Hybrid methods for modelling combustion instabilities

We have developed a set of methods for modelling combustion instabilities that can be called 'hybrid' in the sense that they combine numerical and experimental techniques. The techniques are based on the idea to simulate the acoustics numerically but, within this simulation, to represent the effect of the flame by a flame transfer function obtained from experiments or computational fluid dynamics. The simulation on the one hand can be carried out in the time domain. This approach allows a stability analysis in principle for arbitrary geometries, multi-dimensional acoustics, multiple flames, distributed reaction zones, and non-linearities in the flame. On the other hand, the hybrid method can also be formulated in the frequency domain. This allows the computation of the acoustic field for an acoustically excited system, including the effects of flame dynamics. One application of this method is the accurate determination of burner and flame transfer matrices, which can be used for a stability analysis with a network type code. While the measured frequency response of a flame can directly be included in the frequency domain simulations, it is otherwise often necessary to identify a flame model. We show that for the flame transfer function of a specific swirl burner a well matching model could be found, following a formal approach.