Generation of shock waves by a body during high-speed water entry

The generation and propagation of pressure waves by a body impacting and penetrating into water at subsonic or supersonic velocities are investigated both analytically and numerically. The high-speed water entry of a projectile is accompanied by the generation of two distinct pressure waves: ballistic waves and collapse waves. The ballistic wave is generated by the impulse imparted into water from the kinetic energy loss of a projectile due to drag. An analytical method to estimate the ballistic waves radiated by a projectile moving at subsonic or supersonic velocities from a knowledge of the dynamics of a projectile has been developed here and, in principle, is applicable to any projectile of practical interest. The model also allows us to solve the case of oblique penetration by using a coordinate transformation technique. Numerical investigations were conducted using an existing finite difference code (AutoDyn) and the results are in good agreement with the analytical predictions.;In the late stage of the penetration process, the cavity formed begins to collapse and collapse waves are generated. To describe these collapse waves, the dynamics of the cavity is investigated, and variables such as cavity radius, cavity wall velocity and cavity collapse completion time are determined. The predictive procedure for the collapse waves is based upon spherical bubble dynamics and some modifications for the case of water entry. In summary, the results show that the pressure waves due to the ballistic pulse increase with increased impact velocity, while the collapse waves is nearly independent of impact velocity.