Mathematical Models of the Transient Heat Flow to Fuel Droplets.

Two models for the preheat stage of conventional liquid fuel droplets and of emulsified fuel droplets in combustion gases are analyzed theoretically. These models contain the effects of transient heat conduction to the droplets. In the first model, the droplet and gas temperatures vary temporally hut only the gas temperature varies spatially; i.e., the droplet temperature is spatially uniform. Numerical examples, computed from this model, for both the droplet and gas temperatures are given. In the second model, both the droplet and gas temperatures vary spatially and temporally. Numerical examples computed from this second model for the surface and average temperature of the droplet are given. These analyses show that the temperature gradients inside droplets of oil and water are small compared to those in the combustion gases near the droplet; that temperature profiles given by both models are very similar. In particular, the predicted times at which micro-explosions are expected to occur agree within 10 percent of each other.