A model for puffing/microexplosions in water/fuel emulsion droplets

A new analytical solution to the one-dimensional transient heat conduction equation in a composite spherically symmetric water-fuel emulsion droplet, suspended in a hot gas, is obtained. The Robin boundary condition at the surface of a droplet and conditions at the fuel-water interface are used. A water sub-droplet is assumed to be located at the centre of a fuel droplet, the radius of which was fixed at each time step; it could change at the next time step. The Abramzon and Sirignano model is applied for the approximation of the droplet evaporation process. This solution and the evaporation model are incorporated into a numerical code in which droplet heating/evaporation and the variable thermophysical properties are accounted for. The time instant at which the temperature at the fuel-water interface became equal to the boiling temperature of water is identified with the initiation of puffing, giving rise to microexplosion. This allowed us to compute the minimal microexplosion delay time. The new solution is applied to a typical case of puffing/microexplosion of water/diesel emulsion droplets in high temperature gas. It is shown that the new model allows us to understand better the underlying physics of the processes leading to puffing/microexplosion. The experimental observations of the microexplosion delay time for various initial droplet sizes are shown to be compatible with the predicted values of this time. It is shown that puffing/microexplosions are expected well before the droplet surface temperature reaches the boiling temperature of n-dodecane. The numerical code can be potentially implemented into Computational Fluid Dynamics codes, which can be applied to the modelling of other fuel and water/fuel blends.