Vortex-induced vibration of two circular cylinders at low Reynolds number

Abstract

Vortex-induced vibration of a pair of equal-sized circular cylinders in tandem and staggered arrangements in laminar flow regime is investigated. A stabilized finite element method is utilized to carry out the computations in two dimensions. Both cylinders are free to oscillate in transverse as well as in-line directions. The Reynolds number, based on the free-stream speed, U, and the diameter, D, of the cylinders is 100. To encourage high amplitude of oscillation the structural damping is set to zero and cylinders of low nondimensional mass are considered (m^∗=10). The computations are carried out for various values of reduced speed of the oscillator (2≤U^∗≤15). The cylinders are separated by 5.5D in the streamwise direction. They are separated by 0.7D in the cross-flow direction to study the effect of stagger. The downstream cylinder lies in the wake of the upstream one and experiences an unsteady inflow. The upstream cylinder in both tandem and staggered arrangement responds qualitatively similarly to a single cylinder. Compared to an isolated cylinder, a small increase in transverse oscillation amplitude of the upstream cylinder is observed due to the presence of the downstream cylinder. In both arrangements, the downstream cylinder shows very large amplitude transverse oscillations comparable to that of a single cylinder at higher Re. In the staggered arrangement, very large streamwise oscillations of the downstream cylinder are observed. Compared to an isolated cylinder, the synchronization range for the two-cylinder arrangement is larger. The downstream cylinder in the staggered arrangement undergoes two types of motion: an orbital motion at most of the U^∗ studied, and figure-of-eight motion for a small range of U^∗. In the tandem arrangement, only the figure-of-eight motion is observed. The stagger in the arrangement of the two cylinders is found to have a significant effect on the flow.