A theoretical analysis of thermoacoustics and combustion instability in annular combustors

Abstract

A theoretical analysis of thermoacoustics and combustion instability for a general annular combustor is presented. The combustor consists of an annular plenum and an annular flame chamber, connected by a series of identical nozzles. By applying the discrete Fourier transform to the azimuthal coordinate, we develop a closed-form representation of combustor thermoacoustics as a transfer function matrix that maps vector-valued heat inputs to resulting velocity fluctuations. In the transformed coordinate system, the transfer function matrix is diagonalized, which allows acoustic resonance to be determined through a set of explicit scalar equations. Furthermore, by approximating these scalar equations, we identify the effects of the combustor’s geometry and steady operating conditions on acoustic resonance. Combining the thermoacoustic model with a general flame model enables the assessment of combustion instability through the resonance characteristics of a perturbed thermoacoustic model. Our theoretical findings are demonstrated with numerical examples.