Scalar Dissipation Rate Transport in the Context of Large Eddy Simulations for Turbulent Premixed Flames with Non-Unity Lewis Number

Abstract

The effects of global Lewis number Le on the statistical behaviour of the unclosed terms in the transport equation of the Favre-filtered scalar dissipation rate (SDR) N c have been analysed using a Direct Numerical Simulation (DNS) database of freely propagating statistically planer turbulent premixed flames with Le ranging from 0.34 to 1.2. The DNS data has been explicitly filtered to analyse the statistical behaviour of the unclosed terms in the SDR transport equation arising from turbulent transport T 1, density variation due to heat release T 2, scalar-turbulence interaction T 3, reaction rate gradient T 4, molecular dissipation (−D 2) and diffusivity gradients f(D) in the context of Large Eddy Simulations (LES). It Le has significant effects on the magnitudes of T 1, T 2, T 3, T 4, (−D 2) and f(D). Moreover, both qualitative and quantitative behaviours of the unclosed terms T 1, T 2, T 3, T 4, (−D 2) and f(D) are found to be significantly affected by the LES filter width Δ, which have been explained based on a detailed scaling analysis. Both scaling analysis and DNS data suggest that T 2, T 3, T 4, (−D 2) and f(D) remain leading order contributors to the SDR $\tilde {{N}}_{c} $ transport for LES. The scaling estimates of leading order contributors to the SDR $\tilde {{N}}_{c} $ transport has been utilised to discuss the possibility of extending an existing SDR model for Reynolds Averaged Navier Stokes (RANS) simulation for SDR $\tilde {{N}}_{c} $ closure in the context of LES of turbulent premixed combustion.