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 20 000. 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.