This study describes a simple analytical method to compute the azimuthaludmodes appearing in annular combustion chambers and help analyzing experimental, acoustic and LES (Large Eddy Simulation) data obtained in theseudcombustion chambers. It is based on a one-dimensional zero Mach numberudformulation where N burners are connected to a single annular chamber. Audmanipulation of the corresponding acoustic equations in this configurationudleads to a simple dispersion relation which can be solved by hand when theudinteraction indices of the flame transfer function are small and numericallyudwhen they are not. This simple tool is applied to multiple cases: (1) a singleudburner connected to an annular chamber (N = 1), (2) two burners connectedudto the chamber (N = 2), (3) four burners (N = 4). In this case, the tooludalso allows to study passive control methods where two different types ofudburners are mixed to control the azimuthal mode. Finally, a complete helicopter chamber (N = 15) is studied. For all cases, the analytical resultsudare compared to the predictions of a full three-dimensional Helmholtz solverudand a very good agreement is found. These results show that building veryudsimple analytical tools to study azimuthal modes in annular chambers is anudinteresting path to control them.
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