Turbulent jet ignition (TJI) (Attard et al., 2010; Toulson et al., 2010; Alvarez et al., 2018) is one promising technology that allows ultra-lean combustion with high energy efficiency and low emission. The TJI system adopts a pre-chamber that houses a spark plug and optionally fuel/air injectors, which has already been adopted in natural gas spark ignition engines (Mastorakos et al., 2017). In general, stoichiometric fuel/air mixture can be supplied to the pre-chamber to ensure successful ignition, meanwhile the main chamber can accommodate sufficiently lean mixture for substantially-enhanced thermal efficiency. For the active pre-chamber design, where both fuel and air injectors equipped, accurate fuel/air mixture without EGR can be prepared for the pre-chamber. Disadvantage of this active pre-chamber option is that additional fuel system is required, which increases the cost and complexity of control, packaging, and cooling. In the case of passive pre-chamber, no fuel injector is installed inside the pre-chamber, so that the fuel/air mixture has to rely on natural scavenging during the intake stroke to enter the pre-chamber. Therefore, the passive pre-chamber design causes difficulty for precise charge preparation inside the pre-chamber, which may lead to more severe combustion instabilities and higher chance of misfire. In both options, the fuel and air mixture in the pre-chamber are ignited by the spark plug. The temperature and pressure inside the pre-chamber quickly increase. Consequently, the large pressure difference between the pre-chamber and main chamber forces the hot combustion products out of small orifices at the end of the pre-chamber, forming a hot turbulent jet igniting the compressed lean charge in the main combustion chamber. Combustion induced by this hot reacting turbulent jet occurs much more rapidly due to the spatially distributed flame-fronts (Attard et al., 2010). Less heat is transferred to the engine parts due to the fast combustion and lean mixture. Compared to the conventional SI engines that run at stoichiometric conditions and limited by engine knock, the lean mixture in the main chamber is knock free for most of the conditions and hence allows much higher compression ratio. Furthermore, relatively low combustion temperature occurring in the lean main chamber significantly reduces emissions of NOx and particulate matter (PM).

TJI has been extensively investigated both experimentally and numerically. Toulson and co-workers conducted a series of fundamental studies of TJI using an optical-accessible rapid compression machine (RCM). Toulson et al. (2012) compared conventional spark ignition and TJI in an optical single cylinder engine, and demonstrated that TJI enables faster combustion due to the multiple widely distributed ignition sites produced. Gentz et al. (2015) investigated the orifice size’s effects on TJI in a rapid compression machine (RCM). It was found that for near stoichiometric air to fuel ratios, a large nozzle that produces more spatially distributed jets would result in faster combustion progression. However, at leaner conditions a smaller diameter nozzle that produces a faster and more vigorous jet is required to initiate combustion. Gentz and Toulson (2016) further compared active and passive fueling in TJI. For passive fueling, the single orifice has better performance than the dual orifice with the same cross section area. Karimi et al. (2014) conducted an experimental and computational analysis of the hot jet ignition in a combustion vessel. The hot jet is characterized by three different jets: wall jet, wall impinging jet, and free jet. Li et al. (2019) conducted an experimental study of TJI in a RCM and a single cylinder engine. The study revealed that there are two ignition patterns in the pre-chambers depending on the diameter of orifices: flame ignition pattern with large orifice diameter and auto-ignition pattern with smaller orifice. Biswas et al. (2016) revealed two ignition mechanisms in the main chamber: jet ignition and flame ignition. Biswas and Qiao (2016) conducted an experimental study of the ignition of ultra-lean premixed H2/air mixtures by the hot jet issued by a pre-chamber with a stoichiometric mixture, visualized using simultaneous high-speed Schlieren photography and OH* Chemiluminescence. Three nozzle geometries (straight, convergent and converging-diverging) are compared. Diamond shock structures in the supersonic jets and a high-temperature zone downstream the shocks were observed, which may reduce the flammability limit in the main chamber. Combustion instability becomes noticeable near the lean-limit conditions. Biswas and Qiao (2018) further investigated the effects of spark location and equivalence ratio in pre-chamber on the ignition pattern in the main chamber. The effective ratio describing the spark location governs the flame dynamics in the pre-chamber. Bolla et al. (2019) simulated an automotive-sized scavenged pre-chamber mounted at the head of a rapid compression-expansion machine using RANS and LES. It is shown that the tilted nozzle of the pre-chamber orifice generates a swirl flow inside the pre-chamber. Benekos et al. (2020) conducted a 2D DNS study of the ignition process in the main chamber. The effect of the wall thermal boundary condition, initial mixture temperature, and equivalence ratio in the main chamber was investigated numerically. It was found that the hot jet from the pre-chamber can be broken into small kernels at cold condition of the main chamber, or forms a flame torch at the hot condition. Muller et al. (2018) investigated the ignition mechanism in the main chamber. It was found that both kinetic effects and thermal effects are important for the hot jet induced ignition process. Strong correlations between fluid dynamics, mixing and combustion are observed. Akhtar et al. (2017) investigated the effects of orifice geometry on the performance of pre-chamber using Schlieren imaging. Circular and slit shapes with the same cross-section area were considered. It was found that the slit pre-chamber can accelerate the flame propagation in the early stages. Freeman et al. (2020) developed a new design of pre-chamber with the assistance of 3D combustion CFD. The CFD results show that the pre-chamber SI engine has good improvements over the conventional gasoline SI engine, especially the fuel economy. Based on the pressure difference between main chamber and pre-chamber, the gas exchange process between them can be described by a four-stage process. Shah et al. (2015) experimentally investigated the effects of pre-chamber volume and nozzle diameter on the resultant ignition characteristics. It was found that a larger pre-chamber provides higher ignition energy which results in shortened flame development angle and combustion duration. At a given pre-chamber volume, nozzle diameter mainly affects the combustion duration. Hlaing et al. (2020) reveals a two-stage combustion mechanism in the main chamber where the latter stage is thought to be contributing to the bulk ignition of the main chamber charge. The pre-chamber heat release is correlated to the mixture strength of the pre-chamber, which affects the phasing of the pre-chamber combustion and the initial heat release in the main chamber. Tang et al. (2020) used simultaneous negative PLIF and OH chemiluminescence to visualize the gas exchange process and flame jet from the nozzles of a pre-chamber, which showed that the flame jet penetration length is much shorter than that of the pre-chamber jet. A three-stage gas exchange process is proposed. When the equivalence ratio of the pre-chamber is increased from lean to slightly rich, the pressure difference between main chamber and pre-chamber, ignition timing, and timing of peak pressure difference increases at first and then reaches a plateau. Kim et al. (2019) compared turbulent combustion models (multi-zone well-stirred reactor and G-equation) for pre-chamber ignition. G-equation model gives better predictions than the well-stirred reactor model. From above, although extensive computational and experimental work has been conducted to understand and predict pre-chamber spark ignition, the design of the pre-chamber is still largely experience-based and there is a lack of general strategy that can provide guidance toward an optimal design. Zhang et al. (2020) conducted a comprehensive 3D CFD analysis of a light-duty gasoline engine with a passive pre-chamber. A three-phase phenomenological model is proposed to describe the flame ignition behavior during pre-chamber jet combustion. Pre-chamber with swirl nozzles generates organized and repeatable swirl motion that could be beneficial for combustion. The pre-chamber nozzle umbrella angle and orientation could be further optimized for a given combustion system to achieve reduced combustion heat loss. Hua et al. (2021) compared four pre-chamber designs, passive and active fueling in engine tests. They found that the volume and number of the jet hole are two key parameters for optimizing the structure of the pre-chamber. The pre-chamber with smaller volume has better IMEP and fuel economy due to the lower heat dissipation and combustion loss in the pre-chamber. The single-hole pre-chamber studied generates a stronger hot jet than the 7-hole pre-chambers, which effectively improves the burning rate and extends the lean-burn limit.

From the manufacturing and mechanical design perspective, MAHLE Powertrain has been the leading developer in application of TJI for powertrain of passenger cars. Attard et al. (2010) demonstrated in one single-cylinder engine that the TJI can tolerate up to 54% mass fraction diluent, which results in 18% improvement in fuel economy. Attard and Parson (2010) showed that the spark plug type, orientation and electrode gap have little to no effect on jet ignition combustion. They concluded that it is partially due to the spark discharge in the pre-chamber occupies a much larger fraction of the chamber relative to conventional spark ignition. They also found that the spark plug reach has the greatest effect that is not very important for conventional SI engines.

Coupled with genetic algorithm, 3D combustion CFD has been extensively used in engine development (Shi et al., 2011). Ge et al. (2009) and Ge et al. (2010) developed automated calculation processes to optimize fuel system, piston bowl, and swirl ratio. Ge et al. (2010) developed an optimization method that simultaneously optimizes multiple operating conditions by separating the design parameters into hardware parameters and operating parameters. Ge et al. (2011) and Lee et al. (2012) combined scaling laws with the optimization method in (Ge et al., 2010) for engine combustion optimizations. Machine learning techniques have been applied to many areas of engine combustion. Moiz et al. (2018) combined machine learning with genetic algorithm and 3D CFD for engine combustion optimization. The method was applied to a heavy-duty diesel engine. Kodavasal et al. (2018) used machine learning techniques to analyze the controlling factor of cycle-to-cycle variation in a gasoline spark-ignited engine. Probst et al. (2019) used two machine learning techniques (Gaussian process and SuperLearner) in engine combustion predictions. Different optimization methods were compared. The particle swarm optimization, differential evolution, GENOUD algorithm, and micro-genetic algorithm (GA) were recommended. Badra et al. (2020) optimized the combustion system of a gasoline compression ignition engine using CFD and machine learning-grid gradient algorithm. Shah et al. (2019) used machine learning techniques to predict the ignition delay, flame speed, octane rating, and combustion phasing of multicomponent gasoline surrogates in homogenous charge compression ignition engines.

The design of the pre-chamber is the most critical component of this type of engines, which remains a challenge. The papers in literature usually investigated the effects of one or a few design parameters on engine performance. However, systematic study of the pre-chamber geometry is missing. The present paper reports an automated optimization method for pre-chamber design using 3D combustion CFD. DOE, GA, machine learning is coupled with 3D combustion CFD for optimization of the pre-chamber design for a spark-ignition engine. Different machine learning models are compared. The optimal design is compared with an averaged design and a bad design to understand how the design parameters physically influence the engine performance.

A three-dimensional port fuel injection (PFI) spark-ignition engine was simulated, which is one of the example cases of the CONVERGE. Table 1 lists the parameters of the engine configurations. For all the cases, the global equivalence ratio is set to unity. In the original engine, the spark plug is installed at the center of the cylinder head. In the present work, the spark plug is then replaced by the TJI system (c.f., Figure 1), whose bottom part has the size as the spark plug. Thus, the whole pre-chamber can be directly installed to the SI engine without making a new cylinder head. Full cycle simulations of all the engine cases were conducted, i.e., starting from EVO (exhaust valve opening, which is −579.8° ATDC) to EVO (140.2° ATDC). The gas exchange process is simulated. At the IVC (intake valve closing), the mass fraction of CO2 and H2O in the whole chamber (including main and pre-chamber) is 1.83%, which is equivalent to about 5.4% EGR.

In the present paper, a commercial CFD software CONVERGE (Richards et al., 2017) was used for engine simulation, which is based on the finite volume method. Table 2 lists the primary models used in the present simulations. Adaptive mesh refinement (AMR) and fixed embedding were used to balance efficiency and accuracy. Real fluid model, Redwich–Kwong equation of state, was employed. SAGE combustion model with PRF mechanism (Liu et al., 2012) was used for all the simulations of SI engine cases, in which the fuel is gaseous gasoline. For the simulation of the rapid compression machine, the fuel is methane. The SAGE combustion model with the GRI 3.0 mechanism was used. The SAGE combustion model treats each computational cell as a perfectly stirred reactor, i.e., there is no explicit turbulence chemistry interaction (TCI) models. Recently, Dahms et al. (2019) conducted an asymptotic analysis that showed there is implicit TCI in the multi zone SAGE model. The implicit TCI means that the performance of the combustion model depends on grid size, numeric, etc. The TCI can be fully recovered by SAGE model when the grid size and time step approaches the size of DNS. Although the present grid size and time step are not small enough to fully recover the TCI, local mesh refinement near the flame front can largely recover the TCI. Additionally, the turbulence effects are taken into account through the turbulent diffusivity, through which the TKE affects the mixing processes of energy, species, and momentum. Thus, a certain level of the turbulence effects on the combustion process has been captured by the present simulations. All the combustion simulations use unsteady RANS with RNG k–ε model (Han and Reitz, 1995). Constant diffusivities were assumed, with turbulent Prandtl number of 0.9 and turbulent Schmidt number of 0.78. Spark plug geometry was neglected in the pre-chamber. In both conventional SI engine and pre-chamber, spark ignition was modeled using a point source. Base mesh size is set to 4 mm. Three level embedding based on temperature and velocity was applied to AMR. Boundary of the pre-chamber was refined to 0.5 mm using fixed embedding. Five and three level fixed embedding were used for the nozzle and near nozzle jet flow region, respectively. Level three AMR is activated by both temperature gradient and velocity gradient.

Launder and Spalding wall model (Launder and Spalding, 1974) is employed to treat the boundaries of the solid walls. The temperature of piston, liner, cylinder head, pre-chamber, exhaust valve bottom, exhaust valve stem, exhaust port, intake port, intake valve bottom, and intake valve stem are set to 450, 400, 400, 450, 525, 425, 400, 300, 480, and 350 K, respectively. At the inlet of intake port, the pressure is fixed to 1 atm and a perfect stoichiometric mixture of gaseous gasoline and air is set. The pressure at the outlet of exhaust port is set to 1 atm, too. Backflow with temperature of 610 K and a mixture of N2 (71.9% by mass), CO2 (19.2%), and H2O (8.9%) is applied to the outlet of exhaust port. At the beginning of the simulations (−579.8° ATDC, which is EVO), the mixtures in the main chamber and pre-chamber are assumed to be N2 (71.9% by mass), CO2 (19.2%), and H2O (8.9%). By simulating the whole cycle, the scavenging process of the main chamber and pre-chamber is covered. The predicted residuals in the main chamber and pre-chamber are more reliable. The same numerical model has been used to simulate the MSU single nozzle TJI case, which successfully reproduced in-cylinder images and the averaged pressure trace of the main chamber that will be presented in the next section. It implies that the present numerical model and mesh is able to reproduce the ignition and combustion processes in the pre-chamber and main chamber. Figure 1 shows the surface of one pre-chamber SI engine. The intake ports and exhaust ports are on the two side of x-direction, i.e., the engine is about symmetric of y-plane (y = 0). Figure 2 shows a typical mesh of the pre-chamber SI engine at −2.5° ATDC. Due to the additional volume of the pre-chamber, the compression ratio of the pre-chamber SI engine is reduced from 10.0 for the baseline engine. Fuel injection is neglected for simplification. The intake air/fuel mixture is assumed to be perfectly mixed.

The pre-chamber has 6 holes. The hole size and normal direction of nozzle exit are fixed. In the present study, only the geometry above the nozzle is optimized. An axi-symmetric shape is assumed for the upper part of the pre-chamber that is above the nozzle part. Thus, the geometry of upper part can be simplified as a symmetric 2D profile. The half profile is then parameterized and analytically described using 11 design parameters. Figure 3 (left) shows the sketch of an example design with the 11 design parameters. Point A is fixed and connects with the nozzle part of the pre-chamber. Points B, C, D, and E are flexible. Point B has the same radial coordinate as Point A, i.e., the part AB is vertical. Vertical coordinate of Point B is determined by design parameter “bz”. Points C and D have the same radial coordinates, which is determined by design parameter “cr.” Their vertical coordinates are determined by “cz” and “dz”. Coordinates of Point E is determined by design parameter “er” and “ez.” Radius of the pre-chamber top is set to be larger than the spark plug size to ensure that a regular spark plug can be installed to the pre-chamber. Thus, the radial coordinate of Point E has a minimal value. Design parameter “xde” is used to determine the curvature of DE. Design parameters “gz,” “hz,” and “θ” are used to determine the curve between points B and C. Table 3 lists the range of these 11 design parameters. Bezier curves are applied on the corner to ensure smooth transitions. The parameters “bz,” “dz,” “gz,” “hz,” and “θ” are physically within [0,1]. Except theta, all are set to [0.01, 0.99] to avoid potential singularity issue. For “θ”, a range of [0.2, 0.8] is chosen to avoid too sharp angles for curve BC. The minimal value of parameter “er” indicates the radial size of a conventional spark plug, i.e., the pre-chamber should be at least large enough to host a spark plug. Its maximum value is set to 1.8 based on the experience. The parameter “cr” indicates the ratio of radius at point C and point E, and thus it is larger than 1. Its minimal value is set to 1.02 to leave sufficient space for the curve DE. Its maximal value is set to 1.2 based on the experience. The minimal value of parameter “ez” indicates the minimal heights to host a conventional spark plug. Its maximal value is set to 3.0 based on the experience. The parameter “cz” is a normalized parameter describing the height of point C. Its minimal value is limited by its distance to the cylinder head, i.e., to avoid intersection with the cylinder head and maintain enough thickness of prechamber wall. Its maximal value is set to 2.0 based on the authors’ experience. The curvature parameters “xbc” and “xde” have non-negative values, with 0 for straight line and 1 for circular curve. They are set to the ranges of [0.1, 2.0] to cover a reasonable variety of curvature. Figure 3 (right) shows the three example designs. Black solid line indicates the design with all minimal parameters. Red dashed line indicates the design with all median parameters (which is the design DOE56 in “Combustion Analysis of the Optimal Design” section). Blue dotted line indicates with all maximal parameters.

Figure 4 shows the sketch of the optimization method, which is based on the Bayesian updating strategy (Enright and Frangopol, 1999). The Bayesian updating strategy is a learning-by-practicing approach, in which the Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. In the present application, the machine learning module is updated when more CFD results become available. The optimization starts from a DOE (design of experiment) of all the design parameters. In the present work, the size of the DOE is set to 56, which represents a small size DOE matrix with 11 design parameters. The DOE matrix is generated using Latin hypercube sampling method in Matlab. All the designs in this DOE are simulated using 3D combustion CFD. These CFD results form the first database, which is used in machine learning (ML) module for data training. Thus, the ML module can replace the 3D combustion CFD in the optimization process. Then, a genetic algorithm (GA) coupled with the trained ML module is used for optimization, which will recommend one “optimal” design(s). The “optimal” design(s) are further confirmed in the 3D combustion CFD. Thus, the role of ML+GA approach is to suggest the potential good designs, instead of accurately predicting the objective CA50. All the designs suggested by ML+GA approach will be further confirmed by the 3D CFD simulations. In another words, we judge the ML algorithm based on what design it has suggested, not the CA50 it predicted. The benefit of ML is to reduce the total number of the computational expensive 3D CFD simulations. Thus, the ML is not necessary to be a quantitative prediction tool. Instead, qualitative prediction of CFD results by the ML will be sufficient and actually is more critical than the quantitative prediction. The results of these “optimal” designs are added to the database to further improve the accuracy of the ML module. Compared to the 3D combustion CFD cases that usually take about 20 h using 72 cores, the computational time of the GA+ML option is only about a few minutes using a laptop, which is completely negligible. Thus, this method significantly reduces the computational costs by replacing the 3D combustion CFD with the ML module in the optimization. The ML module also helps to narrow down the optimal domain in the whole design space and reduces the total runs of 3D combustion CFD. The Bayesian updating approach reduces the total number of iterations. Given the nature of the GA, the final “optimal” design is the best design among all the considered designs, not the exact optimum in the whole design space (Shi et al., 2011).

In this work, an efficient optimization method that is based on Bayesian updating strategy is developed for 3D CFD-based optimization of internal combustion engines. The method couples DOE, genetic algorithm, and machine learning method. The method is applied to optimize the pre-chamber design for a spark-ignition engine. The pre-chamber geometry is parameterized by 11 design parameters. CA50 is taken as the primary objective of the optimization. A DOE matrix of these design parameters is generated. The designs in the DOE matrix are simulated using 3D combustion CFD, which generates a database that is used to train the machine learning models. Different machine learning models are evaluated in two stages. The first stage is based on the RMSE of the machine learning models. The second stage is based on the iterations with genetic algorithm and 3D combustion CFD. The optimal design is compared with an averaged design to understand the effects of pre-chamber design on engine performance. The following conclusions can be drawn from the present paper:

The proposed Bayesian updating optimization method based on 3D combustion CFD, parameterization, DOE, GA, and machine learning is efficient and feasible for engine development.

In the future, more design parameters, including nozzle hole number, nozzle hole size, nozzle hole direction, nozzle hole orientation, spark timing, and piston bowl will be taken into consideration. Wider ranges of the design parameters should be explored. The geometry of spark plug needs to be included into the CFD model. More objectives (e.g., CA10, TKE and residual gas fraction of pre-chamber, emissions) and constraints (e.g., peak pressure, peak pressure rising rate) may be taken into account using multi-objective optimization methods.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

HG and PZ made equal contributions to the present paper.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.