Mechanism Analysis And Simulation Study Of Chaotic Rotation Of Circular Truncated Continuous Water Wheel

Chaos is an important research field in nonlinear science.More and more chaotic dynamics are studied by many scientists.The Lorenz equation is the most representative kind of chaotic system.Scientists have found that rotating water truck is a physical model that fully conforms to the Lorenz equation.On the basis of Malkus water wheel and cylinder type discrete water wheel,the rotating liquid membrane reactor device developed by Li Dianqing scientific research team of Beijing University of Chemical Technology to prepare nanomaterials is analyzed and studied.The mathematical model of circular continuous water wheel experimental device is constructed and the dynamic behavior of circular continuous water wheel chaotic rotation is analyzed.Then the energy conversion and corresponding physical meaning of circular continuous water wheel mathematical model are analyzed by Kolmogorov turbulence theory to explain the chaotic rotation phenomenon of circular continuous water wheel.Chapter one introduces the research background of chaotic rotation of continuous water wheel,the history and development of chaos,and the experiment of chaotic water wheel.The mechanical mechanism and energy conversion of fluid flow and Taylor-Couette flow between coaxial rotating platforms are described,and the characteristics and significance of this paper are described.Chapter two,by deducing the moment balance equation of water wheel and the mass conservation equation of the system,the mathematical model of chaotic rotation of circular continuous water wheel is constructed.The mathematical model is simplified by Fourier expansion and low frequency term to obtain the Lorenz equation.Chapter three mainly studies the chaotic system of water wheel deduced in chapter two,uses nonlinear theory to analyze the dynamic behavior of the model,and carries on the numerical simulation research to the analysis result through the Matlab numerical program.Then the chaotic rotation phenomenon of round platform water wheel is revealed.Chapter four analyzes the mechanical mechanism of the Lorenz system.Firstly,the circular continuous water wheel chaotic system is transformed into a Kolmogorov system with different forced power systems with Hamiltonian function,and the different dynamic behaviors of the circular continuous water wheel chaotic system are analyzed in the absence of various moments.The conversion between potential energy and kinetic energy in a circular continuous water wheel is discussed.The results show that the external force moment and the dissipative moment are the basic factors of chaos.Only when the driving moment and the dissipative moment are similar,they compete with each other and match each other,the continuous water wheel of the circular platform will have chaotic rotation.Finally,the paper summarizes the work done,and points out the next research direction.