Mean cell wavelengths of wrinkled premixed flames in weak gravity fields: Spontaneous evolutions

Nonlinear dynamics of flame fronts with large-scale stabilizing effects

“…The longtime dynamics is completely different from the MS ones. The new crest creations start earlier in the propagation process, resulting in a smaller mean cell size (as identified by Boury et al [33]). Moreover, a particular feature is observed here.…”

“…which reduces to (1) in the limit G → 0 through a simple change of frame of reference. Numerical experiments obtained by pseudo-spectral integration of equation ( 9), report a strongly modified dynamics (even for G σ M ) compared to the standard MS model [29][30][31][32][33]. Simulations of this modified MS equation will be compared to experiments in the rest of the paper.…”

“…Here, we demonstrate that these gravity and heat-loss effects are favourably taken into account in the G parameter for continuous flames, even in the absence of thermodiffusive instability. The leading pattern has probably not been observed before in that condition because all the MSG simulations were focused on small size domain [29][30][31][32] except for Boury's studies [33,42]. In the latter, however, the MSG integration was stopped as soon as new crests were starting to appear and the long time dynamics was not studied.…”

“…A stabilising large scale effects G < 0 has thus a destabilising influence for the curved non-linear shape. This new size selection mechanism leads the flame front evolution to a stationary mean cell size d smaller than the size domain, even in the absence of noise [33,42]. For large domain Λ as shown in Fig.…”

“…In §II, we therefore first review the different stabilising effects acting at large scales and we recall their specific influence in the linear regime. From this review, in §III we extract the general component introduced in the dispersion relation by this kind of effect and use a modified MS equation (already proposed by other authors in a different context [29][30][31][32][33]) with an additional term expected to mimic these large scale stabilising effects. We then compare the dynamics described by this equation with propane-air flames propagating in a Hele-Shaw cell and use these comparisons to suggest that this large scale stabilising effect could indeed be responsible for the intriguing features observed experimentally in the non-linear regime of propagation.…”