Statistical Behavior of a Reacting Mixture in Isotropic Turbulence

Abstract

Under the restrictions of (A) isotropy in turbulent velocity and concentration fluctuation fields, (B) negligible effect of reaction on fluid motion, and (C) negligible effect of heat of reaction on local reaction rate, equations have been deduced for some statistical functions of the concentration of reactant. For a first-order reaction the simplest equations do not differ in general character from those of pure mixing without reaction, but the nonlinear nature of second-order reactions introduces decided differences. Solutions for the decay rates of mean concentration and fluctuations have been obtained in some limiting cases and with some simplifying assumptions. The principal hypothesis introduced is that a first-order reaction has no effect on the size structure of the scalar field.