Prediction of Thermoacoustic Limit Cycles during Premixed Combustion using the Modified Galerkin Approach

The present work extends the Generalized Instability Model, which solves the pressure wave equation via the modified Galerkin method, to include nonlinear heat release models in the form of Flame Describing Functions as well as acoustic losses at the boundaries. These extensions are required for limit cycle prediction in premixed combustors. The governing equations are presented in detail followed by the implementation of two Flame Describing Functions obtained experimentally from a bluff body burner and a swirl stabilized burner. For both test cases, multiple operating points are analyzed, with the model predicting correctly the stability in all cases. Good correspondence between modeled and measured limit cycle amplitudes for the unstable modes is also obtained. However, a parametric study shows that the predicted limit cycle amplitude has a strong dependence on the heat release model and on the acoustic losses present in the system. This indicates that both the energy gain due the combustion process and the acoustic losses through the boundaries need to be determined accurately for limit cycle prediction.