A CONTROL-ORIENTED JET IGNITION COMBUSTION MODEL FOR AN SI ENGINE

Proceedings of the ASME 25 Dynamic Systems and Control Conference DSCC25 October 28-3, 25, Columbus, Ohio, USA DSCC25-9687 A CONTROL-ORIENTED JET IGNITION COMBUSTION MODEL FOR AN SI ENGINE Ruitao Song, Gerald Gentz, Guoming Zhu, Elisa Toulson, and Harold Schock Department of Mechanical Engineering Michigan State University East Lansing, MI 48824 USA ABSTRACT A turbulent jet ignition system of a spark ignited (SI) engine consists of pre-combustion and main-combustion chambers, where the combustion in the main-combustion chamber is initiated by turbulent jets of reacting products from the precombustion chamber. If the gas exchange and combustion processes are accurately controlled, the highly distributed ignition will enable very fast combustion and improve combustion stability under lean operations, which leads to high thermal efficiency, knock limit extension, and near zero NOx emissions. For modelbased control, a precise combustion model is a necessity. This paper presents a control-oriented jet ignition combustion model, which is developed based on simplified fluid dynamics and thermodynamics, and implemented into a dspace based real-time hardware-in-the-loop (HIL) simulation environment. The twozone combustion model is developed to simulate the combustion process in two combustion chambers. Correspondingly, the gas flowing through the orifices between two combustion chambers is divided into burned and unburned gases during the combustion process. The pressure traces measured from a rapid compression machine (RCM), equipped with a jet igniter, are used for initial model validation. The HIL simulation results show a good agreement with the experimental data. and homogeneous charge compression ignition (HCCI) combustion [2, 3], provide promising means to achieve these goals. The engine thermal efficiency is improved by increasing the specific heat ratio due to the introduction of additional air. The low lean combustion temperature leads to a significant reduction of NOx emissions, especially when the relative air-to-fuel ratio λ is beyond the lean limit (e.g., at λ >.4) []. However, the application of lean burn technologies to a conventional spark ignition (SI) engine is limited by the poor combustion stability and decreased effectiveness of the three-way catalyst under lean operation conditions. The HCCI combustion, one of the lean burn technologies that have been widely studied in recent years, is initiated by the auto-ignition of the in-cylinder air-fuel mixture, which is similar to the operation of compression ignition (CI) engines. The heat releasing at multiple sites within the combustion chamber results in a very fast rate of combustion, which improves the thermal efficiency. However, the combustion phase control and SI-HCCI combustion mode transition control are two of the key challenges of the HCCI combustion [3,4]. Regulating the charge air temperature is often used to control the start of combustion. However, this technology needs to be further improved for practical applications. The jet ignition system consists of a main-combustion chamber and a small-volume pre-combustion chamber filled with a relatively rich air-fuel mixture. It has two fuel delivering systems: one for the pre-combustion chamber and the other for the main-combustion chamber. The two combustion chambers are connected by a few small orifices. The combustion process is initiated by a spark inside the pre-combustion chamber, and the INTRODUCTION In the recent years, various alternative combustion technologies have been investigated for improving combustion thermal efficiency and meeting the increasingly strict emission regulations. Lean burn technologies, such as jet ignition combustion [] Copyright 25 by ASME

turbulent jets of the reacting mixture from the pre-combustion chamber cause the combustion of the lean air-fuel mixture in the main-combustion chamber. In 98, Harry R. Ricardo developed and patented the 2- stroke Ricardo Dolphin engine that first used the jet ignition system [5]. In the 97s, as strict emission standards appeared, significant amount of research was devoted to the development of jet ignition systems. In 976, Toyota developed a jet ignition engine with no auxiliary fueling system for the pre-combustion chamber [6]. Similar engines were also developed by Ford [7], Volkswagen [8], etc. The compound vortex controlled combustion (CVCC) system developed by Honda is usually considered to be the most successful example of jet ignition technology [9]. It was able to meet the 975 emission standards without a catalytic converter. Jet ignition combustion possesses all the advantages of the lean burn technology mentioned at the beginning of this section. Besides, the distributed ignition source enables a very fast rate if combustion, which is similar to the HCCI combustion. It is capable of up to 8% fuel economy improvement relative to SI engines []. The enhanced ignition provided by the turbulent jets results in a significant improvement of combustion stability under lean operation conditions. Stable combustion can be achieved when λ is up to.8, approaching elimination of NOx emissions []. In addition, a jet ignition system makes it easy to control the combustion phase, compared with the HCCI combustion, due to the simple control of the start of combustion through the spark plug in the pre-combustion chamber. However, the higher heat losses due to the additional surface area of the pre-combustion chamber along with the poor mixture propagation within the small pre-combustion chamber cavity may somewhat compromise thermal efficiency []. The gas exchange and combustion processes within the pre-combustion chamber need to be precisely controlled to provide an optimal turbulent intensity. Therefore, model-based control strategies become necessary for jet ignition systems and a precise control-oriented jet ignition combustion model is the foundation of model-based control of the jet ignition system. The simulation tools, such as GT-Power and WAVE, are widely used in the automotive industry due to their high fidelity and accuracy [2]. However, they can only be used for offline simulations. For model-based control, a simplified model with sufficient accuracy is required for real-time hardware-in-the-loop (HIL) simulations [2, 3]. In this article, a crank-based one-zone gas exchange model is constructed to simulate the gas exchange process in the precombustion chamber. It is based on the assumption that the air, fuel, and residual gas are uniformly mixed in the pre-combustion chamber before ignition. After ignition, the chamber is divided into two zones: the burned and unburned zones. Correspondingly, the gas flowing through the orifices connecting the two combustion chambers is also divided into burned gas and un- FIGURE. BASIC STRUCTURE OF A JET IGNITION SYSTEM. burned gas. The gas in the pre-combustion chamber is assumed to be an ideal gas. The pressure and temperature within the pre-combustion chamber are calculated based on mass and energy conservation principles and the mass fraction burned (MFB) Wiebe function. The main-combustion chamber is modeled in a similar way. However, the ignition time and burn rate of the mixture in the main-combustion chamber are influenced by the combustion condition in the pre-combustion chamber. The main contribution of this article is the formulation and development of the control-oriented jet ignition system model, the implementation of the developed model into a dspace realtime HIL engine simulation environment for model-based control development and validation. The simulation results are validated using the experimental data from a rapid compression machine (RCM). This paper is organized as follows. The next section briefly describes the jet ignition system and modeling framework and the following section provides the governing equations of gas exchange and combustion processes. The developed model was validated using the experimental data from the RCM, and finally, conclusions are drawn at the last section. SYSTEM DESCRIPTION AND MODELING FRAME- WORK System Working Principle Figure shows the basic cylinder architecture of a jet ignition system modeled in this paper. The jet ignition engine model was developed for a four-cylinder engine with a pre-combustion chamber of 2.3 cm 3 located in each cylinder head. The precombustion chamber has an auxiliary fuel system that injects the air-fuel mixture directly into the pre-combustion chamber. The two combustion chambers are connected by a few small orifices. The working process of the jet ignition system can be illustrated by Fig. 2. The valve timing of the system is similar to a conventional SI engine. During the intake stroke, a lean fresh charge flows into the main-combustion chamber until the intake valve closes near bottom dead center. Then, the pressure increases in the main-combustion chamber in the compression stroke. At the same time, premixed fresh charge is injected into 2 Copyright 25 by ASME

Pressure (bar) 5 4 3 2 Intake IVC Compression Spark Expansion Pre chamber pressure Main chamber pressure Fuel Injection EVO Exhaust 5 2 9 6 Mass flow rate (g/s) 3 FIGURE 3. MODELING FRAMEWORK. 8 27 TDC 45 54 Crank position (deg) FIGURE 2. JET IGNITION SYSTEM WORKING PROCESS. the pre-combustion chamber, which pushes the residual gas out, increases the pressure in the pre-combustion chamber, and thus reduces back-flow from the main-combustion chamber to make air-fuel ratio (AFR) control possible. When the piston moves close to the top dead center (TDC), the spark plug ignites the relatively rich air-fuel mixture within the pre-combustion chamber. The released heat from chemical reaction quickly increases the pressure and temperature in the pre-combustion chamber. The great pressure gradient and small orifice size produce high intense turbulent jets of the reacting mixture that ignite the lean mixture in the main-combustion chamber. Modeling Framework As shown in Fig. 3, the jet ignition engine model mainly consists of four subsystem models: piston and crank dynamics model, exhaust gas recirculation (EGR) model, manifold model, and combustion model. The combustion model includes two parts: main-combustion chamber model and pre-combustion chamber model. A two-zone combustion model was developed for the main-combustion chamber. The mass fraction burned is calculated based upon the Wiebe function. The coefficients of the Wiebe function are determined by the gas properties in the pre-combustion chamber. For the pre-combustion chamber, a two-zone combustion model is developed. There is gas exchange through the orifices connecting two combustion chambers. Crank-based combustion related variables are updated every crank degree. The other subsystem models provide the combustion model with crank position, manifold pressures, and other variables. The details of these models can be found in [2, 3]. JET IGNITION SYSTEM MODELING Pre-Combustion Chamber Model In compression stroke, an air-fuel charge is injected into the pre-combustion chamber. The pressure of the charge is assumed to be larger than that of the residual gas within the chamber. Then, the injected air-fuel mixture flow rate can be calculated by the one-dimensional compressible flow equation [4]. where κ ψ (x) = P in j ṁ in j = C d A v ψ RTin j ( Ppre P in j ( ) 2 (κ+)/(κ ) ( 2 x < κ + ),P in j > P pre () κ + 2κ x /κ ( ) ( x (κ )/κ 2 x κ κ + ) κ/(κ ) ) κ/(κ ) (2) The coefficient C d can be determined by experiments, A v is the area of the fuel injector orifice, κ is the ratio of specific heats, P in j and T in j are the charge pressure and temperature, respectively, and P pre is the residual gas pressure in the pre-combustion chamber. The gas exchange between the two combustion chambers is modeled similarly. However, the gas pressure in the precombustion chamber can be either larger or smaller than that in the main-combustion chamber. The pre-combustion chamber is considered as a control volume with mass and energy exchange. In this paper, heat transfer through the walls is not considered during the intake and compression stroke. The following equations can be used for solving the gas pressure and temperature in the pre-combustion chamber during these two strokes. dm pre = ṁ in j ṁ tur (3) du pre = Ḣ in j Ḣ tur where m pre and U pre are the mass and internal energy of the gas in the pre-combustion chamber, respectively, and H is the enthalpy flow. Assuming that the gas can be considered as an ideal gas, the two equations can be coupled by the ideal gas law. 3 Copyright 25 by ASME

make the equations concise, the variables in the following equations in this subsection are for the pre-combustion chamber, if not specified. FIGURE 4. TWO-ZONE COMBUSTION MODEL d(m b T b ) c v dq ch + P dv b + x b dq ht + m u x b dx b c pt u ṁ tur b c p T b (7) The energy balance equation of the unburned zone is represented by = P V = m R T (4) Substituting Eqn. (4) into Eqn. (3), the following two equations are obtained to calculate the gas pressure and temperature. d(m u T u ) c v + ( x b ) dq ht = m (8) u dx b x b c pt u ṁ tur u c p T u + P dv u The masses of the burned zone and unburned zone are obtained based on the mass conservation law. dp pre dt pre = c pr V c v [ṁ in j T in j ṁ tur T tur ] = T prer P pre V c v [c p ṁ in j T in j c p ṁ tur T tur c v (ṁ in j ṁ tur )T pre ] (5) dm b dm u = ṁ tur b + m u dx b x b = ṁ tur u m u dx b x b (9) where c p and c v are the specific heat at constant pressure and that at constant volume, V is the pre-combustion chamber volume, and T tur = { Tpre ṁ tur > T main ṁ tur where T pre and T main are the temperatures in the pre-combustion and main-combustion chamber, respectively. To improve the model accuracy, the pre-combustion chamber is divided into two zones after ignition. Both the burned and unburned zones can be regarded as control volumes. Besides the mass, enthalpy, and work exchange between these two control volumes, there are also mass and enthalpy exchange through the orifices to the main-combustion chamber, shown in Fig. 4. Moreover, the mass flow can be positive, where the gas flows from precombustion to main-combustion chamber, or negative, where the gas flows backwards. In the case of positive mass flow, the gas flow is divided into burned gas and unburned gas. The energy balance equation of the burned zone is shown in Eqn. (7). To (6) The subscripts b and u represent burned zone and unburned zone. Q ht is the heat transfer to the chamber wall. Q ch is the chemical energy released by the combustion. x b is the mass fraction burned. ṁ tur b and ṁ tur u represent the mass flow rates from burned and unburned zones to the main-combustion chamber. They are calculated by P pre ṁ tur b = α b C d2 A v2 ψ RTb ( Pmain ) P pre ( P pre Pmain P pre ṁ tur u = ( α b )C d2 A v2 ψ RTu ) () The coefficient α b is chosen according to x b, shown in Fig. 5. At the start of combustion, because the burned zone is far from the orifices to the main-combustion chamber, α b is much smaller than x b. As the mass fraction of the unburned zone decreases during combustion, α b gets close to or even greater than x b. However, α b is bounded by. The precise value of α b is experimentally determined. The case of negative mass flow, where the gas flows from main-combustion to pre-combustion chamber, is also considered. 4 Copyright 25 by ASME

α b.8.6.4 Ppre>Pmain.8.6.4 Ppre<Pmain where A pre is the pre-combustion chamber surface area, T w is the mean wall temperature, and h c is the heat-transfer coefficient calibrated by the experiment. The mass fraction burned is obtained from the Wiebe function [6]..2.5 Pre chamber x b FIGURE 5..2.5 Main chamber x b THE VALUE OF α b USED IN THE SIMULATION. Before ignition in the main-combustion chamber, all the gas from the main-combustion chamber enters the unburned zone in the pre-combustion chamber. After ignition of the main-combustion chamber, the orifices to the pre-combustion chamber will soon be surrounded by the burned gas in the main-combustion chamber. As a result, most of the gas entering the pre-combustion chamber is assumed to be the burned gas and enters the burned zone in the pre-combustion chamber. Applying the principle of mass conservation, the instant mass of fuel in the pre-combustion chamber can be obtained by dm pre f uel = m ( ) pre f uel dx b ṁ tur u () x b λ(a/f) s + where λ is the relative AFR, and (A/F) s is the stoichiometric AFR. Only the fuel from the unburned zone is considered. From Eqn. () and Eqn. (), the following conclusion can be made. The total amount of fuel burned inside the precombustion chamber is highly influenced by α b. If α b is small, the total amount of fuel flowing out of the pre-combustion chamber is large, and correspondingly, the total chemical energy released inside the pre-combustion chamber is small and more released chemical energy is trapped inside the pre-combustion chamber. The rate of chemical energy release can be obtained by the following equation. dq ch m pre f uel dx b = η pre Q LHV x b (2) where the combustion efficiency η pre is experimentally determined, and Q LHV is the lower heating value of the fuel. The heat transfer to the chamber wall can be modeled by the following relationship [5]. dq ht = A pre h c (T pre T w ) (3) [ ( ) ] θ m+ θign x b = exp a θ d (4) The coefficient a and m are chosen to be 6.98 and 2 respectively, θ ign is the start of ignition, and θ d is the burn duration in crank angles, which is calibrated by spark timing and AFR before ignition. Main-Combustion Chamber Model After the ignition in the pre-combustion chamber, the combustion in the main-combustion chamber will not be initiated until the generation of the turbulent jet from the pre-combustion chamber. During this period, the mass flow from the burned zone in the pre-combustion chamber to the main-combustion chamber is neglected. The unburned gas from the pre-combustion chamber is assumed to be well mixed with the mixture in the maincombustion chamber. As a result, an additional amount of fuel is added into the main-combustion chamber. dm main f uel ( ) = ṁ tur u λ pre (A/F) s + (5) where m main f uel is the fuel mass in the main-combustion chamber. After ignition in the main-combustion chamber, the burned zone is created. Different from the two-zone combustion model in a conventional SI engine, the combustion model of the maincombustion chamber needs to consider the gas flowing through the orifices into the pre-combustion chamber. The burned gas and unburned gas from pre-combustion (main-combustion) chamber are assumed to enter the burned zone and unburned zone in the main-combustion (pre-combustion) chamber, respectively. The mass and energy conservation equations for burned and unburned zones are very similar to those of the pre-combustion chamber model presented in the above subsection and is omitted in this paper. The major difference is that the total volume of the maincombustion chamber is varying. The mass fraction burned in the main-combustion chamber is also calculated by the Wiebe function. In a jet ignition system, the combustion in the maincombustion chamber is initiated by the turbulent jets generated 5 Copyright 25 by ASME

TABLE. ENGINE SPECIFICATIONS. Parameter Value bore/stroke 86 mm / 86 mm connecting-rod length 43.6 mm compression ratio 9.8: pre-combustion chamber volume 2.3 cm3 pre-combustion chamber orifice diameter.25 mm FIGURE 6. HIL SIMULATION PLATFORM. from the pre-combustion chamber. The burn rate is highly dependent on the characteristics of the turbulent jets, which are mainly determined by AFR and total mass of the air-fuel mixture in the pre-combustion chamber right before ignition. As a result, the ignition timing θ ign and burn duration θ d in the Wiebe function of the main-combustion chamber are chosen as functions of spark timing, AFR, and the mass of air-fuel mixture in the pre-combustion chamber before ignition. These functions are realized by lookup tables and experimentally calibrated. The details of the gas exchange model for the maincombustion chamber can be found in [3]. SIMULATION RESULTS AND EXPERIMENTAL VALIDA- TION The simulation of the jet ignition system model was performed using the HIL simulation environment shown in Fig. 6. The dspace based real-time engine simulator interacts with a host computer, which is used for displaying the simulation results and setting the simulation parameters [3]. A breakout box connects to the dspace simulator and an oscilloscope is used for displaying the simulation results. The jet ignition engine modeled in this paper is for a 2.-L four-cylinder engine equipped with turbulent jet igniters for each cylinder. The detailed engine parameters are given in Tab.. Since the experimental metal engine has not been set up yet, the RCM jet ignition experimental data were used to validate the developed model. Fig. 7 shows the basic structure of the RCM at Michigan State University [7]. At the beginning of the experiment, the two combustion chambers were filled with air-fuel mixture with a known AFR. The piston in the RCM rapidly compressed the mixture in the main-combustion chamber. At the same time, fuel was injected into the pre-combustion chamber. At the end of compression, the piston kept still; and, thus, the volume in the main-combustion chamber remained constant. After about 3 ms, the spark is initiated through the spark plug inside the pre-combustion chamber and then the reacting products from the pre-combustion cham- Pressure (bar) 5 4 3 2 FIGURE 7. Main chamber Pre chamber RAPID COMPRESSION MACHINE. 5 5 5 Time (ms) FIGURE 8. MEASURED PRESSURES IN THE RCM. ber ignited the mixture in the main-combustion chamber. The pressures in the combustion chambers were measured by Kistler pressure sensors. Figure 8 shows the measured pressure traces in the RCM with the main-combustion chamber λ =.75. These data cannot be used directly for the model validation since the RCM combustion occurs with a constant volume. To make the experimental data and the simulation results comparable, the following method was used. Assuming the piston is moving the same way as in a real engine, there would be an additional pressure drop in the maincombustion chamber due to the chamber volume increasing. The pressure after considering the pressure drop can be calculated 6 Copyright 25 by ASME

TABLE 2. RCM SPECIFICATIONS. Parameter Value bore/stroke 5.8 mm / 2.2 mm compression ratio 8.5: pre-combustion chamber volume 2.3 cm3 pre-combustion chamber orifice diameter.25 mm according to the adiabatic process equation. Pressure (bar) 5 4 3 2 Main experiment Main two zone Pre experiment Pre two zone Pre one zone 28 3 32 34 36 38 4 42 Crank position (deg) FIGURE 9. COMPARISON OF SIMULATION AND CONVERTED EXPERIMENTAL RESULTS. ( ) γ Vmain r P main c = P main r (6) V main c where P main c is the converted pressure after considering the volume change, P main r and V main r are the pressure and volume of the RCM main-combustion chamber, respectively, V main c is the chamber volume of the engine, and γ is the specific heat ratio, which is considered to be a constant value. Note that only the pressure trace after the RCM piston reached the end of its stroke length is converted. The pressure in the pre-combustion chamber is mainly influenced by combustion and the gas flow through the orifices between the two combustion chambers. As a result, the pressure trace in the pre-combustion chamber is converted by considering the difference between the mass flow rates through these orifices before and after conversion, as shown in Eqn. (7), where it is assumed that the temperatures of the gas flows before and after conversion are the same. dp pre c = dp pre r + c prt tur V pre c v (ṁ tur r ṁ tur c ) (7) where the subscripts c and r denote the converted and original properties, respectively. T tur is calculated by the calibrated RCM model which will be discussed later. Table 2 provides the RCM parameters. The engine model parameters were chosen accordingly to make the simulation results comparable to the RCM experimental data. The engine speed was chosen as follows. Considering the simulation and experimental results of jet-ignition systems in [8, 9], the main-combustion chamber burn duration of our jet ignition system was estimated to be around 2 crank degrees with λ =.75. From the RCM experimental data shown in Fig. 8, the burn duration is about 3.6 ms. Therefore, the corresponding engine speed is about 9 rpm. In this paper, the combustion process in the pre-combustion chamber is simulated by a two-zone combustion model. To analyze the benefit of using the two-zone combustion model over the one-zone one, another jet ignition system model with one-zone combustion model for the pre-combustion chamber was also developed. In the one-zone model, the gas in the pre-combustion chamber is assumed to be homogeneous all the time. So, the gas flowing to the main-combustion chamber is also homogeneous. However, since main-combustion chamber model is unchanged the gas flowing from the main-combustion chamber is still divided into burned and unburned gas. In Fig. 9, the simulation results of the developed jet ignition system models are compared with the RCM data when the pre-combustion chamber relative AFR is. and the maincombustion chamber relative AFR is.75. The model simulation results and converted RCM experimental data show a fairly good match. Moreover, the two-zone model is more accurate than the one-zone model because the two-zone model is able to capture detailed characteristics of the gas exchange process between the two combustion chambers. Converting the RCM experimental pressure traces inevitably causes additional errors. As a result, we used another method to further validate the jet ignition system model. Since the major difference between the jet ignition engine and the RCM is the piston movement, an RCM model can be developed by only changing the piston movement feature of the jet ignition system model. Once the RCM model is validated by the experimental data, the corresponding jet ignition system model is also indirectly validated. The simulation results of the developed RCM model were compared with the experimental data from the RCM in Fig.. The simulation results match the experimental data fairly well, so the jet ignition system model is further validated. The relatively large simulation error occurs at the beginning of the combustion in the main-combustion chamber. One possible 7 Copyright 25 by ASME

Pressure (bar) 5 4 3 2 Main experiment Main two zone Pre experiment Pre two zone Pre one zone 5 5 5 Time (ms) FIGURE. COMPARISON OF SIMULATION AND EXPERI- MENTAL RESULTS. reason is that utilizing Eqn. () could cause large error when the pressure difference between the pre-combustion and maincombustion chambers is small, which was discussed in [4]. And again, the two-zone model is more accurate than the one-zone model. CONCLUSION A control-oriented jet ignition system model is presented in this paper, and the model was implemented into a dspace based HIL (hardware-in-the-loop) engine simulation environment. The simulation results were compared with the RCM (rapid compression machine) experimental data and show a fairly good match, indicating the developed control-oriented model is able to accurately capture the jet ignition system dynamics. This shows that the developed model has the potential to be used for modelbased control. The future work is to further validate and calibrate the developed model using actual engine data and to developed model-based combustion control strategies. REFERENCES [] Toulson, E., Schock, H. J., and Attard, W. P., 2. A review of pre-chamber initiated jet ignition combustion systems. In SAE Technical Paper, SAE International. [2] Zhang, S., Zhu, G., and Sun, Z., 24. A Control- Oriented Charge Mixing and Two-Zone HCCI Combustion Model. Vehicular Technology, IEEE Transactions on, 63(3), March, pp. 79 9. [3] Yang, X., and Zhu, G., 23. SI and HCCI Combustion Mode Transition Control of an HCCI Capable SI Engine. Control Systems Technology, IEEE Transactions on, 2(5), Sept, pp. 558 569. [4] Stanglmaier, R. H., and Roberts, C. E., 999. Homogeneous Charge Compression Ignition (HCCI): Benefits, Compromises, and Future Engine Applications. Tech. rep., SAE Technical Paper. [5] Turkish, M. C., 974. 3-Valve Stratified Charge Engines: Evolvement, Analysis and Progression. Tech. rep., SAE Technical Paper. [6] Noguchi, M., Sanda, S., and Nakamura, N., 976. Development of Toyota Lean Burn Engine. Tech. rep., SAE Technical Paper. [7] Adams, T. G., 979. Torch Ignition for Combustion Control of Lean Mixtures. Tech. rep., SAE Technical Paper. [8] Brandstetter, W., 98. The Volkswagen Lean Burn PC- Engine Concept. Tech. rep., SAE Technical Paper. [9] Date, T., Yagi, S., Ishizuya, A., and Fujii, I., 974. Research and Development of the Honda CVCC engine. Tech. rep., SAE Technical Paper. [] Toulson, E., Huisjen, A., Chen, X., Squibb, C., Zhu, G., Schock, H., and Attard, W. P., 22. Visualization of Propane and Natural Gas Spark Ignition and Turbulent Jet Ignition Combustion. Tech. rep., SAE Technical Paper. [] Attard, W. P., and Blaxill, H., 22. A lean burn gasoline fueled pre-chamber jet ignition combustion system achieving high efficiency and low nox at part load. In SAE Technical Paper, SAE International. [2] Vítek, O., Macek, J., and Polášek, M., 23. Simulation of pre-chambers in an engine combustion chamber using available software. Tech. rep., SAE Technical Paper. [3] Yang, X., and Zhu, G. G., 22. A control-oriented hybrid combustion model of a homogeneous charge compression ignition capable spark ignition engine. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 226(), pp. 38 395. [4] Guzzella, L., and Onder, C., 29. Introduction to modeling and control of internal combustion engine systems. Springer Science & Business Media. [5] Heywood, J. B., 988. Internal combustion engine fundamentals, Vol. 93. Mcgraw-hill New York. [6] Ghojel, J., 2. Review of the development and applications of the wiebe function: a tribute to the contribution of ivan wiebe to engine research. International Journal of Engine Research, (4), pp. 297 32. [7] Allen, C., Valco, D., Toulson, E., Edwards, T., and Lee, T., 23. Ignition behavior and surrogate modeling of jp-8 and of camelina and tallow hydrotreated renewable jet fuels at low temperatures. Combustion and Flame, 6(2), pp. 232 239. [8] Bunce, M., Blaxill, H., Kulatilaka, W., and Jiang, N., 24. The effects of turbulent jet characteristics on engine performance using a pre-chamber combustor. In SAE Technical Paper, SAE International. [9] Toulson, E., Watson, H. C., and Attard, W. P., 29. Modeling alternative prechamber fuels in jet assisted ignition of gasoline and lpg. Tech. rep., SAE Technical Paper. 8 Copyright 25 by ASME