A DNS evaluation of three MMC-like mixing models for transported PDF modelling of turbulent nonpremixed flames

Abstract

Transported probability density function (TPDF) methods are suitable for modelling turbulent reactive flows. One of the main challenges is to accurately model the molecular mixing terms. In TPDF mixing models, it is desired that the principle of localness is satisfied so that the molecular mixing is performed locally in both physical and composition spaces. The multiple mapping conditioning (MMC) mixing model can ensure mixing localness without violating other desired principles. The present study examines three MMC-like mixing models, including the original MMC (OMMC) mixing model, shadow-position mixing model (SPMM) and a conceptually simplified multiple mapping conditioning (SMMC) mixing model. Three direct numerical simulation (DNS) datasets modelling turbulent nonpremixed ethylene flames with increasing levels of extinction are used for model evaluation. The DNS datasets are also used to provide both initial conditions and inputs needed over the course of TPDF runs to remove the uncertainties caused by turbulence closure, allowing the study to focus on the molecular mixing model. The mixing model coefficients are specified analytically by reference to a canonical mean scalar gradient (MSG) flow in order to achieve specifiable dissipation rate and user-controllable localness. The results show that the MMC-like mixing models yield similar prediction of flame extinction and reignition if the coefficients are properly specified. The MMC-like mixing models can also be tuned to achieve a desired level of localness. For conditional statistics, the MMC-like mixing models can yield correct level of conditional variances. By changing localness, the MMC-like models can yield solutions resembling the interaction by exchange with the mean (IEM) or Euclidean minimum spanning tree (EMST) mixing model for extreme parameter choices. The models differ in their abilities to specify unconditional dissipation rates, at least in the flow considered, and in their ease of implementation.