Numerical simulations of steady flow past two cylinders in staggered arrangements

This paper presents a numerical study on steady flow around two identical circular cylinders of various arrangements at a low subcritical Reynolds number ($\mathit{Re}=10^{3}$). The ratio of centre-to-centre pitch distance ($P$) to the diameter of the cylinder ($D$) ranges from 1.5 to 4, and the alignment angle $({\it\alpha})$ between the two cylinders and the direction of the cross-flow varies from 0 to 90°. The detailed flow information obtained from direct numerical simulation allows a comprehensive interpretation of the underlying physics responsible for some interesting flow features observed around two staggered cylinders. Four distinct vortex shedding regimes are identified and it is demonstrated that accurate classification of vortex shedding regimes around two staggered cylinders should consider the combination of the flow visualization with the analyses of lift forces and velocity signal in the wake. It is revealed that the change in pressure distribution, as a result of different vortex shedding mechanisms, leads to a variety of characteristics of hydrodynamic forces on both cylinders, including negative drag force, attractive and repulsive lift forces. Two distinct vortex shedding frequencies are identified and are attributed to the space differences based on the flow structures observed in the wake of the cylinders. It is also found that the three-dimensionality of flow in the gap and the shared wake region is significantly weakened in almost two of the classified flow regimes; however, compared with the flow around a single cylinder, active wake interaction at large ${\it\alpha}$ does not clearly increase the three-dimensionality.