Abstract
Abstract
Highlights
Thermoacoustic instability is the result of the mutual coupling between flow dynamics, the unsteady heat release produced by a flame and the surrounding acoustic environment (Dowling & Stow 2003; Dowling & Morgans 2005; Lieuwen & Yang 2005; Culick 2006; Poinsot 2017)
We connect the existence of a finite radius of convergence to the existence of singularities in parameter space. We identify these singularities as exceptional points, which correspond to defective thermoacoustic eigenvalues, with infinite sensitivity to infinitesimal changes in the parameters
We have established interconnections between several topics that are essential for the investigation of thermoacoustic stability, namely symmetry-induced degeneracies, high-order adjoint perturbation theory, the origin of thermoacoustic modes and exceptional points (EPs)
Summary
Thermoacoustic instability is the result of the mutual coupling between flow dynamics, the unsteady heat release produced by a flame and the surrounding acoustic environment (Dowling & Stow 2003; Dowling & Morgans 2005; Lieuwen & Yang 2005; Culick 2006; Poinsot 2017). Large-amplitude pressure fluctuations develop inside the combustion chamber and affect the entire engine as undesired vibrations. These vibrations affect the normal operation of the system and reduce the lifespan of the engine. Quantitative stability prediction and analysis of thermoacoustic systems require the calculation of complex-valued eigenvalues and their associated eigenvectors. In order to calculate the drift of eigenvalues and eigenvectors due to changes in parameters at an affordable computational cost, high-order adjoint-based perturbation theory can instead be used (Mensah, Orchini & Moeck 2020)
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