## 2 Methods
### Numerical Simulations
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Compression** \\ **Ratio** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Reference** \\ **Point ID** \\ \end{tabular} } & \multirow{2}{*}{**IMEP [bar]**} & \multicolumn{2}{c}{**Intake**} & \multirow{2}{*}{
\begin{tabular}{c} **Temperature** \\ **[\({}^{\circ}\)C]** \\ \end{tabular} } & \multirow{2}{*}{\(\lambda_{\text{global [-]}}\)} & \multicolumn{2}{c}{**ST [\({}^{\circ}\)CA**} & \multicolumn{2}{c}{**Pred**} \\  & & & & **PTDC** & **DOI [ms]** & \multicolumn{2}{c}{**Temperature**} \\  & & & & [\({}^{\circ}\)C] & & [\({}^{\circ}\)C] \\ \hline \multirow{3}{*}{17.5} & R5 & 3.52 & 33.9 & 2.54 & 12 & 1.68 & 122.1 \\ \cline{2-8}  & R6 & 3.49 & 78.5 & 2.75 & 8 & 1.83 & 135.9 \\ \cline{2-8}  & R7 & 3.45 & 100.0 & 2.65 & 6 & 1.10 & 134.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reference points taken from initial measurements of PC-HCCI [22]. Figure 4: The comparison of PC fuel energy and PC air excess ratio profiles between 3D-CFD and 0D PCSI combustion model at \(\lambda=1.6\). Figure 3: The comparison of pressure profiles between experiment, 3D-CFD, and 0D PCSI combustion model at \(\lambda=1.6\). First, the model is validated by comparing the simulated and experimentally obtained pressure profiles in the pre-chamber and the main chamber at the intake temperature of 34 \({}^{\circ}\)C (operating point R5), where it can be safely assumed that the engine operates fully in PCSI combustion mode (Figure 5). It can be seen that a good match between the simulated and experimentally obtained pressure profiles is achieved. Then, the model is applied to simulate the PCSI combustion with the imposed boundary conditions of operating points with increased intake temperatures (R6 and R7), and the comparison of the obtained pressure profiles is shown in Figure 6. Once the experimentally obtained pressure curve starts to deviate from that obtained by simulation, it can be assumed that the HCCI combustion was triggered. Below the pressure curves, the plot of mass fraction burned (MFB) is given and the values of both total MFB and main chamber-only MFB are extracted at the point of clearly visible deviation in the pressure curves. Figure 5: The comparison of pressure profiles between experiment and 0D PCSI combustion model for the operating point R5. Figure 6: The comparison of pressure profiles between experiment and 0D PCSI combustion model for the operating points R6 and R7 and the corresponding MFB profiles obtained by the simulation model. As expected, a larger share of the main chamber charge is consumed by flame propagation prior to the autoignition (AI) at a lower intake temperature. However, it can be seen that even at 100 \({}^{\circ}\)C, a large share of total fuel is combusted in the pre-chamber before the HCCI combustion in the main chamber is triggered. It was already indicated in [22] that the pre-chamber variant used in the initial measurements of PC-HCCI possibly has too large a volume, considering that it was optimized for PCSI combustion at the compression ratio of 12.8 and that this has a negative effect on indicated efficiency, which was approximately 3 percentage points lower than that of HCCI combustion with the compression ratio of 16. That is why, for this study, a smaller pre-chamber was used, whose geometry is listed in Table 2, along with performing a sweep of the duration of fuel injection in the pre-chamber (PC DOI) as a means of reducing the share of energy released in the pre-chamber and thus possibly increasing the overall efficiency.