## 6 Numerical Analysis
### 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. 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 \(\pm\)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]. Figure 10: Numerical/experimental comparisons of ISFC (**a**) and TIT (**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 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 \(\sim\)45% and \(\sim\)55% at 1800 rpm and between \(\sim\)60% and \(\sim\)90%  
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. 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.