In this paper, the vortex-induced vibration (VIV) of a main cylinder with two symmetrically arranged control rods at Reynolds number of 500 is numerically simulated. The control rods and the main cylinder are connected rigidly and can move synchronously, which is modeled as a spring oscillator with double degree of freedom. Seven gap ratios (G/D=0.1~2) and sixteen angles (α=15o~165o) are used to model the cylinder system. Thirteen flow patterns are identified, and the VIV of the cylinder system in every flow pattern is discussed separately. It is found that the characteristics of the VIV of the cylinder system are similar in the same flow pattern, which may give a way to understand the VIV of the multiple cylinders further. Based on the classification in previous researches, some advanced insights into the passive control are achieved. The control rods located in the boundary layer (G/D=0.1) can change the VIV of the main cylinder most effectively, and the effect decreases with increasing gap ratio. The control rods immerged in the wake of the main cylinder may result in sub-harmonic resonance, while the control rods located centrally in front of the main cylinder does not obviously affect the VIV of the main cylinder. As G/D=0.1~0.7, overall, the control rods located nearly side-by-side with main cylinder can amplify the VIV, while the control rods located downstream of the main cylinder can suppress the VIV. As G/D=1~2, the control rods can suppress the VIV slightly, and the effect increases with increasing gap ratio and decreasing angle. For G/D=0.1 & α=105o, the VIV is magnified for maximum effect, and the peak amplitude is about twice that of the single cylinder. For G/D=0.2 & α=45o, the VIV is suppressed for maximum effect, and the peak amplitude is about 0.88% of that of the single cylinder.

中文翻译：

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具有两个对称布置的控制杆的圆柱体的涡激振动

在本文中，数值模拟了雷诺数为 500 时具有两个对称布置的控制杆的主圆柱体的涡激振动 (VIV)。控制杆与主缸刚性连接，可同步运动，建模为双自由度弹簧振子。七个间隙比（G/D=0.1~2）和十六个角度（α=15o~165o）用于对圆柱系统进行建模。确定了 13 种流动模式，并分别讨论了每种流动模式中气缸系统的 VIV。发现同一流型下气缸系统的VIV特性相似，这为进一步了解多气缸VIV提供了一种途径。基于以往研究中的分类，实现了对被动控制的一些高级见解。位于边界层（G/D=0.1）的控制杆可以最有效地改变主缸的VIV，并且随着间隙比的增加，效果减弱。浸入主缸尾流中的控制杆可能会产生次谐波共振，而位于主缸前中央的控制杆不会明显影响主缸的VIV。当G/D=0.1~0.7时，总体而言，与主缸接近并排的控制杆可以放大VIV，而位于主缸下游的控制杆可以抑制VIV。当G/D=1~2时，控制棒对VIV有轻微的抑制作用，并且随着间隙比的增加和角度的减小，效果增强。对于 G/D=0.1 & α=105o，VIV 被放大以获得最大效果，峰值幅度约为单缸的两倍。