandem square cylinders (1.5 ≤ S* ≤ 7) are discussed.