Effect of the flame motion on azimuthal combustion instabilities

In the analysis of combustion instabilities in the annular combustors, especially for the azimuthal combustion modes, the flame motion is usually neglected and the flame is typically regarded as a discontinuity at rest. However, this simplicity may cause severe prediction errors for certain conditions. In this paper, the influence of the flame motion on the entropy, vortex, acoustic, and intrinsic modes in the annular combustion chamber is investigated by constructing an analytical model with the flame motion. Meantime, the influence of flame model parameters is also explored. The flame motion can affect both the frequency and growth rate of the entropy mode, but the growth rate is influenced more significantly. This effect can be damped or enlarged by the inlet Mach number depending on which parameter of flame model remains unchanged. The effect of the flame motion on vortex, acoustic, and intrinsic modes remains small when the inlet Mach number is very small. However, the increase of inlet Mach number can enlarge this effect.