## 4 Compression Ignition Engine Simulations
### Engine Data and Simulation Setup  
The simulation setups were constructed based on experimental data from a heavy-duty (HD) 13.0 L Diesel engine that features a direct injection system capable of injection pressures up to 2000 bar. Although the engine has an in-built external EGR system, the analyzed engine conditions did not include external EGR. A total of 10 operating points from 1000 rpm to 1700 rpm and 6 bar to 22 bar indicated mean effective pressure (IMEP) are used for the present simulation campaign. Details of the operating conditions are outlined in Table 2.  
Figure 5: Error maps for the interpolation error (\(\epsilon_{\text{MSD}}\) as defined in Equation (7)) between online and tabulated chemistry solver under constant pressure reactor conditions (**a**) at 1 bar and (**b**) 35 bar, both at 0% exhaust gas recirculation using \(n\)-heptane as fuel.  
As presented in Figure 6, operating point 10 features a double injection rate profile (pilot + main) while the rest have a single injection event. The crank-angle resolved pressure profiles were measured for one cylinder and used to calibrate the SRM engine model.  
Commercial Diesel fuel was used during experiments, whereas in the simulations a blend of \(n\)-decane and \(\alpha\)-methylnaphthalene (75-25% mass fractions respectively, also noted as IDEA surrogate fuel) was employed as surrogate fuel model. A liquid fuel properties comparison is summarized in Table 3.  
The chemical kinetic scheme employed in this study has been taken from the LOGEfuel database [53]. The mechanism is an improved version of the detailed model from [PERSON] [56]. It features oxidation models for \(n\)-decane, \(\alpha\)-methyl-naphthalene and methyl decanoate as main fuel species as well as a detailed PAH growth mechanism [57] and thermal NOx model. The detailed reaction scheme was reduced to a size of 189 species using the method described in [12].  
The measured pressure history was analyzed using the thermodynamic analysis of LOGEengine [53]. This procedure provided chemical kinetics-based estimations of wall temperature,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case Name** & **Speed (rpm)** & **IMEP (bar)** & **EGR (mass\%)** & **Injection Pulses (\#)** \\ \hline HD01 & 1700 & 19.0 & 4.0 & 1 \\ HD02 & 1300 & 22.0 & 4.0 & 1 \\ HD03 & 1300 & 14.5 & 4.0 & 1 \\ HD04 & 1300 & 6.0 & 4.0 & 1 \\ HD05 & 1200 & 6.0 & 4.0 & 1 \\ HD06 & 1200 & 14.5 & 4.0 & 1 \\ HD07 & 1200 & 22.0 & 4.0 & 1 \\ HD08 & 1000 & 6.0 & 4.0 & 1 \\ HD09 & 1000 & 11.0 & 4.0 & 1 \\ HD10 & 1000 & 22.0 & 4.0 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Heavy-duty engine operating conditions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fuel Name** & **Lower Heating** & **Density at** & **Cetane** & **C (w\%)** & **H (w\%)** & **O (w\%)** \\ \hline EU Diesel & 41.6 & 820.0 & 49 & 86.0 & 13.4 & 0.6 \\ IDEA surrogate fuel & 42.94 & 783.0 & 52.3 & 86.62 & 13.38 & 0.0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Liquid properties of the experimental and surrogate fuel mixture used in the heavy-duty Diesel engine simulation campaign.  
Figure 6: Fuel injection rates as a function of crank angle degree (assuming 0 as firing TDC) for operating conditions (**a**) from 1–5 and (**b**) 6–10, as listed in Table 2.  
in-cylinder temperature at IVC, internal EGR fraction and the apparent rate of heat release (RoHR). In Tables 4 and 5, the main SRM model parameters and the calibrated k-\(\varepsilon\) model constants are presented, respectively [45].  
The SRM model calibration for the presented operating conditions was carried out using the procedure described in [58], and the Curl [50] particle interaction sub-model was used. To ensure consistency during chemistry solver comparisons, the same set of model parameters and constants were applied to both the online and tabulated chemistry solver runs without any re-calibration.