Elimination of numerical damping in the stability analysis of non-compact thermoacoustic systems with linearized euler equations

The hybrid Computational Fluid Dynamics/Computational AeroAcoustics (CFD/CAA) approach represents an effective method to assess the stability of non-compact thermoacoustic systems. This paper summarizes the state-of-the-art of this method, which is currently applied for the stability prediction of a lab-scale configuration of a perfectly-premixed, swirl-stabilized gas turbine combustion chamber at the Thermodynamics institute of the Technical University of Munich. Specifically, 80 operational points, for which experimentally observed stability information is readily available, are numerically investigated concerning their susceptibility to develop thermoacoustically unstable oscillations at the first transversal eigenmode of the combustor. Three contributions are considered in this work: (1) flame driving due the deformation and displacement of the flame, (2) visco-thermal losses in the acoustic boundary layer and (3) damping due to acoustically induced vortex shedding. The analysis is based on eigenfrequency computations of the Linearized Euler Equations with the stabilized Finite Element Method (sFEM). One main advancement presented in this study is the elimination of the non-physical impact of artificial diffusion schemes, which is necessary to produce numerically stable solutions, but falsifies the computed stability results.