Numerical study on vortex-induced vibration of four circular cylinders at low Reynolds number

Vortex-Induced Vibration (VIV) of multiple cylinders has received increasing attention in the ocean engineering field in recent years. In this paper, a two-dimensional numerical model for studying VIV of multiple cylinders is developed. Based on a fixed Cartesian grid with local mesh refinement adopted, the immersed boundary method is utilized to account for the existence of cylinders. Two-degree-of-freedom VIV of a single circular cylinder is simulated to validate the model, and then the model is utilized in the VIV of a four circular-cylinder group with square arrangement. The mass ratio is m* = 2.0, and the spacing ratio L/D is 5.0, where L is the central displacement of two adjacent cylinders and D is the diameter of the cylinders. Reynolds number ranging from 45 to 210 is considered, and the variation of which is achieved by changing the inflow velocity. The corresponding reduced velocity varies from 3 to 14. The influences of Reynolds number on the vibrating frequencies, the response amplitudes, the X–Y trajectories, the vorticity field distribution, and the hydrodynamic coefficients are analyzed in detail. A critical Reynolds number of 105 is observed, at which the X–Y trajectories and the vorticity field distribution change their patterns.