Thermal explosion of particles with internal heat generation in turbulent temperature of surrounding fluid

摘要

We consider the phenomenon of thermal explosion which is exponential rise of temperature of particle with internal heat release in the turbulent field of surrounding fluid with temperature fluctuations. The Arrhenius law approximates the rate of chemical reactions and power of heat release. Diffusion resistance inside the particle is absent. The collective influence of particles on the thermal parameters of the environment is not considered. The problem is investigated by analytical construction of probability density function (PDF) of temperature fluctuations of the particle and by direct numerical simulation. It was established that in a random environment temperature thermal explosion always happen. Results of modeling of development of thermal explosion are presented. Average delay time for thermal explosion in a random environment is calculated. The method of direct numerical simulation of stochastic differential equations for modeling the thermal explosion is developed. Results of analytical and numerical modeling in satisfactory agreement.