## 3 Results and Discussion
### Engine Results  
In Figure 14 the comparison between the in-cylinder pressure, temperature, rate of heat release, and the cumulative heat release are presented. The lower in-cylinder pressure trace in the oxy-fuel cases comes from the differences in the gas properties, due to the absence of nitrogen as already mentioned in Section 2.2.1. Both oxy-fuel combustion cases, baseline cases, and optimized cases have the same CR and the differences in the peak of pressure are due to the differences in the engine settings. For instance, the optimization procedure indicates that for a proper operation in oxy-fuel mode, the start of injection should be delayed, near the top dead center, with a higher injection pressure. The benefit of this strategy is evidenced in the heat-release rate curves, where the start  
Figure 13: Comparison between the baseline and the optimized geometry. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Baseline Case** & \multicolumn{2}{l}{**Oxy-Fuel Combust.**} \\  & **Best Case** \\ \hline Number of injector holes [-] & 10 & 7 \\ Spray angle [deg] & 154 & 164 \\ Swirl number [-] & 2.00 & 1.08 \\ Injection pressure [bar] & 1800 & 2190 \\ SOI [cad aTDC] & \(-\)11.5 & \(-\)4.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Input comparison between the baseline and optimized oxy-fuel combustion cases configuration. of combustion occurs sooner because the ignition delay is shorter because the injection occurs when the gas in the chamber is at a higher temperature and pressure. The wider bowl shape without the re-entrant edge minimizes the wall impingement and avoids the slowdown of the combustion observed in the blue curve around 15 cad. Another factor responsible for this improvement is the higher injection pressure, which atomizes the fuel better and helps to find the oxygen available in the chamber, enhancing the mixture distribution. The cumulative rate of heat-release curves corroborate this behaviour (bottom-right graph in Figure 14). The modifications in the combustion system allow the fuel to burn more efficiently in the engine, with a combustion efficiency more similar to those of conventional air-diesel engines. Moreover, the evolution of the mean temperature along the cycle is analyzed because it is an important parameter for the correct operation of the MIEC. The bottom-left graph in Figure 14 shows that the temperature level in oxy-fuel cases is lower from the IVC and during the compression stroke. However, as soon the combustion starts, the temperature trace in the optimized configuration increases and reaches levels similar to the conventional diesel operation mode, delivering an exhaust gas with temperatures higher than 1500 K, and then this energy can be used for the O\({}_{2}\) separation in the MIEC membrane. This result is consistent with the RoHR curves (see the upper-right plot in Figure 14). This result is representative of the EGR level settled in the boundary conditions for the current study; however this might vary for different EGR rates as was determined by [PERSON] et al. in [PERSON] et al. (2018). The improvement in terms of emissions per cylinder is listed in Table 9. Comparing the combustion system of the optimized oxy-fuel combustion case against the reference diesel case, it is possible to see that the soot emissions are widely reduced, obtaining values near to virtual zero. Regarding the CO emissions, the initial baseline engine operating with an oxy-fuel combustion concept produced an unacceptable level of this pollutant specie, ten times higher than the standard reference diesel. The new chamber hardware combined with adequate engine settings allowed for a decrease in the CO emissions to a lower level than the reference diesel. This result is obtained even with the restricted oxygen quantity in the system (lambda is 1.1, because its production in the membrane is costly).