Flamelet perturbations and flame surface density transport in weakly turbulent premixed combustion

DNS data obtained under conditions of weak turbulence that are well associated with the flamelet combustion regime are analysed in order (i) to assess the widely-accepted linear relation between the mean mass rate (Formula presented.) of product creation and the mean Flame Surface Density (FSD) (Formula presented.) and (ii) to investigate transport of the FSD and the role played by local flamelet perturbations in the FSD transport. While, in line with common expectations, a ratio of (Formula presented.) is found to be close to the unperturbed laminar flame speed S⁰ _L within the largest part of the mean flame brush, this ratio is significantly smaller (larger) than S⁰ _L at the leading (trailing) edge of the flame brush. Nevertheless, under the conditions of the present study, this difference in (Formula presented.) and (Formula presented.) can be disregarded when computing burning velocity by integrating (Formula presented.) over the flame brush, provided that (Formula presented.) is extracted from the DNS data. Even in the case of weak turbulence addressed here, the FSD transport is substantially affected by the difference between local density-weighted displacement speed ρS_d/ρ_u and S⁰ _L. This difference is associated with local perturbations of flamelet structure by turbulent eddies, with the local flamelet curvature (strain rate) playing a significantly more (less) important role in the FSD transport under the conditions of the present study. While the difference between ρS_d/ρ_u and S⁰ _L in the FSD transport equation can be approximated with a linear function of the local flamelet curvature by processing the DNS data, Markstein lengths associated with such an approximation (i) are scattered, (ii) vary within the mean flame brush, and (iii) differ significantly from the counterpart laminar Markstein length.