Using Broad-Band and Narrow-Band Signals to Measure Transfer Functions of Turbulent Flames

We assess the use of broad-band (BB) and narrow-band (NB) forcing signals to retrieve the Flame Transfer Functions (FTF) from experimental measurements in premixed turbulent flames where the latter uses monochromatic and Chirp signals and the former dichromatic and white/coloured noise signals. At low excitation amplitudes, all forcing methods provide similar estimates of the FTF. Although broad-band excitation provides information over a range of frequencies simultaneously, it also promotes nonlinear saturation effects over the whole frequency range. We show that these effects occur due to interactions between the response at high and low frequencies that cause significant amplitude saturation, even for relatively low excitation amplitudes (<2%). High-frequency modes were found to modify the phase distribution at lower frequencies leading to an increase in spatial interference and a reduced global HRR fluctuation amplitude. These results show that saturation must be avoided at all frequencies which significantly limits the use of BB signals without substantial a priori knowledge of the flame response. To circumvent this limitation, we utilise an amplitude modulated Chirp signal to obtain a time-series that sweeps the frequency range over the same total time duration as the applied broad-band signal. We show that this method reliably captures the FTF by avoiding nonlinear frequency interactions and only uses a single time-series measurement. This significantly reduces experimental effort required to retrieve FTFs over a wide range of operating conditions.Novelty and significance statementThis work presents the first systematic experimental comparison of broad-band and narrow-band forcing strategies for measuring flame transfer functions (FTFs) in turbulent premixed flames. The findings highlight a fundamental limitation of broad-band approaches for reliable FTF identification in turbulent flames, as nonlinear cross-frequency interactions cause gain reduction across the entire frequency range. We propose an amplitude-modulated Chirp methodology that preserves narrow-band behaviour while sweeping the full frequency range within a single time-series. This approach enables accurate FTF retrieval without cross-frequency contamination and substantially reduces experimental time, facilitating efficient mapping of FTFs across operating conditions.