Nonlinear Dynamics and Bifurcations of a Supercavitating Vehicle

Abstract

In this effort, a numerical study of the bifurcation behavior of a supercavitating vehicle is conducted. The vehicle model is nonsmooth; this is a result of the planing force acting on the vehicle. With a focus on dive-plane dynamics, bifurcations with respect to a quasi-static variation of the cavitation number are studied. The system is found to exhibit rich and complex nonlinear dynamics including nonsmooth bifurcations such as the grazing bifurcation; smooth bifurcations such as Hopf bifurcations, cyclic fold bifurcations, and period-doubling bifurcations; and aperiodic behaviors such as transient chaotic motions and chaotic crises. The tailslap phenomenon of the supercavitating vehicle is identified as the consequence of a Hopf bifurcation followed by a grazing event. It is shown that the occurrences of these bifurcations can be delayed or triggered earlier by using dynamic linear feedback control laws employing washout filters.