Several new approaches to the modelling of liquid droplet heating and evaporation by convection\ud and radiation from the surrounding hot gas are reviewed. The finite thermal conductivity of the\ud liquid, recirculation within droplets, time dependence of gas temperature and the convection heat\ud transfer coefficient are taken into account. The relatively small contribution of thermal radiation to\ud droplet heating allows us to describe it by a simplified model, which does not consider the variation\ud of radiation absorption inside the droplets. In the case of stationary droplets a coupled solution of\ud the heat conduction equation for gas and liquid phases is obtained. A transient modification of\ud Newton’s law is introduced via a correction to either the gas temperature or convection heat transfer\ud coefficient. The solution is analysed using values of parameters relevant to liquid fuel droplet\ud heating in a diesel engine. Since gas diffusivity in this case is more than an order of magnitude\ud larger than liquid diffusivity, for practical applications in computational fluid dynamics (CFD)\ud codes, this model can be simplified by assuming that droplet surface temperature is fixed.\ud Moreover, if the initial stage of droplet heating (a few μs) can be ignored then the steady-state\ud solution for the gas phase can be applied for the analysis of droplet heating. This solution is\ud described in terms of the steady-state convection heat transfer coefficient. All transient effects in\ud this case are accounted for by liquid phase models. A decomposition technique for the solution of\ud the system of ODEs, based on the geometrical version of the integral manifold method, is described.\ud A comparative analysis of hydrodynamic and kinetic approaches to the problem of diesel fuel\ud droplet evaporation is described. The kinetic approaches are based on a simplified analysis of the\ud Boltzmann equation and its direct numerical solution. Kinetic models predict longer evaporation\ud times and higher droplet temperature compared with the hydrodynamic model. It is recommended\ud that kinetic effects are taken into account when modelling the evaporation process of diesel fuel\ud droplets in realistic internal combustion engines. The preliminary results predicted by deterministic\ud and stochastic models of droplet break-up, both implemented into the KIVA-2 code, are compared\ud with high-speed video images of diesel sprays
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