Simulations of Multi-Mode Combustion Regimes Realizable in a Gasoline Direct Injection Engine

Gasoline engines can be operated under the condition of low-temperature combustion regime in order to benefit from the greater thermal efficiency. To maximize the benefit, an advanced compression ignition (ACI) strategy with lean fuel-air ratio has been widely examined in gasoline engines to achieve their diesel-like efficiency while emitting low levels of nitric oxides (NO_x) and particulate matter [1–3]. However, challenges associated with lacking controllable autoignition in ACI engines may constrain their operation limitedly in low- or part-load conditions [4,5].

Multi-mode (MM) combustion strategies have been shown to meet the demand of wide range of engine operations by utilizing SI engine platforms [6–8]. This type of strategy involves two distinctive combustion modes enabling engines to operate by selectively implementing high-load spark ignition (SI) and low- and part-load ACI at varying runtime engine load demands. A key challenge to achieve multi-mode combustion is to enable mode transition between ACI and SI without losing combustion controllability and thermal efficiency. Toward the goal of retaining their inherent gains of each combustion mode, the mode transition should be optimized in terms of thermochemistry impact of employed fuels and in-cylinder flow characteristics.

Effective mode transition (e.g., ACI to SI or SI to ACI) can be achieved by implementing a proper mixed-mode combustion regime. This in general accommodates flame propagation followed by end-gas autoignition. Major bottleneck to this approach is associated with uncertainties in fuel-specific physiochemical behaviors, such as autoignition, flame propagation, and knock resistance. In addition, random process in turbulent flow and cyclic variability adds one more layer of complexity toward deeper understandings. Mixed-mode combustion has been investigated in numerous studies [9–13]. In such regards, Zigler et al. [9] investigated fundamental properties of ignition assisted by spark ignition in an optical research engine. Sjöberg and coworkers have studied a strategy of lean gasoline mixed-mode combustion extensively [10,12]. They highlighted substantial improvements in fuel economy for lean SI operation with the use of low octane gasoline, which effectively facilitates end-gas autoignition. This end-gas autoignition assists in completing the combustion event, which otherwise leads to unburnt hydrocarbon (UHC) emissions in lean gasoline SI engines.

Computational fluid dynamics (CFD) is an effective tool to investigate key physics, often undiscovered in experimental diagnostics. However, relatively a few CFD activities on mixed-mode combustion have been reported to date. Middleton et al. [14] proposed a hybrid model that combines the Coherent Flamelet Model (CFM) and detailed chemistry solver coupled with multi-zone (MZ) approach, named the CFMZ model to capture the premixed flame propagation followed by the end-gas autoignition process. Pal et al. [15,16] proposed a novel hybrid combustion model to effectively reduce the computational time. In their hybrid model approach, the premixed flame front is captured by a level-set based G-equation model. This approach avoids the necessity of solving detailed chemistry in tracking the premixed flame front; hence, it can dramatically reduce the computational load.

The first objective of this study is to discover important physics governing each of the combustion modes (e.g., ACI and SI) with respect to turbulent mixing and ignition processes. Sensitivity of wall temperature to combustion dynamics reported in a previous study by the authors [17] is also revisited to describe its primary characteristics in a quantitative fashion. Important physiochemical impacts in turbulent combustion behavior in SI combustion are also discussed. The second objective of this study is to discuss the feasibility of mixed-mode combustion using the same engine platform as a mode transition strategy. To this end, a spark ignition-assisted ACI (named SACI) condition was numerically investigated. Such a virtual test condition was created by benchmarking a published mixed-mode engine study. Important insights into the mixed-mode combustion obtained from the SACI simulation are then discussed.

In this study, three-dimensional (3D) full engine open-cycle simulations were performed and validated against experiments accordingly. The experiments were conducted to achieve representative ACI and SI conditions utilizing the same engine platform. However, mixed-mode combustion has yet to be tested experimentally in this engine; hence, a virtual test condition was generated for the mixed-mode combustion. Details of experimental and CFD strategies are summarized in Secs. 2.1 and 2.2.

The experimental activities were performed on a single cylinder GDI engine at Argonne National Laboratory (ANL) which has been fully described in previous studies [18–20]. For ACI operation, the engine was equipped with a high compression ratio piston, but otherwise the standard GDI engine setup was retained. A Motec M800 engine control unit was used to control the injection timing and the fueling rate. Intake air was supplied by an Atlas Copco compressor and throttling was achieved by using a Parker Pilot regulator upstream of the intake manifold. To enable ACI mode, an electric intake air heater was used to maintain constant intake charge temperatures. Low-speed engine and test cell data, such as the intake temperature and pressure, were logged at a sampling rate of 1 Hz using an in-house LabView based data acquisition system. Pertinent engine specification for ACI and SI conditions and their operating parameters are summarized in Table 1.

A commercially available CFD tool package, CONVERGE (v2.4.20) [21], was used to perform full open-cycle simulations of multi-mode engine operations. The adopted computational domain representing the employed Argonne single cylinder engine geometry is depicted in Fig. 1. A modified cut-cell Cartesian method that can facilitate automatic grid generation was utilized with base grid size of 4 mm. Computational cells are dynamically generated or removed in the domain as the piston and valves are in motion. In order to better resolve the small scale (i.e., sub-grid scale) flow motion such as turbulent boundary layer, fixed embedding cells sizing down to 0.5 mm were constantly held in regions where static finer grid resolution is required. Additional finer mesh embedding (0.125–0.25 mm) was added during the initial flame kernel growth for spark ignition process. In addition, the adaptive mesh refinement (AMR) automatically applies finer grids in regions where finer fluid structure becomes substantial on runtime basis, e.g., steep gradient of reactive scalars and liquid spray particles are present. Minimum grid size of 0.5 mm was dynamically adopted in the region of such interests. The total cell count, in turn, reached the peak at 1.3–1.5 million during the simulation depending on the conditions employed. The SI condition requires in general more cell counts due to finer grid resolution in the flame kernel region.

In-cylinder turbulent motion was modeled using the Reynolds-averaged Navier–Stokes (RANS) solver with renormalized group k–ɛ model with wall functions. To account for chemically reacting flow, the CONVERGE is integrated with SAGE detailed chemistry solver. This chemistry solver was then applied to address well-stirred reactor (WSR) concept modeling in the RANS solver platform. The WSR model was also coupled with a MZ [22] approach to further accelerate the computational speed. The MZ approach allows to group together similar computational cells and invoking the chemistry solver once per group. The number of zones is dynamically determined by specifying bin sizes. In this study, two-dimensional bins were predetermined on dimension of equivalence ratio and mixture temperature; 0.05 of equivalence ratio and 5 K of temperature. This combination of WSR-MZ setup was used to model spontaneous ignition of fuel-air mixture where small scale mixing is not dominant, i.e., well-mixed condition.

For turbulent premixed combustion, a hybrid combustion modeling approach that has been recently proposed and validated across different SI engine platforms [15,23] was used to capture SI and mixed-mode combustion. In this approach, level-set based flamelet model, G-equation model [24,25], is employed to track the deflagration flame front initiated by spark ignition. This flamelet model allows to avoid solving stiff ODE calculations for chemistry in a thin reaction zone of premixed flame. The model is then used to explicitly track the turbulent flame brush by a passive scalar transport, G(x,t). This is enabled by resolving large-scale motion of flame brush in turbulent flow, which is derived from the local turbulent flame speed (St) as a function of mixture properties, thermodynamics and turbulent intensity. The turbulent flame speed is then calculated by the combination of laminar flame speed (LFS) and turbulent mixing contribution according to the Peters’ formulation [24]. The fuel-specific laminar flame speed was calculated on 1D coordinate normal to a freely propagating premixed flame front a priori. Separate lookup tables for the laminar flame speed were then created as a function of temperature, pressure and equivalence ratio for currently employed fuels. This approach of tabulated laminar flame speed is therefore beneficial to incorporate fuel-specific effects on flame front motion.

In the current hybrid combustion model approach, burnt gas elements are treated as being in the equilibrium; therefore, stiff ordinary difference equation (ODE) calculation is not required. On the other hand, a separate WSR-MZ model approach is implemented to account for unburnt gas (G < 0); hence the fluid elements may undergo finite rate of chemical kinetics, requiring detailed chemistry solution. Validity of this hybrid model approach has been well demonstrated in knocking propensity of Cooperative Fuel Research SI engine platform [15]. Details of model formulations and descriptions are not repeated in this paper for the sake of brevity. Additional details can be bound in Refs. [15,21,24,25].

The gasoline fuel injection was modeled in an Eulerian–Lagrangian fashion, which treats gas phase and liquid phase in separately defined coordinates. The clouds of liquid particles are treated in a Lagrangian coordinate and coupled with the continuous phase Eulerian solution. In order to address the spray atomization and evaporation process, Kelvin–Helmholtz (KH)-Rayleigh–Taylor breakup model [26] and Frossling correlation [27] were used, respectively. This study adopted Co-Optima core research gasolines designed as part of the Co-Optima Initiative [28]. Two research gasolines, Alkylate and E30, were considered in this study. These fuels were formulated to obtain similar high Research Octane Number (RON), which is suitable for diluted/boosted SI operation. To treat these fuels in the liquid phase, the primary reference fuel (PRF97.3: iso-octane 97.3% and n-heptane 2.7% by volume) was substituted for Alkylate liquid surrogate. For the E30 liquid fuel blend, physical properties were referred to 30%-by-volume blend of ethanol with a certification gasoline that was generated in the previous literature [29].

For chemistry surrogate, on the other hand, four component blends for Alkylate and 8 components for E30 were suggested in the Co-Optima research initiative [28] to match their ignition characteristics with targeted research gasolines. The Table 2 shows details of their chemistry surrogate components. Chemical kinetics behavior of these two chemical surrogates were modeled by using two respective reduced mechanisms for Alkylate and E30; (1) 121 species and 647 reaction steps and (2) 211 species and 1239 reaction steps. The former mechanism (BOB-Alkylate) was developed by researchers at University of Connecticut and first introduced in the preceding ACI study [17]. The second mechanism was newly developed for BOB-E30 fuel in this study by the same kinetics group led by Lu. Details of the new mechanism developed are described in Sec. 2.3.

The chemical kinetics behavior of BOB-E30 was modeled using a 211-species skeletal mechanism for Co-Optima core research fuels, including BOB-Alk, BOB-Aro, and BOB-E30, which is reduced from a 2878-species detailed mechanism for gasoline surrogates developed by the Lawrence Livermore National Laboratory [30]. The reduction was performed based on a large set of reaction states sampled over the parameter range of pressure from 1 to 100 atm, equivalence ratio from 0.3 to 1.5, inlet temperature of 700 K for perfectly stirred reactors (PSR), and initial temperature from 600 to 1600 K for autoignition, covering the low-temperature chemistry which is important for engine combustion. Due to the high efficiency, directed relation graph (DRG) was employed as the first step to reduce the large mechanism [31], with H radical selected as the starting species in DRG and the error tolerance was set to be 0.3. Then the DRG aided sensitivity analysis (DRGASA) [32] was applied to further eliminate unimportant species and reactions by specifying a worst-case relative error of 30% for ignition delay and extinction residence time in PSR, which is a quantification of the errors in the skeletal mechanism. The measured worst-case error tolerances for ignition delay and extinction residence time were 27.87% and 29.22%, respectively. The obtained skeletal mechanism is composed of 211 species and 1023 reaction steps.

The obtained 211-species skeletal mechanism is then validated against the detailed mechanism in evaluating the ignition delay times. The validation study was performed at multi-mode engine relevant conditions: lean mixture and booting part-load ACI operation and stoichiometric SI operation. Selected validation results are displayed in Figs. 2(a) and 2(b) for mixtures of equivalence ratio of 0.3 and 0.4 under 40 bars and stoichiometric mixture under 20 bars, respectively, showing close agreements between the 211-species skeletal mechanism and the detailed mechanism results.

In this paper, primary results from the CFD analysis are organized by the representative engine conditions of multi-mode combustion in sequence of (1) ACI, (2) SI, and finally (3) mixed-mode.

This chapter provides extended analysis of thermal wall-boundary impact that was once discussed in the authors’ preceding study [17]. The authors carried out CFD simulations on several ACI conditions on the same engine platform ranging from low loads (IMEP ∼ 2 bars) to high loads (IMEP ∼ 9 bars). Important initial and boundary conditions were provided by the corresponding experimental data; e.g., intake charge thermodynamics and flow conditions. However, the experiment lacks the thermal wall temperature condition on cylinder wall components; head, liner, valves and piston. This is a commonly encountered problem in engine simulations. Therefore, approximation of temperature range of the wall components was given from the conjugated heat transfer study [33]. This heat transfer study was performed on a different SI engine platform for a range of engine loads considered in this study. Then, an empirical adjustment of temperature was applied to provide best agreement with the measured in-cylinder pressure trace for currently employed ACI conditions. The wall temperature profile was finally defined by finding the following: T_liner = 425 K, T_piston = 475 K, T_head = 455 K, and T_valves = 435 K. With this boundary condition setup, model validation and important findings were discussed in the preceding papers [17,34]; hence, short summary of engine performance metrics listed in Table 3 replaces learnings obtained from the ACI simulations performed in the previous studies.

In the previous ACI engine studies [17,34], essential findings were discussed; i.e. (1) volumetric and spontaneous combustion event and (2) the cylinder wall temperature sensitivity as illustrated in Fig. 3. The spatial distribution of progress variable illustrated in Fig. 3(a) is representative of such a volumetric burning process. Hence, the use of WSR-MZ model seems to be well suited. In addition, numerical experiments in the previous study [17] revealed a certain level of wall temperature perturbation that noticeably shifts the combustion phasing and combustion stability. The numerical experiments applied 25 K temperature perturbation applied across entire cylinder wall components and observed significant shift of pressure trace indicated by cyan curves in Fig. 3(b). However, the earlier study [17] did not yield further quantitative clues on this observation. Hence, the present study put forth a research subject on this finding that can be better understood by exploring multi-variables joint analysis.

In the previous studies [17,34], certain degrees of sensitivity of mixture stratification and thermal stratification in combustion phasing were identified. However, coupled impact of both types of stratifications on detailed ignition process was not considered. To gain an in-depth understanding of ignition process, this study proposes a novel method of analysis that measures autoignition characteristics associated with mixture/thermal stratifications. In this analysis, mass-weighted joint PDF in percentile of temperature and equivalence ratio (ϕ) is overlaid on an ignition delay time map (see Fig. 4). The joint PDF was constructed by averaging mixture quantities over five consecutive cycles constantly at TDC timing where noticeable low-temperature reaction is yet to begin. For constructing the ignition time delay map, the pressure was held constant at 50 bars (mean pressure at TDC). This is reasonable choice since the pressure would not hold as heavy impact as temperature and equivalence ratio would have on the ignition delay. In order to determine whether the mixture element of interest would proceed the high-temperature combustion at desired CA50 timing, a chemical time scale (τ_chem) was introduced to measure time elapsed from TDC to CA50; i.e., $τchem∼1.3ms$ at given engine operating condition (1500 rpm). Therefore, it is reasonable approximation that the mixture elements within the τ_chem limit can undergo high-temperature heat release prior to the designated CA50. This method of analysis can be applied in the discussion of wall temperature sensitivity.

Along with the given test data (baseline), two additional numerical tests were conducted by imposing thermal wall-boundary condition with perturbations of 25 K temperature; see Figs. 3 and 4. In the baseline scenario presented in Fig. 4, only a portion of the mixture elements comes within the chemical reactivity limit (1.3 ms). This portion of mixture quantity may have been responsible for the onset of high-temperature combustion prior to CA50 and transported thermal energy to the neighbor mixture elements, resulting in sequential burning process. It is also noteworthy that wall temperature change by 25 K level can noticeably shift the thermal quantity distribution of mixture while maintaining the nonuniformity of thermal-mixture relatively constant in its PDF shape. In consequence, majority of the mixture charge mass with +25 K wall temperature scenario is found to fall within the time scale (τ_chem) limit and hence resulting in explosively fast reaction process. In contrast, −25 K wall temperature case forces the majority of mixture to be chemically inert and fail to meet desired combustion phasing.

On this map, one can see higher degree of reactivity change in temperature space given the equivalence ratio range of interest (0.25 < ϕ < 0.5), meaning that the employed ACI conditions were operated in the domain of very temperature sensitive region. Conversely, mixture charge stratification in ϕ may have imposed a less influential impact. This is a tendency of T-ϕ sensitivity which is very consistent with observations in the previous study [17].

The hybrid combustion model approach for SI mode combustion is first validated against the experiments in this section. Corresponding engine experiments were performed aiming to produce high-load SI engine conditions (IMEP ∼ 9 bars) with stoichiometric mixture charge. Two different Co-Optima research gasolines (Alkylate and E30) were used to highlight the robustness of the model accuracy and validity. With these two different fuels used, the model empirical constants were not found case-dependent, thus ensuring the robustness of the model setup. Calculated pressure and heat release traces for two fuels are also found to match the trend of experiment. Table 4 summarizes the key engine combustion and performance metrics evaluated by experiments and simulations. Slightly mismatching combustion phasing in Fig. 5 is possibly attributed to the use of simplified ignition kernel growth modeling during the energizing stage. Indeed, to avoid numerical complexity and intense time integration in the ignition modeling, we utilized a simple approach to mimic the ignition kernel formation and growth by imposing an energy source at the spark plug location.

To feature the cyclic engine operations, 11 consecutive cycles were collected at each test condition. The first cycle was then discarded and the remaining ten cycles were used for analysis. The current modeling framework did not seem to suitably capture higher bandwidth of pressure variance from cycle to cycle. This is indicated by underestimated COVimep compared with measurement. This is primarily attributed to the fact that RANS framework tends to smooth out the numerical solution with ensemble averaged scalars and presence of turbulent viscosity term (i.e., Reynolds stress). Hence, small scale turbulent motion may disappear and be merged into the resolved scalar quantities. In such a reason, many of computational studies in the past has leveraged a technique of high-fidelity simulation such as Large Eddy Simulations in order to better capture their transient and stochastic nature [35,36]. However, large-scale fluctuating fluid motion can reasonably be retained and attribute to the cyclic combustion dynamics. Over the past years, several engine CFD studies [37–40] have demonstrated the relevance of using RANS framework in capturing qualitative trend of CCV impact. They addressed that RANS modeling can capture portion of the CCV events and reproduce generic trends of cyclic variability.

Given the validated baseline simulation, this section aims to discuss underlying principles governing the main features observable in high loads SI mode. Figure 6 shows the results obtained from the wall temperature sensitivity analysis. As opposed to ACI mode, the SI mode features marginal influence of wall temperature on key combustion metrics, i.e., IMEP and combustion phasing. While the ACI mode was hugely affected by even a small wall temperature perturbation (25 K), up to 65 K difference in Twall barely makes change in presented combustion metrics in Fig. 6. It only appears to merely affect the combustion phasing in a small range of 3 CAD, which is very small change compared with that of ACI mode condition. It is true that thermal wall-boundary condition would not affect the major source of SI combustion event; rather the energy deposition in spark plug and subsequent flame kernel growth would be more influential.

One of the prominent features of the SI can be noticed by the enlarged cycle-to-cycle (CCV) variation in both experiment and simulation with respect to ACI. The SI mode appears to double the CCV range compared with that of ACI mode. Since the SI combustion features premixed flame propagation, possible sources of the CCV can be found from local variations in (1) mixture thermodynamic state and (2) fluid dynamics. Following discussions explores the CCV impact in these two aspects.

First, potential source of CCV in SI mode may stem from the cyclic/spatial variability of mixture thermodynamic state. This, in turn, changes the local laminar flame speed. In this context, the same type of analysis introduced in Fig. 4 is applied to analysis of the SI combustion. Instead of using ignition delay map, the current analysis used a map of LFS as a function of temperature and pressure as displayed in Fig. 7. The thermal-mixture stratification is apparent as represented by the joint PDF of equivalence ratio and temperature. The mixture elements may feature varying laminar flame speed in association with the joint PDF. From this map, one can roughly spot the LFS values ranging 0.6–0.8 m/s to best represent dominant mixture thermodynamic property. This is too slow for the flame front to travel the half of the bore dimension (44.5 mm) within the effective duration of combustion event (50 deg equivalent to 5.5 ms). The flame front may require around 55.5 ms in order to travel through the combustion chamber (ten times the engine combustion period). In other words, the laminar flame speed may hold a marginal impact toward the flame-travel-through-time. Regarding the CCV tendency, therefore, it can be claimed that the impact of static thermodynamic variation (laminar chemistry) is rather outweighed by the fluid dynamics impact.

Second, from a different aspect, the increased CCV level may be attributed to in-cylinder turbulent flow characteristics. Primary characteristics of CCV tendency in the SI combustion may be attributed to the interaction between flame front and adjacent turbulent mixing. In this context, underlying characteristics of CCV event can be understood in conjunction with the local turbulent mixing intensity. Illustrated graphics in Fig. 8 well represent this scenario; two-fold end-cycle bands (weak/strong cycles: lower-end and upper-end) are selected to compare the turbulent intensity and consequence of flame front propagation. The sequence of flame front development in Fig. 8 identifies the strong correlation of combustion cycle and local turbulent intensity. Further analysis shown in Fig. 9 supports this idea. We gathered three representative cycles of upper-end, lower-end and median cycle. The burnt gas in Fig. 9(a) is measured by the ratio of burnt gas mass over the total gas mixture; thereby standing for the progress rate of turbulent flame brush. Figure 9(b) quantifies the intensity of turbulent mixing filtered at flame front (captured within −0.001 < G < 0) and accordingly tracks the temporal history of the mixing intensity. This suggests strong positive correlation between turbulence intensity and flame propagation speed.

Indeed, this turbulence impact on the CCV is fairly well-known physics in normal SI engine operations and has been discovered in many literatures [41–43]. Nonetheless, this study provides meaningful insights by identifying contribution of turbulent intensity competing with laminar state thermal-mixture charge. To add more insights, additional numerical experiments were performed for the three given cycles at following conditions: (1) laminarized flame and (2) imposed homogeneous turbulence.

The first test, laminarized flame scenario, forces the flame to undergo laminar flame propagation without an impact of turbulence. This could be conducted by turning off the turbulent flame speed (St) contribution to transport of the level-set G scalar. Burnt gas ratio (gold colored lines) in Fig. 9(a) suggests that the contribution by the pure laminar flame speed impact is minimal. Only 1% of unburnt gas was swept by the laminarized flame till 40 CAD aTDC. The slight change (∼4%) between lower- and upper-end cycles can be understood by finding the laminar chemistry variance in thermal-mixture charge. Under the notion that the laminarized flame is merely characterized by LFS shown in Fig. 7, this slight change is an outcome of the stratified charge variance from cycle to cycle.

The second test is to evaluate the contribution from the thermal-mixture state variance to the CCV. The homogeneous turbulence field was artificially imposed identically to the three cycles, such that cyclic variability of turbulence flow impact is removed. Mean turbulent kinetic energy (TKE) and energy dissipation rate values were extracted from the median cycle at 12 CAD bTDC shortly before the spark timing and imposed to these three cycle simulations at the same time. In order to neglect the production of turbulence by the large-scale motion, convective velocity components were also reinitialized with zero values, i.e., u = v = w = 0. Strictly speaking, from energy balance stand-point, the flow field becomes nonstationary and decaying turbulent flow (i.e., no production of turbulence). This feature is evident by finding the monotonously decaying TKE trajectory filtered at flame front (gray colored lines) in Fig. 9(b). Under this circumstance, the impact of turbulence is retained equally across the three different cycles; hence, other competing impact (thermal-mixture state variation) becomes effective. In the result shown in Fig. 9(a), cyclic variation of burnt gas is still present. Therefore, it can be claimed that a part of CCV source comes from the cyclic variation of local thermal-mixture charge.

The validity of the employed combustion model has been ensured by sweeping the two-end modes of multi-mode combustion; low-load ACI and high-load SI. Hence, it is also a reasonable approach to apply the consistent model setup to produce the part-load mixed-mode combustion regime in the same engine platform. In this section, the mixed-mode combustion is taken as a strategy for mode transition between ACI and SI; hence both distinctive combustion modes likely coexist in the transitional mode operation. However, the mixed-mode combustion has yet to experimentally be attempted in the currently employed engine platform; no available experimental data exist to this date. Therefore, following discussions on mixed-mode are made based upon the results obtained from the numerically explored mixed-mode simulation.

Toward the goal of mixed-mode combustion strategy using the consistent engine platform, this study created a virtual test condition for realizing mixed-mode while maintaining the same engine dimensions with the ACI and SI operations. The virtual test condition was intended to benchmark the major engine parametric features used in the published mixed-mode combustion studies [10,23]. The benchmarked engine was featured of direct injection spark ignition and explored to realize the spark ignition-assisted ACI (SACI) operation. Important engine parametric features employed for the current virtual test are listed in Table 5.

Figure 10(a) shows the pressure and heat release rate traces obtained from a single simulation at the virtual test condition. Although no experimental data for direct comparison is available for validation purpose, the simulated condition apparently captures an evidence of finding mixed-mode combustion dynamics. This evidence of mixed-mode combustion propensity was similarly reported in one previous study [23]. The currently simulated engine load (IMEP) yields 4.6 bars, which is very close to the benchmarked experiment, 4.46 bar.

Coordinate transform of heat release rate trace can additionally highlight distinctive feature of mixed-mode combustion regimes. In Fig. 10(b), the mass burned rate replaces the crank angle coordinate. The burned mass fraction was calculated as the integrated heat release rate normalized by total heat release at each cycle. In this figure, first phase of heat release till 65% of mass burned ratio is constantly observed over the entire cycles. Second rise at different rate from cycle to cycle is identified at a later phase (from 65% till the end). One can see the peak heat release found at around 80% of mass burned ratio. This is very close to the finding in the benchmarking experiment [10]. The presence of the second heat release peak identifies a clue of finding the “mixed” two combustion regimes. It is apparent that the SI initiated flame front propagation determines the first rise of heat release. Conversely, the second peak indicates the assisted autoignition, namely, spark ignition-assisted ACI (SACI). However, a portion of captured cycles was observed to skip the second peak of heat release as indicated in blue solid lines. This study is therefore intended to primarily reveal the governing physics behind these distinguished combustion behaviors.

Time sequence of flame structures for two different combustion regimes is illustrated in Fig. 11; upper row with mixed-mode and lower row with SI only mode. These combustion regimes can be distinguished by finding the spontaneous ignition of unburnt gas. The mixed-mode combustion shown here, sequential event of SI initiated deflagration wave and subsequent end-gas autoignition, can also be distinguished by apparently fast flame front progress rate indicated by the dark iso-contour surface. Therefore, it can be hypothesized that the fast burning flame front pushes the end-gas mass toward cylinder wall. This may result in accelerating the end-gas heating and spontaneous combustion.

It should be noted that the principle of the mixed-mode is very similar to the one behind the knocking propensity. The mixed-mode excludes abnormal rise of pressure; otherwise this scenario would become knocking phenomena. Therefore, a method of analysis on end-gas reactivity that has been popularly utilized by the preceding literatures [44–46] can also be used. In this context, pressure and temperature trajectory of the end-gas phase (G < 0) was captured after spark timing and displayed on the fuel-specific (E30 in this test) static ignition delay time. Symbols in Fig. 12 mark sample points of CADs along the trajectory; hence one can see the progress rate of end-gas compression. The aforementioned hypothesis holds in this analysis of P-T trajectory. The mixed-mode appeared to be promoted by the accelerated end-gas pressure rise by the flame front, whereas the SI only mode failed to reach to a state of thermodynamic that can sufficiently initiate high-temperature kinetics.

It is noted that the flame front progress rate is responsible for promoting the mixed-mode occurrence. Therefore, the insight gained from the SI combustion mode also holds valid in the mixed-mode and allow to derive informative understandings. From this perspective, result shown in Fig. 13 accounts for contribution of turbulent mixing at the flame front to the burnt gas progress rate. This derives a solid implication that the mixed-mode cycles were consistently accompanied by increased level of turbulent mixing at the flame front which in turn augmented progress rate of the SI (deflagration wave) mode. In a general notion, autoignition is kinetically driven; hence chemically reactive fuels (e.g., low RON#) may be more compatible with mixed-mode repeatability. However, findings in this section suggest that turbulent mixing can also assist the end-gas autoignition to enhance the mixed-mode combustion potentially with high RON fuels.

Key outcome of this study is to show the model capability of simulating the realizable multi-mode (ACI/SI) combustion strategies and introduce novel method of analysis to understand in-depth physics. Key summaries are listed as follows:

1. In the ACI simulations, the WSR-MZ model approach moderately captures the experimental trend and characterizes the volumetric combustion event. This approach also provides parametric analysis with the wall temperature uncertainty. Such a wall temperature impact plays a role in determining the combustion phasing. This phase control can be greatly influenced by the chemical reactivity variation along with the stratified mixture charge.

2. Standard SI operations in the GDI engine were simulated with a recently proposed hybrid combustion model (level-set G-equation model with WSR-MZ approach). The model was useful to capture major features observed in the SI combustion revealed by the experiment.

3. Major source of CCV in SI operation stem from local turbulence intensity, which greatly affects the progress rate of premixed flame brush. A numerical experiment performed in this study created a cyclic constant homogeneous turbulent flow field. The test revealed a partial source of CCV stemming from the cyclic variation of thermal-mixture charge.

4. As a strategy of mode transition for multi-mode engines, this study discusses a mixed-mode operation that combines major features of ACI and SI operations. A virtual test condition was designed in order to reproduce the mixed-mode combustion that was demonstrated in a preceding experiment. The virtual test condition with the Argonne engine configuration replicated the same findings and consistent level of mixed-mode probability as seen in the previous experimental investigation.

5. The use of the hybrid combustion model provided insightful notions in terms of source of mixed-mode realization and impact of local turbulent mixing. From the result noted from the virtual test, elevated turbulence intensity can enhance the probability of mixed-mode combustion regime. This also suggests the use of high RON (low-reactivity) fuels in the mixed-mode combustion if increased turbulent mixing intensity is ensured near the spark plug location.

The submitted manuscript has been created in part by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science Laboratory, is operated under Contract No. DE-AC02-06CH11357. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.¹ This work is performed under the auspices of the Office of Energy Efficiency and Renewable Energy, Office of Vehicle Technology, U.S. Department of Energy, as part of the Co-Optimization of Fuels & Engines (Co-Optima). Finally, the authors thank the U.S. Department of Energy Vehicles Technology Office (technical manager: Kevin Stork) for financial support.

There are no conflicts of interest.

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