## 4 Compression Ignition Engine Simulations
### Simulation Results  
In Figure 7, comparisons of experimental and simulated in-cylinder pressure histories, rate of heat release, combustion phasing parameters and normalized emissions are presented for a low-load (HD04), a mid-load (HD06) and a high-load (HD07) operating points. The quantities noted in the following figures as CA05, CA10, CA50 and CA90 represent the crank angle location at which 5, 10, 50 and 90 per cent of the total heat has been released, respectively. Detailed comparisons by means of pressure, RoHR and crank angle resolved emissions for all the operating conditions listed in Table 2 can be found in Appendix A. In Figure 8, comparisons of the CA50, peak cylinder pressure location in CAD (PCPCAD), as well as CO, CO\({}_{2}\), unburned hydrocarbons (uHC) and NO at EVO are shown for all operating points. To comply with data confidentiality restrictions, all the results shown in this simulation campaign are presented in a normalized fashion. With respect to engine out emissions, different normalization strategies have been applied to ensure meaningfulness of the shown comparisons. More in detail, for CO\({}_{2}\) and NO, the simulated ppm values have been normalized with respect to the experimental measurements. For CO and uHC instead, the normalization has been computed based on the difference in ppm between simulated and experimental data with a threshold value set to approximately 100 ppm. In other words, if simulated uHC or CO presents a normalized factor of 2.0, it means that the absolute difference between experimental and simulated values is approximately 200 ppm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of particles (-) & 500 \\ Simulation time-step (CAD) & 0.5 \\ Number of consecutive cycles (-) & 30 \\ Woschni constant C1 & 2.28 \\ Woschni constant C2 & 0.0035 \\ Stochastic heat transfer constant (-) & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SRM main model settings for the heavy-duty Diesel engine simulation campaign. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**C\({}_{\text{squish}}\)** & **C\({}_{\text{injection}}\)** & **C\({}_{\text{swirl}}\)** & **C\({}_{\text{dissipation}}\)** & **C\({}_{\text{tau}}\)** \\ \hline
1.0 & 11.0 & 136.0 & 9.1 & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Calibrated constants for the k-\(\varepsilon\) turbulence model. Figure 7: In-cylinder pressure history and apparent rate of heat release (left), combustion phasing parameters (top right) and normalized engine-out emissions (bottom right) comparisons between experimental data and SRM simulations for operating points (**a**) HD04, (**b**) HD06 and (**c**) HD07. On the other hand, if simulated and experimental HC or CO differ by less than 100 ppm, then the factor is set to 1.0, so to underline an acceptable agreement. Such formulation was considered necessary to cope with the fact that the measured CO and uHC are in absolute terms very low. Hence a standard normalization would have resulted in a set of misleadingly high factors for CO and uHC from the engineering standpoint. For uHC, in particular, the difference between experimental and simulated engine-out ppm values never exceeded 30 ppm across all the operating points, and therefore, the set of comparison factors for uHC in Figure 8 is homogeneously set to 1.0. By means of combustion phasing, the SRM results are in good agreement with experimental data for the majority of the analyzed operating conditions. Visible discrepancies can be observed by means of peak cylinder pressure predictions in HD08 and HD09. However, such result was considered acceptable, considering that on the experimental side, these operating points showed a strong cycle-to-cycle variability, as it can be noticed via the large fluctuations of the heat release rate between 0 and 40 crank angle degrees after TDC (see Figures A8 and A9 in Appendix A).