A simplified model for bi-component droplet heating and evaporation S.S. Sazhin a, * , A. Elwardany a , P.A. Krutitskii b , G. Castanet c , F. Lemoine c , E.M. Sazhina a , M.R. Heikal a a Sir Harry Ricardo Laboratories, Centre for Automotive Engineering, School of Environment and Technology, Faculty of Science and Engineering, University of Brighton, Brighton BN2 4GJ, UK b Keldysh Institute for Applied Mathematics, Department 4, Miusskaya Sq. 4, Moscow 125047, Russia c LEMTA, Nancy-Université, CNRS UMR 7563, 2, Avenue de la Forêt de Haye, BP 160, 54504 Vanduvre-lès-Nancy, France article info Article history: Received 15 December 2009 Accepted 22 June 2010 Available online xxxx Keywords: Droplets Multi-component fuel Heating Evaporation Diffusion equation Acetone Ethanol abstract A simplified model for bi-component droplet heating and evaporation is developed and applied for the analysis of the observed average droplet temperatures in a monodisperse spray. The model takes into account all key processes, which take place during this heating and evaporation, including the distribu- tion of temperature and diffusion of liquid species inside the droplet and the effects of the non-unity activity coefficient (ideal and non-ideal models). The effects of recirculation in the moving droplets on heat and mass diffusion within them are taken into account using the effective thermal conductivity and the effective diffusivity models. The previously obtained analytical solution of the transient heat con- duction equation inside droplets is incorporated in the numerical code alongside the original analytical solution of the species diffusion equation inside droplets. The predicted time evolution of the average temperatures is shown to be reasonably close to the measured one, especially in the case of pure acetone and acetone-rich mixture droplets. It is shown that the temperatures predicted by the simplified model and the earlier reported vortex model are reasonably close. Also, the temperatures predicted by the ideal and non-ideal models differ by not more than several degrees. This can justify the application of the sim- plified model with the activity coefficient equal to 1 for the interpretation of the time evolution of tem- peratures measured with errors more than several degrees. Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. 1. Introduction In a number of papers a new model for heating and evaporation of monocomponent droplets, based on the analytical solution of the heat conduction equation inside droplets, has been described [1–3]. The effects described by this model were shown to be partic- ularly important for modelling fuel spray autoignition processes [4,5]. It was shown to be more CPU efficient compared with the model based on the numerical solution of the heat conduction equation inside droplets [6], and was validated against the results of available experimental measurements of droplet temperatures [7,8]. The practical application of the above-mentioned model, how- ever, is limited by the fact that most real-life fuels are multi-com- ponent. The models of multi-component droplet heating and evaporation could be subdivided into two main groups: those based on the analysis of individual components [9–15], applicable in the case when a small number of components needs to be taken into account, and those based on the probabilistic analysis of a large number of components (e.g. continuous thermodynamics ap- proach [16–18] and the Distillation Curve Model [19]). In the sec- ond family of models a number of additional simplifying assumptions were used, including the assumption that species in- side droplets mix infinitely quickly. A model containing features of both these groups of models has been suggested in [20]. The focus of this paper is on the extension of the model devel- oped in [2,3] for monocomponent droplets to the case of multi- component droplets. Only the first group of multi-component droplet heating and evaporation models is considered, which al- lows us to perform the deterministic analysis of individual species. Moreover, at this stage only the simplest case of bi-component droplets is considered, as in [12,13,15], which allows us to develop a better understanding of the underlying physics of the processes involved. The new model is much simpler than the previously sug- gested models (e.g. [15]) which makes it potentially attractive for implementation into computational fluid dynamics (CFD) codes. The predictions of the model are compared with the measured time evolution of droplet temperatures in monodisperse bi-com- ponent (ethanol/acetone) droplet streams. The basic equations and approximations of the new model are described in Section 2. The experimental set-up for measurements of droplet temperatures in monodisperse bi-component (ethanol/ acetone) droplet streams is briefly described in Section 3. In 0017-9310/$ - see front matter Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.06.044 * Corresponding author. Tel.: +44 (0)1273642677; fax: +44 (0)1273642309. E-mail address: S.Sazhin@brighton.ac.uk (S.S. Sazhin). International Journal of Heat and Mass Transfer xxx (2010) xxx–xxx Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Please cite this article in press as: S.S. Sazhin et al., A simplified model for bi-component droplet heating and evaporation, Int. J. Heat Mass Transfer (2010), doi:10.1016/j.ijheatmasstransfer.2010.06.044