Nonlinear Dynamics And Motion Stability Of A Supercavitating Vehicle

Supercavitating projectile technology is an important research direction in the field of weapon science.The application of supercavitating technology to underwater high-speed vehicle can effectively reduce the drag of the vehicle,and has great military application value.During the high-speed movement of underwater vehicle,most of its surface is enclosed by cavity,and the head cavitator and tail are mainly contacted with water.The motion parameters,i.e.cavitation number,initial depth,initial vertical velocity,initial pitch angle,initial pitch rate,affect the size and shape of supercavity,and structural parameters,i.e.deflection angle of the cavitator,the deflection angle of the tail affect the position of the vehicle in the supercavity.Because the contact between the tail of the vehicle and the cavity wall produces complex nonlinear planing force,which not only increase the sailing resistance,but also lead to the vibration and shocks of the vehicle,including complex nonlinear phenomena such as bifurcation and chaos.Therefore,it is of great theoretical significance and engineering application value to study the nonlinear phenomena caused by the changes of motion parameters and structural parameters of supercavitating vehicle,and to analyze the nonlinear dynamic characteristics of supercavitating vehicle in order to further improve the motion stability and quality of the vehicle.In this paper,based on the study of the characteristics of the flow field and the force characteristics analysis,the effects of structural parameters and initial motion parameters on the nonlinear dynamic characteristics and motion stability of supercavitating vehicle are studied by using various nonlinear dynamic analysis methods.The main contents and results are as follows:1.The Logvinovich cavitation model commonly used in the field of cavitation flow is introduced to predict the supercavitation shape under unsteady conditions.The hydrodynamic forces acting on each part of the body are analyzed and deduced,and the generation of nonlinear planing force and its influence on the motion of the vehicle are described.On this basis,the dynamic model of underwater supercavitating vehicle is given.Then the nonlinear dynamics analysis methods are introduced such as phase trajectory diagram method and Poincare? mapping method and so on.2.The bifurcation diagram is used to reveal chaos,bifurcation and other nonlinear physical phenomena occur when supercavitating vehicle changes with the cavitation number.The system is linearized at the equilibrium point,and the Jacobian matrix,the characteristic equation and the characteristic root of the system are obtained.The local stability of the system at the equilibrium point is determined by Routh-Hurwitz criterion,and then the motion state of the system under different cavitation numbers is obtained by time domain analysis.3.In order to solve the problem of motion instability of supercavitating vehicle affected by structural parameters,a variety of nonlinear dynamic analysis methods are used to analyze the dynamic behaviors of the dynamics model with the change of parameters in detail.Firstly,according to Lyapunov exponent criterion,the dynamic maps of the radius of the cavitator with respect to the cavitation number are drawn,which proved that the vehicle has three steady-state motions: stable,periodic and chaotic.The Lyapunov exponents and phase track diagram are used to reveal a special motion state called the transient chaotic and steady-state period.Secondly,the bifurcation diagram shows the nonlinear physical phenomena of the vehicle with the change of the deflection angle of the cavitator,including chaos,bifurcation,coexistence attractor and incomplete Feigenbaum tree.The position of the vehicle can be controlled by adjusting the deflection angle of the cavitator to ensure the stable movement of the vehicle.Finally,the relationship between the tail deflection angle and the cavitation number is determined according to the equilibrium point distribution map.The tail deflection angle is adjusted by bifurcation control method to delay the occurrence of Hopf bifurcation,enlarge the range of the cavitation number that makes the steady motion,and improve the stability of the vehicle.4.In order to solve the problem of instable motion of supercavitating vehicle due to the influence of initial motion parameters,based on lyapunov exponent spectrums,dynamic maps of different structural parameters on the cavitation number are drawn respectively.Moreover,the corresponding system parameters regions of stable motion,periodic oscillation and chaotic oscillation of supercavitating body are determined.Furthermore,by comparing and analyzing the dynamic maps and equilibrium point distribution maps,the parametric regions where the probability of multistable phenomena can be obtained.Finally,different parameter combinations are selected in different parameter regions,and the coexistence of multiple attractors in the system is verified by phase track diagram and time domain diagram.The results show that under the same set of cavitation numbers and structural parameters,different initial motion parameters may lead to different motion states of the vehicle.The above investigation reveals the influence of initial motion parameters on the nonlinear dynamic characteristics of supercavitating vehicle.5.According to different types of coexistence attractors,the corresponding attraction domains are obtained,and the motion stability of supercavitating vehicle is analyzed according to the size and shape of the attraction domains.The larger the area of attraction domain at the stable equilibrium point,the better the motion stability of the vehicle at the parameter combination.Then,the time-domain and frequency-domain simulation methods are used to analyze and verify the motion state of the vehicle with the same parameters and different initial motion parameters.The results show that in the parametric region where the cavitation number does not change much,the stability of the motion decreases with the increase of the control gain of the tail deflection angle.On this basis,the motion stability of supercavitating vehicle can be further improved by parameter optimization.