Abstract Although flow past cylinders has a vast spectrum of applications in various fields of engineering, the existence of flow-induced vibrations (FIVs) add a need for a more precise and thorough approach when studying such flows. In this context, this work investigates the FIVs’ mechanism due to two square cylinders placed in tandem arrangement through a characteristics-based-split (CBS) finite element method. Both cylinders, with a low mass ratio ( m r = 2), are free to oscillate in in-line and transverse directions. The center-to-center distance of 5 D ( D being the cylinder side width) is kept fixed between the cylinders. The Reynolds number ( R e ) is ranged from 40 to 200 with an increment of 40, and computations are carried out for the reduced velocity ( U r ) ranging from 3 to 13 under each R e value. Results show that the effects of Re and U r on the dynamic responses are qualitatively similar for both cylinders. However, effects on the downstream cylinder are stronger due to the upstream wake. For R e equal to or beyond 120, the in-line low-frequency characteristic becomes obvious at some higher values of U r for the upstream cylinder, whereas it exists over a wide range of U r for the downstream cylinder. For lower R e (up to 120), cylinders show steady behavior at U r = 5. However, for higher R e , they vibrate with the maximum amplitudes (especially the in-line amplitude of the downstream cylinder), and show complex wake flow at the same U r . Compared to higher R e , the maximum vibration amplitudes in the transverse direction of lower R e are relatively higher, while the opposite trend is observed for in-line vibration amplitudes. Several unstable trajectories are also identified other than the typical figure-eight trajectories. In context of vortex shedding, different permutation of steady state, 2S, P+S, and complex modes are observed for different values of R e . It is also noted that the vortex shedding pattern keeps changing in the far wake for higher R e .

中文翻译：

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低雷诺数下串联排列的两个方形圆柱体的二自由度涡激振动

摘要 尽管流过圆柱体在各个工程领域都有广泛的应用，但流动诱导振动 (FIV) 的存在增加了在研究此类流动时需要更精确和彻底的方法的需要。在这种情况下，这项工作通过基于特征的拆分 (CBS) 有限元方法研究了由于两个方形圆柱串联排列而导致的 FIV 机制。具有低质量比 (mr = 2) 的两个圆柱体都可以在线和横向自由振荡。5 D 的中心距（D 是圆柱体的边宽）在圆柱体之间保持固定。雷诺数 (Re) 的范围为 40 到 200，增量为 40，并且计算每个 Re 值下的折减速度 (U r ) 范围为 3 到 13。结果表明 Re 和 U r 对两个气缸的动态响应的影响在性质上是相似的。然而，由于上游尾流，对下游圆柱体的影响更大。当R e 等于或超过120 时，在上游气缸的U r 值较高时，串联低频特性变得明显，而下游气缸则存在于较宽的U r 范围内。对于较低的 Re（高达 120），圆柱体在 U r = 5 时表现出稳定的行为。然而，对于较高的 Re ，它们以最大振幅（尤其是下游圆柱体的同轴振幅）振动，并显示出复杂的尾流流在相同的 U r 。与较高的 Re 相比，较低的 Re 横向上的最大振动幅度相对较高，而在线振动幅度则观察到相反的趋势。除了典型的 8 字形轨迹外，还确定了几个不稳定的轨迹。在涡旋脱落的背景下，对于不同的 Re 值，观察到稳态、2S、P+S 和复杂模式的不同排列。还注意到，对于较高的 Re，涡旋脱落模式在远尾流中不断变化。