Wake transitions of six tandem circular cylinders at low Reynolds numbers

Direct numerical simulations for flow over six tandem circular cylinders at Reynolds numbers ( R e ) from 40 to 180 and gap ratios ( G / D) from 0.5 to 18 were conducted. The main aims are to identify vortex transitions from primary to secondary vortices and from secondary to tertiary vortices and to explore the mechanisms for these transitions. In addition, the variations of the force coefficients and Strouhal numbers with the transitions are also examined. Based on the characteristics of vortex shedding frequency, flow patterns, and force coefficients on the cylinders, four flow regimes, namely, no-shedding, primary shedding, secondary shedding, and tertiary shedding regimes, were mapped out in the Re- G / D domain. The three shedding regimes always initiate from the last cylinder. With the increase of Re and/or G/D, the onset locations of the regimes shift upstream. The secondary and tertiary vortices are formed after a region of convective instability characterized by two-row parallel vortex streets or shear layers. Two physical mechanisms for the transition from primary to secondary vortices are identified. The first one is associated with shear layer instabilities developed after the decay of the primary vortices, and the second one is the merging of the primary vortices. The transition from secondary to tertiary vortices involves vortex merging only. Whereas no-shedding or primary shedding regimes occur at smaller gap ratios or lower Reynolds numbers, the three vortex shedding patterns (primary, secondary, and tertiary) can co-exist for larger gap ratios or higher Reynolds numbers, and each pattern dominates a region around the group of cylinders. The variations of the flow patterns, vortex shedding frequency, and force coefficients on the cylinders in each of the flow regimes are quantified and interpreted. When the number of cylinders is increased to more than 6 at a gap ratio of 15, no further transition is observed after the transition to tertiary wake, and the vortex shedding processes on the downstream cylinders become chaotic without a dominant frequency, suggesting that for multiple tandem cylinders, only two transitions, corresponding to the generations of the secondary and tertiary vortices, can be identified. The change in Reynolds number or gap ratio influences the onset locations of the transitions only.

Automated summary

This study uses direct numerical simulations to investigate the flow over six tandem circular cylinders at different Reynolds numbers and gap ratios. The aim is to understand the vortex transitions and explore the mechanisms behind them. Four flow regimes are identified based on vortex shedding frequency, flow patterns, and force coefficients. The transitions from primary to secondary vortices involve shear layer instabilities and vortex merging, while the transitions from secondary to tertiary vortices only involve vortex merging. The onset locations of the transitions are influenced by the Reynolds number and gap ratio.