Modeling of the Tail Slap for an Underwater Projectile within Supercavitation

Abstract

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.

Experimental Investigation into the Tail-Slapping Motion of a Projectile with an Oblique Water-Entry Speed

“…Zhao et al [28] focused on the oblique water-entry process of projectiles with different heads and studied the velocity attenuation and projectile motion stability. Zhao et al [29] studied the tail-slapping law of underwater projectiles with a speed of less than 50 m/s by MATLAB simulation. In addition, by means of computer numerical simulation technology, Akbari et al [30] adopted the numerical simulation method to study the process of oblique water-entry of the stepped head projectile, and briefly described the tail-slapping phenomenon, which mainly analyzed the motion law of the projectile.…”

Analysis and Calculation of the Best Center of Mass for Supercavitating Projectile

“…Affected by the projectile entering water, the high-speed supercavitating projectile rotates in the cavity while advancing, which is this rotation that causes the tail of the projectile to collide with the cavity wall [10]. As shown in the literature [11], as the projectile beats the water wall, the force of the water wall on the projectile tail gradually decreases, and finally, the supercavitation collapses. The literature [12] obtained through theoretical analysis of the force of the projectile: when the projectile has the same shape and other conditions such as the length of the projectile, the forward movement of the center of mass is beneficial to the linear movement of the projectile and is beneficial to keep stability of movement of the projectile underwater.…”