Two Dimensional Numerical Simulation Of Traveling Wave Thermoacoustic Engine

Thermoacoustic engines use thermoacoustic effects to convert thermal energy into sound power.It has outstanding advantages such as no mechanical moving parts,compact structure,long life,reliable operation and environmental protection,and has received extensive attention at home and abroad.Thermoacoustic engines include traveling wave type thermoacoustic engines and standing wave type thermoacoustic engines.The traveling wave type thermoacoustic engine has higher thermal power conversion efficiency than the standing wave type thermoacoustic engine.Therefore,the application and development of traveling wave thermoacoustic engines has become a research hotspot for more than a decade.In addition,in terms of numerical simulation,most of the research work is mainly on the one-dimensional distribution characteristics of thermoacoustics,ignoring the changes of physical quantities in the radial direction.In order to understand the distribution characteristics of the sound field in the thermoacoustic system more clearly,and to provide reference for the development of nonlinear thermoacoustic theory,this paper focuses on the distribution characteristics of thermoacoustic systems in two-dimensional space.Based on Rott’s linear thermoacoustic theory and basic dynamic equations,the two-dimensional first-order and two-dimensional second-order frequency domain theoretical mathematical models of thermoacoustic engine system are established,and according to the weighted residual method in the finite element method,the mathematical model is transformed into a matrix form which is easy to solve.A traveling wave thermoacoustic engine system is simulated by using MATLAB software.The first-order pressure,first-order temperature,first-order velocity distribution and numerical value of the acoustic field in the thermoacoustic system are obtained successfully.Subsequently,the first-order fluctuations are substituted as known variables into the second-order solution model to obtain the distribution characteristics of the second-order fluctuations in the system.The simulation results show that in the resonance tube,both the first-order fluctuations and the second-order fluctuations exhibit a good sinusoidal distribution.Compared with the first-order quantity,the second-order wavelength is reduced by half and the frequency is increased by two times.In the single flow path of the regenerator,the distribution of the first-order and second-order fluctuations is basically the same,but the first-order vibration amplitude is much larger than the second-order quantity.From the cold end to the hot end,due to the large impedance,the amplitude of the fluctuating pressure and the temperature amplitude are significantly reduced,while the amplitude of the fluctuating velocity is gradually increased.The velocity and pressure in the whole thermoacoustic system are calculated by cross-section integral and the distribution of volume flow rate and pressure amplitude along the axial direction in one-dimensional space is obtained.No matter the first or second order quantity,the pressure and volume flow rate have the opposite change phenomenon.At the inlet of regenerator,the pressure reaches the maximum value,while the volume flow rate just reaches the minimum value.The two dimensional model of traveling wave thermoacoustic engine is explored and studied from the time domain angle.The second-order first-dimensional model and the finite element solution model,the two-dimensional second-order model and the finite element solution model are established,which provide a solution method for the time domain analysis of the thermoacoustic system.