Comparison between a numerical model and the classic thermal explosion theories for the calculation of the minimum ignition temperature of dust clouds

Abstract

A numerical model for the calculation of the minimum ignition temperature (MIT) of dust clouds is compared with the classic Semenov and Frank-Kamenetskii thermal explosion theories. The numerical model is developed based on the MIT testing equipment: Godbert-Greenwald furnace. The Semenov theory for uniform temperature system is exploited for the MIT calculation of a single dust particle (MITP). The Frank-Kamenetskii theory for a uniform system with temperature gradient is modified for the MIT calculation of a dust cloud (MITC). At stoichiometric dust concentration with infinite dust cloud residence time, two horizontal asymptotes are discovered along with the variation trend of the numerical ignition temperature against ignition delay time. The higher asymptotic temperature is only discovered for metal dusts. This temperature is almost identical to the MITP value with the Semenov theory. On the other hand, the lower asymptotic temperature for both metal and organic dusts almost equals the calculated MITC value with the Frank-Kamenetskii theory. Thus, there is good agreement between the numerical model and the classic thermal explosion theories. This study can provide reference for the theoretical prediction of the MIT of dust clouds.