Stochastic simulation of the structure and propagation rate of turbulent premixed flames

Abstract

A stochastic simulation model of the wrinkled flamelet regime of turbulent premixed combustion is shown to exhibit several postulated scaling properties governing flame structure and progagation rate. The model, based on the linear-eddy model of molecular mixing in turbulent flow, incorporates laminar burning of flamelets and the resultant decrease of flame surface area, and flamelet convection and surface area growth due to turbulent stirring. Simulated realizations, implemented on a one-dimensional domain representing a longitudinal line through the turbulent flame brush, exhibit (1) linear dependence of the turbulent flame speed u t on the turbulent velocity fluctuation u ′, (2) fractal flame structure, and (3) a lower cutoff of fractal scaling that can be plausibly characterized either by the Kolmogorov scale L k ≈Re −3/4 L , whereRe is the turbulence Reynolds number and L is the integral scale, or by the Gibson scale L G ≈( u′/S L ) −3 L , where S L is the laminar flame speed. The latter ambiguity indicates that the Re values investigated computationally (up to 1000) are not high enough to fully resolve the high-Re limiting behavior, reflecting an analogous limitation of typical experimental configurations. The experimentally observed decrease of the fractal dimension D at low u′/S L is reproduced, and is interpreted as reflecting insufficient dynamic range to fully resolve the fractal regime rather than an intrinsic dependence of D on u′/S L .