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Because the ultimate stages of turbulent mixing take place at the unresolved scales in either Reynolds Average Navier Stokes (RANS) or Large Eddy Simulation (LES) approaches of turbulent reactive flows, the closure of molecular dissipation rates still remains an essential problem in the field of turbulent combustion. In the present study, turbulent flames with premixed reactants are considered in the flamelet regime of turbulent premixed combustion: Damköhler and Karlovitz number's values are such that Da > 1 and Ka < 1. In this situation, the mixing rate clearly depends upon the turbulence characteristics but is also strongly influenced by the laminar flamelet structures that drive the instantaneous gradients of the reactive species. In the present work, the analysis is focused on some among the different unclosed terms that arise in the transport equation of the mean reactive scalar dissipation rate. New closures relying on the fast chemistry assumptions are proposed for these production terms and similarities and differences with existing models are discussed. Previous works devoted to the modeling of the scalar dissipation rate have recently shown that both reactive features and expansion phenomena strongly influence the behavior of some terms with respect to the passive scalar situation of reference, and the present study confirms the relevance of these findings. Finally, Direct Numerical Simulation (DNS) databases are considered to assess the validity of the proposed models. These DNS correspond to the calculations of three-dimensional statistically steady planar turbulent premixed flames obtained for three distinct values of the gas expansion factor τ =(T b − T u )/T u namely 1.5, 4 and 6.5, where subscripts u and b refer to unburned reactants and burned products A. Mura (B) · V. Robin · M. Champion LCD UPR 9028 du CNRS Flow Turbulence Combust (2009) 82:339-358 respectively. With respect to previous studies, these data allow a detailed check of the validity of the different modeling proposals when the gas expansion factor is varied.

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