Azimuthal instabilities in annular combustors: standing and spinning modes

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. We extend this model to take into account the effect that the acoustic azimuthal velocity, u, 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. In an intermediate range of delta, both spinning and standing modes are stable states. For large values of delta, standing modes are the only stable state. This study shows that a flame's response to azimuthal velocity fluctuations plays an important role in determining the type of thermoacoustic oscillations found in annular combustors.