Occurrence of orbital cylinder motion for flow around freely vibrating circular cylinder in uniform stream

In this study flow around a freely vibrating circular cylinder in two-degrees-of-freedom is investigated using two-dimensional numerical approach. The equations of motion, the continuity and the pressure Poisson equations are solved for incompressible constant property Newtonian fluid using the finite difference method. Systematic computations are carried out to investigate the effect of the natural frequency fN of the cylinder on the oscillation amplitudes and aerodynamic force coefficients. The mass ratio and the structural damping coefficient values are fixed at m*=10 and ζ=0, respectively.
In addition to the typical distorted figure-eight motion, a raindrop-shaped path is also found whose range widens with increasing fN. Within this range the streamwise oscillation amplitude reaches higher values compared to figure-eight motions and the curves shift upwards with increasing fN. Different vortex structures belong to each cylinder path: 2S or C(2S) modes are observed for distorted figure-eight and P+S mode is found for raindrop-shaped trajectories. The time-mean values of lift jump abruptly between two solutions. Pre- and post-jump analysis reveals that these solutions are mirror images of each other. The root-mean-square (rms) values of lift plotted against U*St shift upwards in the raindrop-shaped motion range and downwards in the figure-eight motion range, while the rms of drag shifts to higher values in both regimes with increasing fN. Chaotic cylinder paths are observed when increasing the natural frequency over a critical value.

本研究采用二维数值方法，探讨了二维自由振动的圆形圆柱体绕流情况。通过有限差分法求解不可压缩常物性牛顿流体的运动方程、连续性方程以及压力泊松方程。系统性地进行计算，以研究圆柱体自然频率fN对振动幅度和气动力系数的影响。质量比和结构阻尼系数分别固定为m*=10和ζ=0。除了典型的扭曲八字形运动外，还发现了一种雨滴形状的轨迹，其范围随着fN的增加而扩大。在此范围内，流向振动幅度相对于八字形运动达到更高的值，且曲线随fN的增加而向上移动。不同的涡结构属于每个圆柱轨迹：扭曲八字形观察到2S或C(2S)模式，雨滴形状轨迹则发现P+S模式。升力的时均值在两个解之间发生突然跳跃。跳跃前后的分析揭示，这些解互为镜像。将升力的均方根值(U*St)与雨滴形状运动范围相对应，其值随fN的增加而上升，在八字形运动范围内则下降，而拖力的均方根值在两种情况下均随fN的增加而向更高值偏移。当自然频率超过临界值时，观察到混沌圆柱轨迹。