Modeling multiple reactive scalar mixing with the generalized IEM model

Abstract

An outstanding feature of the amplitude mapping closure is its ability to relax an arbitrary initial probability density function (PDF) to a Gaussian PDF asymptotically. Due to the difficulties in computing either the analytical or numerical solution, the mapping closure has never been applied to multiple scalars with finite reaction rates. In this work, the generalized IEM (GIEM) model is combined with the mapping closure to model the molecular mixing terms in the PDF balance equation. The GIEM model assumes a linear relationship between the rates of change of the reactive scalars and an inert scalar (shadow scalar) during the mixing step. By applying the mapping closure for binary mixing to the shadow scalar, the GIEM model yields excellent agreement for both one- and two-step reactions with DNS data, the conditional moment closure (CMC) and reaction–diffusion in a random lamellar system for a wide range of initial volume ratios and reaction rates.