Impact of Heat Release Distribution on the Spinning Modes of an Annular Combustor With Multiple Matrix Burners

Annular combustors of aero-engines and gas turbine are often affected by thermo-acoustic combustion instabilities coupled by azimuthal modes. Previous experiments as well as theoretical and numerical investigations indicate that the coupling modes involved in this process may be standing or spinning but they provide diverse interpretations of the occurrence of these two types of oscillations. The present article reports a numerical analysis of instability coupled by a spinning mode in an annular combustor. This corresponds to experiments carried out on the MICCA test facility equipped with 16 matrix burners. Each burner response is represented by means of a global experimental flame describing function (FDF) and it is considered that the flames are sufficiently compact to interact with the mode without mutual interactions with adjacent burning regions. A harmonic balance nonlinear stability analysis is carried out by combining the FDF with a Helmholtz solver to determine the system dynamics trajectories in a frequency-growth rate plane. The influence of the distribution of the volumetric heat release corresponding to each burner is investigated in a first stage. Even though the 16 burners are all compact with respect to the acoustic wavelength considered and occupy the same volume, simulations reveal an influence of this volumetric distribution on frequencies and growth rates. This study emphasizes the importance of providing a suitable description of the flame zone geometrical extension and correspondingly an adequate representation of the level of heat release rate fluctuation per unit volume. It is found that these two items can be deduced from a knowledge of the heat release distribution under steady state operating conditions. Once the distribution of the heat release fluctuations is unequivocally defined, limit cycle simulations are performed. For the conditions explored, simulations retrieve the spinning nature of the self-sustained mode that was identified in the experiments both in the plenum and in the combustion chamber.