一种基于谱方法的三维热声不稳定模型

Three-dimensional thermoacoustic instability model based on spectral method

研究流体的流动参数,包括热源热释放的周向不均匀分布对热声不稳定现象的影响,将欧拉方程进行线化处理之后,对轴向和径向方向进行基于切比雪夫多项式的谱离散,周向方向则进行基于傅里叶多项式的谱离散,建立了一种三维热声不稳定数值模型.通过对圆柱管道共振频率以及声场的求解,进行了一系列算例的验证,证实了该方法的可靠性,并且通过热释放温度周向非均匀的算例,证实了某些周向对称分布参数下,可以使用截面平均的集总参数来代替非均匀分布参数;而在非对称的分布情况下,当周向不均匀分布很强烈的时候,这种使用截面平均参数的近似算法会带来偏差.

In order to investigate the effect of circumferential non-uniform fluid parameters and heat release on thermoacoustic instabilities, Chehyshev method was applied to axial and radial directions and Fourier method was applied to circumferential direction in the linear Euler equations. Resonant frequencies and acoustic fields of a duct were obtained by this method for validation and further investigations. At last, after some calculation for circumferential non-uniform heat release, it is verified that some symmetrical circumferential non-uniform conditions can be simplified to uniform conditions. But this approximation would bring errors if the circumferential non-uniform distribution is strong in case of asymmetrical distribution.