The impacts of the activity coefficient on heating and evaporation of ethanol/gasoline fuel blends

doi:10.1016/j.icheatmasstransfer.2018.08.018

International Communications in Heat and Mass Transfer

Volume 98, November 2018, Pages 177-182

https://doi.org/10.1016/j.icheatmasstransfer.2018.08.018 Get rights and content

Highlights

•
Effects of the activity coefficient on blended fuel evaporation
•
Effects of ethanol and gasoline fuel blends on droplet lifetimes
•
The evolution of droplet surface temperatures and radii

Abstract

The evolutions of droplet radii and temperatures for ethanol and gasoline fuels and their blends are investigated using a modified version of the Discrete Component (DC) model, taking into account the effect of the activity coefficient (AC). The universal quasi-chemical functional–group AC (UNIFAC) model is used to predict the ACs of the blended ethanol and gasoline fuels approximated by 21 components. In contrast to previous studies, it is shown that droplet lifetimes predicted for pure gasoline are not always shorter than those predicted for ethanol/gasoline blends. They depend on the total vapour pressure of the mixture. It is shown that the original DC model predicts ethanol/gasoline fuel droplet lifetimes with errors up to 5.7% compared to those predicted using the same model but with the ACs obtained from the UNIFAC model.

Introduction

Heating and evaporation of droplets are important processes in numerous applications, including those in internal combustion engines [1,2], spray coating [3], fire suppression [4], the pharmaceutical industry [5], and agriculture [6,7]. This has stimulated intensive research to develop robust models for the description of these processes [1,[8], [9], [10]].

Our analysis is focused primarily on ethanol/gasoline fuel blend droplets, the interest in which has been mainly stimulated by the depletion of fossil fuels and environmental concerns. The heating and evaporation of these blends have been investigated numerically and experimentally [[11], [12], [13], [14]]. In these studies, however, gasoline has been approximated by isooctane or a mixture of isooctane/n-heptane, whilst the commercial gasoline fuels consist of tens of hydrocarbons [15]. The effects of fuel compositions, transient diffusion of species, temperature gradient, and recirculation inside moving droplets on their heating and evaporation have been commonly described using the Discrete Component (DC) model [9,16], and the Effective Thermal Conductivity/Effective Diffusivity (ETC/ED) model [8]. These models have been validated against experimental data [[17], [18], [19]].

The DC model was used previously for the analysis of blended fuel droplet heating and evaporation, including blends of diesel/biodiesel and ethanol/gasoline fuels [17,[20], [21], [22], [23], [24]]. In these studies, however, Raoult's law was assumed to be valid (the activity coefficient (AC) was assumed equal to one). Unlike fossil fuels, ethanol and biodiesel fuels are polar liquids. Therefore, Raoult's law may not be suitable for predicting the vapour pressures of these fuel blends [25]. To address this issue, in our analysis we took into account the contributions of non-unity ACs. In some studies (e.g. [26]), the Wilson equation was used for the predictions of ACs. The Wilson equation is a simple approach, but limited to binary components. In the general case, the universal quasi-chemical functional–group AC (UNIFAC) model is believed to be the most suitable for prediction of the multi-component ACs [11,27].

In [28], the UNIFAC model was used to predict the ACs of 20 components in gasoline FACE C and 98 components in diesel fuel. This approach, however, was based on the initial molar fractions of components and droplet surface temperatures. In the current analysis, we investigate the impact of transient ACs on the evolutions of blended ethanol/gasoline fuel droplet temperatures and radii. The transient droplet surface temperatures and diffusion of 21 components are taken into account using the UNIFAC model. The governing equations and main features of the DC model used in our analysis are summarised in [8,29], and will not be discussed in this paper. The main features of the model and the implementation of UNIFAC equations into relevant equations of the DC model are described in Section 2. The results predicted by the modified DC model, using the corrected ACs, are presented and discussed in Section 3. The main results are summarised in Section 4.

Section snippets

The model

The DC model used in our analysis is based on the analytical solutions to the heat transfer and species diffusion equations inside droplets [9]. The effects of recirculation on species diffusion and heat conduction inside droplets are taken into account, using the Effective Thermal Conductivity/Effective Diffusivity (ETC/ED) model [30]. The evaporation rate of a droplet is described by the following equation: ${\dot{m}}_{d} = - 2 π R_{d} D_{v} ρ_{total} B_{M} {Sh}_{iso},$ where D_v is the binary diffusion coefficient of vapour in gas

Results

The total vapour pressures versus molar fractions of ethanol/gasoline in the liquid phase (indicated as EMX, where X is the percentage of ethanol in the mixture) at 296 K and 350 K are presented in Fig. 1. In this figure, a comparison between the two approaches, Raoult's and UNIFAC, is shown. In Raoult's law, the AC is equal to unity, while in the UNIFAC model, the values of multi-component ACs are used.

As can be seen from this figure, the multi-component ACs have significant impact on the

Conclusion

The heating and evaporation of ethanol/gasoline fuel blend droplets are investigated using the discrete component model, based on the analytical solutions to the heat and mass transfer equations and the effective thermal conductivity/effective diffusivity model. The universal quasi-chemical functional–group AC (UNIFAC) model is used to predict the activity coefficients (ACs) of the components of blended ethanol/gasoline (21 components) fuels. It is found that the droplet lifetimes for the

Acknowledgement

This work was supported by the Institute for Future Transport and Cities, Coventry University. One of the authors (S.S. Sazhin) is grateful to EPSRC (Grant EP/M002608/1) for financial support.

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The impacts of the activity coefficient on heating and evaporation of ethanol/gasoline fuel blends

Highlights

Abstract

Introduction

Section snippets

The model

Results

Conclusion

Acknowledgement

Fuel

Appl. Therm. Eng.

Prog. Energy Combust. Sci.

Int. J. Heat Mass Transf.

Curr. Opin. Colloid Interface Sci.

Environ. Exp. Bot.

Prog. Energy Combust. Sci.

Fuel

Int. J. Heat Mass Transf.

Fuel

Int. J. Therm. Sci.

Fuel

Fuel

Fuel

Fuel

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Fuel

Fuel