## Abstract

In this study, lean mixed-mode combustion is numerically investigated using computational fluid dynamics (CFD) in a spark-ignition engine. A new E30 fuel surrogate is developed using a neural network model with matched octane numbers. A skeletal mechanism is also developed by automated mechanism reduction and by incorporating a NOx submechanism. A hybrid approach that couples the G-equation model and the well-stirred reactor model is employed for turbulent combustion modeling. The developed CFD model is shown to well predict pressure and apparent heat release rate (AHRR) traces compared with experiment. Two types of combustion cycles (deflagration-only and mixed-mode cycles) are observed. The mixed-mode cycles feature early flame propagation and subsequent end-gas auto-ignition, leading to two distinctive AHRR peaks. The validated CFD model is then employed to investigate the effects of NOx chemistry. The NOx chemistry is found to promote auto-ignition through the residual gas, while the deflagration phase remains largely unaffected. Sensitivity analysis is finally performed to understand effects of fuel properties, including heat of vaporization (HoV) and laminar flame speed (SL). An increased HoV tends to suppress auto-ignition through charge cooling, while the impact of HoV on flame propagation is insignificant. In contrast, an increased SL is found to significantly promote both flame propagation and end-gas auto-ignition. The promoting effect of SL on auto-ignition is not a direct chemical effect; it is rather caused by an advancement of the combustion phasing, which increases compression heating of the end-gas.

## Introduction

Lean combustion is beneficial to spark-ignition (SI) engine operation due to the higher efficiency and lower emissions than conventional stoichiometric engine operation. However, applications of lean combustion are challenged by the intrinsically low flame speeds and the susceptibility to static and dynamic instabilities. To overcome these difficulties, spark-assisted compression ignition (SACI) or mixed-mode combustion is a promising strategy, which combines conventional deflagrative flame propagation and controlled end-gas auto-ignition. Thus, the fuel can burn sufficiently fast through auto-ignition, compensating for the low flame speed of lean mixtures, while the engine remains knock free.

Lean combustion under mixed-mode conditions has been extensively studied by experiments [14]. Urushihara et al. [1] studied spark-ignited compression ignition and demonstrated the increased engine load compared to conventional homogeneous charge compression ignition (HCCI) combustion. Zigler et al. [2] studied SACI in an optical engine and identified the presence of spark-initialized turbulent flame propagation and subsequent auto-ignition in the end-gas. Sensitivity of the air preheating and spark timing on various engine performance metrics was also investigated with high-speed imaging. Ma et al. [5] used CH2O and OH chemiluminescence to investigate in-cylinder combustion behaviors in flame-induced auto-ignition. A stoichiometric condition was employed, while the observed flame characteristics—occurrence of auto-ignition in the outer rim of the deflagrative flame front and accelerated reaction front propagation—could hold true for lean engine operations as well. Sjöberg and Zeng [3] studied mixed-mode combustion at lean and diluted conditions with various fuels. Significant cycle-to-cycle variability (CCV) was observed at ultra-lean conditions, which could pose a great challenge for practical engine operation. Reuss et al. [6] demonstrated that the early kernel growth was a major source for CCV under SACI conditions. Hu et al. [4] identified injection strategies that could stabilize the ultra-lean operation and improve combustion efficiency for mixed-mode combustion.

In this context, computational fluid dynamics (CFD) modeling has its unique capabilities to probe into the governing physics of mixed-mode combustion, providing unique opportunities for studying CCV and fuel property effects. Dahms et al. [7] developed a mixed-mode flamelet combustion model, which combines the SparkCIMM ignition model, the G-equation model and multi-zone chemistry, targeting spark-assisted HCCI engines at lean conditions with significant exhaust gas recirculation dilution. The model demonstrated a good agreement between CFD and experiment. However, the target operation was at a relatively low-CCV condition, and the performance under high-CCV conditions remains unclear. Middleton et al. [8] studied SACI combustion at stoichiometric conditions and investigated the effect of spark timing and charge temperature on combustion phasing and heat release rate that are governed by the competition between flame propagation and auto-ignition, using the coherent flamelet model coupled with detailed chemistry. However, few CFD studies till date have focused on mixed-mode combustion under lean and dilute conditions with a high level of CCV.

The objectives of this study are, therefore, twofold. The first goal is to develop an engine CFD model that can accurately capture lean, mixed-mode combustion characteristics. The second objective is to identify effects of chemical and physical fuel properties on mixed-mode engine performance, which can eventually enable co-optimization of fuels and engines.

## Engine Specifications and Operating Conditions

The engine simulated in this study is a single-cylinder, four-valve, direct-injection spark-ignition (DISI) research engine at Sandia National Laboratories. Figure 1 schematically shows the cross section of the combustion chamber at the top dead center (TDC). A long-reach spark plug is adopted to extend the spark plasma to the center of the combustion chamber, which can potentially improve the ignition efficiency, especially for lean operations. The fuel injector is mounted on the pent-roof facing the spark plug allowing for direct injection of fuel into the chamber center. The piston bowl window can provide optical access to the combustion chamber, but in this study, a metal blank was used to enable continuously fired all-metal engine experiments. One of the intake valves was deactivated to enhance the in-cylinder swirl level and thereby the overall mixing process. Relevant engine specifications are provided in Table 1.

Fig. 1
Fig. 1
Close modal
Table 1

Engine specifications

ParameterValue
Bore86.0 mm
Stroke95.1 mm
Connecting rod length166.7 mm
Piston pin offset−1.55 mm
Compression ratio12:1
ParameterValue
Bore86.0 mm
Stroke95.1 mm
Connecting rod length166.7 mm
Piston pin offset−1.55 mm
Compression ratio12:1

The engine is operated at a lean condition (a global fuel/air equivalence ratio of 0.55) using certification gasoline blended with 30% ethanol by volume (referred to as “E30” hereinafter). To achieve a well-mixed charge of fuel, air, and residual gas (∼6%), the fuel was injected using three injections of equal duration during the intake stroke. Research octane number (RON) and motor octane number (MON) of the E30 fuel are 105 and 91, respectively. To achieve mixed-mode combustion with maximum brake torque for such a high-octane fuel, a fairly advanced combustion phasing is necessary, requiring the use of an advanced spark timing (−57 CA ATDC). However, such an early spark timing leads to a significant level of CCV. Capturing CCV for this operating point will be one focus of the present modeling efforts. Engine operation conditions are summarized in Table 2, and more details on engine configuration and operating conditions are presented in Ref. [3].

Table 2

Engine operating conditions

ParameterValue
Engine speed1000 rpm
IMEPg446 kPa
Intake temperature100 °C
Intake pressure87.0 kPa
Exhaust pressure100.1 kPa
Injection timings−318, −303, −288 CA ATDC
Injection duration444 μs
Injected fuel mass17.8 mg/cycle
Spark timing−57 CA ATDC
ParameterValue
Engine speed1000 rpm
IMEPg446 kPa
Intake temperature100 °C
Intake pressure87.0 kPa
Exhaust pressure100.1 kPa
Injection timings−318, −303, −288 CA ATDC
Injection duration444 μs
Injected fuel mass17.8 mg/cycle
Spark timing−57 CA ATDC

## Numerical Approach

### Computational Fluid Dynamics Geometry and Model Setup.

To model the Sandia DISI engine, a full-scale engine geometry, including intake and exhaust runners, the piston head, the piston, the spark plug, and the fuel injector, is used, as shown in Fig. 2. The engine is simulated using the converge code v2.4 [9]. The re-normalized group kε model is used to describe the Favre-averaged turbulent flow. Wall heat transfer is modeled with a temperature wall function from Amsden and Findley [10]. Cylinder wall temperature is set to be 445 K. Experimentally measured high-speed intake and exhaust pressures (varying with time) are specified at the intake port inlet and the exhaust port outlet. Fuel spray and in-cylinder combustion processes are simulated with the Eulerian–Lagrangian approach. The spray injection is described by the blob injection approach [11], while droplet breakup, droplet evaporation, and drag force are modeled using the Kelvin–Helmholtz and Rayleigh–Taylor models [12,13], the Frossling correlation [14], and a dynamic drag model [15], respectively. Liquid properties are taken from a previous study [16] on the same engine platform with the same E30 fuel.

Fig. 2
Fig. 2
Close modal

For turbulent combustion modeling, a hybrid approach is employed to capture mixed-mode combustion. In particular, the G-equation model is employed to track deflagrative flame propagation with tabulated laminar flame speed. A passive scalar G is transported according to the instantaneous turbulent flame speed, which is modeled using Peter’s model [17]. The value of G indicates the distance from a local fluid element to the mean flame front. G = 0 identifies the flame front location, while G < 0 and G > 0 indicate the unburned and burned mixtures, respectively. The laminar flame speed is calculated based on one-dimensional (1D) freely propagating premixed flames and is then tabulated as a function of pressure, unburned temperature, local equivalence ratio, and local dilution ratio. The local dilution ratio is calculated through a separate passive transport equation. The well-mixed model coupled with detailed chemical kinetics is used to predict auto-ignition in the end-gas. The multi-zone model is further employed to accelerate detailed chemistry integration. This hybrid approach has been demonstrated to be able to capture knock in Cooperative Fuel Research engines [18,19] and boosted SI engines [20]. A unique feature of this hybrid approach is that it allows isolated investigation of individual chemical properties such as flame speed and ignition delay.

A modified cut-cell Cartesian grid method for automatic mesh generation is used during runtime [9]. The base grid size is Δ0 = 4 mm, and the minimum grid size is Δ5 = 0.125 mm. In particular, fixed embedding is applied to better resolve in-cylinder dynamics (Δ2 = 1 mm), wall boundary layers (Δ3 = 0.5 mm), spray injection (Δ4 = 0.25 mm), early flame propagation (Δ5 = 0.125 mm), and other small geometrical structures (Δ3 = 0.25 mm). Adaptive mesh refinement based on velocity and temperature fluctuations is further employed to better resolve complex flow and flame structures with a minimum cell size of Δ3 = 0.5 mm. Note that in Δn, n represents the level of mesh refinement with respect to the base grid size. The peak cell count during a full engine cycle is approximately 1.6 million. The computational cost for simulation of one engine cycle is approximately two days.

### E30 Fuel Surrogate.

To generate the surrogate composition for gas-phase modeling, a nonlinear regression model was employed that could relate the ignition chemistry from a detailed chemical kinetics model [21] and other thermophysical properties to RON and MON. In this case, the nonlinear regression model was a feed-forward neural network [22]. The regression was an approximation, but it could balance the error in the chemical kinetic model with the error correlating octane numbers to ignition delay times [2328]. The model could be evaluated in less than 10 s on a single CPU thread for compositions containing any combination of the more than 50 hydrocarbons and biofuels represented in the detailed chemical kinetics model developed by Mehl et al. [21]. This model was then combined with standard optimization routines [29] to find the fuel blend with equivalent octane ratings within the accuracy of the regression.

Two feed-forward neural networks were created, one for each octane number. They both used the same inputs and architecture—a single hidden layer with 24 nodes. The inputs included three ignition delay-related quantities, simulated using the detailed chemistry model [21] in a homogeneous, constant-volume reactor at 825 K and 20 bar. These were the inverse of the ignition delay time to reach 1225 K and the derivative of the normalized ignition delay time with respect to pressure and temperature. The other neural network inputs were the enthalpy of vaporization and liquid density at 298 K, and the mole-averaged atom counts for hydrogen, carbon, and oxygen. A schematic of the neural network architecture is shown in Fig. 3. The neural network was demonstrated to have good predictive capability with root-mean-square errors in RON/MON of approximately 1 ON for the cross-validation data. Further details on the design, implementation, and validation of the neural network can be found in Ref. [30].

Fig. 3
Fig. 3
Close modal

A fuel surrogate based on toluene primary reference fuel (TPRF) and ethanol was obtained using the basic multivariable minimization techniques found in the python scipy library2 in conjunction with the neural network regression models. Specifically, the difference between predicted and target RON (105) and MON (91) with respect to component volume fractions was minimized, subject to the constraints of 30% ethanol volume fraction and the sum of the volume fractions being unity. The resultant TPRF–ethanol surrogate is presented in Table 3.

Table 3

E30 fuel surrogate composition (by mole)

n-Heptaneiso-OctaneTolueneEthanol
6.0%16.8%28.4%48.8%
n-Heptaneiso-OctaneTolueneEthanol
6.0%16.8%28.4%48.8%

### E30 Skeletal Reaction Model.

The detailed chemical kinetic model [21] of the proposed TPRF–ethanol blend consists of 2878 species and 12,839 reactions, which is prohibitive for three-dimensional (3D) engine CFD simulations. Therefore, mechanism reduction based on directed relation graph [31] and sensitivity analysis is employed to systematically reduce the size of the reaction model. The reduction is performed based on a large set of reaction states sampled over the parameter range of pressure from 1 to 100 atm, equivalence ratio from 0.3 to 2.0, inlet temperature of 300 K for perfectly stirred reactors, and initial temperature from 600 to 1600 K for auto-ignition, covering the low-temperature chemistry region that is important for engine combustion. The error tolerance used in the reduction is 0.3, implying that the worst case error of the skeletal mechanism is 30%. The resultant skeletal model consists of 149 species and 640 reactions. A submechanism of NOx chemistry3 is then merged into the skeletal model, resulting in a final rection model containing 164 species and 694 reactions.

Figure 4 compares the ignition delays of the final skeletal model with NOx against the skeletal model without NOx as well as the detailed model at different temperatures and pressures. Excellent agreement is observed between the skeletal models and the detailed model for both ignition delay and flame speed. Laminar flame speeds calculated by the two skeletal mechanisms are also compared in Fig. 5. The addition of NOx has negligible impact on 0D and 1D calculations at the selected conditions. However, NOx chemistry can be important under practical engine conditions due to the presence of the residual gas, as will be investigated in Results and Discussion section.

Fig. 4
Fig. 4
Close modal
Fig. 5
Fig. 5
Close modal

## Results and Discussion

### Model Performance.

The proposed modeling approach is first validated in this section. Table 4 presents the comparison of key engine performance parameters, including peak cylinder pressure (Pmax), gross indicated mean effective pressure (IMEPg), CA10, CA50, and CA90, obtained from simulations and experimental measurements. Predicted values overall agree well with measured ones. A slightly earlier combustion phasing (CA10 and CA50) predicted by simulation is possibly due to the use of a simplified ignition model (a spherical energy source at the center of the spark gap) during the energizing stage. However, the computational cost is significantly reduced with this simplified ignition model.

Table 4

Predicted and measured mean combustion characteristics

QuantityPmax (MPa)IMEPg (MPa)CA10CA50CA90
Experiment3.930.446–8.043.5422.3
CFD4.080.497–14.12.2221.4
QuantityPmax (MPa)IMEPg (MPa)CA10CA50CA90
Experiment3.930.446–8.043.5422.3
CFD4.080.497–14.12.2221.4

Figure 6 shows the pressure and AHRR traces obtained from the experiment (500 cycles) and the simulation (13 cycles). Good agreement is observed between the simulation and experimental data, with the predicted mean pressure being slightly higher than the measured mean pressure. In addition, the moderate level of, but not full range of, CCV is captured by CFD. This is because unsteady Reynolds-averaged Navier–Stokes (RANS) models solve time-averaged Navier–Stokes equations and therefore intrinsically predict lower CCV. Two types of combustion cycles are observed in both experiment and simulation (Fig. 6(b)). The first type of cycles features low in-cylinder pressure and heat release rate, resulting in a single AHRR peak. This type of combustion cycles is similar to those observed in conventional SI engines (although the combustion duration is typically longer due to the lean condition) and is referred to as deflagration-only cycles. The other type of cycles shows higher in-cylinder pressure and heat release rate and exhibits two AHRR peaks. The first and second peaks correspond to the early flame propagation and the subsequent end-gas auto-ignition processes, respectively. This type of cycles is, therefore, referred to as mixed-mode cycles. Figure 7 shows the flame structure and dynamics of the two types of combustion cycles, namely deflagration-only (top) and mixed-mode cycles (bottom). In contrast to the deflagration-only cycle, earlier flame propagation is seen for the mixed-mode cycle, and isolated ignition spots are formed (∼7 CA) followed by volumetric auto-ignition in the end-gas. As end-gas auto-ignition rapidly consumes the reactants ahead of the flame fronts (7–20 CA), turbulent flame propagation due to deflagration is still present, although much slower than auto-ignition.

Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal

The two types of combustion cycles can further be distinguished from each other in the mass burned space as shown in Fig. 8, where burned mass fraction is calculated as the integrated heat release rate normalized by total heat released from each cycle. It is further seen that the initial flame propagation phase in the two types of combustion cycles are very similar to each other, while the mixed-mode cycles feature a second peak at ∼75% mass fraction burned (∼80% in experiment). The presence of the second peak is, therefore, employed as a criterion to systematically distinguish between these two types of cycles, without specifying any empirical threshold. With this criterion, the predicted fraction of mixed-mode cycles from the simulation is 61.5%, closely matching the experimental value 63.2%. Mixed-mode combustion cycles are further characterized by the mean formaldehyde mass fraction ($YCH2O$) inside the cylinder, versus the burned mass fraction, as shown in Fig. 9. Both types of cycles exhibit an initial plateau, indicating stable flame propagation. Compared with deflagration-only cycles, mixed-mode combustion cycles feature a rapid increase in $YCH2O$ near CA50, which leads to fast auto-ignition. The observed difference in evolution of $YCH2O$ can be explained as follows. In the flame propagation mode, CH2O is produced only within a thin layer (the preheat zone) ahead of the flame fronts, and therefore, $YCH2O$ is closely related to the total flame surface area, which does not vary significantly during a large part of the main heat release process. When chemical reactions in the end-gas are nonnegligible, the low-to-intermediate temperature chemistry starts to build up radical pools in the fresh mixture, and thus, $YCH2O$ increases exponentially until volumetric auto-ignition consumes it.

Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal

The difference between mixed-mode and deflagration-only cycles, and their correlations with combustion phasing are further investigated. Figure 10 shows the scatter of CA50 as function of peak heat release rate for all the simulation cycles overlaid on the experimental data. It is clear from both experimental and simulation results that mixed-mode combustion occurs with more advanced CA50. This is mainly because earlier flame propagation promotes auto-ignition by increasing in-cylinder pressure and temperature. The well-predicted correlation between mixed-mode combustion tendency and CA50 therefore further demonstrates the accuracy of the developed CFD model.

Fig. 10
Fig. 10
Close modal

### Effects of NOx Chemistry.

While the overall lean operation would generally reduce the production of thermal NO, the high octane number of the current E30 fuel forces the use of a fairly advanced combustion phasing to achieve mixed-mode combustion, and the associated increase of combustion temperature promotes thermal NO formation. A portion of the formed NOx will be retained in the residuals, potentially affecting the next cycle. Therefore, the effects of NOx on mixed-mode combustion, especially on the end-gas auto-ignition, are investigated in the following. The numerical modeling approach validated earlier allows for such an investigation by activating or deactivating the NOx chemistry in the reaction model, which cannot be achieved in experimental studies.

Figures 11(a) and 11(b) show the pressure and apparent heat release traces calculated using reaction models with and without NOx chemistry. While the flame propagation stage before auto-ignition occurs is not significantly impacted by NOx chemistry, the end-gas behavior is significantly altered. In particular, no end-gas auto-ignition is observed when NOx chemistry is absent, implying that NOx plays a significant role in promoting auto-ignition. Such auto-ignition enhancement by NOx is attributed to enhanced chain branching due to the presence of nonnegligible NOx-related radicals in the residual gas that can alter the reaction pathways during radical explosion and thereby modifying ignition delay. This is demonstrated in Fig. 11(c), showing that $YCH2O$ is produced much earlier and faster with the presence of NOx than that obtained without NOx chemistry. Note that the in-cylinder NO mole fraction at the intake value closing point, averaging over all the cycles, is found to be 2.6 × 10−4.

Fig. 11
Fig. 11
Close modal

Figure 12 further shows the effects of NOx chemistry in 0D homogeneous auto-ignition and 1D flame propagation. As shown in Fig. 12(a), the ignition delay calculated with and without NOx chemistry differs from each other when residual gas fraction (RGF) is not negligible, e.g., 5% (corresponding to the mean RGF for the present engine operation), in contrast to the case without any residual gas. NOx, however, has only a very small effect on the laminar flame propagation regardless of the level of residual gas (Fig. 12(b)), as it is mainly controlled by back diffusion of sensible heat and important intermediates such as H and OH. It is therefore suggested that when RGF is nonnegligible, NOx chemistry has to be accounted for to accurately predict auto-ignition.

Fig. 12
Fig. 12
Close modal

### Sensitivity to Fuel Properties.

Effects of physical and chemical properties of the E30 fuel, including heat of vaporization (HoV) and laminar flame speed (SL), on mixed-mode combustion characteristics are then examined. Local sensitivity analysis was employed by perturbing the fuel properties by $±30%$ with respect to their nominal values.

Figures 13(a) and 13(b) show the pressure and heat release rate traces obtained from simulations using −30%HoV, HoV, and +30%HoV, respectively. A higher HoV is expected to have a negative impact on overall combustion intensity by reducing the overall in-cylinder temperature. It is seen that a perturbation on HoV has a negligible effect on initial flame propagation. The auto-ignition-induced heat release rate is enhanced by a lower HoV, but suppressed with a higher HoV. The reason is that a higher HoV indicates the increased evaporation cooling, which induces a small reduction in in-cylinder temperature far before combustion occurs, as demonstrated in Fig. 13(c). Note that due to this charge cooling effect, changing HoV may also affect charged mass. However, for the perturbation range considered in this study, the effect of HoV on the in-cylinder equivalence ratio is found within 1% and therefore considered negligible.

Fig. 13
Fig. 13
Close modal

In contrast, the effect of laminar flame speed has a much larger impact on mixed-mode combustion. This is shown in Fig. 14 for the pressure and heat release traces calculated using −30%SL, SL, and +30%SL, respectively. Large SL not only advances the combustion phase but also increases the peak heat release rate during deflagrative flame propagation. As a result, subsequent auto-ignition is also advanced and intensified. In contrast, no auto-ignition is predicted for the lower SL and the overall heat release rate is much lower than the two larger SL values. Compared with the case with the nominal flame speed, the mean heat release rate at the first peak decreases by 23% for −30%SL and increases by 22% for +30%SL.

Fig. 14
Fig. 14
Close modal

Results shown earlier not only demonstrate the capability of the current modeling approach in capturing fuel property effects but also guide us to perform more detailed sensitivity analysis over a wider range of fuel properties. In particular, a coupled strategy of the neural network-based surrogate modeling approach, engine CFD, and global sensitivity analysis [32] could facilitate the understanding of the most influential fuel properties that enable mixed-mode combustion and lead to pathways for fuel-engine co-optimization. This topic will be addressed in the future work.

## Conclusions

A CFD model for lean, mixed-mode combustion in a DISI engine is developed in this work. Good agreement is observed between numerical results and experimental data, which demonstrates the capability of the developed CFD model in simultaneously characterizing deflagrative flame propagation and spontaneous auto-ignition for mixed-mode combustion. Moderate level of CCV is captured by simulation using an unsteady RANS approach. Instantaneous 3D flame structure reveals distinct combustion characteristics of deflagration-only cycles and mixed-mode cycles. Cycles with earlier flame propagation tend to produce mixed-mode combustion, since an advanced combustion phasing leads to the increased pressure and temperature which favor auto-ignition. In the mixed-mode cycles, isolated auto-ignition spots are observed which subsequently expand into the entire end-gas mixture. It is also seen that when both deflagration and auto-ignition are present, the deflagrative flame propagation is slightly suppressed by auto-ignition. The presence of auto-ignition is witnessed by the dramatically increased CH2O radical concentration. The positive correlation between occurrence of mixed-mode cycles and advanced CA50 is predicted in good agreement with experimental measurement.

The validated numerical model is then employed to investigate the effects of NOx chemistry and different fuel properties including HoV and laminar flame speed SL. NOx chemistry is found to play an important role in promoting auto-ignition chemistry via retained residual gases, while the effect on flame propagation is minimal. Local sensitivity studies are performed to provide preliminary investigation of fuel property effects on mixed-mode combustion. Overall, flame propagation is not significantly modified with a perturbation in HoV, while a higher HoV reduces the auto-ignition tendency and peak heat release rate in the end-gas. An increase in the laminar flame speed significantly enhances the combustion phasing, for both deflagration and auto-ignition stages. A higher SL promotes flame propagation in terms of both combustion phasing and peak heat release. The enhanced flame propagation further enhances end-gas auto-ignition and raises the second peak in heat release rate since an advanced combustion phasing increases the compression heating of the end-gas. Across the parameter ranges studied here, the impact of SL is found much stronger than that of HoV on mixed-mode combustion.

## Acknowledgment

UChicago Argonne, LLC, operator of Argonne National Laboratory (Argonne), a US Department of Energy (DOE) Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. This research was partially funded by DOE’s Office of Vehicle Technologies, Office of Energy Efficiency and Renewable Energy under Contract No. DE-AC02-06CH11357. The authors wish to thank Gurpreet Singh, Michael Weismiller, and Kevin Stork, program managers at DOE, for their support. This research was conducted as part of the Co-Optimization of Fuels & Engines (Co-Optima) project sponsored by the US DOE’s Office of Energy Efficiency and Renewable Energy (EERE), Bioenergy Technologies and Vehicle Technologies Offices. We gratefully acknowledge the computing resources provided on Bebop, a high-performance computing cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory. The engine experiments were performed at the Combustion Research Facility, Sandia National Laboratories, Livermore, CA. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.

## References

1.
Urushihara
,
T.
,
Yamaguchi
,
K.
,
Yoshizawa
,
K.
, and
Itoh
,
T.
,
2005
, “
A Study of a Gasoline-Fueled Compression Ignition Engine Expansion of HCCI Operation Range Using SI Combustion as a Trigger of Compression Ignition
,”
SAE Trans.
,
114
, pp.
419
425
.
2.
Zigler
,
B.
,
Keros
,
P.
,
Helleberg
,
K.
,
Fatouraie
,
M.
,
Assanis
,
D.
, and
Wooldridge
,
M.
,
2011
, “
An Experimental Investigation of the Sensitivity of the Ignition and Combustion Properties of a Single-Cylinder Research Engine to Spark-Assisted HCCI
,”
Int. J. Engine Res.
,
12
(
4
), pp.
353
375
. 10.1177/1468087411401286
3.
Sjöberg
,
M.
, and
Zeng
,
W.
,
2016
, “
Combined Effects of Fuel and Dilution Type on Efficiency Gains of Lean Well-Mixed DISI Engine Operation With Enhanced Ignition and Intake Heating for Enabling Mixed-Mode Combustion
,”
SAE Int. J. Engines
,
9
(
2
), pp.
750
767
. 10.4271/2016-01-0689
4.
Hu
,
Z.
,
Zhang
,
J.
,
Sjöberg
,
M.
, and
Zeng
,
W.
,
2019
, “
The Use of Partial Fuel Stratification to Enable Stable Ultra-Lean Deflagration-Based Spark-Ignition Engine Operation With Controlled End-Gas Autoignition of Gasoline and E85
,”
Int. J. Engine Res.
,
21
(
9
), pp.
1678
1695
. 10.1177/1468087419889702
5.
Ma
,
X.
,
Wang
,
Z.
,
Jiang
,
C.
,
Jiang
,
Y.
,
Xu
,
H.
, and
Wang
,
J.
,
2014
, “
An Optical Study of In-Cylinder CH2O and OH Chemiluminescence in Flame-Induced Reaction Front Propagation Using High Speed Imaging
,”
Fuel
,
134
, pp.
603
610
. 10.1016/j.fuel.2014.06.002
6.
Reuss
,
D. L.
,
Kuo
,
T. -W.
,
Silvas
,
G.
,
Natarajan
,
V.
, and
Sick
,
V.
,
2008
, “
Experimental Metrics for Identifying Origins of Combustion Variability During Spark-Assisted Compression Ignition
,”
Int. J. Engine Res.
,
9
(
5
), pp.
409
434
. 10.1243/14680874JER01108
7.
Dahms
,
R.
,
Felsch
,
C.
,
Röhl
,
O.
, and
Peters
,
N.
,
2011
, “
Detailed Chemistry Flamelet Modeling of Mixed-Mode Combustion in Spark-Assisted HCCI Engines
,”
Proc. Combust. Inst.
,
33
(
2
), pp.
3023
3030
. 10.1016/j.proci.2010.08.005
8.
Middleton
,
R. J.
,
Olesky
,
L. K. M.
,
Lavoie
,
G. A.
,
Wooldridge
,
M. S.
,
Assanis
,
D. N.
, and
Martz
,
J. B.
,
2015
, “
The Effect of Spark Timing and Negative Valve Overlap on Spark Assisted Compression Ignition Combustion Heat Release Rate
,”
Proc. Combust. Inst.
,
35
(
3
), pp.
3117
3124
. 10.1016/j.proci.2014.08.021
9.
Richards
,
K. J.
,
Senecal
,
P. K.
, and
Pomraning
,
E.
,
2018
, “
CONVERGE Manual (Version 2.4)
10.
Amsden
,
A. A.
, and
Findley
,
M.
,
1997
, “
KIVA-3V: A Block-Structured KIVA Program for Engines With Vertical or Canted Valves
,
Lawrence Livermore National Laboratory
,
Livermore, CA
, Technical Report, Report LA–13313-MS, Los Alamos National Laboratory, CA.
11.
Reitz
,
R. D.
, and
Diwakar
,
R.
,
1987
, “
Structure of High-Pressure Fuel Sprays
,”
SAE Trans.
,
96
, pp.
492
509
.
12.
Reitz
,
R. D.
,
1987
, “
Modeling Atomization Processes in High-Pressure Vaporizing Sprays
,”
Atom. Spray Technol.
,
3
(
4
), pp.
309
337
.
13.
Patterson
,
M. A.
, and
Reitz
,
R. D.
,
1998
, “
Modeling the Effects of Fuel Spray Characteristics on Diesel Engine Combustion and Emission
,”
SAE Trans.
,
107
, pp.
27
43
.
14.
Froessling
,
N.
,
1958
, “
Evaporation, Heat Transfer, and Velocity Distribution in Two-Dimensional and Rotationally Symmetrical Laminar Boundary-Layer Flow
,” Technical Report, Report No. NACA-TM-1432, National Aeronautics and Space Administration, Washington, DC.
15.
Liu
,
A. B.
,
Mather
,
D.
, and
Reitz
,
R. D.
,
1993
, “
Modeling the Effects of Drop Drag and Breakup on Fuel Sprays
,”
SAE Trans.
,
102
, pp.
83
95
.
16.
Van Dam
,
N.
,
Sjöberg
,
M.
, and
Som
,
S.
,
2018
, “
Large-Eddy Simulations of Spray Variability Effects on Flow Variability in a Direct-Injection Spark-Ignition Engine Under Non-Combusting Operating Conditions
,” Technical Report, SAE Technical Paper 2018-01-0196.
17.
Peters
,
N.
,
2000
,
Turbulent Combustion
,
Cambridge University Press
,
Cambridge, UK
.
18.
Pal
,
P.
,
Kolodziej
,
C.
,
Choi
,
S.
,
Som
,
S.
,
Broatch
,
A.
,
Gomez-Soriano
,
J.
,
Wu
,
Y.
,
Lu
,
T.
, and
See
,
Y. C.
,
2018
, “
Development of a Virtual CFR Engine Model for Knocking Combustion Analysis
,”
SAE Int. J. Engines
,
11
(
6
), pp.
1069
1082
. 10.4271/2018-01-0187
19.
Pal
,
P.
,
Wu
,
Y.
,
Lu
,
T.
,
Som
,
S.
,
See
,
Y. C.
, and
Le Moine
,
A.
,
2018
, “
Multidimensional Numerical Simulations of Knocking Combustion in a Cooperative Fuel Research Engine
,”
ASME J. Energy. Res. Technol.
,
140
(
10
), p.
102205
. 10.1115/1.4040063
20.
Yue
,
Z.
,
Edwards
,
K. D.
,
Sluders
,
C. S.
, and
Som
,
S.
,
2019
, “
Prediction of Cyclic Variability and Knock-Limited Spark Advance in a Spark-Ignition Engine
,”
ASME J. Energy. Res. Technol.
,
141
(
10
), p.
102201
. 10.1115/1.4043393
21.
Mehl
,
M.
,
Zhang
,
K.
,
Wagnon
,
S.
,
,
G.
,
Westbrook
,
C. K.
,
Pitz
,
W. J.
,
Zhang
,
Y.
,
Curran
,
H.
,
Rachidi
,
M. A.
,
Atef
,
N.
, and
Sarathy
,
M. S.
,
2017
, “
A Comprehensive Detailed Kinetic Mechanism for the Simulation of Transportation Fuels
,”
10th US National Combustion Meeting
,
College Park, MD
,
Apr. 23–26
.
22.
scikit learn
, “
1.17. Neural network models (supervised)
,”https://scikit-learn.org/stable/modules/neural_networks_supervised.html Accessed May 13, 2019.
23.
Ahmed
,
A.
,
Goteng
,
G.
,
Shankar
,
V. S.
,
Al-Qurashi
,
K.
,
Roberts
,
W. L.
, and
Sarathy
,
S. M.
,
2015
, “
A Computational Methodology for Formulating Gasoline Surrogate Fuels With Accurate Physical and Chemical Kinetic Properties
,”
Fuel
,
143
, pp.
290
300
. 10.1016/j.fuel.2014.11.022
24.
Mehl
,
M.
,
Chen
,
J.-Y.
,
Pitz
,
W. J.
,
Sarathy
,
S. M.
, and
Westbrook
,
C. K.
,
2011
, “
An Approach for Formulating Surrogates for Gasoline With Application Toward a Reduced Surrogate Mechanism for CFD Engine Modeling
,”
Energy. Fuels.
,
25
(
11
), pp.
5215
5223
. 10.1021/ef201099y
25.
Singh
,
E.
,
,
J.
,
Mehl
,
M.
, and
Sarathy
,
S. M.
,
2017
, “
Chemical Kinetic Insights Into the Octane Number and Octane Sensitivity of Gasoline Surrogate Mixtures
,”
Energy. Fuels.
,
31
(
2
), pp.
1945
1960
. 10.1021/acs.energyfuels.6b02659
26.
Naser
,
N.
,
Yang
,
S. Y.
,
Kalghatgi
,
G.
, and
Chung
,
S. H.
,
2017
, “
Relating the Octane Numbers of Fuels to Ignition Delay Times Measured in an Ignition Quality Tester (IQT)
,”
Fuel
,
187
, pp.
117
127
. 10.1016/j.fuel.2016.09.013
27.
Naser
,
N.
,
Sarathy
,
S. M.
, and
Chung
,
S. H.
,
2018
, “
Estimating Fuel Octane Numbers From Homogeneous Gas-phase Ignition Delay Times
,”
Combust. Flame.
,
188
, pp.
307
323
. 10.1016/j.combustflame.2017.09.037
28.
,
J. A.
,
Bokhumseen
,
N.
,
Mulla
,
N.
,
Sarathy
,
S. M.
,
Farooq
,
A.
,
Kalghatgi
,
G.
, and
Gaillard
,
P.
,
2015
, “
A Methodology to Relate Octane Numbers of Binary and Ternary N-Heptane, Iso-Octane and Toluene Mixtures With Simulated Ignition Delay Times
,”
Fuel
,
160
, pp.
458
469
. 10.1016/j.fuel.2015.08.007
29.
SciPy.org
, “
Optimization and Root Finding (scipy.optimize)
,” https://docs.scipy.org/doc/scipy/reference/optimize.html Accessed May 13, 2019.
30.
Whitesides
,
R. A.
, and
McNenly
,
M. J.
,
2018
, “
Prediction of RON and MON of Gasoline Surrogates by Neural Network Regression of Ignition Delay Times and Fuel Properties
,”
,
Lemont, IL
,
Jan. 29–Feb. 1
.
31.
Lu
,
T. F.
, and
Law
,
C. K.
,
2008
, “
Strategies for Mechanism Reduction for Large Hydrocarbons: n-Heptane
,”
Combust. Flame.
,
154
(
1–2
), pp.
153
163
. 10.1016/j.combustflame.2007.11.013
32.
Pal
,
P.
,
Probst
,
D.
,
Pei
,
Y.
,
Zhang
,
Y.
,
Traver
,
M.
,
Cleary
,
D.
, and
Som
,
S.
,
2017
, “
Numerical Investigation of a Gasoline-Like Fuel in a Heavy-Duty Compression Ignition Engine Using Global Sensitivity Analysis
,”
SAE Int. J. Fuels Lubricants
,
10
(
1
), pp.
56
68
. 10.4271/2017-01-0578