Investigation of quasihomogeneous turbulent diffusion combustion using the equation for the probability density distribution function of the concentration

Abstract

In the description of turbulent diffusion combustion, the density, temperature, and completeness of combustion can be expressed in terms of the concentration of the passive admixture. These dependences are nonlinear and in a turbulent flow the concentration pulsates, and therefore some difficulties arise when these parameters are averaged. Usually, the flame front is situated at the edge of the jet, in the region where intermittence is observed and the concentration pulsations have a large amplitude. Therefore, for correct averaging it is necessary to know the probability density distribution P(z) of the concentration of the passive admixture. In calculations of turbulent flows with combustion, it is often assumed that this distribution has a universal dependence on the mean concentration and the pulsations of the concentration, which are determined from the corresponding equations. Such assumptions were used, for example, in [1–5]. Despite its relative simplicity, this approach has some shortcomings. First, the employed approximations of the probability density are not based on known experimental or theoretical data. Second, which is the most important, it is assumed that the dependence of the density on the concentration of the passive admixture does not influence the form of the probability density distribution of the concentration of the passive admixture. The aim of the present paper is to analyze the influence of the concentration dependence of the density on the form of P(z) and to establish effects of the concentration of pulsations on the characteristics of diffusion combustion in a channel.