Application of an Equilibrium Phase (EP) Spray Model to Multi

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Application of an Equilibrium Phase (EP) Spray Model to Multi-component Gasoline Direct Injection (GDI) Zongyu Yue, and Rolf D. Reitz Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04435 • Publication Date (Web): 01 Mar 2019 Downloaded from http://pubs.acs.org on March 5, 2019

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Energy & Fuels

Application of an Equilibrium Phase (EP) Spray Model to Multi-component Gasoline Direct Injection (GDI) Zongyu Yue, Rolf D. Reitz Engine Research Center, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706, USA

Abstract An Equilibrium Phase (EP) spray model for simulating high-pressure diesel fuel injection has recently been proposed, which is based on a local phase equilibrium assumption and jet theory. In this model, spray vaporization is assumed to be a mixing-controlled equilibrium process, while the non-equilibrium processes of droplet breakup, collision and surface vaporization are neglected. The model shows a good grid-independency by introducing a Liquid-Jet model and a Gas-Jet model. In this study, the EP model is applied in simulations of multi-hole gasoline direct injection (GDI). The model validation is performed for two different GDI injectors, i.e., the Engine Combustion Network (ECN) Spray G injector and a GM injector, operated at ambient temperatures from 400 K to 900 K and ambient densities from 3 to 9 kg/m3, with fuel of iso-octane. Good agreement are found between simulation and available experimental data in terms of liquid/vapor penetrations, shape of the vapor envelope, and the axial velocity evolution along the injector centerline for no or slight spray collapse conditions. In addition, a 10-component gasoline surrogate fuel is employed to demonstrate the capability of this model for simulating multi-component spray. The results reveal considerable dependency of vapor distribution on fuel properties and ambient temperature, which is essential for predictions of engine combustion and emissions. Keywords: GDI, ECN, Spray G, CFD, phase equilibrium

1. Introduction Gasoline direct injection (GDI) in spark-ignition engines has been a trend in the light-duty market for the past decade in order to further improve fuel economy and reduce CO2 emission. Compared to the port fuel injection system, the GDI system offers precise fuel delivery, less cyclic variability, improved thermal 1

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efficiency by engine knock mitigation and allowing higher compression ratios, and the potential for unthrottled, stratified lean combustion.1 In recent years, the multi-hole nozzle has been widely used in GDI engines because it provides a spray structure that is more stable and less sensitive to in-cylinder conditions in comparison with pressure-swirl atomizers.2 Different than the multi-hole nozzles in diesel engines, the multi-hole GDI nozzles usually feature a step-hole design with a smaller length/diameter (L/D) ratio and a narrower drill angle, and operated under a relatively lower injection pressure (10-40 MPa) with a less viscous, more volatile fuel being injected into a cooler and lower density chamber. Computational Fluid Dynamics (CFD) modeling of the fuel injection process has long been a focus for diesel applications using the Lagrangian-Drop Eulerian-Fluid (LDEF) framework,3-7 and it has been adapted for GDI spray simulation as well.8 Briefly, the intact liquid core is represented by discrete ‘blobs’ with an initial size of the effective nozzle diameter, and the subsequent processes of primary/secondary breakups, collisions and vaporization are also modeled. A hybrid Kelvin-Helmholtz/Rayleigh-Taylor (KH-RT) instability analysis model is mostly used to predict primary and secondary breakups,3,4 coupled with a concept of breakup length to regulate the competition between two breakup mechanisms,5 in that blobs within the breakup length are only affected by the KH model while both the KH and RT models are applied to blobs beyond the breakup length. Beale et al.6 further improved this model by allowing all the drops outside the intact liquid core of the jet to be affected by the RT model and applying a Rosin-Rammler distribution to specify the sizes of children drops. Recent effort on breakup model improvement also consider the in-nozzle flow effects, e.g. cavitation and turbulence.7 Since gasoline and diesel fuels are complex mixtures that consist of a number of paraffins, cycloalkanes and olefins, etc., a continuous composition model9 or a discrete component model10 with a suitable multi-component surrogate have been used to model the liquid vaporization. These sub-models often contain a number of model constants that can be tuned to optimize the overall accuracy of spray simulations under certain conditions. 11 However, it is still very challenging to accurately predict the fuel injection process across a wide range of operating conditions as well as for different injectors and fuels without the need of case-by-case constant tuning. While the spray model development has been primarily focused on modeling drop breakup/collision and evaporation, the experimental study by Siebers12 suggests that high-pressure fuel injection under diesel engine 2


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conditions is a mixing-controlled process by examining the dependency of liquid length on orifice size and injection pressure. It is indicated that under such conditions, the liquid spray is analogous to a turbulent gas jet, and phase equilibrium state is achieved locally such that the vaporization process is mainly limited by the entrainment of ambient hot gas, instead of drop breakup or finite-rate evaporation at droplet surfaces. A dimensional scaling law of liquid length was subsequently proposed and was successfully applied to liquid length prediction for diesel-type fuel injection under a wide range of operating conditions.12 Parrish13 examined this scaling law for GDI measurements and the results also confirm this mixing-controlled characteristics of sprays for GDI under a certain range of conditions, especially at high ambient temperatures. Iyer et al.14 performed CFD simulations for a diesel spray using a two-fluid model. In their modeling approach, both the liquid and gas phases are resolved as Eulerian fluids with the locally homogeneous flow (LHF) approximation. Thus, the spray vaporization is controlled by turbulent mixing with an empirical model for equilibrium phase calculation. The simulations showed reasonably good predictions for liquid length, which again suggests the mixing-controlled characteristics of diesel sprays. More recently, Matheis et al.15 employed an advanced phase equilibrium model16 in Large Eddy Simulation (LES) of a diesel spray and also concluded that the dense or moderately dense sprays can be properly simulated by the mixing-controlled two-phase mixture model. Based on the mixing-controlled jet theory and the local phase equilibrium assumption, an equilibrium phase (EP) spray model17 has been previously developed for the application of engine CFD simulations. This model has been successfully employed to simulate diesel sprays and has shown excellent predictions in terms of transient liquid and vapor penetrations, spatial vapor distributions and flame lift-off lengths for constant volume chamber sprays, as well as in-cylinder pressures, heat release rates and emissions for engine combustion under a wide range conditions without the need of model constant tuning. Additionally, the model is more computationally efficient than the classical Lagrangian spray modeling approach because consideration of the non-equilibrium processes of drop breakup, collision, and vaporization are bypassed. In this study, the EP spray model is applied for GDI spray simulation. The model is validated against Engine Combustion Network (ECN) Spray G and GM GDI iso-octane spray experiments for liquid and vapor penetrations, plume shape as well as velocity field predictions at multiple operating conditions. Further, a 103


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component gasoline surrogate is employed to simulate multi-component spray using the EP model, and to illustrate the impact of fuel properties and ambient conditions on multi-component vapor distributions.

2. Model description The EP spray model is discussed in detail in Reference (17), and is only briefly described here. In this approach, the role of mixing process is emphasized by introducing an Eulerian phase of liquid, and by solving for the phase equilibrium based on local thermodynamic state. The fuel is injected into the CFD domain as Lagrangian parcels or ‘blobs’ in order to avoid the need to resolve the spray structure at the nozzle scale. The liquid fuel is then gradually released from the injected Lagrangian parcels to the Eulerian liquid as it moves away from the nozzle exit, while the breakup, collision and finite-rate interfacial vaporization are not modeled. The governing equation for the Eulerian liquid reads, ∂𝜌𝑙 ∂𝑡

[ ( )] + 𝑆

+ ∇ ∙ (𝜌𝑙𝐮) = ∇ ∙ 𝜌𝐷∇

𝜌𝑙 𝜌

𝐸𝑃

+ 𝑆𝑟𝑒𝑙𝑒𝑎𝑠𝑒

(1)

𝜌𝑙 is the liquid mass density in Eulerian phase. 𝑆𝐸𝑃 is a source term caused by phase change between the Eulerian vapor and Eulerian liquid achieving local phase equilibrium. 𝑆𝑟𝑒𝑙𝑒𝑎𝑠𝑒 is a source term that describes the liquid conversion from Lagrangian to Eulerian phase, which is governed by the Liquid-Jet model, 𝑆𝑟𝑒𝑙𝑒𝑎𝑠𝑒 = (𝑚𝑝 ― 𝑚𝑝, 𝑖 ∙ (1 ― 𝛾(𝑥))) 𝑑𝑡 1 + 16𝑥2 ― 1

𝑚𝑎(𝑥)

𝛾(𝑥) = 𝑚𝑎(𝐿) =

2 1 + 16(𝐿/𝑥 + ) ― 1

(2) (3)

where 𝑚𝑝 is the Lagrangian parcel mass, and 𝑚𝑝, 𝑖 is the mass of the same parcel when initially injected. 𝑚𝑎 (𝑥) is the entrainment mass flow rate as a function of axial distance, 𝑥. 𝑥 = 𝑥 𝑥 + is the axial distance normalized by 𝑥 + = 𝜌𝑓 𝜌𝑎 ∙ 𝐶𝑎 ∙ 𝑑/tan (𝜃 2). 𝜌𝑓 and 𝜌𝑎 are the densities of fuel and ambient gas, respectively. 𝑑 is the nozzle diameter, and 𝐶𝑎 is the area-contraction coefficient which is set to be 0.8 in this study. The term 𝛾(𝑥) describes the ratio of the entrainment mass flow rate as a function of axial distance and the total entrained gas required at that liquid length tip (𝐿) to fully vaporize the fuel. In a mixing-controlled spray, 𝛾(𝑥) is also the upper limit for the fraction of liquid being possibly vaporized along the axial distance. 𝐿 is the liquid length and it is estimated by a scaling law,12 4


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Energy & Fuels

𝐿 = 𝐶𝐿 ∙

𝜌𝑓

𝜌𝑎 ∙

𝐶𝑎 ∙ 𝑑 tan (𝜃 2)

(

2

2

)

𝐵(𝑇𝑎,𝑃𝑎,𝑇𝑓) + 1

―1

(4)

𝐶𝐿 = 0.62 is a model constant. The term 𝐵(𝑇𝑎,𝑃𝑎,𝑇𝑓) describes the saturated vapor condition at liquid length tip, which is a function of ambient temperature, 𝑇𝑎, ambient pressure, 𝑃𝑎, and fuel temperature, 𝑇𝑓. The cone angle 𝜃 is modeled as a function of gas/liquid density ratio, 𝜌𝑓 𝜌𝑎, Reynolds number, 𝑅𝑒𝑓 and Weber number, 𝑊𝑒𝑓, based on the aerodynamic surface wave theory of jet breakup,18 tan 𝜃 2 = 𝐶𝜃4𝜋

𝜌𝑎

𝜌𝑓 𝑅𝑒𝑓 2

𝜌𝑓𝑓(𝜌𝑎(𝑊𝑒𝑓) )

(5)

𝐶𝜃 is a model constant that depends on in-nozzle configuration and flow condition and 𝑓 is a weak function. The EP model was implemented in the KIVA-3vr2 code,19 with several improvements in sub-models for engine combustion simulations. A Gas-jet model20 is used to improve grid-independency by calculating the Lagrangian parcel drag force with a sub-grid velocity from turbulent gas-jet theory that allows a more accurate liquid/gas momentum coupling when coarse meshes are used. A generalized-RNG k-ε turbulence model21,22 that considers the effects of flow compressibility and flow strain rate is used for turbulence modeling and provides improved predictions for several types of pure compression of interest in engine flows compared to the original RNG model. An advanced phase equilibrium solver16 that is based on Gibbs free energy minimization is employed for calculating 𝑆𝐸𝑃 in Equation (1) and 𝐵(𝑇𝑎,𝑃𝑎,𝑇𝑓) in Equation (4), which tests phase stability using the tangent plane distance (TPD) method23 and solves for flash calculation with the Rachford-Rice algorithm24. This solver has been successfully applied to study multiphase dynamic flash, condensation, as well as supercritical fluids, etc.25-27 The Peng-Robinson equation of state28 is applied for both the phase equilibrium solver and the gaseous phase Pressure-Volume-Temperature relationship to account for real gas effects under engine conditions.29

3. Results and discussion 3.1. ECN Spray G The model was first validated at the standard ECN Spray G condition.30 The Spray G injector has eight holes with stepped-hole structure. The drill angle is 37˚, but a measured value of 33˚ 31 was used for the plume 5


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direction in this study. The nozzle diameter is 165 μm and the length/diameter ratio is 1.03. In both the experiments and simulations, iso-octane was used as a surrogate for gasoline. The injected fuel temperature was 363 K and the injection pressure was held at 20 MPa. The injection duration was 780 μs and a measured rate of injection as shown in Figure 1 was used in simulation. The constant volume spray chamber was maintained at 573 K, 3.5 kg/m3 with nitrogen. For the simulation setup, a cylindrical domain with diameter of 10 cm and height of 10 cm was considered using a 360˚ full mesh to simulate eight spray plumes, as well as a 45˚ sector mesh with periodic boundary on the sides to simulate just one spray plume, as shown in Figure 2. The red cloud represents the spray plumes and illustrates the injector location as well as plume direction. In the case of the sector mesh, plume-to-plume interaction is approximated by assuming that each plume is identical. The mesh resolution is 0.5 mm × 0.5 mm × 4.5˚ in the near-nozzle region, and smoothly transitions to 2.75 mm × 2.75 mm × 4.5˚ at the far sides, for both mesh setups.

Figure 1. Rate of injection measurement and spray cone angle prediction from Equation (5).

(a) 360˚ full mesh

(b) 45˚ sector mesh

Figure 2. Computational domain with the full mesh and sector mesh. Red cloud represents the spray plume and indicates the injector location.

6


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Due to lack of experimental measurement of the cone angle, 𝐶𝜃 was determined to be 1.2 to optimize the prediction of jet penetration, and the cone angle prediction is also shown in Figure 1. Since the cone angle is modeled as function of Reynolds number and Weber number that depend on the instantaneous injection velocity, the transient periods are also captured at the start and end of injection. A cone angle of 25 degrees is predicted for the quasi-steady period, and a widened cone angle is seen at the start and end of injection due to the slower injection velocity. Figure 3 shows the comparison of predicted radial distribution of fuel mass density obtained with the full mesh against experimental measurements by x-ray tomography,32 at 2 mm downstream of the injector tip and 0.5 ms after the start of injection (ASI). The measurement shows the mean value of the eight plumes of the ECN Spray G injector #29 as a black solid line, with the standard deviation indicated by the dash lines. Only the mean value is shown for the prediction as a red line, since the relative standard deviation is less than 1%. Reasonably good agreement is found between the prediction and measurement in terms of peak value, peak location and spray width, indicating that the cone angle is well predicted, as well as that the plume direction is well captured with the measured value.

Figure 3. Radial profile of fuel mass density 2 mm downstream of the injector tip, 0.5 ms ASI. Black solid line is the averaged result of 8 plumes from X-ray tomography measurements for ECN Spray G #29, with black dash lines indicating results +/- standard deviation. Red line is the averaged result of 8 plumes from CFD simulation.

Schlieren and Mie-scattering imaging were used in the experiments to measure the vapor and liquid envelopes, respectively. The penetrations of vapor and liquid phases are defined as the distance from the nozzle exit to the jet tip along the injector axis. In the CFD simulation, the vapor penetration is defined as the distance from the nozzle exit to the tip region where the fuel vapor mass fraction is 0.1%., and the liquid penetration length is determined as the distance from the nozzle exit to the farthest axial position for a 0.01% liquid volume 7


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fraction. Figure 4 shows the spray penetration predictions in comparison with the available experimental measurements. Several experimental measurements made by different institutes are plotted with black lines.30 It is seen that vapor penetration measurements are relatively consistent, while the liquid penetration shows more variations, especially for the period after the end of injection. The red solid lines are the present CFD predictions by the sector mesh with 0.5 mm resolution, and the red dash lines are the predictions using the full mesh with the same resolution. Both meshes show consistently good agreement with the measurements for both the vapor and liquid penetrations. However, a discrepancy in the liquid length is seen after the end of injection, which can be partly attributed to the large uncertainty in the measurements. With the sector mesh, finer resolution of 0.3 mm and coarser resolutions of 1 mm and 2 mm were also tested in the simulations, and are shown as magenta, blue and green lines in Figure 4. It is seen that the liquid length is less sensitive to the mesh resolution, which is attributed to the Liquid-Jet and Gas-Jet models that enable accurate liquid/gas momentum exchange predictions that are independent of mesh resolution. However, more discrepancy is seen in the vapor penetration in that the coarser mesh has a slower penetration rate at later stages, but grid convergence is achieved for 0.5 mm and 0.3 mm resolution. Despite the accurate momentum exchange with the liquid, fine spatial meshing in the near-nozzle region is still required to correctly resolve the velocity profile, which can also be illustrated by examining the axial velocity.

Figure 4. Liquid and vapor penetrations for ECN Spray G. Circles with labels indicate results of liquid and vapor, respectively. Black lines are experimental measurements performed by different institute. Colored solid lines are model predictions using the sector mesh with different mesh resolutions. Red dash line is prediction using the full mesh.

The evolution of the axial velocity component along the injector centerline 15 mm downstream of the injector tip is shown in Figure 5. The black line and shadow areas are the ensemble average and standard 8


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deviation of Particle Image Velocimetry (PIV) measurements,33 respectively, which present a recirculation period during the injection where the flow is moving upward to the injector with a negative axial velocity. The recirculation velocity starts to decelerate at 0.75 ms ASI, slightly after the point when the rate of injection starts to drop. With the plume slowing down and widening and collapsing along the centerline after the end of injection, the flow at the measured location reverses to be directed downward with a positive axial velocity. This transient velocity profile is well predicted by the current model using both the sector and full mesh with 0.5 mm mesh resolutions, in terms of velocity magnitude and phasing with a slight delay in the plume arrival time, as shown by the red solid and dash lines in Figure 5. Similar to the penetration predictions, the grid convergence is reached for 0.5 mm and 0.3 mm mesh, with a small difference in the downward-directed velocity after the end of injection. The blue line and green line show the velocity predictions with coarse meshes, which under-predict the recirculation velocity and significantly over-predict the downward-directed velocity with an early reversal time.

Figure 5. Temporal axial velocity on the centerline 15 mm downstream of the injector tip. Black line is the PIV measurement,33 with standard deviation indicated by the shadow area. Colored solid lines are model predictions using the sector mesh with different mesh resolutions. Red dash line is prediction using the full mesh.

Figure 6 gives the distribution of the velocity field on a cut-plane through the plume centerline for the sector mesh with 0.5 mm and 2 mm mesh resolution, respectively. The red spheres represent the injected Lagrangian parcels. Black arrows indicate velocity vectors, and the size of the arrow tip is proportional to the velocity magnitude. The location of the hole exit is 0.79 mm in the radial direction from the injector axis, which means that with a mesh resolution larger than 0.79 mm, the hole exit is within the cell that is adjacent to the axis of symmetry of the cylindrical domain. This results in excessive momentum transfer to the gas phase along the injector centerline because the radial velocity along the axis of symmetry is zero with axisymmetric structure. 9


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The over-predicted axial velocity suppresses the recirculation flow and leads to an unrealistic collapse along the axis after the end of injection. The dispersed velocity profile seen in Figure 6 (b) also results in a slow penetration rate, as found in Figure 4. It is interesting to note that this grid dependency has not been seen when applying the present EP spray model to diesel spray simulations, which is likely due to the wider hole drill angle and less interaction between the plumes for diesel injectors.

Figure 6. Velocity field for 0.5 mm and 2 mm mesh resolution with the sector mesh. Red spheres represent Lagrangian parcels. Black arrows indicate the velocity vectors and the size of the arrow tip is proportional to the velocity magnitude.

With the narrow hole drill angle and close periphery between plumes, multi-hole GDI spray usually features strong plume-to-plume interaction, and spray collapse can happen under certain conditions where individual plumes are attracted to each other or even merge into a single plume.33-35 The axial velocity measurement for the ECN Spray G injector at different ambient temperatures and densities are presented in Figure 7 and Figure 8 by solid lines, respectively. A trend of spray collapse is indicated by reduction in the recirculation motion and increase in the downward motion at increased ambient temperatures and densities. The CFD prediction with the full mesh, as shown by the dash lines, captures the trend qualitatively, but with significant deviation from the measurements for the strong collapse conditions. It should be noted that a plume angle of 33° was used for all the simulations, and it was reported that the plume direction varies during the injection event, and also changes considerably with ambient condition.33 To illustrate the effect of plume angle direction, the result at 800 K using a plume direction of 28°, which is the measured value at the end of injection at that condition,33 is also presented in Figure 7 by the dash dot line, and shows improved agreement over the baseline case. However, further model improvement is needed to capture the behavior of strong collapse for the current model, which has also been seen in other state-of-art Lagrangian spray modeling work.31 One possible solution would be to couple the spray simulations with in-nozzle simulations36,37 to provide more detailed boundary conditions at the nozzle outlet. Recent experimental study38 has shown that injectors with nominally identical geometries but different 10


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manufacturing methods show completely different behavior of spray collapse, which shed lights on the importance of internal nozzle flow on the external spray development, especially when a counter-bore design is used where the ambient gas can interact with the fuel.

Figure 7. Axial velocity on the centerline 15 mm downstream of the injector tip for different ambient temperatures. Solid lines are the PIV measurements. Dash lines are model predictions with the full mesh. Dash dot line is model prediction using 28˚ plume angle.

Figure 8. Axial velocity on the centerline 15 mm downstream of the injector tip for different ambient densities. Solid lines are the PIV measurements. Dash lines are model predictions with the full mesh.

3.2. GM GDI Optimization of the injection strategy in engines using CFD tools requires the spray model to be predictive across a wide range of in-cylinder conditions, covering from cold start, early injection during the intake stroke, to late injection for mixture stratification. While further model development is needed for the prediction of spray collapse, validation under a wide range of conditions with no or slight collapse is still challenging and is a better indication that the key underlying physics of spray vaporization are being correctly modeled, compared to validation at a single condition where a good result can usually be achieved by optimizing model constants. In this section, the EP model is validated against experiments by Parrish at GM13 at 18 operating conditions, as 11


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shown in Figure 9. Temperature varies from 400 K to 900 K under three ambient densities, with no strong spray collapse observed at all conditions. The GDI nozzle used here is also an eight-hole counter-bore injector, similar to the ECN Spray G injector, but has a larger L/D ratio of 1.8 and narrower plume direction of 25°. The sector mesh was used in this section due to its consistent performance to the full mesh as seen in last section and its better computational efficiency. The injection pressure was maintained at 20 MPa with 766 μs injection duration. The fuel temperature was 363 K. Since 𝐶𝜃 is negatively correlated with L/D ratio,18 a smaller value of 0.6 was used for 𝐶𝜃 for the GM injector under all conditions, which was determined by best match of the liquid length at 6 kg/m3, 700 K. All the other model details were kept the same as for the Spray G simulation setup, and also unchanged across the different conditions in this section.

Figure 9. Operating conditions for GM GDI experiments. Black squares: ambient density at 3 kg/m3; Red circles: 6 kg/m3; blue triangles: 9 kg/m3.

Figure 10, Figure 11, and Figure 12 compare the predictions of vapor and liquid envelopes against the experimental measurements at ambient temperatures of 500 K, 700 K and 900K, respectively. For each ambient temperature, three ambient densities are presented. For each condition, the results are shown at 0.5 ms, 1.0 ms and 1.5 ms ASI, with the experimental results on the left and the simulation results on the right. For the experimental line-of-sight measurements, green and red lines represent the boundaries of the vapor and liquid envelopes, respectively, while the black dash lines mark the spray included angle. For the CFD results, white clouds represent iso-volumes where the vapor mass fraction is larger than 0.1%, and red clouds represent isovolumes where the liquid volume fraction is larger than 0.01%. Since the sector mesh was used in this section, the simulation result of a single plume is replicated and rotated to form an eight-plume image for comparison 12


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with experiment. As can be seen, the shapes and projected areas of vapor plumes and liquid jets are well predicted by the model for most of the time instants and operating conditions.

Figure 10. Comparisons of experiment and simulations for liquid and vapor envelopes at 500 K conditions. White cloud: iso-surface of 0.1% vapor mass fraction. Red cloud: iso-surface of 0.01% liquid volume fraction.

Figure 11. Comparisons of experiment and simulations for liquid and vapor envelopes at 700 K conditions. Similar to Figure 10.

It is observed in the experimental measurement that as ambient temperature and density increase, the liquid jet penetrate slower and evaporate faster with decreased liquid residence time. This trend is captured in current CFD simulations, and is also in agreement with the characteristics of mixing-controlled sprays. Higher ambient temperature leads to higher internal energy per unit gas entrainment, while higher ambient density results in a wider spray cone angle as indicated in Equation (5) and subsequently a faster entrainment rate. Both of these two factors contribute to a higher evaporation rate in a mixing-limited condition. It is noted that while the liquid

13


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jet varies significantly with both ambient temperature and density, the evolution of vapor plume is only sensitive to the ambient density and much less affected by the ambient temperature.

Figure 12. Comparisons of experiment and simulations for liquid and vapor envelopes at 900 K conditions. Similar to Figure 10.

Figure 13. Liquid (a, b, c) and vapor (d, e, f) penetrations at 500 K, 700 K, and 900 K ambient temperatures, respectively. Black, red, and blue lines are results at 3, 6, and 9 kg/m3 ambient densities, respectively. Solid lines are experiments, and dash lines are CFD predictions.

More quantitative comparison for the vapor and liquid penetrations are presented in Figure 13, in which the experimental measurements are shown by the solid lines, and the CFD predictions are shown by the dash lines, 14


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with line colors indicating the different ambient densities. Consistent with Figure 10, Figure 11, and Figure 12, the prediction of transient vapor penetration is seen to match well with the experiment results with deviation less than 5% even at 3.5 ms ASI. A quasi-steady state of the liquid length can be found at high ambient temperature and high ambient density conditions as indicated by the plateau region in the liquid penetration profiles. However, the injection events studied here are considered to be mostly transient, especially at low ambient temperature and low ambient density that a quasi-steady state is not reached for such a short injection duration. It is seen that the transient evolution of the short injection is captured by the CFD simulations very well in terms of predictions of liquid length profiles, although the Liquid-Jet model used in the current modeling approach was initially developed for predicting quasi-steady fuel injection with long duration.

Figure 14. Maximum liquid penetrations. Black, red, and blue lines are results at 3, 6, and 9 kg/m3 ambient densities, respectively. Solid symbol lines are experiments, and open symbol lines are CFD predictions.

The maximum liquid length is plotted in Figure 14, with experimental data by the solid symbol lines and model predictions by the open symbol lines, which agree very well considering the wide range of tested conditions. Large error of model predictions is seen at low ambient density and temperature conditions, i.e. low ambient pressure conditions. This is possibly attributed to the accuracy in the prediction of spray cone angle θ. Particularly, the effect of cavitation is not accounted for in the current model, which is likely to affect 𝐶𝜃 in Equation (5).39 The cavitation number K, defined as 𝐾 = (𝑃𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛 ― 𝑃𝑎𝑚𝑏𝑖𝑒𝑛𝑡) (𝑃𝑎𝑚𝑏𝑖𝑒𝑛𝑡 ― 𝑃𝑣𝑎𝑝𝑜𝑟), is estimated to vary from 7.5 to 70.4 for the studied cases using 𝑃𝑣𝑎𝑝𝑜𝑟 of 0.78 bar for iso-octane at 363 K, indicating a higher cavitation propensity and possibly wider cone angle at the low ambient pressure condition. Therefore, inclusion of cavitation effect could further improve the prediction in liquid length at low ambient 15


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pressure conditions. Nonetheless, the current form of the EP spray model provides satisfying results under most of the engine-relevant conditions, especially for the vapor phase that is critical for accuracy in simulations of engine combustion.

3.3. Multi-component gasoline surrogate simulation Gasoline and diesel fuels are complex mixtures that consist of a number of paraffins, cycloalkanes and olefins, etc. While a single component surrogate is sometimes used in experimental and numerical research of IC engine combustion for simplicity, the use of a multi-component surrogate that considers both light-end and heavy-end components is favored to represent the complicated vaporization behavior of gasoline and diesel fuels. Because the present phase equilibrium solver is capable of dealing with multi-component mixtures, the EP spray model can readily be extended to simulate multi-component fuel injection. To demonstrate this ability, a 10-component fuel surrogate for RON 91 gasoline40 was used for the ECN Spray G condition. The surrogate composition was obtained by a novel methodology based on local optimization and sensitivity analysis with objectives of matching the distillation curve, mass fraction of family group (saturates, aromatics and olefins), hydrogen-to-carbon ratio, Cetane Number, and Research Octane Number. All the simulation setups described above for the ECN Spray G with single component fuel were unchanged except for the fuel composition. The composition of the multi-component surrogate is listed in Table 1, along with properties for each species. A simulation with an elevated ambient temperature at 800 K was also performed to investigate the temperature effect on spray evaporation and vapor distribution. Figure 15 (a) shows the 2D distribution of mixture fraction and mass fractions for selected components, which are iso-pentane, a light-end species with the lowest boiling temperature, n-heptane, a species with moderate boiling temperature and m-cymene, an aromatic and the least volatile species in the surrogate model, at 0.3 ms and 0.7 ms ASI. A small portion of vapor is seen to travel along the injector centerline at 0.3 ms and disappears at later time. This is because the widened spray cone angle during the initial transient stage, as illustrated in Figure 1, results in mass and momentum transferred to the center region. The vapor distribution patterns are found to be significantly different depending on the fuel properties at both times. M-cymene shows the most distinct distribution and concentrates in a horseshoe shaped region at the jet head, while the other two 16


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Energy & Fuels

species, as well as mixture fraction, present a normal distribution in the transverse direction with concentration peaks at the spray centerline. Iso-pentane concentrates more narrowly along the spray centerline compared to n-heptane, which has a distribution almost identical to the mixture fraction distribution. The vapor composition in mass fraction is shown in Figure 16 for all the components at three locations, as marked in Figure 15 (a) at 0.7 ms ASI. The components listed on the x-axis from left to right are in the order from low to high boiling temperature. Similar to the observation in the 2D contours, the light-end species (iso-pentane, 1-hexene, isoheptane) concentrate in the upstream region (Location 1) and downstream center of the plume (Location 2) due to their quick evaporation after being injected, even in these relatively colder regions. The heavy-end species (m-xylene, 2,2,3,3 tetramethylhexane, n-decane, m-cymene) dominate the jet head periphery (Location 3) due to the locally high temperature from ambient gas entrainment. The remaining species (n-heptane, iso-octane, toluene) show almost unchanged mass fractions throughout the spray, which is attributed to their moderate volatility. Table 1. 10-component surrogate for 91 RON gasoline.40

Component name

Chemical formula

Molecular weight (g/mol)

Boiling temperature at 1 bar (K)

Critical temperature (K)

Critical pressure (bar)

Mass fraction (-)

n-heptane

n-C7H16

100

371.6

540.2

27.4

0.05921

n-decane

n-C10H22

142

447.2

617.7

21.1

0.06023

2,2,3,3 tetramethylhexane

C10H22

142

413.5

623

25.1

0.02935

iso-pentane

i-C5H12

72

301.2

460.4

33.8

0.31702

iso-heptane

i-C7H16

100

363.2

530.4

27.4

0.13954

iso-octane

i-C8H18

114

372.5

543.8

25.7

0.09062

toluene

C7H8

92

383.8

591.8

41.1

0.09932

m-xylene

C8H10

106

412.2

617.1

35.4

0.07041

m-cymene

C10H14

134

448.2

657

29.3

0.10484

1-hexene

C6H12

84

336.2

504

32.1

0.02888

17


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(a) 573 K, 3.5 kg/m3 condition

(b) 800 K, 3.5 kg/m3 condition Figure 15. Distribution of mixture fraction and mass fraction for iso-pentane, n-heptane and m-cymene at 0.3 and 0.7 ms ASI, respectively.

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Energy & Fuels

The 2D distribution of mixture fraction and mass fraction of selected species for 800 K ambient temperature condition is shown in Figure 15 (b). The ambient density is kept at 3.5 kg/m3 by adjusting the chamber pressure. It is seen that the spray shape is similar to the prediction at the 573 K condition, meaning that the vapor penetration and dispersion are less sensitive to the ambient temperature, which is the same as the observation made in the iso-octane spray simulations in Figure 13. However, the ambient temperature is shown to play a bigger role in determining component evaporation and distribution details. As the ambient temperature increased and the extent of the cold region reduced, m-cymene presented a distribution pattern similar to the light-end species, instead of the horseshoe shape seen in Figure 15 (a). Thus, at elevated temperature, the vaporization process becomes less location dependent, and the vapor composition is more consistent throughout the spray and is close to the fuel surrogate composition.

Figure 16. Local vapor composition at three positions as marked in Figure 15 (a) for 573 K, 3.5 kg/m3 condition at 0.7 ms ASI.

Figure 17. Global vapor composition in mass fraction as function of time for iso-pentane, n-hpetane and m-cymene. Solid line is the 573 K, 3.5 kg/m3 condition and the dash line is the 800 K, 3.5 kg/m3 condition.

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The impact of fuel volatility and ambient temperature on evaporation not only affects the spatial distribution, but is also reflected in the transient profile, as presented in Figure 17, where the global mass fractions for the selected species are plotted as a function of time. At the beginning, the mass fractions of iso-pentane and mcymene in the vapor phase start at values above and below their mass fractions in the fuel surrogate, respectively. Then the vapor composition gradually approach steady values at later stages as the fuel is fully vaporized, which are also their mass fractions in the fuel surrogate. This transient behavior can be mitigated by increasing the ambient temperature, as illustrated by the comparison of the solid and dash lines, and this is attributed to the overall faster evaporation at the high ambient temperature condition.

4. Summary and Conclusions In this study an Equilibrium Phase (EP) spray model, which was previously developed for diesel engine CFD simulation based on mixing-controlled jet theory and local phase equilibrium assumption, was applied to GDI spray simulations. In this approach, an Eulerian liquid phase is introduced into the LDEF framework. A Liquid-Jet model is used to govern the conversion of liquid from Lagrangian to Eulerian phase. A detailed phase equilibrium solver is adopted for the phase change calculation without the need to model spray non-equilibrium processes, such as drop breakup, collision and coalescence, and finite rate vaporization. The model was validated extensively for two GDI injectors under ambient conditions from 3 kg/m3 to 9 kg/m3 and 400 K to 900 K, which covers the situations of interest to GDI engines from cold start, early injection, to late injection near TDC for charge stratification. The model shows good accuracy in its vapor penetrations and plume envelope predictions for all the simulated conditions, as well as in liquid penetrations for most of the conditions from medium to high ambient density. The prediction of the liquid length could potentially be improved even further by employing a comprehensive spray cone angle model that accounts for effects of innozzle flow and cavitation at low ambient pressure conditions, etc. Moreover, the EP model can also be used for flashing jets, provided that a model is available to give the correct spray cone angle at the nozzle exit, which accounts for the near nozzle expansion due to flashing. The results in this study indicate that the GDI spray vaporization process is also dominated by turbulent mixing under most of the engine-relevant conditions.

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Compared to diesel simulations where a relative coarse mesh can provide satisfactory prediction of the spray process, use of the EP model for GDI spray simulation requires the near-nozzle region to be appropriately spatially resolved to accurately capture the velocity field distribution due to the narrow included angle and close periphery between the plumes of GDI injectors. Further improvement including modelling the in-nozzle flow is needed to capture the strong collapse behaviour, which has also been noted in studies using standard Lagrangian spray models. A 10-component gasoline fuel surrogate was applied in the present simulations to demonstrate the capability of the present EP model to simulate multi-component fuels. The component distribution is shown to be sensitive to the species properties, in that the light-end species are found to dominate both the spatial distribution upstream in the cold region of the spray and the early stage of the transient global vapor composition, while the heavyend species vapor are located at the plume downstream periphery, hot region. The temporal and spatial vapor distribution is less dependent on fuel properties at elevated ambient temperatures due to the overall fast evaporation. The sensitivity of the vaporization process to fuel properties and ambient temperature as illustrated by the EP model indicates that there is significant impact on charge stratification, and thus on ignition and emission formation in the GDI engine combustion processes.

Acknowledgements This work was finished during the Ph.D project of the corresponding author, Yue, Z., at the University of Wisconsin-Madison. The authors would like to acknowledge the financial support provided by the China Scholarship Council (CSC). The authors would like to acknowledge Daniel J. Duke, Alan L. Kastengren, Katarzyna E. Matusik, and Christopher F. Powell from Argonne National Laboratory to share the fuel density data for ECN Spray G. The authors are also thankful for support from ANSYS for use of EnSight software.

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(4) Su, T. F. Patterson MA, Reitz RD, Farrell PV. Experimental and numerical studies of high pressure multiple injection sprays. SAE technical paper, 1996, 960861. (5) Ricart, L. M.; Xin, J.; Bower, G. R.; Reitz, R. D. In-cylinder measurement and modeling of liquid fuel spray penetration in a heavy-duty diesel engine. SAE technical paper, 1997, 971591. (6) Beale, J. C.; Reitz, R. D. Modeling spray atomization with the Kelvin-Helmholtz/Rayleigh-Taylor hybrid model. Atomization Spray, 1999, 9, 623–650. (7) Som, S.; Aggarwal, S. K. Effects of primary breakup modeling on spray and combustion characteristics of compression ignition engines. Combust. Flame, 2010, 157, 1179–1193. (8) Van Dam, N.; Rutland, C. Adapting diesel large-eddy simulation spray models for direct-injection sparkignition applications. Int. J. Eng. Res. 2016, 17, 291–315. (9) Ra, Y.; Reitz, R. D. The application of a multicomponent vaporization model to gasoline direct injection engines. Int. J. Eng. Res. 2003, 4, 193-218. (10) Ra, Y.; Reitz, R. D. A vaporization model for discrete multi-component fuel sprays. Int. J. Multiph. Flow, 2009, 35, 101–117. (11) Perini, F.; Reitz, R. D. Improved atomization, collision and sub-grid scale momentum coupling models for transient vaporizing engine sprays. Int. J. Multiph. Flow, 2016, 79, 107–123. (12) Siebers, D. L. Scaling liquid-phase fuel penetration in diesel sprays based on mixing-limited vaporization. SAE Technical Paper, 1999, 1999-01-0528. (13) Parrish, S. E. Evaluation of Liquid and Vapor Penetration of Sprays from a Multi-Hole Gasoline Fuel Injector Operating Under Engine-Like Conditions. SAE Int. J. Eng. 2014, 7, 1017-1033. (14) Iyer, V. A.; Post, S. L.; Abraham, J. Is the liquid penetration in diesel sprays mixing controlled? P. Combust. Inst. 2000, 28, 1111–1118. (15) Matheis, J.; Hickel, S. Multi-component vapor-liquid equilibrium model for LES of high-pressure fuel injection and application to ECN Spray A. Int. J. Multiph. Flow, 2017, 99, 294–311. (16) Qiu, L.; Wang, Y.; Jiao, Q.; Wang, H.; Reitz, R. D. Development of a thermodynamically consistent, robust and efficient phase equilibrium solver and its validations. Fuel, 2014, 115, 1-16. (17) Yue, Z.; Reitz, R. D. An Equilibrium Phase (EP) spray model for high pressure fuel injection and engine combustion simulations. Int. J. Eng. Res. 2019, 20(2), 203-215. (18) Reitz, R. D.; Bracco, F. V. On the Dependence of the Spray Angle and Other Spray Parameters on Nozzle Design and Operating Conditions. SAE Technical Paper, 1979, 790494. (19) Amsden, A. A. KIVA-3V, Release 2: Improvements to KIVA- 3v. Report No. LA- UR99-915, 1999. (20) Abani, N.; Reitz, R. D. Unsteady turbulent round jets and vortex motion. Phys. Fluids, 2007, 19, 125102. (21) Wang, B.-L.; Miles, P. C.; Reitz, R. D.; Han, Z.; Petersen, B. Assessment of RNG Turbulence Modeling and the Development of a Generalized RNG Closure Model. SAE Technical Paper, 2011, 2011-01-0829. (22) Perini, F.; Zha, K.; Busch, S.; Reitz, R. D. Comparison of Linear, Non-Linear and Generalized RNGBased k-epsilon Models for Turbulent Diesel Engine Flows. SAE Technical Paper, 2017, 2017-01-0561. (23) Michelsen, M. L. The Isothermal Flash Problem .1. Stability. Fluid Phase Equilibr. 1982, 9, 1-19. (24) Rachford Jr., H. H.; Rice, J. D. Procedure for Use of Electronic Digital Computers in Calculating Flash Vaporization Hydrocarbon Equilibrium. J. Pet. Technol. 1952, 4, 1952. (25) Qiu, L.; Reitz, R. D. Simulation of supercritical fuel injection with condensation. Int. J. Heat Mass Tran. 2014, 79, 1070-1086. (26) Qiu L.; Reitz, R. D. Investigation fuel condensation processes in low temperature combustion engines. J. Eng. Gas Turb. Power, 2014, 137, 101506. 22


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Application of an Equilibrium Phase (EP) Spray Model to Multi

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