Decomposition of swirling flame transfer function in the complex space

Guoqing Wang, Thibault Guiberti, Xi Xia, Lei Li, Xunchen Liu, William L. Roberts, Fei Qi

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this work, we propose an analytical decomposition of the flame transfer function (FTF) in the complex space. The decomposition provides new insight into the relationship between the local heat release oscillator and the global flame response of a periodically oscillating system in the linear regime. The FTF of a premixed methane-air swirling flame is decomposed using two-region and pixel-by-pixel division of the chemiluminescence images. The two-region decomposition uses horizontal or vertical dividing lines to examine the effects of dividing positions and orientations. The complex curves of the two-region division are more sensitive to the dividing line's position than its orientation. The pixel-by-pixel decomposition provides detailed distributions of the weighting factor, weighted gain, and phase of all local oscillators. The weighted gain distribution highlights the inner fluctuating region (IFR) and outer fluctuating region (OFR), as well as the node region. These regions are mainly controlled by the radial velocity and its fluctuations induced by the vortices in the inner and outer shear layers. The unwrapped phase, which gradually increases as the downstream distance from the injector increases, highlights the convective characteristics of the oscillating heat release rate. Angular wavenumbers and phase velocities are deduced from the phase distribution. The phase velocities agree well with the mean velocities measured with particle image velocimetry. Sorting all the local oscillators in the ascending phase allows constructing complex curves that favorably represent the FTF. The algebraic sum of weighted gain and the efficiency of phase interference are calculated to examine the phase interference. Phase interference plays a large role in suppressing the global fluctuating amplitude of the heat release rate. The local extrema at low and intermediate frequencies are attributed to in- or out-of-phase interference, while the reduced local response also explains why small FTF gains are observed at high frequencies.
Original languageEnglish (US)
Pages (from-to)29-41
Number of pages13
JournalCombustion and Flame
StatePublished - Feb 2 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-02-16
Acknowledged KAUST grant number(s): BAS/1/1370–01–01
Acknowledgements: This research is supported by National Natural Science Foundation of China (91941301) and King Abdullah University of Science and Technology (KAUST) (BAS/1/1370–01–01).


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