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Numerical Investigation of a Gasoline-Like Fuel in a Heavy-Duty Compression Ignition Engine Using Global Sensitivity Analysis.


The transportation industry accounts for around 20% of the total energy consumed globally [1]. It is expected that the global demand for transport energy will rise by ~40% by 2040. Moreover, in the foreseeable future, internal combustion (IC) engines using liquid fuels made from petroleum are expected to dominate the transport sector [2, 3, 4, 5, 6]. Given the focus on reducing greenhouse gas (GHG) emissions in the transportation industry, there is a need for more efficient IC engines for both passenger and commercial applications. This pursuit of higher efficiency has led to a stronger interest in advanced compression-ignition (CI) engines. CI engines are more fuel-efficient than the spark-ignited (SI) engines due to their relatively high compression ratios and lack of throttling losses. However, conventional CI engines suffer from higher emissions of nitrogen oxides (N[O.sub.x]) and particulate matter (PM) due to local fuel-rich combustion and higher in-cylinder temperatures. Modern diesel engines use exhaust gas recirculation (EGR) to lower the in-cylinder temperature and oxygen content so that N[O.sub.x] is reduced. However, this adversely affects the oxidation of any soot that is formed in the cylinder.

To address the combined needs of further emissions reduction, improved efficiency and cost, alternative forms of CI combustion are being explored [7, 8]. Gasoline compression ignition (GCI) [9] is one of the most attractive alternative combustion strategies, and can use fuels in the gasoline auto-ignition range (RON > 60) instead of a diesel fuel in a CI engine. The longer ignition delay of such fuels allows more time for mixing before combustion starts [10, 11, 12]. In addition, sufficient inhomogeneity in the fuel-air mixture can be ensured by late fuel injection so that combustion will occur somewhere in the cylinder and will promote combustion of the rest of the charge. At the same time, the in-cylinder mixture is "homogeneous enough" everywhere in the cylinder before combustion starts so that soot formation is circumvented [8]. Therefore, GCI has the potential to offer diesel-like efficiency at lower cost by using low-octane, low-cetane, gasoline-like fuels that may require less processing in the refinery compared to today's fuels. Utilization of such fuels could lead to significant energy savings in fuel manufacturing. In addition, the fuel injection pressures need not be as high as with diesel fuel [13, 14, 15] as longer fuel ignition delay already facilitates better mixing. This can reduce the cost of the fuel injection system for GCI.

However, GCI combustion is dependent on a number of engine design parameters such as fuel injection strategies, EGR levels, intake temperature and pressure, and injector configuration. Different combinations of these parameters can lead to a variety of combustion characteristics, emissions and pressure rise rates. Engine simulation is a valuable tool that can aid the development of advanced combustion strategies such as GCI. Computational fluid dynamics (CFD) is being commonly used in the industry, thereby serving to shorten product development cycle and delivering significant cost savings as compared to experimental prototyping.

The influence of a large number of input parameters on specific targets of interest can be assessed using sensitivity analysis. Sensitivity analysis has been used in the chemical kinetics community as a technique for uncertainty quantification [16, 17, 18]. The goal in these studies was to identify reactions in large chemical kinetic mechanisms which influenced the ignition delay timing the most, so that the rate constants for those reactions could be computed with greater fidelity. This, in turn, led to the development of improved and more predictive chemical kinetic mechanisms.

In the past, diesel engine simulations have employed the local sensitivity analysis method to study the effect of a few parameters sequentially such as spray breakup and combustion model constants [19] to provide a guideline on how to calibrate the models under these conditions. However, this approach inherently cannot incorporate any non-linear effects. In this regard, global sensitivity analysis (GSA) has significant advantages over the traditional local sensitivity analysis approaches such as brute force methods [20], It provides a more realistic picture by accounting for the uncertainties in all the relevant parameters considered simultaneously. Moreover, it captures the non-linear response of targets to the input parameters. Pei el al. [21] applied global sensitivity analysis to an engine simulation for the first time to quantify the sensitivities of various target functions such as ignition delay, combustion phasing and emissions to various inputs such as experimental boundary conditions, fuel properties and CFD model constants. Later, Pei et al. [22] carried out a similar study using GSA to quantify the uncertainties for the Engine Combustion Network (ECN) Spray A [23]. More recently, Kodavasal et al. [24, 25] explored the effect of uncertainties in experimental boundary conditions and fuel properties on GCI operation with conventional gasoline fuel using a similar approach for a light-duty engine. These studies demonstrated that GSA could be employed as a valuable tool to readily identify important parameters which have the greatest influence on engine combustion behavior. However, the engine combustion sensitivity to various design parameters when utilizing a low-octane gasoline-like fuel is expected to be different and hasn't been explored previously.

Therefore, in the present work, GSA was applied to CFD simulation of a heavy-duty CI engine at medium load conditions operating with a low-octane gasoline-like fuel. A number of key design parameters are considered and their relative influences on specific targets of efficiency, emissions and heat release rate are quantified. The main objective is to provide direction on which control variables have the highest impact on the combustion characteristics, thereby requiring the highest attention during engine design and optimization phase. The paper is arranged as follows. Firstly, the engine setup is briefly discussed and details of the numerical model are provided. This is followed by a brief overview of the GSA methodology employed in this work. Next, the input parameters and their respective ranges of variation are prescribed. Then, the CFD model setup is validated against experimental data. Subsequently, the results of the GSA are discussed in terms of the sensitivity of target variables to the input parameters. Brute force sensitivity analysis is also performed on some important variables to gain additional insights. The paper concludes with a summary of the main findings.


Engine Setup

The experimental data were generated using a four-stroke, six-cylinder, heavy-duty Cummins test engine with a variable-geometry turbocharger, high-pressure cooled EGR loop and charge air cooler. A nine-hole mini-sac injector nozzle was used. The details of the engine geometry and operating conditions for the baseline case on which the GSA was performed are listed in Table 1. The in-cylinder pressure and emissions data were used to validate the CFD model described in the next section.

Numerical Model Setup

A commercial 3-D CFD code, CONVERGE (version 2.3.8) [26], is used to perform numerical simulations for the closed part of the cycle, from intake valve closing (IVC) to exhaust valve opening (EVO). Assuming axisymmetry, the simulation domain is considered to be a sector mesh representing a single cylinder and accounting for only one spray plume in order to reduce the computational expense. Periodic boundary conditions are imposed in the azimuthal direction. A uniform mixture and temperature distribution is specified at IVC.

CONVERGE uses a modified, cut-cell Cartesian method for grid generation directly during runtime. In addition, it has the capability to include fixed embedding of cells, i.e., increasing the grid resolution with respect to base grid size a priori along the cylinder walls and near the nozzle, and adaptive mesh refinement (AMR) to refine areas where the sub-grid field is largest [26]. In the present work, a base mesh size of 1.4 mm is used. One level of fixed embedding is prescribed near the cylinder head and piston, while two levels of fixed embedding are employed to resolve the flow near the fuel injector. In addition, two levels of AMR are employed based on the velocity and temperature sub-grid scales of 1 m/s and 2.5 K, respectively. This results in the minimum grid size of 0.35 mm. The computational mesh for the baseline case at top-dead-center (TDC) is shown in Figure 1. The simulation time step is automatically adjusted in the simulations based on the maximum convective, diffusive and mach Courant-Friedrichs-Lewy (CFL) numbers of 1, 2 and 50, respectively.

In-cylinder turbulence is modeled using the Reynolds-Averaged Navier Stokes (RANS) based re-normalized group (RNG) k-[epsilon] model [27] with wall functions. The liquid spray is treated in a Lagrangian fashion and the "blob" injection model by Reitz and Diwakar [28] is used, which initializes the diameter of a liquid droplet to the effective nozzle diameter. The Kelvin Helmholtz (KH)--Rayleigh Taylor (RT) breakup model [29, 30] and "no-time counter" collision model of Schmidt and Rutland [31] are employed to describe the subsequent spray atomization and collision processes, respectively. Droplet evaporation is modeled using Frossling correlation [32] and models are also included for dynamic drop drag [33] and droplet turbulent dispersion [34]. A reduced chemical kinetic mechanism for primary reference fuel (PRF) consisting of 48 species and 152 reactions based on Liu et al. [35] is used in this work. A RON70 two-component surrogate comprising of 70% iso-octane by mass and 30% n-heptane by mass is employed [36], In addition, the N[O.sub.x] formation is modeled by the extended Zel'dovich mechanism [37]. The empirical Hiroyasu soot model [38] coupled with the Nagle and Strickland-constable model [39] are used to determine the soot formation and oxidation rates and acetylene (C2H2) is considered as the precursor for soot formation. For combustion modeling, the SAGE detailed chemistry solver [40] is employed along with a multi-zone (MZ) approach, with bins of 5 K in temperature and 0.05 in equivalence ratio [26, 41], Although it doesn't utilize an explicit turbulent combustion closure [42, 43, 44], the SAGE-MZ model has been demonstrated to perform well to simulate spray combustion in the context of RANS in some previous studies [45].

GSA Methodology

GSA is used as a tool to explore the relations between the input parameters and the outputs/targets of a model. This approach is more insightful than the local sensitivity analysis methods [46], where only a single input parameter is varied, as it captures the relative sensitivity of different variables on the targets of interest over the whole input parameter space. In doing so, it also accounts for the non-linear response of targets to the input variables. The details of the GSA methodology can be found in Ref. [16]. However, a brief discussion is provided as follows.

Assume that there are 'n' input parameters and each one of them is equally likely to lie anywhere within a prescribed range of variation:

[mathematical expression not reproducible] (1)

where [v.sub.1] is the ith variable, [??] and [??] are the lower and higher limits of its range of variation, respectively. It is assumed that the probability distribution of the parameters is uniform within the n-dimensional hypercube [16]:

[mathematical expression not reproducible]

The Monte Carlo method is used to generate a large number 'N' of independent random parameter sets within the above hypercube for CFD simulations. In the present study, 256 simulations are used, i.e., N = 256. The targets obtained from the simulations can be written as:

f = f(v), (3)

where f is the vector of targets of interest and v is the vector containing one set of the sampled n input parameters. The GSA is implemented based on the analysis of variance using an ordinary least squares (OLS) method through the following expansion:

[mathematical expression not reproducible] (4)

where m is the order of expansion. Here, m = 2. The sensitivity coefficient of each input parameter ([S.sub.i]') can then be computed as the ratio of the partial variance to the total variance as shown below:

[mathematical expression not reproducible] (5)

[mathematical expression not reproducible] (6)

where the brackets "< >" indicate the mean value over N simulations. In Eq. (5). [[sigma].sup.2.sub.i] denotes the partial variance of ith parameter based on the expansion shown in Eq. (4). The larger the sensitivity coefficient, the greater the impact an input variable has on a particular target function. It must be noted that the range of variation imposed on the inputs can influence the relative values of the sensitivity coefficients.

Control Variables and Their Ranges

The design parameters used as control variables in the present study along with their respective ranges of variation are listed in Table 2. In total, eleven input variables are chosen pertaining to fuel injector design (number of nozzle holes, total nozzle area, nozzle inclusion angle), fuel injection strategy (injection pressure, start-of-injection (SOI) timing) and initial conditions (IVC temperature and pressure, EGR fraction, initial turbulence level and swirl). Each parameter is assigned a minimum and maximum value. The ranges of variation include the baseline conditions. The total nozzle area and initial turbulence kinetic energy (TKE, k) are normalized with respect to the respective baseline values, therefore the baseline values are 1. Figure 2 shows the distributions generated for [P.sub.IVC] and EGR. It is evident that these variables are randomly distributed using the MC method over the sample space identified by their ranges of variation. The other input parameters also have similar random distributions.

Automated Simulation Case Setup

The initial turbulence length scale ([L.sub.turb]) is used in the calculation of turbulent dissipation rate (e in the k-[epsilon] turbulence model). The dissipation rate is inversely proportional to [L.sub.turb]. The composition at IVC is computed based on the EGR fraction, [T.sub.IVC], [P.sub.IVC] and total mass of fuel injected. Also, it must be noted that in the CONVERGE CFD code, nozzle diameter, duration of injection (DOI) and injection velocity rate-shape are the inputs that need to be prescribed. These CFD model inputs are computed from the first three input parameters listed in Table 2 as follows. For a particular simulation case, first the nozzle diameter is calculated based on the total nozzle area and number of nozzle holes. The number of nozzle holes also determines the sector mesh to be used for that particular case, which is generated using CONVERGED Make Surface utility [26]. In addition, this also provides the fuel mass injected in the sector domain because the total mass injected is constant and each nozzle hole injects the same mass of the fuel. Now, due to the [A.sub.noz] and [P.sub.inj] scaling, the fuel mass flow rate-shape changes from the baseline case. Hence, in order to meet the updated mass injected per nozzle hole, the baseline mass flow rate-shape is modified by iteratively removing (or adding) data points from (or to) the "quasi-steady" portion of the rate-shape, thereby causing the DOI to change accordingly. Finally, the DOI is again adjusted slightly to match the injection pressure. Figure 3 shows the resultant injection velocity and injection pressure profiles for two extreme scenarios over the input parameter space (Scenario A: [N.sub.holes] = 8, [A.sub.noz] =1.3, [P.sub.inj].= 1800 bar) and (Scenario B: [N.sub.holes] =10, [A.sub.noz] = 1, [P.sub.inj] = 1400 bar), along with the corresponding baseline profiles.

A standalone code is developed using the CONVERGE genetic optimization utility, CONGO [26], to perform all the operations described above in this section for each of the 256 simulation cases sequentially and generate the respective input files. All the simulations were run concurrently on half of a rack of Mira, an IBM BG/Q supercomputer at Argonne Leadership Computing Facility (ALCF) and Office of Science User Facility at Argonne, with each case running on 32 cores (2 nodes, 16 cores per node). The average runtime per simulation was around 72 hours. In order to ensure that the sample size provided convergent results, the GSA was performed on a smaller subset (128 simulations) as well. It was found that the relative sensitivities of various targets to the inputs did not change between the two sets. This confirmed that 256 simulations provided a big enough sample set for the present study. Moreover, 20 simulation cases based on the maximum, minimum and baseline values of each input variable from Table 2 were also run for brute force sensitivity analysis to further quantify the influence of independent variations in input parameters on the targets. We note that independent variations are not practical but they do provide us with further insights.


Model Validation

The CFD model predictions were validated against experimental data for RON70 naphtha at the baseline conditions. As seen in Figure 4, cylinder pressure traces and heat release rates predicted by the CFD model were in good agreement with the experimental results. In addition, Figure 5 showed that the model was also able to capture the engine-out N[O.sub.x] and soot emissions reasonably well.

GSA Results

A number of targets such as ignition timing, combustion phasing, burn duration, emissions, fuel consumption, peak cylinder pressure and maximum pressure rise rate are discussed and their responses to the input parameters are analyzed. The results are presented in terms of bar plots showing the sensitivity of targets to different inputs and scatter plots with regression fits of the targets versus the input variables they are most sensitive to.

Ignition Timing

CA2 and CA 10 can be used as the two definitions for ignition timing. They correspond to the crank angles when 2% and 10% of the total integrated heat release occur, respectively. CA10 is typically easier to measure from experiments and is a more conventional definition of ignition timing. However, CA2 is indicative of the first stage of heat release, which is interesting from a chemical kinetics viewpoint.

The sensitivity coefficients for the input variables affecting CA2 and CA10 are reported in Figure 6. Clearly, both quantities are predominantly sensitive to SOI timing. Other input variables play negligible roles in influencing ignition timing with sensitivity coefficients less than 0.1. Figure 7 shows the scatter plots of CA2 and CA10 versus SOI and the corresponding regression fits. As the SOI is delayed, ignition timing expectedly gets retarded. Also, the spread in CA10 is higher than that in CA2. The spread is influenced by other input variables and higher spread means a larger effect of others at a certain SOI timing. Higher spread for CA10 is expected due to greater combustion progress in the cylinder. Unlike CA2, CA10 also shows some degree of controllability through EGR, [T.sub.IVC] and [P.sub.IVC], as shown in Figure 6.

Combustion Phasing and Burn Duration

The next set of targets are for combustion phasing, CA50 and CA90, which are key indicators of the progress in combustion. These correspond to the crank angles for 50% and 90% of total heat release, respectively.

Figure 8 shows the sensitivity of these two target quantities towards the control variables. CA50 is found to be strongly correlated to SOI, which is also suggested by the very narrow spread in Figure 9. Increasing SOI linearly increases the CA50 as depicted in Figure 9. This is consistent with the effect of SOI on CA2 and CA10 as observed earlier. Figures 8 and 9 indicate that CA90 is most sensitive to SOI as well, with a trend similar to CA50. The spread is higher for CA90 compared to CA50 though, which is consistent with the findings corresponding to Figure 7. CA90 is also significantly influenced by EGR and [T.sub.IVC]. In particular, the sensitivities of CA90 to SOI and EGR are nearly equal. It can be seen in Figure 10 that CA90 gets delayed with both increasing EGR fraction and higher [T.sub.IVC]. An increase in either of these input parameters would lead to higher residual (C[O.sub.2] and [H.sub.2]O) mass fraction in the cylinder at IVC. This would tend to lower the in-cylinder temperatures and cause slower rate of overall heat release. It is also noted from Figure 8 that CA90 is more sensitive to EGR as compared to [T.sub.IVC]. This is probably due to the fact that with an increase in [T.sub.IVC], the in-cylinder mixture would be at a higher temperature at IVC. Hence, the net cooling effect is expected to be less pronounced as compared to a scenario where EGR fraction is raised while keeping [T.sub.IVC] constant.

In addition to combustion phasing, the impact of input parameters on overall combustion burn duration is also assessed, as shown in Figure 11. Here, CA 2-90 is used as a metric for burn duration. Clearly, it is most sensitive to EGR and [T.sub.IVC]. Higher EGR and [T.sub.IVC] result in more prolonged burn duration as shown in Figure 12. These trends are similar to those observed for CA90 and can be justified based on similar reasoning as above. Burn duration also shows a moderate level of sensitivity to [P.sub.IVC] and [P.sub.inj].

Emissions and Fuel Consumption

First, N[O.sub.x] and soot emissions are examined. The sensitivity coefficient results in Figure 13 clearly indicate that N[O.sub.x] emissions are primarily sensitive to EGR fraction, whereas both [T.sub.IVC] and EGR have a pronounced effect on soot emissions. A scatter plot of N[O.sub.x] with respect to EGR is shown in Figure 14. N[O.sub.x] emissions tend to be lowered by a higher percentage of EGR, which has also been observed for conventional diesel combustion. This is primarily attributed to the lowering of burned gas temperatures due to higher residual fraction. On the other hand, as depicted in Figure 15 (a) soot emissions increase with increase in EGR, which is mainly the result of suppressed soot oxidation due to lower combustion temperatures and lower oxygen concentration.

Soot emissions are also influenced by [T.sub.IVC] in that higher [T.sub.IVC] leads to more soot as shown in Figure 15 (b). This can be explained by Figure 16 which shows the in-cylinder distributions of equivalence ratio and soot mass fraction at 15 [degrees]CA aTDC, from brute force sensitivity analysis performed for the minimum and maximum [T.sub.IVC] in the prescribed range of variation as noted in Table 2. It is observed that higher [T.sub.IVC] results in lower oxygen content in the in-cylinder mixture and thereby more fuel-rich regions ([PHI] > 1) during the combustion phase. This promotes higher soot formation. This fact is further demonstrated in Figure 17, which shows the temporal evolution of in-cylinder soot for the bounded values of [T.sub.IVC].

Next, the impact of input parameters on carbon monoxide (CO) and unburned hydrocarbon (UHC) emissions is explored. The sensitivity coefficient results in Figure 18 show that CO emissions are mostly influenced by EGR with some minor sensitivity to swirl ratio and nozzle inclusion angle. Higher amount of residuals in the in-cylinder mixture favors CO formation as indicated by Figure 19. Higher EGR causes lower oxygen concentration resulting in more fuel-rich combustion and thereby an increased CO production. At the same time, it causes lower bulk gas temperatures leading to incomplete CO-C02 conversion. It is noted that the regression fit in Figure 19 shows a non-linear effect.

Figure 18 also shows that UHC emissions are most sensitive to [T.sub.IVC]. It is observed that UHC emissions decrease as [T.sub.IVC] is raised (Figure 20). This trend is further investigated using brute force sensitivity analysis. Figure 21 shows the in-cylinder distributions of equivalence ratio and temperature at 30 [degrees]CA aTDC for two different cases. These cases have the exact same inputs as in the baseline case, except for different values of [T.sub.IVC], representing the extremes of the range over which [T.sub.IVC] was varied for the GSA. It can be seen that for both cases, there are fuel-lean regions (0.3 < [PHI] < 0.6) present near the cylinder head. However, these regions are smaller when [T.sub.IVC] is higher (case (b)). In addition, the temperatures in these regions are higher for case (b). In fact, the minimum temperature in case (b) is around 100 K higher than case (a). These factors lead to a lower UHC production for case (b) (not shown here).

In addition to IVC temperature, EGR and SOI are also found to have a considerable influence on UHC emissions. Figures 22 and 23 depict the scatter plots of UHC emissions versus EGR and SOI respectively, along with corresponding regression fits. Clearly, UHC emissions are positively correlated to residual fraction and SOI timing.

Finally, the effect of the control variables on indicated specific fuel consumption (ISFC) is also assessed. The sensitivity coefficients are plotted in Figure 24. [T.sub.IVC] and EGR seem to have the highest impact on ISFC, along with some minor influence of SOI timing and [P.sub.IVC]. The scatter plots of ISFC versus [T.sub.IVC] and EGR are shown in Figures 25 and 26, respectively. Clearly, ISFC is positively correlated to both these design parameters. This is mainly attributed to the fact that with higher [T.sub.IVC] or higher EGR, the amount of oxygen in the cylinder gets lowered, with the effect of [T.sub.IVC] being more pronounced. As a result, the indicated mean effective pressure (IMEP) decreases, thereby leading to an increase in ISFC.

Peak Pressure and Maximum Pressure Rise Rate

The last set of targets comprises peak cylinder pressure and maximum pressure rise rate (MPRR), which define the mechanical limit of the engine. Figure 27 shows the sensitivities of both targets to the design variables. It can be seen that SOI timing has the highest impact on both of them. Earlier, it was found that retarding the SOI timing delayed both ignition timing and combustion phasing. This also leads to lower peak pressure and MPRR as shown in Figure 28. In addition, peak pressure is also influenced by [P.sub.IVC]. As expected, higher IVC pressure leads to higher peak in-cylinder pressure (Figure 29). On the other hand, MPRR is found to be positively correlated to total nozzle area as reported in Figure 30. This is mainly due to better air utilization obtained with larger total nozzle area for gasoline-like fuels. Note that it is not the case for diesel as it requires smaller nozzle diameter for enhanced mixing [47], Higher injection pressure, as shown in Figure 30, leads to higher maximum pressure rise rate.

This can be explained by the fact that an increase in injection pressure shortens the duration of fuel injection and increases injection velocity, thereby resulting in faster and better fuel-air mixing.

Finally, it is noted that the number of nozzle holes ([N.sub.holes])do not affect any of the target variables investigated in the present study. This is not clear but could be possibly due to the fact that simulations were run only for a sector mesh with a single spray plume. This might not have been able to capture the effect of potentially different plume-to-plume interactions for different injector nozzle configurations. More studies using full engine cylinder geometry will be conducted in the future to investigate this aspect. Secondly, initial turbulence characteristics (TKE and [L.sub.turb]) also play a negligible role. Indeed, brute force sensitivity analysis indicates that TKE is reduced to less than 1% of its initial value at IVC before SOI timing (not shown here). In addition, the GSA results also show that within the range of variation prescribed to all the input parameters, swirl ratio and nozzle inclusion angle have negligible impact on the target variables except CO emissions. Hence, the GSA methodology clearly shows parameters that may have a more profound influence on performance and emission characteristics of an engine.


In the present work, a GSA study was applied to heavy-duty CI engine combustion simulations with a gasoline-like fuel aimed at guiding engine design and optimization. A number of engine operating conditions, initial conditions and injector design parameters were chosen and their impact on multiple targets such as ignition timing, combustion phasing, overall burn duration, emissions and pressure rise rate was assessed. The GSA tool was used to screen key input parameters that affected various targets of interest most significantly and also provided guidance on the operating ranges of control variables to achieve combustion and performance robustness while pursuing higher efficiency. A total of 256 three-dimensional CFD simulations were used in the GSA. The sensitivity of the targets to each input variable was quantified in terms of sensitivity coefficients. The main findings of the study are as follows.

* It was found that ignition timing (CA2, CA10) was affected by SOI timing the most and a positive correlation was observed between them, similar to conventional diesel combustion. Unlike CA2 which was solely dominated by SOI, CA10 displayed a certain degree of controllability through EGR, [T.sub.IVC] or [P.sub.IVC] besides SOI.

* For combustion phasing (CA50, CA90), although SOI was again found to be the most sensitive variable, EGR fraction and IVC temperature also played an important role, especially for CA90. Moreover, SOI and EGR were found to be equally effective in influencing CA90.

* EGR was the most effective way of controlling burn duration. However, [T.sub.IVC], [P.sub.IVC] and injection pressure could also be considered to achieve the optimal fuel efficiency.

* NOx was primarily affected by EGR similar to conventional mixing-controlled combustion. SOI might play a certain role more towards relatively lower EGR level. EGR and [T.sub.IVC] were the major players in controlling soot and it might be able to find a window of low soot levels at relatively lower EGR and [T.sub.IVC].

* Unlike NOx and soot, [T.sub.IVC] was the dominant factor for HC emissions. To maintain a lower level of HC emissions, low [T.sub.IVC] should be avoided.

* [T.sub.IVC] and EGR were the most important input variables affecting ISFC as a result of their direct impact on the amount of oxygen present in the in-cylinder mixture.

* In addition, peak in-cylinder pressure and MPRR were most significantly affected by the SOI timing. However, MPRR was also influenced by total nozzle area and injection pressure by way of modulating fuel-air mixing in the cylinder. The corresponding scatter plots provided additional insights that could be useful in determining a smaller design parameter space spanned by narrower ranges of only the important control variables, for a more rigorous design optimization.

In the future work, a more detailed investigation of the important inputs identified in this GSA will be carried out and coupled with engine piston bowl design to optimize engine efficiency and emissions. In addition, it is noted that the present work didn't investigate the impact of uncertainties in CFD model parameters and chemical kinetics. These aspects will also be explored in future studies.


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Pinaki Pal, Ph.D.

Post-doctoral appointee

Argonne National Laboratory

9700 S.Cass Avenue

Lemont, IL- 60439


The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (Argonne). Argonne, a U.S. Department of Energy Office (DOE) of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

This research used resources of the Argonne Leadership Computing Facility (ALCF), which is a DOE Office of Science User Facility supported under contract DE-AC02-06CH11357. Fusion and Blues High Performance LCRC cluster facilities at Argonne National Laboratory were also used for some of the simulations.

The authors would like to thank Aramco Services Company: Aramco Research Center - Detroit, for funding the project that led to this work; We also thank Dr. Noah Van Dam and Dr. Muhsin Ameen from Argonne National Laboratory for many helpful discussions and Convergent Science Inc. for providing the Converge CFD software licenses.

Pinaki Pal

Argonne National Laboratory

Daniel Probst

Convergent Science Inc.

Yuanjiang Pei

Aramco Research Center

Yu Zhang

Aramco Services Co.

Michael Traver

Aramco Research Center

David Cleary

Aramco Services Co.

Sibendu Som

Argonne National Laboratory
Table 1. Engine specifications and operating conditions.

Engine model               Cummins ISX15
Cylinders                     6
Displacement                 14.91
Bore                        137 mm
Stroke                      169 mm
Connecting Rod              262 mm
Compression ratio            17.3:1
Engine speed               1375 rpm
Intake valve closing       -137 [.sup.0]CA aTDC
Exhaust valve opening       148 [degrees]CA aTDC
Start of injection timing    -9 [degrees]CA aTDC
Injection duration           15.58 [degrees]CA
Mass of fuel injected         0.1245 g/cycle/cylinder
Fuel injection temperatu    360 K
Injection pressure         1600 bar
Nozzle inclusion angle       15[degrees]
IVC pressure                323 K
IVC temperature               2.15 bar
EGR                          41%
Global equivalence ratio      0.57

Table 2. Control variables and respective ranges of variation along
with the baseline setup.

Variable           Description

[N.sub.holes]      Number of nozzle holes
[A.sub.noz]        Total nozzle area
[P.sub.inj]        Injection pressure [bar]
SOI                Start-of-injection timing
                   [[degrees]CA aTDCl
[[theta].sub.noz]  Nozzle inclusion angle [[degrees]]
EGR                EGR fraction
[T.sub.IVC]        IVC temperature [K]
[P.sub.IVC]        IVC pressure [bar]
TKE, k             Initial turbulent kinetic
[L.sub.urb]        Initial turbulence length
                   scale [mm]
SR                 Swirl ratio

Variable           Baseline  Min.     Max.

[N.sub.holes]         9         8       10
[A.sub.noz]           1         1        1.3
[P.sub.inj]        1600      1400     1800
SOI                  -9       -13       -5
[[theta].sub.noz]   152       148      156
EGR                   0.41      0.35     0.50
[T.sub.IVC]         323       323      373
[P.sub.IVC]           2.15      2.0      2.3
TKE, k                1         0.7      1.3
[L.sub.urb]           4.5       1        8
SR                    1         1        2.4
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Author:Pal, Pinaki; Probst, Daniel; Zhang, Yu; Traver, Michael; Cleary, David; Som, Sibendu
Publication:SAE International Journal of Fuels and Lubricants
Article Type:Technical report
Date:Apr 1, 2017
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