Physical and numerical realizability requirements for flame surface density approaches to large-eddy and Reynolds averaged simulation of premixed turbulent combustion

In the flamelet regime of turbulent premixed combustion, flame surface density (FSD) models for Reynolds averaged and large-eddy simulation (LES) should satisfy the realizability requirement Sigma greater than or equal to \del(c) over bar \ . Some commonly employed FSD models are analysed from this perspective and it is found that several models may not satisfy the criteria under all flow conditions. Suggestions are made for adjustments to the models and for the choice of model parameters such that realizability is guaranteed in the one-dimensional constant density case. The suggestions are supported with physical arguments based on the links between the progress variable and the FSD. Another and rather different realizability issue concerns the local simulated flame thickness in LES. This is important both physically and numerically. Physically it is expected that the local simulated flame thickness should be of approximately the same order as the filter size, Delta. In most approaches to LES of premixed combustion, the shape of the turbulent flame profile must be resolved on the computational grid, i.e. there is a numerical requirement for a minimum number of computational grid points within the simulated flame thickness. Some recently suggested approaches for LES based on the FSD concept and the filtered G-equation are analysed from the perspective of the simulated flame thickness. It is found that current approaches may not produce a flame thickness of order Delta under all flow conditions. Suggestions are made for models that can overcome this difficulty. One-dimensional simulations are presented that show the inadequacies of current approaches and the potential of the modified methods.