An evaluation of gas-phase micro-mixing models with differential mixing timescales in transported PDF simulations of sooting flame DNS

The use of transported probability density function (TPDF) models to predict soot has the strong advantage that the effects of turbulent fluctuations on soot source terms can be rigorously accounted for. However, soot processes are closely coupled to gas-phase composition. Among the open issues for gas-phase micro-mixing is the species-dependence of mixing timescales. The objective is to carry out an evaluation on the effect of incorporating differential mixing timescales among gas-phase species in a TPDF simulation for soot prediction. A DNS having the configuration of a temporally evolving, non-premixed ethylene flame with a four-step, three-moment soot model is considered as the target for evaluation. The DNS dataset is applied to provide key inputs for TPDF simulations to limit the sources of error to micro-mixing. TPDF simulations with the interaction by exchange with the mean (IEM) and modified Curl (MC) models, which impose the same mixing timescale to all species, underpredict soot mass fraction and overpredict extinction levels regardless of the prescribed mixing frequency. By incorporating differential mixing timescales among gas-phase species, IEM-DD and MC-DD models yield notable improvement in predictions of the overall extinction and soot levels, highlighting the benefit of accounting for differential mixing timescales. A TPDF simulation with the Euclidean minimum spanning tree (EMST) model yields even better predictions, illustrating that the localness in composition space remains a critical issue. The indicated species mixing frequencies by the EMST model are shown to follow the DNS results qualitatively, illustrating that the micro-mixing process based on the Euclidean distance in composition space reproduces to a certain extent the differential mixing timescales due to reaction. Finally, it is shown that incorporating differential mixing timescales of soot moments is expected to have limited value as the mixing timescales of soot moments are sufficiently large to safely neglect soot mixing.