On Local Equivalence Ratio Dependence of the Burning Rate in Premixed Turbulent Lean Hydrogen/Air Flames: A Direct Numerical Simulation Analysis

Abstract This study investigates preferential diffusion effects on the volume-integrated burning rate in turbulent premixed lean hydrogen/air flames, using 3D direct numerical simulations (DNS) to analyze flames at two global equivalence ratios and varying turbulence intensities. By examining the statistical distributions of local equivalence ratios, the analysis confirms pronounced preferential diffusion effects across all cases. Intenser turbulence tends to amplify these effects. Probability density functions (PDFs) of the local equivalence ratio further confirm stronger preferential diffusion at lower global equivalence ratios and significant sensitivity to the choice of reaction progress variable definitions, particularly between hydrogen-based and water-based definitions. To predict the impact of preferential diffusion, the volume-integrated burning rate is estimated by multiplying the laminar burning velocity for the local equivalence ratio with the probability density function of the local equivalence ratio distribution. The subsequent estimates are compared to corresponding values directly obtained from DNS data. Results show that, in cases where preferential diffusion effects are more pronounced, i.e. at lower global equivalence ratios and relatively higher turbulence intensities, the DNS-derived burning rates based on water and temperature progress variables are best approximated using burning rates computed from the local equivalence ratio field conditioned on positive mean curvature. In contrast, cases less affected by preferential diffusion yield burning rate per unit area values comparable to those in the unstretched laminar flames when evaluated using water- and temperature-based definitions. The findings suggest that the burning rate per unit flame area could be modeled using the laminar burning velocity corresponding to the local equivalence ratio, and presumed PDFs representing the distributions of the local equivalence ratio. The gamma (or beta) distribution has been found to reasonably approximate the PDF of the local equivalence ratio, which can be utilized for the modeling of the volume-integrated burning rate in premixed turbulent lean hydrogen/air flames.