Identification of flame transfer functions in the presence of intrinsic thermoacoustic feedback and noise

The Large Eddy Simulation/System Identification (LES/SI) approach is a general and efficient numerical method for deducing a Flame Transfer Function (FTF) from the LES of turbulent reacting flow. The method may be summarised as follows: a simulated flame is forced with a broadband excitation signal. The resulting fluctuations of the reference velocity and of the global heat release rate are post-processed via SI techniques in order to estimate a low-order model of the flame dynamics. The FTF is readily deduced from the low-order model. The SI method most frequently applied in aero- and thermo-acoustics has been Wiener–Hopf Inversion (WHI). This method is known to yield biased estimates in situations with feedback, thus it was assumed that non-reflective boundary conditions are required to generate accurate results with the LES/SI approach. Recent research has shown that the FTF is part of the so-called Intrinsic ThermoAcoustic (ITA) feedback loop. Hence, identifying an FTF from a compressible LES is always a closed-loop problem, and consequently one should expect that the WHI would yield biased results. However, several studies proved that WHI results compare favourably with validation data. To resolve this apparent contradiction, a variety of identification methods are compared against each other, including models designed for closed-loop identification. In agreement with theory, we show that the estimate given by WHI does not converge to the actual FTF. Fortunately, the error made is small if excitation amplitudes can be set such that the signal-to-noise ratio is large, but not large enough to trigger nonlinear flame dynamics. Furthermore, we conclude that non-reflective boundary conditions are not essentially necessary to apply the LES/SI approach.