Quantification of wake unsteadiness for low- Re flow across two staggered cylinders

This work performs a numerical investigation on the two-dimensional flow across two circular cylinders in staggered arrangement at Re = 100. The seaparting distances between the centers of the cylinders are D/d = 4–10 with ΔD/d = 2 and T/d = 0.0–2.0 with ΔT/d = 0.5 in the streamwise and transverse directions, respectively, in which d is the cylinder diameter. Although the low-Re flow across staggered cylinders has been studied in a number of works, the authors mainly concerned about the identification and transition of various flow patterns. In this work, our objective is to quantitatively reveal the characteristics of flow unsteadiness as affected by the two separating distances. The flow unsteadiness is assessed from several aspects, including the spatial distributions and temporal variations of instantaneous flow patterns, fluctuating characteristic quantities, and fluctuating flow in the gap and in the near- and far-wake regions. To investigate the inherent instability of the flow, the global linear stability and sensitivity analysis is further carried out to demonstrate the unstable mode of perturbation growth and the critical flow patterns that destabilize the flow. The numerical results reveal that the wake flow between the two centerlines and beside the upstream cylinder is the most intensely perturbed. The flow around the downstream cylinder exhibits great fluctuation as perturbed by the destabilized shear layer of the upstream cylinder. The flow downstream of both cylinders shows multiple peak fluctuation of velocity because of the complex interactions between the destabilized shear layer and the wake vortices, resulting in the bidirectional transverse propagation of fluctuation. The stability analysis demonstrates that the unstable mode of perturbation growth is more significant in the far-wake region as the two cylinders are placed in proximity; the sensitivity analysis shows that the gap flow is crucial for the flow destabilization at small D, while the wake flow of cylinder-B is more significant for large D.