# Engine Optimization Model for Accurate Prediction of Friction Model in Marine Dual-Fuel Engine
## 4 Results and Discussions
### Simulation of Marine Diesel Engine
This is achieved by maintaining a high air-to-fuel ratio within the cylinders, which not only enhances combustion efficiency but also significantly reduces NO\({}_{\text{x}}\) emissions, ensuring compliance with IMO Tier II regulations. Additionally, the R\({}^{2}\) for the fuel burn rate reaches an impressive 99.99%, indicating smooth and consistent combustion behavior throughout the process. This ensures optimal performance while meeting stringent emission standards. To validate engine performance, key parameters--P\({}_{\text{B}}\), brake-specific fuel consumption (BSFC), air mass flow, and T\({}_{\text{exh}}\)--are compared with real engine data. The first three parameters demonstrate excellent accuracy, with deviations of just 0.05%. The T\({}_{\text{exh}}\) in the simulated results is slightly higher than the real data, with a deviation of 2.31%. This difference falls within an acceptable range and is likely attributed to the rescaling of existing performance maps to align with the characteristics of the current engine. These results confirm the reliability of the simulation model for engine performance evaluation. After validating the engine model at the rated operating point, the optimized constant parameter values are used to simulate performance across three partial operating points. The same optimization methodology is applied to these reduced-variable cases, ensuring consistency and reliability in the approach. The computed results for all operating points are systematically summarized in Table 3. These results show the adaptive behavior of the turbocharger speed, injection timing, and FMEP under varying engine speeds and loads. The increasing AFR at low load highlights the impact of reduced fuel demand, while consistently high R\({}^{2}\) values confirm combustion stability. The TS decreases as the load is reduced, achieved by lowering the air supply and boosting pressure. The SOI is adjusted between 0\({}^{\circ}\) and \(-\)5\({}^{\circ}\) BTDC to ensure optimal combustion and achieve maximum in-cylinder pressure. At lower loads, the injection duration is shortened to account for the decreased cylinder combustion temperature and pressure, promoting smooth combustion. The AFR remains stable up to 31:1 for load ratios \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & **Parameter** & **Unit** & **Case 1** & **Case 2** & **Case 3** \\ \hline  & Engine & & & & \\  & speed & & & & \\  & Loading & & & & \\  & ratio & & & & \\ \hline  & TS & [rpm] & 120,659 & 67,592 & 35,956 \\ Optimized & SOI & [BTDC] & \(-\)3.69 & \(-\)2.23 & \(-\)1.69 \\ variables & IN\({}_{\text{Dur}}\) & [degree] & 25.68 & 23.99 & 17.31 \\  & FMEP & [bar] & 2.48 & 1.86 & 1.17 \\ \hline  & T\({}_{\text{AfterCylinder}}\) & [K] & 808 & 758 & 494 \\ Constraints & T\({}_{\text{max}}\) & [K] & 1717 & 1706 & 1334 \\ parameters & P\({}_{\text{max}}\) & [bar] & 168.5 & 94.2 & 73.0 \\  & AFR & [-] & 30.19 & 31.03 & 68.89 \\  & R\({}^{2}\) & [-] & 0.9999 & 0.9998 & 0.9999 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimized engine parameters and corresponding combustion constraint values at three partial load points. up to 30%, but it increases significantly at lower loads to enhance combustion efficiency. At 600 rpm, the engine operates at a very low load (4.5%), which results in a significantly reduced fuel injection quantity. However, the air supply remains comparatively high due to the turbocharger configuration and intake system dynamics. This imbalance leads to a high AFR of 68.89. While this value may appear high, such AFRs are typical during idle or low-load conditions in dual-fuel or lean-burn engines, where excess air improves combustion stability and reduces NOx emissions. This behavior has been observed in similar low-load engine studies and is consistent with expected thermodynamic trends under minimal fueling scenarios. The R\({}^{2}\) exceeds 0.9996, indicating smooth combustion with no misfires detected, ensuring reliable engine operation.