1/4波长驻波型热声发动机的非线性模型

为研究声波在热声系统开口端和负载构成的阻抗间断面上的声反射问题，针对一端开口的1/4波长驻波型热声发动机建立了一种基于截面平均的准一维非线性热声模型，并采用具有频散保持特性的高精度计算格式进行数值求解。在发动机开口端采用了对于系统共振频率具有一定选择自适应性的宽频时域声阻抗边界条件。宽频阻抗模型写成共轭复数对的留数和极点分式之和的形式，其时域形式可用递推卷积方法进行快速高效的求解，共轭复数系数采用优化拟合方法近似得出。模型可对一端开口的1/4波长驻波型发动机进行临界起振温度的预测，能够描述热声系统的瞬态压力波由初始小扰动经过非线性增长，最终达到饱和的全过程，计算结果与某微小型驻波热声发动机的实验结果相符。最后分析讨论了板叠的形状对热声系统的影响。

A quasi-one-dimensional nonlinear model of an open-closed standing-wave thermoacoustic engine

A quasi-one-dimensional nonlinear model of a standing-wave thermoacoustic engine with a quarter-wavelength resonator is presented. The model is based on cross-sectional averaged equations and is solved by high-order low-dispersion numerical schemes. Considering the acoustic reflection and radiation at the open end, broadband time-domain impedance boundary conditions are employed so that oscillation frequency can be self-adaptive. The impedance is expressed in the mathematical form of partial fraction expansion with complex-conjugate residues and poles, so that the convolution of the impedance with the velocity can be calculated by efficient and causal recursive convolution. Pole-residue pairs of the impedance can be optimized in the frequency domain. Critical temperature difference of an open-ended standing-wave thermoacoustic engine can be predicted and the time-domain simulation shows that the pressure oscillation undergoes a nonlinear amplifying process and eventually reaches saturation amplitude. Numerical results agree very well with the experiment for a small-scale thermoacoustic engine. The simulation results for different stack geometries are included.