Stability of Oblique Water Entry of Cylindrical Projectiles

Water entry is an interesting subject but many of its physical aspects have remained unknown so far. Using computational fluid dynamics (CFD), this study investigates the dynamic stability of cylindrical projectiles in the oblique water entry at shallow angles in the presence of three phases of air, water and water vapor. The three-dimensional and transient numerical model has been verified using the former experimental results in the literature. In this study, the effects of projectile length-to-diameter ratio (L/D) and water entry angle on the projectile stability within cavity were investigated. Accordingly, the water entry of six projectiles was simulated with aspect ratios of 2 to 6 at three water entry angles of 6, 9 and 12 degrees with respect to the free surface with an initial velocity of 280 m/s. At each of the aforementioned angles, the critical L/D, where the projectile avoids tumbling inside the cavity at a larger value, was determined. This study showed that in the oblique water entry of a cylindrical projectile at the angles of 6, 9 and 12 degrees, the projectile tumbled within the cavity with a L/D of less than 5, 4 and 3.5, respectively. The simulation results showed that increasing the L/D as well as the water entry angle relative to the free surface resulted in the improvement of the cylindrical projectile motion stability, which is in agreement with the experimental results. By analyzing the details of each simulation, it was found that the projectile stability within the cavity is correlated with the magnitude of the angular momentum which is generated in the projectile by the impact of the cavitator on the free surface and it was shown that the projectile with a specific L/D can withstand destabilizing angular momentum to a certain extent. Considering the fact that the atmospheric ballistics of gyroscopically stabilized projectiles lead to a limit for increasing L/D, this study showed that, for aluminum cylindrical projectiles in which air stability is achieved via the gyroscopic effect, the minimum water entry angle is 6° to attain the gyroscopic stability of the projectile in the air and stable motion inside the cavity. This fact is very important from a practical point of view.