Analysis of Algebraic Closures of the Mean Scalar Dissipation Rate of the Progress Variable Applied to Stagnating Turbulent Flames

In the turbulent premixed reactive flows considered in this study, i.e. large Damkohler and Reynolds numbers, the flamelet regime of turbulent combustion applies and the scalar dissipation rate and mean reaction rate are inter related. In this situation various algebraic models for the mean chemical rate that are obtained from an equilibrium of the dominant terms of the transport equation for the scalar dissipation rate, are evaluated through their application to flames stabilized in a turbulent stagnating flow. An asymptotic analysis is first performed and results obtained through the resulting one-dimensional calculation are compared with the experimental data of Li et al. (Proc Combust Inst 25:1207-1214, 1994). Eventually, three-dimensional CFD calculations including suited algebraic closures to represent the turbulent transport terms are carried out. Results are satisfactorily compared to the experimental data of Cho et al. (Proc Combust Inst 22:739-745, 1988). As a first outcome, the analysis confirms the interest and the relevance of the corresponding algebraic closures to deal with turbulent premixed combustion in such conditions. In the search of a satisfactory representation of such premixed impinging flames, the computational results also clearly emphasize the strong intertwinment that exits between the mean reaction rate, i.e. scalar dissipation rate or micro-mixing taking place at the smallest scale of the reactive flowfield, and the Reynolds fluxes modelling, i.e. turbulent macro-mixing.