Transverse flow-induced vibrations of a sphere in the proximity of a free surface: A numerical study

TL;DR

This numerical study investigates how a sphere's transverse flow-induced vibrations are affected by proximity to a free surface, revealing that free surface interactions can significantly alter vibration amplitude and vortex dynamics.

Contribution

The paper provides new insights into the effects of free surface proximity on FIV of spheres, including the impact of piercing the surface and the role of vorticity flux and surface deformation.

Findings

Amplitude decreases near free surface due to energy sink effect.

Piercing the free surface increases vibration amplitude and surface deformation.

Free surface interaction alters vortex shedding and synchronization.

Abstract

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.