Intensity distribution of shock waves generated in water-filled tanks subjected to subsonic-velocity projectiles impact

This research effort focuses on examining the intensity distribution of shock waves produced by subsonic projectiles impacting water-filled containers through an integrated approach that combines theoretical modeling, numerical simulations, and experimental validation. First, the original source-strength formulation in the potential-flow-based analytical model is re-examined and corrected by introducing an angular correction function into the effective source-strength formulation to account for the observed angular variation of the initial shock-wave intensity, especially in the near-free-surface region where the original model tends to overestimate the pressure amplitude, and a semi-empirical improved model for the shock-wave intensity is established. Experimental validation was then carried out using high-velocity shadowgraph imaging and pressure sensors, which confirmed that the improved model provides a more physically consistent description of the initial shock-wave intensity than the original formulation. In particular, the dimensionless initial shock intensity exhibits a clear angular dependence, which can be approximately represented by a sinusoidal variation and is supported by both the present numerical results and trends reported in previous studies. On this basis, the proposed formulation offers a practical analytical framework for estimating the spatial distribution of initial peak pressure in confined water systems under subsonic impact. Furthermore, based on the modified model, it was found that the iso-intensity distribution of the initial shock wave exhibits a circular shape at different initial water entry velocities. Analytical implications of the proposed model for idealized container geometries are also discussed. This research contributes to a more comprehensive understanding of the HRAM effects and the damage mechanism of initial shock waves in confined systems.