Parametric Investigation on the Influence of Turbocharger Performance Decay on the Performance and Emission Characteristics of a Marine Large Two-Stroke Dual Fuel Engine

Abstract

Identifying and analyzing the engine performance and emission characteristics under the condition of performance decay is of significant reference value for fault diagnosis, condition-based maintenance, and health status monitoring. However, there is a lack of relevant research on the currently popular marine large two-stroke dual fuel (DF) engines. To fill the research gap, a detailed zero-/one-dimensional (0D/1D) model of a marine two-stroke DF engine employing the low-pressure gas concept is first established in GT-Power (Version 2020) and validated by comparing the simulation and measured results. Then, three typical types of turbocharger performance decays are defined including turbine efficiency decay, turbine nozzle ring area decay, and turbocharger shaft mechanical efficiency decay. Finally, the three types of decays are introduced to the engine simulation model and parametric runs are performed in both diesel and gas modes to identify and analyze their impacts on the performance and emission characteristics of the investigated marine DF engine. The results reveal that turbocharger performance decay has a significant impact on engine performance parameters, such as brake efficiency, engine speed, boost pressure, etc., as well as CO₂ and NOx emissions, and the specified limit value on certain engine operational parameters will be exceeded when turbocharger performance decays to a certain extent. The changing trend of engine performance and emission parameters as turbocharger performance deteriorates are generally consistent in both operating modes but with significant differences in the extent and magnitude, mainly due to the distinct combustion process (Diesel cycle versus Otto cycle). Furthermore, considering the relative decline in brake efficiency, engine speed drop, and relative increase in CO₂ emission, the investigated engine is less sensitive to the turbocharger performance decay in gas mode. The simulation results also imply that employing a variable geometry turbine (VGT) is capable of improving the brake efficiency of the investigated marine DF engine.

1. Introduction

In order to meet the increasingly stringent environmental regulations, engine manufacturers and researchers in recent years have carried out extensive research on the employment of alternative energy in marine engines. Typical alternative energy sources include hydrogen, methanol, biofuel, ammonia, and natural gas [1,2,3,4,5]. Among them, natural gas has been proven to be a promising energy source as it can effectively mitigate both greenhouse and non-greenhouse gaseous emissions [6,7]. The sulfur content in natural gas is almost zero, thus resulting in extremely low levels of sulfur oxides (SOx). Due to its lower carbon-to-hydrogen ratio, the carbon dioxide (CO₂) emissions from burning natural gas can be reduced by 20% to 25% compared to heavy fuel oil (HFO) or marine gas/diesel oil (MGO/MDO). Furthermore, the nitrogen oxides (NOx) emissions can be reduced by up to approximately 80% for engines employing the low-pressure gas concept. Given these advantages, marine engine manufacturers have developed various types of DF engines that can burn either conventional diesel fuel in diesel mode or natural gas in gas mode.

Currently, in the international market, marine two-stroke DF engines can be classified into two categories based on the gas admission pressure level, namely engines employing the high-pressure gas concept (e.g., MAN ME-GI series) and engines employing the low-pressure gas concept (e.g., MAN ME-GA series and WinGD X-DF series) [8,9,10]. In both diesel and gas modes, the combustion process of DF engines employing a high-pressure gas concept follows the Diesel cycle. This enables the use of a higher compression ratio; therefore, a high thermal efficiency can be achieved. However, it only meets the Tier II NOx limit and requires additional after-treatment devices to comply with the Tier III NOx limit. For DF engines employing the low-pressure gas concept, the combustion process also follows the Diesel cycle in diesel mode, while in gas mode, the combustion process follows the Otto cycle, complying with the Tier III NOx limit without requiring any after-treatment device. However, there are also notable drawbacks, such as low thermal efficiency in the diesel mode, knocking, and methane slip in gas mode.

In recent years, in order to improve the power, economy, and emission performance of marine DF engines, researchers have carried out extensive experimental and simulation research covering various aspects including fuel injection strategies [11,12,13], performance analysis and optimization [14,15,16,17], knock control [11,18,19,20], combustion modeling methodologies [21,22,23,24], etc. Compared to traditional marine diesel engines, marine DF engines have higher requirements for safety, reliability, and stability due to the use of gas fuel. Therefore, conducting research on the performance and emission characteristics of marine DF engines under fault conditions is necessary, which is of significant reference value for fault diagnosis, condition-based maintenance, and health status monitoring. However, by reviewing the literature databases, including Web of Science, Engineering Village, and Scopus, it can be found that relevant studies regarding the performance and emission characteristics of marine DF engines under fault conditions are scarce. Only several relevant studies can be found for traditional marine diesel engines. These studies simulated several typical faults experienced in marine diesel engines and analyzed their impact on engine operational characteristics. Hountalas [25] built a simulation model to predict the performance of a marine large two-stroke diesel engine under fault conditions. The faults examined included compression fault, injector fault, injection timing error, air cooler efficiency fault, air cooler excessive pressure drop, turbine fault, compressor fault, turbine inlet nozzle effective area change, exhaust port fault, and exhaust pipe fault. Rubio et al. [26] developed a marine diesel engine failure simulator based on the thermodynamic model, which was capable of reproducing the effect of several typical thermodynamic failures on both measured and non-measured engine performance parameters. Livanos et al. [27] developed an engine simulation model to investigate the effect of fire in the scavenging space on the operation of the engine and turbocharger. Benvenuto and Campora [28] built a simulation model for a marine four-stroke turbocharged diesel engine, which was capable of predicting engine performance under fault conditions. Particularly, the influence of different engine governor settings on engine performance was analyzed and compared. Matulić et al. [29] developed a marine two-stroke diesel engine model by using AVL’s real-time software platform Cruise M (Version 2015) for failure simulation. Typical faults, including exhaust valve opening and closing timing and injection timing malfunction, were simulated and analyzed. In [30], turbocharger fouling for a marine two-stroke diesel engine was simulated using a Wärtsilä-Transas 5000 engine room simulator. Based on the simulation results, engine performance under fault conditions was presented and analyzed.

The above studies are helpful for engineers and researchers to understand the impact of faults on the performance and emission characteristics of marine engines. However, it should be noted that these studies are only focused on traditional marine diesel engines. Compared to traditional marine diesel engines, marine DF engines, when operating in gas mode, especially those employing the low-pressure gas concept, exhibit significant differences in the combustion process, emission characteristics, and turbocharger matching. As a result, when the performance of a certain engine component deteriorates, the impact trend and magnitude on traditional diesel engines and DF engines are also likely to be different. For both traditional marine diesel engines and DF engines, the turbocharger has a significant impact on the engine’s steady-state performance and transient response. It is also of great importance for increasing engine power density, reducing fuel consumption, and mitigating emissions. However, the working environment of the turbocharger is quite harsh, especially the turbine, which operates in a high-temperature environment for extended periods. Furthermore, particulate matter and soot produced by fuel burning accumulate on the turbine nozzle ring and blades, leading to efficiency deterioration and a change in the turbine nozzle ring area. Considering the complex interaction between the turbocharger and the engine, the turbocharger performance decay will inevitably affect the engine performance and emission characteristics. Based on the above discussion, it is necessary to carry out research to identify and analyze the effect of turbocharger performance decay on the performance and emission characteristics of marine DF engines. However, no relevant studies have been found by the extensive literature survey. To fill the research gap, a simulation model of a marine two-stroke DF engine employing the low-pressure gas concept is first established in GT-Power and validated by comparing the simulation and measured results. Then, three common types of turbocharger performance decays are defined including turbine efficiency decay, turbine nozzle ring area decay, and turbocharger shaft mechanical efficiency decay. Finally, the three types of decays are introduced to the engine simulation model to analyze their impacts on the performance and emission characteristics of the investigated marine two-stroke DF engine.

The novelty of this study stems from the following point. The research gas is filled in this study and the effect of turbocharger performance decay on performance and emission characteristics of a marine two-stroke DF engine in both operating modes is identified and analyzed. Furthermore, this study provides insights into the mechanisms causing the different sensitivity of engine performance and emission characteristics to turbocharger performance decay in the two operating modes. The findings of this study have significant reference value for the design and improvement in fault diagnosis algorithms oriented toward marine two-stroke DF engines. In addition, the established engine simulation model can also serve as a tool for generating fault data, thereby meeting the purpose of training or verifying fault diagnosis algorithms.

2. Engine Modeling

2.1. Investigated Engine

In this study, a marine large low-speed two-stroke DF engine is selected for the investigation. This engine is designed for merchant ships, such as liquefied natural gas (LNG) carriers, Suezmax tankers, Panamax and Sub-Panamax containers, and Capesize bulkers, and has been widely used in recent years due to stable combustion, inherently low NO_x emissions, high overall system efficiency, and safe gas operation. The engine’s main specification is presented in

Table 1. Engine main specification.

Parameter	Unit	Value
Engine model	-	W6X72DF
Number of cylinders	-	6
Cylinder bore	mm	720
Stroke	mm	3086
Speed at MCR 1	RPM	69.1
Power at MCR	kW	13265
BSFC 2 at MCR-diesel mode	g/kW·h	190.5
BSEC 3 at MCR-gas mode	kJ/kW·h	6685.6
Firing order	-	1-6-2-4-3-5
Scavenging type	-	Uniflow scavenging
Number of turbochargers	-	1
Number of auxiliary blowers	-	2
Number of exhaust valve each cylinder	-	1

¹ MCR: Maximum Continuous Rating. ² BSFC: Brake Specific Fuel Consumption. ³ BSEC: Brake Specific Energy Consumption.

.

The investigated DF engine is capable of operating in two distinct modes, namely diesel and gas mode. In diesel mode, the engine can burn either HFO or MGO/MDO, which is directly injected into the cylinder around the top dead center (TDC) by the main fuel injectors. The fuel is ignited by the compressed hot gas and the combustion proceeds as a Diesel cycle. In diesel mode, the engine is only compliant with the Tier II limit. In gas mode, during the period from scavenging port close (SPC) to exhaust valve close (EVC), natural gas at a pressure below 16 bar is injected into the cylinder through the gas admission valve (GAV) located at the lower part of the cylinder liner. It then mixes with the fresh air inside the cylinder and a lean premixed mixture is formed. Approximately at a 9° crank angle before TDC, the lean mixture is ignited by the flame jet, which is initiated by the pilot fuel in the pre-chamber. When operating in gas mode, the combustion proceeds as an Otto cycle, which achieves an extremely low level of NOx emissions, fully meeting the Tier III limit without requiring additional after-treatment devices.

2.2. Model Description

In this study, the engine simulation model is built by using the 0D/1D simulation software GT-Power, which is widely used in both industrial and academic fields due to its excellent simulation capabilities, satisfying simulation accuracy as well as fast computational speed [14,16,17,19,24,31]. Typical applications of this software include engine cycle simulation, thermal management as well as acoustic analysis, etc. In GT-Power, 1D gas dynamics is employed to represent the flow in pipes, while the 0D approach is used to simulate the working process within engine cylinders. To set up the engine simulation model, appropriate components are selected from the component library and connected by using pipe/flowsplit components according to the engine layout. The developed engine simulation model in GT-Power is illustrated in Figure 1, which includes blocks for the cylinder, turbocharger (compressor, turbine, and turbocharger shaft), crank train, propeller, air cooler, auxiliary blower, scavenging receiver, scavenge port, exhaust valve, exhaust receiver, injectors (main fuel, pilot fuel, natural gas), and pre-chamber. The modeling approach of these blocks is described in the following section.

It should be noted that marine engines are always equipped with a proportional-integral-derivative (PID) governor, which is capable of stabilizing the engine’s actual speed at the setting speed by adjusting the cycle fueling quantity. It is implied that even if turbocharger performance deteriorates, the engine’s actual speed will gradually restore to the setting speed under the control of the governor and so will the other engine operational parameters. Therefore, to identify the effect of turbocharger performance decay on engine speed and other performance parameters without the influence of the governor, the cycle fueling quantity is chosen as the model input instead of the engine speed. In each operating condition, the cycle fueling quantity is set according to the actual value measured in the shop trial. Actually, in many marine engine remote control systems, such as the AC600 developed by Norway’s Kongsberg, a constant fuel mode is provided [32]. In this mode, the engine cycle fueling quantity is fixed and not affected by the governor.

2.2.1. Cylinder Model

The cylinder model consists of several sub-models mainly including combustion, NO_x emission, heat transfer, friction, and scavenging sub-models. Among all the sub-models, the combustion model has a significant impact on the overall prediction accuracy of the engine simulation model. GT-Power totally provides three types of combustion modeling methods, namely non-predictive, semi-predictive, and predictive combustion models [33]. The non-predictive combustion model simply imposes a burn rate as a function of crank angle regardless of the in-cylinder conditions. The most prominent advantage of a non-predictive combustion model is fast computational speed. However, the non-predictive combustion model is not appropriate for studying an engine operating/setting parameter (ignition timing, residual fraction, injection pressure, etc.) that has a direct and significant influence on the burn rate. As for the predictive combustion model, it is capable of adapting to the changes in engine operating/setting parameters, which, in theory, is the ideal choice for all types of simulations. Nevertheless, two practical factors constrain the employment of predictive combustion models. First, a sufficient amount of measured data is required for model calibration to ensure prediction accuracy. Second, the model’s computational speed is generally slower than the non-predictive combustion model. By defining the relationship between model parameters and engine operating/setting parameters, the semi-predictive combustion model provides a good compromise between the non-predictive and predictive combustion models. The investigated DF engine in this study exhibits completely distinct combustion characteristics in the two operating modes. Therefore, different combustion models should be used for the diesel and gas modes.

In the diesel mode, the combustion proceeds as a Diesel cycle and the predictive combustion model named DIPusle, proposed by Gamma Technologies, is used to predict the burn rate [33]. The DIPulse model is a phenomenological multi-zone combustion model, which discretizes the cylinder volume into three thermodynamic zones, i.e., main unburned zone, spray unburned zone, and spray burned zone, each with its own temperature and composition. The main unburned zone consists of all cylinder-trapped mass at EVC, the spray unburned zone consists of injected fuel and entrained gas, and the spray burned zone consists of burnt combustion products. The basic idea of the DIPulse is to track the fuel as it is injected and as it evaporates, mixes with surrounding gas, and burns. In total, four model parameters in DIPulse need to be calibrated, i.e., the entrainment rate multiplier, ignition delay multiplier, premixed combustion rate multiplier, and diffusion combustion rate multiplier.

In gas mode, the combustion proceeds as an Otto cycle similar to conventional SI gasoline engines. However, for the DF engine investigated in this study, the lean premixed mixture is ignited by the flame jet emanated by the pilot fuel in the pre-chamber rather than the spark. Furthermore, the combustion process is also different from the SI engines as discussed in [24]. Therefore, the predictive combustion model named SITurb, which is designed specifically for SI engines in GT-Power, is not appropriate for the investigated DF engine. In the 2020 version of GT-Power, a phenomenological multi-zone predictive combustion model named JetIgnition is provided. The JetIgnition model is capable of predicting the burn rate in the main cylinder chamber for engines where combustion is initiated in the pre-chamber and the resulting flame jet ignites the premixed air–fuel mixture in the main chamber. The JetIgnition model discretizes the cylinder volume into three thermodynamic zones, i.e., the main unburned zone, jet zone, and burned zone. The airflow from scavenging ports and the natural gas injected via GAV are added to the main unburned zone. Once combustion starts in the pre-chamber, the jet zone is formed in the main chamber consisting of the flame jet flow from the pre-chamber nozzle. As the jet penetrates inside the main chamber, it expands and slows down by entraining mass from the surrounding gas. When ignition begins in the jet zone, the burned zone is introduced in the main chamber. Both mass and energy are transferred from the main unburned and jet zone to the burned zone. Meanwhile, at the tip of the flame jet, a spherical-like flame is initiated, which entrains mass from both the main unburned and jet zone and propagates it into the main chamber like a conventional turbulent flame. In summary, two modes of combustion are activated after ignition, i.e., combustion inside the jet and combustion by the propagating spherical turbulent flame brush. For more details on the JetIgnition model, refer to reference [24]. As reported in [24], the JetIgnition model has already been validated in a WinGD marine two-stroke DF test engine and satisfying prediction accuracy was achieved.

For the marine two-stroke DF engine investigated in this study, the JetIgnition model is the ideal choice for predicting the burn rate in gas mode. It should be noted that the JetIgnition model requires a large amount of experimental data to calibrate the total seven model parameters for achieving satisfying prediction accuracy. However, this study is lacking in such a large number of experimental data due to the constraint on experimental conditions. For marine large two-stroke engines, this situation is quite common in other studies as well. Therefore, it is decided to use the non-predictive combustion model to predict the burn rate in gas mode. As can be observed from the measured data of a WinGD two-stroke DF engine, the shape of the heat release rate curve in the main cylinder chamber exhibits two peaks at low loads, whereas only one peak is observed at high loads [24]. Therefore, when operating in gas mode, a double Wiebe function can be employed to predict the burn rate in the main cylinder chamber, which represents the combustion in the jet and the combustion by the propagating spherical turbulent flame brush, respectively. Based on the model validation results presented in Section 3, it can be observed that using a double Wiebe function is capable of achieving satisfactory prediction accuracy. The improvement in prediction accuracy by using a triple Wiebe function is not expected to be significant. Furthermore, having too many model parameters makes model calibration difficult. Therefore, choosing the double Wiebe function is a better compromise between prediction accuracy and model calibration difficulty. As for the pilot fuel combustion in the pre-chamber, a single Wiebe function is used as suggested in [24].

As for the fuels used in the combustion models, their main properties are shown in

Table 2. Main properties of diesel fuel and natural gas used in combustion models.

Fuel Type	Molecular Formula	Lower Heating Value	Stoichiometric A/F Ratio
Diesel fuel	C13.5H23.6	43.25 MJ/kg	15.5
Natural gas	CH4	50 MJ/kg	17.2

. It should be noted that the diesel fuel used in diesel mode is of the same type as the pilot fuel used in the gas mode.

For predicting the NO_x emission, the extended Zeldovich mechanism is employed and only thermal nitrous oxide (NO) is considered [34]. As for the brake specific NO_x emission, it is calculated using the following equation [33]:

$$bsNOx={\displaystyle \frac{60n_{eng}{\displaystyle \sum _{i=1}^{6}1.533m_{\mathrm{NO},\mathrm{EVO},\mathrm{i}}\left(1-\frac{m_{\mathrm{burned},\mathrm{cs},\mathrm{i}}}{m_{\mathrm{tot},\mathrm{EVO},\mathrm{i}}}\right)}}{P_{\mathrm{b}}}}$$

(1)

where n_eng denotes engine speed; P_b denotes engine brake power; m_NO,EVO,i denotes mass of NO in cylinder i when exhaust valve opens, which is calculated based on the extended Zeldovich mechanism; m_burned,cs,i denotes mass of burned species in cylinder i at start of cycle; and m_tot,EVO,i denotes total mass of all species in cylinder i when exhaust valve opens.

It should be noted that most experimentally measured NO_x data are reported with the assumption that all sensed NO_x has the molecular weight of NO₂. To maintain consistency with this convention for reporting NO_x, the mass of NO is scaled by a factor of 1.533, as shown in Equation (1).

As for the brake specific CO₂ emission, it is calculated using the following equation [33]:

$$bsC{O}_2={\displaystyle \frac{60n_{eng}{\displaystyle \sum _{i=1}^6{m}_{{\mathrm{CO}}_2,\mathrm{EVO},\mathrm{i}}\left(1-\frac{m_{\mathrm{burned},\mathrm{cs},\mathrm{i}}}{m_{\mathrm{tot},\mathrm{EVO},\mathrm{i}}}\right)}}{P_{\mathrm{b}}}}$$

(2)

where m_CO2,EVO,i denotes the mass of CO₂ in cylinder i when exhaust valve opens, which is calculated based on the fuel consumption quantity and the mass of CO₂ produced per unit mass of fuel burned.

A modified version of classical Woschni correlation, which is named WoschniGT and proposed by Gamma Technologies, is employed to calculate the in-cylinder heat transfer coefficient [33]. Compared to the original Woschni correlation, the WoschniGT model specifically enhances the heat transfer during the valve overlap period when the exhaust valve and scavenging ports are opening simultaneously. The Chen–Flynn model is employed in this study to calculate the friction mean effective pressure (FMEP) [35]. During simulation, the engine simulation model calculates the cylinder peak pressure and the average piston speed for each cycle and passes them to the Chen–Flynn model as the input. The Chen–Flynn model then calculates the FMEP as the output.

The flow rate through the scavenging ports and exhaust valve is calculated by employing a 1D quasi-steady adiabatic flow equation. A “S-shaped” scavenging function, which establishes the relationship between the cylinder residual ratio and exhaust residual ratio, is employed to describe the scavenging process [33]. Due to the lack of experimental data, the “S-shaped” scavenging function is calibrated by referring to the computational fluid dynamics (CFD) simulation results for marine two-stroke diesel engines as reported in [36,37,38]. For all the injectors (gas, pilot fuel, and main fuel injectors) in the engine simulation model, they are modeled with the same method. By providing the amount of fuel injected per cycle as the input, the injection timing, injection pressure profile, and respective injection mass flow rate profile are derived as the output.

2.2.2. Turbocharger Model

The turbocharger model consists of three sub-models, i.e., the compressor, turbine, and turbocharger shaft sub-model. For the compressor and turbine, modeling methods with different levels of complexity and accuracy can be found in the literature. Among these methods, the lookup table method is adopted in this study because this method is capable of providing a good compromise between prediction accuracy and computational cost, which is very suitable for the 0D/1D engine cycle simulation [39,40,41]. To apply the lookup table method, the compressor and turbine performance maps are extracted from the turbocharger-engine matching test report and then they are digitized and stored in a lookup table.

For the compressor model, the turbocharger shaft speed and pressure ratio are provided as the input. The mass flow rate and efficiency are calculated by interpolating the lookup table as the output. Based on these parameters, the post-compressor temperature and the power absorbed by the compressor are derived by the following equations:

$$T_{\mathrm{c},\mathrm{out}}=T_{\mathrm{c},\mathrm{in}}+{\displaystyle \frac{T_{\mathrm{c},\mathrm{in}}}{{\eta }_{\mathrm{c}}}}\left\{{\left({\displaystyle \frac{p_{\mathrm{c},\mathrm{out}}}{p_{\mathrm{c},\mathrm{in}}}}\right)}^{{\displaystyle \frac{{\gamma }_{\mathrm{c}}-1}{{\gamma }_{\mathrm{c}}}}}-1\right\}$$

(3)

$$P_{\mathrm{c}}=G_{\mathrm{c}}{c}_{\mathrm{p},\mathrm{c}}\left(T_{\mathrm{c},\mathrm{out}}-T_{\mathrm{c},\mathrm{in}}\right)$$

(4)

where T_c,in and T_c,out denote the pre- and post-compressor temperature, respectively; p_c,in and p_c,out denote the pre- and post-compressor pressure, respectively; G_c denotes the compressor mass flow rate; η_c denotes the compressor efficiency; γ_c and c_p,c denote the specific heat ratio and the constant-pressure specific heat of boost air flowing through the compressor, respectively; and P_c denotes the compressor absorbed power.

It should be noted that the compressor operating point may move into the unstable surge region when turbocharger performance deteriorates. As the scope of the present study does not focus on the compressor operational characteristics in the surge region, the modeling of compressor operation in the surge region is simplified in this study. As illustrated in Figure 2, the extension of the mass flow rate into the surge region is handled by imposing a straight line with a very small negative slope from the surge line to the point at which the mass flow rate equals zero, whereas the extension of efficiency is handled by extrapolating the efficiency quadratically from the surge line to the minimum efficiency at a zero mass flow rate [42]. The minimum efficiency is taken from the highest speed line with the lowest pressure ratio in the compressor performance map. Additionally, an index known as surge margin is used to quantitatively assess the risk of surge, which is calculated by the following equation:

$$SG={\displaystyle \frac{G_{\mathrm{c}}-G_{\mathrm{c},\mathrm{sg}}}{G_{\mathrm{c},\mathrm{sg}}}}$$

(5)

where SG represents the surge margin and G_c,sg represents the compressor mass flow rate at the surge line.

For modeling the turbine, it is simplified as an equivalent nozzle and the exhaust gas flow rate can be estimated by assuming the actual flow process as a 1D quasi-steady adiabatic flow process. From the turbine performance map, it can be found that the turbine efficiency and the nozzle discharge coefficient only depend on the expansion ratio across the turbine. Therefore, for the turbine model, the expansion ratio is provided as the input and the discharge coefficient and efficiency are calculated by interpolating the lookup table as the output. Consequently, the post-turbine temperature and the turbine output power are calculated by the following equations:

$$T_{\mathrm{t},\mathrm{out}}=T_{\mathrm{t},\mathrm{in}}-{\eta }_{\mathrm{t}}{T}_{\mathrm{t},\mathrm{in}}\left\{1-{\left({\displaystyle \frac{p_{\mathrm{t},\mathrm{out}}}{p_{\mathrm{t},\mathrm{in}}}}\right)}^{{\displaystyle \frac{\gamma -1}{\gamma }}}\right\}$$

(6)

$$P_{\mathrm{t}}=G_{\mathrm{t}}{c}_{\mathrm{p},\mathrm{t}}\left(T_{\mathrm{t},\mathrm{in}}-T_{\mathrm{t},\mathrm{out}}\right)$$

(7)

where T_t,in and T_t,out denote the pre- and post-turbine temperature, respectively; p_t,in and p_t,out denote the pre- and post-turbine pressure, respectively; G_t denotes the turbine mass flow rate; η_t denotes the turbine efficiency; γ_t and c_p,t denote the specific heat ratio and the constant-pressure specific heat of exhaust gas flowing through the turbine, respectively; and P_t denotes the turbine output power.

For the turbocharger shaft model, the angular momentum conservation equation is adopted to calculate the shaft speed by the following equation:

$${\displaystyle \frac{d{\omega }_{\mathrm{tc}}}{dt}}={\displaystyle \frac{1}{J_{\mathrm{tc}}}}\left({\displaystyle \frac{P_{\mathrm{t}}}{{\omega }_{\mathrm{tc}}}}{\eta }_{\mathrm{m}}-{\displaystyle \frac{P_{\mathrm{c}}}{{\omega }_{\mathrm{tc}}}}\right)$$

(8)

where ω_tc denotes the turbocharger shaft rotational angular velocity; J_tc denotes the turbocharger shaft inertia; and η_tc denotes the turbocharger shaft mechanical efficiency.

For the marine DF engine investigated in this study, a waste-gate valve is used to bypass a proportion of exhaust gas along the turbine mainly for air–fuel ratio control in gas mode. Furthermore, as reported in the engine project guide, the waste-gate valve is also used for surge control. The exhaust gas mass flow rate through the waste-gate valve is calculated by employing the 1D quasi-steady adiabatic flow equation.

2.2.3. Air Cooler Model

In this study, the air cooler is modeled as a bundle of multiple pipes connected in parallel [33]. The pipe wall temperature is imposed as the desired air outlet temperature and a high heat transfer multiplier is set. This setting will allow a sufficient amount of heat transfer between the air and pipes so that the air outlet temperature is able to reach the pipe wall temperature. The desired air outlet temperature is calculated based on the air cooler’s effectiveness, cooling water inlet temperature, and air inlet temperature. A lookup table consisting of the measured effectiveness and corresponding air volumetric flow rate is established and the effectiveness is estimated by interpolating the lookup table. The pressure drop across the air cooler is modeled as surface friction loss, which is calibrated based on the measured pressure drop provided in the engine shop trial report.

2.2.4. Auxiliary Blower Model

At low engine loads, the compressor cannot provide a sufficient amount of boost air due to low exhaust gas energy. Therefore, the electric auxiliary blower downstream of the air cooler is activated to assist the boosting process. For the auxiliary blower, it is simplified as a centrifugal compressor running at a fixed rotational speed [43]. Therefore, the modeling method for the compressor can be employed to model the auxiliary blower.

2.2.5. Engine Receivers and Connecting Piping Model

The engine receivers and connecting pipes between engine components are modeled by using the 1D approach [42]. Based on the imposed discretization length, these pipes are discretized into many volumes and connected by boundaries. The scalar variables (temperature, pressure, density, etc.) over each volume and the vector variables (mass flux, velocity, mass fraction flux, etc.) for each boundary are calculated by solving the continuity, momentum, and energy conservation equations.

2.2.6. Propeller Model

For investigating the influence of turbocharger performance decay on engine speed, a propeller model is integrated into the engine simulation model. In this study, the propeller is simplified assuming that the propeller power only depends on the engine speed.

2.3. Model Calibration

After building the engine simulation model in GT/Power, meticulous calibration is necessary to ensure a good match between the predicted and measured results. Model calibration is carried out in two steps.

In the first step, the turbocharging-related blocks are removed from the simulation model. The measured temperature and pressure of the scavenging and exhaust receivers are used as the boundary conditions for the cylinder. During this stage, the cylinder-related sub-models are calibrated. Among these sub-models, the combustion model significantly influences the prediction accuracy of the engine simulation model. For the diesel mode, four model parameters in the DIPulse model need to be calibrated. These parameters are calibrated only at 75% load, yielding a set of model parameters. Benefiting from the robust physical foundation of the DIPulse model, satisfactory predictive accuracy is also obtained at other load points by directly applying this single set of model parameters. Regarding the combustion in the pre-chamber in gas mode, which is modeled using a single Wiebe function, the start of combustion can be estimated to be a few crank angles after injection begins and the combustion duration can be approximated to be three to five crank angles [24]. As for the combustion in the main chamber in gas mode, a double Wiebe function is used to predict the burn rate and the model parameters are calibrated for each load point. Since the investigated marine DF engine operates according to the propeller law, a specific relationship exists between the engine speed and brake power. Consequently, the obtained Wiebe function parameters are stored in a lookup table as a function of engine speed and quadratic interpolation is employed to calculate the Wiebe function parameters at other engine speeds [19]. The calibration task is performed based on genetic algorithm-based multi-objective optimization with the measured cylinder peak pressure and BSFC as the target values in the objective function. As for the optimization tool, the GT-Optimizer provided by GT-Power software is used. In the second step, turbocharging-related blocks are added to form a complete engine simulation model. During this stage, the remaining engine model parameters are calibrated.

3. Model Validation

In this section, the developed engine simulation model is validated by comparing the simulation results with measured results in both operating modes at four steady-state load points, e.g., 25%, 50%, 75%, and 100% of MCR, covering the entire operating envelope. The measured results provided by the engine shop trial report are presented in

Table 3. Measured results provided by the engine shop trial report.

Engine Load [%]	25	50	75	100
	Diesel Mode
Engine speed [RPM]	43.5	54.8	62.8	69.1
Brake power [kW]	3316	6633	9949	13265
BSFC [g/kW·h]	192.3	188.3	182.8	190.5
Peak pressure [bar]	65.9	86.9	100.5	112.9
Turbocharger shaft speed [RPM]	7229	10756	12678	14175
Post-compressor pressure [bar]	1.56	2.68	3.66	4.68
Post-compressor temperature [K]	348	413	453	493
Pre-turbine temperature [K]	520	598	643	721
Post-turbine temperature [K]	448	473	483	523
Pre-turbine pressure [bar]	1.59	2.53	3.45	4.52
Boost Pressure [bar]	1.63	2.63	3.66	4.59
	Gas Mode
Engine speed [RPM]	43.5	54.8	62.8	69.1
Brake power [kW]	3316	6633	9949	13265
BSEC-pilot fuel [kJ/kW·h]	61.3	30.6	15.3	13.4
BSEC-natural gas [kJ/kW·h]	7903.1	7534.4	7166.3	6685.6
Peak pressure [bar]	63.2	111.2	144.9	172.3
Turbocharger shaft speed [RPM]	6726	9772	11776	13206
Post-compressor pressure [bar]	1.18	2.25	3.2	4.03
Post-compressor temperature [K]	350	397	438	476
Pre-turbine temperature [K]	526	571	612	660
Post-turbine temperature [K]	473	464	473	486
Pre-turbine pressure [bar]	1.52	2.27	3.02	3.9
Boost Pressure [bar]	1.55	2.34	3.16	3.98

. It should be noted that the engine shop trial is carried out by the engine manufacturer and the provided shop trial report does not include the uncertainty of each measured parameter, making it impossible to carry out uncertainty analysis in this study. Nevertheless, the shop trial report has been approved by Lloyd’s Register of Shipping, which to some extent ensures the accuracy and reliability of the measurement results.

The predicted engine operation parameters are compared to the respective measured results as presented in Figure 3 and the relative errors are calculated and reported in

Table 4. Relative errors between simulation results and shop trial measured results.

Engine Load [%]	25	50	75	100
	Diesel Mode-relative error [%]
Engine speed	0.02	0.29	−0.38	−0.46
Brake power	−0.3	1.01	−1.07	−1.26
BSFC	0.33	−0.71	0.68	0.8
Peak pressure	−0.91	−0.58	−1.39	0
Turbocharger shaft speed	0.1	1.03	0.6	1.37
Post-compressor pressure	1.28	−0.37	−0.82	−1.5
Post-compressor temperature	2.87	2.66	3.31	4.26
Pre-turbine temperature	7.5	2.51	1.87	0.69
Post-turbine temperature	13.84	6.55	4.55	3.06
Pre-turbine pressure	−2.52	0	0.29	−2.43
Boost pressure	0	0.76	−1.37	−0.22
	Gas Mode-relative error [%]
Engine speed	0.05	−0.05	−0.11	0.26
Brake power	−0.3	0.05	−0.2	0.97
BSEC-pilot fuel	0.31	−0.01	−4.27	−0.93
BSEC-natural gas	0.28	−0.06	0.2	−0.96
Peak pressure	−0.16	−1.44	−2.28	−0.93
Turbocharger shaft speed	3.67	2.11	0.76	1.29
Post-compressor pressure	29.66	4	−1.56	−0.74
Post-compressor temperature	1.14	2.02	2.05	1.89
Pre-turbine temperature	2.47	2.98	0.49	−1.36
Post-turbine temperature	4.44	7.11	2.75	0.41
Pre-turbine pressure	−0.66	−2.64	−0.99	−2.31
Boost pressure	1.94	−0.85	−0.95	−0.25

.

To better explain the reasons causing the prediction errors as well as to interpret the operational difference between the diesel and gas mode, several additional engine operational parameters not measured in the shop trial are also examined. These parameters, including compressor and turbine efficiency, engine brake efficiency, the maximum temperature in the burned zone, and brake-specific NO_x and CO₂ emissions, are presented in Figure 4. Additionally, the compressor operating points superimposed on the compressor performance map for both modes are illustrated in Figure 5.

Although the engine brake efficiency is not directly provided in the shop trial report, it can be calculated by the following equation:

$${\eta }_{\mathrm{b}}={\displaystyle \frac{P_{\mathrm{b}}}{G_{\mathrm{eng},\mathrm{d}}LH{V}_{\mathrm{d}}+G_{\mathrm{eng},\mathrm{p}}LH{V}_{\mathrm{p}}+G_{\mathrm{eng},\mathrm{g}}LH{V}_{\mathrm{g}}}}$$

(9)

where η_b denotes the engine brake efficiency; P_b denotes the engine brake power; G_eng,d, G_eng,p, and G_eng,g denote the average fueling rate of diesel fuel, pilot diesel fuel, and natural gas, respectively; and LHV_d, LHV_p, and LHV_g denote the lower heating value of diesel fuel, pilot diesel fuel, and natural gas, respectively, which are provided in Table 2. The measured average fueling rate and calculated engine brake efficiency at each operating condition are presented in

Table 5. Measured average fueling rate and respective calculated engine brake efficiency for engine operation at different loads in both modes.

Engine Load [%]	25	50	75	100
	Diesel Mode
Geng,d [g/s]	177.1	346.9	505.2	701.9
ηb [%]	43.28	44.20	45.53	43.69
	Gas Mode
Geng,d [g/s]	0	0	0	38
Geng,p [g/s]	1.3	1.3	0.93	1.1
Geng,g [g/s]	145.6	277.6	396.1	492.7
ηb [%]	45.07	47.57	50.13	50.80

.

From the data presented in Table 4 and Figure 3, it can be observed that for most of the examined engine operation parameters, the relative errors are within the range of approximately ±3% in both modes, with the predicted results closely following the variation trend of respective shop trial measured results. However, large deviations between the predicted and measured results for certain parameters are also observed. The most pronounced discrepancy is observed for the post-compressor pressure at 25% load in gas mode with a relative error of as high as 29.66%. Such a large prediction error is unacceptable for an engine cycle simulation study. Based on the measured temperature and pressure, the compressor efficiency at this operating point is calculated to be 32.19%, which is unrealistically low. In fact, the compressor can achieve an efficiency of around 80% in the entire operating envelope when matched with a marine large two-stroke engine, which is consistent with the predicted compressor efficiency, as shown in Figure 4b. Moreover, as demonstrated in Figure 3g, the measured post-compressor pressure at this operating point noticeably strays from the general trend. Given the influence of the pressure ratio on the calculated compressor efficiency, it is highly possible that the large prediction error of post-compressor pressure at 25% load in gas mode is caused by the measurement error during the shop trial. As observed from Table 4 and Figure 3i,j, for most operating points, the developed engine simulation mode tends to over-predict both the pre- and post-turbine temperatures, with a relatively larger prediction error compared to other parameters. Based on the measured temperature and pressure, the turbine efficiency at each operating point is calculated and compared to the respective prediction result, as shown in Figure 4a. The predicted turbine efficiency is around 85%, whereas the calculated turbine efficiency varies within a relatively broad range from 78.84% to 116%. For the turbine in this study, its efficiency varies only within a small range from 83% to 88% according to the performance map provided by the turbocharger manufacturer. Moreover, the turbine efficiency will never exceed 100%. Considering the impact of pre- and post-turbine temperatures on calculated turbine efficiency, it can be inferred that the prediction errors are likely attributed to the heat transfer phenomenon between the turbine, compressor, surrounding atmosphere, and coolant oil, which is not accounted for in the study. To accurately characterize the heat transfer within the turbocharger, a comprehensive mathematical model is required along with a sufficient amount of experimental data for model calibration [44,45]. However, this is already out of the scope of the present study. Although the heat transfer within the turbocharger is not modeled in this study, the turbocharger performance, including turbocharger shaft speed, compressor, and turbine efficiency, is predicted with adequate accuracy. Furthermore, the prediction accuracy of the overall engine performance is also not influenced. Based on the above discussions, it can be concluded that the developed engine simulation model can represent the engine performance with satisfactory accuracy and can be used as a reliable tool for subsequent investigation.

There are several points that also need to be clarified regarding the model validation:

• It can be observed from Figure 3a that there is a deviation between the measured and predicted engine speed. This is because the model input chosen in this study is the cycle fueling quantity rather than the engine speed. Ideally, when the cycle fueling quantity is set according to the actual value measured in the shop trial, the predicted engine speed should be identical to the measured result. However, due to factors such as model assumptions and simplifications, prediction errors in engine speed are inevitable;
• As observed from Table 4, in diesel mode, although the combustion model parameters at 25% load are set by directly employing the calibration results of 75% load, the relative error in brake power at 25% load is slightly lower than that at 75%. It should be noted that the engine brake power can be considered as a model output under the combined effect of all engine sub-models. Therefore, it is possible that at a 25% load, the slightly inferior accuracy in the combustion model is compensated by other sub-models, resulting in a slightly higher prediction accuracy of brake power at a 25% load compared to a 75% load;
• From Table 4, it can be observed that the prediction accuracy of brake power in gas mode is slightly higher than that in diesel mode. This may be due to the different calibration methods for the combustion model in the two operating modes. In diesel mode, the combustion model used is a predictive, phenomenological, multi-zone model named DIPulse, whose model parameters are calibrated only at 75% load. The obtained model parameters are directly applied to other load points. However, in gas mode, the combustion mode used is the Wiebe function, which is an empirical model. It is not possible to find a single set of model parameters that are applicable to all of the operating conditions. Therefore, in gas mode, the model parameters in the Wiebe function are individually calibrated for each load point.

Based on the obtained simulation results, the operational differences between the two operating modes for the investigated marine DF engine will be analyzed in the following.

As shown in Figure 3a, under the control of the engine governor, the engine is capable of achieving the same speed in diesel and gas mode at each load point. Since the marine engine operates according to propeller law (the propeller power is approximately proportional to the square of the engine speed), the brake power will also be the same when the engine speeds are identical. Both the engine speed and brake power are predicted with satisfactory accuracy. However, as observed in Figure 4e, there is an obvious difference in brake efficiency between the two operating modes. In the entire operating envelope, the brake efficiency in gas mode is always higher than that in the diesel mode at each load point. It should be noted that in order to avoid knock in the gas mode, the engine compression ratio was significantly reduced. The diesel version of the investigated engine has a compression ratio of 18.8, while it ranges from 12 to 14 for the respective DF version. This explains why the break efficiency of the investigated DF engine in diesel mode is lower than traditional marine diesel engines.

Turbocharger matching is more challenging for DF engines because the engine exhibits distinct operating characteristics between the two operating modes. Despite this fact, it can be observed from Figure 4a,b that the compressor can achieve a high efficiency ranging from 80% to 85% in both modes and that the turbine efficiency is also above 85%. Moreover, as shown in Figure 5, a sufficient surge margin is also obtained for the compressor in both modes. Particularly, at 100% load, the surge margin in diesel and gas modes is 19% and 23.2%, respectively, which is sufficient for a reliable and stable operation of the turbocharger in service. At 100% load, the turbocharger shaft speed in diesel mode is close to the maximum limit speed; however, the risk of turbocharger over-speeding can be effectively controlled by opening the waste-gate valve. Therefore, it can be inferred that the selected turbocharger is well matched with the DF engine because it can not only provide a sufficient amount of boost air in both modes but also provide enough surge margin to avoid the occurrence of surge.

As shown in Figure 3f, the turbocharger shaft speed in the gas mode is lower than that in diesel mode at each load point. This is mainly because the exhaust gas energy in gas mode is lower than that in diesel mode. Figure 6 presents a comparison of the in-cylinder average temperature under two operating modes at 75% load. Due to the characteristics of lean premixed combustion in gas mode, the in-cylinder average temperature during the gas exchange process is lower than that in diesel mode. Furthermore, as shown in Figure 3k, the pre-turbine pressure in gas mode is lower than that in diesel mode at each load point; hence, the exhaust gas flow rate through the turbine is also lower. Consequently, lower exhaust gas energy is available upstream of the turbine in gas mode, which leads to slower turbocharger shaft speed when compared to the diesel mode.

Due to the slower turbocharger shaft speed at each load point, the boost pressure in gas mode is therefore lower than that in diesel mode. Consequently, the compression pressure, defined as the pressure at TDC estimated based on the assumption of a polytropic process for the engine compression process, is also found to be lower in gas mode. However, due to the faster combustion speed and advanced ignition timing in gas mode as shown in Figure 7, the peak pressure is much higher than that in diesel mode as shown in Figure 3e.

In gas mode, the predicted brake-specific CO₂ emission is 438.43, 415.09, 395.13, and 397.99 g/kW·h at 25%, 50%, 75%, and 100% load, respectively, while in diesel mode, it is 616.47, 596.41, 585.69, and 609.18 g/kW·h, respectively. The significant reduction in CO₂ emissions in gas mode is mainly due to the lower carbon-to-hydrogen ratio of natural gas compared to diesel fuel. Moreover, the higher brake efficiency in gas mode further contributes to the reduction in CO₂ emissions. Although the brake-specific NO_x emission is not provided by the shop trial report, the predicted results, as shown in Figure 4d, are consistent with the measured data presented in [46]. In gas mode, the predicted specific NO_x emission is 1.08, 1.31, 1.34, and 1.3 g/kW·h at 25%, 50%, 75%, and 100% load, respectively, fully complying with the Tier III limit. In diesel mode, the predicted specific NO_x emission is 11.7, 10.08, 9.55, and 10.15 g/kW·h at 25%, 50%, 75%, and 100% load, respectively, only meeting the Tier II limit. The lower NO_x emission in gas mode is primarily due to the lower in-cylinder temperature level. Although it is illustrated in Figure 6 that the peak average in-cylinder temperature in gas mode is much higher than in diesel mode, the shorter combustion duration leads to a more rapid decrease in temperature. Moreover, as shown in Figure 4f, the maximum temperature in the burned zone in gas mode is significantly lower than in diesel mode at each load point. As a result, the NOx emission is effectively reduced in gas mode.

4. Definition of the Turbocharger Performance Decay

In this study, a total of three types of typical turbocharger performance decays are defined as follows:

• Turbine efficiency decay is expressed by the decrease in turbine efficiency with the degree of decay varying between 0% and 40%;
• Turbine nozzle ring area decay is expressed by the change in turbine nozzle ring area with the area multiplier varying between 0.7 and 1.3;
• Turbocharger shaft mechanical efficiency decay is expressed by the decrease in mechanical efficiency with the degree of decay varying between 0% and 40%.

Based on the fundamental principles of turbocharging machinery, the turbine efficiency is expressed by the following equation:

$${\eta }_{\mathrm{t}}={\displaystyle \frac{P_{\mathrm{t}}}{P_{\mathrm{t},\mathrm{ideal}}}}$$

(10)

where P_t,ideal represents the turbine power delivered by an ideal process.

The compressor efficiency is expressed by the following equation:

$${\eta }_{\mathrm{c}}={\displaystyle \frac{P_{\mathrm{c},\mathrm{ideal}}}{P_{\mathrm{c}}}}$$

(11)

where P_c,ideal represents the compressor power required by an ideal process.

The turbocharger shaft mechanical efficiency is expressed by the following equation:

$${\eta }_{\mathrm{m}}={\displaystyle \frac{P_{\mathrm{c}}}{P_{\mathrm{t}}}}$$

(12)

By multiplying both sides of Equations (10)–(12), the turbocharger efficiency can be derived as the following equation:

$${\eta }_{\mathrm{tc}}={\eta }_{\mathrm{t}}\cdot {\eta }_{\mathrm{c}}\cdot {\eta }_{\mathrm{m}}={\displaystyle \frac{P_{\mathrm{t}}}{P_{\mathrm{t},\mathrm{ideal}}}}\cdot {\displaystyle \frac{P_{\mathrm{c}}}{P_{\mathrm{t}}}}\cdot {\displaystyle \frac{P_{\mathrm{c},\mathrm{ideal}}}{P_{\mathrm{c}}}}={\displaystyle \frac{P_{\mathrm{c},\mathrm{ideal}}}{P_{\mathrm{t},\mathrm{ideal}}}}$$

(13)

Equation (13) integrates the turbine efficiency, compressor efficiency, and shaft mechanical efficiency into the turbocharger efficiency η_tc, which can be used to quantitatively assess the turbocharger’s ability to convert the energy from the exhaust gas to the boost air. As implied by Equation (13), with the same degree of decay, the impact of turbine and shaft mechanical efficiency decay on the turbocharger’s energy conversion capability is identical. Consequently, the influence on engine performance and emission characteristics is also expected to be the same. Therefore, for the sake of brevity, this paper will only present the relevant results in the case of turbine efficiency decay. Additionally, during actual engine operation, two or more types of turbocharger performance decay may happen simultaneously. However, for better identifying the influence of each type of turbocharger performance decay on engine performance and emission characteristics, only one type of decay is accounted for in each parametric run in this study.

To ensure safe and reliable operation, engine manufacturers always set limit values for certain operation parameters, such as in-cylinder peak pressure, pre-turbine temperature, and turbocharger shaft speed. When these parameters exceed respective limit values, it is likely to cause the engine to experience excessive thermal and mechanical load, significantly affecting engine safety and durability. Additionally, Tier II and III also regulate the level of NOx emission produced by marine engines. When the engine is operating normally, engine operating parameters will be within the normal range. However, when turbocharger performance deteriorates, it will inevitably cause the engine operation parameters to deviate from their normal range. In this study, limit values are defined for three engine operating parameters and NOx emission as shown in

Table 6. Engine operation parameters limit values.

Parameter	Unit	Upper Limit Value
Turbocharger shaft speed	rpm	15,000
Pre-turbine temperature	K	893
Peak pressure	bar	180
Tier II limit on NOx emissions	g/kW·h	14.6
Tier III limit on NOx emissions	g/kW·h	3.4

, which are derived from the engine project guide, turbocharger user manual, and the pertinent literature [47].

5. Results and Discussions

In this section, the developed marine two-stroke DF engine model is utilized to investigate the influence of turbocharger performance decay on engine performance and emission characteristics. Parametric runs are performed for each load point (specifically, 25%, 50%, 75%, and 100% of the engine MCR) in both operating modes by manually varying the type of decay and the degree of decay. The simulation results, including engine speed, turbocharger shaft speed, boost pressure, peak pressure, pre-turbine temperature, air–fuel equivalence ratio, brake efficiency, and brake-specific CO₂ and NOx emissions, are presented for analysis.

5.1. Turbine Efficiency Decay

The turbine efficiency decay is primarily attributed to the change in turbine blade geometry caused by deposition and wear [25]. In this section, the influence of turbine efficiency decay on engine performance and emission characteristics is investigated with the corresponding results illustrated in Figure 8 and Figure 9 for diesel and gas modes, respectively. In Figure 8e,i and Figure 9e,i, the corresponding black dashed line is used to indicate the extent to which turbine efficiency decay will cause the engine operation parameter to exceed the specified limit value.

By comparing the results presented in Figure 8 and Figure 9, it can be found that when the turbine efficiency deteriorates, the overall changing trend in engine performance and emission characteristics in diesel and gas modes is similar. However, the two operating modes exhibit different sensitivities to the turbine efficiency decay.

As the turbine efficiency decays, the amount of exhaust gas energy that can be utilized and recovered by the turbine decreases, resulting in more energy being wasted. Consequently, the turbocharger shaft speed gradually drops, resulting in lower boost pressure and peak pressure. Therefore, the limit value on the turbocharger shaft speed and peak pressure will be not exceeded in both modes. When turbine efficiency deteriorates, due to the lower exhaust gas energy in gas mode, the turbocharger shaft speed and boost pressure are still lower than those in the diesel mode at each operating point. Despite the lower boost pressure in gas mode, the peak pressure is higher than that in diesel mode, mainly due to faster combustion speed and advanced ignition timing. By comparing the results presented in Figure 8d and Figure 9d, it can be found that the relative decrease in peak pressure in gas mode is less compared to diesel mode as the turbine efficiency decays. When the degree of efficiency decay increases from 0% to 40%, the peak pressure in the diesel mode decreases by 19.6%, 35.19%, 34.21%, and 30.2% at 25%, 50%, 75%, and 100% load, respectively, while in gas mode, it is 15.69%, 26.28%, 28.6%, and 26.13%, respectively. It should be noted that the peak pressure, to some extent, is representative of the in-cylinder pressure level. Higher in-cylinder pressure levels may allow more fuel energy to be converted into useful work, thereby improving the engine efficiency. Therefore, the relative decline in brake efficiency in gas mode is less than the diesel mode, as shown in Figure 8g and Figure 9g. When the degree of efficiency decay increases from 0% to 40%, the brake efficiency in gas mode declines by 6.01%, 10.54%, 9.88%, and 9.04% at 25%, 50%, 75%, and 100% load, respectively, while in diesel mode, it is 7.67%, 14.49%, 15.28%, and 14.47%, respectively. As the engine cycle fueling quantity is chosen as the model input and fixed at each load point in this study, the engine speed will inevitably drop due to the decline in brake efficiency. As expected, the engine speed drop in diesel mode is greater than that in gas mode, as shown in Figure 8a and Figure 9a. In diesel mode, when the degree of efficiency decay increases from 0% to 40%, the engine speed drops by 2.76%, 7.86%, 8.06%, and 7.39% at 25%, 50%, 75%, and 100% load, respectively, whereas in gas mode, it is 2.21%, 5.61%, 5.17%, and 4.55%, respectively. In the case of constant cycle fueling quantity, a decrease in brake efficiency will be accompanied by an increase in brake-specific CO₂ emission. As presented in Figure 8h and Figure 9h, the relative increase in brake-specific CO₂ emission in diesel mode is higher than that in gas mode. In diesel mode, when the degree of efficiency decay increases from 0% to 40%, the CO₂ emission increases by 8.2%, 15.91%, 15.98%, and 14.24% at 25%, 50%, 75%, and 100% load, respectively, while in gas mode, it is 6.3%, 11.52%, 10.98%, and 9.97%, respectively.

Due to the interaction between the compressor and turbine, the decline in turbine efficiency will influence the compressor operating point. As shown in Figure 10, in both operating modes, the compressor operating point gradually moves toward the surge line as the degree of decay increases, implying that the risk of compressor surge increases. Particularly, when the turbine efficiency decays by 40%, the surge margin at 100% load in diesel mode is 4.9%, while it is 5.43% in gas mode. Although the surge has not occurred, the surge margin is relatively small. Therefore, when the engine operates under transient conditions, the compressor may experience a surge.

The pre-turbine temperature, which is representative of the exhaust gas temperature, is mainly influenced by the air–fuel equivalence ratio. As can be observed from Figure 8f and Figure 9f, in both operating modes, the air–fuel equivalence ratio monotonically decreases as the turbine efficiency decays. Consequently, the pre-turbine temperature monotonically increases as presented in Figure 8e and Figure 9e. Due to the characteristics of lean premixed combustion in gas mode, the pre-turbine temperature remains lower than that in diesel mode at each operating point when turbine efficiency deteriorates. By comparing the result presented in Figure 8e and Figure 9e, it can be found that at 50%, 75%, and 100% load points, the degree of turbine efficiency decay, causing the pre-turbine temperature to exceed the specified limit value in gas mode, is higher than that in diesel mode. In both operating modes, at 25% load, even if the turbine efficiency deteriorates by 40%, the pre-turbine temperature will not exceed the limit value. This is mainly because the activation of the auxiliary blower at this load point leads to a relatively higher air–fuel equivalence ratio compared to other load points.

Figure 8i and Figure 9i illustrate the influence of turbine efficiency decay on brake-specific NO_x emission. Overall, the NO_x emission increases as the turbine efficiency decays in both operating modes. This is primarily because NO_x emission is highly dependent on the in-cylinder temperature level. As the turbine efficiency deteriorates, the in-cylinder temperature rises due to the decrease in air–fuel equivalence ratio, thus leading to increased NO_x emission. Although the influence of in-cylinder pressure level on NO_x emission is much less than temperature, the decrease in pressure (indicated by the reduction in peak pressure) also contributes to the increase in NO_x emission. This is because the reduction in pressure enhances the dissociation of oxygen and nitrogen molecules [48]. In diesel mode, the NO_x emission exhibits a continuously rapid increased trend as the turbine efficiency deteriorates. By fitting the simulation results, it can be found that the NO_x emission will exceed the Tier II limit when the turbine efficiency deteriorates by 11.68%, 13.72%, 16.6%, and 18.11% at 25%, 50%, 75%, and 100% load, respectively. However, it can be observed that when the turbine efficiency decays to a certain extent, the rate of increase in NO_x emission slows down and the NO_x emission may even begin to decrease as the turbine efficiency decays. This is because an overly low air–fuel equivalence ratio results in an extremely low oxygen concentration within the cylinder, unable to provide sufficient oxygen for the formation of NO_x. In gas mode, for engine operation at 50%, 75%, and 100% load, the NO_x emission will exceed the Tier III limit when the turbine efficiency declines by 25.75%, 26.39%, and 23.81%, respectively. It is worth noting that at the three load points, NO_x emission initially increases slowly as the turbine efficiency decays; however, once the turbine efficiency deteriorates to a certain extent, NO_x emission exhibits a rapidly increasing trend. This phenomenon is mainly due to the fact that the NO_x formation rate approximately follows an exponential trend with temperature [49]. In the gas mode, due to the characteristics of lean premixed combustion, the in-cylinder temperature remains at a relatively low level. Therefore, in the early stage of turbine efficiency decay, although the in-cylinder temperature continuously rises, NO_x emission only increases slowly due to the exponential relationship between the NO_x formation rate and temperature. It is only when turbine efficiency decays to a certain extent, causing the in-cylinder temperature to rise above a “threshold” value, that NO_x emission exhibits a considerable increase with temperature. At 25% load, NO_x emission does not exhibit an obvious change within the entire variation range of turbine efficiency decay and always meets the Tier III limit. This is primarily because, at this load point, the activation of the auxiliary blower keeps the in-cylinder temperature at a low level due to the relatively high air–fuel equivalence ratio.

5.2. Turbine Nozzle Ring Area Decay

For turbocharged engines, deposition on the turbine nozzle ring typically leads to a reduction in the nozzle ring area, which is a frequently encountered issue primarily resulting from the use of low-quality HFO [25]. On the other hand, in some cases, the nozzle ring area may increase due to the change in geometry caused by wear and corrosion [25]. In this section, the influence of a change in turbine nozzle ring area on engine performance and emission characteristics is investigated with the corresponding results illustrated in Figure 11 and Figure 12. In the two figures, an area multiplier greater than 1 indicates an increase in nozzle ring area, while an area multiplier less than 1 indicates a reduction in nozzle ring area. The corresponding black dashed lines in Figure 11e,i and Figure 12e,i are used to indicate the extent to which change in the turbine nozzle ring area will cause the engine parameter to exceed the specified limit value.

Figure 13 presents the movement trajectory of the compressor operating point with the change in turbine nozzle ring area for both operating modes. It can be found that as the nozzle ring area decreases, the compressor operating point gradually approaches the surge line and ultimately enters into the surge region. Furthermore, Figure 14 presents the fitting result of the nozzle ring area multipliers and respective surge margins at each load point for both modes. This figure indicates that in diesel mode, an area multiplier of 0.79, 0.86, 0.88, and 0.92 will lead to a compressor surge at 25%, 50%, 75%, and 100% load, respectively, while in the gas mode, it is 0.78, 0.85, 0.87, and 0.9, respectively. The result reveals that as the turbine nozzle ring area decreases, the compressor is more prone to surge at high load conditions. In addition, at the same load point, the area multiplier at which the surge will occur is almost the same in both modes. In the engine project guide, two methods are recommended by the engine manufacturer for surge control. The first one is to temporarily slow down the engine when a surge occurs and the second one is to open the waste-gate valve to bypass a portion of exhaust gas along the turbine. In this study, the second method is utilized to ensure a surge margin of at least 10% for the operating point at which surge already occurs caused by the decrease in the nozzle ring area. It should be noted that, as the severity of the surge intensifies, the opening of the waste-gate valve must be progressively enlarged for effective surge control. Particularly, for engine operation at 100% load with an area multiplier of 0.7 in both modes, surge control by the waste-gate valve becomes unfeasible because stable combustion cannot be sustained due to an extremely low air–fuel equivalence ratio. Therefore, corresponding results are not presented in Figure 11 and Figure 12.

As shown in Figure 11b and Figure 12b, before the waste-gate valve is opened, the turbocharger shaft speed continuously increases with the reduction in the turbine nozzle ring area in both operating modes. Meanwhile, as shown in Figure 13, the compressor operating point gradually moves toward the region with a higher pressure ratio. As a result, the boost pressure monotonically increases, which consequently leads to a higher air–fuel equivalence ratio, as well as a rise in both the compression pressure and peak pressure. Although the change in nozzle ring area will not cause the peak pressure to exceed the limit value in both modes as presented in Figure 11d and Figure 12d, for engine operation at 100% load in gas mode, the peak pressure is only slightly below the specified limit value if the nozzle ring area decreases to a certain value. Therefore, the chance that the limit value on peak pressure may be exceeded during transient operation should be cautiously approached. Once the waste-gate valve is opened for surge control, the turbocharger shaft speed, boost pressure, compression pressure, and peak pressure all decrease accordingly.

From Figure 11g and Figure 12g, it can be observed that at each load point for both modes, the nozzle ring area at which the engine achieves the highest brake efficiency is not always at the original area but rather in its vicinity.

Table 7. Nozzle ring area multiplier at which the engine achieves the highest brake efficiency at each load point for both modes.

Engine Load [%]	25	50	75	100
Diesel Mode	0.9	0.95	1.05	1.05
Gas Mode	0.85	0.95	0.95	1.05

presents the area multiplier at which the engine achieves the highest brake efficiency. The result implies that the application of VGT has the potential to improve engine efficiency by appropriately increasing the nozzle ring area under high load conditions and decreasing it under low load conditions, just similar to what is conducted in automotive engines [50]. From Figure 11g and Figure 12g, it can also be observed that near the original nozzle ring area, the change in area does not cause a significant change in engine brake efficiency. Only when the nozzle ring area increases or decreases to a certain extent does the brake efficiency exhibit a considerable change. The cylinder pressure–volume (P–V) diagrams, which are commonly used to analyze and calculate engine-indicated power, can provide insights into this phenomenon. Figure 15 illustrates the P–V diagrams with seven different nozzle ring area multipliers (specifically, 0.8, 0.9, 0.95, 1, 1.05, 1.1, and 1.3) at 75% load in diesel mode. From this figure, it is evident that when the area multiplier is 0.9, 0.95, 1, 1.05, or 1.1, the total area enclosed by the P–V curve does not change greatly. Therefore, the engine indicated power will not change significantly. As the engine friction does not fluctuate greatly with the change in turbine nozzle area, the final engine brake power and brake efficiency will not exhibit significant variation as well. However, when the area multiplier is 1.3 or 0.8, the area enclosed by the P–V curve significantly decreases, thus leading to a noticeable decline in brake efficiency, as demonstrated in Figure 11g. The reduction in brake efficiency in the former case (area multiplier equals 1.3) is mainly due to the reduction in boost pressure caused by the increased nozzle ring area. As for the latter case (area multiplier equals 0.8), the reason for the decline in brake efficiency lies in the fact that the decreasing trend of boost pressure caused by the opening of the waste-gate valve outweighs the increasing trend of boost pressure caused by the reduction in the nozzle ring area. From the perspective of energy utilization, whether it is the increase or decrease in the nozzle ring area, both will affect the turbocharger efficiency, which can be considered as the utilization efficiency of exhaust gas energy, thereby impacting the engine brake efficiency. Figure 16 presents the variation trend of brake efficiency and turbocharger efficiency with the change in nozzle ring area at 75% load for both modes. From this figure, it can be observed that the variation trend of brake efficiency and turbocharger efficiency are roughly consistent. In addition, the turbocharger efficiency also does not change significantly near the original nozzle ring area. From the above discussion, it can be deduced that when the nozzle ring area changes, the fundamental reason affecting the engine brake efficiency lies in the change in turbocharger efficiency.

Similar to the changing trend of brake efficiency, the turbine nozzle ring area at which the engine achieves the highest speed at each load point in both modes is also not always at the original area but rather in its vicinity, as shown in Figure 11a and Figure 12a.

Table 8. Relative change in engine speed with the change in turbine nozzle ring area.

	Area Multiplier Increase from 1 to 1.3
Engine Load [%]	25	50	75	100
Diesel Mode	−1.84%	−5.35%	−4.94%	−3.37%
Gas Mode	−1.7%	−3.87%	−3.44%	−2.5%
	Area Multiplier Decrease from 1 to 0.75
Engine Load [%]	25	50	75	100
Diesel Mode	−0.92%	−7.39%	−10.18%	−11.73%
Gas Mode	−0.53%	−4.36%	−5.69%	−6.87%

presents the relative change in engine speed when the turbine nozzle ring area multiplier increases from 1 to 1.3 and decreases from 1 to 0.75, respectively. It can be found that the engine speed drop in gas mode is always lower than that in diesel mode at each load point. This is mainly because the relative decline in brake efficiency in gas mode is less than in diesel mode, as presented in Figure 11g and Figure 12g.

Due to the fact that the brake-specific CO₂ emission is inversely proportional to the brake efficiency, the variation trend of brake-specific CO₂ emission with the change in turbine nozzle ring area is opposite to that of brake efficiency as shown in Figure 11h and Figure 12h.

Table 9. Relative change in brake-specific CO₂ emission with the change in turbine nozzle ring area.

	Area Multiplier Increase from 1 to 1.3
Engine Load [%]	25	50	75	100
Diesel Mode	5.19%	10.46%	9.08%	5.82%
Gas Mode	4.68%	8.03%	7.12%	5.36%
	Area Multiplier Decrease from 1 to 0.75
Engine Load	25	50	75	100
Diesel Mode	2.52%	14.84%	21.34%	23.98%
Gas Mode	1.43%	9.12%	12.28%	15.32%

presents the relative change in brake-specific CO₂ emission when the turbine nozzle ring area multiplier increases from 1 to 1.3 and decreases from 1 to 0.75, respectively. It can be found that, regardless of whether the nozzle ring area is increased or decreased, the relative increase in CO₂ emission in gas mode is always lower than that in diesel mode.

In general, as illustrated in Figure 11e and Figure 12e, the pre-turbine temperature increases when the turbine nozzle ring area deviates (either increases or decreases) from its original value, which is mainly attributed to the reduction in air–fuel equivalence ratio. It can be observed that a slight variation around the original nozzle ring area does not cause a significant change in air–fuel equivalence ratio and, consequently, the pre-turbine temperature. In addition, when the nozzle ring area changes in the vicinity of its original value, an apparently counter-intuitive trend appears for certain cases, where the pre-turbine temperature and the air–fuel equivalence ratio either both increase or both decrease simultaneously. This is mainly because, although the air–fuel equivalence ratio significantly affects the exhaust gas temperature, its impact may be offset or even surpassed by other factors if the change in air–fuel equivalence ratio is relatively small. Obvious changes in pre-turbine temperature can only be observed with a relatively large area deviation. In both modes, for engine operation at medium to high load conditions, when the nozzle ring area decreases to a certain extent, the pre-turbine temperature rapidly increases and may exceed the specified limit value. This is mainly because the waste-gate valve is opened for surge control at these operating points, leading to a significant decrease in the air–fuel equivalence ratio. However, although the pre-turbine temperature also increases as the turbine nozzle ring area increases, there is no occurrence of pre-turbine temperature exceeding the specified limit value. It can also be found from Figure 11e and Figure 12e that the limit on pre-turbine temperature is not exceeded within the entire operating envelope at 25% load for both modes. This is because the auxiliary blower is activated at this load point, keeping the air–fuel equivalence ratio at a relatively high level.

It can be clearly observed from Figure 11i that with the increase in turbine nozzle ring area, the brake-specific NO_x emission in diesel mode exhibits a significant increasing trend. This is mainly because NO_x formation is highly dependent on the in-cylinder temperature level. In diesel mode, the combustion proceeds as a Diesel cycle and the temperature within the cylinder remains at a high level. As the nozzle ring area increases, the air–fuel equivalence ratio decreases accordingly, leading to a further increase in in-cylinder temperature, which in turn causes a noticeable increase in NO_x emission. By fitting the simulation results, it can be found that the Tier II limit is exceeded with an area multiplier of 1.06, 1.11, 1.16, and 1.17 at 25%, 50%, 75%, and 100% load, respectively. In the case of a decrease in the turbine nozzle ring area, the NO_x emission does not exhibit a monotonic variation trend. For engine operation at 25% load, the NO_x emission initially decreases as the turbine nozzle ring area decreases. This is primarily because the increased air–fuel equivalence ratio leads to a reduction in in-cylinder temperature. Once the waste-gate valve opens for surge control, the air–fuel equivalence ratio rapidly decreases, causing the in-cylinder temperature to rise and subsequently leading to an increase in NO_x emission. For engine operation at 50%, 75%, and 100% load conditions, a slight decrease in the nozzle ring area results in a less significant change in the air–fuel equivalence ratio compared to 25% load, thus leading to a minor change in in-cylinder temperature and consequently the NO_x emission. Once the waste-gate valve opens for surge control, the NO_x emission initially increases significantly and then rapidly decreases. The initial significant increase is due to the rapid decrease in air–fuel equivalence ratio, which causes a sharp rise in in-cylinder temperature. If the waste-gate valve opens too much, although the in-cylinder temperature still rises sharply, the excessively low air–fuel equivalence ratio results in insufficient oxygen concentration for NO_x formation. When the influence of decreased oxygen concentration on NO_x formation outweighs that of increased in-cylinder temperature, the NO_x emission will begin to decrease.

In gas mode, for engine operation at 25% load, the NO_x emission does not exhibit a significant change in the entire variation range of the turbine nozzle ring area and always meets the Tier III limit, as shown in Figure 12i. This is primarily because, at this load point, the air–fuel equivalence ratio remains at a relatively high level due to the activation of the auxiliary blower as presented in Figure 12f. Consequently, the in-cylinder temperature remains at a low level regardless of the change in the turbine nozzle ring area. Considering that the NO_x formation rate changes approximately exponentially with the temperature, the low in-cylinder temperature level implies that the increase in temperature will not lead to a significant change in NO_x emission. Similarly, for engine operation at 50%, 75%, and 100% load, although the change in turbine nozzle ring area in the vicinity of the original area will cause the variation in in-cylinder temperature, the in-cylinder temperature still remains at a relatively low level due to the Otto cycle combustion process in gas mode. Therefore, the NO_x emission does not change significantly. Only when the nozzle ring area significantly increases or decreases will the NO_x emission exhibit a noticeable change. In the case of nozzle ring area increase, by fitting the simulation results, it can be found that the Tier III limit is exceeded with an area multiplier of 1.2, 1.22, and 1.22 at 50%, 75%, and 100% load, respectively. On the other hand, if the nozzle ring area is excessively decreased, the waste-gate valve is opened for surge control. This results in a rapid decrease in the air–fuel equivalence ratio, thus leading to a considerable increase in NO_x emission. Consequently, the Tier III limit is exceeded when the nozzle ring decreases to a certain extent. It should be noted that, at 100% load, although an excessive opening of the waste-gate valve causes a significant increase in in-cylinder temperature, the in-cylinder oxygen concentration decreases to a very low level at the same time. As a result, the NO_x emission begins to decrease with an area multiplier of 0.8 due to the combined effect of in-cylinder temperature and oxygen concentration.

6. Conclusions

In the present study, a 0D/1D simulation model of a marine large two-stroke DF engine is built in GT-Power. Parametric runs are performed and the derived results are used for analyzing the influence of turbocharger performance decay on engine performance and emission characteristics in both diesel and gas modes. The main findings are summarized as follows:

• As the turbine efficiency decays, a decreasing trend is observed for turbocharger speed, air–fuel equivalence ratio, boost pressure, peak pressure, brake efficiency, and engine speed in both operating modes, while there is an increasing trend in pre-turbine temperature and CO₂ and NO_x emissions. In addition, the compressor operating point moves toward the surge line as the turbine efficiency decays;
• In both operating modes, as the nozzle ring area multiplier gradually decreases from the specified maximum value, the engine speed, turbocharger speed, boost pressure, peak pressure, air–fuel equivalence ratio, and brake efficiency all show an increasing trend, while the pre-turbine temperature and CO₂ and NO_x emissions show a decreasing trend. In addition, the compressor operating point gradually approaches the surge line. When the waste-gate valve is opened for surge control, these parameters show an opposite changing trend;
• It is only when the turbine nozzle ring area increases or decreases to a certain extent that a noticeable change in brake efficiency can be observed for both modes. This phenomenon is highly related to the changing trend in turbocharger efficiency as the turbine nozzle ring changes;
• Under each load condition in both modes, the nozzle ring area at which the engine achieves the highest brake efficiency and highest speed is not always at the original area but rather in its vicinity. This implies the potential of employing a VGT to improve the engine efficiency for the investigated marine DF engine;
• Due to the advanced ignition timing and faster combustion speed in gas mode, the in-cylinder pressure level is significantly higher than in diesel mode. As a result, when the turbocharger performance decays, the relative decline in brake efficiency, along with the resulting engine speed drop and relative increase in CO₂ emission, is lower than in diesel mode;
• Due to the characteristics of lean premixed combustion in gas mode, the degree of turbocharger performance decay at which the pre-turbine temperature exceeds the limit is lower than that in diesel mode;
• For both types of turbocharger performance decay, the NO_x emission in diesel mode shows a noticeable change, while in gas mode, NO_x emission only shows a significant change when the turbocharger performance decays to a certain extent. This is mainly related to the significant difference in combustion temperature caused by the distinct combustion process (Diesel cycle versus Otto cycle) in the two operating modes.

In summary, when the turbocharger performance deteriorates, the changing trend in engine performance and emission characteristics in both operating modes are generally consistent but there are significant differences in the extent and magnitude of these changes mainly due to the completely different combustion characteristics of the two operating modes. Moreover, the engine is less sensitive to the turbocharger performance decay in gas mode in terms of relative decline in brake efficiency, engine speed drop, and relative increase in CO₂ emission.

In future research, the effect of compressor performance decay on the performance and emission characteristics of the investigated marine DF engine will be analyzed. In addition, the effect of turbocharger performance decay on engine knocking in gas mode will be also studied.