The hierarchy of low-dimensional manifolds in the context of multiple mapping conditioning mixing model

Abstract

A new model to couple the multiple mapping conditioning (MMC) mixing model with manifold based simplified chemistry is proposed. The concept is based on the fact that the system state can be locally confined to a manifold with lower dimension, which is embedded in the manifold with higher dimension. Therefore, in the framework of the MMC mixing model, particles to be mixed must be selected such that they are localized in the reference variable space with the dimension which corresponds to the minimum number of the progress variables describing the thermo-kinetic states locally. This can be achieved by comparing the physical mixing time-scale with the chemical time-scales describing the movement on the slow manifold, and the dimension of the necessary reference variables can be determined automatically. The present work uses an IEM-based MMC mixing model and Reaction-Diffusion Manifolds (REDIMs) as the simplified chemistry, but it can be extended easily to other mixing models. The proposed methodology is validated by testing the well-known non-premixed Sandia Flame D and F, and the results show good agreement with experimental results and those obtained using the detailed chemistry.