Determination of 3D flame surface density variables from 2D measurements: Validation using direct numerical simulation

Abstract

Three-dimensional compressible direct numerical simulation (DNS) data of freely propagating statistically planar turbulent premixed flames have been used to assess the accuracy of the isotropy- derived correction factors, which relate the two-dimensional projections of the different terms of the Reynolds averaged flame-surface density (FSD) transport equation with their corresponding actual three-dimensional counterparts for different values of Karlovitz number Ka, Lewis number Le, heat release parameter τ, and turbulent Reynolds number Ret. It is shown that the isotropic distribution of the surface area weighted probability density function (pdf) of the angle φ between the normal vectors on the measurement plane and on the flame surface provides a simple algebraic relation between the generalised FSDs evaluated in two and three dimensions (i.e., Σ2D and Σ3D), irrespective of the values of Ka,τ,Le, and Ret. Isotropic relations between two-dimensional and three-dimensional counterparts of the surface-averaged curvature and the FSD propagation term are also found to work well for all the values of Ka,τ,Le, and Ret considered in this study. However, the relations between the value obtained from two-dimensional projection and the actual three-dimensional value for the tangential strain rate and curvature terms in the FSD transport equation work well only for the high values of turbulent Reynolds number. The reasons behind the disagreement between the predictions of the relations derived based on isotropy arguments for both the tangential strain rate and curvature terms of the FSD transport equation are explained in detail. It is found that the threshold value of Ret above which the assumption of isotropy yields an accurate relation between two-dimensional projection and three-dimensional values for the tangential strain rate and curvature terms of the FSD transport equation depends on the values of heat release parameter, Lewis number, and the regime of the prevailing combustion process.