Propagation and generation of acoustic and entropy waves across a moving flame front

In analytical models of the propagation and generation of acoustic and entropy waves across a premixed flame, the relations that couple upstream and downstream flow variables often consider the flame as a discontinuity at rest. This work shows how the model of a flame at rest can misrepresent the generation of entropy waves, and how it leads to paradoxical results concerning the conservation of mass and volume flow rates across the flame. Such inconsistencies can be resolved by taking into account the movement of the flame in the coupling relations for flow perturbations. Analysis in a quasi-1D framework shows that in the absence of perturbations in equivalence ratio, the magnitude of the entropy waves generated across the flame are first order in Mach number and derive from interactions between the upstream acoustics and the mean heat release rate. For non-perfectly premixed flames, fluctuations in equivalence ratio may generate perturbations in entropy of leading order in Mach number. Furthermore, for the moving flame model conservation of volume flow rate across a passive, perfectly premixed flame appears as a natural consequence of mass and energy conservation.