Numerical investigation of the water entry of a hydrophobic sphere with spin

The process of water entry is a complex and attractive field of research, since from more than a century ago there are wide applications in industry, nature science, bionics, and naval technology. The objective of this work is to investigate the cavity dynamics during water entry of a spinning sphere by numerical simulations. The algorithm of these simulations uses the Boundary Data Immersion Method (BDIM) to model the solid/fluid interactions, and the interface between the liquid and the gas is tracked by the volume-of-fluid (VOF) method. The uniform Cartesian-grid is used, and the effect of surface wettability is considered. The governing meta-equations for the full domain ensure the stable and accurate prediction on the pressure value on the solid boundary. Numerical results are validated with experiments, and good agreement between numerical and experimental results has been obtained for the transient cavity formation and the motion of the sphere. To further investigate the influence of the spin rate on the splash and cavity evolution and hydrodynamic characteristics, five different spin rates with a constant impact velocity are considered. Results reveal that the spin rate has significant influence on the cavity and splash asymmetry as well as the moment of pinch-off, while the depth of pinch-off is almost constant. The vortex structures show that both effects of rotation and shear play a role on the evolution of splash and cavity. The hydrodynamic forces fluctuate dramatically both at the moment of impact and the pinch off of the cavity. They gradually tend to be constant as the sphere descent with an open cavity.