# Engine Optimization Model for Accurate Prediction of Friction Model in Marine Dual-Fuel Engine
## 4 Results and Discussions  
### Simulation of Marine Diesel Engine  
Based on the developed optimization model, the engine's performance is first computed and optimized at its rated power to identify the optimal combination of adjustable parameters such as the TS, SOI, FMEP, and INJ\({}_{\text{Dur}}\) and a constant parameter such as the BRPM. The constant parameter is subsequently fixed while performing optimization at partial load conditions. This initial step serves as a calibration process, where critical factors such as air intake, fuel supply, exhaust temperature, and defined constraints significantly influence the determination of the optimal values for the adjustable variables. To ensure accuracy and engine stability, each iteration involves simulating 40 cycles. Depending on the number of optimization variables involved, the simulation of each operating point takes approximately 4 to 8 h to reach optimal conditions. The results, including the values of optimized variables, constraint parameters, and validation parameters, are presented in Table 2. These validation parameters quantify the percentage error between the manufacturer's real-world data and the simulation results, ensuring the model's accuracy and reliability. Based on the optimized variables, the TS is adjusted at a higher engine speed to enhance airflow, resulting in a compressor efficiency of 78%, as derived from the performance maps. The SOI is optimized to occur a few degrees before the top dead center (TDC), with an injection duration of approximately 33\({}^{\circ}\), ensuring high combustion pressure and a smooth, consistent fuel burn rate. The FMEP is optimized at 2.54 bar, a value deemed appropriate for this type of diesel engine, balancing efficiency and reliability. The intake and exhaust valve lift ratios are \begin{table}
\begin{tabular}{l l l c c c} \hline \hline  & **Parameter** & **Unit** & \begin{tabular}{c} **Real** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Simulated** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Percentage of** \\ **Error [\%]** \\ \end{tabular} \\ \hline \multirow{4}{*}{\begin{tabular}{l} Optimized \\ variables \\ \end{tabular} } & TS & [rpm] & - & 131,529 & - \\  & SOI & [BTDC] & - & \(-\)1.406 & - \\  & INJ\({}_{\text{Dur}}\) & [degree] & - & 32.98 & - \\  & FMEP & [bar] & - & 2.54 & - \\  & BRPM & [rmp] & - & 2957 & - \\ \hline \multirow{4}{*}{\
\begin{tabular}{l} Constraints \\ parameters \\ \end{tabular} } & T\({}_{\text{AfterCylinder}}\) & [K] & - & 915 & - \\  & T\({}_{\text{max}}\) & [K] & - & 1771 & - \\  & P\({}_{\text{max}}\) & [bar] & - & 168.4 & - \\  & AFR & [-] & - & 26.2 & - \\  & R\({}^{2}\) & [-] & - & 0.9999 & - \\ \hline \multirow{4}{*}{
\begin{tabular}{l} Validation \\ parameters \\ \end{tabular} } & P\({}_{\text{B}}\) & [kW] & 749 & 748.74 & 0.034 \\  & BSFC & [g/kW.h] & 208 & 208 & 0 \\  & \(\hat{\text{m}}_{\text{a}}\) & [kg/h] & 4084 & 4082.56 & 0.035 \\  & T\({}_{\text{exh}}\) & [K] & 711 & 733 & 3.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computed results from the optimization model and percentage of error between real and simulation data at 100% rated power and 100% engine speed. carefully calculated, with the intake valve having a higher lift to maximize fresh air intake and improve the replacement of exhaust gases in the cylinder. Additionally, the BRPM is set near the midpoint of its operational range, a critical factor in determining combustion duration and ensuring stable engine performance. These optimizations collectively contribute to enhanced engine efficiency and operational stability. The constraint parameters adhere to the predefined safety limits, ensuring reliable engine operation. The P\({}_{\text{max}}\) remains below 180 bar, while both the T\({}_{\text{AfterCylinder}}\) and T\({}_{\text{max}}\) are kept below their respective limits.