numerical research of the water entry of hyperelastic spheres within low froude numbers

The water-entry process of solid and hollow hyperelastic spheres was numerically simulated using the arbitrary lagrange–euler method, based on the finite element analysis software ls-dyna. the effect of the different initial velocities on the cavity evolution and deformation of the sphere in a range of low froude (fr) numbers was investigated. the evolution of the cavity, deformation of the hyperelastic sphere and parameters at the time of cavity closure were analysed. in addition, the difference in the water-entry process between solid and hollow spheres was given. the numerical results shows that the size of the cavity, fluctuation on the cavity profile, closure time and closure depth increased with fr and that the closure time was proportional to fr1/2 for both solid and hollow spheres. however, the relationship between the closure depth and fr of the hollow sphere differed from that of the solid one. within the investigated low froude numbers, whether for the solid or hollow spheres, the deformation amplitude increased with the froude number. however, the deformation period remained nearly the same for different conditions. under the same physical and motion parameters, the hollow sphere exhibited larger deformations compared with the solid sphere. the deformation period for the hollow sphere was also longer than that for the solid one.