Inclusion of higher harmonics in the flame describing function for predicting limit cycles of self-excited combustion instabilities

The Flame Describing Function (FDF) is widely used to model non-linear thermo-acoustic phenomena, e.g. limit cycle oscillations in a combustor. The FDF is a weakly non-linear approach, because it accounts for the amplitude dependence of the flame response, but besides that relies on quasi-linear assumptions. In particular, it neglects the excitation of higher harmonics – a typical non-linear feature, which may play a major role in certain...