Nonlinear dynamics of premixed flames: from deterministic stages to stochastic influence

Abstract

Abstract

Nonlinear dynamics of flame fronts with large-scale stabilizing effects

“…As can be seen, the differences between the fit obtained here (red line) and the one obtained in [27] on the same data but with the standard dispersion relation (black line) are small. In particular, the dispersion relation is slightly shifted towards the large wavenumbers and a new cutoff wavenumber is introduced on the left side of the dispersion relation.…”

“…The dynamics described by MS equation was even succesfully compared to DNS results [18] and experiments [25,26] on a quantitative level for moderate time of propagation (≈ 10 × 1/σ M ). At larger time, we have argued in a recent study that the background noise and sensitivity to initial conditions play an important role in the observed dynamics, therefore limiting a face to face comparison between experiments and numerical simulations [27]. However, we have suggested that the MS equation could still be relevant in predicting some statistical features of the flame front topology.…”

“…The dynamics described by (9) will now be compared to experimental flames. For this purpose, we make use of the Hele-Shaw burner employed in our recent studies [27,34,45,46]. This apparatus is made of two borosilicate glass plates (1500 × 500 × 5mm) oriented vertically and separated by a 5mm gap.…”

“…These data are then used as an indirect measurements of the parameters σ M , k c and G involved in (9). The procedure to obtain their value is the same as the one employed in [27], but the modified dispersion relation (8) instead of the standard one associated with (1), is fitted on the growth-rate measurements using a Levenberg-Marquardt algorithm (see Fig. 2).…”

“…2. This corresponds to the standard MS equation exploited in [27] (G = 0). The second one 3 (c) is obtained using the parameters corresponding to the best fit of (4) on our growth rate data (red line on fig.…”