Dynamic responses and flow-induced vibration mechanism of three tandem circular cylinders in planar shear flow

Abstract

Numerical study is conducted on flow-induced vibrations (FIVs) of three circular cylinders arranged in tandem with spacing ratio L/D = 5.5 in planar shear flow. The cylinders are free to vibration in both in-line and transverse directions. A four-step semi-implicit Characteristic-based split (4-SICBS) finite element method is adopted to solve the governing Navier-Stokes equations. The mass ratio of each cylinder is set as mr = 2.0, and the structural damping ratio as zero to maximize the flow-induced responses of the cylinders. The effects of three main parameters, such as the Reynolds number (Re = 80, 120, 160), the shear ratio (k = 0.0, 0.05, 0.1), and the reduced velocity (Ur = 3–21), are considered. The changes of vibration amplitudes, frequency characteristics, motion trajectories and flow characteristics are analyzed. The results show that, the dynamic responses of the upstream cylinder are similar to those of an isolated cylinder. The Re, k and Ur play a more important role in the FIVs of the midstream and downstream cylinders. As Re ≤ 120, the dynamic responses of the cylinders change slightly with the increasing of Re, while they present a dramatic increase because of the unstable flow characteristic at Re = 160. Additionally, with the increasing of Re, the vibration response mechanism of the cylinders in the in-line direction will change from resonance phenomenon into the vortex interference. For the motion orbits of the circular cylinders, in additional to the eight-figure, raindrop, oval and irregular shape, the dual-raindrop, dual-eight and dual-oval sharp are observed. Finally, regarding the flow field, it is found that the interference of the wake vortex is highly affected by the shear ratio of the incoming flow, resulting in great changes on the wake pattern and dynamic responses. Especially, the “2T”wake pattern is observed.