采用基于嵌入式迭代的浸入边界法对均匀流场中圆柱群的横向流致振动进行了二维直接数值模拟。圆柱群中相邻柱体正交排列，间距比为L/D = 3.2, 8，折合流速为Ur = 2-11，Re = 100，圆柱质量比m* = 2。研究发现：不同间距比下，圆柱群前排和后排的圆柱分别呈现出涡激振动和尾流驰振的响应特征。后排圆柱的振幅普遍大于前排圆柱，小间距比圆柱群的最大振幅高于大间距比的情况。不同间距比下，前排相邻圆柱（横流向）的脱涡模式为稳定的同相同步和反相同步模式，或者两种同步模式的切换。顺流向上，小间距比前排相邻圆柱分别呈现延展体和重附着模式，而大间距比下均为共同脱涡模式。各圆柱的主频f*、振幅与升力-位移相位差之间存在紧密的联系。随Ur的增大，圆柱升力-位移相位差会从0°跳转到180°，分别对应流体对圆柱振动的激励和抑制作用，其中后排圆柱完成相位转换需要过渡的折合流速区间更大。相邻并列圆柱之间存在微小的振动频率差，其位移之间的相位差不稳定。随Ur的增大，大间距比圆柱群相位差稳定的范围总体向上游缩窄，而小间距比时则向下游扩张。
Abstract
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.
关键词
圆柱群 /
流致振动 /
尾涡模式 /
相位差
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Key words
cylinder array /
flow-induced vibration /
wake mode /
phase difference
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