Turbulent diffusion of chemically reacting flows: theory and numerical simulations

TL;DR

This paper extends the theory of turbulent diffusion for chemically reacting flows to higher Reynolds numbers and validates it through detailed DNS simulations, revealing how reactions influence turbulent mixing.

Contribution

It generalizes the turbulent diffusion theory to finite Reynolds numbers and confirms predictions with direct numerical simulations of reaction waves.

Findings

Good agreement between DNS results and theoretical predictions.

Reactions significantly affect turbulent diffusion coefficients.

The dependence on Reynolds and Damköhler numbers is characterized.

Abstract

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously (Phys. Rev. E {\bf 90}, 053001, 2014) is generalized for large yet finite Reynolds numbers, and the dependence of turbulent diffusion coefficient versus two parameters, the Reynolds number and Damk\"ohler number (which characterizes a ratio of turbulent and reaction time scales) is obtained. Three-dimensional direct numerical simulations (DNS) of a finite thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in a good agreement with the developed theory.