Assessment of the performances of sub-grid scalar flux models for premixed flames with different global Lewis numbers: A Direct Numerical Simulation analysis

The statistical behaviours of sub-grid flux of reaction progress variable has been assessed for premixed turbulent flames with global Lewis number Le (=thermal diffusivity/mass diffusivity) ranging from 0.34 to 1.2 using a Direct Numerical Simulation (DNS) database of freely propagating statistically planar flames. It is known that the sub-grid scalar flux shows counter-gradient transport when the velocity jump across the flame due to heat release overcomes the effects of turbulent velocity fluctuation. The results show that the sub-grid scalar flux components exhibit counter-gradient transport for all cases considered here. The extent of counter-gradient transport increases with increasing filter width Δ and decreasing value of Le. This is due to the fact that flames with Le ≪ 1 (e.g. Le = 0.34) exhibit thermo-diffusive instabilities, which in turn increases the extent of counter-gradient transport. The effects of heat release and flame normal acceleration weaken with increasing Le. Several established algebraic models have been assessed in comparison to the sub-grid scalar flux components extracted from explicitly filtered DNS data in terms of their correlation coefficients at the vector level and their mean variation conditional on the Favre-filtered progress variable. The gradient transport closure does neither capture the quantitative nor the qualitative behaviour of the different sub-grid scalar flux components for all filter widths in all cases considered here. Models which account for local flame normal acceleration perform better, especially when the flame remains completely unresolved. In particular those models that account for the alignment of local resolved velocity and scalar gradients by using a tensor diffusivity, perform relatively better than the other alternative models irrespective of Le.