Analysis of the combined modelling of sub-grid transport and filtered flame propagation for premixed turbulent combustion

Flame surface density (FSD) based reaction rate closure is an important methodology of turbulent premixed flame modelling in the context of Large Eddy Simulations (LES). The transport equation for the Favre-filtered reaction progress variable needs closure of the filtered reaction diffusion imbalance (FRDI) term (i.e. filtered value of combined reaction rate and molecular diffusion rate) and the sub-grid scalar flux (SGSF). A-priori analysis of the FRDI and SGSF terms has in the past revealed advantages and disadvantages of the specific modelling attempts. However, it is important to understand the interaction of the FRDI and SGSF closures for a successful implementation of the FSD based closure. Furthermore, it is not known a-priori if the combination of the best SGSF model with the best FRDI model results in the most suitable overall modelling strategy. In order to address this question, a variety of SGSF models is analysed in this work together with one well established and one recent FRDI closure based on a-priori analysis. It is found that the success of the combined FRDI and SGSF closures depends on subtle details like the co-variances of the FRDI and SGSF terms. It is demonstrated that the gradient hypothesis model is not very successful in representing the SGSF term. However the gradient hypothesis provides satisfactory performance in combination of a recently proposed FRDI closure, whereas unsatisfactory results are obtained when used in combination with another existing closure, which was shown to predict the FRDI term satisfactorily in several previous analyses.