*5.2. Simulation Setup*

Concerning the 1D model setup, at low loads, the experimental IMEP is reproduced by a Proportional-Integral-Derivative (PID) controller acting on the throttle (THR) valve opening, while the WG valve is fully opened. At high loads, the measured IMEP is obtained by another PID controller adjusting the WG valve opening and considering the fully opened throttle valve. In each operating condition, the injected fuel mass is monitored to reproduce the different experimental λ level for each cylinder. The experimental EGR rate is replicated by regulating the EGR valve opening with an additional PID controller. The spark advance is automatically modified in the cycle-by-cycle calculation to realize the measured combustion phasing (MFB 50%). The above-discussed model setup is taken into account in the numerical analysis, and the related outcomes are presented in the next section.

## **6. Numerical Analysis**

The accuracy of the developed 1D engine model is proved for the entire set of measurements (Table 2). In a first stage, the model capability is tested in replicating the main performance variables such as the in-cylinder pressure peak and combustion core duration for both cylinders, the Indicated Specific Fuel Consumption (ISFC) and the Temperature at Turbine Inlet (TIT). A detailed analysis is also presented with the aim to demonstrate the model proficiency in reproducing the main gaseous emissions (NO, CO and HC). Particular care was paid to the numerical/experimental assessment of the single cylinder performance and emissions in order to reproduce the effect of cylinder-by-cylinder variation. In a second phase, the validated model is applied to evaluate the improvements in terms of ISFC and pollutant emissions resulting from the suppression of the cylinder-by-cylinder A/F ratio imbalance.

## *6.1. Model Validation*

Referring to the performance parameters, the following figures, Figures 8–10, report the numerical/experimental comparisons for the overall set of measured operating points, including the variations in load level, speed, EGR rate and cylinder-related air/fuel ratio. The figures also present the average absolute or percent error between the numerical and the experimental outcomes.

The results plotted in Figure 8a,b show that the model is capable to capture with similar accuracy the experimental pressure peak of both cylinders, denoting very limited absolute percent errors of numerical predictions. These assessments also highlight the good reliability of the combustion modeling for the individual cylinders.

**Figure 8.** Numerical/experimental comparisons of in-cylinder pressure peak for Cyl #1 (**a**) and Cyl #2 (**b**) at various operating conditions.

**Figure 9.** Numerical/experimental comparisons of combustion core duration MFB 10–50% for Cyl #1 (**a**) and Cyl #2 (**b**) at various operating conditions.

**Figure 10.** Numerical/experimental comparisons of ISFC (**a**) and TIT (**b**) at various operating conditions.

To further prove the model capability in reproducing the combustion process evolution, the numerical/experimental assessment of the combustion core duration (MFB 10–50%) is reported in Figure 9. Combustion duration of both engine cylinders is adequately described by the model, as demonstrated by the reduced average difference between predicted and experimental data (1.17 CAD and 0.93 CAD for Cyl #1 and Cyl #2, respectively). The above outcomes demonstrate the model ability to sense the effect of cylinder-by-cylinder differences in thermodynamic state (pressure and temperature), mixture quality and composition (A/F ratio and EGR content).

As a relevant global engine performance, Figure 10a presents the numerical/experimental assessment for the ISFC. A satisfactory correlation with the measurements is found for the overall data set with an average percent error of 4.3%. Greater ISFC differences are detected for points at speed of 1800 rpm, mainly due to the model overestimation of the air flow rate. ISFC errors are lower at speed of 3000 rpm. However, most of the computed points are included in the considered allowable error band ±5%, thus demonstrating an acceptable model capability for the ISFC prediction.

Good numerical/experimental agreements for TIT (Figure 10b) are reached, thanks to the refined thermal modeling, which also includes the FE approach for cylinders and exhaust pipes. Indeed, the computed TIT shows a good correlation with the experimental data (mean absolute temperature error of 37.3 K). Although not visible in Figure 10b, the model correctly reproduces the trend of TIT reduction at increasing the EGR rate and lowering the IMEP.

Even if not reported here for brevity, the in-cylinder pressure traces and the other global performance variables are reproduced with accuracy similar to a previous authors' work [15].

As for pollutants, Figures 11–13 show the comparison between numerical and experimental levels of regulated gaseous emissions: NO, CO and HC, respectively. Consistently with the presentation of the experimental results, the variations of considered pollutant emissions are reported as a function of the EGR rate.

**Figure 11.** Numerical/experimental comparisons of nitrogen oxide (NO) for engine (**a**) and Cyl #1 (**b**) at various operating conditions.

**Figure 12.** Numerical/experimental comparisons of percent carbon monoxide (CO%) for both engine and Cyl #1 at various operating conditions.

**Figure 13.** Numerical/experimental comparisons of engine unburned HC at various operating conditions.

Figure 11a,b show the NO emissions at the engine exhaust (Figure 11a) and at the exit of exhaust valve of Cyl #1 (Figure 11b), at different points and EGR rates. At each investigated operating condition, engine NO emission decreases at increasing the EGR rate with a reduction between ~45% and ~55% at 1800 rpm and between ~60% and ~90% at 3000 rpm when the maximum charge dilution is adopted. Looking at Figure 11b, the Cyl #1 NO emission strongly increases compared to the overall level at the engine exhaust. This behavior can be explained considering the relevant difference in the A/F ratio of two cylinders: running the engine at stoichiometric conditions the relative A/F ratio in Cyl #1 ranges between ~1.03 and ~1.08 and the higher oxygen content speeds up the NO formation reactions. The comparison between experimental and numerical data demonstrates that the employed NO modeling approach is capable to adequately reproduce the EGR-induced trend of the NO emission reduction for both the single cylinder (Cyl #1—lean A/F ratio) and the engine exhaust (stoichiometric A/F ratio). Indeed, the NO sub-model correctly senses the formation mechanism, which is primarily affected by the in-cylinder temperature and by the presence of some species (CO2, H2O, N2 and O2) in the fresh air/fuel mixture [29].

The model demonstrates to well capture the level of the engine NO emissions (Figure 11a) even if a limited model underestimation (average error around 15%) is observed in most of the analyzed conditions. Conversely, greater errors in the prediction of NO emissions coming out of Cyl #1 are obtained (Figure 11b). In this case, the model average error in predicting the measured Cyl #1 NO emission is of about 30%. Indeed, higher differences between the computed NO emissions of Cyl #1 and of Engine are obtained by the model, when compared to the same experimental differences. This consideration highlights the prediction limitations of NO sub-model in the range of lean A/F mixtures, as in the case of Cyl #1. The numerical inaccuracies reported in Figure 11b may be probably attributed to the high sensitivity of NO sub-model to the relative air/fuel ratio variations.

CO emissions are plotted in Figure 12, where a good prediction of the experimental values for both the engine and the Cyl #1 is obtained. Engine CO is reproduced by the model with an average error of about 30% over the tested operating conditions.

Very low CO emissions are measured for Cyl #1, because of lean mixture operations. The model systematically underestimates the CO levels for Cyl #1 at varying the EGR. This could be attributed to a model limitation which does not include the CO generated by the partial oxidation of unburned HC at the cylinder walls under lean conditions.

However, the experimental/numerical correlation of CO levels for Cyl #1 is taken as satisfactory, also considering the experimental errors in recording small emission levels. The outcomes in Figure 12 sugges<sup>t</sup> that the numerical CO emissions of Cyl #2 are also reliable even if they cannot be compared to any measured data.

Figure 13 proposes the numerical/experimental assessment for the sole engine unburned HC emission. Unfortunately, the single cylinder HC data cannot be proposed here, because the Cyl #1 exhaust probe is located very close the exhaust valves, and, as clearly discussed in Reference [30], a relevant instantaneous peak of unburned HC emission is realized at the event of exhaust valve opening. This phenomenon involves some difficulties to furnish a reliable measure of the HC level for Cyl #1 with the available gas-emission analyzer.

According to Figure 13, the HC sub-model demonstrates to be able to reproduce the experimental trend of the engine unburned HC emissions at varying the EGR rate. In particular, the model provides an average error of 18% in the prediction of engine unburned HC species. Concerning the set of EGR-sweep operating points, only for the highest investigated IMEP (3000@13) a slight HC reduction is observed at increasing the EGR. As known, the engine load and A/F ratio are found to be the main parameters influencing the quenching phenomenon, through the quenching distance variations [27]. Since the quenching distance is proportional at first order to the laminar flame thickness, at increasing the IMEP the wall-flame quenching furnishes a gradually reduced in-cylinder HC production. It is very likely that, at 3000@13, the quenching exerts a limited impact on the HC emission. Therefore, at 3000@13, the EGR-related HC reduction has to be ascribed to the spark timing advance (Table 2). In addition, at 3000@13, the rise in boost pressure at increasing the EGR content, required to restore the engine IMEP, is more prominent than the other load conditions. This also means that higher temperature levels are expected to

occur during the expansion phase, thus improving the HC post-oxidation and contributing to reduce its overall level.

For all the other points, higher HC emissions are obtained as the EGR rises, and the model well captures this trend, mainly thanks to the contribution of the wall flame quenching.

In light of the above-discussed results, the proposed modeling approach shows the capability to satisfactorily take into account the influence of both engine operation and cylinder-by-cylinder variations on the main pollutant emissions, without the need of a case-dependent tuning.

#### *6.2. Model Application: Suppression of A/F Ratio Imbalance between Cylinders*

Once validated, the model is utilized to evaluate the engine behavior in the case of the virtual suppression of the cylinder-by-cylinder variation. To this aim, the experimental A/F ratio imbalance between cylinders for the examined engine is removed and a stoichiometric A/F ratio is imposed in each cylinder, while preserving the measured combustion phasing as input data. As a consequence, variations in the performance and emissions of the engine are expected to occur and can be easily estimated. It is the case to underline that authors focused on showing the single effect related to the suppression of A/F ratio imbalance between cylinders. Of course, a more refined engine calibration also requires a control of combustion phasing to reach the optimal levels at both low and medium/high loads. The main numerical outcomes of the above-discussed investigation are plotted in the Figures 14 and 15. In each figure, the 1D results obtained by imposing the measured A/F ratio for individual cylinder (labeled as "Unbalanced A/F ratio") are compared with the 1D outcomes resulting from the imposition of a stoichiometric A/F ratio as input data for two cylinders (labeled as "Balanced Stoichiometric A/F ratio").

Figure 14 shows the ISFC comparisons in the analyzed engine operating points. Interestingly, this figure highlights that not negligible ISFC improvements are realized and the lower ISFC levels resulting from the balanced A/F ratio (blue bars in Figure 14) mostly follow the EGR related trend. A maximum ISFC percent benefit equal to 5% (ΔISFC = 12.4 g/kWh at 3000@7, EGR% = 9%) is attained, while the average percent gain is around 2%.

**Figure 14.** ISFC comparisons: Unbalanced A/F ratio vs. Balanced Stoichiometric A/F ratio at varying the engine operating condition.

**Figure 15.** Comparisons of NO (**a**), CO (**b**) and HC (**c**): Unbalanced A/F ratio vs. Balanced Stoichiometric A/F ratio at varying the engine operating condition.

Referring to the main pollutants, the results plotted Figure 15a–c demonstrate that the cylinder-by-cylinder variation exerts a certain influence on both NO, CO and unburned HC emissions. CO improvements are substantially independent from the EGR variation (Figure 15b). The engine CO emission is strongly affected by the cylinder variability with a percent average reduction of about 50%. A peak of CO reduction (about 97%) is observed at 1800@10 and EGR% = 14.4% corresponding to an absolute ΔCO% of 0.36% (Figure 15b). Conversely, NO and unburned HC emissions exhibit reduced benefits (Figure 15a,c, respectively) and the optimized NO and HC species continue to follow the expected trend with EGR. The percent advantage for the HC emission reaches a peak of 8% (ΔHC = 171 ppm at 3000@13, EGR% = 10%) while the average benefit in HC emission is of 2.5%. Similar and only slightly greater benefits are observed for the NO emission: mean percent gain around 5% and peak advantage of 21% (ΔNO = 730 ppm at 1800@8 with EGR% = 0%). It is the worth to underline that the obtained advantages cannot be considered as a general case, but they should be taken as a prediction related to the analyzed engine and the measured points. Hence, the results illustrated in Figure 15 are solely related to the analyzed engine configuration and they lose their meaning in the case of mature commercial SI unit. As a final remark, a refined engine calibration which includes a control on both A/F ratio and combustion phasing can lead to further performance advantages, especially in terms of fuel consumption.
