Simulation of thermal explosion on the base of solution of the equation for the probability density function of particle temperature fluctuations

Abstract

The influence of temperature fluctuations of gas on the thermal explosion of particles with internal exothermic reactions is considered. The dependence of the rate of a chemical reaction on the concentration of a gas reagent is taken into account. Based on a rigorous system of heat and mass transfer equations, equations for the average temperature and concentration of the reagent inside the particle are obtained. A study of the dynamics of changes in the concentration of reagents and temperature inside the particle in a random field of temperature is carried out on the basis of the probability density function. Based on the solution of the systems of stochastic ordinary differential equations, a method of direct numerical simulation of random temperatures and reagent concentration in a particle is developed. A method for solving the equation for the probability density function is created. The results of comparing the empirical probability density function obtained by direct numerical simulation and the results of solving the equation for the probability density function are presented.