The group combustion of a spherical cloud of monodisperse fuel droplets

Abstract

The vaporization and combustion of a spherical, uniform monodisperse cloud of fuel drops in equilibrium with a quiescent atmosphere is considered. For typical fuel sprays in which the drops are separated by five to ten drop diameters only the droplets within a thin inwardly propagating vaporization wave at the edge of the cloud will vaporize. In analogy with single drop theory the cloud radius is found to decrease acording to a “ d 2 law,” although with a modified vaporization constant for both purely vaporizing and burning clouds. The cloud interior in all cases remains in saturated, non vaporizing equilibrium at a temperature determined by ambient conditions. Burning occurs at a spherical diffusion flame front outside the cloud. The flame radius to cloud radius ratio is found to be constant and independent of the cloud radius and the droplet radius and number density within the cloud. An external ignition temperature is determined by considering the bifurcation of steady state solutions for single step, irreversible Arrhenius kinetics. At ignition the cloud interior reaches a new equilibrium which is still too cool and rich for single drop ignition. Under conditions of the present analysis a fuel cloud, if it burns at all, will do so with an external diffusion flame.