The time evolution of the size distribution of droplets effects on the thermal explosion of polydisperse fuel spray

In this paper we investigate the problem of thermal explosion in a two-phase polydisperse combustible mixture (oxygen and fuel concentrations are takes into account). The current work presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a probability density function (PDF). The evolution of the size distribution of droplets due to the evaporation process is described by the kinetic equation for the PDF. An explicit expression of the critical condition for thermal explosion limit is derived analytically and represents a generalization of the critical parameter of the classical Semenov theory.