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

Abstract

Flamelet models have been widely applied to predict premixed turbulent combustion, such as for instance, the Bray-Moss-Libby (BML) model in which spatial flamelet statistics and, thus, mean reaction rate were deduced from a mean reaction progress variable (c) and a mean crossing frequency. Recently, Shy et al. introduced a methodology based upon a downward propagating premixed flame through a near-isotropic turbulent flow field in a cruciform burner with a pair of specially designed ion probes for quantitative measurements of turbulent burning velocities. In this work, we report detailed measurements of important spatial statistical properties of these propagating turbulent methane-air flames for experimental analysis of the BML model using high-speed laser sheet tomography technique. Four cases are studied, including both lean and rich conditions, with equivalence ratio φ = 0.9 and 1.2, and two different turbulent intensities u′/SL ≈ 1.4 and 4.1 where SL is the laminar burning velocity. Each case contains up to five hundred runs at the same experimental conditions, so that sufficient images in the central near-isotropic region can be obtained to extract contours of reaction progress variable (c), flamelet crossing lengths, crossing frequencies, flame wrinkling lengths (L̂y), flamelet crossing angles (θ), coefficient g in the BML model, and flame surface density (Σ).The symmetric profile of flamelet crossing frequency νy as a function of c is found for diffusionally stable flames, where the maximum value of νy occurs at c = 0.5. For diffusionally unstable flames, the profile of νy tends to be asymmetric (skewed to the burned side), revealing the effect of Lewis number on νy. It is found that L̂y, evaluated along contours of c, is almost constant for all values of c. Its magnitude decreases with increasing turbulent intensities and is much smaller than the integral length scale in the unreacted turbulent flow. As Lewis number is varied, values of L̂y for diffusionally unstable flames are larger than that for diffusionally stable flame. These results differ from those obtained with Bunsen flames and liquid flames, indicating that the BML model needs a precise closure for L̂y. The overall mean cosine value of θ (= σy) is measured to be 0.61 for u′/SL ≈ 1.4 and 0.67 for u′/SL ≈ 4.1, in contrast to 0.5 found for Bunsen flames but very close to 0.65 measured in liquid flames, suggesting that σy is probably not a universal constant as assumed by the BML model. The coefficient g is found to be better described by an exponential relationship (g = 2) than a gamma-two relationship (g = 1), a result consistent with previous Bunsen flame measurements. Other quantities of interest, such as crossing frequencies, auto-correlations of c, and distributions of actual crossing angle along c contours, are also examined. These results may be used to improve the BML model.