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Abstract
The strain rate contribution in the generalized flame surface density (FSD) transport equation remains a leading order unclosed source term, which plays a pivotal role in the modeling of
transport for all filter widths
in the context of large eddy simulations (LES). To date, most FSD-based closures have been proposed for flames without differential diffusion effects of heat and mass, characterized by a global Lewis number equal to unity (i.e.,
). The effects of differential diffusion arising due to non-unity Lewis number on the FSD transport have rarely been analyzed in existing literature. In the present analysis, the statistical behaviors of the strain rate term of the FSD transport equation have been analyzed using a DNS database of freely propagating statistically planar turbulent premixed flames with a global Lewis number ranging from 0.34 to 1.2 (i.e.,
= 0.34–1.2). The FSD strain rate term has been split into components originating from the gradients of Favre-filtered velocity components (i.e.,
), strain rate contribution due to chemical heat release (i.e.,
) and sub-grid processes (i.e.,
). The contributions of
and
assume positive values throughout the flame brush for all values of
. The performances of the existing models for
and
have been assessed for flames with different values of global Lewis number
. The contribution of
remains positive throughout the flame brush for the
= 0.6, 0.8, 1.0, and 1.2 flames but the variation of
towards the burned gas side of the flame brush for the
flame remains qualitatively different in comparison to the other cases considered here. The effects of
on the local alignment of reaction progress variable gradient with principal strain rates are responsible for the observed influences of Lewis number on the sub-grid strain rate term
. The existing models have been found to be inadequate for the purpose of capturing the qualitative behaviors of the sub-grid strain rate term
for
flames. Here a new model has been proposed based on a-priori analysis of explicitly filtered DNS data, which has been demonstrated to capture both the qualitative and quantitative behaviors of
for all values of
for flames with
ranging from 0.34 to 1.2.