Modeling pre-spark heat release and low temperature chemistry of iso-octane in a boosted spark-ignition engine

Combustion and Flame 212 (2020) 39–52

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Modeling pre-spark heat release and low temperature chemistry of iso-octane in a boosted spark-ignition engineR Dan A. DelVescovo a,∗, Derek A. Splitter b, James P. Szybist b, Gurneesh S. Jatana b a b

Department of Mechanical Engineering, Oakland University, 115 Library Drive, Rochester, MI 48309, USA Fuels, Engines, and Emissions Research Center, Oak Ridge National Laboratory, 2360 Cherahala Blvd, Knoxville, TN 37932, USA

a r t i c l e

i n f o

Article history: Received 6 June 2019 Revised 23 July 2019 Accepted 6 October 2019

Keywords: Low temperature chemistry Chemical kinetics Knock Spark ignition Engine modeling

a b s t r a c t Recent trends among automotive manufacturers towards downsized, boosted engines make it imperative to understand specific fuel chemistry interactions encountered in this new operating regime. At these elevated pressure conditions a phenomenon called pre-spark heat release has recently been discovered, and is characterized by kinetically controlled heat release before spark, with resultant changes in endgas thermodynamic state and composition. These reactions typically occur in the end-gas during normal operation, but are obscured by the deflagration heat release and therefore cannot be easily studied. A 2-zone spark-ignition engine model was utilized to determine whether chemical kinetic mechanisms are able to predict this phenomenon, and whether they accurately capture end-gas thermodynamic history. Experimental engine data at a range of boosted operating conditions demonstrating pre-spark heat release were compared with simulations using mechanisms representing the latest developments in gasoline kinetic modeling. The results demonstrated significant discrepancies between mechanisms, and between experimental and simulated results in terms of low-temperature heat release magnitude, end-gas thermodynamic state, and autoignition propensity. The results highlight shortcomings in low-temperature reaction pathways, and indicate the necessity of simultaneously matching first-stage ignition delay and heat release magnitude, in addition to second-stage ignition delay, in order to accurately predict end-gas thermodynamics and autoignition. © 2019 The Authors. Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction Concerns over global carbon dioxide (CO2 ) emissions and pressure from regulatory agencies have driven engine manufacturers in recent decades towards engine technologies such as gasoline direct injection, variable valve timing, engine downsizing, and turbocharging. These technologies have resulted in significant improvements in vehicle fuel economy to date, while further efficiency gains are possible with improved knock resistance from

R This manuscript has been authored by UT-Battelle, LLC, under contract DEAC05-00OR22725 with the US Department of Energy (DOE). The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retainsa non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/ downloads/doepublic- access- plan). ∗ Corresponding author. E-mail address: [email protected] (D.A. DelVescovo).

the fuel [1]. In the US, gasoline fuels are sold based on the AntiKnock Index (AKI), which represents the average of the Research Octane Number (RON) [2] and Motor Octane Number (MON) [3] of the fuel. These two test conditions represent different pressure– temperature trajectories due to variations in the inlet mixture temperature; MON representing a higher temperature condition [4–6]. The difference between RON and MON is referred to as the Octane Sensitivity, and is a relative measure of the sensitivity of a fuel to operating conditions compared to the primary reference fuels used to define the RON and MON scales [2,3]. Many researchers have shown the benefits of both high octane and high sensitivity fuels on engine performance and thermal efficiency in boosted engines [4,7], and Splitter et al. [1] discusses potential efficiency improvements through the adoption of higher ethanol (which has high octane sensitivity) blending fractions to increase octane number, allowing for the use of higher compression ratios. Szybist and Splitter [4] identified a phenomenon called prespark heat release (PSHR) for low octane number sensitivity fuels such as iso-octane and most current U.S. commercial gasoline fuels at elevated intake pressure and temperature conditions, and found

https://doi.org/10.1016/j.combustflame.2019.10.009 0010-2180/© 2019 The Authors. Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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D.A. DelVescovo, D.A. Splitter and J.P. Szybist et al. / Combustion and Flame 212 (2020) 39–52 Table 1 GM Ecotec 2.0 L LNF engine geometry and experimental operating conditions. Bore [mm] Stroke [mm] Conrod length [mm] Wrist pin offset [mm] IVC [°CA ATDC] EVO [°CA ATDC] Compression ratio [dimensionless] Speed [r/min] Airflow [g/min] External EGR [%] Residual [%] CA50 [°CA ATDC] IMEPg [bar] Injection timing [°CA ATDC] a

86.0 86.0 145.5 0.8 −141 130 9.2:1a 2000 804, 684 0, 14 7–8 32–35, 47–51 11–15 −280

Reduced to 8.7:1 in post-processing.

that the tendency towards PSHR decreased with increasing octane sensitivity. They demonstrated that PSHR is a kinetically-controlled phenomenon, and not caused by an independent deflagration event. In a subsequent work, Splitter et al. [8] showed that PSHR magnitude correlated with LSPI frequency, but that the occurrence of PSHR was not necessarily an indicator of LSPI potential. Further work demonstrated that operating conditions demonstrating PSHR actually improve fuel knock resistance under high intake manifold temperature conditions [9]. Additionally, Vuilleumier and Sjöberg [10] showed that the magnitude of charge heating in the end-gas due to low temperature heat release (LTHR) plays a significant role in the knock tolerance of a given fuel, and that the magnitude of this LTHR is strongly influenced by the fuel’s chemical composition, while further work [11,12] found that LTHR reduced end-gas thermal stratification, thereby increasing knock intensity. Because PSHR is a distinct process from deflagration, it can be used as a tool to assess kinetic mechanism thermodynamic and knocking predictions at stoichiometric conditions for gasolinerelevant fuels without needing to model the deflagration process in significant detail. A mechanism which adequately predicts end-gas thermodynamic conditions for cases demonstrating PSHR would then provide confidence when simulating cases where low temperature heat release takes place in the end-gas during the main deflagration event where it would otherwise be obscured. The simulations could then provide valuable information regarding the controlling mechanisms of this behavior, including identifying important reaction pathways, and determining whether PSHR, a fuel-specific phenomena, is desirable or undesirable in terms of flame propagation, knocking tendencies, and efficiency, and thereby potentially informing desirable fuel compositions under boosted operating conditions. 2. Methodology 2.1. Experimental approach Iso-octane was chosen for the preliminary analysis because its chemical kinetics have been extensively studied by numerous researchers including [13–15], due to its relevance in the standard RON [2] and MON [3] test methods, and because it is a fuel which exhibits negative temperature coefficient (NTC) behavior [13]. Iso-octane also comprises a significant portion of many gasoline surrogate fuels [16], representing various iso-alkane components. The experimental data utilized in this work was collected on a single-cylinder version of a 2.0 L GM Ecotec LNF engine, the specific geometry and operating conditions studied in this work are shown in Table 1. A more complete description of the laboratory configuration, data collection, and post-processing routines can be found in [4].

A wide range of non-knocking operating conditions with and without exhaust gas recirculation (EGR) were experimentally tested, though this work focuses only on non-knocking cases at two fixed combustion phasings of 33±1° and 48±1° after top dead center firing (ATDC), at 6 intake temperatures between 41 °C and 131 °C with 0% and 14% EGR. Additionally, the cases with 14% EGR were operated under two distinct conditions, one which displaced fresh air with EGR, thus effectively matching intake pressure, and the second which matched air flowrate with the addition of EGR, leading to higher intake pressures. The combustion phasing was defined by the CA50 value, which corresponds to the crank angle of 50% mass fraction burned (MFB). These conditions represent stoichiometric, boosted, moderately high load operation with a nominal indicated gross mean effective pressure (IMEPg ) of 11– 15 bar depending on combustion phasing and air flowrate. The operating conditions studied in this work utilize combustion phasings significantly retarded from typical SI engine operation in order to study PSHR behavior. These late combustion phasings are typically avoided due to reduced engine efficiency. The LTHR behavior which causes PSHR typically occurs in the end-gas concurrent with deflagration during normal SI operation for fuels exhibiting two-stage ignition, particularly under boosted operating conditions, but is obscured by the magnitude of the deflagration heat release. Thus, late combustion phasings were investigated in order to decouple the kinetic behaviors from the deflagration-driven combustion event. 2.2. Modeling approach The modeling results shown in this work utilize the builtin zero-dimensional, two-zone Spark Ignited (SI) engine model R associated with the Chemkin Pro package in ANSYS v18.1. This model utilizes detailed chemistry to predict end-gas autoignition, but the solver will predict any chemical heat release, including LTHR. The two zones represent the unburned fuel/air/EGR and the burned gases respectively. Mass is transferred between the zones at the rate and timing specified by a user inputted Wiebe function. For each operating condition, a best-fit Wiebe function was determined from the experimental MFB profile between 1% (CA1) and 98% (CA98) mass fraction burned with a least-squared error approach by iterating the Wiebe parameters θ o , θ , and m, shown in Eq. (1), and minimizing the error between the calculated and experimental profiles. In general, this single-Wiebe function approach provided a very good fit for cases without EGR and non-knocking cases. Cases with EGR exhibit slow burn rates which are poorly fit by a single Wiebe function at these operating conditions, whereas knocking cases distort the heat release shape even when the ensemble averaged curve is utilized. For cases exhibiting PSHR behavior in excess of 1% of the total fuel energy, this fitting procedure introduces a small amount of error in the “best fit” Wiebe function due to over-fitting of the initial burn rate. Additionally, any end-gas chemical energy release that occurs during deflagration should ideally be omitted from the burn-rate fit, however it is unclear how to accomplish this a priori.



MFB = 1 − exp −6.908



CA − θ0

θ

m+1 

(1)

The heat transfer correlation utilized in this work was the Woschni formulation [17], with the scaling parameter and cylinder wall temperature tuned to match the experimental pressure, and the heat transfer coefficients used in this work are shown in Table 2. With a fixed scaling parameter, the cylinder wall temperature was made to be a linear function of intake temperature according to Eq. (2) to adequately match the experimental data. Minor tuning to the IVC temperature was required to match the

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Table 2 Woschni heat transfer correlation parameters. Head area ratio Piston area ratio a b c C11 C12 C2

1.136 1.0 0.06 0.8 0 2.28 0.308 0.324

experimental pressure, on the order of 5–15 K from the experimentally calculated IVC temperatures, illustrating good overall agreement with the data. The methods used to calculate experimental quantities such as trapped mass, IVC temperature, and residual fraction (RF) are discussed in [4]. Residual gas composition was assumed to be identical to the measured exhaust emissions at each operating condition, comprised of only CO2 , water vapor, oxygen, nitrogen, carbon monoxide, hydrogen, nitrogen oxide (NO), and unburned hydrocarbons (uHC), which was assumed to be composed entirely of unburned fuel (i.e. iso-octane). All of the experimental measurements and model parameters utilized in this work for the cases studied can be found in the Supplementary Materials.

Twall = 535 + Tintake

(2)

3. Results and discussion

Fig. 2. Apparent heat release vs. crank angle in region of potential PSHR for isooctane at λ = 1, 804 g/min airflow, 0% EGR, and CA50 of 33±1 o ATDC.

3.1. Experimental results Figure 1 shows the 20 0 0 cycle ensemble averaged experimental pressure and heat release rate profile for a case which demonstrates fully-developed PSHR, with spark timing denoted on the heat release line. A clear and distinct LTHR event, reminiscent of that commonly observed in purely kinetically controlled combustion strategies such as Homogeneous Charge Compression Ignition and Partial Fuel Stratification [18], is present before spark. This phenomenon is clearly shown in the inset axis. The PSHR at this operating condition ends just after the spark, before any appreciable heat release from deflagration occurs. The evolution of PSHR as a function of intake temperature can be seen in Fig. 2, where for the lowest intake temperature investigated (41 °C), no discernable PSHR is observed, but for the highest intake temperature (131 °C), a clear and distinct PSHR event is observed. Between these extremes (77 °C to 117 °C), there is evidence of developing PSHR that is not associated with the main de-

flagration event. At a sufficiently high temperature (117 °C), PSHR reaches a local maxima, but at lower temperatures the LTHR blends into the main deflagration. At these elevated pressure conditions it is very likely that all cases exhibit some amount of LTHR in the end-gas. This process cannot easily be deconvoluted in experimental data for cases where LTHR overlaps the much higher magnitude deflagration heat release, but cases which exhibit LTHR before deflagration provide the decoupled data necessary to validate the models with a 2-zone methodology so that the models can then be used to elucidate the LTHR process that is currently obscured by deflagration. 3.2. Initial simulation results The first step in analyzing the effects of PSHR was ensuring that the thermodynamic conditions (i.e. temperature and pressure) of the end-gas can be accurately modeled, given the sensitivity of phenomena like knock and LSPI on the thermodynamic state of the end-gas [8]. Four recent chemical kinetic mechanisms [16,19–21] were selected from the literature to determine whether any of the mechanisms could accurately match the experimental PSHR magnitude and phasing, and selected mechanism details are shown in Table 3. Each of the selected mechanisms were developed to simulate gasoline surrogate fuel mixtures in engine applications, and as such they all contain reaction pathways for iso-octane, n-heptane, and toluene at a minimum, representing the iso-alkane, n-alkane, and aromatic components of gasoline Table 3 Selected gasoline surrogate kinetic mechanisms.

Fig. 1. Ensemble averaged pressure and apparent heat release rate vs. crank angle, one standard deviation in shaded grey region for iso-octane, at λ = 1, Tin = 131 °C, 804 g/min airflow, and 0% EGR. Inset axis (top left) showing the PSHR behavior.

Mechanism

Andrae

Cai

Mehl

Ren

Year Species Reactions NOx chem Reference

2016 125 583 None [19]

2015 335 1610 GRIv3.0 [20]

2011 312 1488 None [16]

2017 178 758 GRIv3.0 [21]

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Fig. 3. Pressure and apparent heat release vs. crank angle, at three intake temps (41 °C, 98 °C, and 131 °C) with CA50 of 33±1 o ATDC, and Chemkin predictions for 4 kinetic mechanisms.

respectively. These reduced gasoline surrogate mechanisms were chosen for analysis in this work with an eye towards modeling this behavior for real gasoline blends including the behavior observed in [4,6,9], and for modeling this behavior in high fidelity 3-D computational fluid dynamics simulations, which are unable to utilize detailed chemical kinetic mechanisms without excessive computational costs. Each of the kinetic mechanisms was validated directly against neat iso-octane/air ignition delay data at some point in their development. For the Cai and Pitsch [20] and Ren et al. [21] mechanisms, this validation can be found directly in the referred to work, while for the Mehl et al. [16] and Andrae and Kovacs [19] mechanisms this can be found in their original formulations, Mehl et al. [22] and Andrae et al. [23], respectively. Figure 3 shows the results of the simulations for each kinetic mechanism compared to the ensemble-averaged pressure and heat release rate at three intake temperature conditions and a combustion phasing of 33±1 o ATDC. Spark timing was varied in each case to achieve the desired combustion phasing. The representative conditions shown were chosen to demonstrate cases with no PSHR (41 °C), PSHR that blends into the deflagration (98 °C), and fully

decoupled PSHR (131 °C). Each mechanism predicts significant differences in the LTHR magnitude and phasing. The Mehl et al. [16] mechanism predicts no LTHR for any of the cases shown, while Cai and Pitsch [20] and Ren et al. [21] predict similar LTHR phasing to the experiments at 98 °C and 131 °C, and Andrae and Kovacs [19] predicts a delayed LTHR event, and even predicts high-temperature auto-ignition in the 131 °C case despite no evidence of auto-ignition or knock in the experimental data (experimental knock limit at 131 °C was 9 °CA more advanced than present analysis). For the mechanisms that show PSHR, there is a small peak due to low-temperature reactions in the unconsumed end-gas near the peak heat release rate for the 41 °C case, though this LTHR is indiscernible from the deflagration heat release in the experimental data. Based on emissions measurements and residual fractions, the highest residual NO levels were about 100 ppm at IVC. Given the important role of NOx in the fuel oxidation and radical formation processes even in low concentrations [24], it is not surprising that the two mechanisms that include NOx chemistry (i.e. Ren-2017 and Cai-2015) provide the best predictions of LTHR phasing and magnitude, while the mechanisms that do not (i.e. Mehl-2011 and Andrae-2016) do not agree well. This result reinforces the importance of the inclusion of NOx chemistry in chemical kinetic mechanisms for end-gas thermodynamic and autoignition prediction. In an effort to represent the end-gas thermodynamic state for each of the three intake temperature conditions (i.e. 41 °C, 98 °C, and 131 °C) shown in Fig. 3, the predicted pressure– temperature trajectories using the Ren-2017 kinetic mechanism are plotted in Fig. 4. Additionally as a point of reference, the predicted pressure and heat release rate as a function of crank angle are shown in the same figure. The end-gas trajectories are overlaid on contour plots of ignition delay from constant volR ume simulations performed in Matlab using Cantera over a wide range of initial conditions used to generate the contours. Ignition here was defined as a 50 K temperature rise from the initial state, thus providing a consistent metric representing measurable energy release via chemical reactions in the unburned mixture (which could correspond to first-stage or second-stage ignition depending on thermodynamic conditions), and was chosen to be consistent with a previous related work [4]. The controlling mechanism of temperature/pressure change (i.e. piston compression/expansion, deflagration compression, or low-temperature heat release) for each portion of the trajectory is denoted in the figure by the accompanying linestyle, and trajectories were truncated at the crank angle of 98% MFB. This same convention is utilized in the plot of predicted pressure and heat release rate as a function of crank angle. Portions of the paths where dotted and dashed lines overlap (e.g. for the 41 °C case) indicate LTHR occurring during the main deflagration event. As can be seen in the zoomed axis for the 41 °C case, the late combustion phasing utilized in this work results in a brief decrease in end-gas temperature and pressure as the gases expand after TDC resulting in a local pressure maximum near TDC. During expansion, the end-gas temperature is lower for a corresponding compression pressure due to heat transfer to the cylinder walls, causing the trajectory to “hook” to the left on these axes. The effect of the deflagration process on the unburned zone is to increase the temperature and pressure via compression heating in a polytropic manner. Because the 2-zone model in Chemkin utilized in this work does not account for heat transfer between the burned and unburned zones, the only mechanism capable of shifting the trajectory away from pure polytropic compression/expansion behavior is chemical energy release in the end-gas. In order to evaluate the choice of kinetic mechanism on the predicted end-gas thermodynamics, the unburned temperature/pressure trajectories were plotted separately for each mechanism at the three intake temperature conditions (i.e. 41 °C,

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Fig. 4. Ren-2017 predicted unburned P–T trajectories overlayed on ignition delay contours (ignition defined as 50 K temperature rise) (top) and pressure and AHRR vs. crank angle (bottom) for three intake temperatures at constant CA50 of 33±1 o ATDC. Mode of P–T changes denoted by linestyle. Zoomed windows magnified 4.5×.

98 °C, and 131 °C) in Fig. 5. These trajectories are overlaid on contour plots of ignition delay derived from constant volume simulations for each mechanism utilizing the methodology previously described. From the figure, it is clearly seen that the choice of kinetic mechanism has a strong effect on the predicted end-gas thermodynamic state due to differences in low-temperature chemistry, as each of the mechanisms predicts a distinctly different thermodynamic trajectory after the onset of low-temperature reactions for each operating condition. Additionally, the ignition delay contours vary drastically between the given mechanisms with respect to the onset of chemical energy release. LTHR is characterized in these trajectories by a distinct change in slope, shifting the end-gas into a higher temperature regime than would otherwise be predicted by the polytropic nature of the compression/expansion and deflagration processes. In general at these engine operating conditions, the end-gas becomes chemically reactive when the ignition delay for that mixture is between 1 and 3 ms. To better understand the discrepancies observed in Figs. 3 and 5, ignition delay simulations were performed for the four tested kinetic mechanisms via two additional methods. The first utilized rapid compression machine (RCM) simulations performed in Chemkin Pro using a closed homogeneous batch reactor model to simulate RCM experiments for iso-octane collected from literature [15]. This dataset in particular was chosen because the authors

Fig. 5. Predicted unburned P–T trajectories for three intake temperatures overlayed on ignition delay contours (ignition defined as 50 K temperature rise) for each tested mechanism. Mode of P–T changes denoted by linestyle.

provided both calculated RCM volume traces, and measured pressure data, allowing for a more rigorous comparison than ignition delay alone. The variable volume profile was specified in the reactor model, and the initial temperature and pressures were set to achieve the appropriate end-of-compression (EOC) state. Three EOC temperatures were simulated (704 K, 814 K, and 852 K), all at an EOC pressure of 20 bar. In a recent work, Salih et al. [25] showed that the same 814 K, 20 bar case’s thermodynamic

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Fig. 6. Temperature (top) and rate of temperature change (bottom) vs time for CV ignition of iso-octane at initial conditions of 750 K and 20 bar and λ = 1.0 using the Ren et al. [21] mechanism.

trajectory matches well with the trajectory for iso-octane under RON operating conditions until the EOC state, while the 704 K, 20 bar case would represent a “beyond RON” condition, more representative of the engine operating conditions in this work. The second set of ignition delay simulations utilized a constant volume (CV), homogeneous, adiabatic reactor model solved using R the Cantera toolbox in Matlab at an initial pressure of 20 bar, and a wide range of initial temperatures. Ignition (corresponding to “2nd Stage Ignition”) was defined as the time of maximum rate of temperature change, while “1st Stage Ignition” was defined if a local maxima in the rate of temperature change was detected before the main ignition event. Additionally, if a distinct 1st stage ignition event was detected, the magnitude of this event (in K) was defined as the difference in temperature between the point of local minima in rate of temperature change between 1st and 2nd stage ignition, and the initial temperature. This definition criterion is depicted graphically for a representative condition in Fig. 6. All simulated ignition delay cases presented here were at stoichiometric conditions with no residual gas or EGR considered. Figure 7 shows the results of the RCM simulations, and the CV simulation results are shown in Fig. 8 at the conditions described. For reference, the three RCM simulation EOC temperatures, and experimental ignition delay values (for the 2nd stage ignition) are highlighted on the CV ignition delay simulation plots. It can clearly be seen from both figures that significant differences can be observed between mechanisms for even a well-studied fuel like iso-octane, including large differences in 1st and 2nd stage ignition timing, particularly in the NTC region, as well as 1st stage magnitude. From the RCM simulations, a similar trend to the engine simulations shown in Fig. 3 can be observed for the 704 K case with respect to the LTHR magnitude and phasing (i.e. that the Ren-2017 and Cai-2015 mechanisms match LTHR phasing, but over-predict the magnitude). The Andrae-2016 and Cai-2015 mechanisms exhibit good prediction of the 2nd stage ignition delay for the 704 K, 20 bar case, but arrive at this value via distinctly different pathways. This implies that at engine operating conditions resembling this RCM condition, these two mechanisms would likely provide reasonable “knocking” predictions, but via different end-gas thermodynamic paths, neither of which representing the true end-gas conditions. These results highlight some obvious and significant discrepancies that exist in mechanisms

Fig. 7. RCM simulations for the four tested mechanisms compared to experimental RCM data from Nour et al. [15] for iso-octane at 704 K, 814 K and 852 K and EOC pressure of 20 bar, and λ = 1.0.

available in the literature, as well as limitations which exist in current mechanism validation procedures. To determine the predicted kinetic state of the unburned region based on the Chemkin 2-zone engine simulations, autoignition integrals utilizing a Livengood–Wu approach [26] were calculated based on the simulation results. Cantera was used to determine the ignition delay of the unburned zone by supplying the unburned zone temperature, pressure, and composition at each crank angle index from the Chemkin results. In this approach, ignition delay was defined as the location of maximum rate of temperature change (corresponding to 2nd stage ignition). For each operating condition, two simulations were performed. In the first set of simulations (referred to as non-reacting), the unburned zone chemistry was turned off such that the unburned zone composition remained constant through the simulation, and the thermodynamics were only influenced by compression/expansion processes (including compression induced by the deflagration) and heat transfer. The second set of cases utilized the reacting unburned zone simulations previously shown here. Figure 9 shows the autoignition integral (AI) value at CA98 for the three intake temperature conditions previously shown. The figure depicts the AI values for the non-reacting unburned zone cases colored by kinetic mechanism, with the change in AI value from the reacting case in white stacked on top of each bar. Thus, the difference between the top of each white bar and the top of each colored bar indicates the change in autoignition propensity of the unburned region due to the combined thermodynamic and compositional changes induced by LTHR.

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the Mehl mechanism penetrate into the NTC region, leading to increased ignition delay with increasing temperature. The Cai mechanism shows non-monotonic behavior, as considering reactions in the unburned zone actually decreased the AI value relative to the non-reacting conditions in the 131 °C case. This indicates that the thermodynamic and compositional changes induced by PSHR in this case would actually decrease the autoignition tendency of the end-gas. This result is consistent with the experimental work of Splitter et al. [9], which showed operating conditions demonstrating PSHR can actually improve the knock tolerance of the fuel. Second, the results show several cases with AI values greater than the general autoignition criteria of 1.0, while from Fig. 3, the only obvious autoignition event predicted by any of the models was for the 131 °C case using the Andrae mechanism. For this case, the predicted AI value was 9.0 at CA98, far in excess of the value that would normally be considered necessary for autoignition. However, upon close examination of Fig. 5, all of the cases with AI values > 1.0 (i.e. all Andrae cases, Cai 98 °C, and Ren 98 °C and 131 °C) show a positive inflection near the end of the trajectory, indicating energy release in the unburned region. It is unclear whether this is due to intermediate temperature heat release, or the start of autoignition that is then quenched by the rapid expansion induced by the moderate engine speed and late combustion phasing. Regardless, the tested mechanisms exhibit significant levels of disagreement between predicted autoignition propensities, even with respect to the general trends in autoignition tendency as a function of engine operating conditions. 3.3. Model parameter tuning

Fig. 8. Constant volume ignition delay simulations highlighting second stage (hightemperature) ignition delay (top), and first stage (low-temperature) ignition delay (middle), and low-temperature magnitude (bottom) for iso-octane at initial pressure of 20 bar and λ = 1.0.

Fig. 9. Livengood–Wu autoignition integral value at CA98 for three intake temperature conditions (41 °C, 98 °C, and 131 °C) for the 4 tested kinetic mechanisms with non-reacting (colors) and reacting (white) unburned zone. Dotted line indicates an AI value of 1.0 (i.e. autoignition).

From the figure, several interesting and contradictory trends emerge. First, when considering the reacting cases, the Andrae and Ren mechanisms exhibit monotonically increasing autoignition propensity with increasing intake temperature as would generally be expected, while the Mehl mechanism shows a slightly decreasing trend in AI value with increasing temperature. From Fig. 5, the pressure–temperature trajectories of the unburned region for

Given the significant discrepancies observed between the experiments and simulations in the previous section, and in order to determine the best methodology to employ towards accurate modeling of low-temperature heat release in the end-gas of spark ignition engines, each of the experimental operating conditions that serve as inputs to the engine model were considered for any potential inaccuracy or variability which may be present. In-cylinder pressure can be accurately measured with high speed piezo-electric pressure transducers as long as the transducers are well-calibrated and operating properly. Additionally, the high speed of propagating pressure waves relative to typical piston speeds means that the in-cylinder pressure can be treated as uniform with negligible error, and the experimental pressure data did not show significant cyclic variability in terms of the cylinder pressure during compression or expansion. Only during the deflagration heat release does the in-cylinder pressure demonstrate significant cyclic variability, induced by variations in flame propagation rate caused by variations in-cylinder turbulence and mixing [27]. Other parameters such as engine speed, fuel and air flowrates, and engine geometry can be directly measured independent of other operating conditions, and thus the errors associated with these experimental measurements and their related calculated quantities are typically minimal, and thus were not considered to be appropriate tuning parameters. The experimental parameters important for engine modeling which are difficult or impossible to measure directly in a typical experimental setting include the IVC temperature, the residual gas fraction (RF), and the residual gas composition. In experimental work, these parameters are not generally measured, and typically employ several assumptions or simplifications in their calculation, thus increasing the potential for error propagation and inaccuracy. The most chemically active and significant residual gas species considered in this work was nitrogen oxide [28], and thus this species was investigated with regards to the residual gas concentration and its effect on low-temperature chemistry. As such, a sensitivity study was performed on each of these parameters to

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Fig. 10. Pressure and apparent heat release rate as a function of crank angle at λ = 1, Tin = 131 °C, 804 g/min airflow, and 0% EGR, showing variations in IVC temperature (top), residual gas fraction (middle), and NO concentration (bottom) using the Ren et al. [21] mechanism.

determine if the discrepancies observed between the experimental and predicted LTHR could be accounted for by one or more of these experimental operating parameters. This was accomplished by independently varying each of the uncertain parameters within a range that could be expected given the uncertainty in each parameter (±12.5 K for TIVC , factor of 0.5 to 2 for RF, factor of 0 to 2 for NO) from the nominal values of 412 K, 7.91%, and 1421 ppm respectively. Here, the nominal value for NO concentration corresponds to the exhaust gas measurement, and additionally, for the varying NO concentration, a corresponding change in N2 and O2 concentration was made to preserve mass conservation. The results of these simulations can be seen in Fig. 10 for the 131 °C intake temperature case that exhibited fully decoupled PSHR. Assuming all IVC conditions, including pressure, equivalence ratio, and volume are fixed in an engine model, varying the IVC temperature has the unintended consequence of altering the charge density, and thus affecting the trapped mass. Because the equivalence ratio is fixed to stoichiometric in this work, (and measured experimentally by 3 independent measurements including exhaust emissions, fuel and air flowrates, and an exhaust lambda

sensor), this change in trapped mass leads to a corresponding change in predicted fuel mass and therefore fuel energy. This change manifests itself as more or less heat released during deflagration, which affects the peak in-cylinder pressure accordingly. This variation in charge density could be easily accounted for with a corresponding adjustment to the IVC pressure in the model to offset this effect, however, as discussed previously, the experimental in-cylinder pressure is measured directly and accurately, so little justification exists for this approach. Additionally, while the LTHR phasing is a strong function of temperature as shown in Fig. 10, it does not significantly affect the LTHR magnitude within the range of expected variability or inaccuracy in the IVC temperature. As such, IVC temperature represents a poor tuning parameter for modeling the LTHR process in this work, and does not adequately explain the observed discrepancies. The residual gas fraction has a small effect on the PSHR phasing and magnitude as shown in the middle plot of Fig. 10, however it also affects the quantity of fresh air and fuel, and thus total energy released due to the constraints of the simulation (i.e. constant IVC pressure and equivalence ratio). Because of this, residual gas fraction also serves as a poor tuning parameter for modeling the PSHR behavior. The NO concentration has a significant effect on the PSHR magnitude, and a small effect on the phasing, however even if NO is removed entirely from the residual gas, the PSHR magnitude was still overpredicted in the simulation results. Given this, NO concentration could serve as a reasonable tuning parameter to match PSHR behavior given small differences between experimental and simulation predictions, but the discrepancies observed in this work could not be accounted for by NO concentration alone. One additional limitation of the modeling work presented is the lack of any thermal stratification effects on the end-gas conditions imposed by software limitations in Chemkin Pro’s SI engine simulation utility, which does not allow for multi-zone simulations. In order to study the effect of thermal stratification on PSHR behavior, and to evaluate whether this could explain the discrepancies previously observed, the HCCI engine model in Chemkin Pro was employed via two means, the first utilized a single initialized zone similar to the SI engine model, and the second, which utilized the multi-zone HCCI engine model with 5 discrete zones to represent a thermally stratified end-gas. The mass fractions of each zone were assigned by integrating a normal distribution based on temperature with a standard deviation of 10 K with zones centered at −2, −1, 0, 1, and 2 standard deviations from the mean IVC temperature, which is within the range of variability that may be expected in the end-gas region [29]. The HCCI engine simulations do not consider deflagration heat release, so any effects related to deflagration on the end-gas thermodynamics (such as compression heating) are not accounted for in these simulations. Figure 11 shows the results of these HCCI simulations, comparing the pressure and apparent heat release results for two intake temperature conditions (98 °C and 131 °C) which exhibit partially and fully decoupled PSHR respectively. The thermally stratified 5zone simulations show a clear trend towards a longer duration of heat release with a lower peak as expected. The increased chemical reactivity induced by the elevated temperature in the hottest zone causes this zone to react first, and these reactions progress through the remaining zones along the thermal gradient. Additionally, distinct local peaks corresponding to the specific thermal zones can be observed, and their magnitude is a function of the mass fraction contained within that zone. Figure 12 shows the resultant heat release as a function of crank angle for the 1-zone and 5-zone cases compared to the experimental ensemble averaged heat release curves. As can be clearly seen from these figures, the implementation of thermal stratification via this methodology does not significantly impact the overall magnitude or phasing of energy released, but does influence the rate and duration of en-

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Fig. 11. Pressure and apparent heat release rate as a function of crank angle comparing experimental data (solid lines) and single-zone (dotted) and multi-zone (dash dotted) homogeneous simulations using the Ren et al. [21] mechanism.

ergy release. In both cases shown, the simulations overpredict the magnitude of energy released via low-temperature reactions, thus, thermal stratification effects alone are unable to account for the discrepancies observed between the simulations and experimental results in terms of LTHR magnitude. However, it should be noted that there are several phenomena which are not well captured with this modeling approach which may be resulting in some of the observed discrepancies, including in-cylinder mass trapped in crevice volume and quench zones, inaccuracies in the experimental heat release calculation due to uncertain wall heat transfer modeling, and transport processes including heat transfer and diffusion between burned and unburned regions. Nevertheless, while the multizone simulation approach provides an improved prediction of LTHR behavior under these conditions, further improvements can be made by modifying the chemical kinetic mechanism itself. 3.4. Kinetic mechanism tuning Given the level of disagreement observed between kinetic mechanisms shown in Figs. 7 and 8, as well as the inability of experimentally uncertain parameters to account for the poor predictions of observed PSHR behavior shown in the previous sections, and given the uncertainty associated with kinetic rate parameters [30], it is reasonable to assume that the kinetic mechanism itself may need to be tuned in order to accurately model this PSHR behavior, and thus accurately predict end-gas thermodynamic conditions. Likewise, it is reasonable to assume that if a kinetic mechanism could accurately predict the LTHR phasing and magnitude for cases which exhibit PSHR at a wide range of temperature–pressure

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Fig. 12. Heat released as a function of crank angle comparing experimental data and homogeneous simulations at two intake temperatures.

histories and mixture compositions, then the same mechanism should predict LTHR in the end-gas for cases where it is obfuscated by the main deflagration, as would be the case in typical knocking conditions, and in this way, modeling PSHR behavior could serve to improve kinetic mechanism development and predictive capability. The Ren-2017 mechanism was chosen for further study to determine whether specific reactions could be tuned to better match the experimental results in order to improve the prediction of the end-gas thermodynamic conditions. This mechanism was chosen over the Cai-2015 mechanism since it tended to accurately predict the phasing of the PSHR event for all the tested cases, but with a systematically elevated magnitude, while Cai-2015 demonstrated non-linearity in the agreement between the simulations and experiments, and therefore would likely require a more involved tuning procedure. The approach utilized was to first identify the important pathways in the low-temperature oxidation process. These have been well defined in literature, including Zhao and Law [31], who outlined the dominant chemical reactions and pathways in the firststage ignition of n-heptane which, while not studied in the current work, follows the same general processes as iso-octane. Given the general trend in the simulations (i.e. accurate LTHR timing, but elevated magnitude), it was necessary to decrease the amount of fuel that decomposed via low-temperature reactions. The approach that worked most universally was to decrease the rate of hydrogen abstraction by OH radicals (i.e. iC8 H18 + OH → aC8 H17 + H2 O) by decreasing the pre-exponential factor from 7.5 × 106 to 2.5 × 106 . This reaction was chosen due to the high sensitivity of low-temperature heat release to this reaction as observed by Kukkadapu et al. [32]. This change tended to decrease the magni-

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Table 4 iC8 H18 + OH → aC8 H17 + H2 O reaction rate constants. Mechanism

A

n

Ea

Andrae Caia Mehla Ren

1.5 × 1013 3.96 × 109 2.63 × 107 7.5 × 106

0 0.97 1.8 1.8

3000 1590.11 1431 1431

a Cai and Mehl mechanisms contain additional OH abstraction reactions to b, c, and d isomers of C8 H17 .

tude without changing the timing of the LTHR event. It should be noted that the 3× reduction in the OH abstraction reaction utilized in this work is beyond the uncertainty factor of 2 for this reaction class reported by Goldsborough et al. [30]. However, examining the rate constants for this reaction from the mechanisms tested in this work listed in Table 4, shows a significant level of disagreement between all three Arrhenius equation parameters. Note that the Ren mechanism primary reference fuel chemistry was based on the work of Wang et al. [33,34], which began with the same detailed chemistry [22] prior to reduction as the Mehl mechanism. In the Ren mechanism, the reaction rate was already reduced by a factor of 3.5 from the baseline chemistry [22]. To add to the complexity however, the Cai and Mehl mechanisms also contain reactions for additional hydrogen abstraction sites by OH as noted in the table. It is also worth noting that the reaction rate modification utilized in this work has a significant effect on the 2nd stage ignition delay prediction under conditions where LTHR is relevant, particularly for “beyond RON conditions”, as discussed in Salih et al. [25] which utilized this same tuning. This tuned mechanism thus provides worse knock prediction capability under the conditions studied here, however, the focus of this work is on the end-gas thermodynamics, and not knock prediction. Figure 13 shows comparisons between the experimental traces and the original and tuned Ren-2017 predictions. The tuned mechanism provides significantly better agreement, demonstrating the validity of the tuning approach. While the phasing agrees well, the duration of the LTHR events are not well captured despite very similar pressure traces. This discrepancy is primarily a result of the single, lumped unburned zone in the Chemkin 2-zone model as demonstrated in the previous section. Despite this, it is reasonable to assume that the mean unburned thermodynamic conditions are matched well given the excellent agreement between the experimental and tuned mechanism pressure traces. Additional comparisons between experimental and modeled pressure and HRR data for the cases studied in this work can be found in the Supplementary Materials. Constant volume ignition delay simulations were again perR formed in Matlab using Cantera over a wide range of conditions this time using the tuned Ren-2017 mechanism to develop the ignition delay contours shown in Fig. 14. As can be seen in the figure, the LTHR acts as a nearly iso-baric temperature increase in the end-gas, while the compression/expansion and deflagration processes act via polytropic compression/expansion. The inflection depends on whether the pressure was increasing or decreasing when the LTHR event occurred, and whether the LTHR magnitude offsets the pressure change due to expansion. Though difficult to distinguish due to the relative magnitude of the LTHR event compared to the deflagration heat release, for the 41 °C case the LTHR event occurs near the location of maximum heat release rate where the cylinder pressure is increasing due to deflagration, while for the 98 °C case, the LTHR occurs after TDC during expansion, and in the 131 °C case, LTHR occurs before TDC during compression. As is clearly shown, the phasing and magnitude of the LTHR event strongly influences the temperature–pressure history of the end-gas. For iso-octane, which demonstrates strong NTC behavior at these conditions, the temperature increase actually results in an in-

Fig. 13. Pressure and apparent heat release vs. crank angle comparing experimental data at three intake temperatures (41 °C, 98 °C, and 131 °C) to original and tuned mechanism predictions.

crease in the first-stage ignition delay, thus it seems as if this process is self-regulating for fuels with NTC, i.e. that as the end-gas releases heat via low-temperature reactions, thus increasing temperature, the ignition delay increases to a point where the lowtemperature reactions will not occur before the deflagration event consumes the remaining end-gas. Szybist and Splitter [4] noted that for fuels with NTC, once LTHR developed, combustion phasing did not need to be retarded to mitigate knock. For fuels with positive temperature coefficient (PTC) behavior, LTHR could accelerate end-gas chemistry, making these fuels more knock prone, and more susceptible to cycle-to-cycle variations in end-gas composition and state. High octane sensitivity fuels (which tend to have no NTC, or strong PTC [16]) are less knock prone and more suitable for high boost conditions [4,7], but it is unclear whether LTHR is a positive, negative, or neutral property in terms of a fuel’s ability to resist auto-ignition. Szybist and Splitter [4] demonstrated that at high load, high temperature conditions, LTHR-prone fuels operated at higher loads than would be expected based on their RON and MON values, but that a high sensitivity fuel was preferable because it allowed more advanced combustion phasing before

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Fig. 15. Percent of total energy released in unburned (UB) zone from Chemkin simulations as a function of intake temperature condition for two combustion phasings with 0% EGR, and 804 g/min airflow.

Fig. 14. Predicted unburned P–T trajectories for three intake temperatures overlayed on ignition delay contours (50 K temperature rise).

reaching the knock limit. However, Splitter et al. [9] demonstrated that conditions demonstrating PSHR improved the knock tolerance of the fuel. Many questions remain, such as whether a fuel that derives a significant amount of its octane sensitivity from heat of vaporization, instead of low-temperature chemistry suppression, may perform worse than a fuel with equivalent or even lower sensitivity at these conditions. As such, the effects of LTHR may help explain discrepancies between predicted and observed octane index values such as those in [4]. 3.5. Effect of combustion phasing Combustion phasing, controlled by spark timing in SI engines, is an important parameter in terms of engine efficiency and knocking behavior. Under knock-limited operating conditions, spark is retarded in order to decrease end-gas pressure and temperature, thus avoiding end-gas autoignition, but at the cost of reduced efficiency [35–39]. The combustion phasings analyzed in this work are significantly retarded from max brake torque (MBT) timing or knock limited spark advance (KLSA) timing where SI engines would typically operate in order to maximize efficiency, however these operating conditions enable the decoupling of the low-temperature chemistry from the deflagration process as shown throughout this work. Figure 15 shows the simulation results in terms of unburned fuel energy as a percentage of total energy release as a function of experimental intake temperature using the tuned Ren-2017 mechanism discussed in the previous section for cases matching the experimental operating conditions for two combustion phasings (33±1 and 48±1 o ATDC). Once the PSHR event becomes decoupled from the deflagration process, the combustion phasing has no effect on the fraction of energy released in the unburned zone. At these operating conditions, this occurs beyond an intake temperature of 75 °C as can be seen in the figure. Prior to this, the deflagration process competes with the end-gas chemistry, consuming some or all of the available fuel energy prior to the end-gas becoming chemically active. Intake temperatures less than 75 °C are more representative of typical engine operation, and thus combustion phasing plays a significant role on the magnitude of energy release and corresponding temperature change of the end-gas during the deflagration event, in turn, this could have a significant effect

on the knocking tendency of fuels that is separate from the differences in compression heating induced by changes in combustion phasing. Figure 16 shows the effect of combustion phasing on the endgas pressure/temperature trajectory for the 3 intake temperature cases discussed throughout this work. The combustion phasing affects the penetration of the end-gas thermodynamic trajectory into the LTHR peninsula. From the figure, there does not seem to be a specific ignition delay time that corresponds to the start of LTHR in the end-gas, instead the residence time of the end-gas within the chemically active region is the controlling parameter in terms of LTHR onset in the end-gas, which implies that engine speed, through its influence on chemical residence time, is, in addition to combustion phasing, also an important parameter in terms of LTHR onset and magnitude, as shown in [9]. 3.6. Effect of EGR dilution Dilution with EGR can be used to reduce in-cylinder temperatures and NOx formation, and for knock mitigation [40], though this effect may be reduced under boosted operating conditions [5], including those utilized in this work. As discussed previously, EGR was added via two methods, the first which fixed fresh airflow rate, and added 14% EGR to the mixture, and the second which displaced fresh air with EGR. The additive method matches fuel energy and nominal engine load, but at increased intake pressure, while the displacement method matches intake pressure, but results in a reduced fuel energy and engine load. The EGR composition was assumed to be equivalent to the measured exhaust gas composition. Figure 17 shows the percent of energy released in the unburned zone from the simulation results as a function of the intake temperature condition for the case without EGR compared to the cases with EGR. In all three cases, the maximum fraction of energy release occurs at the same intake temperature condition just above 75 °C, and the general trends are similar in all three cases. Comparing the nominal 0% EGR case to the displacement method with reduced airflow, there is a reduction of approximately 50% in the unburned zone energy released at intake temperatures which may exhibit partially or full decoupled PSHR (>75 °C at these conditions). The increased pressure in the EGR additive case (with matched airflow) recovers approximately half of difference between the nominal and EGR displacement case at the high intake temperature cases. At the lowest tested intake temperature condition (41 °C), all three cases exhibit a similar fraction of en-

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Fig. 17. Percent of total energy released in unburned (UB) zone from Chemkin simulations as a function of intake temperature condition for fixed CA50 of 33±1 o ATDC with air flowrate and EGR rate denoted in legend.

Fig. 16. Predicted unburned P–T trajectories for three intake temperatures overlayed on ignition delay contours (50 K temperature rise) for two combustion phasings.

ergy released in the unburned region, though this energy release occurs during the deflagration event at this condition, and thus its overall magnitude is reduced by the reduced fuel energy available in the unconsumed end-gas. Figure 18 depicts the pressure–temperature trajectories for the cases without EGR, with 14% EGR addition, and with 14% EGR dilution. The increased pressure required to add EGR with matched airflow can be clearly seen in the elevated trajectory for the EGR addition cases. Small differences in pressure–temperature trajectories can be observed between the nominal 0% EGR case and the EGR dilution cases prior to LTHR due to differences in compression γ , and small differences in IVC temperature. While the fraction of energy released in the unburned zone is similar at 41 °C for all three cases, the EGR displacement case with reduced fresh airflow has a corresponding reduction in total fuel energy, and thus

Fig. 18. Predicted unburned P–T trajectories for three intake temperatures for fixed CA50 of 33±1 o ATDC.

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the increase in temperature of the end-gas due to LTHR is less in this case than the nominal case with no EGR. The EGR addition cases exhibit similar P–T trajectories as the nominal cases without EGR, but shifted to higher pressure. Additionally, the increase in end-gas temperature due to LTHR is somewhat reduced compared to the nominal case. For all three cases shown, the EGR dilution cases show a significantly reduced effect of LTHR on the end-gas temperature, caused by a combination of the reduced fuel energy available, and the reduction in end-gas O2 concentration due to the introduction of EGR.

4. Conclusions Experimental conditions exhibiting PSHR were modeled with a 2-zone SI engine model in Chemkin Pro to determine whether literature kinetic mechanisms could accurately capture this phenomena, and thereby end-gas thermodynamic conditions and autoignition tendencies. Four chemical mechanisms representing the state of the art in gasoline surrogate modeling were chosen, and none were able to adequately match experimental results in terms of LTHR magnitude and phasing universally without modification, leading to vastly different predictions of end-gas thermodynamic trajectory and autoignition tendencies. The two tested mechanisms which incorporated NOx chemistry were the best performing in terms of LTHR magnitude and phasing, highlighting the importance of NOx chemistry in SI engine modeling. Variations in experimental parameters with the largest uncertainty, including IVC temperature, residual gas fraction, and residual gas NO concentration were unable to account for the observed discrepancies. However, by tuning a single reaction rate controlling the rate of hydrogen abstraction by OH, the most recent mechanism was able to match the experimental pressure traces with excellent agreement for a range of operating conditions. Combustion phasing was found to have an effect on the fraction of total energy released in the unburned zone for cases where LTHR occurred during deflagration. Combustion phasing influences the penetration in terms of P–T trajectory of the end-gas into the chemically active LTHR peninsula, and affects the corresponding residence time spent in this region, thereby influencing end-gas temperature. The use of EGR was shown to reduce the percentage of energy released via low-temperature reactions in the end-gas, and resulted in a correspondingly smaller change in the end-gas temperature than for cases with no EGR. The results allude to the notion that it may be insufficient for robust chemical mechanisms to match only high temperature ignition delay for autoignition prediction in boosted SI engines, as a mechanism must match the low temperature ignition delay and heat release magnitude in order to accurately predict the thermodynamic conditions of the end-gas. The methodology presented in this work provides a pathway towards more robust chemical kinetic mechanism development, since a wide range of operating conditions exhibit distinct and decoupled PSHR, which can be adequately modeled with a simple 2-zone approach as demonstrated here, providing a procedure which is more directly relevant to SI engine autoignition prediction and kinetic mechanism validation than constant volume ignition delay simulations, or validation based solely on rapid compression machine and shock tube experiments.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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