Nonlinear combustion instabilities analysis of azimuthal mode in annular chamber

Thermo-acoustic combustion instabilities are due to the coupling mechanism between acoustic pressure oscillations and heat release rate fluctuations. This phenomenon is of great interest because combustion instabilities cause recurrent problems in modern gas turbines. The case of annular chambers largely diffused in gas turbines for power generation is of particular interest. In this work, the azimuthal modes of a three-dimensional annular combustion chamber are studied by means of a finite element (FEM) code. For each burner, the coupling between heat release fluctuations (q′) and the velocity fluctuations (u′) is modeled by means of a non-linear analytical Flame Describing Function (FDF) consisting of a third order and fifth order polynomial expression. A delay time between (q′) and (u′) is considered. The dissipation of acoustic energy of the system due to viscous and thermal boundary layer is directly modeled in the code. The weakly nonlinear analysis is performed to determining the bifurcation diagrams for these flame models, considering the acoustic-combustion interaction index n as the control parameter. The influence on the bifurcations diagram of the time delays (τ) and of the damping coefficient (ζ) is analyzed.