We seek to ascertain and understand source terms that drive thermoacoustic instability and acoustic radiation. We present a new theory based on the decomposition of the Navier-Stokes equations coupled with the mass fraction equations. A series of solutions are presented via the method of the vector Green’s function. We identify both combustion-combustion and combustion-aerodynamic interaction source terms. Both classical combustion noise theory and classical Rayleigh criterion are recovered from the presently developed more general theory. An analytical spectral prediction method is presented, and the two-point source terms are consistent with Lord Rayleigh’s instability model. Particular correlations correspond to the source terms of Lighthill, which represent the noise from turbulence and additional terms for the noise from reacting flow.

中文翻译：

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反应声湍流的热声不稳定性源和声辐射解析方程

我们力求确定和理解驱动热声不稳定性和声辐射的源术语。我们提出了一种基于Navier-Stokes方程与质量分数方程的分解的新理论。通过矢量格林函数的方法给出了一系列解。我们确定了燃烧-燃烧和燃烧-空气动力相互作用的源术语。古典燃烧噪声理论和古典瑞利准则都可以从目前发展起来的更通用的理论中获得。提出了一种解析谱预测方法，其两点源项与瑞利勋爵的不稳定性模型相一致。特殊的相关性对应于Lighthill的源项，这些源项表示来自湍流的噪声以及来自反应流的噪声的其他项。