Vortex-induced vibration of four cylinders in an in-line square configuration in steady flow

Vortex-induced vibration (VIV) of four rigidly connected circular cylinders in an in-line square configuration at a Reynolds number of 150 and a low mass ratio of 2.5 is investigated numerically for spacing ratios (L) of 1.5, 2, 2.5, 3 and 4. Among all the studied spacing ratios, the lock-in regime for L=1.5 is found to be the widest and the corresponding maximum amplitude is the largest. The response amplitudes in the lock-in regime for L=2 are the smallest, because of the strong interaction among the vortices. For L=2.5, 3 and 4, the lock-in regime is similar to that of a single cylinder and the response amplitudes in the lock-in regime are slightly higher than that of a single cylinder. The critical spacing ratio for vortex shedding to occur from the two upstream cylinders is much smaller than that for flow past a four stationary cylinders. The vortex shedding flows outside the lock-in regime for large spacing ratio of L=4 are in an anti-phase pattern, which is similar to that of flow past four stationary cylinders and leads to zero cross-flow displacement.