## 6 Numerical Analysis
### Model Validation
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 (CO\({}_{2}\), H\({}_{2}\)O, N\({}_{2}\) and O\({}_{2}\)) 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 suggest 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.