Distillation-based Droplet Modeling of Non-Ideal Oxygenated Gasoline Blends: Investigating the Role of Droplet Evaporation on PM Emissions.
The combustion of fossil fuel used for transportation of people and goods in the United States is the second largest contributor to C[O.sub.2] emissions (31%) and contributes to 25% of the total greenhouse gas emissions . Demand for liquid fossil fuels is continuously increasing,  motivating the need for vehicles that run on low-net-carbon biofuels (or biofuel blends) with high efficiencies. One such biofuel is ethanol that has been shown to reduce life-cycle greenhouse gas emissions . Pump gasoline can contain up to 15% ethanol per volume in the US - although 10% blends are most common. In addition to reducing fossil fuel consumption, ethanol has the potential to enable improved spark ignition engine performance through higher compression ratio, higher boost pressure and/or optimizing spark timing (i.e. combustion phasing) [4, 5., 6, 7]. These benefits are partly a result of ethanol's comparatively high octane ratings, but also stem from ethanol's high heat of vaporization (HOV), which is a fluid property that describes the necessary energy to evaporate a prescribed amount of liquid. Direct Injection Spark Ignition (DISI) engines utilize the fuel's evaporative cooling potential to lower combustion chamber temperatures allowing higher loads to be achieved without knock, [8, 9, 10, 11] which in turn allows for higher compression ratios or increased pressure from forced induction. Due to higher HOV, increased ethanol content should lead to greater evaporative cooling allowing engine designers to further leverage these effects which in turn can increase efficiency and ultimately reduce greenhouse gas emissions.
Particulate matter (PM) is a combustion product that can present serious health and environmental risks, is formed in fuel-rich zones when fuel and air are not fully premixed, and in particular in a DISI engine when the fuel spray impinges on the cylinder wall or piston [12, 13, 14]. Research has shown that increasing the ethanol percentage in gasoline produces in most cases a reduction in PM [9, 13, 15] but in other cases elevated PM levels [16, 17]. General observations suggest that for fuels containing low ethanol concentrations (e.g. E0 - E15) PM emissions are insensitive to ethanol content . For moderate ethanol concentrations (e.g. E20-E40), increased PM emissions relative to EO have been observed [9, 17]. PM is reduced at high ethanol concentrations, such as E85, because it is likely that blending with ethanol dilutes PM precursors such as aromatic compounds in the gasoline .
The fundamental cause of the PM increase seen for moderate ethanol concentrations is not well understood. Current theories suggest that the high HOV of ethanol can cool the cylinder environment slowing the evaporation rate and preventing the highest boiling compounds in gasoline from fully vaporizing and mixing with air in the combustion chamber. The formation of this non-homogenous mixture would be even more likely if there was impingement of the fuel spray on the cylinder wall or piston. The pool or film of fuel can burn in a diffusion flame where these high boiling species are more concentrated in the rich zone leading to hydrocarbon molecular weight growth and increased PM production [16, 17]. Additionally, ethanol as well as other potential biofuels can form azeotropes when blended with gasoline. These non-ideal interactions can alter the boiling temperatures (i.e. the distillation curve) of the fluid as well as the time dependent vapor and liquid composition that can dictate the in-cylinder reactant composition distribution. For example, these interactions can enrich the heavy fractions of the liquid droplet with certain species such as aromatics which have shorter kinetic pathways and greater potential to form PM [9, 18].
A numerical model was created to simulate the droplet evaporation dynamics of ethanol/gasoline fuel blends to explore the role of these unique behaviors and properties (i.e. azeotropes and increased HOV) on recent observations linking ethanol content to PM emissions. Validation of the model's ability to predict the fuel's vapor liquid equilibrium and evolving thermophysical properties is carried out through comparisons with data gathered from experiments with the Advanced Distillation Curve . Following validation, an isentropic single cylinder engine model was developed to evaluate droplet evaporation under dynamic temperature and pressure conditions for a set of ethanol-gasoline blends. Results from these simulations, including the net droplet evaporation times, are then compared and used to explain the link between the HOV of ethanol and reported PM emissions.
The base gasoline used in this work was the Fuels for Advanced Combustion Engines reference gasoline B (FACE B) . FACE B was chosen because of its relative simplicity as compared to a commercially available gasoline. This simplified composition reduced model run times, yet still provided enough complexity to capture the physics experienced in a real life pump fuel.
A detailed hydrocarbon analysis (DHA) of the neat FACE B revealed that 29 compounds were required to describe 99.9% of the fuel's mass. DHA was performed using ASTM Method D6729  and Hydrocarbon Expert 5.  The result of the DHA for the neat FACE B is provided in Table 2 in Appendix A.
Distillation experiments were carried out to provide comparison data for model development using the well documented Advanced Distillation Curve (ADC) approach.  ADC experiments were performed on three FACE B/ethanol blends containing 0% (EO), 15% (E15), and 30% (E30) ethanol by volume. Distillation curves were measured for the three fuel blends and the evolving composition of the distilling fuels was quantified by sampling and performing a DHA on the condensate during the distillation. This condensate composition data was then used to determine the changing mixture averaged properties of the fuel to compare with model predictions. The distillations and corresponding simulations were performed at an average ambient pressure of 81.2 kPa (1760 m elevation).
In the case of some models, a wider gamut of gasoline ethanol blends was used. These represent EO to E85 in 5 percent increments by volume. The volume fraction of gasoline was multiplied by a normalized composition of FACE B as measured by DHA, so that the volume fractions of the components in the model summed to unity. Differences in composition between FACE B samples and errors due to mixing were thus controlled in order to directly quantify the effect of increasing ethanol content.
Ideal Distillation Model
Ideally, vapor-liquid equilibrium (VLE) can be determined from
Raoult's Law and Dalton's Law, as in Eq. (1). The mole fraction of each component in the liquid is defined as [x.sub.i] and the mole fraction within the vapor as [y.sub.i]. The ratio of these values defines the equilibrium constant ([K.sub.i]) which can be found knowing the ratio of the species' vapor pressure ([P.sub.i.sup.0])to the total pressure of the system (Ptot), multiplied by an interaction term ([[gamma].sub.i]) to account for non-ideal vaporization behaviors (typical of biofuels). If molecular interactions are neglected, the interaction term [gamma] can be ideally assumed to be unity.
[mathematical expression not reproducible] (1)
To predict the distillation curve of a complex fuel, one needs to be able to predict the change of composition of the fluid as it evaporates. This change in the liquid composition can be described as a function of the instantaneous vapor composition , and simplified using the equilibrium ratio to the ordinary differential equation provided in Eq. (2). where L is the fraction of total moles in the system that are in the liquid state.
[mathematical expression not reproducible] (2)
The set of differential equations describing the change of the liquid mole fraction of each species, Eq. (2), are then solved for set increments of L with the convergence criteria described by the equilibrium condition that all the species' vapor pressures sum to the system's total pressure as described in Eq. (3).
[mathematical expression not reproducible] (3)
Assuming the total pressure remains constant, a Newton-Raphson Method is used to find the liquid temperature which dictates each species' vapor pressure to satisfy the equilibrium condition described in Eq. (3) . Vapor pressure is calculated using coefficient lookup tables based on DIPPR empirical relationships,  which are shown in Appendix C. This application of the Newton-Raphson Method is summarized by Eq. (4).
f(T) = [p.sub.tot] -[P.sub.[infinity]] = 0 & [T.sub.i+1] = [T.sub.i]-[f([T.sub.i])]/f([T.sub.i])]] (4)
For both the modeling and the experiments, the HOV of the mixture is calculated as a composite sum weighted by the mole fraction of each component as described by Eq. (5) . The HOV of each component is calculated with the empirical relationship provided by DIPPR . Other mixture properties, such as thermal conductivity and specific heat capacity, were also calculated as a composite based on mole fraction.
[mathematical expression not reproducible] (5)
In the ideal case, the gamma term in the set of differential equations previously defined can be assumed to be equal to unity This is acceptable for gasolines and other hydrocarbons, but is inaccurate when ethanol is present in the mixture. The UNIFAC group contribution theory is one of several methods that are used to quantify the correct gamma values to model realistic vapor liquid equilibrium for chemically dissimilar compounds. It consists of geometric and polarity-driven pieces, referred to as combinatorial and residual, which both contribute to the total non-ideal coefficient, Eq. (6) [23, 25].
In [gamma] = In [[gamma].sub.r] + In [[gamma].sub.c] (6)
The combinatorial component of the UNIFAC group contribution theory, [[gamma].sub.c], deals with geometric interaction between molecules, and is applicable even in the absence of non-ideal interactions. The residual UNIFAC term, [[gamma].sub.r], is a function of polarity and temperature. Unlike the combinatorial portion, the main interaction parameters, [a.sub.mn], are purely empirical in nature. These terms describe the effect that the polarity of one structure has on another. Because this term is a function of polarity, and there is zero residual interaction between structures of the same category, alkane blends have no residual term [[gamma].sub.r]. This term is thus only needed when oxygenates and, to a far lesser extent, aromatics are present in the mixture. It can otherwise be omitted for the sake of performance, as in the case of pure FACE B. The residual parameter [[PSI].sub.mn], as defined in Appendix B Eq. (12). is a function of droplet temperature and [a.sub.mn], and must be determined at every step of the solver.
In order to model the distillation process as a droplet, energy transfer must be taken into account. A zero-dimensional form is used that includes heat conduction, sensible heat of the droplet, and latent heat of vaporization. As this is zero-dimensional, composition and temperature within the droplet are assumed to be uniform. This assumption has been shown to accurately predict the droplet evaporation dynamics for fuels and conditions similar to those reported here .
When modelling distillation, the system of differential equations depended on the changing composition. (Eq. 2) When modeling a droplet, the Newton-Raphson Method is no longer needed to solve for saturation temperature, but vapor pressure must still be calculated as shown in Eq. (3). It is also necessary to include a term for the change in volume fraction, which allows radius to be calculated, and the change in mass fraction, which allows the elapsed time to be determined based on the diffusion equation. Equations 7 and 8 show the change in volume fraction distilled and mass fraction distilled, respectively. These are negative, as they describe, in nondimensional form, the volume and mass leaving the droplet. The term c is the molar concentration of each component .
[mathematical expression not reproducible] (7)
[mathematical expression not reproducible] (8)
The time rate of mass change, Eq. (9). is found using diffusion. In this expression, [[gamma].sub.F] represents the vapor mass fraction of the fuel at the droplet surface. An approximation was used to solve for the diffusivity term as a function of molecular weight of the fuel air mixture surrounding the droplet, which is shown in Eq. (10) . The change in mass with respect to L, Eq. (8). and the change in mass with respect to time, Eq. (9). can be combined to find the change in time with respect to L. This allows for time to be calculated as an independent variable. Conservation of energy is used with latent heat, sensible heat, and conduction terms. The sensible heat term is used to find transient temperature change, Eq. (11). Change in time with respect to L was calculated as shown in Eq. (12). so Eq. (11) can be redefined with respect to L to add a dT/dL term to the system of equations. Heat conduction, as shown in Equations 13 and 14, is the only form of heat transferring to the droplet from the environment, with radiation and convection neglected.
[mathematical expression not reproducible] (9)
[mathematical expression not reproducible] (10)
[mathematical expression not reproducible] (11)
[mathematical expression not reproducible] (12)
[mathematical expression not reproducible] (13)
Z = [[c.sub.p],gas/4[pi]k](14)
The system of ordinary differential equations used to model an evaporating droplet defines changes of the liquid molar concentrations for each species, time, temperature, mass fraction distilled, and volume fraction distilled with respect to changes in L. The resulting ODE is shown below, Eq. (15). A stiff ODE solver was utilized in MATLAB to integrate this system.
[mathematical expression not reproducible] (15)
Direct Injection Engine Model
In order to predict how the dynamic temperature and pressure inside of a direct injection engine may affect the relative timescales of the ethanol evaporation, an isentropic Otto cycle was used to provide ambient pressure and temperature as a function of time. Dimensions representative of a 2.OL DISI 4-cylinder engine were used at an assumed rotational velocity of 1000 revolutions per minute. These dimensions allowed the volume of air within the piston to be determined as a function of time, assuming constant radial velocity. Therefore, the pressure and the temperature in the cylinder were calculated based on an isentropic ideal gas. This ramped temperature droplet model does not account for cooling of the combustion chamber by the droplet evaporation and remains an open model with diffusivity along an infinite scale. Table 1 provides the engine dimensions and conditions used to calculate the transient temperature/pressure traces.
Comparisons between the measured and predicted distillation curves and HOV for E15 are shown in Figure 1. Results from simulations assuming ideal interactions and non-ideal interactions determined using the UNIFAC approach are provided for comparison. It should be noted that the use of UNIFAC resulted in a 45 fold increase in computation time compared to the ideal distillation model. The predicted distillation curves and HOV accounting for non-ideal interactions agree well with data from the ADC experiments. Assuming ideal interaction behavior for these fuel blends, however, significantly under predicts the HOV and over predicts boiling temperatures in the early part of the distillation. Not shown here, the ideal interaction assumption did accurately predict experimental measurements performed on the neat FACE B (E0).
Despite the good overall agreement, there is a noticeable over prediction in the HOV for the initial sample of condensate. This is likely a result of the sampling process during the experiments not being able to collect the highly volatile species which are the first compounds to distill, namely n-butane. Nevertheless, the initial boiling temperature is accurately predicted based on the composition of the neat fuel blend, which implies that the composition at this point is properly reflected by the UNIFAC model. While the distillation model with UNIFAC followed the experimental temperature trends for ethanol blends, it consistently under predicted the saturation temperature of the mixture across the distillation. The magnitude of this shift, not shown in this paper, is roughly equal for the E0 and E30 blends, suggesting an error in van der Waals surface calculation from the combinatorial function of UNIFAC, and not a product of non-ideal behavior.
The composition by hydrocarbon group was measured by DHA for condensate samples throughout the distillation process and compared with the compositions calculated by the UNIFAC model. A representative comparison for E15 is shown in Figure 2. Firstly, comparison between Figures 1 and 2 points to the fact that the presence of ethanol is responsible for the reduced boiling temperatures and increased HOV in the early part of the distillation. Additionally, the presence of ethanol can be seen to suppress the distillation of the aromatic and isoparaffm species, noted by the sharp increase in these species concentration at the moment ethanol is completely evaporated from the boiling mixture.
Ideal Multicomponent Droplet
Following successful validation of the modeled vapor-liquid equilibrium, these methods were employed in a droplet model to determine how the combined increased HOV and altered VLE affect the evaporation dynamics of the droplet. Transient droplet evaporation results from the model with UNIFAC were compared to an empirical study of droplets consisting of a ternary alkane mixture . The comparison of the predicted and experimental data are provided in Figure 3. The experimental measurements were performed by Jochen et al using optical droplet levitation. It is important to note that compared to the reference data, the model slightly under predicted the total evaporation time. The source of the discrepancy is likely differences in diffusion, perhaps due to natural convection present in the experiment. However, the inflection points that result in slowing of vaporization which occur as octane and dodecane are eliminated from the droplet were accurately captured, implying that the droplet composition and the resulting effect of heat of vaporization on the temperature of the droplet are properly reflected by the model.
Non-Ideal Multicomponent Droplet
While the results with the ternary alkane blend demonstrate the predictive capabilities of the model, and its ability to account for the HOV to predict the transience of an evaporating droplet, the VLE of this mixture behaves ideally. The effect of non-ideal VLE behavior in the presence of a biofuel species must also be demonstrated. The model predicted droplet regression was compared to to experiments conducted by Corsetti et al . The empirical droplet regression data was measured employing an electrodynamic balancing (EDB) technique to levitate droplets comprised of gasoline-ethanol blend surrogates. These mixtures were blended based on mass fractions of ethanol corresponding to nominal ethanol content, with the remainder of the composition being equal parts by mass of heptane and isooctane . The time scales predicted by the model were substantially different than those measured by EDB. These differences are most likely due to the model not incorporating effects of electrically charging the droplet, which may affect diffusivity and surface composition, nor ambient humidity, which was present in the experiment. In order to compare these results, both time scales were normalized with respect to the total evaporation time when the E30 droplet was at 32 percent of its original diameter, the point at which it failed to remain suspended by electrodynamic balance. This allowed the effect of ethanol content on relative evaporation time to be validated.
As illustrated in Figure 4, the normalized transient response shows agreement between the droplet model and EDB experiments, with some differences observed for E100. Corsetti et al concluded that ambient humidity did impact the droplet vaporization behaviors, particularly with higher ethanol concentrations, and attributed the inflection point around 50 percent diameter for the E100 case to be the result of absorption of water by the droplet. Overall, the model reflects the observed trends in vaporization time for different ethanol-hydrocarbon fuel blends. These agreements, illustrated in Figures 3 and 4, provide confidence that the model is accurately predicting the physics to the extent required to compare complex fuel blends and help explain observations linking ethanol content to PM emissions.
FACE B and Ethanol Droplets
Blends of FACE B and ethanol were then modeled as 50 [micro]m droplets in a constant ambient temperature. A diameter of 50 [micro]m was chosen to ease future experimental validation with optical levitation, as larger droplets allow time and diameter to be more readily resolved, and allow stable levitation to be maintained for longer periods. [28, 29] The composition of these blends as measured by DHA were used as the initial droplet compositions. Unidentified components accounted for less than 0.1 percent of the FACE B composition, and were neglected.
Figure 5 shows the temperature of the E0, E15, and E30 droplets during evaporation with an initial droplet and surrounding air temperature of 298 K. Clearly, ethanol increases the HOV of the mixture, resulting in a greater initial temperature drop. The temperature remains low until ethanol is depleted, at which point the temperatures for the E15 and E30 droplets converge with that of the E0 droplet. The group-based compositions of these droplets are shown in Figure 7. Compared to the E0 and E15 blends, E30 exhibits a distinct increase in mono-aromatic concentration for both phases towards the end of droplet vaporization.
The droplet model was repeated for various ethanol concentrations ranging from 0 to 85 percent by volume and for various ambient temperatures ranging from 298K to 360K. The final evaporation time was defined to be the time at which the droplets were 99.9 percent (by mole) vaporized. The normalized evaporation times with respect to pure FACE B for these blends and ambient temperatures are shown in Figure 6. Generally, evaporation time increases with increased ethanol content because the droplet temperature is depressed, resulting in less rapid diffusion. It is also interesting to note that at lower temperatures, namely 298 K, for cases with low to moderate ethanol concentrations (E0-E30) evaporation time actually reduces as compared to the pure FACE B droplets. The reasoning for this scenario is that the increased volatility of the fuel promotes evaporation more so than the increased HOV resists evaporation, resulting in a temperature dependent balance between the two phenomena. This dependence on in-cylinder temperature conditions may provide some explanation for the inconsistent conclusions from engine testing relating ethanol to PM.
Direct Injection Engine Model
A 0-dimensional model was created to incorporate changing isentropic temperature and pressure conditions around the droplet, as there would be in a reciprocating internal combustion engine. While not reflective of typical fuel injection droplet size for DISI, a droplet size of 40 [micro]m was chosen to represent the largest droplets that can occur in a fuel spray, as these droplets are likely to play a significant role in PM formation. [30, 31]
For simplicity, the model begins with a closed combustion chamber with the piston in the bottom dead center (BDC) position and all fuel in the liquid phase, with a single droplet at 40 [micro]n. The resulting diameter and droplet temperature for E15 are shown in Figure 8 as a function of crank angle. An initial decrease in the droplet temperature is observed for E15 followed by a rapid heating as the chamber temperature and pressure rise corresponding to an isentropic compression. This increase in droplet temperature leads to an increase in droplet evaporation rate resulting in complete vaporization of the E15 droplet at -15[degrees] after top dead center (ATDC).
These simulations were repeated for E0 to E85 to determine the final crank angle at the time of complete vaporization, the results of which are shown in Figure 9. If the time between complete droplet evaporation and TDC is assumed to be an indicator of total mixing time for the air and fuel vapor blend and final vapor homogeneity, the difference in mixing based on ethanol concentration can be significant. Figure 9 demonstrates that increasing the ethanol content blended with FACE B can be correlated with decreased mixing times for air and fuel vapor. Droplets that are not vaporized before ignition may impinge on the piston and cylinder wall, which has been previously correlated with increased PM emissions . Furthermore, as illustrated in Figure 10, similar to the constant ambient temperature model, aromatic concentrations in both phases are increased with increasing ethanol content towards the end of vaporization. In combination with the effect on overall vaporization time, this means that not only could there be fuel-rich pockets in the cylinder (or pre-evaporated liquid droplets) as ethanol concentration is increased, but that these fuel-rich pockets (or liquid droplets) can be enriched with higher concentrations of aromatics when ignition occurs, which could result in increased PM emissions. It is also interesting to note that non-ideal behavior in the presence of ethanol changes the vapor phase concentrations of paraffins and mono-aromatics, however isoparaffms do not show a change in vapor concentration between E15 and E30 until ethanol is exhausted. This suggests that the difference in vapor concentration of isoparaffms for E0 and E15 results from dilution by ethanol rather than non-ideal behavior. It should be noted that the dynamics of fuel spray break-up, evaporation, and air mixing within the engine cylinder are far more complicated than simulated here. Nevertheless, the intrinsic evaporation tendencies of fuels are a dominant component that can be studied as demonstrated here to explore trends and observed differences in combustion behavior between multiple fuels.
A droplet evaporation model validated against experimentally measured distillation curve and droplet regression data was developed to determine the impact of increasing HOV when ethanol is blended with gasoline on the evaporation of the fuel and its potential to produce PM. While increasing the HOV of the fuel by increasing the ethanol concentration did not cause the droplet vaporization time to increase at room temperature, particularly for mixtures containing less than 40% ethanol, higher temperatures and especially ramped temperature environments did lead to predicted longer vaporization times as the HOV was increased. These results suggest that the competition between the increased fuel volatility and the increased HOV, which occur when ethanol is blended with gasoline, can vary as engine conditions are altered. Furthermore, as confirmed by ADC experiments, there was a clear effect that as the blended ethanol concentration increased there was an increase in the aromatic concentration in both the vapor and liquid phases towards the later stages of distillation and droplet evaporation - aromatic evaporation was shifted to later in the distillation.
The increase in aromatics towards the end of vaporization, along with the decreased mixing time produced by the ramped temperature and pressure model, suggest that increased ethanol content could be causing regions locally rich in aromatics in direct injection engines which would heighten PM emissions. Note that the aromatics in FACE B all boil below 150[degrees]C, while the T90 limit for gasoline is 185 or 190[degrees]C and the endpoint limit is 225[degrees]C. In fuels containing high boiling aromatics these trends would likely be significantly enhanced. The trends predicted here advocate that it may be favorable to design a petroleum blend stock that has low concentration of heavy aromatics to lessen PM emissions and, furthermore, that port injection, with its lower intake temperatures which show little to no deviation in evaporation time versus ethanol content, would be less effected by the elongation of the vaporization process. It is possible that this method could be used to evaluate the susceptibility of various gasoline compositions to decreased mixing times and local richness of PM precursors in the presence of ethanol. Ultimately, this could aid in identification of gasoline blend stocks with favorable vaporization and emission behavior tailored for use with desired concentrations of ethanol. A reduction in aromatic content would need to be balanced with the role that aromatics play in knock resistance. However, the high octane and HOV of ethanol may serve to offset the octane decrease from a reduction in aromatics if this reduction allows for a greater concentration of ethanol.
Future work will need to confirm that these effects would not be counteracted/exaggerated by increased combustion chamber cooling in DISI engines and to employ the evaporation physics described here within computation fluid dynamic simulations to account for realistic in-cylinder fluid dynamics, heat transfer, and droplet interactions on the mixing/in-cylinder composition distribution. Nevertheless, the evaporation tendency of a fuel is a time limiting process which can dictate a fuel's ability to mix with air, and can be used explore trends and observed differences in combustion behavior between multiple fuels.
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[32.] Constantinescu, D. and Gmehling, J., "Further Development of Modified UNIFAC (Dortmund): Revision and Extension 6," Journal of Chemical & Engineering Data 61(8):2738-2748, 2016, 10.1021/acs.jced.6b00136.
Colorado State University
This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists under the Visiting Faculty Program.
Research performed by National Renewable Energy Laboratory staff was conducted as part of the Co-Optimization of Fuels & Engines (Co-Optima) project sponsored by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy, Bioenergy Technologies and Vehicle Technologies Offices. Co-Optima is a collaborative project of multiple National Laboratories initiated to simultaneously accelerate the introduction of affordable, scalable, and sustainable biofuels and high-efficiency, low-emission vehicle engines. Work at the National Renewable Energy Laboratory was performed under Contract No. DE347AC36-99GO10337.
ATDC - After top dead center
BDC - Bottom dead center
D - Diameter
[D.sub.0] - Initial diameter
DHA - Detailed hydrocarbon analysis
DIPPR - Design Institute for Physical Properties
DISI - Direct-injection spark ignition
EDB - Electrodynamic balancing
FACE - Fuels for Advance Combustion Engines
HOV - Heat of vaporization
ODE - Ordinary differential equation
PM - Particulate matter
TDC - Top dead center
UNIFAC - UNIQUAC functional-group activity coefficients
UNIQUAC - Universal quasichemical
VLE - Vapor-liquid equilibrium
Those items with a k subscript are calculated for each structure, while those with an i subscript are calculated for each component in the mixture.
[mathematical expression not reproducible] (1)
[[theta].sub.i]= [[q.sub.i][x.sub.i]/[[sigma].sub.j][q.sub.j][x.sub.j]] (2)
[[theta].sub.i]= [[r.sub.i][x.sub.i]/[[sigma].sub.j][r.sub.j][x.sub.j]] (3)
[l.sub.i] = [z/z]([r.sub.i] - [q.sub.i]) ([r.sub.i]-1) (4)
[mathematical expression not reproducible] (5)
[mathematical expression not reproducible] (6)
[R.sub.k] = [[v.sub.k]/15.17]
[Q.sub.k] = [[A.sub.k]/2.5 x [10.sup.9]]
[V.sub.k] and [A.sub.k] are van der Waals group volume and surface area. The selection of the z coefficient is largely arbitrary , and is often stated as being equal to 5. No significant differences were observed from changing this factor.
Those items with a k subscript are calculated for each structure, while those with an i subscript are calculated for each component in the mixture.
[mathematical expression not reproducible] (9)
[mathematical expression not reproducible] (10)
[[PHI].sub.mn] = [exp(-[U.sub.mn]-[U.sub.mn])/RT] = exp (-[a.sub.mn]/T) (12)
[[THETA].sub.m] = [[q.sub.m][X.sub.m]/[[SIGMA].sub.n][q.sub.n][X.sub.n]] (13)
[mathematical expression not reproducible] (18)
Stephen C. Burke
Colorado State University
Matthew Ratcliff and Robert McCormick
National Renewable Energy Laboratory
University of Colorado - Colorado Springs
Colorado State University
Table 1. Engine operating parameters Bore 83.5 mm Stroke 91.2 mm Connecting Rod 159.6 mm Compression Ratio 13.0:1 Rotation Velocity 1000 RPM Pressure at BDC 101.325 kPa Temperature at BDC 315K Initial droplet diameter 40 [micro]m Table 2. Normalized composition of FACE B used for simulation Component Group Percent Weight i-Butane I-Paraffins 0.045 n-Butane Paraffin 2.305 i-Pentane I-Paraffins 8.013 n-Pentane Paraffin 2.942 2,3-Dimethylbutane I-Paraffins 0.806 2-Methylpentane I-Paraffins 0.234 3-Methylpentane I-Paraffins 0.105 2,4-Dimethylpentane I-Paraffins 4.241 2-Methylhexane I-Paraffins 9.265 3-Methylhexane I-Paraffins 0.156 2,2,4-Trimethylpentane I-Paraffins 40.732 2,2,3-Trimefhylpentane I-Paraffins 0.673 2,5-Dimethylhexane I-Paraffins 1.353 2,4-Dimethylhexane I-Paraffins 1.939 2,3,4-Trimethylpentane I-Paraffins 9.078 2,3,3-Trimethylpentane I-Paraffins 6.116 2,3-Dimethylhexane I-Paraffins 1.856 4-Methylheptane I-Paraffins 0.129 3,4-Dimethylhexane I-Paraffins 0.147 2,2,5-Trimethylhexane I-Paraffins 1.266 2,3,5-Trimethylhexane I-Paraffins 0.212 Ethylbenzene Mono-Aromatics 1.200 m-Xylene Mono-Aromatics 3.693 p-Xylene Mono-Aromatics 1.573 2,3-Dimethylheptane I-Paraffins 0.065 o-Xylene Mono-Aromatics 1.516 2,2,4-trimethylheptane I-Paraffins 0.193 n-Nonane Paraffin 0.092 2,3-Dimcthy loctanc(1) I-Paraffins 0.054 Table 3. Combinatorial UNIFAC parameters for the structures utilized for FACE B and ethanol. Structure k Group [R.sub.k] [R.sub.k] CH3 1 1 0.9011 0.848 CH2 2 1 0.6744 0.540 CH 3 1 0.4469 0.228 C 4 1 0.2195 0.000 CH=CH 6 2 1.1167 0.867 ACH 10 3 0.5313 0.400 ACCH3 12 4 1.2663 0.968 ACCH2 13 4 1.0396 0.660 ACCH 14 4 0.8121 0.348 OH 15 5 1.0000 1.200 CH20 26 13 0.9183 0.780 Table 4. Interaction parameters [a.sub.mn] quantifying the polarity-driven interaction of group m (arranged by row) with group n (arranged by column). Group 1 2 3 4 5 13 1 0 86.02 61.13 76.5 986.5 251.5 2 -35.36 0 38.81 74.15 524.1 214.5 3 -11.12 3.446 0 167 636.1 32.14 4 -69.7 -113.6 -146.8 0 803.2 213.1 5 156.4 457 89.6 25.82 0 28.06 13 83.36 26.51 52.13 65.69 237.7 0 Table 5. Physical properties and the corresponding DIPPR correlations that were used to calculate each . Property DIPPR Equation Liquid specific heat capacity 100 Liquid vapor pressure 101 Liquid molar concentration 105 Heat of vaporization 106 Ideal gas specific heat 107 capacity Vapor thermal conductivity 102