Influence of Lewis number on the surface density function transport in the thin reaction zone regime for turbulent premixed flames

Abstract

The effects of tangential strain rate and curvature on the surface density function ͑SDF͒ and on different terms within the SDF transport equation in the thin reaction zone regime are studied for statistically planar turbulent premixed flames with global Lewis numbers Le= 0.8, 1.0, and 1.2 by using three-dimensional direct numerical simulations with simplified chemistry. A positive correlation is observed between the SDF and tangential strain rate, and this is explained in terms of the local statistical behaviors of tangential strain rate and dilatation rate. Curvature is shown to affect the SDF through the curvature response of both tangential strain rate and dilatation rate on a given flame isosurface. The correlation between the curvature and SDF is positive in the Le= 0.8 flame and negative in the Le= 1.2 flame. The curvature dependence of the SDF is weak in the case of unity Lewis number. Strain rate and curvature are found to have an appreciable effect on different terms of the SDF transport equation. The SDF strain rate term arising from tangential strain rate contribution in all the flames is positively correlated with tangential strain rate as expected and is also negatively correlated with curvature. For the Le= 1.0 and 1.2 flames, the SDF propagation term is found to negatively correlate with flame curvature toward the reactant side of the flame and positively toward the product side. By contrast, for the Le= 0.8 flame, the SDF propagation term is negatively correlated with curvature throughout the flame brush. The variation of the SDF curvature term with local flame curvature for all the flames is found to be nonlinear due to the additional stretch induced by the tangential diffusion component of the displacement speed. Physical explanations are provided for all of these effects, and the modeling implications are discussed in detail.

Effects of Lewis number on vorticity and enstrophy transport in turbulent premixed flames

“…Several analyses [44][45][46][47][48][49][50][51][52][53] attributed large values of A T /A L or R T /R L for turbulent premixed flames with Le < 1 to the thermo-diffusive instability of laminar flamelets which separate the unburned and burned gases. An alternative concept 54,55,69,80 of the Lewis number effects in premixed turbulent combustion emphasizes the propagation of highly stretched leading reaction zones into the unburned gas (the so-called leading edge concept).…”

“…It is shown elsewhere 48,50 that the flame thickness decreases, though the probability of finding high temperature spots (including super-adiabatic temperature values) increases with decreasing Le in turbulent flames, because the molecular diffusion of reactants into the reaction zone overwhelms conductive heat flux out from the zone for small values of Le. Accordingly, the magnitude of density gradient |∇ρ| increases with decreasing Le, which can be confirmed from Fig.…”

“…32 In the past, the significant effects of characteristic Lewis number Le on various aspects of premixed combustion (e.g., thermo-diffusive instability of laminar flames, burning rate, scalar gradient statistics, and combustion modelling) have been addressed analytically, [33][34][35][36] experimentally, [37][38][39][40][41][42][43] and numerically. 18,[44][45][46][47][48][49][50][51][52][53] Various concepts, which have been developed in order to explain such effects in turbulent flames, are reviewed elsewhere. 54,55 However, the influences of Le on vorticity ⃗ ω and enstrophy Ω transport are yet to be analysed in detail in the existing literature.…”

A Direct Numerical Simulation-Based Analysis of Entropy Generation in Turbulent Premixed Flames

“…Single step chemistry has been used successfully to obtain fundamental physical insight and to develop high-fidelity models in several analyses in the past [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] and the same methodology has been followed here. In the context of simplified chemistry the species field is characterized by a reaction progress variable c , which can be defined in terms of a suitable reactant mass fraction R Y as follows:…”

“…It is worth noting that Soret and Dufor effects are ignored here following several previous analyses on entropy generation in turbulent reacting flows [4][5][6][7][8][10][11][12][13][14][15]17]. Moreover, there have been several previous DNS based computational analyses [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], which ignored Dufor and Sorret effects without much loss of generality. These effects are not expected to play important roles in most hydrocarbon-air and hydrogen-air flames [35] unless extremely lean hydrogen-air flames are considered.…”