Interaction dynamics of gap flow with vortex-induced vibration in side-by-side cylinder arrangement

A numerical investigation of the vortex-induced vibration (VIV) in a side-by-side circular cylinder arrangement has been performed in a two-dimensional laminar flow environment. One of the cylinders is elastically mounted and only vibrates in the transverse direction, while its counterpart remains stationary in a uniform flow stream. When the gap ratio is sufficiently small, the flip-flopping phenomenon of the gap flow can be an additional time-dependent interference to the flow field. This phenomenon was reported in the experimental work of Bearman and Wadcock [“The interaction between a pair of circular cylinders normal to a stream,” J. Fluid Mech. 61(3), 499–511 (1973)] in a side-by-side circular cylinder arrangement, in which the gap flow deflects toward one of the cylinders and switched its sides intermittently. Albeit one of the two cylinders is free to vibrate, the flip-flop of a gap flow during VIV dynamics can still be observed outside the lock-in region. The exact moments of the flip-flop phenomenon due to spontaneous symmetry breaking are observed in this numerical study. The significant characteristic vortex modes in the near-wake region are extracted via dynamic modal analysis and the interference between the gap flow and VIV is found to be mutual. In a vibrating side-by-side arrangement, the lock-in region with respect to reduced velocity becomes narrower due to the interference from its stationary counterpart. The frequency lock-in occurs and ends earlier than that of an isolated vibrating circular cylinder subjected to an identical flow environment. Similar to a tandem cylinder arrangement, in the post-lock-in region, the maximum vibration amplitudes are escalated compared with those of an isolated circular cylinder configuration. On the other hand, subjected to the influence from VIV, the biased gap flow deflects toward the vibrating cylinder quasi-stably during the frequency lock-in process. This behavior is different from the reported bi-stable regime in a stationary side-by-side arrangement. The analyses show that the flip-flop is associated with a characteristic low flip-flopping frequency, which is dependent upon the values of gap ratio, Reynolds number and the symmetry of the gap flow strength in a time-averaged sense. The disappearance of the flip-flop during the frequency lock-in of vibrating side-by-side arrangements is further investigated through a critical-point concept and a critical vortex merging distance.