A numerical study on nested cavities during the water entry of deformable elastic spheres

Among the three typical cavities formed by elastic spheres, the nested cavities are investigated, including the formation moment, influencing factors, size and quantities. To achieve this, a fluid-solid interaction model is used to describe the water entry of elastic spheres. The results show that the formation moment is related to the sphere diameter, density and material shear modulus, but not to the impact velocity. The formation moment and number of nested cavities can be predicted from the material properties. Additionally, we have shown the change characteristics for the dimension parameters of the nested cavity with the dimensionless ratio of material shear modulus to impact hydrodynamic pressure and the sphere density. The higher the sphere density, the longer the nested cavity. The results also show that the cavity pinch-off time is modulated by the sphere size and density. With the increase of the dimensionless parameter for time D/(μ₀/ρ_S)^1/2, the pinch-off time grows rapidly first and then slowly.