Two-dimensional numerical simulations of transverse flow-induced vibrations of cylinder arrays in uniform flow field are carried out using the iterative immersed boundary method. The cylinders are arranged orthogonally with the spacing ratios of L/D = 3.2, 8, the reduced velocity Ur = 2-11, Re = 100, and the mass ratio of the cylinders m* = 2. It is found that the cylinders in the front row and the rear row of the arrays exhibit the response characteristics of vortex-induced vibration and wake-induced galloping, respectively, for different spacing ratios. The amplitudes of the rear row of cylinders are generally larger than that of the front row of cylinders, and the maximum amplitudes of the cylinder arrays with small spacing ratios are higher than that of the case with large spacing ratios. For different spacing ratios, the vortex-shedding patterns of the neighboring cylinders in the front row (in the cross-flow direction) are stable in-phase-synchronized pattern and anti-phase-synchronized pattern, or the switching of the two patterns. In the in-line direction, the front-row neighboring cylinders at small spacing ratios show extended-body and reattachment modes, respectively, whereas they were all in co-shedding mode at large spacing ratios. There is a strong connection between the dominant frequency f*, amplitude and lift-displacement phase difference of each cylinder. With increasing Ur, the cylinder lift-displacement phase difference jumps from 0° to 180°, which corresponds to the excitation and suppression effects of the fluid on the cylinder vibration, respectively, where the rear row of cylinders need to transition to a larger reduced velocity interval to complete the phase transition. There is a small vibration frequency difference between neighboring side-by-side cylinders, and the phase difference between their displacements is unstable. With the increase of Ur, the range of the stabilized phase difference in the group of cylinders with large spacing ratio generally narrows upstream, while it expands downstream with small spacing ratio.
Key words
cylinder array /
flow-induced vibration /
wake mode /
phase difference
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