# 2013 - Stability of spinning and standing azimuthal modes in symmetric annular chambers : model for transversal forcing

Author’s copy

Abstract: This theoretical study investigates spinning and standing modes in azimuthally symmetric annular combustion chambers. Both modes are observed in experiments and simulations, and an existing model predicts that spinning modes are the only stable state of the system (Noiray, Bothien {\&} Schuermans, 2011, Comb. Theory Modelling 15(5) 585–606). We extend this model to take into account the effect that the acoustic azimuthal velocity has on the flames, and propose a phenomenological model based on experiments performed on transversely forced flames. This model contains a parameter, $\delta$, that quantifies the influence that the transversal excitation has on the fluctuating heat release. For small values of $\delta$, spinning modes are the only stable state of the system, while for large values of $\delta$, standing modes are the only stable state. There is also an intermediate range of $\delta$ for which both spinning and standing modes are stable. 1