Water impact of deformable spheres with vertical and oblique entries

Abstract

At low Froude numbers, vertical and oblique impacts of deformable spheres into water are performed. The dependence levels of the hydrodynamics, cavity formations, and stress responses on the oblique angle are investigated. Based on theoretical and numerical analyses, the differences between the vertical and oblique impacts in sphere deformations and cavity formations are clarified. Elastic forces inside the sphere induce different models of the deformation behaviors during oblique water entry, and the sphere with a smaller oblique angle extends the formation time of the oblate deformation and nested cavity. Over a single deformation period, the vertical hydrodynamic forces do not continuously increase with the oblique angle, and they depend on the deformation behavior. Additionally, the evolution in the high-stress area at the bottom of the sphere caused by the oblique motion is similar to a solar eclipse. Over the first deformation period, the energy change in the sphere with different oblique angles can be predicted from the dimensionless ratio of the material shear modulus to the impact hydrodynamic pressure.