On hydrodynamic loads and stability of projectile during small-angle water entry in waves

This study develops a three-phase flow solver in OpenFOAM to simulate phase change between vapor and liquid for the small-angle high-speed water entry of a projectile into regular waves. Validation is performed using experimental data for high-speed entry of a projectile. The results demonstrate that the wave phase significantly influences the hydrodynamic loads on the projectile during water entry. Larger phase angles reduce the effective entry angle, defined as the sum of the initial angle and the wave-induced inclination, leading to earlier instability, cavity deformation, and trajectory deviation. By analyzing the lift force, pitching moment, and drag experienced by the projectile during water entry at different wave phases, the study reveals that instability is triggered by a “whip angular velocity” generated upon the initial impact of the projectile with the water surface. Stability is maintained if this angular velocity decays to zero before the second shoulder impact. Based on this criterion, the stable and unstable entry regions for the projectile under the specified wave conditions are delineated. Extending this classification across various wave conditions and entry angles reveals that the likelihood of stable motion increases with the effective entry angle. These findings provide insights into predicting the trajectory stability of slender projectiles entering and moving within cavities under ocean wave conditions.