1. Introduction
Marine DF engines use cleaner fuels, such as natural gas, as the primary fuel, which effectively solves the emission problem and reduces pollution to the atmosphere and the marine environment [
1,
2]. However, they have the same energy waste and environmental heat pollution problems as traditional diesel engines. The thermal efficiency of modern large marine diesel propulsion devices is generally only 45–50%, and the unused heat accounts for nearly half of the heat generated by fuel combustion, which is discharged into the atmosphere in various forms [
3]. At present, studies on DF engines mainly focus on combustion characteristics, emission characteristics, turbocharged technology, electronic regulation, and control of fuel and gas, etc., but few studies have been conducted on the utilization of the flue gas waste heat of DF engines [
4]. An exhaust gas turbocharger is the most common energy recovery and utilization device. The turbine converts the kinetic energy of exhaust gas to drive the turbocharger and improve the engine intake gas. Similarly, power turbines are converted into electricity by connecting them directly to a generator [
5,
6].
In addition to the abovementioned flue gas energy recovered from turbines, waste heat refrigeration, Rankine cycle, temperature difference power generation, seawater desalination, and other technologies also exist. Waste heat refrigeration is a kind of absorption refrigeration that is compensated by the consumption of heat energy, mainly low heat energy. The exhaust gas and the energy of cooling water on the marine engine can be recovered and utilized by absorption refrigeration [
7]. Fernandez-Seara et al. used exhaust gas to power ammonia absorption refrigeration units. Using heat conduction oil as the intermediate heat transfer medium can effectively reduce ships’ brake-specific fuel consumption (BSFC) by 2–4% [
8]. When the Rankine cycle is used for waste heat recovery of large marine engines, water is generally selected as the working medium for comprehensive consideration of safety, tightness, and economy. Organic working medium can also replace water as the intermediate medium for heat exchange, namely the organic Rankine cycle (ORC), as a means of waste heat utilization [
9]. Simone Lion et al. used Ricardo Wave, an engine modeling software, to establish a two-stroke engine model and calculated and analyzed that the addition of ORC devices could save ships’ fuel costs by about 5% per year [
10]. Ahmed G redesigned the heat exchanger by replacing cooling water with R34a and R245fa. The results showed that the heat waste of the system would be reduced by 18% [
11]. Based on the 4-stroke DF engine V18 MAN 51/60DF, Douvartzides compared and analyzed 37 kinds of ORC working medium, and selected the best working medium and ORC conditions to improve the efficiency of the whole system by 5.52% and reduce the BSFC by 12.69% [
12]. Teng et al. built an experiment platform for water and waste heat recovery from flue gas. The experimental results showed that the water and waste heat recovery characteristics are enhanced with the gas flow increases. Increasing the flue gas temperature can increase the water recovery and heat recovery power [
13]. Ouyang et al. studied the waste heat boiler utilization system of a MAN 6S50ME-C8.2 marine low-speed two-stroke diesel engine. The results showed that the waste heat utilization capacity increases gradually with the increase in the ambient temperature and main engine load, and the maximum power is 1288.7 kW [
14].
The optimization of DF engines with waste heat recovery systems is more complex and is a multi-parameter multi-objective problem. Heuristic algorithms, such as genetic algorithms, are widely used in engineering and have achieved good results. In the field of engines, Li et al. directly controlled the parameters of compression ignition engines and a direct DF stratification combustion mode, multi-objective optimization, and detailed comparison were conducted [
15]. However, the direct use of multi-objective optimization requires computationally significant computational resources, which limits its application in more complex systems, such as combining genetic algorithms with computational fluid dynamics (CFD-GA). The optimization process can be accelerated by using the surrogate model approach, and has achieved excellent results in practical applications, especially in the optimization of experimental parameters. Statistical methods are very effective in the application of constructing surrogate models and are very effective in the engineering field [
16,
17,
18]. Ji et al. employed the genetic algorithm to optimize the engine performance based on support vector machine intelligent regression. The engine showed a higher performance and lower emission with a hydrogen volume fraction of 5.06%, excess air ratio of 1.09%, and ignition timing of 34.37 °CA before the top dead center [
19]. Li et al. employed an online optimization approach for a methanol-diesel DF engine by combining an artificial neural network with genetic algorithms (ANN-GA). It showed that ANN-GA can save over 75% in computational time compared to CFD-GA [
20]. Tian et al. used the multi-objective genetic algorithm (MOGA) to optimize the performance and ORC thermal economy of DF engines on liquefied nature gas ships The results showed that R1150-R1234yf-R600a and R170-R1270-R152a are the two most promising combinations [
21]. Guan et al. developed a general simulation-optimization platform on the performance and emissions of an engine, and based on NSGA-II to optimize the BSFC and NOx emission of an engine. The result shows that BSFC and NOx is reduced by 16.37% and 75.18% [
22]. Hu conducted a comparative study of the engine design parameters using the NLPQL algorithm and the MOGA. The results show that the MOGA provides more feasible pareto optimality [
23]. Stoumpos used GT-Power simulation software to establish a marine four-stroke DF engine model with multiple Wiebe functions in order to study the transient response of the engine when the mode switches and load changes and optimized it with MOGA [
24]. Response surface method (RSM) is relatively simple and reliable, and has a good alternative effect, so it is applied more often in marine engines. Kamarulzaman et al. used RSM to optimize the performance and emission parameters of a compression ignition engine [
25]. Hatami et al. applied RSM based on a central composite design to obtain an optimization design of finned-type heat exchangers to recover waste heat from the exhaust of a diesel engine. The results showed that fin numbers have a maximum effect to enhance the heat recovery [
26].
In conclusion, it is necessary to optimize the waste heat recovery system to improve fuel economy. However, most of the research on the waste heat recovery of large marine engines has focused on large low-speed two-stroke diesel engines while studies on DF engines are relatively few. As the exhaust temperature generated by DF engines in gas mode is higher than that of large low-speed 2-stroke diesel engines, the exhaust temperature of large 2-stroke diesel engines after the turbocharger is basically around 220 °C under full load conditions [
27]. Compared with the 2-stroke engine, the bench report of the 4-stroke DF engine shows that the exhaust temperature of the turbocharger under a 100% load in gas mode can reach 32 °C. Therefore, the unit flue gas contains more energy [
28]. Therefore, in this paper, a waste heat recovery system for a four-stroke DF engine is constructed and optimized by combining RSM with GA.
Consequently, GT-Power and Simulink were employed to simulate the DF engine and waste heat boiler, respectively. They comprise the waste heat recovery system. A regression model based on RSM, with the intake temperature, compression ratio, and pilot fuel injection timing as input parameters, was built to conduct a multi-objective optimization of the BSFC, engine power, and exhaust gas waste heat generation of the waste heat recovery system with MOGA. This paper provides theoretical guidance for the practical application of waste heat recovery systems.
2. Modeling Methodology
This section focuses mainly on the implementation of the modeling.
Section 2.1 discusses the modeling of the DF marine engine.
Section 2.2 discusses the modeling of the waste heat boiler.
Figure 1 shows the whole DF engine flue gas waste heat recovery system flow chart.
The exhaust gas waste heat recovery system consists of a DF engine, a waste heat boiler, and a steam turbine. The exhaust gas from the DF engine flows through the waste heat boiler and heats the water in the waste heat boiler, which absorbs the waste heat and vaporizes into superheated steam, driving the steam turbine to generate electricity, and the steam from the steam turbine enters the hot water well after being cooled by the condenser, and the water in the hot water well is pumped to the waste heat boiler through the feed pump, completing the whole cycle.
2.1. DF Engine Modeling Methodology
The engine studied in this paper belongs to a MAN 51/60DF series 8 cylinder 4-stroke DF engine, with a design power of 1000 kW for a single cylinder. DF refers to diesel and natural gas, mainly divided into gas, oil, oil and gas mixture, and other working modes [
29].
GT-power is suitable for a spark plug ignition internal combustion engine, compression combustion internal combustion engine, and two-stroke/four-stroke internal combustion engine. This paper uses the MAN 8L51/60DF engine as the research object and was based on GT-power for the simulation. The engine’s main technical parameters are shown in
Table 1 [
28]. In this paper, the vibe heat release model is used for combustion heat release [
24], and the calculation formula is as follows:
The heat transfer model is used to calculate heat loss, and the complicated heat transfer process is transformed into a heat transfer coefficient model. According to the instantaneous average heat transfer coefficient of the working medium to the cylinder wall [
30], the heat transfer coefficient of working medium to the cylinder wall is calculated as follows:
The instantaneous heat transfer coefficient adopts the Woschni formula, which is accurate and straightforward to calculate [
31], and the form is as follows:
This engine is a propulsion power device applied to LNG electric propulsion ships. The engine runs at constant speed, which can recover the waste heat of flue gas more stably and effectively than traditional models that directly use a diesel engine as the main propulsion power device of ships.
2.2. Waste Heat Recovery Simulation Methodology
The modular partition modeling of a waste heat boiler was carried out with Simulink, which is divided into a convection zone, metal heat exchange zone, soda, and water zone [
32]. The convection zone is taken as an example to establish a mathematical model, and other modules refer to the convection zone.
In mass conservation, the amount of flue gas flowing into the convection zone is equal to the amount of smoke flowing out. The formula is as follows:
In the conservation of energy, the change in the energy in the convection zone is related to the energy of the flue gas entering the convection zone, the energy carried by the flue gas out of convection zone, and the convective heat transfer from the flue gas to the boiler metal wall in the convection zone. The formula is as follows:
where
is the energy of the flue gas entering convection zone per unit time,
is the energy of the flue gas flowing out of the convection zone per unit time,
is the convective heat exchange between the flue gas and the metal wall of the boiler per unit time, and
is the flue gas energy of convection zone. Steady-state algebraic equations are used to describe the variation in the working conditions of the steam turbine. When the working conditions of the steam turbine change, the steam flow of the steam turbine can be calculated by the Flugel formula [
33]. The formula is as follows:
where
is the steam mass flow rate,
is the steam mass flow rate under design working conditions,
is the inlet steam temperature,
is the inlet steam temperature under design working conditions,
is the inlet steam pressure,
is the outlet steam pressure,
is the inlet steam pressure under design working conditions, and
is the outlet steam pressure under design working conditions.
The outlet enthalpy of a steam turbine is derived from the ideal enthalpy by the following procedure, and then corrected by the efficiency, whose inlet entropy can be determined by the other parameters of the inlet steam. The formula is as follows:
where
is the steam outlet’s enthalpy,
is the steam inlet’s enthalpy,
is the stage efficiency, and
is the ideal steam outlet’s enthalpy.
The output power of the steam turbine is the power generation power of flue gas waste heat [
34]. The formula is as follows:
Simulink allows modeling and simulation of continuous and discrete systems based on the mathematical logic that has been constructed. Simulink is used to simulate the waste heat boiler. The exhaust temperature of the engine determines the steam temperature of the waste heat boiler. The exhaust gas turbocharger outlet temperature of the DF engine studied in this paper is 326 °C under full load gas mode, regarded as the flue gas inlet temperature of the waste heat boiler. The steam temperature is set to 270 °C. Considering the temperature drop effect of the pipeline, the intake temperature of the steam turbine needs to be reduced by 5 °C on this basis. The steam pressure of the waste heat boiler needs to refer to the inlet pressure corresponding to the inlet temperature of the turbine. Under the condition of satisfying the turbine’s relative internal efficiency and exhaust humidity, the steam pressure is selected as 0.7 MPa [
35]. In order to improve the utilization rate of waste heat, it is necessary to reduce the exhaust temperature of the waste heat boiler as much as possible. However, the exhaust temperature of the waste heat boiler affects the equivalent thermal efficiency and is limited by the acid dew point of flue gas and smoke wind resistance. When the temperature is too low, sulfur retention produces sulfur corrosion. After comprehensive consideration, the exhaust temperature of the waste heat boiler is chosen as 170 °C [
36]. The design parameters are shown in
Table 2.
5. Conclusions
This paper optimized the performance of a marine four-stroke DF engine MAN 51/60DF based on MOGA, including the engine BSFC, power, and flue gas waste heat generation.
The 1-D model of the DF engine was established based on the GT-Power simulation modeling tool. The simulation data were checked and verified before the optimization study of the DF engine, and the maximum error was 1.96% in gas mode. Then, the main parameters of the waste heat boiler were designed, the Simulink simulation model was established, and the power generation of flue gas waste heat was calculated according to the mathematical model of the steam turbine.
The effects of the intake temperature, compression ratio, and pilot fuel injection timing on flue gas waste heat generation in the DF engine gas mode were studied. Through the analysis of the simulation data, it can be seen that with the increase in the intake temperature, the BSFC decreased first and then increased, the power decreased gradually, and the power generation decreased gradually. With the decrease in the compression ratio, the BSFC, power, and power generation increased gradually. With the advance of the pilot fuel injection timing, BSFC, power, and power generation were gradually reduced.
MOGA was used to obtain the optimal parameter settings under the condition of maximum power and flue gas waste heat generation and minimum BSFC. First, RSM transformed the data into a nonlinear regression model for the analysis and optimization. The optimal solution set was obtained by optimizing the algorithm, and then the optimal solution was selected artificially. The reduction of BSFC is most important, so the final optimal solution was 306.18 K (intake temperature), 14.4 (compression ratio), and −16.68 °CA ATDC (pilot fuel injection timing). This corresponded to 155.18 g/kWh (BSFC), which was reduced by 3.24%, 8025.62 kW (power), and increased by 0.32%. At the same time, an additional 280.98 kW (flue gas waste heat generation) was obtained.
In conclusion, this study provides a methodology for the modeling and optimization of four-stroke DF engines for ships. The results contribute to a better understanding of the effects of operating parameters on performance and exhaust gas waste heat utilization. RSM was applied to engine performance and exhaust gas waste heat utilization, and combined with the MOGA optimization algorithm, the engine parameter settings were derived under the condition that performance and exhaust gas waste heat generation were satisfied.
In future work, the operating parameters of the DF engine under full load will be optimized by machine learning, including linear regression, support vector machine, and Gaussian process regression. Then, their optimization results will be compared.