Large Eddy Simulation (LES) has potential to address unsteady phenomena in turbulent premixed flames and to capture turbulence scales and their influence on combustion. Thus, this approach is gaining interest in industry to analyse turbulent reacting flows. In LES, the dynamics of large-scale turbulent eddies down to a cut-off scale are solved, with models to mimic the influences of sub-grid scales. Since the flame front is thinner than the smallest scale resolved in a typical LES, the premixed combustion is a sub-grid scale (SGS) phenomenon and involves strong interplay among small-scale turbulence, chemical reactions and molecular diffusion. Sub-grid scale combustion models must accurately represent these processes.

When the flame front is thinner than the smallest turbulent scale, the flame is corrugated by the turbulence and can be seen as an ensemble of thin, one-dimensional laminar flames (flamelets). This allows one to decouple turbulence from chemistry, with a significant reduction in computational effort. However, potentials and limitations of flamelets are not fully explored and understood. This work contributes to this understanding. Two models are identified, one based on an algebraic expression for the reaction rate of a progress variable and the assumption of fast chemistry, the other based on a database of unstrained flamelets in which reaction rates are stored and parametrised using a progress variable and its SGS variance, and their potentials are shown for a wide range of premixed combustion conditions of practical interest. The sensitivity to a number of model parameters and boundary conditions is explored to assess the robustness of these models. This work shows that the SGS variance of progress variable plays a crucial role in the SGS reaction rate modelling and cannot be obtained using a simple algebraic closure like that commonly used for a passive scalar. The use of strained flamelets to include the flame stretching effects is not required when the variance is obtained from its transport equation and the resolved turbulence contains predominant part of the turbulent kinetic energy. Thus, it seems that SGS closure using unstrained flamelets model is robust and adequate for wide range of turbulent premixed combustion conditions.