Mathematical Model of Soot Formation Under Toluene’s Diffusion Combustion

Abstract

An approach to mathematically model the nucleation and growth of soot particles during the diffusion combustion of hydrocarbon fuel is presented. The chain of transformations of hydrocarbon fuel is modeled using a Markov process with a finite number of states, which is described by a stiff system of Kolmogorov’s ordinary differential equations (ODEs). As a result of numerical modeling, the set of functions describing the change in concentrations of various soot fractions in a laminar diffusion flame of toluene depending on time is obtained. Based on the results of the numerical solution of the ODE system, discrete particle size distributions (relative diameters) are constructed for different times. Continuous Weibull distributions approximating discrete distributions are constructed using the least squares method. The results obtained are in qualitative agreement with the experimental data.