## 6 Numerical Analysis
### 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% (\(\Delta\)ISFC = 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 \(\Delta\)CO% 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% (\(\Delta\)HC = 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% (\(\Delta\)NO = 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.