International Journal of Thermal Sciences 46 (2007) 779–789 www.elsevier.com/locate/ijts A numerical study of the effect of turbulence on mass transfer from a single fuel droplet evaporating in a hot convective flow M.M. Abou Al-Sood, M. Birouk ∗ Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, R3T 5V6 Manitoba, Canada Received 13 July 2006; received in revised form 13 October 2006; accepted 16 October 2006 Available online 29 November 2006 Abstract A three-dimensional numerical model is developed to investigate the effect of turbulence on mass transfer from a single droplet exposed to a freestream of air. The freestream temperature, turbulence intensity and Reynolds number are varied to provide a wide range of test conditions, whereas the ambient pressure is kept atmospheric. The turbulence terms in the conservation equations of the gas-phase are modelled by using the shear-stress transport (SST) model. A Cartesian grid based blocked-off technique is used in conjunction with the finite-volume method to solve numerically the governing equations of the gas and liquid-phases. This study showed that the vaporization Damköhler number proposed in the literature to correlate the effect of turbulence on the droplet’s vaporization rate is invalid at air temperatures higher than room temperature. Additionally, an attempt is made to correlate the effect of the freestream turbulence on the droplet’s mass transfer rate by using Sherwood number over a wide range of freestream temperatures.  2006 Elsevier Masson SAS. All rights reserved. Keywords: Numerical modeling; Freestream turbulence; Droplet; Vaporization; Heat transfer 1. Introduction The effect of the freestream turbulence intensity on sphere/ droplet mass transfer is investigated first by Maisel and Sher- wood [1] and then followed by other researchers (see, for ex- ample, Refs. [2–11]). Almost all these early studies reported an increase in sphere/droplet mass transfer due to turbulence. The exception concerns Hsu and Sage [2] who claimed that turbulence had a negligible effect especially at low Reynolds numbers. A recent review [12] revealed that these early stud- ies correlated the effect of turbulence on sphere (or droplet) mass transfer by using a dimensionless number, i.e. Sher- wood number. These correlations have the following general form [12] Sh = A ′ + B ′ Re 1/2 d Sc 1/3 (C T ) (1) where C T is a turbulent coefficient, A ′ and B ′ are constants, and their values are given in Table 1. The correlations reported in Table 1 are plotted in Fig. 1 to illustrate the change of * Corresponding author. Tel.: +1 204 474 8482; fax: +1 204 275 7507. E-mail address: biroukm@cc.umanitoba.ca (M. Birouk). (Sh − A ′ )/(Re 1/2 d Sc 1/3 ) versus C T . The latter varies between 1.00 and 2.10 for 2  Re d  1.33 × 10 6 and 0  I ∞  0.6, which are the ranges covered by the investigations reported in Table 1. As reported in Birouk and Gökalp [12] almost all recent studies investigated the effect of turbulence on the droplet evap- oration rate [13–19]. Birouk et al. [16,17] studied the effect of pure turbulence (i.e. with zero-mean velocity) on droplet vaporization rate and developed an interesting correlation be- tween the droplet turbulent vaporization rate and flow turbulent Reynolds number. Park [13] developed a two-dimensional nu- merical model to predict the effect of freestream turbulence on the evaporation of n-hexane droplet. Although Park’s nu- merical model lacked experimental validation, Park [13] con- cluded that the freestream turbulence enhances the evaporation rate particularly at elevated Reynolds number. In an experi- mental investigation, Gökalp et al. [14] proposed a vaporiza- tion Damköhler number to explain the influence of turbulence on droplet mass transfer rate and concluded that the effect of turbulence on the droplet normalized vaporization rate is more pronounced at lower values of this number. Hiromitsu and Kawaguchi [15] measured the evaporation rates of sev- 1290-0729/$ – see front matter  2006 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2006.10.007