Calculations of steady state droplet vaporization at high ambient pressures

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A mathematical model of a spherically symmetric quiescent droplet undergoing quasi-steady vaporization in the region of its thermodynamic critical point was investigated. By steady state it is implied that all the energy arriving at the droplet surface is carried away entirely by the mass transfer. Calculated steady state temperatures and rates of vaporization of a liquid carbon dioxide droplet vaporizing in a nitrogen atmosphere are reported for ambient temperatures of 500–1600°K and pressures of 70–120 atm. The calculations include the effects of non-ideal mixtures, solubility of nitrogen in the carbon dioxide liquid, variation of the properties through the boundary layer, the effect of total pressure on vapor pressure, and the non-ideality of the enthalpy of vaporization. All of these effects were found to be important. The theory indicates that at sufficiently high pressures, steady state conditions cannot be attained. This implies that the droplet vaporizes unsteadily from its injection conditions until complete vaporization takes place. At a fixed pressure, the thermal boundary layer increases with increasing ambient temperature and at a fixed droplet temperature decreases with increasing total pressure. The steady state mass vaporization rate increases with increased pressure and/or increased ambient temperature. The droplet temperature increases slowly with ambient temperature, the rate of increase being slowest in the region near the critical pressure.