This study investigates the mode transition phenomenon in a standing-wave thermoacoustic engine (TAE) by means of computational fluid dynamics (CFD). Firstly, the steady-state responses of the TAE at selected temperature ratios are examined via continuous wavelet transform. The bifurcation diagram and spectral map indicate that, as the temperature ratio increases, the TAE experiences a series of bifurcations, through which first-mode periodic oscillations, quasiperiodic oscillations and second-mode periodic oscillations occur. Secondly, the TAE performances in the initial decay/build-up, nonlinear saturation and steady states are studied. The onset of the first and/or second acoustic mode is identified via dynamic mode decomposition. The oscillation frequencies and growth/attenuation rates from CFD agree well with those from the reduced-order network model. Nonlinear mode competition takes place during saturation in which the growth of one acoustic mode is affected or even totally inhibited by the growth of the other. At steady state, periodic oscillations exhibit a closed loop in the phase space whilst quasiperiodic oscillations generate a torus. The time-averaged acoustic energy density, acoustic intensity and efficiency increase with increasing temperature ratio. Finally, parametric studies are conducted to investigate the effects of the gap between stack plates and stack position on mode transition. It is found that the TAE will exhibit second-mode oscillations if the stack is near the closed end or the gap is small. Results in this study indicate that mode transition could become a novel approach to match the TAE with external loads for higher electric power outputs.

本研究通过计算流体力学（CFD）研究驻波热声发动机（TAE）的模式转变现象。首先，通过连续小波变换研究了TAE在选定温度比下的稳态响应。分叉图和频谱图表明，随着温度比的增加，TAE经历了一系列分叉，通过这些分叉会发生第一模式周期性振荡，准周期振荡和第二模式周期性振荡。其次，研究了TAE在初始衰减/累积，非线性饱和和稳态下的性能。经由动态模式分解来识别第一和/或第二声学模式的开始。CFD的振荡频率和增长率/衰减率与降阶网络模型的振荡频率和增长率/衰减率非常吻合。非线性模式竞争发生在饱和期间，其中一种声学模式的增长会受到另一种声学模式的增长的影响，甚至完全被另一种声学模式的增长所抑制。在稳态下，周期性振荡在相空间中表现出闭环，而准周期振荡则产生圆环。时间平均声能密度，声强和效率随温度比的增加而增加。最后，进行参数研究以研究叠层板之间的间隙和叠层位置对模式转换的影响。已经发现，如果堆叠靠近封闭端或间隙很小，则TAE将表现出第二模式振荡。