Closures for Multi-Component Reacting Flows based on Dispersion Analysis

TL;DR

This paper develops algebraic closure models for multi-component reacting flows, extending dispersion analysis to nonlinear reactions, and demonstrates improved predictive accuracy through numerical simulations.

Contribution

It introduces a novel dispersion-based closure model for nonlinear reacting flows that explicitly incorporates reaction kinetics into eddy diffusivity calculations.

Findings

Model improves prediction of mean quantities in turbulent reacting flows.

Derived eddy diffusivity matrix captures reaction kinetics effects.

Model reduces to classical gradient diffusion models in limiting cases.

Abstract

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters (Turbulent Combustion, 2000) and based on work by Corrsin (JFM, vol. 11, p.407-416) beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly-nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two- and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of non-reactive species and linear reactions, respectively.