An analytical study of the effect of flame response to simultaneous axial and transverse perturbations on azimuthal thermoacoustic modes in annular combustors

Abstract

Transverse mean flows and transverse acoustic perturbations are factors that may influence the flame response, and thus change the frequency, growth rate and mode nature (standing, spinning or mixed) of the azimuthal thermoacoustic modes in annular combustors. Previous analytical and low-order network models for annular combustors usually consider only axial flame response. This work identifies the linear response of an asymmetric planar Bunsen flame under simultaneous axial and transverse perturbations. A linearized analytical method for studying the response of an inclined flame under perturbations using G-equation is applied. The relation between the flame responses under a 2-D perturbation and separate axial/transverse perturbations is studied to identify a linear 2-D flame response superposition, with the response under simultaneous perturbations being equal to the sum of two responses under each single perturbation. The effect of this linear 2-D flame response on the azimuthal thermoacoustic modes is then investigated by incorporating it into a linear low-order network methodology [19]. An annular combustor both with and without mixing burners and transverse mean flows is studied. The results are verified by comparing with FEM (Helmholtz solver) simulations. It is found that even though the transverse flame response is usually much smaller than the axial flame response, it may strongly affect the spin ratio of the azimuthal thermoacoustic modes. The asymmetries (e.g. due to burner difference) in both the transverse and axial flame response, and the effect of transverse mean flow on the acoustic propagation may all significantly change the spin ratio of the azimuthal modes, and thus need to be considered simultaneously.