Numerical Study Of Nonlinear Phenomenon In Thermoacoustic Resonant Tubes And Microscale Effects

Many key factors affecting the application of thermoacoustic technology are more or less closely related to many nonlinear problems caused by high-amplitude acoustic oscillations or miniaturization.The nonlinear thermoacoustic theory has become an urgent need for the application development of thermoacoustic devices.In the development of thermoacoustic devices and other acoustic devices,nonlinear resonance technology and micro-scaled technology have become the key elements to improve the sound-amplification and thermoacoustic conversion efficiency.The development of its theoretical and analytical models is of utmost importance.In this thesis,the dynamic acoustic behavior of equal crosssection area resonator tubes and exponential resonance tubes are studied using gas kinetic scheme.At the same time,taking into account the influence of micro-scale factors,a general-purpose thermoacoustic network analysis model has been established.Description of transmission parameters of nonlinear network elements is made.The specific research content of this article is summarized as follows.(1)The gas kinetic scheme is used to simulate the spatiotemporal evolution of sound field and the axial distribution of acoustic intensity in a standing-wave resonator with constant cross-sectional area.The results are in good agreement with the existing experimental results.The influence of the driving displacement amplitude of the piston on the formation of harmonics and shock waves was studied and the energy cascade process from fundamental to higher harmonics was revealed by harmonic component analysis from the mechanism.These provides a corresponding theoretical basis for nonlinear phenomena such as nonlinear acoustic saturation and shock suppression.(2)Based on the one-dimensional approximate expressions obtained by the progressive expansion method,the acoustic field distribution in the exponential resonant tube is theoretically analyzed.The influence of velocity-driven amplitude on acoustic field is studied and the optimal shape parameters of exponential resonant tube is given.It is concluded that the analytical results of the approximate solution and the simulation results of the gas kinetic scheme are consistent on one dimension,thus mutually validating the analytical method and the aerodynamic simulation method.Finally,the phenomenon of beat in the m=3.0 exponential resonance tube is analyzed and a method to improve the accuracy of the calculation of the first-order eigenfrequencies of the resonance tube using the beat phenomenon is proposed.(3)Considering the Navier-Stokes equations with slip velocity boundary condition and temperature jump boundary condition,the internal flow of a micro-scale thermoacoustic apparatus is theoretically modeled by the linearization method and the model unifies the thermoacoustic theory of Kn≤0.1.Based on the theoretical model,a network model in a micro-scale thermoacoustic engine is established and the expressions of transmission parameters and network transmission matrix of stack in the unit length transmission matrix are deduced.The influence of hydraulic radius of stack on the transmission parameters such as unit length impedance,admittance,pressure source parameters and flow source parameters are studied under different Kn.