Modelling of Lewis Number dependence of Scalar dissipation rate transport for Large Eddy Simulations of turbulent premixed combustion

The influences of differential diffusion of heat and mass on the Favre-filtered scalar dissipation rate (SDR) transport have been analysed and modelled using a-priori analysis of Direct Numerical Simulations (DNS) data of freely propagating statistically planar turbulent premixed flames with different values of global Lewis number Le. The DNS data has been explicitly filtered using a Gaussian filter to obtain the unclosed terms of the Favre-filtered SDR transport equation, arising from turbulent transport (T1), density variation due to heat release (T2), strain rate contribution due to the alignment of scalar and velocity gradients (T3), correlation between the gradients of reaction rate and reaction progress variable (T4), molecular dissipation of SDR (-D2) and diffusivity gradients f(D) . The statistical behaviours of these terms and their scaling estimates reported in a recent analysis have been utilised here to propose models for these unclosed terms in the context of Large Eddy Simulations (LES) and the performances of these models have been assessed using the values obtained from explicitly filtered DNS data. These newly proposed models are found to satisfactorily predict both the qualitative and quantitative behaviours of these unclosed terms for a range of filter widths for all Le cases considered here.