Nonlinear responses of the premixed V-flame subjected to dual-frequency disturbances
File(s)
Accepted version
Author(s)
Type
Journal Article
Abstract
The two-way interaction between the unsteady flame heat release rate (HRR) and acoustic waves can lead to combustion instability within combustors. Previous studies have typically characterised premixed flame responses to pure harmonic forcing, assuming dynamically linear or weakly nonlinear behaviour, to quantify flame–acoustic interactions. By combining third-order asymptotic analysis with numerical simulations of the 𝐺-equation, this study investigates the nonlinear response of laminar premixed V-flames subjected to dual-frequency velocity perturbations (𝑆𝑡1 and 𝑆𝑡2, dimensionless frequencies). The positive correlation between disturbance propagation speed 𝑢𝑐 and frequency 𝑆𝑡 is captured by integrating a velocity-potential model with calibration against existing experimental data. The mechanism by which the disturbance at one forcing frequency, say 𝑆𝑡2, affects the flame dynamic response at the other forcing frequency, 𝑆𝑡1, is studied in detail. The perturbation at 𝑆𝑡2 couples with that at 𝑆𝑡1 to induce third-order nonlinear terms, giving rise to a non-monotonic suppression mechanism that smooths out the flame’s spatial wrinkling owing to the positive correlation between 𝑢𝑐 and 𝑆𝑡. As a result, excitation at 𝑆𝑡2 modifies the HRR response at 𝑆𝑡1, delineating an effective region bounded on the left by the frequency threshold of the linear response and on the right by the aforementioned non-monotonicity. Within this region, excitation at 𝑆𝑡2 can markedly attenuate the HRR gain at 𝑆𝑡1 compared with the case where the flame is driven solely by the perturbation at 𝑆𝑡1. For instance, once both perturbation amplitudes exceed a certain threshold, excitation at 𝑆𝑡2 can attenuate the flame response at 𝑆𝑡1 by more than 40 % compared with the case without excitation at 𝑆𝑡2. These findings contribute to the development of a quantitative framework for understanding how targeted frequency perturbations modulate the flame dynamics via nonlinear interactions, which may inform open-loop approaches for mitigating thermoacoustic instabilities in combustion chambers.
Date Issued
2026-07-10
Date Acceptance
2026-05-13
Citation
Journal of Fluid Mechanics, 2026, 1038
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
1038
Copyright Statement
Copyright © The Author(s), 2026. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Article Number
A2
Date Publish Online
2026-06-29