ON THE INITIAL-STAGE SLAMMING OF A RIGID SPHERE IN A VERTICAL WATER ENTRY

Analytic expressions are obtained for the small-time slamming coefficient and wetting factor of a rigid spherical shape in a vertical water entry. The theoretical model neglects gravity, compressibility and viscous effects with respect to inertia, which is usually the dominant effect during the early stages of water impact. Replacing the free-surface by a flat equipotential surface enables us to solve the incompressible inviscid flow problem about a double spherical bowl for the Stokes stream function expressed in terms of toroidal coordinates 12. A semi-Wagner approach is then used to compute the wetting factor and the Lagrange equations are employed in order to determine the slamming force from the kinetic energy of the fluid. Good agreement between theoretical model and available experimental measurements has been obtained, both for the early-stage impact force and the free-surface rise at the vicinity of the three-phase contact line (wetting correction factor).