A Computational Investigation of Two-Stage Combustion in a Light-Duty Engine

A Computational Investigation of Two-Stage Combustion in a Light-Duty Engine Sage L. Kokjohn and Rolf D. Reitz University of Wisconsin-Madison, Engine Research Center Abstract. The objective of this investigation is to optimize light-duty diesel engine operating parameters using Adaptive Injection Strategies (AIS) for optimal fuel preparation. A multi-dimensional Computational Fluid Dynamics (CFD) code with detailed chemistry, the KIVA-CHEMKIN code, is employed and a Multi-Objective Genetic Algorithm (MOGA) is used to study a Two-Stage Combustion (TSC) concept. The combustion process is considered at a light load operating condition (nominal IMEP of. bar and high speed (2 rev/min)), and two combustion modes are combined in this concept. The first stage is ideally Homogeneous Charge Compression Ignition (HCCI) combustion and the second stage is diffusion combustion under high temperature and low oxygen concentration conditions. Available experimental data on a 1.9L single-cylinder research engine is used for model validation. The results show that the computations are able to adequately predict the emissions trends and quantities over an injection timing sweep for the Partially Premixed Compression Ignition (PCCI) cases investigated. A preliminary investigation was performed to gain an understanding of two-stage combustion in the light duty engine. At this condition it was found that pure HCCI combustion could yield very low engine out emissions, but extreme pressure rise rates would lead to excessive combustion noise. A multi-dimensional optimization code, NSGAII, was used for optimization of six objectives (NOx, soot, CO, HC, ISFC, and peak PRR) by adjusting four parameters (boost pressure, EGR rate, fraction of premixed fuel, and start of late injection timing). The optimization has shown that two-stage combustion is a feasible concept for noise reduction while maintaining reasonable emissions and fuel consumption. A Pareto solution yielding a peak pressure rise rate of 4.3 bar/deg was found using a high EGR rate (4%), relatively low IVC pressure (1.74 bar), premixing 36% of the total fuel, and injecting the remainder of the fuel at 2.9 degrees after TDC. Introduction Since its introduction in the late 18 s, the diesel engine has been utilized in almost every aspect of modern life, from transportation to energy generation to food production. Several emissions are of prime concern for air pollution: nitrogen oxides (NOx), carbon monoxide (CO), unburned hydrocarbons (HC), and particulates (soot). These pollutants are damaging to the environment and human health. Reduction of these harmful pollutants while maintaining fuel economy has been a primary driving factor for internal combustion engine research in recent years. Homogeneous Charge Compression Ignition (HCCI) and Premixed Charge Compression Ignition (PCCI) concepts have been shown as promising techniques for simultaneous NOx and soot reduction [1-3]. However, a major concern for light duty engines is noise generated during the combustion process. HCCI combustion tends to produce high rates of pressure rise and therefore can result in higher combustion noise than conventional diesel operation. Sun [4, ] has shown the possibility of emissions reduction using a Two-Stage combustion concept in a heavy-duty diesel engine. The first stage is HCCI combustion and the second stage is diffusion combustion under high temperature and low oxygen concentration conditions. Because only a fraction of the total fuel is burnt in pure HCCI combustion it may be possible to use the TSC concept for noise reduction. This study aims to apply the TSC concept to a light-duty diesel engine in order to minimize pollutant emissions and to improve fuel economy while maintaining low engine noise. A multi-dimensional CFD code with detailed chemistry, the KIVA-CHEMKIN code, was employed in this investigation. Model validation was performed using experimental data of Opat et al. [3]. After model validation, a preliminary investigation was performed to gain a basic understanding of the two-stage combustion concept in a light-duty diesel engine. With a basic understanding of two-stage combustion, a multi-objective genetic algorithm (MOGA) was used to optimize engine parameters to minimize pollutants, engine noise, and fuel consumption. Computational Model Computations were performed using the KIVA-3v release 2 code [6] with improvements to many physical and chemistry models developed at the ERC [7-11]. The KIVA-3v code was coupled with the CHEMKIN II solver for 1

detailed chemistry calculations. A 34 species and 74 reaction mechanism for n-heptane [12] was used to simulate diesel fuel chemistry. Droplet breakup was modeled using a hybrid Kelvin Helmholtz (KH) Rayleigh Taylor (RT) model [9]. Gasjet theory was employed to model the relative velocity between the droplets and gas phase in the near nozzle region in order to reduce grid dependency [7, 8]. Turbulence was modeled using the RNG k-ε model [1]. An unsteady droplet vaporization model considering droplet temperatures ranging from flash boiling to normal evaporation was employed [11]. The droplet collision model is based on O Rourke s model; however, a radius of influence method is used to determine the possible collision partners to further remove mesh dependency [7]. Parameter optimization was performed using a multi-objective genetic algorithm (MOGA). Shi [13] has shown that the Nondominated Sorting Genetic Algorithm (NSGAII) proposed by Deb et al. [14] performs well in engine optimizations; therefore, NSGAII was selected as the optimization tool for this study. A multi-objective approach was favored over the use of a merit function based single-objective optimization scheme in order to generate a set of solutions from which the engine designer may choose an in-cylinder strategy which best accompanies the available aftertreatment system. The computational grid used in this study was a 1.4º sector mesh which represents a single nozzle hole of the 7-hole Bosch injector used in the engine. Figure 1 shows the computational mesh. To allow the use of a sector mesh consisting of a single injector nozzle hole and in order to minimize computational expense, the early injection was not modeled, but instead it was assumed that a perfectly homogeneous charge was created at IVC. Sun [] has shown this assumption yields similar results to a full 3d simulation of the early injection event. Model Validation Figure 1 Computational grid with crevice volume, shown at TDC. The grid is a 1.4 degree sector consisting of 11, cells at BDC. Engine Specifications The engine used in this study was a single cylinder version of the GM 1.9 L engine with specifications and operating conditions given in Table 1. Engine experiments performed by Opat et al. [3] were used for computational model validation. The experiments were conducted using a single injection PCCI approach at the same operating condition investigated in the present study (. bar nominal IMEP and 2 rev/min). To achieve PCCI combustion, Opat utilized an early injection to attain adequate mixing prior to the start of combustion and a high EGR rate (~6%) to suppress in-cylinder temperatures. Table 1 engine specifications and operating condition Engine type GM 1.9 L Bore x Stroke (cm) 8.2 x 9.4 Connecting Rod Length (cm) 16.1 Displacement (L).4774 Compression Ratio 16.:1 Swirl Ratio 2.2 Injection Pressure [bar] 86 Included Angle [ ] 1 Number of holes 7 Nozzle hole diameter [µm] 141 Engine speed (rev/min) 2 IMEP (bar). Fuel flow rate (kg/hr).89 EGR rate (%) 6 IVC Temperature (K) 3 IVC Pressure (bar) 1.91 Cylinder Pressure [kpa] 12 1 8 6 4 2 Experiment Simulation SOI -29.2 datdc - -4-3 -2-1 1 2 3 4 1 12 Crank [degrees] Figure 2 Comparisons of computed and measured cylinder pressure and heat release rate. The start of injection was 29.2 degrees before TDC. 2 9 6 3 Heat Release Rate [J/deg]

Model validation was performed over a start of injection (SOI) sweep from 34.2 to 16.2 deg before TDC. Figure 2 shows the cylinder pressure and heat release rate comparison from a representative case with an SOI of 29.2 degrees before TDC. The location of the cool flame and main heat release is predicted very accurately; however, the simulation predicts slightly higher cylinder pressure than the experiment. This difference in cylinder pressure can be attributed to an over-prediction of the evaporation process during the injection event. Figure 3 shows comparisons of predicted and measured soot and NOx emissions. The simulation soot results do not show as much sensitivity to start of injection timing as the experimental data. Nevertheless, the soot trend is predicted reasonably well for all but the earliest injection timings. At an SOI of 34 degrees before TDC the experiments show a sharp increase in soot levels; however, the simulation results show a flattening out of the soot versus SOI curve. The simulation captures all of the NOx trends exhibited by the experimental data; however the results show the simulation slightly under predicts NOx for all injection timings. Figure 4 shows comparisons of measured and predicted CO and HC emissions. The CO trend shows good agreement for injection timings later than 28.2 degrees before TDC. As SOI is further advanced the experimental data shows an increase in CO levels while the simulation shows a flattening off and then a decrease in CO levels. Significant wall impingement is observed as the SOI is advanced beyond 3 degrees before TDC. Therefore, the discrepancy between the simulation and experimental results may be due to limitations of the wall film model. Because the present investigations were primarily concerned with cases with little wall film, this discrepancy is not likely to significantly impact the results of this study. HC emissions are over-predicted for a majority of the injection timings considered. Similar to CO, a discrepancy between simulation and experimental HC trends becomes present as the SOI is advanced to very early injection timings. NOx [g/kgf].8.6.4.2 Experiment Simulation 16 18 2 22 24 26 28 3 32 34 Start of Injection [deg. before TDC].1.1.. Soot [g/kgf] HC [g/kgf] 3 2 2 1 1 Experiment Simulation 16 18 2 22 24 26 28 3 32 34 Start of Injection [deg. before TDC] 3 2 2 1 1 CO [g/kgf] Figure 3 Tailpipe NOx and Soot emissions computed by KIVA compared with measured values over an injection timing sweep. Figure 4 Tailpipe HC and CO emissions computed by KIVA compared with measured values over an injection timing sweep. Simulation Results and Discussion This section consists of two parts. In the first part an investigation is performed to determine if two-stage combustion is a feasible means of lowering combustion noise while maintaining reasonable emissions. In the second part a multi-objective genetic algorithm is employed to optimize engine parameters in a two-stage combustion operating condition. Preliminary Investigation A preliminary investigation was performed to gain an understanding of two-stage combustion in the present light-duty diesel engine. Boost, IVC timing, EGR, start of late injection timing (SOLI), and total fueling were held constant at 1.91 bar, 132 ºBTDC, %, top dead center, and.89 kg/hr respectively. The fraction of fuel participating in HCCI combustion was varied from % (diesel combustion) to 1% (pure HCCI combustion). Figure shows cylinder pressure traces for each case. As the quantity of fuel participating in HCCI combustion was decreased from pure HCCI combustion, a decrease in peak cylinder pressure was observed. Decreasing the quantity of premixed fuel also resulted in a retardation of the first stage combustion phasing. 3

Cylinder Pressure [MPa] CO [g/kgf] 14 12 1 8 6 4 2 Diesel 1% 2% 3% 4% % 6% 7% 8% 9% HCCI - -4-3 -2-1 1 2 3 4 Crank [degrees] Figure Cylinder pressure for each case. The percentages shown are the fraction of total fuel premixed at IVC. 12 1 8 6 4 2 Increasing premix fraction CO Eff 1..98.96.94.92.9 Diesel 1 2 3 4 6 7 8 9 1 HCCI Fraction of Fuel Participating in HCCI Combustion [%] Combustion Efficiency [-] Figure 7 Effects of fraction of fuel premixed at IVC on CO and combustion efficiency. NOx and HC [g/kgf] 6 4 3 2 1 NOx HC PRR Diesel 1 2 3 4 6 7 8 9 1 HCCI Fraction of Fuel Participating in HCCI Combustion [%] Figure 6 Effects of fraction of fuel premixed at IVC on NOx, HC, and peak pressure rise rate. Heat Release Rate [J/deg] 3 2 2 1 1 Cool Flame Heat Release HCCI Heat Release Late Injection Heat Release -2-2 -1-1 - 1 1 Crank [degrees] Figure 8 Heat release rate as a function of crank angle for each case. The percentages shown are the fraction of total fuel premixed at IVC. 3 2 2 1 1 Peak Pressure Rise Rate [bar/deg] Diesel 1% 2% 3% 4% % 6% 7% 8% 9% HCCI Figure 6 shows the corresponding NOx, HC, and maximum pressure rise rates for each case and Figure 7 shows CO and combustion efficiency. Soot is not presented because soot was very low for all cases. The HCCI case shows the lowest NOx and HC emissions; however, the pressure rise rate is much greater than the target of. bar/deg. As fuel is removed from the HCCI combustion event and introduced to the cylinder via a late injection, the combustion phasing shifts towards TDC, a decrease in peak pressure rise rate is observed, NOx and CO increase dramatically, and HC increases slightly. As greater than % of the total fuel is removed from the HCCI event and placed in the late injection, combustion is delayed until after TDC, an increase in pressure rise rate is observed, NOx remains almost constant, while HC and CO show an initial increase, then rapid decrease. The increase in pressure rise rate as the fraction of fuel participating in HCCI combustion is decreased beyond % is due to ignition delay of the late injection. Figure 8 shows the heat release rates for each case. When greater than % of the total fuel participates in HCCI combustion a cool flame heat release is observed followed by premixed heat release of the first stage fuel and a late injection diffusion burn near TDC. As the fraction of fuel participating in HCCI combustion is decreased past % very little cool flame heat release is observed and no first stage heat release is present. The ignition delay of the late injection increases as the fraction of fuel participating in HCCI combustion decreases. The increase in ignition delay allows significant time for mixing, resulting in rapid heat release and high pressure rise rates. 4

Late Injection Optimization The previous investigation showed that while pure HCCI combustion yields extremely low emissions and high efficiency, the pressure rise rate is excessive and engine noise would be problematic. It has also been shown that pressure rise rates can be reduced to acceptable levels by utilizing a two-stage combustion strategy [4, ]; however, engine out emissions were much greater than the pure HCCI case. Accordingly, the present study employed a Multi-Objective Genetic Algorithm (MOGA) to optimize the engine parameters to seek a set of solutions which simultaneously result in low emissions, low noise, and high efficiency. Optimization Parameters The set of optimization parameters and their ranges are shown in Table 2. The late injection timing range was selected based on the findings of Sun [] where the optimum injection timing occurred at 17 degrees ATDC. The range of fraction of fuel premixed at IVC was selected such that the minimum injected fuel would be ~1% of the total fueling at the baseline condition. This value was chosen to yield a result that could be achieved with existing hardware. Throughout the optimization the total trapped mass was held constant by varying the intake valve closure timing with boost pressure and EGR. Optimization Results The four engine parameters of Table 2 were optimized using the NSGAII code with the aim of minimizing six objectives: NOx, soot, CO, HC, peak pressure rise rate, and ISFC. As the optimization progressed the location of the Pareto front was monitored. The optimization was said to have converged after 1 generations because the Pareto front had stopped making significant advances. Each generation consisted of 24 members, giving a total of 36 runs. Each run took about 1 hours on a 3. GHz AMD Athalon processor and each generation was processed in parallel. Because the optimization contained six unique objectives, the Pareto front contains the set of solutions which minimizes these six objectives differently. The overall Pareto front consisted of 171 designs with varying NOx, soot, HC, CO, ISFC, and peak pressure rise rate (PRR) performance. Obviously, the visualization of six dimensional space is difficult; therefore, the results are presented on just two Pareto fronts, as shown in Figure 9 (a) and (b). Furthermore, emissions are presented on brake specific basis; thus, ISFC is implicitly included in the figures. Note that stray values (e.g. unacceptable emissions results) have been removed from the plots for clarity. Five cases are selected from the overall Pareto front, which each optimizes the competing parameters differently, shown in Table 3. The net indicated work used to determine ISFC was calculated as the work from IVC to EVO minus the work required for a compressor operating with an isentropic efficiency of.8 to compress air from 1 atm to the IVC pressure. The baseline case is a low temperature combustion PCCI case utilizing very high EGR levels. This case is adapted from the cases presented by Opat et al [3]. The initial conditions of the baseline case have been modified slightly from the case of Opat in order to permit a direct comparison with the optimization results (i.e. the initial composition at IVC was specified as N 2, O 2, CO 2, and H 2 O only). Peak PRR [bar/deg] 3 3 2 2 1 1 2 4 NOx [g/kw-hr] 6 8 1 All Citizens Pareto Citizens Selected Cases...1.1.2.2 Soot [g/kw-hr] (a) (b) Figure 9 Pareto Solutions for the optimization of premixed fuel fraction, start of late injection timing, EGR rate, and boost pressure. (a) All Pareto solutions and citizens shown in NOx, soot, and peak PRR space. (b) All Pareto solutions shown in HC, CO, and peak PRR space. The cases selected for further discussion are shown in green (see Table 3). Peak PRR [bar/deg] 3 3 2 2 1 1 Table 2 Optimization parameters and ranges SOLI (deg. ATDC) -1. ~ 2. IVC Pressure (bar) 1.7 ~ 3. Fraction of fuel premixed at IVC (-).1 ~.9 EGR rate (%) ~ 6 1 HC [g/kw-hr] 1 2 All Citizens Pareto Citizens Selected Cases 1 2 3 CO [g/kw-hr] 4

Table 3 Parameters and results of selected cases from the overall Pareto front and parameters for the baseline case. SOLI Boost Frac EGR IVC NOx Soot HC CO ISFC PRR Case (ºATDC) (bar) (-) (%) (ºATDC) (g/kgf) (g/kgf) (g/kgf) (g/kgf) (g/kw-hr) (bar/deg) Low ISFC -7.87 2.7.9 1-96.7.73 1.E-4 43 66 179 11.2 low NOx -9.23 2.4.9 43-97.6.2 1.E-4 81 367 27. Low PRR 2.89 1.74.36 4-11.1.73 6.8E-2 6 173 228 4.3 Low HC -3.4 1.78.88 3-14.7.97 6.6E-3 31 34 2 12.3 Low CO 2.89 1.74.89 3-11.1.2 9.9E-3 33 32 23 12. Baseline 28.2 1.92 6-13.7 2.E-2 23 118 2 7.4 Figure 1 shows the pressure traces and heat release rates for each of the selected cases. The low ISFC case has a high boost pressure, resulting in late intake valve closure, high fraction of premixed fuel, and relatively early start of injection timing. The late intake valve closure reduces the duration of the compression process and decreases the temperature in the compression stroke, which delays the start of combustion until TDC, resulting in a minimum in compression work. The injection timing is ~ 8 degrees before TDC with a duration of only 2.7 CAd; consequentially the fuel and air are very well mixed prior to the start of combustion. The high quantity of premixed fuel and low EGR rate of the low ISFC case result in very rapid heat release, causing a high peak pressure rise rate (~11 bar/deg). Although the low EGR rate resulted in high temperatures near the spray plume, the remainder of the combustion process occurred at very lean premixed conditions (equivalence ratio of ~.24), resulting in combustion temperatures below 2 K for most of the domain. Thus, NOx levels remained reasonably low. The low NOx case has very similar parameters as the low ISFC case, except that the EGR rate is increased in order to suppress in-cylinder temperatures. The increased EGR rate of the low NOx case causes combustion to be further retarded after TDC compared to the low ISFC case. The delay in combustion causes combustion efficiency to suffer, resulting in higher HC and CO emissions. The low PRR case has 36% of fuel Cylinder Pressure [MPa] Heat Release Rate [J/deg] 12 1 8 6 4 2 14 12 1 8 6 4 2 Low NOx Low HC Low CO Low ISFC Low PRR Baseline - -4-3 -2-1 1 2 3 4 Crank [degrees] Figure 1 Cylinder pressure and heat release rates for each of the selected Pareto solutions and the baseline case. 6 premixed at IVC with the remainder injected shortly after TDC. The fuel which burns in the first stage combustion has a very slow heat release, resulting in a low pressure rise rate. The second stage heat release occurs around 1 degrees ATDC and is gradual enough to yield a maximum pressure rise rate of only 4.3 bar/deg. The low HC and low CO cases have very similar parameters and combustion characteristics. The high EGR rates and premixed fuel fractions of these cases maintained combustion temperatures below that of traditional diesel combustion to maintain reasonable NOx levels. However, the low boost pressure requires a very early IVC timing; thus increasing the temperature in the compression stroke, resulting in early combustion phasing and higher temperatures than the other selected cases. The higher combustion temperatures allowed reduced HC and CO emissions compared to the other cases. Although these cases show reasonably low emissions and relatively low fuel consumption, the early combustion phasing resulted in excessive pressure rise rates. All of the selected cases show higher HC emissions than the baseline case. To understand the high HC levels of the Pareto solutions, fuel contours are presented for the baseline case, the

low HC case, and the low NOx case in Figure 11. From the fuel contours, it can be seen that unburnt fuel exists in the piston-liner crevice region. Because the optimization considered a perfectly premixed charge at IVC, fuel was dispersed throughout the computational domain, including into the crevice region. Temperatures in the crevice region remained low over the entire computation; therefore, this fuel remained unburnt and contributed to the HC emissions at the end of the cycle. From the spray visualization it is seen that significant quantities of liquid fuel droplets exist late in the cycle for the optimized cases and very little liquid fuel is present in the baseline case. The presence of liquid fuel late in the cycle indicates that the late injection may also be a major source of HC emissions. All of the selected cases aside from the low PRR case have premixed fuel quantities at or near the upper limit of the design space. This result suggests that a pure HCCI case may be the best solution. To investigate this hypothesis and as a limiting case, the low NOx, low HC, low CO, and low ISFC cases were repeated with the same parameters except with 1% of the fuel premixed at IVC. NOx and soot emissions were found to be very low for all the pure HCCI cases. HC and CO were reduced to approximately half of the values from the Pareto solutions, confirming that a significant portion of HC emissions were coming from the late injection. ISFC remained relatively constant except for the low NOx case were it was reduced by ~1%. Although the emissions results with pure HCCI are very promising, the peak pressure rise rate was increased substantially in all cases. Thus, the results of this investigation are consistent with the preliminary investigation and suggest that pure HCCI yields very low emissions levels, but is unable to produce acceptable pressure rise rates. Conclusions This investigation has explored two-stage combustion as a means of yielding low emissions and low combustion noise in a light duty engine operating at a part load condition. Model validation was performed and it was found that the models are able to qualitatively and quantitatively predict the emissions results at the operating condition investigated. A preliminary investigation was performed to gain an understanding of two-stage combustion in the light duty engine. At this condition, it was found that pure HCCI combustion could yield very low engine out emissions, but has extreme pressure rise rates that would lead to excessive combustion noise. As fuel was removed from the first stage combustion and placed in a late injection, the peak pressure rise rate was reduced; however, emissions and combustion efficiency suffered. The minimum pressure rise rate corresponds to a case where % of the total fuel is premixed, with the remaining fuel being burnt in a diffusion flame. As the quantity of premixed fuel is decreased beyond % the result is a longer ignition delay of the late injection and an increased peak pressure rise rate. A multi-dimensional optimization code, NSGAII, was used to optimize of six objectives (NOx, soot, CO, HC, ISFC, and peak PRR) by adjusting four parameters (boost pressure, EGR rate, fraction of premixed fuel, and start of late injection timing). The NSGAII code produced a set of Pareto solutions which each optimized the objectives in a different way. The results of the optimization were consistent with those of the preliminary investigation and suggest that high levels of premixed fuel can yield very low emissions. However, pressure rise rates for cases with very high levels of premixed fuel were excessive. The optimization has shown that two-stage combustion is a feasible concept for noise reduction while maintaining reasonable emissions and fuel consumption. A low NOx and soot Pareto solution yielding a peak pressure rise rate of only 4.3 bar/deg was found using a high EGR rate (4%), low IVC pressure (1.74 bar), premixing 36% of the total fuel, and injecting the remainder of the fuel at 2.9 degrees after TDC. However, these improvements came at the expense of increased ISFC and CO emissions. Acknowledgements Figure 11 Fuel mass fraction contours and liquid droplets for two selected cases and the baseline case. Financial support from the US Department of Energy (DOE) HCCI contract # DE-FC4-2AL67612 and from the Engine Research Center s Diesel Emissions Reduction Consortium (DERC) member companies is gratefully acknowledged. 7

References [1] G. Bression, D. Soleri, S. Savy, S. Dehoux, D. Azoulay, H. Ben-Hadj Hamouda, L. Doradoux, N. Guerrassi, and N. Lawrence, "A Study of Methods to Lower HC and CO Emissions in Diesel HCCI," SAE Technical Paper 28-1-34, 28. [2] W. L. Hardy and R. D. Reitz, "A Study of the Effects of High EGR, High Equivelance Ratio, and Mixing Time on Emisssions Levels in a Heavy-Duty Diesel Engine for PCCI Combustion," SAE Technical Paper 26-1-26, 26. [3] R. Opat, Ra, Y., Gonzalez D., M.A., Krieger, R.,Reitz, R.D., Foster, D.E., Siewert, R., Durrett, R., "Investigation of Mixing and Temperature Effects on HC/CO Emissions for Highly Dilute Low Temperature Combustion in a Light Duty Diesel Engine," SAE Technical Paper 27-1-193, 27. [4] Y. Sun and R. D. Reitz, "Modeling Diesel Engine NOx and Soot Reduction with Optimized Two-Stage Combustion," SAE Technical Paper 26-1-27, 26. [] Y. Sun, "Diesel combustion optimization and emissions reduction using adaptive injection strategies (AIS) with improved numerical models," University of Wisconsin--Madison, 27. [6] A. A. Amsden, "KIVA-3V, Release 2, Improvements to KIVA-3V," in LA-UR-99-91, 1999. [7] N. Abani, A. Munnannur, and R. D. Reitz, "Reduction of Numerical Parameter Dependencies in Diesel Spray Models," in ASME Internal Combustion Engine Division 27 Fall Technical Conference, 27. [8] N. Abani, S. Kokjohn, S. W. Park, M. Bergin, A. Munnannur, W. Ning, Y. Sun, and R. D. Reitz, "An improved Spray Model for Reducing Numerical Parameters Dependencies in Diesel Engine CFD Simulations," SAE Technical Paper 28-1-97, 28. [9] J. C. Beale and R. D. Reitz, "Modeling Spray Atomization With the Kelvin-Helmholtz/Rayleigh-Taylor Hybrid Model," Atomization and Sprays, vol. 9, pp. 623-6, 1999. [1] Z. Han and R. D. Reitz, "Turbulence Modeling of Internal Combustion Engines Using RNG k-e Models," Combustion Science and Technology, vol. 16, 199. [11] Y. Ra and R. D. Reitz, "The Application of a Multi-component Droplet Vaporization Model to DI Gasoline Engines," International Journal of Engine Research, vol. 4, pp. 193-218, 23. [12] A. Patel, S.-C. Kong, and R. D. Reitz, "Development and Validation of a Reduced Reaction Mechanism for HCCI Engine Simulations," SAE Technical Paper 24-1-8, 24. [13] Y. Shi and R. D. Reitz, "of Optimization Methodologies to Study the Effects of Bowl Geometry, Spray Targeting and Swirl Ratio for a Heavy-Duty Diesel Engine Operated at High-load," SAE Technical Paper 28-1-949, 28. [14] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II," in IEEE Transactions on Evolutionary Computation. vol. 6, 22, pp. 182-197. 8