Spark Timing Optimization through Co-Simulation Analysis in a Spark Ignition Engine

Abstract

The automotive industry is experiencing radical changes under the pressure of institutions that are increasingly reducing the limits on CO₂ and pollutant emissions from road vehicles powered by internal combustion engines (ICEs). A way to decarbonize the transport sector without disrupting current automotive production is the adoption of alternative fuels for internal combustion engines (ICEs). Hydrogen is very attractive, thanks to the zero-carbon content and very high laminar flame speed, allowing for extending the lean burn limit. Other alternative fuels are methanol and ethanol. This work deals with the conversion of a small-sized passenger car powered by a three-cylinder spark ignition (SI) engine for the use of alternative fuels. In particular, the spark timing has been optimized to improve the fuel economy under every operating condition. The optimization procedure is based on the MATLAB/Simulink^® R2024a-GT-Power co-simulation analysis and minimizes the fuel consumption by varying the spark timing independently for each cylinder. In particular, at full load, the algorithm reduces the spark timing only for the cylinder in which knock is detected, reducing fuel consumption by about 2% compared to the base calibration. This approach will be adopted in future activities to understand how the use of alternative fuels affects the ignition control strategy.

1. Introduction

The automotive industry is experiencing a period of radical changes under the pressure of institutions, which are increasingly reducing the limits on CO₂ and pollutant emissions from road vehicles powered by internal combustion engines (ICEs). The current Euro 6 D legislation limits the CO₂ to 95 g/km for light duty vehicles (LDVs), a category including passenger cars and light commercial vehicles [1]. Moreover, the proposed Euro 7 standard, scheduled for 2026, imposes a further limitation for NO_x emissions to 15 mg/km for passenger cars and 23 mg/km for vans [2]. However, this is only an intermediate step. The European Green Deal aims to ban the sale of vehicles powered by ICEs from 2035 to achieve carbon-neutrality by 2050 [3]. This goal can be achieved only through the rapid growth of zero-emission vehicles’ (ZEVs) market share, particularly battery electric vehicles (BEVs).

However, the complete electrification of road vehicles in such a short time is very challenging and involves a lot of unknowns, which are also associated with the energy source from which the electricity for vehicle recharging is produced [4].

A way to decarbonize the transport sector while maintaining the current vehicle fleet is the use of alternative fuels in ICEs. Among these is hydrogen, whose combustion does not produce CO₂, thanks to the zero-carbon content [5,6,7]. Moreover, hydrogen’s very high laminar flame speed and low minimum ignition energy compared to fossil fuels allow for extending the lean burn operation limit without flame propagation issues [6]. Another advantage of hydrogen fueling is the high specific mass energy density of hydrogen, which is due to its high lower heating value (119.7 MJ/kg, against 46 MJ/kg for the CNG and 44.8 MJ/kg for the gasoline) [5]. However, like any other gaseous fuel, hydrogen use in ICEs leads to a reduction in the power density due to the lower volumetric efficiency resulting from the fuel partial pressure in the mixture, which is proportional to the air partial pressure [8]. Furthermore, due to its very low minimum ignition energy, hydrogen can be easily ignited by hot spots, thus resulting in pre-ignition and engine failure [9].

The progress in the use of hydrogen as a pure fuel in SI engines up to 2013 was reviewed by Verhelst in [10]. They found that thanks to the high laminar flame speed, hydrogen is a viable solution in such applications in which ultra-lean combustion is required to achieve very high efficiency and low NO_x emissions. This is particularly useful if the engine is adopted as a range extender in a series of hybrid electric architectures [11,12,13].

Other alternative fuels for SI engines are oxygenated hydrocarbons, like methanol (CH₃OH) and ethanol (C₂H₅OH). These alcohols present similar octane numbers, high heat of vaporization, and low stoichiometric air–fuel ratios [14]. Methanol can be obtained sustainably either from biomass or from the synthesis of carbon and green hydrogen. In the last case, methanol can be considered the simplest liquid “electrofuel” (e-fuel) [14,15]. Ethanol, otherwise, is currently produced from sugar cane and beets, both of which are very rich in sucrose [16].

As stated above, both methanol and ethanol are characterized by a high heat of vaporization, which results in a strong charge cooling effect, especially for methanol. The latter, in turn, leads to improved volumetric efficiency and, thus, better performance, as well as a reduced knock tendency [14,17]. On the other hand, both methanol and ethanol present a low lower heating value compared to gasoline, which reduces the energy content by volume [14]. Therefore, to introduce the same energy content per cycle as gasoline, longer injection durations are needed; thus, larger fuel tanks should be adopted to ensure an acceptable driving range.

The benefits of the methanol fueling of ICEs were reviewed by Verhelst et al. [14]. Moreover, Li et al. [18] employed pure methanol in a heavy-duty direct-injection SI engine, with a compression ratio of 16:1, achieving indicated efficiencies of up to 50%. Iodice et al. [19] investigated the impact of increasing ratios of ethanol (up to 30% vol) in gasoline–ethanol blends on fuel consumption and pollutant emissions in SI engines. They reported a significant reduction in CO and NO_x emissions compared to gasoline, especially for the E20 blend (20% v/v ethanol content).

Given the different laminar flame speeds of the alternative fuels mentioned above compared to gasoline, their use in SI engines requires a dedicated spark timing calibration to enhance performance and reduce fuel consumption. Yoo et al. [20] optimized the spark timing in a 1.6 l gasoline–ethanol flexible fuel engine. They achieved an improvement in the delivered torque of 5.4% and 1.8% for E30 and E50 fuel blends, respectively, by optimizing the spark timing. Gong et al. [21] optimized the injection and spark timings in a high-compression ratio stratified-charge methanol engine, under lean burn operating conditions, obtaining a reduction in ignition delay and combustion duration, as well as lower CO, unburned methanol, and soot emissions.

As shown by the abovementioned considerations, the adoption of alternative fuels in SI engines represents an effective way to decarbonize the transport sector while maintaining the current vehicle fleet.

Within this context, this work deals with the conversion of a small-sized passenger car powered by a three-cylinder SI engine for the use of alternative fuels, focusing on the spark timing optimization for each speed and load. Like in [22,23,24], 1-D engine model simulations have been performed to investigate the operating conditions that are most representative of urban and highway driving. Particular attention has been devoted to the development of the predictive turbulent combustion sub-model, containing a correlation for the knock prediction. The 1-D engine model has been coupled with an offline optimization algorithm based on the integration of a commercial solver for engine simulation into the MATLAB/Simulink^® environment [25,26]. This algorithm minimizes the fuel consumption by varying the spark timing independently for each cylinder, also taking into account the risk of knock onset. The optimization procedure adopted proved to be effective between 2000 and 4000 rpm, which are operating conditions often encountered during urban driving, for which the vehicle under study is designed. In particular, at full load, the algorithm delays the spark timing only for the cylinder in which knock is detected, thus improving the fuel economy compared to the baseline engine calibration. The methodology introduced here will be adopted in future activities to understand how the use of alternative fuels, like hydrogen, methanol, or ethanol, in the same engine affects the control strategy regarding the choice of the optimal spark timing and considering the different octane numbers of these fuels.

2. Materials and Methods

2.1. Experimental Setup

For this activity, a small passenger car powered by a three-cylinder SI engine delivering a rated power of 40 kW has been considered [23,24]. The main engine specifications are listed in

Table 1. Engine technical data [23].

Description
Displacement [cm3]	599
Number of cylinders [-]	3 in-line
Rated power [kW]	40 (@ 5250 rpm)
Rated torque [Nm]	80 (@ 2000–4000 rpm)
Bore [mm]	63.5
Stroke [mm]	63
Connecting rod length [mm]	114 mm
Compression ratio [-]	9.5
Number of valves per cylinder [-]	2
Intake valve opening/closure	363/164 °CA bTDC
Exhaust valve opening/closure	157/349 °CA a/bTDC
Injection system	Port fuel injection at 3.5 bar for gasoline and 5 bar for hydrogen
Ignition	Inductive discharge; 2 spark plugs per cylinder

.

During the experimental campaign, the engine has been assembled into a fully instrumented test bench. In particular, the engine has been coupled to an active dynamometer, which is speed-controlled by custom software. The experimental campaign was aimed at measuring the characteristic curves of torque and power.

Regarding the fuel injection system, port fuel injection (PFI) has been adopted for both gasoline and hydrogen, given its easier implementation due to the reduced number of components. In particular, the hydrogen injectors have been placed downstream of the gasoline injectors, close to the intake valves (i.e., at the end of the intake runners). For this activity, the engine under study has been fueled with commercial gasoline.

A schematic representation of the engine under study is shown in Figure 1.

Further details about the engine test bench can be found in [22,23].

2.2. 1-D Engine Model

A 1-D model of the engine described in Section 2.1 has been developed by using the commercial software GT-Power v2024, in which the engine is discretized into many sub-volumes connected by boundaries [27]. In particular, the geometrical features of all the engine components in the model have been measured from a disassembled engine available during the initial stage of model development. Other OEM data have been used to impose the valve lift, as well as to build equivalent turbine and compressor maps [28,29]. Moreover, the blow-by losses have been considered using three orifices connecting each cylinder to the intake system, upstream of the compressor. Their diameter has been set at 0.5 mm. A schematic of the 1-D engine model is shown in Figure 2.

As can be observed, some PID controllers have been implemented in the 1-D engine model to control the injection and ignition, as well as the throttle angle and the boost pressure. In particular, the PID for the injection imposes the injected fuel mass per cycle based on the error between the actual λ value, measured in the exhaust line before the three-way catalyst, and the λ target. On the other hand, the PID for the ignition timing has been fed with a CA50 target of 9 °CA aTDC, which is a good compromise of optimized spark control in various conditions [30]. A condition has been also implemented to limit the risk of knocking combustion events, which reduces the spark timing of 0.2 °CA for the next cycle if knock is predicted by the model [23].

The engine load has been jointly controlled by the PIDs for the boost pressure and the throttle. In particular, for part loads, the PID of the boost pressure is set to achieve a certain boost level for each load and adjusts the wastegate accordingly, while the PID for the throttle is set to achieve a certain power level. On the other hand, for boosted conditions, namely, at full load, a wide-open throttle (WOT) has been imposed.

Regarding the combustion, this process has been simulated through a predictive multi-zone quasi-dimensional model, which simulates the development of the flame kernel and the subsequent propagation of the flame front into a homogeneous charge as a turbulent entrainment process, followed by the combustion [13].

In a quasi-dimensional framework, the combustion chamber is modeled as a volume divided into two zones, namely, the unburned and burned mixture. These two zones are separated by a spherical flame front of infinitesimal thickness centered in the spark plug and truncated by the combustion chamber walls, which propagates throughout the combustion chamber [27,31,32]. More details about the governing equations and the model tuning parameters can be found in [13,33].

As stated above, the model can predict the risk of knock onset. In particular, a knock sub-model has been embedded into the turbulent combustion model based on the methodology described by Douaud and Eyzat [34].

To calibrate the combustion model, four tuning parameters must be identified. The parameter identification has been performed by comparing the simulated maximum power curve at full load with that measured at the engine test bench [13,27].

2.3. Spark Timing Optimization

As stated above, the main purpose of the present work is the development of a methodology for specific fuel consumption minimization by varying the spark timing independently for each of the three cylinders. To achieve this, a co-simulation analysis has been performed, in which the 1-D engine model, which was developed in GT-Power, has been interfaced with the optimization algorithm, which was developed in a MATLAB/Simulink^® environment. This coupling takes place through a dedicated function in Simulink, which gives the inputs to the GT-Power model and launches the simulation. On the other hand, the results of the engine model simulation are exported to MATLAB by a GT-Power component called “Simulink Harness”. This methodology allows us to easily design the control strategy, as the engine model simulation results can be post-processed by the control system model in MATLAB/Simulink^®, whose outputs are given in input to the GT model for the next cycle.

The Simulink function and the Simulink Harness block in GT-Power, enabling the co-simulation analysis, are shown and highlighted in Figure 3.

In this case, for each operating condition investigated, the indicated specific fuel consumption (ISFC) and indicated mean effective pressure (IMEP), as well as the CA50 and the unburned mass fraction at knock onset for each cylinder, obtained from the GT-Power model simulations, are processed by the optimization algorithm in MATLAB. The latter minimizes the ISFC for each simulated cycle and provides the control variables for the engine model, namely, the spark timing for each cylinder. In this case, the algorithm sets the optimal spark timing independently for each cylinder, minimizing fuel consumption. A schematic representation of the co-simulation analysis described above is shown in Figure 4.

Regarding the optimization procedure adopted, the ISFC has been minimized through a search algorithm based on the Nelder–Mead method, otherwise known as the simplex method [35,36,37]. The latter is a heuristic direct search methodology, which finds the minimum or maximum of an objective function without computing its derivatives but by using the concept of a simplex, a polytope of n + 1 vertices in n dimensions, in which the objective function is evaluated.

As stated above, the ISFC evaluated at the engine crank train in the GT-Power model has been assumed as the objective function to be minimized by choosing the optimal values for the spark timing in each cylinder. The optimization procedure can be expressed as follows:

$$F_{obj}=\underset{{\mathit{ST}}_{\mathit{cyl}.i}}{\min }ISFC \left({ST}_{cyl.i}\right)$$

(1)

where ${ST}_{cyl.i}$ is the spark timing for the i-th cylinder.

In the first step, the set of spark timing values that minimizes the specific fuel consumption has been found for different operating conditions. Therefore, no constraints to the objective function have been imposed.

However, to avoid the risk of knocking combustion in one of the three cylinders, the optimal spark timing should be chosen considering the knock probability of each cylinder. To achieve this, in a further step, the unburned mass fraction at the knock onset for each cylinder ${umf}_{knock, cyl.i} (i=1, \dots ,3)$ has been considered to monitor the risk of knocking combustion, as it represents the maximum amount of fuel energy that can be released during a knock [38,39].

The unburned mass fraction at knock onset for each cylinder has been considered to formulate the constraints for the objective function. In particular, such constraints have been imposed on the objective function in the form of a penalty function, as follows:

$$F_{obj}=\underset{{\mathit{ST}}_{\mathit{cyl}.i}}{\min }\left\{ISFC \left({ST}_{cyl.i}\right)+p {\sum }_{i=1}^3{c}_i^2\right\}$$

(2)

where the second term on the right-hand side refers to the penalty function. In particular, $p$ is a penalty factor set to 1000, and $c_i (i=1, \dots ,3)$ are the constraints on the objective function. In this case, the upper threshold for ${umf}_{knock, cyl.i}$ has been set to 10% [39,40]. Therefore, the constraints can be defined as follows:

$$c_i={umf}_{knock, cyl.i}-0.10, i=1, \dots ,3$$

(3)

The penalty functions allow for solving a constrained optimization problem as an unconstrained one.

The procedure described above has been adopted to find the optimal spark timing in all the operating conditions investigated.

3. Results and Discussion

3.1. Engine Model Validation

Firstly, the 1-D engine model has been validated against the experimental data measured at the test bench. Since the in-cylinder pressure data are not available yet at this stage, the engine model has been validated by comparing the simulated engine power and torque curves at full load against those measured at the test bench. The comparison between the experimental and simulated maximum power and torque curves is shown in Figure 5.

As can be observed, the model accuracy in predicting the engine performance at full load is good over the whole range of speeds investigated. This result is also due to the implementation of a PID controller of the boost pressure in the model, which allows for reaching the target power level at every speed and load condition by adjusting the wastegate valve. Moreover, it should be noted that the maximum torque is already achieved at 2000 rpm, and it is maintained for a wide range of speeds, which is particularly suitable for urban driving.

The experimental performance curves have been employed to identify the combustion model tuning parameters, given the lack of experimental in-cylinder pressure and HRR traces. The values of the tuning parameters identified at full load have been retained to perform further simulations at part load.

3.2. Spark Timing Optimization at Full Load

Once the model has been validated against the experimental data, it is coupled with MATLAB/Simulink^® to optimize the spark timing through the co-simulation analysis described in Section 2.3. To achieve this, the PID controllers for injection, ignition, and wastegate included in the original model have been removed, and their outputs at the end of the simulations have been directly imposed in the GT-Power model. In particular, the output of the PID for the ignition has been used as a starting point for the spark timing optimization. Figure 6 shows a comparison between the base and optimized values (both from unconstrained and knock-limited optimization) of spark timing (a), CA50 (b), and ${umf}_{knock}$ (c) for each cylinder and at different engine speeds.

As can be noted, the base spark timing assumes positive values at 2000 rpm. This is due to the knock-limited spark advance (KLSA) condition implemented in the PID for the ignition in the baseline model, which reduces the spark timing if a knock is detected. This speed is characterized by a high knock tendency, as evidenced by the high values of the ${umf}_{knock}$. In particular, cylinders 2 and 3 show a greater knock tendency compared to cylinder 1 due to the higher in-cylinder temperature at the intake valve closing (IVC) for these cylinders (379.4 K and 379.7 K, respectively, compared to 364.4 K for cylinder 1). The knock tendency decreases when the speed is gradually increased, given the higher in-cylinder turbulence, promoting a faster flame propagation, which reduces the risk of knock onset. This allows for adopting more advanced spark timing, which in turn, results in better-phased combustion, as evidenced by lower values of CA50.

The optimized spark timing is more advanced than the base value for all the cylinders, with negligible variations between cylinders, from 2000 to 4000 rpm. This advance of the optimal spark timing with respect to the base value is particularly evident at low to medium speeds, given the higher knock probability occurring in such conditions. As stated above, the KLSA condition in the PID for the ignition limits the spark timing if a knock is detected.

The optimization of the spark timing leads to a reduction in CA50 but an increased knock tendency (higher ${umf}_{knock}$), especially for cylinders 2 and 3, compared to the base calibration.

However, in the case of 5000 rpm, the optimized spark timing is slightly delayed with respect to the base value in cylinders 1 and 2, while it is slightly advanced in cylinder 3.

Regarding the knock-limited optimal spark timing, it is delayed compared to the optimal spark timing without any limitation from 2000 to 4000 rpm, providing higher values of CA50 compared to the latter. In particular, the knock-limited optimization provides positive spark timings at 2000 rpm, like the base calibration. Moreover, in this case, the knock-limited optimization provides more delayed spark timings for cylinders 2 and 3 compared to the base calibration, resulting in slightly higher values of CA50.

It is interesting to note that the algorithm provides more delayed knock-limited spark timings for the cylinders showing a higher knock tendency. This behavior is particularly evident at 2000 and 3000 rpm, for which higher values of ${umf}_{knock}$ are observed. In these cases, the knock-limited optimized spark timing is more advanced in cylinder 1 than in cylinders 2 and 3. This is due to the higher values of ${umf}_{knock}$ in these cylinders with the base calibration, compared to the value in cylinder 1. Moreover, the algorithm returns ${umf}_{knock}$ values around 10%, which has been assumed as the upper threshold for this parameter.

At 5000 rpm, the knock-limited optimal spark timing is almost equal to that without limitation thanks to the higher in-cylinder turbulence, which reduces the risk of knocking combustion. In this case, the base, optimal, and knock-limited optimal spark timings provide ${umf}_{knock}$ values below 10% for all three cylinders.

Figure 7 shows the crank train-based IMEP (a) and ISFC (b) resulting from the base, optimal, and knock-limited optimal spark timings at different speeds.

For each calibration, the IMEP increases with the speed, achieves a maximum at 3000 rpm, and then decreases. On the other hand, the ISFC is significantly reduced when the speed is increased from 2000 to 3000 rpm, achieves a minimum around 4000 rpm, and then slightly increases.

As expected, moving from the base to the optimal spark timing results in improved engine performance (higher IMEP) and reduced fuel consumption (lower ISFC), especially from 2000 to 4000 rpm. This is due to the better combustion phasing, as evidenced by the more advanced CA50 in each cylinder with respect to the base value, resulting from the optimized spark timing (Figure 6b).

On the other hand, the knock-limited optimization of the spark timing improves the performance and fuel consumption with respect to the base calibration only at 3000 and 4000 rpm. At 2000 rpm, the knock-limited optimization provides too delayed spark timings for cylinders 2 and 3 (Figure 6a) due to the high knock tendency (see Figure 6c), which results in delayed combustion (high CA50 values) and, thus, worse performance and efficiency compared to the unconstrained optimization.

At 5000 rpm, the IMEP and ISFC values achieved with both the unconstrained and constrained optimization are like those obtained from the base calibration. This happens because the spark timing values in the three cases are not very different from each other (Figure 6a).

Figure 8 shows the ISFC as a function of the control variables, namely, the spark timing in each cylinder, together with its optimal values, at 3000 and 5200 rpm. Those speeds have been here considered, as the former represents the maximum torque speed, while the latter represents the maximum power speed.

For both speeds considered, the ISFC achieved with the optimal spark timing corresponds to the minimum value. Moreover, the cylinder-to-cylinder variations of the optimal spark timing are more evident in the case of 3000 rpm, confirming what is observed in Figure 6a. Such variations become even more evident when considering the spark timing obtained from the knock-limited optimization. In particular, the knock-limited optimized spark timing is more delayed for cylinders 2 and 3 compared to cylinder 1, given the higher knock tendency of these cylinders observed in Figure 6c.

On the other hand, at 5200 rpm, the cylinder-to-cylinder variations of the optimal spark timing are almost negligible. Moreover, the knock-limited optimal spark timing is roughly equivalent to that resulting from the unconstrained optimization for all three cylinders.

3.3. Effect of Load Reduction

In this work, the effect of load reduction on the spark timing optimization at different speeds has been also investigated. In particular, the same analysis has been performed at 50% and 25% load. Given that the spark timings provided by the optimization procedure at 5000 rpm are almost equal to the base values, speeds between 2000 and 4000 rpm have been considered for part load simulations. Moreover, these speeds represent urban driving conditions well, in which medium to low power levels are requested from the engine. Also, in these cases, the outputs of the PIDs have been directly imposed on the engine model.

Figure 9 shows a comparison between the base and optimized values (both from unconstrained and knock-limited optimization) of spark timing (a) and CA50 (b) for each cylinder and at different engine speeds.

It is worth noting that the comparison of ${umf}_{knock}$ resulting from the base and optimized spark timing at 50% load is missing, contrary to cases at full load (see Figure 6c). The reason for this choice is that ${umf}_{knock}$ is below 5% at 2000 rpm and 0% at higher speeds, for both the base and optimized spark timing. This can be explained through the lower intake pressure in this load condition compared to cases at full load, resulting in lower maximum in-cylinder pressure and thus reducing the end-gas temperature and knock tendency. As expected, the base and optimized values of the spark timing (Figure 9a) are more advanced than those obtained at full load (Figure 6a) in all the speeds investigated. Moreover, the optimization procedure gives more advanced spark timings compared to the base calibration, especially at 3000 and 4000 rpm. Of course, in this case, there is no difference between the results of unconstrained and knock-limited optimization. Furthermore, there are no relevant cylinder-to-cylinder variations of the optimal spark timing for each speed.

Regarding the combustion phasing, an advanced spark timing results in lower CA50 values compared to the cases at full load (Figure 6b). In particular, at 50% load, the spark timing optimization results in a significant reduction in CA50 at 3000 and 4000 rpm compared to the base calibration.

The crank train-based IMEP and ISFC at 50% load resulting from the base, optimal, and knock-limited optimal spark timings are shown in Figure 10.

As expected, at 50% load, the IMEP is about half of the cases at full load (Figure 7a) at any speed. On the other hand, the load reduction results in a significant decrease in ISFC at 2000 rpm with respect to a full load (Figure 7b). This is due to the better combustion phasing achieved by the more advanced spark timing at 50% load, which is allowed by the reduced knock probability. On the other hand, for the other two speeds, the ISFC values are like those observed at full load. Moreover, the optimization of the spark timing results in improved performance and reduced fuel consumption, mainly due to the reduced CA50 (Figure 9a). This behavior becomes more evident as the speed increases, given the possibility of the optimization algorithm advancing the spark timing with respect to the base value, especially at medium to high speed.

Figure 11 shows the base and optimal (both unconstrained and knock-limited) spark timing as a function of engine load for each cylinder and at two different speeds, namely, 2000 and 3000 rpm.

As expected, both the base and optimized spark timings are delayed for increasing load at both speeds, given the higher knock probability in medium to high load conditions. The spark timing delay is very evident at 2000 rpm (Figure 11a), when the load is increased from 50% to 100%, as the latter condition is particularly critical for knock, given the very low turbulence intensity. The spark timing delay for increasing load is reduced at 3000 rpm (Figure 11b), as the higher turbulence intensity promotes a faster flame propagation, thus reducing the knock risk.

The optimization procedure provides more advanced spark timing compared to the base strategy, at 25% and 50% load for both speeds, either in the unconstrained or knock-limited case. At full load, this can be observed only at 3000 rpm (Figure 11b). At 2000 rpm, the knock-limited optimal spark timing at full load is slightly delayed than the base value for cylinders 2 and 3 (see also Figure 6a), given the high knock tendency of this case.

Figure 12 shows the base and optimal (both unconstrained and knock-limited) values of CA50 as a function of engine load for each cylinder and at 2000 and 3000 rpm.

It should be noted that, at 3000 rpm (Figure 12b), the spark timing optimization results in very early combustion phasing (around 5 °CA aTDC) at 25 and 50% load. On the other hand, the CA50 is slightly more delayed than the base value at 2000 rpm and full load (Figure 12a) for cylinders 2 and 3 as a direct consequence of the choice of the spark timing in such cylinders (see Figure 11a). This behavior is not confirmed at 3000 rpm, although the CA50 values achieved by the knock-limited optimization are about 30% lower than those provided by the unconstrained optimization.

Figure 13 shows the crank train-based ISFC as a function of engine load resulting from the base, optimal, and knock-limited optimal spark timings at 2000 and 3000 rpm.

It is worth noting that the 25% load condition features a very poor fuel economy, especially at 2000 rpm, due to the increased throttling losses. However, the spark timing optimization results in a slight reduction in ISFC, which is more evident at 2000 rpm despite the less advanced spark timing.

The increase in engine load from 25% to 50% results in significantly improved fuel economy for both speeds. However, at 50% load, the ISFC reduction achieved by the spark timing optimization is relevant at 3000 rpm (Figure 13b), while it is almost negligible at 2000 rpm (Figure 13a). This can be explained by the better combustion phasing achieved at 3000 rpm by the optimization, rather than at 2000 rpm (see Figure 12).

The ISFC increases again when the load is swept from 50% to 100% at 2000 rpm (Figure 13a), given the very high knock probability characterizing the latter case. As stated above, for the base strategy, the KLSA condition delays the spark timing if a knock is detected. Moreover, the knock-limited spark timing optimization results in only a slight reduction in ISFC (below 1%) compared to the base value. On the other hand, the worsening of fuel consumption is not observed at 3000 rpm (Figure 13b), given the strongly reduced knock tendency. In particular, the optimization at 100% load results in a more evident reduction in ISFC compared to the base value (2% and 1% for the unconstrained and knock-limited case, respectively). This can be ascribed to the improved combustion phasing compared to the base value.

4. Conclusions and Future Developments

This paper deals with the conversion of a small-size passenger car powered by a small three-cylinder SI engine for the use of alternative fuels, like hydrogen or methanol. In particular, a methodology for the spark timing optimization has been developed based on the MATLAB/Simulink^®–GT-Power co-simulation. The methodology allows for setting the optimal spark timing independently for each cylinder, with the goal of minimizing the ISFC while considering the risk of knock onset.

The analysis has been performed at different speeds and load conditions.

At full load, both the base and optimized spark timings are very delayed at 2000 rpm in each cylinder, given the high risk of knocking combustion, mainly due to the high in-cylinder pressure and low turbulence intensity of this condition. This leads to delayed combustion phasing (high CA50) and high fuel consumption. In this case, the unconstrained optimization provides more advanced spark timings, especially for cylinder 1, resulting in a reduction in CA50 (around 20%) and ISFC (around 1%). On the other hand, the knock-limited optimization does not lead to significant reductions in ISFC, given the high knock tendency of this case. However, the algorithm can provide more delayed knock-limited spark timings only for the cylinders with higher knock tendency. In particular, the knock-limited optimized spark timing is more advanced in cylinder 1 than in cylinders 2 and 3, given the higher values of ${umf}_{knock}$ for these cylinders with the base spark timing. The algorithm returns ${umf}_{knock}$ values around 10% for all the cylinders, assumed as an upper threshold for this parameter. The same behavior can be observed at 3000 and 4000 rpm. However, the reduced knock tendency with increasing speed resulting from the improved turbulence intensity allows the algorithm to choose more advanced spark timings, both in unconstrained and knock-limited cases. This results in performance improvement and fuel consumption reduction compared to the base strategy, which is more evident at 3000 rpm (reduction in ISFC around 2% and 1.1% for the unconstrained and knock-limited optimization, respectively). At 5000 rpm, the knock-limited optimal spark timing is almost equal to that without limitation thanks to the reduced risk of knocking combustion. In this case, the base, optimal, and knock-limited optimal spark timings provide ${umf}_{knock}$ values below 10% for all three cylinders. Moreover, the performance and fuel consumption improvement with respect to the base calibration is not significant. For these reasons, the spark timing optimization at part load has been performed considering the cases of 2000 and 3000 rpm.

As expected, the reduction of engine load results in a more advanced base and optimized spark timings for both speeds thanks to the reduced knock tendency resulting from the lower maximum in-cylinder pressure and end-gas temperature. Moreover, the load reduction leads to lower cylinder-to-cylinder variations of the optimal spark timings compared to the full load cases.

The optimization algorithm advances the spark timing compared to the base value, both at 25% and 50% load. This behavior is more evident at 3000 rpm, given the higher turbulence intensity. In this case, the spark timing optimization results in very early combustion phasing (CA50 around 5 °CA aTDC). The increase in load up to 100% results in more delayed spark timing and combustion phasing, confirming what is stated above. Regarding the improvement in the fuel economy resulting from the spark timing optimization, it is particularly relevant at 3000 rpm and 50% load due to the improved combustion phasing compared to the other cases.

This analysis, performed here considering commercial gasoline as fuel, will be useful in future activities, in which the impact on performance and combustion of different low- and zero-carbon fuels, like hydrogen and methanol, will be assessed. In particular, the approach described here can be adopted to find the most suitable spark ignition calibration when the same engine is run on fuels with very different octane numbers than gasoline. In this way, it is possible to maximize engine efficiency while reducing pollutant emissions with any fuel, even under lean burn operating conditions.