The Scalar Gradient Alignment Statistics of Flame Kernels and its Modelling Implications for Turbulent Premixed Combustion

The effects of mean flame curvature on reaction progress variable gradient, $nabla c$ , alignment with local turbulent strain rate are studied based on three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame kernels with different initial radii under decaying turbulence. A statistically planar flame is also considered in order to compare the results obtained from the kernels with a flame of zero mean curvature. It is found that the dilatation rate effects diminish with decreasing kernel radius due to defocusing of heat in the positively curved regions. This gives rise to a decrease in the extent of reaction progress variable gradient alignment with most extensive principal strain rate with decreasing kernel radius. The modelling implications of the statistics of the alignment of $nabla c$ with local strain rate have been studied in terms of scalar dissipation rate transport. A new modelling methodology for the contribution of the scalar-turbulence interaction term in the transport equation for the mean scalar dissipation is suggested addressing the reduced effects of dilatation rate for flame kernels and the diminished value of turbulent straining at the small length scales at which turbulence interacts with small flame kernels. The performance of the new models is found to be satisfactory while comparing to DNS results. The existing models for the dilatation contribution and the combined chemical reaction and molecular dissipation contributions to the transport of mean scalar dissipation, which were originally proposed for statistically planar flames, are found to satisfactorily predict the corresponding quantities for turbulent flame kernels.