Determination of three-dimensional quantities related to scalar dissipation rate and its transport from two-dimensional measurements: Direct Numerical Simulation based validation

Abstract

Three-dimensional compressible Direct Numerical Simulation (DNS) data of freely propagating statistically planar and statistically stationary slot-jet turbulent premixed flames has been used to assess the accuracy of the isotropy-derived correction factors, which relate the two-dimensional projections of the different terms of the Favre-averaged scalar dissipation rate transport equation with their corresponding actual three-dimensional counterparts. The accuracy of these correction factors is assessed using both simplified and detailed chemistry-based DNS data, for a range of values of Karlovitz number Ka, heat release parameter τ, and turbulent Reynolds number Ret. It is shown that the isotropic distribution of the probability density function (pdf) of the angle, ϕ, between the normal vectors of the measurement plane and of the flame surface provides a simple algebraic relation between the scalar dissipation rates evaluated in two and three dimensions (i.e. N∼c and N∼c2D), independent of the considered values of Ka, τ and Ret. The isotropic relations between two-dimensional and three-dimensional counterparts of the curvature and propagation terms in the transport equation of N∼c are also found to work well for all the values of Ka, τ and Ret considered here. However, the relation between the value obtained from two-dimensional projection and the true three-dimensional value for the strain rate term in the N∼c transport equation works well only for large values of Ret and the reasons for this behaviour 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 strain rate term of the dissipation rate transport equation depends on the regime of the prevailing combustion process.