## 2 Methodology
### CFD Model Description and Model Validation
#### 2.2.1 Oxy-Fuel Combustion Model  
The feasibility of the oxy-fuel combustion concept was analyzed in a preliminary work performed by [PERSON] et al. [22]. As previously commented, they implemented a numerical methodology to assess oxy-fuel combustion features and the potential of this concept in optimal conditions. They simulated a conventional CI engine with a 0D-1D in-house simulation software named Virtual Engine Model (VEMOD) [23], in which they also integrated the oxygen membrane (MIEC) model technology. In that preliminary study [17], the composition of the gas that entered the cylinder was formed by O\({}_{2}\), CO\({}_{2}\), and H\({}_{2}\)O, avoiding the presence of N\({}_{2}\). The concentration of each species depends on the operating condition and the EGR rate. It was observed that the optimal operative conditions and the original volumetric compression ratio of the engine (with a CR of 16) operating in oxy-combustion mode, with an EGR rate of 70% and without N\({}_{2}\), had a lower trapped mass than conventional air combustion, which means lower in-cylinder pressure if the temperature of the charge is maintained. For this reason, they performed a sensitivity study, increasing the CR value in order to maximize the engine torque and effective efficiency, varying different parameters in the engine, like intake pressure and temperature, among others (to fulfill the restriction of the exhaust temperature at 1000 \"C and respecting the in-cylinder pressure limit). The outcome was that the CR was changed from 16 to 28, and indirectly the conditions at the IVC changed slightly from the initial case, improving the trapped mass. Moreover, the minimum area of the MIEC required for supplying an appropriate amount of oxygen was calculated, obtaining a value of 10 m\({}^{2}\) for delivering the necessary O\({}_{2}\) amount for the engine. As a consequence, the value of the oxygen-fuel ratio (\(\lambda\)), based on the mass ratio, was maintained as a constant and with a relatively low value of 1.1 (compared to traditional CI values). The reason for this low value is because the oxygen separation onboard is costly, due to the high surface and thermal requirements of the MIEC to operate correctly. The information obtained from this 0D-1D evaluation, in terms of optimum compression ratio, EGR rate and gas composition, is used for defining the boundary conditions for the CFD calculations performed in current work. Specifically, the calibrated case presented in Section 2.2, was updated considering the oxy-fuel operation characteristics and parameters from the 0D-1D simulations. The boundary conditions for the 3D model (so-called \"baseline oxy-combustion\") are presented in Table 5. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **NO\({}_{x}\)** & **YSOot** & **Gross Efficiency** \\  & **[ppm]** & **[-]** & **[\%]** \\ \hline Experimental data & 1253 & \(4.18\times 10^{-6}\) & 44.8 \\ Fine mesh simulation & 1277 & \(3.03\times 10^{-6}\) & 43.4 \\ Coarse mesh simulation & 1459 & \(2.09\times 10^{-6}\) & 43.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between the experimental and CFD simulation values. A comparison of the in-cylinder pressure, RoHR, and the HR between the reference diesel case and the baseline oxy-combustion case is presented in Figure 3. The in-cylinder thermodynamic conditions are different in both cases, due to differences in the gas composition, promoting a higher delay in the start of combustion in the oxy-fuel concept. In terms of in-cylinder pressure (top graph in Figure 3), the reduction in the pressure values when the oxy-fuel combustion concept is used can be explained by the differences between CO\({}_{2}\) and N\({}_{2}\) properties, the different trapped masses and the different volumetric compression ratio. In spite of the higher CR, the oxy-fuel combustion case shows lower peak pressure values in both compression and combustion phases.