Lock-in study of two side-by-side cylinders of different diameters in close proximity in steady flow

Lock-in of the vortex-induced vibration of two side-by-side circular cylinders of different diameters (diameter ratio d/D=0.1) is investigated numerically. The cylinders are located in close proximity and free to oscillate in the cross-flow direction. The initial gap between the two cylinders is set the same as the small cylinder diameter (d). The mass ratios of both cylinders (m⁎) are fixed to be 5 and the damping ratios are small enough to be negligible. Simulations are first carried out for two cases where the large-to-small-cylinder natural frequency ratio is 1. Case 1 is focused on the lock-in of the large cylinder and Case 2 is focused on the lock-in of the small cylinder, which is far narrower than that of the large cylinder. Then simulations are carried out at a natural frequency ratio (small-to-large-cylinder) of 0.1, where both cylinders are expected to lock on to their own natural frequencies (referred to be Case 3). The interference between the two cylinders under these conditions is investigated in detail. The widening of the lock-in range of the reduced velocities for the large cylinder in Case 1, the beating behavior of the small cylinder in its lock-in range in Case 2 and the dual lock-in behavior of the small cylinder during the simultaneous lock-in of both cylinders in Case 3 are some of the key findings of this study.