In this section, the previously described four models (ITC, AS, FTC, ETC) were first evaluated against widely used experimental data of four different fluids namely water (Ranz
& Marshall, 1952b), hexane (Downingm, 1966), heptane (Nomura et al., 1996), and decane (Wong & Lin, 1992) to compare the transient increase in droplet temperature and decrease in droplet size. Also these models were used to predict vaporization times of typical FCC feed stock i.e. vacuum gas oil for different droplet sizes. In the absence of any published experi- mental data on vaporization time of FCC feed droplets, present model predictions were com- pared with available modelling data (Buchanan, 1994). All the modelling calculations were performed at constant ambient gas temperature (TG).
Chapter 3 58 Figure 3.2 Validation of the four homogeneous model predictions with the vaporization data
of water (Ranz & Marshall, 1952b). Conditions are: Td0 = 282 K. TG = 298 K. TB = 373.15 K. dd0 = 1.1 mm. Red0 = 0 (a). Vaporization data of hexane (Downingm, 1966). Conditions are: Td0 = 281 K. TG = 437 K. TB = 344.6 K. dd0 = 1.76 mm. Red0 = 110 (b). Vaporization data of heptane (Nomura et al., 1996). Conditions are: Td0 = 298 K. TB = 371.42 K. TG = 741 K. dd0 = 0.80 mm. Red0 = 0 (c). Vaporisation data of decane (Wong & Lin, 1992). Conditions
are: Td0 = 315 K. TG = 1000 K. TB = 447.1 K. dd0 = 2 mm. Red0 = 17 (d).
A summary of the model validation results presented in Figure 3.2 reveals that classi- cal d2 law (linear decrease of the squared diameter or surface area of droplet with time) is on- ly valid at low ambient temperature. This trend could be seen in Figure 3.2a where all model predictions for water droplet vaporization rate at 298 K collapse on a single line. At higher temperature, however significant deviation from d2 law could be observed. This deviating
Chapter 3 59 trend could be noticed in all the cases, particularly in the early part of the vaporization as the ambient gas temperature increases. The effect is minimal for hexane (TG = 473K) and maxi- mum for decane (TG = 1000K). Among others, ITC model always predicts the smallest vapor- ization time due to no correction factor applied on the heat transfer coefficient. Since ITC model predicts maximum heat transfer, this model should be used to determine the lowest theoretical vaporization time. The FTC model on the other hand constitutes the higher bound of the vaporization time due to minimum heat transfer coefficient (smallest value of correc- tion factor G multiplied to the heat transfer coefficient). For a non-zero Reynolds number case, internal recirculation in the droplet is accounted for the ETC model. A slight difference in vaporization time (0.8 % for hexane and 2 % for decane) could be observed compared to FTC model due to internal recirculation induced enhanced thermal conductivity. The AS model, among others provides the most reasonable prediction when compared to experiments (minimum RMSE) which is primarily due to the fact that Nu number formulation using the correction factors from the film theory matches well with the experimental (Sazhin, 2006).
Figure 3.3 Comparison of transient change of decane droplet temperature predicted by homo- geneous models and experimental data of Wong and Lin (1992). Conditions are: Td0 = 315 K.
TG =1000 K. TB =447.1 K. dd0 =2 mm. Red0 =17 (a). Temporal change of volume averaged
Chapter 3 60 temperature Td versus surface temperature Tds of decane droplet predicted by FTC model.
Conditions are: Td0 =315 K. TG =1000 K. TB = 447.1 K. dd0 =2 mm. Red0 =17 (b).
Figure 3.3a compares model predictions of temporal evolution of the decane droplet temperature with experimental data (Wong & Lin, 1992). Noticeably, all models predict complete vaporization of droplet below the saturation point. The droplet temperature could be seen rising quickly during the heating up period and reaches saturation temperature at around one third of the whole droplet lifetime. Due to theoretically maximum possible heat transfer, only the ITC model predicts the droplet temperature (~ 440K) close to its saturation tempera- ture limit (447.1 K) while the other models consistently under-predict the droplet temperature during vaporization. Predicting saturation temperature during vaporization depends critically on the choice of reference temperature [Eq. (3.21) and Eq. (3.22)] at which the thermophysi- cal properties of carrier gas are determined. For the purpose of model validation in this study, Eq. (3.21) (based on wet bulb temperature) was used to compute the carrier gas properties which was observed to estimate lower temperature compared to Eq. (3.22) (based on 1/3rd rule).
All the models were observed to predict saturation temperature closely during the va- porization period if Eq. (3.22) was used (not shown). However use of Eq. (3.22) produced significant deviations from the experimentally reported droplet diameter reduction
(dd /dd0)2 data which was also noted by R. Miller et al. (1998) in their study.
Figure 3.3b presents the prediction of FTC model for same operating conditions illus- trating the difference between volume averaged droplet temperature Td and the droplet sur- face temperature Tds. The droplet surface temperature rises faster than the volume average temperature due to more heat transfer occurring at the interface however the difference van- ishes as the droplet reaches towards the complete vaporization state.