Temporal structure of gas temperature fluctuations and ignition of fine particles

Abstract

The paper studies ignition of fine particles, i.e., irreversible growth of particle temperature from an exothermal heterogeneous reaction, with the rate approximated with the Arrhenius law. The particles are suspended in gas with fluctuating temperature, and heat transfer from the particle surface occurs according to the Newtonian law. The equations take into account the temporal structure of gas temperature fluctuations. Modern methods of functional analysis were applied for deriving a closed equation for the probability density function for the particle temperature distribution. The gas temperature fluctuations lessen the threshold for the particle ignition in the hot gas as compared with the deterministic variant. The equations for probability density function produce a closed system of conjugate equations for the average temperature and dispersion of particle temperature fluctuations. The results of simulation illustrate the phenomenon of self-speeding drift of particle temperature towards the temperature of ignition startup.