Numerical simulation of vortex-induced vibration of four circular cylinders in a square configuration

Two-degree-of-freedom Vortex-Induced Vibration (VIV) of four rigidly coupled circular cylinders in a square configuration is investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations and SST k-ω turbulence equations are solved using a finite element method. Simulations are carried out for flow approaching angles of α=0°, 15°, 30° and 45° and the reduced velocities ranging from 1 to 20 with an interval of 1. The Reynolds number ranges from 1000 to 20000. The numerical results show that the approaching angle has significant effects on the response of the four-cylinder system. The lock-in region for α=15° is the widest (between 3≤Vᵣ≤12) among the other cases investigated, while the lock-in region for α=45° is the narrowest (between 2≤Vᵣ≤4). For α=0°, the vibration is generally irregular in the lock-in region. Regular and periodic vibrations are observed in the lock-in zone for approaching angles except α=0°, although the hydrodynamic forces, especially those on the two downstream cylinders, are very irregular.