Numerical Study on Vortex Induced Vibrations of Four Cylinders in an In-Line Square Configuration

The two-dimensional numerical simulation of the vortex induced vibrations of four cylinders in an in-line square arrangement is investigated at low Reynolds number in this paper. The mean and fluctuating aerodynamic forces, Strouhal number (St) and vortex shedding pattern in the wake for each cylinder are analyzed with the six spacing ratio L/D changing from 2.5 to 6.0. The results indicate that the mean drag force and the fluctuating lift forces and the transverse displacements of the upstream cylinders are relatively larger than the downstream cylinders, and the downstream cylinders usually undergoing serious fluctuating streamwise displacement. The dominant frequency of drag coefficient is equal to St of downstream cylinders for all spacing ratio, so the simultaneous resonance in the in-flow and cross-flow directions may occur for downstream structures of multi-body oscillating system. The streamwise oscillation of downstream cylinders which is free to move in two degrees of freedom could be as large as 0.75 diameter, and the maximum transverse amplitude of upstream cylinders may achieve 0.82 diameter, is much higher than the transverse amplitude of flow around a single cylinder at same parameter setting.