热声现象的一种非线性模型的研究

The STUDY OF A NONLINEAR THERMOACOUSTIC MODEL

本文对一种准一维非线性热声模型进行研究,利用该模型初步预测了一种热声驱动器的工作特性,并采用一种更简便的差分格式对系统中发生的非线性现象进行了数值模拟。结果表明,在频域内和线性条件下,该模型简化为经典的线性热声模型,可以预测热声驱动器的起振温度梯度;在时域内和非线性条件下,该模型可以模拟热声系统内的瞬态压力波由初始增长,经过非线性演化,最终达到饱和的全过程;最后,还讨论了板叠上的温度差对饱和压力波的影响。

The focus of this thesis is the study of a general time-domain, fully nonlinear, quasi-one- dimensional thermoacoustic model. The work characteristics of a standing-wave prime mover is forecasted by the model, and a more simply numerical method is developed to numerically simulate the nonlinear processes in the device. The result is that in the frequency domain and for small amplitudes the model reduces to the standard linear theory and it can forecast the critical temperature gradient; in the time domain and for large amplitudes explicit results for the initial growth, nonlinear evolution, and final saturation are obtained. Finally, the depenence of the saturation amplitude upon the temperature difference in the stack is illustrated.