Dynamics and energetics of a sphere during water exit

By using a multi-phase Navier–Stokes solver combining the volume of fluid approach for water–air interface, the large-eddy simulations method for turbulence effect, and the overset mesh technique for moving boundary, we investigate the dynamics and energetics of a neutrally buoyant sphere during water exit process. The sphere is launched vertically with various initial velocities. In our analysis, the water exit process is divided into three distinct phases, fully submerged, partially submerged, and airborne. The focus is on the roles of the gravity, buoyancy, viscous, and wave-radiation forces in determining the motion and energy exchange/dissipation. During the fully submerged phase, the energy loss of the sphere is caused by the viscous force and the wave-radiation force, with the former playing the dominating role. In the partially submerged phase, the buoyancy force decreases as the submerged volume is reduced. However, under certain conditions, there could be an additional supporting force on the sphere caused by upward water flow beneath it. Once the sphere is fully airborne, its motion is primarily governed by gravity, and the maximum height it attains correlates strongly with the water-exit speed. These findings offer deeper insights into optimizing underwater launch parameters and understanding energy transfer mechanisms in water exit scenarios.