Abstract
Little is known about the movement characteristics of the supercavitating vehicle navigating underwater. In this paper, based on a four-dimensional dynamical system of this vehicle, its complicated dynamical behaviors were analyzed in detail by numerical simulation, according to the phase trajectory diagram, the bifurcation diagram, and the Lyapunov exponential spectrum. The influence of control parameters (such as various cavitation numbers and fin deflection angles) on the movement characteristics of the supercavitating vehicle was mainly studied. When the system parameters vary, various complicated physical phenomena, such as Hopf bifurcation, periodic bifurcation, or chaos, can be observed. Most importantly, it was found that the parameter range of the vehicle in a stable movement state can be effectively determined by a two-dimensional bifurcation diagram and that the behavior of the vehicle in the supercavity can be controlled by selecting appropriate control parameters to ensure stable navigation.
Highlights
Liquid vaporization of a liquid occurs at any point when the pressure at that point is reduced below a critical value
The boundary between the green and yellow areas indicates the switch between the periodic and chaotic states, where the physical phenomena, such as tangent bifurcation and period doubling bifurcation, can occur. It can be observed from (1) that, in the four-dimensional dynamical system of the underwater vehicle, only the planing force Fplaning is the nonlinear force associated with the system state variable and the vertical velocity w
The nonlinear dynamic characteristic movement states under different control parameters of the supercavitating vehicle were analyzed based on a four-dimensional dynamical model of the vehicle
Summary
Liquid vaporization of a liquid occurs at any point when the pressure at that point is reduced below a critical value. Once the supercavity becomes stable, most of the vehicle’s surface is surrounded by gases and the resistance of the vehicle decreases sharply. This increases the navigation velocity and the distance travelled by the vehicle [2,3,4]. When coming into contact with the cavity wall, the fin will produce complex nonlinear planing force, which will increase the frictional resistance of the vehicle, causing vibrations and impact to the vehicle [5,6,7,8,9,10]. To the best of our knowledge, it is very difficult to find any related work in this paper up till
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