Numerical investigation on the cavity dynamics and deviation characteristics of skipping stones

The unsteady characteristics for the water-skipping problem of a spinning stone, including the cavity dynamics, velocity field distribution, deviation and hydrodynamics, are investigated numerically for the stone with different attack angles and spinning velocities. A three-dimensional numerical model with six degrees of freedom is established based on the large eddy simulation (LES) model and the volume of fluid (VOF) model. Both the symmetry of cavity and velocity field are destroyed by the spin. More than one saddle appears on the cavity surface for the stone with low attack angle, but mild ripple appears for the stone with high attack angle. Time histories of cavity depth and size difference, and the effects of attack angle and spinning velocity on the maximum depth and size difference are analyzed. Furthermore, time histories of deviation and hydrodynamic force in the z-axis are presented and analyzed to reveal the relationship between deviation and hydrodynamics. Compared to the shear stress F_s, the normal stress F_n appears to plays a more dominant role in the deviation in the z-axis. The maximum shear stress increases linearly with Ω₀² at almost the same rate of change for the stone with different attack angles, and a good sine fitting is presented between the maximum normal stress and Ω₀.