The acoustic transmissions and reflections of plane waves at duct singularities can be represented with so-called scattering matrices. This paper shows how to extract scattering matrices utilizing linearized compressible flow equations and provides a comparative study of different governing equations, namely the Helmholtz, linearized Euler and linearized Navier–Stokes equations. A discontinuous Galerkin finite element method together with a two-source forcing is employed. With this method, the scattering matrix for a radial swirler of a combustion test-rig is computed and validated against the results of a fully compressible Large-Eddy-Simulation. Analogously, the scattering behavior of an axial swirler is investigated. The influence of acoustic-hydrodynamic interactions, viscous effects as well as unsteady boundary layers on the results is investigated for both configurations. A thermoacoustic stability analysis of the combustion test-rig housing the axial swirler is carried out, utilizing the scattering matrix of the swirler. Major influence of the reflections coming from the swirler on the thermoacoustic eigenfrequencies is found.

中文翻译：

---

从线性可压缩流动方程确定声散射矩阵并应用于热声稳定性分析

平面波在管道奇点处的声学传输和反射可以用所谓的散射矩阵来表示。本文展示了如何利用线性化可压缩流动方程提取散射矩阵，并提供了不同控制方程的比较研究，即亥姆霍兹方程、线性化欧拉方程和线性化 Navier-Stokes 方程。采用不连续 Galerkin 有限元方法和双源强迫。使用这种方法，可以计算燃烧试验台径向旋流器的散射矩阵，并根据完全可压缩的大涡模拟的结果进行验证。类似地，研究了轴向旋流器的散射行为。声-流体动力学相互作用的影响，研究了两种配置的粘性效应以及不稳定边界层对结果的影响。利用旋流器的散射矩阵对装有轴向旋流器的燃烧试验台进行热声稳定性分析。发现了来自旋流器的反射对热声本征频率的主要影响。