## Abstract

Growing environmental concerns and demand for a better fuel economy are driving forces that motivate the research for more advanced engines. Multi-mode combustion strategies have gained attention for their potential to provide high thermal efficiency and low emissions for light-duty applications. These strategies target optimizing the engine performance by correlating different combustion modes to load operating conditions. The extension from boosted spark ignition (SI) mode at high loads to advanced compression ignition (ACI) mode at low loads can be achieved by increasing the compression ratio and utilizing intake air heating. Further, in order to enable an accurate control of intake charge condition for ACI mode and rapid mode-switches, it is essential to gain fundamental insights into the autoignition process. Within the scope of ACI, homogeneous charge compression ignition (HCCI) mode is of significant interest. It is known for its potential benefits, operation at low fuel consumption, low NOx, and particulate matter (PM) emissions. In the present work, a virtual Cooperative Fuel Research (CFR) engine model is used to analyze fuel effects on ACI combustion. In particular, the effect of fuel octane sensitivity (S) (at constant Research Octane Number (RON)) on autoignition propensity is assessed under beyond-RON (BRON) and beyond-MON (BMON) ACI conditions. The three-dimensional CFR engine computational fluid dynamics (CFD) model employs a finite-rate chemistry approach with a multi-zone binning strategy to capture autoignition. Two binary blends with Research Octane Number (RON) of 90 are chosen for this study: primary reference fuel (PRF) with S = 0 and toluene–heptane (TH) blend with S = 10.8, representing paraffinic and aromatic gasoline surrogates. Reduced mechanisms for these blends are generated from a detailed gasoline surrogate kinetic mechanism. Simulation results with the reduced mechanisms are validated against experimental data from an in-house CFR engine, with respect to in-cylinder pressure, heat release rate, and combustion phasing. Thereafter, the sensitivity of combustion behavior to ACI operating condition (BRON versus BMON), air-fuel ratio (λ = 2 and 3), and engine speed (600 and 900 rpm) is analyzed for both fuels. It is shown that the sensitivity of a fuel’s autoignition characteristics to λ and engine speed significantly differs at BRON and BMON conditions. Moreover, this sensitivity is found to vary among fuels, despite the same RON. It is also observed that the presence of low-temperature heat release (LTHR) under BRON condition leads to more sequential autoignition and longer combustion duration than BMON condition. Finally, the study indicates that the octane index (OI) fails to capture the trend in the variation of autoignition propensity with S under the BMON condition.

## 1 Introduction

Currently, the transportation sector is predominantly powered by hydrocarbon-based fuels. It is predicted that they will continue to contribute a significant share (∼70%) to power transportation across the world even in 2050.2 On the flip side, the transportation sector accounted for nearly 40% of total CO2 emissions in 2019, and certainly, with the increase in demand for mobility, this share is estimated to increase in the near future. This stands as the prime motivation for continuous research in identifying new combustion strategies and develop engines with improved efficiency and lower emissions.

Two representative modes of operation in engines are spark ignition (SI) and compression ignition (CI). SI engines are characterized by flame propagation and with small modifications can achieve low tailpipe soot and NOx emissions, but they are compromised to operate at lower efficiencies due to limitations associated with cyclic variability and knocking [1,2]. CI engines operate at relatively higher compression ratios, which make them more fuel-efficient at all load conditions. However, conventional CI diesel engines suffer from relatively high tailpipe emissions of nitric oxides (NOx) and particulate matter (PM). In this context, an efficient way to optimize engine performance and lower emissions is to implement multi-mode strategies. These strategies target optimizing the engine performance by correlating different combustion modes to load operating conditions. This allows to capitalize on advantages from different (existing or new) combustion modes of operation. Thus, within the scope of light-duty vehicles, multi-mode combustion strategies have gained attention for their ability to provide high thermal efficiency and low emissions. A potential multi-mode strategy would entail mode-switching from boosted SI at high loads to an advanced compression ignition (ACI) mode at low loads. Several ACI modes are under consideration, while the interest lies in engines operating in the low-temperature combustion (LTC) regime. LTC is a very promising technology that has attracted significant interest in recent developments of internal combustion engines. It is known for its potential to achieve high efficiencies along with ultra-low NOx and soot emissions. The main idea is to deploy highly diluted, nearly homogeneous fuel-air mixtures by using combustion products and other means [3]. Homogenous charge compression ignition (HCCI), Premixed charged compression ignition (PCCI), and reactivity controlled compression ignition (RCCI) are some of the known variants of this strategy [48]. Among these ACI strategies, HCCI is the most preliminary mode explored and has gained significant interest as this mode of operation can itself be considered a combination of SI and CI engine modes. Fuel and air are premixed like SI engines; however, the mixture is leaner in HCCI mode, while it is compressed to allow autoignite like CI engines. This means the combustion phenomena and associated heat release are mainly governed by the autoignition characteristics of the fuel. In other words, the HCCI mode of operation is mainly governed by chemical kinetics of the fuel, which is known to depend on the fuel chemical composition, in addition to operating conditions like engine speed, intake pressure (Pin), and intake temperature (Tin) of the fuel/air mixture. Even though this mode has potential benefits like low emissions and high thermal efficiency, there are limitations associated with control over the autoignition of such lean fuel/air mixtures. Thus, in order to fit in the HCCI mode of operation within the scope of a multi-mode strategy, it is essential to gain fundamental insights into the autoignition process. These insights will feed in to control the intake charge condition for ACI operation and hence, to achieve smooth, rapid mode-switches in a multi-mode engine configuration.

Homogenous charge compression ignition-like conditions have been of interest for several decades. Some potential parameters and phenomena that impact autoignition are thermal stratification, fuel/mixture stratification, fuel composition, and associated fuel properties [923]. In order to better understand the effects of the addition of biofuels and associated changes in fuel properties on autoignition performance, Calam et al. [6] investigated the impact of mixing different alternative fuels, such as ethanol, methanol, fusel oil, butanol, and iso-propanol, with n-heptane on combustion performance under HCCI engine conditions. Combustion performance was observed to be strongly related to fuel properties—the heat of vaporization, evaporation temperature, and octane number. However, it must be noted that each of these properties is strongly dependent on the fuel composition. Yao et al. [14] in an experimental study tested different fuels, including gasoline, PRF, and mixtures of PRF and ethanol, at different operating conditions. It was observed that in addition to fuel composition effects, the combustion characteristics of a fuel also significantly depend on the operating condition. Moreover, it was found that autoignition and HC and CO emissions have a good correlation with the octane index (OI) at all conditions, and for all fuel blends other than the one with ethanol. Kalghatgi [1] introduced OI, defined as
$OI=RON−K*(RON−MON)$
(1)
where RON and MON are the Research Octane Number and Motor Octane Number, respectively, while K is an empirical constant representative of the pressure–temperature (P–T) history of the unburnt mixture. Further, studies [2426] have shown that a change in fuel chemical composition has a significant effect on low-temperature (LTHR) and intermediate temperature (ITHR) heat release, which subsequently impacts the main-stage heat release or autoignition characteristics. It was observed that the presence of LTHR allows for stable combustion and extension of HCCI operation to higher load limits. In addition, Sjöberg and Dec [26] showed that LTHR is highly dependent on engine speed. For instance, for PRF80 fuel, the LTHR decreased by a factor of 15 or nearly vanished when engine speed increased from 1050 to 1500 rpm. In a more recent study, Waqas et al. [27] observed through a series of experiments that for a given fuel, the LTHR phenomena primarily depend on the intake valve closing (IVC) conditions, implying that LTHR varies significantly with operating conditions (Tin and Pin). In addition, two other factors that have a prominent impact on autoignition characteristics are thermal and fuel stratification. Thermal stratification to some extent is naturally induced by wall heat transfer and turbulent convection. This allows the mixture to autoignite sequentially from the hottest regions to the coldest, thereby resulting in lower heat release rates and longer combustion duration. Several studies [9,2834] have characterized the significance of thermal stratification using experimental and computational (0-D and CFD) techniques. It was observed that thermal stratification has a more dominant effect when compared to fuel stratification [9,32]. Further, it was shown that thermal stratification can be artificially enhanced by inducing higher turbulent intensity [30], by using negative valve overlap (NVO) [9,31,32], and through direct injection of water in the form of thermally stratified compression ignition (TSCI) concept [29]. On the other hand, several studies also highlighted the effect of fuel stratification on combustion control in HCCI engines [3537]. Fuel stratification becomes effective for fuels that show high ϕ sensitivity, a fuel characteristic defined based on the relationship between ignition delay timing and equivalence ratio [35]. Tao et al. [36] and Pintor et al. [37] have investigated the effect of equivalence ratio on ignition delay under representative P-T trajectories for various gasoline-like fuels. It was observed that fuels having high ITHR and those exhibiting negative temperature coefficient (NTC) behavior show strong ϕ-sensitivities, while fuels that have no NTC behavior displayed small or zero ϕ-sensitivity. Studies have also shown that fuel octane sensitivity (S) depends on NTC behavior [12,3840]. Fuel propensity to exhibit ITHR and/or NTC behavior significantly depends on the IVC pressure and temperature conditions [36,37]. Both higher intake pressures and low temperatures tend to increase ITHR and thus, increase the ϕ-sensitivity.

Based on the above discussion, it is well understood that the autoignition behavior of fuel under HCCI mode has a complex dependency on fuel composition, properties, and engine operating conditions. Therefore, in order to extend the applicability of HCCI to multi-mode strategies, it is of paramount importance to explore the properties/conditions that optimize fuel-engine interaction. The Co-Optimization of Fuels and Engines, or the “Co-Optima” initiative of the US Department of Energy3 aims to explore pathways to enable such synergistic development of advanced fuels and engines for higher efficiency and lower emissions. Within the context of the Co-Optima initiative, the central fuel property hypothesis (CFPH) states that for a given engine platform, fuel properties are sufficient to characterize the performance of the engine, irrespective of the fuel chemical composition. Recently, Szybist and Splitter [41] and Pal et al. [42] have explored this hypothesis for boosted SI conditions, through experiments and CFD simulations, respectively. Several fuel blends of interest to Co-Optima were investigated, and the results showed that OI was a reasonably good indicator of knock propensity. Overall, they found that the fuels generally behaved in accordance with CFPH, except that some fuels consistently outperformed (or underperformed) the OI expectations. Further, in the context of HCCI engines, there is also continuous interest in understanding the performance of OI in LTC engines for various operating conditions [43,44]. Pintor and Dec [43] have explored this hypothesis experimentally and investigated gasoline-like fuels for four P-T trajectories, which include beyond-MON (BMON), MON, RON, and beyond-RON (BRON) HCCI conditions. It was observed that equivalence ratio and speed had a significant impact on the capability of OI to characterize autoignition propensity. The OI performed reasonably well for all operating conditions, other than BRON. However, the reasons for the same were not investigated.

The objective of the present numerical work is to provide insights related to fuel effects on autoignition propensity under HCCI combustion mode. Two binary fuel mixtures with a constant RON of 90, but different S, are examined under BRON and BMON conditions. As a first step, the numerical setup is validated against experimental data for PRF and TH fuels under BRON and BMON conditions. Thereafter, the validated numerical setup is used to characterize combustion behavior under two global equivalence ratios (ϕ = 0.3 and 0.5) and at two engine speeds (600 and 900 rpm). In addition, the effects of thermal stratification on ignition and rate of heat release are also analyzed.

## 2 Experimental and Modeling Setups

### 2.1 Cooperative Fuel Research Engine Platform.

The experimental results shown in this work are based on the tests performed on an in-house cooperative fuel research (CFR) F1/F2 engine at Argonne National Laboratory (ANL). This is a carbureted single-cylinder engine that is used to measure a fuel’s RON and MON based on ASTM protocols [45,46]. In order to make it suitable for the HCCI mode of operation, the standard knockmeter was replaced by a Kistler 6045-AU20 pressure transducer, which allowed to acquire cylinder pressure data. In addition, the standard carburetor horizontal jet was made smaller to achieve lean (near air-fuel ratio (lambda, λ) of 3) premixed HCCI operation. An absolute measurement of the air-fuel ratio was obtained by adding a wide-band lambda sensor in the standard ASTM exhaust line between the port and exhaust surge tank. Flush-mounted high-speed pressure transducers were used to obtain intake and exhaust port pressures with crank-angle resolution. Cycle-averaged intake and exhaust temperatures were obtained with K-type thermocouples. The local crank angle resolved in-cylinder pressure data was triggered using a crankshaft encoder with a resolution of 0.1 crank-angle degrees. Table 1 shows some of the key specifications of this engine, while more details are discussed elsewhere [27,47].

Table 1

CFR engine specifications

 Stroke/bore (mm) 114.3/82.55 Connecting rod (mm) 254 Intake valve open (IVO) 10 deg ATDC Intake valve close (IVC) 34 deg ABDC Exhaust valve open (EVO) 40 deg BBDC Exhaust valve close (EVC) 15 deg ATDC
 Stroke/bore (mm) 114.3/82.55 Connecting rod (mm) 254 Intake valve open (IVO) 10 deg ATDC Intake valve close (IVC) 34 deg ABDC Exhaust valve open (EVO) 40 deg BBDC Exhaust valve close (EVC) 15 deg ATDC

### 2.2 Fuels and Operating Conditions.

The autoignition characteristics of two binary blends, PRF and TH (toluene/n-heptane), are studied in this work. Research Octane Number (RON) of both fuels is the same (=90), while S values are 0 and 10.8, respectively. Table 2 shows the composition (in terms of the mass fraction) of the fuel blends.

Table 2

Composition of the fuel surrogates

PRFTH
Iso-octane (mass fraction)0.90
n-heptane (mass fraction)0.10.249
Toluene (mass fraction)00.751
PRFTH
Iso-octane (mass fraction)0.90
n-heptane (mass fraction)0.10.249
Toluene (mass fraction)00.751

For each fuel blend, experimental data are obtained for λ = 3 and engine speed = 600 rpm, under both BRON (Pin = 1.3 bar, Tin = 52 °C) and BMON (Pin = 1.0 bar, Tin = 149 °C) conditions. Figure 1 shows a comparison of the P-T trajectories (during compression) of the two operating conditions with those of the standard CFR RON and MON 90 tests [39]. 300 pressure cycles were recorded for each test condition. The compression ratio (CR) is adjusted to ensure that CA50 (crank angle of 50% fuel mass fraction burned) is fixed at ∼3 CAD (±1 CAD) ATDC for all operating conditions under consideration. This dataset is utilized for CFD model validation. Subsequently, for the numerical study, a broader test matrix is considered, as shown in Table 3, to investigate the effects of lambda and engine speed.

Fig. 1
Fig. 1
Close modal
Table 3

Operating conditions for the numerical study

Intake pressure (bar)Intake temperature (°C)λSpeed (rpm)
BRON1.3523.0, 2.0600, 900
BMON1.01493.0, 2.0600, 900
Intake pressure (bar)Intake temperature (°C)λSpeed (rpm)
BRON1.3523.0, 2.0600, 900
BMON1.01493.0, 2.0600, 900

### 2.3 Numerical Model.

A virtual CFR engine model developed at ANL has been extensively employed in previous studies to study SI engine combustion characteristics [42,4850]. This model, with minor modifications, is used in the present study to investigate the HCCI mode of operation. The key modification adopted in the engine geometry is the removal of the spark plug.

Figure 2 shows the computational domain representing the engine geometry. A commercial 3D CFD code CONVERGE (version 2.3) [51] is used to perform full-cycle engine simulations. The grid generation in the computational domain is performed by COVERGE during runtime, with the capability of increasing the grid resolution via fixed embedding and adaptive mesh refinement (AMR). Fixed embedding enables the use of high grid resolution in regions of interest a priori, while AMR refines the grid during runtime based on gradients of temperature and velocity. In this study, a base grid of 2 mm is used outside the cylinder, while a 1 mm base grid is used inside the cylinder. Two levels of fixed embedding (cell size of 0.5 mm) are adopted near the cylinder head, piston, and liner. Additionally, the AMR of two levels is employed based on the sub-grid criterion of 1 m/s and 2.5 K for velocity and temperature, respectively [52,53]. This results in a peak cell count of around 1.3 million cells. The in-cylinder turbulence is modeled using unsteady RANS-based re-normalized group (RNG) k–ε model [54] with wall functions. The wall heat transfer is accounted for by using the Han and Reitz model [55]. A second-order central differencing scheme is used for spatial discretization and a first-order implicit scheme is employed for temporal discretization. The time-step is controlled using the diffusive and convective Courant–Friedrichs–Lewy (CFL) numbers with a maximum value of 1.0 between IVC and EVO. Realistic intake/exhaust boundary conditions were prescribed based on experiments. Wall temperatures were estimated by a 1D GT-Power model.

Fig. 2
Fig. 2
Close modal

In-cylinder combustion is modeled using a finite-rate chemistry approach combined with the multi-zone strategy. The Co-Optima gasoline detailed kinetic model developed by Mehl et al. [56], containing nearly 2300 chemical species and 10,000 chemical reactions, is used to generate skeletal mechanisms for each fuel blend; reduction techniques based on directed relation graph (DRG), DRG-aided sensitivity analysis (DRGASA), and isomer lumping are employed [5760]. The resulting skeletal mechanisms for PRF and TH blends contain 178 and 181 species, respectively. These mechanisms are validated against a wide range of experimental data available for homogenous ignition delay timing as well as CFR engine data as discussed in Sec. 3.

### 2.4 Numerical Methodology.

The homogeneous ignition delay calculations presented in this paper are based on simulations of homogeneous fuel-air mixtures under constant volume conditions, performed using CHEMKIN-Pro [61]. The state of first-stage ignition delay (FIDT) is defined as the interval from the initial time to the instant of the first peak in temperature rise rate. The total or main-stage ignition delay (MIDT) is defined as the time interval from the initial point to the time instant when the mixture temperature increases by 400 K over one computational time-step [3,12,13].

Each CFD simulation is run using 80 processors on the Blues computing cluster at ANL. The approximate run time for each engine cycle is around 40 h. Six consecutive cycles are simulated for each fuel and every operating condition. However, the first two cycles were neglected to remove any effect of initial conditions. Thus, all observations made in this paper are based on results for cycles 3–6. Moreover, in order to remain consistent with CFR engine experiments, the CA50 for each fuel, at every condition is fixed at ∼3 CAD (±1 CAD) by adjusting the CR.

The operating condition is referenced as “#fuelname-#condition-#L-#Speed.” For instance, PRF-BRON-L3-600 rpm indicates that the fuel is PRF, P-T trajectory is BRON (boosted condition), λ = 3, and engine speed is 600 rpm. In addition, throughout the discussion, the two terms λ and ϕ are used interchangeably. Physically both indicate the degree of fuel-air premixing, and they are related as λ = 1/ϕ.

## 3 Model Validation

The skeletal mechanisms developed for PRF and TH have been validated against different types of experimental data. Figure 3 presents a comparison between shock-tube ignition delay measurements for PRF91 [62] and TH [63] blends with the respective numerical results obtained from simulations performed using CHEMKIN-Pro. Overall, there is a good agreement between the measurements and predictions from the skeletal mechanisms. Figure 4 presents a comparison of experimental in-cylinder pressure and heat release rate (HRR) profiles with those obtained from CFD simulations for BRON-L3-600 rpm condition. Figure 5 presents the corresponding results for the BMON-L3-600 rpm condition. The experimental pressure trace shown is an average of 300 consecutive cycles, while the CFD results are based on cycle 4. We noticed a negligible cycle-to-cycle variation in CFD, and hence, only results of one cycle (cycle 4 here) are presented. Once again, the CFD simulations capture the evolution of in-cylinder pressure and HRR reasonably well for both fuels. Also, the trends in low-temperature heat release (LTHR) under BRON conditions are well captured. In addition, the compression ratios required in experiments and simulations to achieve a CA50 of ∼3.0 CAD ATDC are very similar, with the values for simulations lower than those in experiments. Under BRON-L3-600 rpm conditions, experimental compression ratios for PRF and TH blends are 12.84 and 13.62, while those used in simulations are 11.5 and 12.2, respectively. Similarly, under BMON-L3-600 rpm conditions, experimental compression ratios for PRF and TH blends are 14.05 and 13.33, while for CFD simulations these are 11.92 and 11.42, respectively. Hence, the trends in compression ratio are well captured by the simulations.

Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal
Fig. 5
Fig. 5
Close modal

## 4 Results and Discussion

To elucidate the importance of S and OI in characterizing the autoignition propensity of gasoline-like fuels under different P-T trajectories, this section is broadly divided into four sub-sections. The first sub-section addresses the importance of fuel composition and associated LTHR on autoignition characteristics by comparing the PRF and TH blends under BRON and BMON conditions. Further, the subsequent sub-sections discuss the effects of thermal stratification, equivalence ratio, and engine speed, respectively, on the fuel autoignition behavior.

### 4.1 Effects of Fuel Composition.

Figures 4 and 5 depict the in-cylinder pressure traces and HRR profiles for PRF and TH blends, under BRON-L3-600 rpm and BMON-L3-600 rpm conditions, respectively. It is evident that under BRON conditions, both the fuels show a significant amount of LTHR. However, there are differences in terms of the start and amount of LTHR. The reason for these differences can be explained by comparing the P–T trajectories and first-stage ignition delay contours (Fig. 6a). Figure 6 shows the first-stage and main-stage ignition delay iso-contours for PRF and TH fuels at ϕ = 0.3 and 600 rpm operating conditions. In addition, a comparison of P–T trajectories from engine simulations at ϕ = 0.3 are shown for both BRON and BMON conditions. It can be noticed that the first-stage ignition delay retards with an increase in S, which indicates earlier timing of LTHR occurrence under BRON conditions for the fuel with smaller S. This is consistent with the CFD results where the start of LTHR occurs earlier (by ∼1.2 CAD) for PRF (S = 0) when compared to TH blend (S = 10.8), where the start of LTHR is defined by a criterion of 0.2 J/CAD [27]. On the other hand, due to high temperatures and low pressures associated with BMON conditions, the P–T trajectories tend to avoid the low-temperature regime or the region that exhibits prominent LTHR. Therefore, there is no evidence of LTHR for both fuels under BMON conditions in CFD. These observations are also consistent with results published in recent studies [27,36].

Fig. 6
Fig. 6
Close modal

Further, under both BRON and BMON conditions, CFD results suggest that CA10 (the crank angle at 10% mass burned), which is used as an indication of autoignition in CI engines, occurs earlier for the PRF. In particular, CA10 for PRF occurs earlier than TH fuel by ∼1.85 CAD and ∼0.85 CAD, under BRON-L3-600 rpm and BMON-L3-600 rpm conditions, respectively. The higher reactivity of PRF can be justified with the help of main-stage ignition delay calculations. Figure 6(b) presents a comparison of MIDT iso-contours for both fuels along with the P–T trajectories for BRON-L3-600 rpm and BMON-L3-600 rpm conditions. Large differences in MIDT can be observed between the two fuels at intermediate pressures (20–40 bar) and intermediate temperatures (700–900 K). This is a typical NTC region for any fuel. PRF has significantly higher MIDT than TH blend in these regions. However, the trend reverses under high temperatures (>920 K) where PRF has lower MIDT values. This suggests that PRF is more reactive than TH fuel in the high-temperature regions (>920 K), irrespective of pressure. Further, this is the region of autoignition based on CFD simulations (as seen from P–T trajectories) for both BRON and BMON conditions. Thus, the observation from CFD that PRF is more reactive or has advanced CA10 than TH blend, is consistent with the analysis of P-T trajectories and MIDT iso-contours.

Lastly, the difference in CA10s of PRF and TH blends decreases when transitioning from BRON (∼1.85 CAD) to BMON (∼0.85 CAD) conditions. This change in behavior is predominantly a consequence of LTHR. To elaborate, a higher amount of LTHR for the PRF-BRON-L3-600 rpm condition also results in a higher fraction of mass-consumed between start and end of LTHR. The fraction of mass-consumed during LTHR in PRF and TH blends is ∼4.9% and 3.6%, respectively. In addition, as discussed earlier, PRF is more reactive than TH blend under high-temperature regions. Both these effects add up resulting in the overall advancement in CA10 of PRF relative to TH blend under BRON condition. However, LTHR is not present under BMON conditions. Thus, the difference in CA10 observed under BMON conditions is only a consequence of MIDT differences. Hence, the CA10s for PRF and TH blends are much closer under BMON conditions.

Based on previous studies [1,41,43], it is evident that the value of K in the OI definition (Eq. (1)) is <0 for BRON conditions and >0 for BMON conditions. In terms of the autoignition quality of fuel, this indicates that the fuel with higher S is more resistant to autoignition under BRON conditions, while the same fuel tends to ignite much earlier (less resistant) under BMON conditions. However, based on the CA10 results from CFD, the fuel with higher S is more resistant to autoignition under both BRON and BMON conditions. Thus, it violates OI prediction under BMON conditions. This indicates that fuel response is highly dependent on the ACI strategy being used.

### 4.2 Significance of Thermal Stratification.

The analysis of thermal stratification and its impact on the autoignition phenomenon is also carried out. Figure 7 illustrates the temporal evolution of thermal stratification in terms of coefficient of variance (CoV) up to CA10 for PRF90 under BRON and BMON L3-600 rpm conditions. CoV is defined based on Eqs. (2) and (3), where Ti is the local temperature in the cylinder at a grid cell and n is the total number of grid points in the cylinder. In general, CoV can be interpreted as the relative variability of the data around the mean. A higher value of CoV indicates a greater level of dispersion around the mean. In other words, higher CoV for temperature indicates greater thermal stratification in the cylinder.
$CoV=StandardDeviation(Tstd)Mean(T¯)×100$
(2)
$Tstd=(∑i=1n(Ti−T¯)2n−1)1/2$
(3)
Fig. 7
Fig. 7
Close modal

As seen in Fig. 7, thermal stratification to some degree is observed under both BRON and BMON conditions. However, it is significantly higher under BRON conditions. The increase in CoV under BRON conditions is associated with the occurrence of LTHR (as seen in Fig. 4). The higher thermal stratification results in longer CA10-CA50 under BRON condition (5.66 CAD) compared to BMON conditions (2.8 CAD). This is a characteristic of enhanced sequential autoignition, suggesting that heat release rate during ACI operation under BRON conditions may be more controllable (via LTHR) than operation under BMON conditions.

### 4.3 Effects of Equivalence Ratio.

Figure 8 shows the autoignition sensitivity of PRF and TH blends (in terms of ΔCA10) to changes in equivalence ratio (ϕ = 0.3 and 0.5, at 600 rpm) under BRON and BMON conditions. ΔCA10 associated with a change in ϕ is greater for PRF. Also, ΔCA10 becomes less significant when transitioning from BRON to BMON conditions, irrespective of the chosen fuel. This suggests that the fuel with higher octane sensitivity (S) is less sensitive to varying ϕ, and BRON conditions are more susceptible to equivalence ratio variations.

Fig. 8
Fig. 8
Close modal

To better understand the behavior of fuels under different P–T trajectories, an attempt is made to relate the CFD results with that of 0D ignition delay calculations. Figure 9 shows the first-stage and main-stage ignition delay iso-contours for PRF at ϕ = 0.3 and 0.5. In addition, a comparison of P-T trajectories at ϕ = 0.3 and 0.5 is also shown for both BRON and BMON conditions. It can be clearly seen that FIDT is nearly insensitive to change in ϕ, while the MIDT considerably decreases for richer mixtures. However, the differences in MIDT are higher under low temperatures and the NTC regimes. Consequently, it is expected that a larger variation of chemical reactivity and fuel ignition performance will be observed for BRON conditions compared to BMON conditions. The TH blend also shows similar behavior (not shown here for the sake of brevity). Therefore, this analysis based on 0D simulations is consistent with that observed from CFD simulations, which indicates that the fuels are more ϕ-sensitive under BRON conditions as evident from higher ΔCA10s.

Fig. 9
Fig. 9
Close modal

### 4.4 Effects of Engine Speed.

In this section, the effect of increasing engine speed from 600 to 900 rpm on autoignition characteristics under BRON and BMON-L3 conditions is discussed. The critical CR required to achieve a CA50 of ∼3.0 CAD ATDC increases with engine speed. Figure 10 shows a comparison of critical CRs for PRF and TH blends under different operating conditions. For instance, the critical CRs required at 600 rpm and 900 rpm engine speeds are 11.5 and 13.49, respectively, or ΔCR = 1.99, for PRF under BRON conditions. On the other hand, the ΔCR for PRF under BMON condition is 1.2. Evidently, ΔCR reduces when transitioning from BRON to BMON conditions. This is due to the fact that the lower residence time at higher engine speed suppresses LTHR (as shown in Fig. 11). Hence, the BRON conditions that show more LTHR than BMON conditions exhibit a larger ΔCR with engine speed. This reasoning also explains the observation from Fig. 10 that the difference in critical CR between the two blends decreases with engine speed, irrespective of the operating condition.

Fig. 10
Fig. 10
Close modal
Fig. 11
Fig. 11
Close modal

## 5 Conclusions

In the scope of multi-mode strategies, a computational study was carried out to evaluate fuel effects under ACI (HCCI) conditions using the virtual CFR engine model. Two blends, PRF and TH, having the same RON (=90) and octane sensitivities (S) of 0 and 10.8, respectively, were chosen. Skeletal reaction mechanisms for these blends were developed from a detailed mechanism and were validated against experimental data. Effect of varying operating conditions (BRON versus BMON relevant conditions), ϕ (0.3 versus 0.5), and engine speed (600 rpm versus 900 rpm) were investigated. It was observed that the occurrence of LTHR has a significant impact on the overall combustion behavior. The presence of LTHR increased the thermal stratification, which resulted in a more stable or controlled combustion process in the cylinder. While the LTHR was quite evident under BRON conditions, there was no evidence of its occurrence under BMON conditions. The higher amount of LTHR under all BRON P-T trajectories helped to achieve desirable longer combustion phasing when compared to BMON P-T trajectories. Further, the significance of LTHR under BRON increased with an increase in ϕ (0.3 to 0.5), while it reduced at higher engine speeds due to lower residence time available under low-temperature regimes. Both the fuels were more ϕ-sensitive under BRON conditions. It was also shown that the OI fails to capture the trend in the variation of autoignition propensity with S under BMON conditions.

## Acknowledgment

The submitted paper has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (Argonne). 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 and Office of Energy Efficiency and Renewable Energy under Contract No. DE-AC02-06CH11357. The authors wish to thank Gurpreet Singh, Kevin Stork, and Michael Weismiller, 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 U.S. Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy (EERE), Bioenergy Technologies and Vehicle Technologies Offices. The authors would like to acknowledge the computing facilities, the Laboratory Computing Resource Center (LCRC) at Argonne National Laboratory and the University of Illinois at Chicago, for computing time used in this research.

### Conflict of Interest

There are no conflicts of interest.

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