Mathematical modeling of velocity and number density profiles of particles across the flame propagation through a micro-iron dust cloud

In this study, an attempt has been made to analytically investigate the concentration and velocity profiles of particles across flame propagation through a micro-iron dust cloud. In the first step, Lagrangian particle equation of motion during upward flame propagation in a vertical duct is employed and then forces acting upon the particle, such as thermophoretic force (resulted from the temperature gradient), gravitation and buoyancy are introduced; and consequently, the velocity profile as a function of the distance from the leading edge of the combustion zone is extracted. In the resumption, a control volume above the leading edge of the combustion zone is considered and the change in the particle number density in this control volume is obtained via the balance of particle mass fluxes passing through it. This study explains that the particle concentration at the leading edge of the combustion zone is more than the particle agglomeration in a distance far from the flame front. This increase in the particle aggregation above the combustion zone has a remarkable effect on the lower flammability limits of combustible particle cloud. It is worth noticing that the velocity and particle concentration profiles show a reasonable compatibility with the experimental data.