Elimination of Numerical Damping in the Stability Analysis of Noncompact Thermoacoustic Systems With Linearized Euler Equations

Abstract

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.

On the convective wave equation for the investigation of combustor stability using FEM-methods

“…Models used for predicting system’s stability range from low-order network models (e.g. Bloxsidge et al, 7 Keller 8 or Evesque and Polifke 9 ) up to higher-order, three-dimensional models employing the Linearized Euler Equations (LEE) 10,11 or the Linearized Navier-Stokes Equations (LNSE). 12,13 Low-order network models are usually not capable of satisfactorily describing the three-dimensional wave propagation of high-frequency (HF) thermoacoustics in complex geometries.…”

“…As a result, the acoustic velocity is not necessarily irrotational if density gradients are present. These may constitute baroclinic effects if the cross product of the density gradient and the acoustic velocity does not vanish, which is discussed by Hofmeister et al 11 This effect may be considered a refraction of acoustic waves passing density gradients, which is not considered in classical acoustics but may play an important role in performing stability analyses of thermoacoustic systems. The LHS of eq. (43b) and (43c) of the APE system are not depending on the density fluctuations.…”