## 2 Numerical Models
### Model Validation  
The BSFC is a superimposed effect of the indicated efficiency and mechanical losses. For the combined model, the verification of the BSFC between calculation and experiment data is not enough to guarantee simulation accuracy. In addition, to analyze the impact of these indicators on engine performance with CDA operation, both the indicated efficiency and mechanical losses need to be validated separately. The comparisons between the simulated and experimental indicated efficiency for four different engine speeds are depicted in Figure 4. A good agreement between simulation and experimental results is observed with the differences, which are less than 4%. Mechanical losses in engines are estimated by mechanical mean effective pressure (MMEP). The predicted mean mechanical loss pressure is extremely close to the experimental values. Mechanical losses generally increase with increasing engine speed; at the constant speed, the change in mechanical losses is not obvious as the load grows from part load to full load. However, the BMEP is small at light-load conditions or idle, so the change in mean mechanical loss pressure on mechanical efficiency cannot be ignored. Figure 3: The 3D computational mesh of the combustion chamber at TDC. The accuracy of the 3D CFD model was evaluated by comparing the indicated diagram and engine emissions between simulation and experimental data. The initial and boundary conditions of the simulated operating condition obtained from GT-SUITE are shown in Table 2. Based on the experimental cylinder pressure curve, the parameter values of the breakup model and combustion model were successfully set and are shown in Table 3 after numerous corrections. The validation of the indicated diagram for the combustion model at a speed of 300 rpm is shown in Figure 5. The maximum relative errors of cylinder pressure between simulation and experiment do not exceed 5%. The validation of the emission formation models was performed by comparing the brake-specific carbon monoxide (BSCO) and the brake-specific nitrogen oxides (BSNOx) with experimental data at a speed of 450 rpm and under different engine loads. As shown in Table 4, the relative errors for the BSNOx prediction are less than 4%, and the maximum relative error for the BSCO prediction is 5.3% at a load of 4000 N\(\cdot\)m. These comparisons confirm that the 3D CFD model can guarantee high accuracy and be used for following investigations. Figure 4: Comparisons of simulations and experiments at engine speed: (**a**) 450 rpm; (**b**) 556 rpm; (**c**) 742 rpm; (**d**) 1000 rpm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Engine Load**} & \multicolumn{2}{c}{**BSNOx, g/(kW\(\cdot\)h)**} & \multirow{2}{*}{**Relative Error**} & \multicolumn{2}{c}{**BSCO, g/(kW\(\cdot\)h)**} & \multirow{2}{*}{**Relative Error**} \\ \cline{2-2} \cline{5-6}
**N\(\cdot\)m** & **Simulation** & **Experiment** & **(\%)** & **Simulation** & **Experiment** & **(\%)** \\ \hline
4000 & 12.17 & 12.66 & 3.9 & 4.40 & 4.64 & 5.0 \\
5940 & 12.60 & 12.91 & 2.4 & 3.60 & 3.80 & 5.3 \\
8210 & 13.28 & 13.16 & 0.9 & 2.27 & 2.21 & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The comparison of the BSNOx and BSCO emissions between simulation and experiment. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & **Value** \\ \hline Initial air pressure & 1.18 bar \\ Initial air temperature & 322 K \\ Cylinder wall temperature & 345 K \\ Cylinder head temperature & 354 K \\ Piston top temperature & 358 K \\ Start and end of injection & \(-8\)\({}^{\circ}\)CA\(/-7.5\)\({}^{\circ}\)CA \\ The cycle injection mass & 80 mg/cycle \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The initial and boundary conditions of the simulated engine operating condition from GT-SUITE. Figure 5: The comparison of the simulated in-cylinder pressure based on the crank angle when idle with experiment data.