Modeling of the Tail Slap for an Underwater Projectile within Supercavitation

Detailed process of the tail slap for an underwater projectile in supercavitation is studied in this paper. Firstly, the horizontal equation of motion for the projectile and a dynamic model of the projectile’s tail slap are introduced through a mathematical derivation, including a simple harmonic motion model of the projectile within the supercavitation layer and the tail slap reflection movement model inside the cavity. Subsequently, the MATLAB software package is used to model the projectile’s motion. Characteristics for force from the projectile tail on the water layer during a single tail slap and the behavior of the projectile’s angular motion as well as the characteristics of projectile tail motion through multiple tail slaps are investigated. It is found that the force magnitude of the water on the projectile tail decreases gradually while the relative motion angle of the projectile tail into the water layer and the contact time increase obviously as the projectile repeatedly slaps the cavity interface. When the projectile velocity decreases into a certain range, i.e., less than 50 m/s, the contact time of the tail in the water layer increases dramatically, and the supercavitation can tend to collapse and lead to unstable projectile motion. With increasing lateral deviation and angular velocity of the projectile tail, the number of tail slaps and the angle of reflection both increase significantly. In the case of supercavitation, the parameters of different tail slap points tend to be stable with time.