# Engine Optimization Model for Accurate Prediction of Friction Model in Marine Dual-Fuel Engine
###### Abstract  
This paper presents an innovative engine optimization model integrated with a friction fitting tool to enhance the accuracy of computed performance for a marine dual-fuel engine. The focus is on determining the terms of the Chen-Flynn correlation--an empirical engine friction model--to improve the precision of friction and performance predictions. The developed model employs WAVE, a 1D engine simulation software, coupled with a nonlinear optimizer to identify the optimal configuration of key parameters, including the turbocharger, injection system, combustion behavior, and friction model. The optimization procedure maximizes the air-fuel ratio (AFR) within the engine while adhering to various predefined constraints. The model is applied to four operational points along the propeller curve, with the optimized results subsequently integrated into a friction fitting tool. This tool predicts the terms of the Chen-Flynn correlation through an updated procedure, achieving highly accurate results with a coefficient of determination (R\({}^{2}\)) value of 99.88%, eliminating the need for experimental testing. The optimized friction model provides a reliable foundation for future studies and applications, enabling precise friction predictions across various engine types and fuel compositions. F 2025 12 June 20253  
To compute the friction losses in a marine diesel engine, the resistance from the moving components inside the engine must be accounted for. Frictional forces in a marine diesel engine arise from different parts, such as the piston assembly (piston rings and cylinder liner), crankshaft and bearings, valve train (camshafts and rocker arms), and auxiliary components (pumps and turbochargers). In a typical fired engine (diesel or spark-ignition), mechanical friction accounts for approximately 4% to 15% of the total fuel energy [8]. This estimate reflects the average engine performance across a range of operating conditions. However, under extreme conditions, such as idling or very light loads, nearly all the fuel energy may be consumed to overcome friction, resulting in little to no net power output. The thermal efficiency of modern engines generally ranges between 38% and 50%, with 45-50% being a common target in engine development. Mechanical friction typically consumes 10% to 30% of the engine's power output, but under idling conditions, it can approach 100%, highlighting the importance of minimizing friction to improve overall efficiency and performance. The friction power calculation method is a straightforward approach in which the friction mean effective pressure (FMEP) is determined by subtracting the indicated mean effective pressure (IMEP) and the brake mean effective pressure (BMEP) from each other, as in Equation (1). \[\text{FMEP}=\text{IMEP}-\text{BMEP} \tag{1}\]  
An alternative approach to estimating friction is through the measurement of mechanical efficiency (\(\eta_{\text{m}}\)), as in Equation (2). This equation highlights the direct relationship between friction losses, fuel consumption, and power output; minimizing friction not only decreases fuel consumption but also enhances engine performance by maximizing usable power. \[\text{h}_{\text{m}}\,=\,\frac{\text{IMEP}-\text{FMEP}}{\text{IMEP}} \tag{2}\]  
Thus, the FMEP is calculated using Equation (3). \[\text{FMEP}\,=\text{IMEP}(1-\text{h}_{\text{m}}) \tag{3}\]  
Over the years, various technologies have been implemented and refined in diesel engines to enhance performance and reduce friction [9]. For example, the installation of one or more turbochargers has optimized the air-fuel ratio (AFR), indirectly lowering friction by allowing engine downsizing [10; 11]. Variable Geometry Turbines (VGTs) have also been introduced to improve the efficiency of turbocharged engines, reducing mechanical stress and internal friction [12]. Optimizing the fuel injection system is critical to maintaining smooth combustion and minimizing unnecessary mechanical loads [13; 14; 15].