A multi-scale asymptotic scaling and regime analysis of flamelet equations including tangential diffusion effects for laminar and turbulent flames

Recently, the relevance of tangential diffusion effects has been identified for laminar flames. These effects are not considered in the classical flamelet equations. In the present work, flamelet equations including these effects are derived, and their relevance is investigated by a multi-scale asymptotic scaling analysis. The analysis yields characteristic ratios dependent on the local curvature of the mixture fraction field, the scalar dissipation rate, and the flame thickness, which indicate whether tangential diffusion effects become important. By comparing relevant scales, a regime diagram is developed and three different flamelet regimes are identified. In regime I, the classical flamelet equations are valid. In regime II, differential diffusion of species and temperature in flame-tangential direction becomes relevant. In regime III, additional transport along mixture fraction isosurfaces exhibits an influence on the flame structure. In the latter case it is not sufficient to condition species mass fractions and temperature on the mixture fraction alone since these quantities are not represented by a one-dimensional structure.The asymptotic scaling is verified against fully resolved numerical data of a laminar non-premixed methane–air flame and a turbulent lifted hydrogen jet flame. Budgets of different flamelet solutions of the laminar flame reveal that tangential diffusion effects are dominant over the classical flamelet terms near the flame centerline, while in regions away from it, standard flamelet terms are prevailing. For the turbulent flame, the results show that tangential diffusion effects are more localized and can exceed flame-normal transport, although, unsteadiness is more likely the key factor of the configuration.While the classical flamelet model is applicable for certain flames, this study shows that tangential diffusion effects may require consideration for general flame configurations.