Non-Steady Planing and Advection Delay Effects on the Dynamics and Control of Supercavitating Vehicles

Cavity-vehicle interactions play a significant role in the dynamics of supercavitating underwater vehicles. To date, in the vast majority of planing force models for supercavitating vehicle dynamics, a steady planing assumption is utilized, wherein the vehicle-cavity interaction is only dependent on the vehicle’s position relative to the cavity. In this work, a framework to properly account for the vehicle radial motions into and out of the fluid is presented. This effectively introduces damping or velocity related dependence into the planing force formulation. The planing force is applied to cavity sections that are described by a previous (or delayed) position and orientation of the cavitator. The physical basis for the advection delay and the expressions used to determine the vehicle immersion and immersion rate are presented. Analysis and simulations for the time-delayed, non-steady planing system are carried out, and the delay effect in this system is shown to be stabilizing for certain values of the cavitation number that is contrary to previous results that have assumed steady planing force models.