The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in the streamwise and cross-flow directions, and forced to rotate about its axis, are investigated via two-and three-dimensional simulations. The Reynolds number based on the body diameter and inflow velocity is equal to 100. The impact of the imposed rotation on the flow-structure system behavior is explored over wide ranges of values of the rotation rate (ratio between the cylinder surface and inflow velocities, α ∈ [0, 5.5]) and of the reduced velocity (inverse of the oscillator natural frequency non-dimensionalized by the inflow velocity and body diameter, U ⋆ ∈ [1, 25]). Flow-induced vibrations are found to develop over the entire range of α, including in the intervals where the imposed rotation cancels flow unsteadiness when the body is rigidly mounted (i.e. not allowed to translate). The responses of the two-degree-of-freedom oscillator substantially depart from their one-degree-of-freedom counterparts. Up to a rotation rate close to 2, the body exhibits oscillations comparable to the vortex-induced vibrations usually reported for a non-rotating circular cylinder: they develop under flow-body synchronization and their amplitudes present bell-shaped evolutions as functions of U ⋆. They are however enhanced by the rotation as they can reach 1 body diameter in each direction, which represents twice the peak amplitude of cross-flow response for α = 0. The symmetry breaking due to the rotation results in deviations from the typical figure-eight orbits. The flow remains close to that observed in the rigidly mounted body case, i.e. two-dimensional with two spanwise vortices shed per cycle. Beyond α = 2, the structural responses resemble the galloping oscillations generally encountered for non-axisymmetric bodies, with amplitudes growing unboundedly with U ⋆. The response growth rate increases with α and amplitudes larger than 20 diameters are observed. The cylinder describes, at low frequencies, elliptical orbits oriented in the opposite sense compared to the imposed rotation. The emergence of subharmonic components of body displacements, leading to period doubling or quadrupling, induces slight variations about this canonical shape. These responses are not predicted by a quasi-steady modeling of fluid forcing, i.e. based on the evolution of the mean flow at each step of body motion; this suggests that the interaction with flow unsteadiness cannot be neglected. It is shown that flow-body synchronization persists, which is not expected for galloping oscillations. Within this region of the parameter space, the flow undergoes a major reconfiguration. A myriad of novel spatio-temporal structures arise with up to 20 vortices formed per cycle. The flow three-dimensional transition occurs down to α ≈ 2, versus 3.7 for the rigidly mounted body. It is however shown that it has only a limited influence on the system behavior. 2 R. Bourguet

中文翻译：

---

旋转圆柱体的二自由度流激振动

通过二维和三维模拟研究了弹性安装的圆柱体的流动引起的振动，该圆柱体在流向和横向流动方向上自由振荡，并被迫绕其轴旋转。基于主体直径和流入速度的雷诺数等于 100。在广泛的旋转速率值（圆柱表面和流入速度之间的比率， α ∈ [0, 5.5]) 和减小的速度（振荡器固有频率的倒数，由流入速度和主体直径无量纲化，U ⋆ ∈ [1, 25]）。发现流动引起的振动在整个 α 范围内发展，包括在刚性安装（即不允许平移）时施加的旋转抵消流动不稳定性的间隔。二自由度振荡器的响应与一自由度振荡器的响应大不相同。在接近 2 的旋转速率下，物体表现出的振荡与通常为非旋转圆柱体报告的涡激振动相当：它们在流体同步下发展，并且它们的振幅呈现为 U 的函数的钟形演变 ⋆ . 然而，它们通过旋转得到增强，因为它们可以在每个方向上达到 1 个主体直径，这代表了 α = 0 时横流响应峰值幅度的两倍。 由于旋转而导致的对称性破坏导致与典型的 8 字形的偏差轨道。流动保持接近在刚性安装的车身情况下观察到的流动，即二维，每个周期有两个展向涡旋脱落。超过 α = 2，结构响应类似于非轴对称物体通常遇到的飞驰振荡，振幅随 U ⋆ 无限增长。响应增长率随 α 增加，并且观察到大于 20 个直径的幅度。圆柱体在低频下描述了与强加旋转方向相反的椭圆轨道。身体位移的次谐波分量的出现，导致周期加倍或四倍，引起关于这个规范形状的轻微变化。这些响应不是由流体强迫的准稳态模型预测的，即基于身体运动每一步平均流量的演变；这表明不能忽略与流动不稳定的相互作用。结果表明，流-体同步持续存在，这在飞驰振荡中是不存在的。在参数空间的这个区域内，流动经历了重大的重新配置。无数新的时空结构出现，每个周期形成多达 20 个漩涡。流动三维过渡发生在 α ≈ 2，而刚性安装的主体为 3.7。然而，它表明它对系统行为的影响有限。2 R.布尔盖 无数新的时空结构出现，每个周期形成多达 20 个漩涡。流动三维过渡发生在 α ≈ 2，而刚性安装的主体为 3.7。然而，它表明它对系统行为的影响有限。2 R.布尔盖 无数新的时空结构出现，每个周期形成多达 20 个漩涡。流动三维过渡发生在 α ≈ 2，而刚性安装的主体为 3.7。然而，结果表明它对系统行为的影响有限。2 R.布尔盖