A model for high-pressure vaporization of droplets of complex liquid mixtures using continuous thermodynamics Guang-Sheng Zhu 1 , Rolf D. Reitz * Engine Research Center, University of Wisconsin-Madison, 1011 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706, USA Received 5 May 2000; received in revised form 9 May 2001 Abstract This paper presents a comprehensive model for the transient high-pressure vaporization process of droplets of complex liquid mixtures with large number of components in which the mixture composition, the mixture properties, and the vapor±liquid equilibrium VLE) are described by using the theory of continuous thermodynamics. Transport equations, which are general for the moments and independent of the distribution functions, are derived for the semi- continuous systems of both gas and liquid phases. A general treatment of the VLE is conducted which can be applied with any cubic equation of state EOS). Relations for the properties of the continuous species are formulated. The model was further applied to calculate the sub- and super-critical vaporization processes of droplets of a representative petroleum fuel mixture ± diesel fuel. The results show that the liquid mixture droplet exhibits an intrinsic transient vaporization behavior regardless of whether the pressure is sub- or super-critical. The regression rate of the liquid mixture droplet is reduced signi®cantly during the late vaporization period. The comparison with the results of a single- component substitute fuel case emphasizes the importance of considering the multi-component nature of practical mixture fuel and the critical vaporization eects in practical applications. This paper provides a practical means for more realistically describing the high-pressure vaporization processes of practical fuels. Ó 2001 Elsevier Science Ltd. All rights reserved. 1. Introduction Droplet vaporization has been the focus of numerous studies for decades due to both its theoretical and practical signi®cance. In most engineering applications the vaporization process takes place in high-pressure environments. The liquids employed, such as petroleum fuels in internal combustion engines, are a complex mixture which is typically composed of hundreds of components. This complex mixture exerts a signi®cant eect on the vaporization process which, as shown by Sirignano and Law [1], cannot be readily described by a single-component fuel substitute. Several investigations have been conducted on droplet high-pressure vaporization, as reviewed by Givler and Abraham [2]. More recent studies include the works of Stengele et al. [3], Curtis et al. [4], Zhu and Aggarwal [5,6], and Abraham and Givler [7]. Most of this work has concentrated on the vaporization of single-component liquid droplets. Very little work ap- pears in the literature on liquid mixtures with more than one component, and typical studies include the calcu- lations of Lazar and Faeth [8] using quasi-steady mod- els, and those of Stengele et al. [3] and Hsieh et al. [9] using unsteady models. In these studies the liquid mix- ture was represented by just two components with dis- tinctly dierent boiling temperatures. The methods are developed for treating a small number of discrete com- ponents. However, it is very dicult or practically im- possible to apply these methods to practical fuels based on the fact that either the number of components is too large to be numerically accounted for or there is no way to isolate and identify the dierent chemical species. International Journal of Heat and Mass Transfer 45 2002) 495±507 www.elsevier.com/locate/ijhmt * Corresponding author. Tel.: +1-608-262-0145; fax: +1-608- 262-6707. E-mail addresses: zhugs@erc.wisc.edu G.-S. Zhu), reitz@engr.wisc.edu R.D. Reitz). 1 Tel.: +1-608-265-6432; fax: +1-608-262-6707. 0017-9310/02/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 7 - 9 3 1 0  0 1 ) 0 0 1 7 3 - 9