1. Introduction
The energy demand is sharply increasing along with the increases in worldwide population and global fossil fuel consumption. Currently, more than 99% of the transport sector is powered by combustion engines, which contribute to around 14% of greenhouse gas emissions (GGE) [
1]. Due to the need for reducing GGE, which contribute to global warming, and the depletion of fossil fuels, governments and industries are aiming to shift from the dependency on fossil fuels to renewable energy sources (e.g., biofuels) [
2,
3]. The mixture of biofuels (e.g., biodiesel and ethanol) with fossil fuels in standard propulsion systems can reduce GGE and lead to complete combustion [
4,
5,
6]. According to the UK Department for Transport, the British Government has increased the percentage of bio/fossil fuel blends from 4.75% (currently) to 9.75% in 2020 [
7]. Therefore, it is important to investigate the feasibility of increasing the bio-/fossil-fuel fractions.
There have been numerous studies on bio-fossil fuel blends for automotive applications, such as ethanol–gasoline, biodiesel–diesel, and ethanol–diesel (ED) blends [
8,
9,
10]. The ED blend, however, is found to be not practical due to the poor solubility of ethanol in diesel and the negative impact of ethanol on the Cetane Number (CN) [
11,
12,
13,
14,
15]. Therefore, researchers have started to add some agents to stabilize the mixture and attain the required CN [
16,
17]. Dimethyl ether (C
2H
6O) is a suitable CN booster when it is mixed with diesel, as it has a CN of greater than 55 [
18]. However, we believe that this molecule cannot be used in diesel engines effectively due to its lower values of molecular weight, boiling point, and density, which makes it evaporate much faster than diesel fuel molecules. Among other different agents, biodiesel is a chemically-convenient additive to mix with ED fuel [
19].
The most recent studies conducted have focused on the ethanol–biodiesel–diesel (EBD) fuel blend. For instance, Kwanchareon et al. [
17] studied the GGE and the CN of this fuel blend. The presence of biodiesel in EBD blend resulted in a significant reduction in the Carbon monoxide (CO) and Hydrocarbon (HC) emissions of internal combustion engines (ICE) compared to the ED blend. In [
20], the solubility of EBD blend was investigated at two different temperatures, which showed that the solubility of ethanol increased when increasing the temperature. Beatrice et al. [
21] studied the influence of blending 10% biodiesel, 20% ethanol, and 70% diesel fuels on ICE performance. In the latter study, the smoke and Nitrogen Oxides (NO
X) emissions were found to be significantly less than those of pure diesel. The impact of EBD blend on emissions was investigated experimentally in [
22], where results showed that the EBD blend had lower NO
X emissions compared to those of pure diesel. Similarly, in [
23,
24,
25,
26,
27], the EBD blend was CN-richer and its combustion produced less NO
X emissions than diesel combustion. According to [
19,
28], up to 25% of biodiesel and 10% of ethanol could be blended with diesel effectively. In brief, previous studies on EBD blends only focused on the solubility, toxic emissions, heating value and CN of these blends. The impact of such blends on droplet heating and evaporation, with consideration to full fuel compositions, has not been investigated to the best of our knowledge.
The heating and evaporation of multi-component fuel droplets are essential processes for various combustion applications [
29,
30]. These processes have been widely investigated and different models have been proposed in [
31,
32], and validated in [
33,
34,
35,
36]. Some studies have been made to envisage the feasibility of blending biofuels with fossil fuels in terms of heating and evaporation [
35,
37]. In this paper, the new key findings are the investigation into mixing different fractions of EBD blends with consideration of their droplet lifetimes and surface temperatures, viscosities, and CN. The basic equations of heating and evaporation model and types of fuels, used in the current analysis, are described in
Section 2. The results and their discussion are provided in
Section 3. The findings are concluded in
Section 4.
2. Model
Our analysis of the blended fuel droplet heating and evaporation is based on the Discrete–Component (DC) model for a spherically symmetric droplet. The heat and mass transfer equations are solved analytically in this model, using the Effective Thermal Conductivity (ETC) and Effective Diffusivity (ED) models, as will be described later in this section. In the latter models, several physics inside droplets associated with fuel heating and evaporation are considered, for example, temperature and species gradient, and recirculation due to moving droplets [
29,
32].
The transient heat transfer equation for the temperature
in the liquid phase in a spherical droplet is [
32]:
where
is the distance from the center of the droplet (assumed to be spherical),
is the temperature,
is time in seconds, and
is effective thermal diffusivity accounting for the recirculation inside droplet, defined as:
is the liquid specific heat capacity,
is the liquid density, and
is the effective thermal conductivity, defined as:
where
is the liquid thermal conductivity, and
is the recirculation coefficient [
38].
varies between 1 (when Peclet number
and 2.72 (for
). The analysis based on Equation (3) is described as the Effective Thermal Conductivity (ETC) approach.
The initial and boundary conditions are introduced as:
where
is the surface temperature of droplet,
is the droplet radius,
is the heat transfer coefficient, and
is the ambient temperature. To take into account the effect of evaporation, the ambient temperature (
) is replaced by the so-called effective temperature (
):
where
is the latent heat of evaporation and
is the rate of change of droplet radius due to evaporation. The mass fraction diffusion of liquid species
is described as:
where
is the effective diffusivity. The
and the diffusion coefficient in the liquid phase are correlated by the following equation:
is the coefficient of recirculation inside droplet. The analysis based on Equation (7) is known as the Effective Diffusivity (ED) approach. The droplet evaporation is estimated using the following correlation:
where
is the coefficient of vapor diffusion in the gas phase,
is the total mixture density of vapor and gas,
is the Sherwood number of isolated droplets,
is the Spalding mass transfer number,
is the vapor mass fraction in the vicinity of the droplet, and
is the far-field vapor mass fraction, with
and
being the vapor mass fractions of group and individual species
, respectively.
is determined using the vapor molar fractions on the surface of droplet (
), as:
where
is the ambient air pressure,
is the molar fraction in the liquid phase of
species at the droplet surface,
is the Activity Coefficient (AC) of the
species, and
is the saturated pressure of the
species in the absence of other species.
Due to the presence of ethanol, which forms a highly non-ideal solution when it mixes with diesel fuel, the Universal Quasi-Chemical Functional group Activity Coefficients (UNIFAC) model is used to predict the AC of 106 components of the EBD blends. In fact, AC is used to correct the vapor pressure of each individual component. The UNIFAC model is presented in greater detail in [
39]. However, as this is the first study to deal with the UNIFAC model for the EBD blend to the best of our knowledge, we have included two tables in
Appendix A for the UNIFAC groups’ parameters and their interaction parameters [
40].
The diesel fuel used in this work conforms to standard European Union fuel (EN590). It consists of 98 components divided into nine groups according to their chemical structures. Molar fractions of various components of this fuel and their physical properties are inferred from [
41]. Biodiesel is represented by soybean, formed of seven methyl ester components. The molar fractions and physical properties of these components are inferred from [
42,
43]. Soybean is a type of biodiesel fuel which refers to single alkyl esters of a long-chain fatty acid derived from vegetable oils. The physical properties of ethanol (anhydrous) are inferred from [
35]. The physical properties for each component are calculated, with appropriate blending rules, to form the average properties of the blend.
4. Conclusions
The combining of biofuels with fossil fuels has received significant attention during the last two decades due to the depletion of fossil fuels and the need for reducing the GGE which contribute to global warming. In this study, we investigated the feasibility of mixing different fuel fractions of biodiesel and ethanol with diesel in terms of heating and evaporation characteristics, Cetane Number (CN), viscosity, and heating value. The aforesaid characteristics and properties are essential for the design of engines to ensure their good performance.
Predictions revealed that the presence of biodiesel at the expense of ethanol (e.g., 5% biodiesel and 5% ethanol, instead of only 10% of ethanol) compensated the reduction in droplet lifetime, surface temperature, CN, viscosity, and even the heating value. It was found that a blend of 15% biodiesel, 5% ethanol, and 80% diesel fuels led to less than 1.2%, 0.2%, 2%, and 2.2% reduction in droplet lifetime, CN, viscosity and heating value, respectively, compared to those of pure diesel fuel.
It can be concluded that the presence of biofuels with up to 20% in diesel fuel can be used in engines designed for pure diesel with minimal, or no, modification requirement.