NUMERICAL INVESTIGATION OF VORTEX-INDUCED VIBRATIONS OF FOUR CIRCULAR CYLINDERS CONSIDERING DIFFERENT INTER-CYLINDER MASS RATIOS

Two-degree-of-freedom vortex-induced vibrations (VIV) of four circular cylinders arranged in a square configuration are numerically investigated with a partitioned strong coupling algorithm using an arbitrary Lagrangian-Eulerian smoothed finite-element formulation. The emphasis is placed on the effect of inter-cylinder mass ratio M, which is defined as the ratio of mass of the upstream cylinder to that of the downstream cylinder. Here, M is set to 2.0 and 0.5 and the solid-to-fluid mass ratio m* is categorized into low mass ratio (m*<5) and high mass ratio (m*≥5). To this end, three different cases of the VIV event are examined: (1) the low-mass-ratio case (both upstream and downstream cylinders have low mass ratios); (2) the mixed-mass-ratio case (cylinders in a row have a high mass ratio whereas those in the other row have a low mass ratio); (3) the high-mass-ratio case (both upstream and downstream cylinders have high mass ratios). The relevant numerical results are summarized as follows. In Case (1), the vibration trajectories of all cylinders are disordered and asymmetric responses are clearly observed. In Case (2), the mass ratio of the upstream cylinders governs the vortex-shedding mode of the downstream cylinders and, importantly, changing this ratio leads to abrupt variation in stream-wise amplitude of the downstream cylinders. For Case (3), the vibration responses of all cylinders become relatively weak. It is also found that the mass ratio of the upstream cylinder dominates flow-induced motions of the downstream cylinders. Overall, the larger upstream ratio (M = 2.0) results in the regularization of the downstream cylinders’ wake and also suppresses their vibration amplitudes. In contrast, the smaller upstream mass ratio (M = 0.5) enhances the wake disorder and amplifies the vibration responses of the downstream cylinders. The current findings are expected to offer guidance on the optimized design of multiple immersed cylindrical structures.