The response of a one-dimensional laminar premixed flame to an inlet velocity forcing is investigated within the disturbance energy budget (DEB) framework. It is evidenced that the flame behaviour can be characterized through two dimensionless numbers. The first is a Strouhal number St , which is related to the flame motion and compares the flame front flapping length scale to the laminar premixed flame thickness delta(0)(L) . The second is the normalized velocity forcing level 77, i.e., the ratio between the amplitude of the inlet velocity variation and the laminar flame speed. Among the various disturbance energy sources, three terms, which do involve temperature (entropy) fluctuations, have significant growth-rates. These are: (i) the thermoacoustic source, (ii) an entropic term related to the coupling between entropy and temperature gradient variations, and finally (iii) a sink term relevant to thermal diffusion effects. For moderate forcing levels, the sole knowledge of these three terms together with St are sufficient to describe the flame dynamics. However, for larger forcing levels, the aforementioned contributions are no longer predominant over the transient variations of the disturbance energy that are induced by velocity fluctuations. Indeed, although the growth-rates of the corresponding source terms remain marginal - regardless of forcing amplitude and frequency - they must be taken into account so as to predict the evolution of the system, and the second non-dimensional number 77 becomes necessary to proceed with its precise characterization. (c) 2023 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
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