Thermoacoustic Spectrum of a Swirled Premixed Combustor With Partially Reflecting Boundaries

This study investigates the effect of partial acoustic reflection at inlet or outlet of a combustor on thermoacoustic stability. Parametric maps of the thermoacoustic spectrum are utilized for this purpose, which represent frequencies and growth rates of eigenmodes for a wide range of model parameters. It is found that a decrease of the acoustic reflection at the boundaries does not always imply an increase in the stability margin of the thermoacoustic system. As a matter of fact, a reduction in the acoustic reflection may sometimes destabilize a thermoacoustic mode. Additionally, we show that perturbed passive thermoacoustic modes may become intrinsic thermoacoustic (ITA) modes in the fully anechoic case. We briefly discuss the mode definitions “acoustic” and “intrinsic” commonly found in the literature. The computational analysis is based on a state-space formulation of the linearized Navier–Stokes equations (LNSEs) with discontinuous Galerkin discretization. This approach allows to describe the thermoacoustic system as a linear combination of internal acoustics, flame dynamics, and acoustic boundaries. Such a segregation grants a clear analysis of the respective effects of the individual subsystems on the general stability of the system, expressed in terms of adjoint-based eigenvalue sensitivity. The state-space formulation of the LNSE proposed in this paper offers a powerful and flexible framework to carry out thermoacoustic studies of combustors with arbitrary geometry and acoustic boundary conditions.