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ISSN Print: 1064-2285
ISSN Online: 2162-6561

# Heat Transfer Research

DOI: 10.1615/HeatTransRes.v39.i1.20
pages 51-64

## Numerical Modeling of Droplet Transient Heating and Evaporation

Sergei S. Sazhin
Advanced Engineering Centre, School of Computing, Engineering and Mathematics, University of Brighton, Brighton, BN2 4GJ, UK
Walid A. Abdelghaffar
Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt; School of Engineering, Faculty of Science and Engineering, University of Brighron, Cockroft Building, BN 2 4GJ, UK
P. A. Krutitskii
Faculty of Physics, Moscow State University, Vorobyovy Gory, Moscow, 119899, Russia
Elena M. Sazhina
School of Engineering, Faculty of Science and Engineering, University of Brighton, Cockcroft, Building, Brighton BN2 4GJ, United Kingdom
Morgan R. Heikal
Advanced Engineering Centre, School of Computing, Engineering and Mathematics, University of Brighton, Brighton, BN2 4GJ, UK

### ABSTRACT

Several approaches to numerical modeling of liquid droplet heating and evaporation by convection and radiation from the surrounding hot gas are discussed. The finite thermal conductivity of liquid, recirculation in droplets, and time dependence of gas temperature and the convection heat transfer coefficient are taken into account. For the constant and almost constant convection heat transfer coefficient the new analytical solutions of the heat conduction equation inside droplets are incorporated into the numerical code. For the arbitrary convection heat transfer coefficient the numerical solution of the latter equation is replaced by the numerical solution of the Volterra integral equation of the second kind. Direct comparison between these approaches shows that the solution based on the assumption of constant convective heat transfer coefficient is the most computer efficient for implementation into numerical codes. The results of the application of this approach to the numerical modeling of fuel droplet heating and evaporation in conditions relevant to diesel engines are briefly discussed. This approach is more effective that the approach based on the numerical solution of the discretized heat conduction equation inside the droplet, and more accurate that the solution based on the parabolic temperature profile model. The relatively small contribution of thermal radiation to droplet heating allows us to take into account using a simplified model, which does not consider the variation of radiation absorption inside droplets.