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

A semiempirical closure, which is an extension of the closure of the velocity probability distribution, for an equation for the probability distribution given in (2-7) of the velocity and concentration of an inert impurity in a subsonic turbulent combustion of previously unmixed gases is proposed. An equation for the density of the combined velocity and concentration probability distribution during diffusion combustion is obtained. A numerical solution of the equation for the probability density in self-similar incompressible jet fluid flows is derived. Probability distribution in homogeneous turbulence and in the domain of fundamental fluctuation generation and dissipation is studied. Finally, computation of a turbulent hydrogen diffusion flare in a quasi-self-similar approximation is undertaken. On the basis of the computations performed, it is deduced that the influence of variability of the density is insignificant within the framework of the approach developed.