One-dimensional flame subject to periodic and sinusoidal motion: frequency domain analysis and flame-motion contribution to combustion instability - Genot, Aurelien; Boulal, Stéphane; Klein, Jean-Michel; Vincent-Randonnier, Axel; Mura, Arnaud (Combustion and flame, 2025)
Combustion instabilities are often an outcome of the interaction between fluctuations in the flame-induced heat release rate (HRR) and acoustic modes of the combustor. Thus, they are a direct consequence of the flame unsteady dynamics, which itself features multiple contributions. The present study is focused on one of them, namely that of the flame motion. Two distinct spatial distributions of the HRR subject to a periodic and sinusoidal motion (slower than the speed of sound) are analyzed in terms of its normalized motion amplitude. For these two distributions, a frequency domain analysis is conducted and the presence of peaks at the motion frequency, together with higher harmonics, are put into evidence. Thus, it is established that, even in (i) a simplified one-dimensional situation and (ii) with a slow periodic and sinusoidal motion featuring moderate amplitudes, flame motions can drive an energy transfer from the fundamental frequency to upper harmonics. This serves as a basis for the development of a simplified model, which is found able to retrieve the corresponding response in terms of its fundamental and harmonic frequencies. Flame-flow couplings are subsequently analyzed on the basis of stability criteria based on the Rayleigh index, the Chu index and a nonlinear index. This leads to the identification of a threshold value of the normalized motion amplitude with the flame motion contribution acting either as a source term below this value or as a damping term once it is exceeded. Novelty and significance This manuscript is focused on the flame motion contribution to flame dynamics and brings some new insights to the current state of the art: (i) for a periodic and sinusoidal motion, the flame response displays several harmonics that are triggered regardless of the motion amplitude and HRR distribution, (ii) a nonlinear and multi-harmonic model of the HRR fluctuations is presented for a boxcar HRR distribution moving periodically, and (iii) a threshold amplitude of the order of twenty times the flame thickness defines the flame motion contribution to combustion instabilities.