Scalar dissipation rate modelling for Large Eddy Simulation of turbulent premixed flames

Abstract

The statistical behaviours of scalar dissipation rate (SDR) in the context Large Eddy Simulations (LES) of turbulent premixed combustion have been analysed using a simplified chemistry based Direct Numerical Simulations (DNS) data of a turbulent V-flame. The filter size dependence of the SDR is analysed in detail and it has been demonstrated that the filtered reaction rate can be satisfactorily closed using the Favre filtered SDR provided the filter width, Δ, remains greater than the thermal flame thickness, δth. Due to the close relation between the SDR and generalised Flame Surface Density (FSD), the dependence of the FSD on filter size has also been addressed. It has been found that a fractal dimension based power-law model satisfactorily captures the global and local behaviours of the generalised FSD in the context of LES. The fractal dimension and the inner cut-off scale for flame surface based on the volume-averaged value of the FSD are found to be in good agreement with previous analytical, experimental and DNS studies. The ratio of the volume-integrated filtered value of density-weighted SDR to its resolved component exhibits a power-law in terms of Δ with an inner cut-off scale scaling with δth. A power-law based model with a global exponent and inner cut-off scale is found to be insufficient to capture the local variations of SDR possibly due to its multi-fractal nature. An algebraic model for SDR, which was originally proposed for Reynolds Averaged Navier Stokes simulations, has been extended here for LES, which is found to satisfactorily capture both the global and local behaviours of SDR.