A direct numerical simulation is applied to investigate three-dimensional unsteady flow characteristics around a finite wall-mounted square cylinder with an aspect ratio of 7 at a Reynolds number (Re) of 40-250. Determination of Re for the onset of vortex shedding and Re influence on the wake structure and integral parameters are the major objectives of the current research. The results show that the vortex shedding inception occurs within the range of 75 < Re < 85. Re has a considerable effect on the mean wake topology and integral parameters. As such, the wake flow changes from a dipole to a quadrupole type, when the flow changes from steady to unsteady. A transition flow commences at Re = 150-200, where the wake instabilities are intensified with increasing Re, and the force signal oscillation alters from a sinusoidal to a chaotic type. Finally, the wake flow becomes turbulent at Re > 200.

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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.

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