Abstract
This study describes an analytical method to compute azimuthal modes due to ame/acoustics coupling in annular combustors. It is based on a quasi- one-dimensional zero-Mach number formulation where N burners are con- nected to an upstream annular plenum and a downstream chamber. Flames are supposed to be compact and are modeled using identical Flame Trans- fer Function for all burners, characterized by an amplitude and a phase shift. Manipulation of the corresponding acoustic equations leads to a sim- ple methodology called ANR (Annular Network Reduction). It allows to retain only the useful information related to the azimuthal modes of the annular cavities. It yields a simple dispersion relation which can be solved numerically and allows to construct coupling factors between the di erent cavities of the combustor. A fully analytical resolution can be performed in speci c situations where coupling factors are small (weak coupling). A bifurcation appears at high coupling factors leading to a frequency lock-in of the two annular cavities (strong coupling). This tool is applied to an aca- demic case where four burners connect an annular plenum to a chamber. For this con guration, analytical results are compared to a full three-dimensional Helmholtz solver to validate the analytical model in both weak and strong coupling regimes. Results show that this simple analytical tool allows to predict modes in annular combustors and investigate strategies to control them.