Pressure–time history scaling for hypervelocity water entry

Numerical simulations are performed for hypervelocity water entry of spherical projectiles, validated against experimental data. The scaling of principal phenomena is investigated using time histories of the pressure at the stagnation point, the axial portion of the shock wave, and the radial portion of the shock wave. The scaling analysis of the pressure is performed via a parameter sweep of projectile impact velocity, density, diameter, and impact kinetic energy. The pressure in all these regions scales most strongly with impact velocity. For the stagnation point and the axial shock wave, the pressure also scales strongly with the projectile density and to a lesser extent with diameter and kinetic energy. The radial shock wave pressure scales only with the projectile diameter at a given impact velocity. Lastly, these pressure histories are non-dimensionalized using a combination of dimensional parameters, i.e., the reference dynamic pressure, a kinetic energy-based characteristic length scale, the impact Mach number, and the water sound speed. Empirical fits are obtained that can be used as predictive tools, with the curves from the computations collapsing well for all locations investigated.