This work discusses from a system theoretic point of view the low order modeling and identification of the acoustic scattering behavior of a ducted flame.
In this context, one distinguishes between black-box and grey-box models. The former rely on time series data only and do not require any physical modeling of the system that is to be identified. The latter exploit prior knowledge of the system physics to some extent and in this sense are physically motivated.
For the case of a flame stabilized in a duct, a grey-box model is formulated that comprises an acoustic part as well as sub-models for the flame dynamics and the jump conditions for acoustic variables across the region of heat release. Each of the subsystems can be modeled with or without physical a priori knowledge, in combination they yield a model for the scattering behavior of the flame.
We demonstrate these concepts by analyzing a CFD model of a laminar conical premixed flame. The grey-box approach allows to optimize directly the scattering behavior of the identified model. Furthermore, we show that the method allows to estimate heat release rate fluctuations as well as the flame transfer function from acoustic measurements only.