### Abstract

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

Original language | English |
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Title of host publication | 13th International Heat Transfer Conference |

Publication status | Published - 13 Aug 2006 |

Event | 13th International Heat Transfer Conference - Sydney, Australia Duration: 13 Aug 2006 → … |

### Conference

Conference | 13th International Heat Transfer Conference |
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Period | 13/08/06 → … |

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## Cite this

Sazhin, S., Martynov, S., Shishkova, I., Crua, C., Karimi, K., Gorokhovski, M., Sazhina, E., & Heikal, M. (2006). Modelling of droplet heating, evaporation and break-up: Recent developments. In

*13th International Heat Transfer Conference*http://www.dl.begellhouse.com/journals/IHTC13,3bec42fb4bc82e89,5437ab8628f501fa.html