Simultaneous identification of transfer functions and combustion noise of a turbulent flame

The Large Eddy Simulation/System Identification (LES/SI) approach allows to deduce a flame transfer function (FTF) from LES of turbulent reacting flow: Time series of fluctuations of reference velocity and global heat release rate resulting from broad-band excitation of a simulated turbulent flame are post-processed via SI techniques to derive a low order model of the flame dynamics, from which the FTF is readily deduced. The current work investigates an extension of the established LES/SI approach: In addition to estimation of the FTF, a low order model for the combustion noise source is deduced from the same time series data. By incorporating such a noise model into a linear thermoacoustic model, it is possible to predict the overall level as well as the spectral distribution of sound pressure in confined combustion systems that do not exhibit self-excited thermoacoustic instability. A variety of model structures for estimation of a noise model are tested in the present study. The suitability and quality of these model structures are compared against each other, their sensitivity regarding certain time series properties is studied. The influence of time series length, signal-to-noise ratio as well as acoustic reflection coefficient of the boundary conditions on the identification are examined. It is shown that the Box-Jenkins model structure is superior to simpler approaches for the simultaneous identification of models that describe the FTF as well as the combustion noise source. Subsequent to the question of the most adequate model structure, the choice of optimal model order is addressed, as in particular the optimal parametrization of the noise model is not obvious. Akaike's Information Criterion and a model residual analysis are applied to draw qualitative and quantitative conclusions on the most suitable model order. All investigations are based on a surrogate data model, which allows a Monte Carlo study across a large parameter space with modest computationally effort. The conducted study constitutes a solid basis for the application of advanced SI techniques to actual LES data.