自由表面附近球体的横向流致振动：数值研究
Transverse flow-induced vibrations of a sphere in the proximity of a free surface: A numerical study
摘要：
本文对亚临界雷诺数下弹性支承球体在自由表面附近的横向流激振动进行了数值研究。首先，我们验证并分析了雷诺数达到$30\,000$时全淹没球体在各个方向自由振动的模态转换和运动轨迹。其次，研究了横向振动球体在三种归一化浸没比下的响应动力学（$h^*=h/D$，其中$h$是从球体顶部到未扰动自由表面水平的距离，$D$是球体直径），在$h^*=1$（完全浸没的球体，无自由表面效应），$h^*=0$（球体顶部接触自由曲面）和$h^*=-0.25$（球体穿透自由曲面）。在锁定范围内，我们观察到$h^*=0$的振幅响应与$h^*=1$的情况相比显著降低。据发现，涡通量扩散由于自由表面边界和自由表面作为一个汇的能量，导致减少的横向力和振幅响应。当球体以$h^*=-0.25$穿透自由表面时，发现锁定状态下的振幅响应大于以最大峰间振幅$\sim2D$研究的所有浸没情况。我们发现，穿刺球与空气-水界面的相互作用引起了相对较大的表面变形，并对涡脱落和振动频率的同步性有显着的影响。流向涡量的增加对$h^*=-0.25$处的穿刺球产生了相对较大的横向力，从而导致每个循环的正能量传递更大，以维持大振幅振动。最后，我们研究了FIV响应对锁定状态下质量比$m^*$和弗劳德数$Fr$的敏感性。
英文摘要：
We present a numerical study on the transverse flow-induced vibration (FIV) of an elastically mounted sphere in the vicinity of a free surface at subcritical Reynolds numbers. To begin, We verify and analyze the mode transitions and the motion trajectories of a fully submerged sphere vibrating freely in all directions for the Reynolds number up to $30\,000$. Next, the response dynamics of a transversely vibrating sphere is studied for three values of normalized immersion ratio ($h^*=h/D$, where $h$ is the distance from the top of the sphere to undisturbed free-surface level and $D$ is the sphere diameter), at $h^*=1$ (fully submerged sphere with no free-surface effect), $h^*=0$ (where the top of the sphere touches the free surface) and $h^*=-0.25$ (where the sphere pierces the free surface). At the lock-in range, we observe that the amplitude response at $h^*=0$ is decreased significantly compared to the case at $h^*=1$. It is found that the vorticity flux is diffused due to the free-surface boundary and the free surface acts as a sink of energy that leads to a reduction in the transverse force and amplitude response. When the sphere pierces the free surface at $h^*=-0.25$, the amplitude response at the lock-in state is found to be greater than all the submerged cases studied with the maximum peak-to-peak amplitude of $\sim2D$. We find that the interaction of the piercing sphere with the air-water interface causes a relatively large surface deformation and has a significant impact on the synchronization of the vortex shedding and the vibration frequency. Increased streamwise vorticity gives rise to a relatively larger transverse force to the piercing sphere at $h^*=-0.25$, resulting in greater positive energy transfer per cycle to sustain the large-amplitude vibration. Lasty, we study the sensitivity of FIV response on the mass ratio, $m^*$, and Froude number, $Fr$, at the lock-in state.
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