Vortex-induced vibration of a sphere close to or piercing a free surface

Vortex-induced vibration (VIV) of an elastically mounted sphere placed close to or piercing a free surface (FS) was investigated numerically. The submergence depth ( $h$ ) was systematically varied between $1$ and $-$ 0.75 sphere diameters ( $D$ ) and the response simulated over the reduced velocity range $U^*\in [3.5,14]$ . The incompressible flow was coupled with the sphere motion modelled by a spring–mass–damper system, treating the free-surface boundary as a slip wall. In line with the previous experimental findings, as the submergence depth was decreased from $h^* = h/D =1$ , the maximum response amplitude of the fully submerged sphere decreased; however, as the sphere pierced the FS, the amplitude increased until $h^* = -0.375$ , and then decreased beyond that point. The fluctuating components of the lift and drag coefficients also followed the same pattern. The variation of the near-wake vortex dynamics over this submergence range was examined in detail to understand the effects of $h^*$ on the VIV response. It was found that $h^* = 1$ is a critical submergence depth, beyond which, as $h^*$ is decreased, the vortical structures in the wake vary significantly. For a fully submerged sphere, the influence of the stress-free condition on the VIV response was dominant over the kinematic constraint preventing flow through the surface. For piercing sphere cases, two previously unseen vortical recirculations were formed behind the sphere near times of maximal displacement, enhancing the VIV response. These were strongest at $h^* = -0.375$ , and much weaker for small submergence depths, explaining the observed response-amplitude variation.

Performance assessments of the fully submerged sphere and cylinder point absorber wave energy converters

Fully submerged sphere and cylinder point absorber (PA), wave energy converters (WECs) are analyzed numerically based on linearized potential flow theory. A boundary element method (BEM) (a radiation–diffraction panel program for wave-body interactions) is used for the basic wave-structure interaction analysis. In the present numerical model, the viscous damping is modeled by an equivalent linearized damping which extracts the same amount of wave energy over one cycle as the conventional quadratic damping term. The wave power capture width in each case is predicted. Comparisons are also made between the sphere and cylinder PAs which have identical geometrical scales and submerged depths. The results show that: (i) viscous damping has a greater influence on wave power performance of the cylinder PA than that of the sphere PA; (ii) the increasing wave height reduces wave power performance of PAs; (iii) the cylinder PA has a better wave power performance compared to the sphere PA in larger wave height scenarios, which indicates that fully submerged cylinder PA is a preferable prototype of WEC.

Force Decomposition of Medium Reynolds Number Oscillating Flow Over a Submerged Sphere

A variety of engineering applications involve medium Reynolds number (Re) oscillating flow around spherical objects (e.g. aerosol dispersion, microorganism motion, sedimentation of small particles, etc.), and they usually require accurate prediction of the movement of particles and the forces. Currently, the popular model of predicting forces acting on an accelerated submerged sphere was developed more than 100 years ago, but only limited to Stokes flow (Re << 1). In the 1960s, Odar and Hamilton conducted experiments and extended the model for Re number up to 64 (OH-64 law). The aim of this study is to further extend the Re number to 300 via numerical simulations using ANSYS Fluent, so that the model is more capable for more varieties of engineering applications. It is expected that the results of this study will be beneficial to advance the fundamental understanding of oscillating flow over spheres and the potential applications.