Model equation for the probability distributions of the velocity and concentration during turbulent mixing and diffusion combustion of gases

Abstract

This article derives an equation for the combined probability distribution of the velocity and concentration of an inert (e.g. not participating in reactions) impurity in order to solve the problem of the subsonic turbulent combustion of previously unmixed gases with combustion limited by the process of fuel and oxidizer mixing. Topics considered include fundamental equations, closing relationships, the selection of empirical constants, probability distribution in homogeneous turbulence and in the domain of fundamental fluctuation generation and dissipation, the numerical solution of the equation for the probability density in self-similar incompressible jet fluid flows, and the computation of a turbulent hydrogen diffusion flare in a quasi-self-similar approximation. The exact equation for the mentioned probability distribution is given.