This paper seeks to advance linear stability analyses of thermoacoustic systems conducted with a stabilized Finite Element Method (sFEM). Specifically, this work analyzes and quantifies the impact of the Streamline Upwind Petrov Galerkin (SUPG) artificial diffusion scheme on (eigen)mode shapes and damping rates of the isentropic Linearized Euler Equations (LEE) in frequency space. These damping rates may significantly be affected by the numerical stabilization scheme in a non-physical manner. The LEE (eigen)mode shapes are separated into acoustic and vortical perturbation components via a Helmholtz decomposition and their sensitivity on the employed stabilization scheme is investigated separately. The regions, where numerical stabilization principally acts on the respective perturbation types, are allocated and explanations for the observations are provided. Furthermore, a methodology is established, which allows the quantification of the impact of artificial diffusion on the acoustic field in terms of a damping rate. This non-physical damping rate is used to determine the acoustic LEE damping rate, which is compensated by the contribution of artificial diffusion and thus represents the physically meaningful damping rate component only. Hence, the presented method eliminates a main shortcoming of LEE eigenfrequency analyses with the sFEM and, as a result, provides more accurate information on the stability of a (thermo-) acoustic system.


Impact of the Stabilized Finite Element Method on Acoustic and Vortical Perturbations in Thermoacoustic Systems

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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