1   Introduction

International trade is heavily reliant on maritime transportation, with nearly 90% of import and export trade in Europe (Karl et al., 2019) and over 80% of global goods transported via seaborne logistics. Maritime transportation, despite its significant economic benefits, poses environmental challenges due to its contribution to greenhouse gas emissions.

Although maritime transportation is the most efficient mode of transport in terms of carbon dioxide emissions per distance and weight ("European Maritime Transport Environmental Report 2021—European Environment Agency", 2021), it still accounts for 2.89% of global greenhouse gases. This figure has been steadily increasing, with a 4.7% rise from 2012 to 2018 (International Maritime Organization, 2020). Moreover, exhaust gases from maritime propulsion systems contain harmful emissions, such as 0.25% to 0.4% sulfur oxides (SO_x), nitrogen oxides (NO_x), and particulate matter (PM) (Latarche, 2021).

Between 2012 and 2018, greenhouse gas emissions in the shipping industry increased by 9.6% (expressed in terms of CO₂e) (International Maritime Organization, 2020). CO₂e encompasses carbon dioxide CO₂, methane CH₄, and nitrous oxide N₂O. CO₂ alone increased by 8.4% in the same period, which reached 919 million tons in 2018. The International Maritime Organization (IMO) anticipates a further increase in GHG of 30% to 130% by 2050 compared with that in 2008 (International Maritime Organization, 2020).

Various methods have been developed to reduce noxious emissions from maritime vessels below the 0.25% threshold for addressing pressing environmental concerns (Latarche, 2021). These approaches mainly include exhaust gas after-treatment techniques (e.g., selective catalytic reductions and scrubbers), exhaust gas recirculation, water addition, novel turbocharging techniques, advanced combustion strategies, the Miller cycle, and low steaming.

Dual-fuel engines have emerged as a promising technology in the maritime propulsion industry. These engines allow the use of various fuels that can withstand high pressures and temperatures without knocking. However, many fuels of high octane number (or methane number for gaseous fuels) have a low cetane number, which measures the reactivity of the fuel. Consequently, a high reactivity fuel, usually diesel, must be injected to trigger combustion. In low-pressure dual-fuel engines, the low reactivity fuel is typically port-injected at low-pressure close to the inlet valve (Agarwal et al., 2022; Chen et al., 2021; Krishnamoorthi et al., 2021; Latarche, 2021; Ma et al., 2020; Wang et al., 2015). This approach reduces NO_x emissions and PM abatement (Chmielniak and Sciazko, 2003).

Several studies (Al-Aboosi et al., 2021; Cardoso et al., 2021; Reiter and Kong, 2011) suggest that ammonia could be a better choice than liquefied natural gas (LNG) for ships. Unlike LNG, ammonia emits no carbon dioxide (CO₂) when burned. Thus, it can significantly reduce air pollution. In terms of energy stored per unit weight, ammonia is comparable to other fuel options like methanol and ethanol. Another advantage is that ammonia is easy to store as a liquid. It can be liquefied with moderate pressure (8 bar) at room temperature or by simply cooling it to −33 ℃ at normal pressure. In addition, large-scale ammonia production is already established, with over 150 million tons produced annually in 2019. The high octane rating of ammonia enables it to burn smoothly in engines.

The maritime industry and academia are actively pursuing new technologies to improve the environmental performance of internal combustion engines. The objective is to reduce the environmental impact of maritime transportation without compromising its economic vitality. Numerous investigations have explored the use of dual-fuel engines as a potential solution to this challenge. For instance, Carlucci et al. (2008) modified a single-cylinder diesel engine to implement the dual-fuel mode by injecting compressed natural gas using a customized gas injector. The authors observed that NO_x and CO emissions rely on the pressure and the amount of the pilot fuel injected, whereas unburned hydrocarbon emissions are sensitive mainly to the pilot fuel. Regarding PM emissions, dual-fuel mode significantly outperforms diesel mode. Li et al. (2015) successfully converted a marine diesel engine to run on diesel–LNG by adding a fuel supply and control system. Tests showed that the new system yields a stable operation, reduces fuel consumption by up to 13.4%, and significantly lowers particle matter and NO_x emissions while causing slight increases in carbon monoxide and hydrocarbon emissions. Ritzke et al. (2016) suggested a two-step approach for simulating a four-stroke dual-fuel marine engine. They used a simpler 0D/1D model in AVL Boost software to define the initial and boundary conditions, which were then fed into a more complex 3D CFD model (AVL FIRE) for a more detailed analysis. Benvenuto et al. (2017) created a computer model to simulate a four-stroke marine engine that can operate on either diesel or natural gas. They studied the behavior of the turbocharger system under various fuel types. The model was confirmed accurate using real engine data from the manufacturer under various operating conditions. Stoumpos et al. (2018) conducted a numerical simulation on a Wärtsilä dual-fuel engine (9L50DF) using methane and diesel. The dual-fuel mode is more efficient in terms of engine thermal efficiency at full load, while the diesel mode is more efficient at 75% load. According to this study, dual-fuel combustion reduces NO_x emissions by 85% and CO₂ emissions by 25% compared with conventional diesel mode, as higher temperatures and pressures in diesel combustion contribute majorly to the former. Mavrelos and Theotokatos (2018) conducted a parametric study using low-pressure port injection of LNG into a two-stroke marine diesel engine. Although each department achieves excellent optimizations, finding the overall optimal performance is challenging due to interdepartmental tradeoffs. Theotokatos et al. (2020) developed a GT-ISE model to predict engine behavior under constant and changing load conditions. Their study showed that effective matching of the engine and turbocharger, along with optimal wastegate control, is crucial to prevent compressor stalls when transitioning from gas to diesel fuel. Stoumpos et al. (2020) created a model that simulates the performance of a marine four-stroke dual-fuel engine under changing loads and fuel types. The model accurately depicts the behavior and control systems of the engine. They found that proper turbocharger selection, wastegate design, and fuel control are essential for smooth engine operation. Selmane et al. (2021) built a mathematical model to analyze the effect of common engine settings (compression ratio, turbocharger boost, fuel ratio, and engine speed) on the performance of a marine diesel–hydrogen dual-fuel engine. The model considers the changing gas composition after combustion and temperature dependence of the specific heat of the working fluid. The results showed significant effects of these operating parameters on engine performance. Moreover, most exergy losses (88.2%) occur within the engine due to the inherent irreversibility of mixing and combustion. The remaining components (turbocharger, intercooler, mixer, catalytic converter, and turbine) contribute only 11.2% of the exergy loss of the entire system. Altosole et al. (2021) compared the performance of a marine dual-fuel engine with a new hybrid turbocharger (HTC), which generates electricity, with that of a traditional turbocharger. The alteration caused by the HTC to the compressor does not affect engine performance or exhaust properties. Therefore, the turbocharger type will not impede installing waste heat recovery systems for added efficiency. Frerichs and Eilts (2022) created an accurate combustion model for GT-Power that accurately predicts combustion behavior (ignition, performance, and emissions) across various engine conditions. Yu et al. (2022) simulated a marine engine using natural gas at varying injection timing conditions. Earlier injection (up to 4℃A BTDC) increases power, efficiency, and NO_x emissions while reducing methane emissions. The methane and NO_x emissions can be optimally minimized by around 4°–6℃A BTDC.

Despite the maturity and popularity of natural gas as a primary fuel in dual-fuel engines, it still faces challenges, such as methane slip and cryogenic storage requirements. Therefore, numerous alternative fuels have gained traction as viable substitutes for natural gas as a marine fuel.

Liu et al. (2021) developed a hydrogen–diesel dual injection engine to address the limitations of past hydrogen engines. They altered the diesel engine to inject hydrogen directly into the cylinder. They attained a 50% hydrogen substitution while maintaining efficiency (47%), reducing noise (6 dB), and limiting NO_x emissions (under 11 g/kWh) by fine-tuning diesel and hydrogen injection timings.

Nadimi et al. (2023) experimentally studied the effect of replacing diesel fuel with ammonia on the performance of a dual-fuel engine. The findings indicated that ammonia energy share can reach 84.2%. Furthermore, an increase in thermal efficiency is observed by maximizing diesel substitution. Moreover, energetic share augmentation of ammonia shortens combustion duration and phasing by 6.8° and 32℃A, respectively. However, the nitrogen content in ammonia leads to higher NO_x emissions.

Shen et al. (2023) investigated the effect of varying injection times for methanol in a high-power engine. They tested five injection timings and found that injecting methanol at −180° crank angle with a moderate dose (4.6%– 8.9%) produces the optimal balance of power, knock, and emissions. Emissions are kept in check by maximizing power and minimizing knock simultaneously. Overall, the study demonstrates that optimizing methanol injection significantly improves engine performance.

Wang et al. (2023) explored the implementation of a substance called DTBP in methanol fuel. They found that DTBP helps methanol burn at lower temperatures (around 550 K) by generating additional OH radicals. The effect weakens as the temperature rises and DTBP concentration increases. Their research suggests that DTBP improves methanol combustion at low temperatures.

Li et al. (2023) explored the effect of incorporating low-carbon fuels (hydrogen, methanol, and methane) into n-heptane (simulating diesel) on engine efficiency. Their research indicated that these blends reduce exergy loss and improve efficiency in engines with low temperatures or rich fuel mixtures. This improvement stems from the blends slowing down the energy-wasting reactions of n-heptane, with hydrogen being the most effective. These blends promote more efficient reactions involving radicals, which are particularly beneficial when the engine is cold or has too much fuel. Overall, the study suggests that low-carbon fuels enhance engine efficiency, especially under less-than-ideal combustion conditions.

Müller et al. (2024) assessed the potential of ammonia and hydrogen as energy carriers. They found that ammonia is as efficient as hydrogen, especially for long-term storage. The most efficient way to use ammonia for energy storage involves breaking it down and then using a solid-oxide fuel cell, which achieves a round-trip efficiency of around 28%. This performance is comparable to the best performing hydrogen pathway.

These studies provide valuable insights into the capability of dual-fuel engines to improve the environmental performance of marine transportation. However, thermodynamic analysis of medium-speed marine diesel engines has been largely overlooked in past research, with existing studies often omitting a second-law analysis of internal engine processes. This study fills the gap by examining the thermodynamic aspects of a marine dual-fuel engine. The aim is to assess the effect of various operating parameters on the energetic and exergetic performance of the engine. This study also explores the potential of methanol and ammonia as lower-emission alternatives to LNG in light of increasingly stringent IMO regulations. With fuel prices and availability becoming more unstable, ship owners are increasingly drawn to fuel-flexible engines. These engines can use multiple fuels, which mitigates the effect of price fluctuations and bunkering infrastructure limitations.

2   Methodology

2.1   System description

This work investigates the thermodynamic performance of a medium-speed marine engine. To achieve this goal, a turbocharged and intercooled V12 Wärtsilä 50DF is used as a case study (Figure 1).

Figure  1  Schematic representation of the system

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2.2   Thermodynamic analysis

The first law of thermodynamics facilitates the measurement of energy exchange between a system as heat and work. However, it does not provide insights into the quality or grade of this energy or the various irreversibilities that occur within the system. This study employs exergy analysis as a complementary approach to traditional energy analysis to address these limitations.

For systems under steady-state conditions, mass, energy, and exergy balances can be expressed as follows:

The turbocharger unit consists of two primary components: the charger and the turbine. The charger is installed to forcibly push air into the engine cylinders at a higher pressure (1–2). However, this compression process inherently raises the air temperature, which reduces its density. The air is cooled down to T₃ in the intercooler to counteract this effect (2–3). At this stage, the fuel is injected at low pressure into the airstream close to the inlet valve (3–4–5). The resulting premixed air–fuel mixture is then introduced into the engine cylinder to complete a thermodynamic cycle (5 – 6). The hot exhaust gases exiting the engine at state 6 are expanded in the turbine (6–7). The wastegate vane is used to regulate the work produced by the turbine and match it to the requirements of the charger.

The exergy balance, which is represented by the third equation, introduces the concept of exergy destruction, which is denoted by Ėx_D (kW). It quantifies the total exergy lost due to irreversibilities within the control volume. The magnitude of exergy destruction can be determined using the Gouy–Stodola equation (Kotas, 1985):

The entropy production rate, ΔṠ_prod (kW/K), represents the rate at which entropy is generated during the process between states i+1 and i. The thermal entropy flux, $\sum \frac{\dot{Q}_j}{T_j}$ (kW/K), represents the transfer of entropy to or from the thermal energy reservoirs interacting with the system.

Excluding potential, nuclear, electrical, magnetic, and surface tension effects, the exergy of a stream can be divided into physical and chemical exergies, Ėx^ph (kW) and Ėx^ch (kW), respectively:

The physical or thermo-mechanical exergy can be determined using the following formula:

where h (kJ/kg) and s (kJ/(kg·K)) denote the specific enthalpy and entropy of the working fluid, respectively. The subscript 0 refers to the dead state, which is assumed to have a temperature of 298.15 K and a pressure of 1.013 25 bars.

The chemical exergy contained in the exhaust gases and injected fuel is given by (Moran et al., 2014)

where y_i and y_i^e represent the mole fraction of individual components in the product mixture and the environment, respectively.

For gaseous fuels, the fuel chemical exergy rate, Ėx_f^ch(kW), is given by (Bejan, 2016)

where ṁ_f (kg/s) is the fuel mass flow rate, LHV (kJ/kg) denotes the lower heating value of the fuel, and x and y are the numbers of carbon and hydrogen atoms, respectively.

For liquid fuels, the fuel chemical exergy rate, Ėx^ch_f (kW), is given by (Kotas, 1985)

where α₁, α₂, α₃, and α₄ denote the mass fractions of carbon, hydrogen, oxygen, and sulfur in the fuel, respectively.

2.2.1   Turbocharger compressor

The compressor draws air from the surroundings of the engine to compress it to a pressure higher than its ambient pressure, which is denoted as p₂ (kPa). This compression increases the pressure in the air according to the compressor pressure ratio. Under isentropic conditions, the entropy in the air at the compressor outlet (s_2is) remains unchanged from its inlet entropy (s_1is). This assumption allows for the determination of the actual properties of the air at the compressor outlet, including temperature and enthalpy, using the definition of isentropic efficiency:

By applying energy and exergy balances to the compressor, the work required for air compression and the amount of exergy destructed during the process can be determined using

The mass flow rate of air delivered by the compressor, ṁ_a (kg/s), will be determined in the subsequent sections.

2.2.2   Charge air cooler

The charge air cooler consists of two heat exchangers, HEX1 and HEX2, which are arranged in series. HEX1 is cooled by a high-temperature water circuit (HT), while HEX2 is circulated by a low-temperature water circuit (LT). The temperature difference of the two cooling water circuits, ΔT_{W, HT} (K) and ΔT_{W, LT} (K), is maintained at a constant value of 15 K by adjusting the flow rates.

Assuming negligible pressure losses in the heat exchangers and with known inlet and outlet temperatures for the high-temperature water in the first stage, the intermediate temperature in the heat exchanger can be determined (Cengel, 2003; Lienhard and Lienhard, 2008):

where C (kW/K) denotes the heat capacity rate, the subscript "hot" represents the hot fluid, and C_min is the minimum between C_hot and C_cold. In this case, the cold fluid is freshwater:

The temperature at the exit of HEX1 can be determined by

The exergy destruction rate within the charge air cooler is given as follows:

2.2.3   Mixer

Wärtsilä Corporation employs a low-pressure timed port injection in its four-stroke engines. Fuel is injected through an intake valve at a pressure slightly higher than that of the air charge (Karim, 2015; Latarche, 2021; Wärtsilä, 2019).

The temperature at the mixer outlet can be determined by applying energy balance:

The air–fuel mixing process results in exergy losses due to various irreversibilities within the mixer. The total exergy destruction rate in the mixer can be expressed as

2.2.4   Engine

In this study, a Wärtsilä 12V50DF engine is selected. For gas mode operation, an Otto cycle better represents the behavior of the engine (Latarche, 2021).

When the inlet valves open, the premixed charge is introduced into the engine at a mass flow rate given by (Heywood, 2018)

T₀ (K) and p₀ (kPa) represent the temperature and pressure of the gas before it enters the engine, which is similar to a waiting room. C_d captures the efficiency of the valve opening (discharge coefficient) in gas flows. A_c (m²) signifies the size of the gas passage (valve curtain area). p_T (kPa) simply refers to the pressure of the gas inside the engine cylinder. Finally, γ represents a property of the gas (ratio of specific heats).

The air and fuel mass flow rates can be calculated using the following equations:

where f is the residual gas fraction.

The presence of residual gas at the outset of the compression process causes a temperature rise (Heywood, 2018):

where p_e/p_i denotes the exhaust-to-inlet pressure ratio.

The exergy balance accurately accounts for the losses caused by various irreversibilities. The total exergy destruction rate during the compression process can be calculated using

The compression process is followed by the combustion of the reactants. A small amount of high cetane pilot fuel initiates the combustion, and the flames subsequently spread to the premixed air-primary fuel (Latarche, 2021). This study focuses on determining the thermal energy extracted from the fuel; thus, one-step combustion is sufficient:

The combustion is assumed to be rapid, which keeps the chemical composition of the mixture in equilibrium (Heywood, 2018). Combining the assumptions and the mass balance principle yields a numerically solvable set of non-linear equations (Ferguson and Kirkpatick, 2001).

An engine cooling system is necessary to maintain cylinder temperatures within acceptable limits. The heat transfer through the cylinder walls to the cooling medium can be quantified using Newton's equation of cooling:

where A (m²) stands for the heat transfer area and T_w (K) is cylinder wall temperature.

The convection heat transfer coefficient, h_c (kW/(m²·K)), is calculated using a Hohenberg correlation (Watson and Janota, 1982):

where ω stands for the mean gas velocity, and p_avg (kPa) and T_avg (K) are the gas average pressure and temperature.

Numerical methods based on the following equation determine the highest temperature of the engine at state 3′

where η_comb is the combustion efficiency, and LHV (kJ/kg) is the lower heating value of the fuel.

Exergy destruction in the combustion process is given as

where T_comb (K) is the combustion source temperature.

The expansion stroke starts from state 3′ ends at state 4′. During this process, the working fluid expands, which generates power that exceeds the compression requirements. The final state properties of the expansion process are initially determined assuming isentropic conditions, followed by a second step that considers isentropic efficiency.

Similarly, a portion of the exergy input is destroyed during expansion through entropy production and heat transfer:

At the exhaust gas valve opening, the working fluid at T_4′ (K) and p_4′ (kPa) is significantly higher than its counterparts in the exhaust manifold. As a result, the burned gases expand until they reach state 5′. The temperature and pressure at this state can be determined using the same method as for state 4′. The exergy destruction rate can be written as

The engine indicated power is equal to the difference between the expansion and compression powers:

The indicated efficiency, indicated mean effective pressure, and mean effective pressure are determined as follows:

A portion of the indicated power of the engine is lost due to the movement of mechanical components. This loss is often expressed in terms of friction mean effective pressure "fmep (bar)", which represents the sum of pumping, mechanical rubbing, and auxiliary mean effective pressures. In this study, the Millington and Hartles method (Millington and Hartles, 1968) is used to calculate fmep (bar):

where S_p (m/s) is the mean piston speed.

The brake mean effective pressure is defined as the power output divided by the displaced volume per unit of time. Therefore, the engine brake power can be expressed as

Thus, the brake-specific fuel consumption can be determined using the following equation:

The engine brake efficiency can be written as

Similarly, the exergetic efficiency is defined as the ratio between the brake power and the chemical exergy of the fuel:

As mentioned earlier, each process within the engine contributes to the overall exergy destruction. The total exergy destruction can be calculated as the sum of exergy destruction in each process:

2.2.5   Turbine

The turbine generates power for the attached compressor. In case of power excess, a portion of the exhaust gases bypasses the turbine through a wastegate valve. This valve regulates the fuel–air equivalence ratio in dual-fuel engines. This study explores the application of pulse turbocharging. In Figure 1, the hatched area on the pressure–volume diagram represents the maximum usable energy from the exhaust gases by the turbine using this method.

The maximum power output of the turbine can be calculated using

The rate of exergy destruction in the turbine can then be expressed as

3   Model verification

The reliability of the proposed model is evaluated against data from the manufacturer due to the limited availability of experimental and theoretical research on four-stroke medium-speed marine engines (Wärtsilä, 2019; Wärtsilä, 2016).

As shown in Table 2, the results obtained by the current model align closely with the data of the manufacturer. Across all load conditions, the maximum errors relative to the mean effective pressure, brake-specific consumption, and air mass flow rate are 1.99, 3.77, and 3.17%, respectively. These discrepancies are mostly due to the simplified combustion process and empirical correlations used in this study. However, the utilization of actual manufacturer data plays a crucial role in achieving satisfactory results.

4   Results and discussion

The previously described thermodynamic model is utilized to develop a Fortran program for a comprehensive parametric investigation. This study aims to evaluate the effect of various engine plant operating parameters, including compressor pressure ratio, intercooler (HEX2) exit temperature, compression ratio, and fuel equivalence ratio, on the energy and exergy performance of the system. Table 3 summarizes the program inputs employed throughout this study.

Figure 2 illustrates the effect of the key engine parameters, –namely engine compression ratio, compressor pressure ratio, air receiver temperature (T₃), and equivalence ratio, on engine performance.

Figure  2  Effect of engine parameters on engine performance

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Boosting the engine compression ratio linearly escalates end-compression temperature, which intensifies compression work. Increased compression ratios boost pressure and temperature at combustion, which further increases due to the combustion process itself. Higher peak pressure and temperature allow for extracting more work through an increasingly efficient expansion process. For compression ratios between 4 and 13 (14 for ammonia), the balance shifts toward higher net power output, which leads to improved energetic and exergetic efficiencies and fuel economy. Surpassing the optimal compression ratio causes more power to be spent on compression and heat transfer than is gained from engine expansion, which deteriorates engine performance.

By maintaining a constant air cooler outlet temperature, increasing the compressor pressure ratio enhances the intake of air mass for the engine. This way substantially enhances the volumetric efficiency, which enables the combustion of more fuel with better economy while generating increased thermal energy convertible into mechanical work.

The air charge cooler reduces the inlet air temperature to increase the air mass admitted into the engine. Regulating engine load by controlling the combustion air amount in dual-fuel engines results in less fuel consumption and reduced heat conversion into useful power. Higher engine inlet temperatures decrease energetic and exergetic efficiencies and increase brake-specific fuel consumption.

The equivalence ratio determines engine load at a constant engine speed. Raising the equivalence ratio boosts a higher end-combustion temperature due to increased thermal energy release from the combustion of more fuel. Consequently, with increasing equivalence ratio, power grows while energetic efficiency and brake-specific fuel consumption decrease.

Among methanol, ammonia, and LNG, methanol exhibits superior performance. This behavior stems from the intrinsic thermophysical properties of fuels: the heat of vaporization, lower heating value, stoichiometric air–fuel ratio, and adiabatic temperature. The combination of these properties favors methanol over the other fuels. The liquid injection of methanol and ammonia improves volumetric efficiency compared with the gaseous injection of LNG. Moreover, the latent heat of vaporization absorbs some heat of the reactant charge, which reduces the working fluid volume and allows for more fresh air and fuel to be burned.

Figure 3 depicts the exergy destruction distribution among the internal processes of the engine, namely compression, combustion, expansion, and exhaust blowdown, for the three investigated fuels and various operating parameters.

Figure  3  Exergetic performance mapping of engine internal processes

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Combustion is the dominant source of exergy destruction, which accounts for a significant portion of the overall engine exergy destruction. For methanol at specific conditions (r_c = 12, r_p = 4, T₃ = 318.15 K, and ϕ = 0.5), combustion exergy destruction reaches 81.37% of the total, followed by expansion, compression, and exhaust blowdown at 9.96%, 6.72%, and 1.95%, respectively. This hierarchy stems from the irreversible nature of converting chemical energy into thermal energy through atomic rearrangement during combustion. High temperatures during combustion cause increased entropy production and heat transfer across cylinder walls, which contribute to exergy destruction. This explanation also elucidates why the expansion process is only slightly more exergy destructive than compression and exhaust blowdown. Methanol, as an oxygenated fuel, destroys combustion exergy to the tune of 237.52 kJ/kg. The simple gaseous fuel structure and higher entropy of mixing for methanol result in less exergy destruction during combustion.

Ammonia, with its simple molecular structure and lightweight, ranks second with 261.57 kJ/kg of combustion exergy destruction, followed by LNG at 310.59 kJ/kg. The higher end-combustion temperature of LNG contributes to increased heat transfer and entropy generation during combustion.

The destruction sequence of exergy for non-reactive processes, namely, compression, expansion, and exhaust blowdown, corresponds to that of combustion. The compression exergy destruction rates for methanol, ammonia, and LNG are 19.61, 22.53, and 24.46 kJ/kg, respectively. The behavior of thermodynamic properties (temperature, pressure, and mixture composition) during compression influences exergy destruction. The specific heat ratio γ plays a crucial role in compression exergy destruction. Higher γ values lead to greater compression work, higher end-compression temperatures, and increased exergy destruction.

Similar to compression, the specific heat ratio γ significantly influences exergy destruction during expansion and exhaust blowdown. A higher γ value corresponds to less energy being extracted and more exergy being wasted, as suggested by Equation (25).

Higher compression ratios generate increasing in-cylinder maximum pressures, which potentially reduces combustion exergy destruction. However, at relatively low engine speeds, the benefits of higher compression ratios are offset by increased engine temperatures and the subsequent higher entropy production and heat transfer, which results in increased exergy destruction.

Effective air charge cooling slightly reduces exergy destruction across the engine cycle. At lower inlet temperatures, more air can be admitted to promote increased combustion of fuel and greater exergy input conversion to work. Lowering the cycle initiation temperature reduces subsequent state point temperatures, which minimizes heat transfer through cylinder walls.

Boosting pressure enhances the exergetic performance of all engine internal processes. Increasing pressure raises pressure and temperature. Given that the intercooler controls inlet temperature, any compression ratio increase results in heightened pressure throughout the engine cycle and reduced entropy production. Elevated pressure at the start of expansion improves the potential for extracting useful work, which further minimizes exergy destruction. This section examines the influence of key engine parameters, including engine compression ratio, charger pressure ratio, inlet temperature, and equivalence ratio, on the exergy destruction of the components of the system (Figure 4).

Figure  4  Impact of engine operating parameters on system components

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As expected, the engine is the primary source of exergy destruction, which accounts for 78.77% of the total under reference conditions (compression ratio of 12, pressure ratio of 4, air receiver temperature of 318.15, and equivalence ratio of 0.5 for LNG). The turbine, charger, intercoolers (HEX1 and HEX2), and mixer have efficiencies of 9.95%, 5.75%, 4.27%, and 1.26%, respectively.

The exergy destruction caused by fluid shear and throttling in the charger and turbine exceeds that of the intercooler. The irreversibilities in the latter primarily result from the temperature difference between the air and cooling medium.

The compression ratio does not affect exergy destruction in upstream engine components, as depicted in Figure 4. However, it affects exergy destruction in the engine and turbine in opposite ways. Increasing the compression ratio causes more heat transfer to the cooling fluid and higher exergy destruction due to raised temperatures within the engine. Conversely, the turbine destroys less exergy as the compression ratio increases due to enhanced work extraction.

Exergy destruction in the charger and turbine occurs primarily due to flow restriction and friction. As air pressure increases, flow rates rise, which leads to greater exergy destruction. Each increment in the compressor pressure ratio raises pressures, temperatures, and exergy destruction. For instance, a pressure ratio increase from 2 to 4 results in a 79.63% rise for the compressor and a 54.36% increment for the turbine.

The air charge cooler also exhibits increasing exergy destruction with rising air pressure. This phenomenon stems from increased flow rate, temperature, and pressure. Moreover, the mass flow rate of the cooling fluid increases proportionally with air pressure boosting, which further contributes to exergy destruction. For instance, a pressure ratio increase from 2 to 4 leads to a 79.63% increase for the compressor and a 54.36% enhancement for the turbine.

Following Equation (15), the irreversibilities in reactant mixture preparation increase as the pressure ratio rises, which results in higher air flow rates and more fuel injection. The increased pressure and temperature lead to nearly double exergy destruction in the mixer when the compressor pressure ratio rises from 2 to 4.

Unlike other components, the dual-fuel engine undergoes less exergy destruction due to reduced exergy destruction in its internal processes. Specifically, increasing the pressure ratio from 2 to 4 diminishes engine destruction by 9%.

While keeping other parameters constant, fluctuations in the charge air cooler outlet temperature cause changes in exergy destruction in all system components except for the compressor and HEX1. The exergy destruction of the compressor is unchanged, but HEX2 operates more efficiently under a decreased thermal load.

The mixer slightly increases exergy destruction when exposed to higher air stream temperatures, which is attributed to intensified stream-to-stream heat transfer. The engine, with higher charge air cooler exit temperatures, experiences increased exergy destruction due to elevated temperatures throughout the cycle, which hinders compression and expansion processes.

Exergy destruction in the mixer amplifies with a rising equivalence ratio. This phenomenon is due to higher fuel injection and mixing rates, which leads to greater entropy of mixing and stream-to-stream heat transfer. For instance, increasing the equivalence ratio from 0.5 to 0.7 leads to 74.91% and 42.98% increases in flow rates and entropy of mixing, respectively. Higher equivalence ratio values also result in escalated exhaust gas temperatures and pressures, which augment exergy destruction in the turbine (18.61% increase from ϕ = 0.3 to ϕ = 0.5).

Ammonia exhibits the highest exergy destruction in the mixer, followed by methanol and LNG. This result is attributed to the lower air–fuel ratio and greater fuel quantity required for a given ϕ in ammonia, which lead to more efficient stream-to-stream heat transfer and molecular intermingling.

Methanol demonstrates the lowest exergy destruction in the turbine due to its oxygen content and simple molecular structure. It also benefits from lower entropy of mixing at lower air–fuel ratios.

5   Conclusions

This study developed a detailed thermodynamic model that effectively simulates the operation of a turbocharged and intercooled dual-fuel engine using LNG, methanol, or ammonia. The model accurately predicted engine performance and was validated using data from the manufacturer. The following main points are noted:

1) Performance enhancement in compression reaches a limit with further increases. The optimal ratios for methanol and ammonia are 13 and 14. Further improvements result in unfavorable outcomes.

2) Increasing the fuel–air ratio (richer mixture) and turbocharger pressure enhances engine performance. However, maintaining a cool intake of air is crucial to preserve fuel efficiency.

3) A total of 70.3%–78.8% of energy loss (exergy destruction) occurs within the engine for methanol and LNG. Methanol, with a simpler molecular structure, offers the highest combustion efficiency (least exergy destruction). Methanol has a lower combustion exergy loss of 56.4% than ammonia (62.1%) and LNG (73.8%).

Although this study is theoretical, its conclusions have several practical applications:

1) The study identified an optimal compression ratio for each fuel (13 for methanol and 14 for ammonia). Engine engineers can follow this information to achieve maximum performance.

2) Operators can optimize the compression based on engine adjustments and fuel type.

3) The compressed air should stay dense for optimal combustion. Therefore, engine designers need to incorporate or consider appropriate intercooling systems in their designs.

4) Proper operation of existing intercooling systems is crucial for maintaining air density and achieving optimal combustion.

5) The study suggests that methanol could be a more cost-effective fuel option than ammonia because of its higher combustion efficiency.

6) Ship owners and maritime companies can use these findings to make economical fuel choices for their operations.