低雷诺数下串联双圆柱涡激振动机理的数值研究

利用有限元数值方法求解不可压缩粘性流体的Navier-Stokes方程，结合任意拉格朗日-欧拉（ALE）动网格方法，对低雷诺数下（Re = 150）等直径串联圆柱的涡激振动问题进行了数值模拟研究。其中上游圆柱固定，下游圆柱在弹簧和阻尼作用下允许同时发生顺流向和横流向的运动。在约化速度Ur = 3.0 ~ 12.0的范围内（阻尼比ξ = 0.007）研究了两圆柱圆心间距比（LX / D = 3.0、5.0、8.0）及圆柱质量比（m* = 5.0、10.0、20.0）对下游圆柱的运动响应及受力的影响。数值结果表明，圆柱间距比的变化会导致锁定区间的变化，进而影响到圆柱涡激振动的位移响应和受力特性。这些方面都与尾流区涡旋脱落模式密切相关，体现了双圆柱间干涉作用对涡激振动的影响。进一步的研究表明，圆柱质量比的变化对以约化速度表征的锁定区间、运动响应和尾流模式等都有一定的影响作用。

Numerical investigation of vortex-induced vibration of twin tandem circular cylinders at low Reynolds number

Based on the FEM solution of incompressible viscous Navier-Stokes equations in the frame of Arbitrary Lagrangian-Eulerian (ALE), a two-dimensional numerical model is developed to investigate the vortex-induced vibration of twin tandem circular cylinders at low Reynolds number. In the numerical simulations, the upstream cylinder is fixed, while the rear cylinder is allowed to freely oscillate in both transverse and stream-wise directions. The damping ratio 0.007 and the reduced velocity varying from 3.0 to 12.0 are used for the computations. The effects of the in-line center-to-center distance (LX / D = 3.0、5.0、8.0) and the mass ratio (m* = 5.0、10.0、20.0) on the displacement and forces of the downstream cylinder are examined. The numerical simulations indicate that the spacing ratio (LX / D) has great influence on the VIV responses in terms of the lock-in band, displacement and fluid forces. Several flow modes under different spacing ratios and reduced velocities are observed, which are closely related to the VIV responses. It was also found that the change of the mass ratio may give rise to different characteristics of VIV responses for the twin cylinders in tandem at low Reynolds number.