Mechanism Analysis And Simulation Study Of Chaotic Rotation Of Cone-type Continuous Water Wheel

Chaos research is a world-famous research hotspot in the world.Chaotic dynamics is an important field involving a wide range.Many scholars at home and abroad have conducted more in-depth research and Discussion on this subject.Lorenz equation and Lorenz like equation are typical chaotic systems.Many scientific researchers have studied Lorenz equation,Lorenz like equation and corresponding physical devices countless.This master's degree thesis is divided into a total of four sections: at the head section is the introduction,which describes the development process of water wheel device,in which the physical devices of five different water wheels are briefly introduced.Two representative chaotic water wheel devices,water wheel made by Lorenz and Water wheel made by Malkus,as well as cylindrical and dome continuous water wheel.Influenced and inspired by these water wheel experimental devices,this paper proposes and briefly introduces the conical continuous water wheel device.Then the history of chaos research at home and abroad and the current development state of chaos research,as well as the characteristic content of this paper.In the second chapter,the mathematical model of chaotic rotation of conical continuous water wheel is deduced and simulated.The mathematical model of conical continuous water wheel is deduced from the mass conservation equation and moment balance equation in physical knowledge.The model system is further simplified by Fourier expansion method to obtain the mathematical model of conical continuous water wheel-Lorenz like equation.Combined with the numerical simulation results of MATLAB,the bifurcation and chaotic behavior of the model system are analyzed to further explain that the rotation phenomenon of conical continuous water wheel is related to the water injection rate and water leakage rate.When the water leakage rate is determined and the water injection is in a range,the chaotic rotation phenomenon of conical continuous water wheel can be produced.In Chapter 3,the global exponential synchronization and stability analysis of chaotic system of conical continuous water wheel are studied.The global exponential synchronization theory is used to illustrate the effectiveness of the global synchronization of the mathematical model of conical chaotic continuous water wheel.By solving the equilibrium point of the mathematical model of conical continuous water wheel,the stability of the equilibrium point is used to explain the bifurcation and chaotic behavior of the model system.It shows that the conical continuous water wheel has unstable rotation and chaotic rotation in the process of motion in the meantime.The fourth chapter analyzes the chaotic rotation of water wheel from the perspective of turbulence theory and mathematical model,conjectures and analyzes four ideal situations,and finds that these four ideal situations can not make the chaotic behavior of water wheel system.Then it analyzes the fifth situation,that is,the actual situation,and draws the motion trajectory diagram and energy evolution diagram of the system in combination with Matlab mathematical drawing software,By comparison,it is found that the chaotic rotation of water wheel can only occur when it exists in reality,and then the internal mechanism of chaotic rotation of conical continuous water wheel is revealed.This energy always exists in the water wheel system in the whole rotation process.When the number of participating energy is greater than one time,there will be energy conversion.