Spatially resolved flamelet statistics for reaction rate modeling using premixed methane-air flames in a near-homogeneous turbulence

Flamelet models have been widely applied to predict premixed turbulent comb ustion, such as for instance, the Bray-Moss-Libby (BML) model in which spat ial flamelet statistics and, thus, mean reaction rate were deduced from a m ean reaction progress variable ((c) over bar) and a mean crossing frequency . Recently, Shy et al. introduced a methodology based upon a downward propa gating premixed flame through a near-isotropic turbulent flow field in a cr uciform burner with a pair of specially designed ion probes for quantitativ e measurements of turbulent burning velocities. In this work, we report det ailed measurements of important spatial statistical properties of these pro pagating turbulent methane-air flames for experimental analysis of the BML model using high-speed laser sheet tomography technique. Four cases are stu died, including both lean and rich conditions, with equivalence ratio phi = 0.9 and 1.2, and two different turbulent intensities n'/S-L approximate to 1.4 and 4.1 where S-L is the laminar burning velocity. Each case contains up to five hundred runs at the same experimental conditions, so that suffic ient images in the central near-isotropic region can be obtained to extract contours of reaction progress variable ((c) over cap), flamelet crossing l engths, crossing frequencies, flame wrinkling lengths ((L) over cap (y)), f lamelet crossing angles (theta), coefficient g in the BML model, and flame surface density (Sigma). The symmetric profile of flamelet crossing frequency v(y) as a function of (c) over bar is found for diffusionally stable flames, where the maximum va lue of v(y) occurs at (c) over bar = 0.5. For diffusionally unstable flames , the profile of v(y) tends to be asymmetric (skewed to the burned side), r evealing the effect of Lewis number on vy. It is found that v(y), evaluated along contours of (c) over bar, is almost constant for all values of (c) o ver bar. Its magnitude decreases with increasing turbulent intensities and is much smaller than the integral length scale in the unreacted turbulent f low. As Lewis number is varied, values of (L) over cap (y) for diffusionall y unstable flames are larger than that for diffusionally stable flame. Thes e results differ from those obtained with Bunsen flames and liquid flames, indicating that the BML model needs a precise closure for (L) over cap (y). The overall mean cosine value of theta (= sigma (y)) is measured to be 0.6 1 for u'/S-L approximate to 1.4 and 0.67 for u'/S-L approximate to 4.1, in contrast to 0.5 found for Bunsen flames but very close to 0.65 measured in liquid flames, suggesting that sigma (y) is probably not a universal consta nt its assumed by the BML model. The coefficient g is found to be better de scribed by an exponential relationship (g = 2) than a gamma-two relationshi p (g = 1), a result consistent with previous Bunsen flame measurements. Oth er quantities of interest, such as crossing frequencies, auto-correlations of c, and distributions of actual crossing angle along (c) over bar contour s, are also examined. These results may be used to improve the BML model. ( C) 2001 by The Combustion Institute.