The Reaction of a Molten Sodium Spray with Air in an Enclosed Volume Part II: Theoretical Model

A mathematical model was developed to predict the burning rate and burning temperature of a single spherical sodium particle moving through air or air depleted in oxygen. The model is based on the assumption that the reaction rate is controlled by the diffusion of oxygen to a combustion zone surrounding the particle. A quasi-steady state approach and an averaging technique were used to correlate the reaction rates of individual spray particles with the theoretical burning rate of a spray and the theoretical pressure rise in an enclosing volume. The theory correctly predicted the direction and magnitude of experimentally observed variations in reaction rate with respect to oxygen content, spray velocity, and particle size. The spray particle size was found to be the most important parameter when considering the sprayed sodium-air reaction.