A priori analysis of a power-law mixing model for transported PDF model based on high Karlovitz turbulent premixed DNS flames

Abstract

Accurate modeling of mixing in large-eddy simulation (LES)/transported probability density function (PDF) modeling of turbulent combustion remains an outstanding issue. The issue is particularly salient in turbulent premixed combustion under extreme conditions such as high-Karlovitz number Ka. The present study addresses this issue by conducting an a priori analysis of a power-law scaling based mixing timescale model for the transported PDF model. A recently produced DNS dataset of a high-Ka turbulent jet flame is used for the analysis. A power-law scaling is observed for a scaling factor used to model the sub-filter scale mixing timescale in this high-Ka turbulent premixed DNS flame when the LES filter size is much greater than the characteristic thermal thickness of a laminar premixed flame. The sensitivity of the observed power-law scaling to the different viewpoints (local or global) and to the different scalars for the data analysis is examined and the dependence of the model parameters on the dimensionless numbers Ka and Re (the Reynolds number) is investigated. Different model formulations for the mixing timescale are then constructed and assessed in the DNS flame. The proposed model is found to be able to reproduce the mixing timescale informed by the high-Ka DNS flame significantly better than a previous model.