A mixing timescale model for differential mixing in transported probability density function simulations of turbulent non-premixed flames

Abstract

The modeling of scalar mixing timescale remains a primary challenge in the transported probability density function (TPDF) method. The variation of scalar mixing timescale among species, i.e., differential mixing, results from the difference in molecular diffusivity and reaction-induced scalar gradient. Nevertheless, the vast majority of TPDF studies on turbulent non-premixed flames simply apply a single mixing timescale determined by the mixture fraction. In this work, a reaction-induced differential mixing timescale (RIDM) model for the mixing timescale of individual species in turbulent non-premixed flames is proposed. The key idea of the RIDM model is to approximate the relative magnitude of the species dissipation rates by using their values in laminar flamelets. A direct numerical simulation dataset of a temporally evolving non-premixed ethylene flame is employed to thoroughly evaluate the model performance via a priori and a posteriori tests. Results show that specifying a single mixing timescale for all species results in a poor prediction of the species dissipation rate and thus the failure to predict the overall combustion process. By accounting for the difference in molecular diffusivity, a slightly better prediction can be obtained, but the improvement is very limited, illustrating that simply modeling the difference due to molecular diffusivities for differential mixing is not sufficient. In comparison, the RIDM model exhibits superior performance in both a priori and a posteriori tests. Moreover, all the components of the RIDM model are readily available in the TPDF method, making the RIDM model a promising candidate employed in practice.