Effect of vorticity waves on azimuthal instabilities in annular chambers

Azimuthal instabilities are the thermoacoustic oscillations that appear in the annular chambers of gas turbines. In previous investigations, the vorticity waves that can be generated by the interaction of acoustic waves and flame have typically been neglected. The present paper studies how vorticity waves affect the azimuthal instability in a simple annular chamber with a compacted flame sheet. An analytical model with the effect of the vorticity wave is constructed. To validate this analytical model with the vorticity wave, a linear Euler equation method, in which all forms of flow disturbances are included, is introduced. The results from the analytical method without the vorticity wave are also given, on the analogy of the network model and finite element method. Good agreement is found between the numerical simulation on the basis of the linear Euler equation and the analytical method with vorticity disturbance. Moreover, for the pure azimuthal mode, the difference between the results with and without vorticity disturbance is significant. For axial and azimuthal mixed-mode, the effect of vorticity disturbance is weak. These results show that the calculation of azimuthal instabilities using a network model and finite element method may lead to severe prediction errors when the mean flow is considered. The generation of vorticity disturbance is also studied based on both numerical method and dimensional analysis. It is concluded that in the present case, the generation of vorticity disturbance is due to the circumferential velocity continuity across the flame.