The Application of a Complex Equation of State for Hypervelocity Water Entry Simulations

In this study, axisymmetric numerical simulations of hypervelocity water entry by spherical projectiles were performed and compared to experimental images. Two equations of state (EOS), the single-phase Stiffened Gas (SG) EOS and the more realistic AQUA EOS with equilibrium phase change, were used for an entry velocity of 2314 m/s. It was found that both EOS could accurately capture the projectile and shock wave trajectories along with the trailing cavity, with the AQUA EOS reproducing the smooth cavity walls observed in experiments. Conversely, for the SG EOS, the walls of the cavity exhibited Kelvin-Helmholtz instabilities due to a large velocity shear between the entrained air in the cavity and the surrounding liquid water. By examining streamlines for both EOS, it was found that for the AQUA EOS, the low pressure found behind the projectile caused cavitation allowing water vapor to flow into the cavity, preventing the large velocity gradients necessary for Kelvin-Helmholtz instabilities. A phase plot of the AQUA EOS showed a trailing cavity consisting largely of a two-phase water-vapor mixture instead of entrained air. Finally, the SG EOS produced an artificial trailing oblique recompression shock wave attached to the back of the projectile that was absent both for the AQUA EOS and in experiments. It was determined that this oblique shock was caused by entrained air redirecting the supersonically expanding water away from the cavity.