Low-Speed Marine Diesel Engine Modeling for NO_x Prediction in Exhaust Gases

Abstract

Knowing the process of generating exhaust emissions and the determination of influential parameters are important factors in improving two-stroke slow-speed marine engines, particularly for further reductions in fuel consumption and stringent regulations on the limitation of nitrogen oxide emissions. In this article, a model of a marine low-speed two-stroke diesel engine has been developed. Experimental and numerical analyses of the nitrogen monoxide formations were carried out. When measuring the concentration of nitrogen oxides in the exhaust emissions, the amount of nitrogen dioxide (NO₂) is usually measured, because nitrogen monoxide is very unstable, and due to the large amount of oxygen in the exhaust gases, it is rapidly converted into nitrogen dioxide and its amount is included in the total emission of nitrogen oxides. In this paper, the most significant parameters for the formation of nitrogen monoxide have been determined. Model validation was performed based on measured combustion pressures, engine power, and concentrations of nitrogen oxides at 50% and 75% of maximum continuous engine load. The possibilities of fuel consumption optimization and reduction in nitrogen monoxide emissions by correcting the injection timing and changing the compression ratio were examined. An engine model was developed, based on measured combustion pressures and scavenging air flow, to be used on board by marine engineers for rapid analyses and determining changes in the concentration of nitrogen oxides in exhaust emissions. The amount of nitrogen oxide in exhaust emissions is influenced by the relevant features described in this paper: fuel injection timing and engine compression ratio. The presented methodology provides a basis for further research about the simultaneous impact of changing the injection timing and compression ratio, exhaust valve opening and closing times, as well as the impact of multiple fuel injection to reduce consumption and maintain exhaust emissions within the permissible limits.

1. Introduction

The impact of exhaust emissions on the environment and air pollution from ships has attracted a great deal of attention in the last few decades, especially from 1995 until today. Due to the properties of the combustion process typical of marine two-stroke slow-speed engines and the use of heavy fuels, merchant fleets release a significant amount of nitrogen oxides, NO_x. Knowledge of the generation, quantity and impact of exhaust emissions on human health and the environment is an important factor in the improvement of marine engines, and thus for the adoption of legislation to limit the emission of harmful substances.

Studies show that emissions of harmful substances from land-based sources are gradually declining, whereas emissions of harmful substances in maritime transport show a steady increase. Emissions of pollutants from ships in international transport in the European Union (Baltic Sea, North Sea, Northeast Atlantic, Mediterranean and Black Sea) in 2000 were estimated at 3.3 million tons of nitrogen oxides (NO_x). The estimated “produced” amount of pollutants for 2020, based on the same maritime transport from 2000, showed an increase of about 40–50%. This means that in 2030, emissions of pollutants from international maritime transport in European waters will reach or even exceed the total amount of pollutants from all land-based sources in all EU Members together (Figure 1).

Nitrogen oxides (NO_x) are the most significant pollutants in exhaust emissions. NO_x is the common name for all nitrogen oxides in exhaust emissions, which are represented by nitrogen monoxide, NO, and nitrogen dioxide, NO₂. In the exhaust emissions of a diesel engine, NO is the most common nitric oxide and makes up more than 70–90% of the total NO_x; nitrogen dioxide (NO₂) makes up 5 to 10% of the volume; and nitrous oxide (N₂O), dinitrogen trioxide (N₂O₃) and dinitrogen pentoxide (N₂O₅) occur in traces. Nitrogen dioxide causes a number of harmful effects on the lungs, such as severe airway inflammation, cough and breathing difficulty, a decrease in lung function, asthma attacks (especially in children), increased likelihood of emergency interventions and hospital treatment, and increased susceptibility to respiratory infections.

Nitrogen dioxide is one of the six most important pollutants in the air because it contributes to the formation of smog, which can have significant impact on human health. The constant increase in maritime traffic density and knowledge about the harmful effects of pollutants on human health and the environment has necessitated the introduction of legislation to limit the emission of harmful substances [2].

On 10 October 2008, Resolution MEPC.176 (58) Amendments to the 1997 Protocol amending the International Convention for the Prevention of Pollution from Ships was adopted. The resolution entered into force on 1 July 2010. One of the main changes, in Rule 13, concerns the progressive reduction in NO_x emissions. The amendment of Annex VI of MARPOL 1973/78 Convention from the point of view of NO_x emissions consists of the introduction of two new tiers in addition to the existing restrictions in force since 19 May 2005, as shown in

Table 1. Different tiers of control apply based on the ship construction date and engine revolution per minutes [4].

Tier	Ship Construction Date on or After	rpm < 130	130 < rpm < 2000	rpm ≥ 2000
I	1 January 2000	17.0 g/kWh	45·n−0.2, e.g., 720 rpm= 12.1 g/kWh	9.8 g/kWh
II	1 January 2011	14.4 g/kWh	44·n−0.23, e.g., 720 rpm = 9.7 g/kWh	7.7 g/kWh
III	1 January 2016 *	3.4 g/kWh	9·n−0.2, e.g., 720 rpm = 2.4 g/kWh	2.0 g/kWh

* Controls apply only to the specified ships while operating in Emission Control Areas (ECAs).

. The table shows that Tier II compared to Tier I requires a reduction in NO_x emissions by about 15%, and Tier III compared to Tier I requires about 80%.

The requirements presented in Table 1 apply to each diesel engine with a power output of more than 130 kW which is installed on every ship constructed, or undergoes a major conversion, on or after 1 January 2000, except when it is proved to the satisfaction of the Maritime Administration that such an engine is an identical replacement for the engine being replaced. The requirements of this item do not apply to an engine which is used solely in response to emergencies on the ship on which the engine is installed [3].

Previous research has shown that the most effective method for reducing the concentration of nitrogen oxides in exhaust emissions from marine two-stroke low-speed marine diesel engine is to subsequently process exhaust gases, change fuel oil injection timings, or to change the compression ratio of the engine as the most effective primary method for reducing the peak combustion pressures, and thus for reducing the peak temperatures, which leads to a decrease in the concentration of nitrogen oxides.

Lamas and Rodriguez [5] concluded that the most effective way to reduce nitrogen oxide exhaust gases emission is to use a selective catalytic reactor (SCR). Nevertheless, for marine engines, exhaust gas recirculation is more acceptable, as is fuel emulsification for operating costs and easier installation.

A mean value engine model (MVEM) of a large two-stroke diesel engine with EGR was investigated by Llamas, X. et al. [6]. A parameterization procedure that deals with the small amount of measurement data available was proposed. After parameterization, the model was shown to accurately capture the stationary operation of the real engine. Models for the ship propeller and resistance were also investigated, showing good agreement with the measured ship sailing signals during maneuvers.

Foteinosa, M.I., made a semi-empirical zero-dimensional three zone scavenging model applicable to two-stroke uniflow scavenged diesel engines and updated it using the results of CFD (computational fluid dynamics) simulations. In this 0D model, the engine cylinders are divided in three zones (thermodynamic control volumes), namely, the pure air zone, mixing zone, and pure exhaust gas zone. The entrainment of air and exhaust gas in the mixing zone is specified by time varying mixing coefficients [7].

A computational fluid dynamics (CFD) analysis was used (Llamas, X., et al. [8]) to simulate the scavenging process in a two-stroke diesel engine with uniflow scavenging. The in-cylinder pressure was successfully compared with experimental measurements, indicating that the proposed CFD approach can simulate the compression/expansion process with a good degree of accuracy. These results provide interesting information to improve two-stroke engines because the scavenging process plays a crucial role in pollution levels, performance, and efficiency.

Lalić, Komar and Nikolić [9] described the process of fuel injection and combustion in marine two-stroke low-speed marine diesel engines, as well as the formation of harmful exhaust emissions as a product of the fuel combustion process, and also described the use of fuel injection timing as a very effective method for lowering combustion temperature and thus the formation of thermal nitric oxide.

In [10], Hountalas, Raptotasios, Antonopoulos and others also studied the onset of fuel injection and its effect on maximum combustion pressure, and thus in a brake specific fuel consumption. They came to the conclusion that correct operation of the fuel injection timing device is essential for the correct operation of two-stroke low-speed marine diesel engines, and thus in the formation of nitrogen monoxide due to the change in maximum combustion temperatures.

Forero, Valencia and Obregon [11] defined their model on combustion pressure and temperature brake-specific fuel consumption, crank shaft speed rotation, injection pressure, compression ratio and environmental conditions in small-volume cylinder engines, showing that the measurement results enable checking the influence of the compression ratio on the heat release rate, finding that the heat release rate increases with increasing the compression ratio.

Serin and Yildizhanin [12] presented their experimental study which investigated the performance and emission characteristics of a variable compression diesel engine when using different types of fuels. Experimental results have shown that increasing the compression ratio improves the engine thermal efficiency and specific fuel consumption, but also causes an increase in NO_x emissions.

Changing the compression ratio of the engine also leads to a reduction in peak pressures and combustion temperatures. The influence of the compression ratio on the concentration of nitrogen oxides in the emission of exhaust gases is described in [13].

The research of this paper is based on the development of a theoretical analytical model based on the recorded indicated pressures on engine acceptance records. A computer simulation model of the marine two-stroke low-speed marine diesel engine was developed, which was then verified and validated on the measured results from the engine acceptance records.

The novelty of this paper is the development of an engine model based on measured combustion pressures to be used on board by marine engineers for fast analyses and determining the changes in the concentration of nitrogen oxides in exhaust emissions. One working cycle of a two-stroke diesel engine is divided into 720 points, i.e., a pressure and temperature change is observed for every 0.5° of the crank angle. Additionally, each small time period of 0.5° of the crank angle was observed as a separate combustion reactor for the formation of nitric oxide. Due to the change in the piston speed, the influence of temperature on the formation of nitric oxide also changes, and greatly influences the formation of nitric monoxide. This model will be used for determining NO_x emissions during the diagnosis and optimization of two-stroke low-speed marine engines.

2. Description of the Simulation Model

A computer program has been written in MS Excel using VBA. At the beginning, it was necessary to enter the engine design characteristics and the values of chemical analysis of the used fuel, in order to calculate the stoichiometric amount of air needed to burn the injected fuel and the value of the heat energy released. By entering the engine design characteristics in the program, the change in cylinder volume according to Equation (1) was determined, and the rate of change of the cylinder volume was calculated with Equation (2).

$$V=\frac{V_s}{2}\left[\frac{2}{\epsilon -1}+\left(1-\cos \alpha \right)+\frac{1}{{\lambda }_m}\left(1-\sqrt{1-{\lambda }_m^2\cdot {\sin }^2\alpha }\right)\right],$$

(1)

where V_S is the cylinder volume, m³; ε is the compression ratio; and λ_m is the ratio of crank radius to the connecting rod length.

$$\frac{\mathrm{d}V}{\mathrm{d}\alpha }=\frac{V_s}{2}\left[\sin \alpha +{\lambda }_m\cdot \frac{\sin \alpha \cdot \cos \alpha }{\sqrt{1-{\lambda }_m^2\cdot {\sin }^2\alpha }}\right],$$

(2)

According to [14], one of the most common ways to obtain the necessary information regarding the work process is to record the pressures of the work cycle. Even in the absence of a calculation of pressure development, the recorded indicator diagram provides important information concerning combustion, such as peak pressure and its position, pressure rise rate, etc.

During changes in the state gas between two consecutive recorded positions of the crankshaft, the combustion of fuel releases a certain amount of chemical energy, dQ_ch. If losses through unsealed places are neglected, the heat is partly transferred to the gas dQ and partly to the combustion chamber surface dQ_wall, and can be written as

$$d{Q}_{ch}=dQ+d{Q}_{wall},$$

(3)

During the high-pressure part of the working cycle, the scavenging ports and the exhaust valve are closed, and the mass flow through the system is very low and can be neglected, provided that the all the sealing components of the cylinder are in good condition. This simplification is based on the fact that pressures are measured depending on the position of the crankshaft. This data set of pressure/angle of the crankshaft position is easily converted into a data set of pressure/cylinder volume. Modern readers of the current position of the crankshaft allow a very small change in the crank angle (Δα), so that pressure and cylinder volume changes are small. It is very convenient to determine the amount of heat released on the basis of the recorded indicator pressures, neglecting the losses, according to Equation (4).

$$\frac{d{Q}_{ch}}{d\alpha }=\frac{\gamma }{\gamma -1}\cdot p\cdot \frac{dV}{d\alpha }+\frac{1}{\gamma -1}\cdot V\cdot \frac{dp}{d\alpha }+\frac{d{Q}_{wall}}{d\alpha },$$

(4)

where p is the engine recorded combustion pressures, bar; V is the cylinder volume, m³; dV is the cylinder volume change, m³/°α; dp is the pressure change, bar/°α; γ is the ratio of specific heat capacities; and dQ_wall is the heat transferred to the combustion chamber surface, J/°α.

The amount of heat energy released from the fuel must be reduced by the value of heat transferred to the walls of the combustion chamber, with the adoption of the value of the heat transfer coefficient according to Woschni. To calculate the amount of heat energy released from the fuel, neglecting the losses through the gaps, it is necessary to adopt the ratio of specific heat capacities, γ, which is a function of the combustion temperature, which can be approximated according to Equation (5) [14].

$$\gamma =1.35-6\cdot {10}^{-5}\cdot T+{10}^{-8}\cdot T^2,$$

(5)

The amount of heat energy released calculated on the basis of recorded indicated pressures was used as a basis for determining the parameters of fuel combustion, with the Vibe function form factors, m, combustion duration, and the amount of burned fuel during the first and second Vibe functions with default parameters of injected fuel mass and fuel net specific energy. The selection of the above parameters, which best describes the heat energy released from the experimentally measured pressure, was determined by means of the determination of the error by the method of least squares.

Model combustion pressure can be ascertained after determinations of the most acceptable parameters of fuel combustion, Vibe function form factors, m, combustion duration and amount of burned fuel during the first and second Vibe function, with given parameters of injected fuel mass and fuel net specific energy and adopted engine specific heat ratio capacity, γ, from Equation (4). Knowing the change in combustion pressures and cylinder volume with the initial temperature, the combustion temperature of the model is determined from the ideal gas equation of state where the mass of products in the cylinder is determined by the sum of delivered air mass and injected fuel and the gas constant of combustion products. During the combustion process, nitrogen oxides are formed only from air that is not used for combustion of fuel. The amount of air delivered to the engine can be read from the engine acceptance record from [12], or from the turbocharger compressor map. The stoichiometric amount of air required to burn one kilogram of fuel was calculated using Equation (6).

$$A_o=\frac{2.67\cdot \hspace{0.17em}c+8\hspace{0.17em}\cdot h+s-o}{0.232}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\frac{{\mathrm{kg}}_{air}}{{\mathrm{kg}}_{fuel}},$$

(6)

where c is the amount of carbon, kg_c/kg_fuel; h is the amount of hydrogen, kg_h/kg_fuel; s is the amount of sulfur, kg_s/kg_fuel; and o is the amount of oxygen, kg_o/kg_fuel.

In the combustion process, a larger amount of air than is stoichiometric must be supplied to the fuel, because it is not possible to supply an ideal amount of air for each particle of fuel and mix them ideally, in order to complete combustion. Today’s modern low-speed, two-stroke, diesel engines operate with an air excess ratio of over three [15,16]. Equation (7) represents the excess air ratio λ_air supplied to the engine for complete combustion and cylinder scavenging. The mass of delivered air is adopted from test bed records.

$${\lambda }_{air}=\frac{m_{air,\hspace{0.17em}d}}{m_{air,\hspace{0.17em}\hspace{0.17em}stoich}},$$

(7)

where m_{air, d} is the mass of delivered air, kg/kWh; and m_{air, stoich} is the mass of air required for stoichiometric combustion, kg/kWh.

Knowing the amount of fuel injected and the amount of air delivered, the remaining amount of air from which nitrogen oxides are formed was calculated. The greatest influence on the rate of nitric oxide formation is the first chemical forward reaction rate coefficient k₁ of the first chemical reaction of the Zeldovich mechanism (25); therefore, the most favorable reaction rate coefficient was adopted as described in Section 3.1.1 for loads of 50% and 75% of MCR. The rate of formation the nitrogen monoxide was calculated according to Equation (33), and the concentration of nitrogen and oxygen is obtained by multiplying the quantitative proportions of oxygen and nitrogen by pressure and dividing by the product of the universal gas constant and temperature. The change in the formation of nitrogen oxides due to the change in the injection timing is achieved by changing the injection start φ and the combustion duration φ_CD of the Vibe function according to Equation (15). Changes in the thickness of the compression shim affect the compression ratio according to Equation (45), and its change affects the air temperature inside the cylinder at the time of fuel injection and the further development of combustion temperatures, and thus, the concentration of nitrogen oxides.

During the working cycle calculation, heat exchange between the gas mixture and the combustion chamber wall must be considered. Heat is transferred to the walls by convection, and during combustion by radiation. The heat transfer in the cylinder is exposed to the piston crown, the inner surface of the cylinder cover and the cylinder liner. The exposure of the cylinder liner to heat transfer depends solely on the position of the piston during the operating cycle. During the operating cycle, in stationary mode, the temperature field on the surfaces of the cylinder elements generally does not change; therefore, the average surface temperature can be accepted [17,18] and the value of heat transfer to the walls of the combustion chamber is calculated according to the following expression:

$$\frac{\mathrm{d}{Q}_{wall}}{\mathrm{d}\alpha }={\alpha }_{wall}\cdot {\displaystyle \sum _{i=1}^n{A}_{wall,i}\left(T_{wall,i}-T_{sp}\right)}\frac{\mathrm{d}t}{\mathrm{d}\alpha },$$

(8)

The total heat transfer surface A_wall is the total combustion chamber surface (cylinder liners, cylinder cover and piston crown), increased by the area between the piston crown and the first compression ring

$$A_{wall}={\displaystyle \sum _i{A}_{wall,i}}+2\cdot d_c\cdot \pi \cdot \frac{h_k}{3},$$

(9)

where A_{wall, i} is the combustion chamber surface, m²; d_c is the cylinder diameter, m; and h_k is the height from the piston crown and the first compression ring, m. The equations for the mean value of the heat transfer coefficient according to Woschni [16,17,18] are as follows:

$${\alpha }_{wall}=130.5\cdot d_c{}^{-0.2}\cdot p_c^{0.8}\cdot T_{{}^c}^{0.53}\cdot w^{0.8},$$

(10)

$$w=C_1\cdot c_m+C_2\cdot \frac{V_s\cdot T_{c,UZ}}{p_{c,UZ}\cdot V_{c,UZ}}\cdot \left(p-p_{mot}\right),$$

(11)

where w is the average velocity of the gas mixture, m/s; d_c is the cylinder diameter, m; p is the cylinder pressure, bar; p_mot is the motoring pressure (cylinder pressure without combustion), bar; c_m = s·n/60 is the mean piston speed, m/s; p_c,UZ, T_c,UZ, V_c,UZ are the pressure, temperature and volume at the time of closing the exhaust valve, respectively; and V_s is the clearance volume, m³.

The constants C₁ and C₂ refer to the change in the velocity of the gas mixture during the cycle, and are expressed in m/sK, where the coefficient c₀ according to the original expression for the Woschni coefficient for the mean value of heat transfer is c₀ = 130. Considering only the coefficient c₀, it became apparent that it needed to be adjusted in order to achieve the most accurate results. The adjustment could be performed when the Woschni heat transfer coefficient was applied for the purpose of estimating the combustion pressure and calculating the heat transfer. For constants C₁ and C₂, the following values apply [15,19] during the working fluid exchange

$$C_1=6.18+0.417\cdot \frac{c_{vr}}{c_m},$$

(12)

during the compression or expansion

$$C_1=2.28+0.308\cdot \frac{c_{vr}}{c_m},$$

(13)

for direct injection diesel engines

$$C_2=0.00324,$$

(14)

where c_vr/c_m is the ratio of the mean vortex flow of a mixture of gases and mean piston speed.

To calculate the high-pressure part of the process, it is necessary to know the flow of energy supply by fuel combustion dQ_ch/d_φ. The parameters of the combustion law can be determined experimentally or approximately according to Vibe [20]. The model includes the combustion of the homogeneous phase and the diffusion phase of combustion, and it is assumed that both phases begin simultaneously. The ignition delay depends directly on the pressure and temperature in the cylinder.

$$\frac{d{x}_g}{d\phi }=C\left(m+1\right)\cdot {\left(\frac{\phi -{\phi }_{ID}}{{\phi }_{CD}}\right)}^m\cdot \exp \left(-C{\left(\frac{\phi -{\phi }_{ID}}{{\phi }_{CD}}\right)}^{m+1}\right),$$

(15)

where m is the Vibe function form factors; φ is the start of fuel injection, °α; φ_ID is the ignition delay, °α; φ_CD is the combustion duration, °α; and where C = 6.901 (for 99.9% of burned fuel) [21,22].

The heat release occurs according to the exponential function, where the Vibe exponent m determines the place of the highest intensity of heat release. Vibe exponent m depends on the operating parameters of the engine, i.e., the ignition delay, the mass of the working medium and the engine speed (Figure 2 and Figure 3).

The combustion flow in a diesel engine with direct injection, with a high combustion rate of the homogeneous phase and relatively slow combustion of the diffusion phase, can be represented more accurately by the so-called double Vibe functions (Figure 4), which, in this case, is shown by the results obtained [22,23].

In the approximate determination of combustion by the double Vibe function, the entire combustion process is divided into two parts. The sum of both parts represents the total combustion flow.

$$x=x_1\left(\phi \right)+x_2\left(\phi \right)=\left\{1-\exp \left[-C{\left(\frac{\phi -{\phi }_{ID}}{{\phi }_{CD}}\right)}^{m_1+1}\right]\right\}+\left\{1-\exp \left[-C{\left(\frac{\phi -{\phi }_{ID}}{{\phi }_{CD}}\right)}^{m_2+1}\right]\right\}$$

(16)

The start of combustion depends on the initiation of the fuel supply by the high-pressure fuel pump, the injection start delays and the fuel ignition delay. Ignition delay in a diesel engine is defined as the time interval (or crankshaft rotation angle) between the start of injection and the start of combustion. The start of the injection is usually the moment when the fuel injector needle is lifted from its seat. Empirical Equation (17) for predicting the duration of the ignition delay φ_ID, developed by Hardenberg and Hase [24], gives the ignition delay expressed in degrees of the crankshaft as a function of temperature and pressure during the ignition delay.

$$\Delta {\phi }_{ID}=\left(0.36+0.22\cdot c_m\right)\hspace{0.17em}\cdot \exp \hspace{0.17em}\left[E_a\left(\frac{1}{R\cdot T}-\frac{1}{17190}\right)\cdot {\left(\frac{2.21}{p-12,4}\right)}^{0.63}\right],$$

(17)

where c_m is the mean piston speed, m/s; and R is the universal gas constant, J/kmolK. The E_a activation energy is obtained from [13]:

$$E_a=\frac{618840}{CN+25},$$

(18)

where CN is the fuel cetane number.

Activation energy decreases with increasing cetane number and vice versa. The amount of heat released calculated on the basis of engine recorded indicator pressures was used as a basis for determining the parameters of starting fuel combustion, Vibe functions form factors m, the duration of combustion and amount of fuel burned during the first and second Vibe functions using the MS Excel Solver function with the specified parameters of the injected fuel mass, and the fuel net specific energy. After determining the most acceptable parameters for initiating fuel combustion, Vibe functions form factors m, combustion duration and amount of burned fuel according to the first and second Vibe functions, with given parameters of injected fuel mass and fuel net specific energy from Equation (2), and adopted specific heat capacity ratio γ of the engine, the combustion pressure of the model can be determined. Knowing the change in combustion pressures and cylinder volume with the initial temperature, the combustion temperature of the model is determined from the gas state equation where the mass of products in the cylinder is determined by the sum of delivered air mass and injected fuel mass, and the gas constant of combustion products [25]:

$$R_{cp}=290.65-0.5\cdot {\lambda }_{air},$$

(19)

where λ_air is the excess air ratio.

The mean indicated pressure is determined by integrating the gas pressure curve in the engine cylinder, where the angle of the crankshaft crank α is expressed in radians according to the expression:

$$p_i=\frac{1}{s}{\displaystyle \underset{x\left({\alpha }_{\min }\right)}{\overset{x\left({\alpha }_{\max }\right)}{\int }}p\left(x\right)}dx=\frac{1}{2}{\displaystyle \underset{{\alpha }_{\min }}{\overset{{\alpha }_{\max }}{\int }}p\left(x\right)\cdot \left(\sin \alpha +\frac{{\lambda }_m}{2}\cdot \frac{\sin 2\alpha }{\sqrt{1-{\lambda }_m^2{\sin }^2\alpha }}\right)}\cdot d\alpha ,$$

(20)

The indicated engine power, for one cylinder, is calculated based on the mean indicated pressure, p_i, and the mean piston speed, v_m, according to the equation

$$P_i=\frac{\pi }{4}\cdot d^2\cdot p_i\cdot c_m\cdot \frac{1}{\tau },$$

(21)

where τ is the number of strokes per engine cycle (for two-stroke cycle τ = 2, for four-stroke cycle τ = 4); d is the cylinder diameter, m; p_i is the mean indicated pressure, bar; and c_m is the mean piston speed, m/s.

The mean effective pressure and the effective power of the engine (for one cylinder) are determined from the mean indicated pressure and the indicated power by means of the mechanical efficiency of the engine η_m according to the equation

$$p_e={\eta }_m\cdot p_i\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em};\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_e={\eta }_m\cdot p_e\hspace{0.17em},$$

(22)

3. Marine Diesel Engines Exhaust Emissions

The main pollutants in the exhaust emissions occur as a direct result of the combustion process in the engine cylinder. The quality of the fuel used, scavenging air delivered, and engine speed play the most important roles in determining the exhaust emission content.

3.1. Nitrogen Oxides

The molecules, atoms and ions react with each other only if they come into contact and every successfully collision leads to the products. All chemical reactions proceed at a certain rate. Chemical kinetics is the science of the rate of chemical reactions and describes the transient states of product formation or decomposition during the combustion process. The main factors influencing the rate of a chemical reaction are the nature of the reactants, the concentration of reactants, temperature, and surface area of solid reactants, radiation and catalysts. Chemical kinetics of the combustion process are very complex. Based on a series of papers, a modern theory of chain reactions has been proposed. The chemical reaction can start by breaking O-O or H-H bonds to generate reactive molecules called “radicals”, which then react with O₂ or H₂ to produce more radicals. The slowest reaction determines the speed of the whole process. Chain termination occurs when radicals react among themselves or when the third bodies are presented [26,27].

An elementary reaction can be described by the following expression: aA + bB → cC + dD.

The rate of reaction progress is given as

$$v\to \hspace{0.17em}=k\to {\left[A\right]}^a\cdot {\left[B\right]}^b,$$

(23)

where k represents a constant of proportionality known as the Arrhenius rate constant. The Arrhenius rate constant, k, is one of the most important relationships in physical chemistry and is represented by the following expression:

$$k=A\cdot T^n\cdot e^{\left(-\hspace{0.17em}\frac{E_a}{R\cdot T}\right)},$$

(24)

where A represents the frequency of collisions of molecules (exponential factor); T is the temperature exponent; and R·T is the average kinetic energy; therefore, the exponent is simply the ratio of the activation energy E_a to the average kinetic energy. This means that high temperature and low activation energy favor larger rate constants, which speed up the reaction. These terms occur in an exponent; therefore, their effects on the rate are quite essential. Nitrogen oxides (NO_x) are highly dependent on the combustion temperature, local oxygen concentration and the combustion duration. Other dependencies include fuel injection timing, scavenging air temperature, mixture quality and fuel quality. Studies show that nitrogen oxides (NO_x) are mostly formed during the diffusion period of combustion, but to a lesser extent during the homogeneous combustion phase. Nitrogen oxides (NO_x) can also cause ozone formation (O₃). Nitrogen monoxide (NO) produced by combustion in an engine cylinder is unstable and easily converted to nitrogen dioxide (NO₂). When measuring the content of nitrogen compounds in exhaust emissions, usually only the content of nitrogen dioxide (NO₂) is measured because nitrogen monoxide is very unstable, and quickly converts into nitrogen dioxide due to the large amount of oxygen in the exhaust gases. Therefore, its amount is adopted as the total emission of all nitrogen compounds. Nitrogen monoxide (NO) can be formed in the combustion process in four different ways [26,28]:

• Thermal NO;
• Prompt NO;
• N₂O route;
• Fuel-bound nitrogen (FBN).

3.1.1. Thermal NO

The kinetic process for nitrogen reactions is generally accepted as a free radical chain reaction. Atomic nitrogen is formed by the Zeldovich free radical chain mechanism. Three reactions are responsible for the formation of nitric oxide. Equations (25) and (26) are based on the Zeldovich mechanism [26,27,28,29,30,31]; a third Equation (27) is included in the mechanism, which is known as extended Zeldovich mechanism (with all three equation):

$$N_2+O\stackrel{k_1}{\to }NO+N\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{k}_1=1.8\cdot {10}^{14}\cdot e^{\left(\frac{-38370}{T}\right)},$$

(25)

$$N+O_2\stackrel{k_2}{\to }NO+O\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{k}_2=1.8\cdot {10}^{10}\cdot T\cdot e^{\left(\frac{-4680}{T}\right)},$$

(26)

$$N+OH\stackrel{k_3}{\to }NO+H\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{k}_3=7.1\cdot {10}^{13}\cdot e^{\left(\frac{-450}{T}\right)},$$

(27)

The reactions of the extended Zeldovich mechanism take place slowly under combustion conditions in a diesel engine when compared to the combustion reactions of hydrocarbons. This behavior is sometimes called kinetical behavior. Consequently, a chemical equilibrium for the concentration of nitrogen oxides will not be obtained under conditions prevailing during combustion in a diesel engine (at local temperatures and local excess air ratio, as well as at short retention times during combustion). The reactions described by Equations (25) and (26) show the formation of nitric oxide in the region of the lean mixture, whereas the reaction shown by Equation (27) shows the formation of nitric oxide in the region of the rich mixture. Equation (25) also determines the reaction rate due to a very high activation temperature. At such high temperatures, a large activation energy occurs, which is necessary for breaking the triple covalent bond in the nitrogen molecule (: N≡N :) Therefore, thermal nitrogen monoxide (NO) is the appropriate name.

Once the nitrogen atom (N) is formed via Equation (25), it is immediately consumed in Equation (26). Equation (27) is important in the rich part of the flame front. We can assume that the nitrogen atom (N) is in the so-called quasi-steady state. The rate of formation of the nitrogen atom is approximately equal to the rate of depletion [26]. The reaction is very slow; therefore, equilibrium is reached later than usual in the part near the front of the flame. From Equations (25)–(27), the reaction rate law is obtained:

$$\frac{d\left[N\right]}{dt}=k_1\left[N_2\right]\left[O\right]-k_2\left[N\right]\left[O_2\right]-k_3\left[N\right]\left[OH\right]\approx 0,$$

(28)

where [N₂] is the molecular nitrogen concentration; [N] is the atomic nitrogen concentration; [O₂] is the molecular oxygen concentration; [O] is the atomic oxygen concentration; and [OH] is the hydroxyl radical concentration.

The nitrogen formed in Equation (25) is converted into nitrogen monoxide (NO) in the second (26) and third reactions (27). The nitrogen atom is in the so-called quasi-steady state, because the concentration of the nitrogen atom (N) remains unchanged. Equation (28) leads to the following expression for the atomic nitrogen (N) concentration:

$$\left[N\right]=\frac{k_1\left[N_2\right]\left[O\right]}{k_2\left[O_2\right]-k_3\left[OH\right]},$$

(29)

From Equations (25)–(27), the expression for the rate of formation of nitrogen monoxide (NO) becomes

$$\frac{d\left[NO\right]}{dt}=k_{1,f}\left[N_2\right]\left[O\right]+k_{2.f}\left[N\right]\left[O_2\right]\cong 2k_{1,f}\left[N_2\right]\left[O\right],$$

(30)

where [NO] is the concentration of nitric oxide molecules; [N₂] is the molecular nitrogen concentration; [O] is the atomic oxygen concentration; and k₁ is the rate constant of Equation (25).

The atomic oxygen concentration [O] can be eliminated from the equilibrium approximation

$$K_p=\frac{{\left[O\right]}^2}{\left[O_2\right]}\cdot \frac{R\cdot T}{p},$$

(31)

which leads to

$$\left[O\right]={\left[\left[O_2\right]\cdot \frac{K_p\cdot p}{R\cdot T}\right]}^{\frac{1}{2}},$$

(32)

and the expression for the rate of formation of nitric oxide (NO) becomes [26,31]

$$\frac{d\left[NO\right]}{dt}=2k_{1,f}\cdot {\left(\frac{K_p\cdot p}{R\cdot T}\right)}^{\frac{1}{2}}\left[N_2\right]{\left[O_2\right]}^{\frac{1}{2}},$$

(33)

Thus, it can be concluded that the reduction in nitrogen monoxide emissions can be obtained by reducing the reaction rate constant, which means by lowering the combustion temperature, and reducing the concentrations of oxygen (O) and nitrogen (N). This is possible if oxygen (O) is used for combustion instead of nitrogen-containing air (N₂). Nitrogen monoxide is formed only at high temperatures (T > 1800 K); therefore, it is assumed that the oxygen radical (O) is in the partial equilibrium state with the oxygen molecule (O₂).

The gas equilibrium constant K_P depends only on temperature and is determined by the equation

$$K_P=e^{\left(\frac{G}{R\cdot T}\right)},$$

(34)

where G is the Gibbs potential at standard pressure, kJ/kmol.

The molecular nitrogen concentration is determined as

$$\left[N_2\right]=x{N}_2\cdot \frac{p}{R\cdot T},$$

(35)

where xN₂ is the mole fraction of nitrogen.

The molecular oxygen concentration can be obtained as

$$\left[O_2\right]=x{O}_2\cdot \frac{p}{R\cdot T},$$

(36)

where xO₂ Gibbs potential mol fraction of oxygen.

The formation of thermal nitric oxide (NO) is very sensitive to the combustion temperature; therefore, the reduction in the maximum flame temperature is the basic mechanism for reducing the amount of nitric oxide (NO) formed. At combustion temperatures above 1800 K and reducing the combustion temperature by about 70 K, the formation of nitrogen monoxide (NO) can be reduced to half the total concentration. As evident in Equation (33), the kinetic coefficient rate k₁ of the first chemical Equation (25) of the Zeldovich mechanism is crucial in the formation of nitric oxide, and it again depends exclusively on the temperature and duration of the reaction.

Today, various suggestions for calculating the first chemical reaction forward rate constants k₁ can be found in the literature [31,32,33,34,35,36,37,38]. Its calculation depends on the type of numerical simulation and the method which is carried out, and the results obtained are comparable to actual measurements on a real diesel engine.

Nevertheless, regardless of which method is applied, they all have in common that the value of the first chemical reaction forward rate constants k₁ is either constant, or a value that depends on the temperature prevailing within the observed volume.

Table 2. Zeldovich mechanism first chemical reaction kinetic coefficient rates.

First Chemical Reaction Forward Rate Constants, mol/cm3s	First Chemical Reaction Backward Rate Constants, mol/cm3s	Reference
$k_{1,f}=6.68\cdot {10}^{12}\cdot T^{0.4}\cdot \exp \left(-\frac{37707}{T}\right)$	$k_{1,b}=3.3\cdot {10}^{12}\cdot T^{0.3}$	[31]
$k_{1,f}=7.6\cdot {10}^{13}\cdot \exp \left(-\frac{38000}{T}\right)$	$k_{1,b}=3.3\cdot {10}^{12}\cdot T^{0.3}$	[32]
$k_{1,f}=7.6\cdot {10}^{13}\cdot \exp \left(-\frac{38000}{T}\right)$	$k_{1,b}=3.2\cdot {10}^7$	[33]
$k_{1,f}=7.6\cdot {10}^{13}\cdot \exp \left(-\frac{38000}{T}\right)$	$k_{1,b}=1.6\cdot {10}^7$	[34]
$k_{1,f}=3.8\cdot {10}^9\cdot T^{1.0}\cdot \exp \left(-\frac{20820}{T}\right)$	$k_{1,b}=3.8\cdot {10}^{13}\cdot \exp \left(-\frac{844}{R\cdot T}\right)$	[35]
$k_{1,f}=1.473\cdot {10}^{13}\cdot \exp \left(-\frac{315000}{R\cdot T}\right)$	$k_{1,b}=3.3\cdot {10}^{12}\cdot T^{0.3}$	[36]
$k_{1,f}=3.0\cdot {10}^{-10}\cdot \exp \left(-\frac{38400}{T}\right)$	/	[37,38]

presents the expressions for calculating the first chemical reaction forward rate constants, k₁, of the first chemical reaction of the Zeldovich mechanism by different authors.

In order to adopt the most favorable first chemical reaction forward rate constants k₁, for use in the model,

Table 3. Nitric oxide emission formation using different kinetic coefficients k₁, _f at 50% MCR [22].

First Chemical Reaction Forward Rate Constants, mol/cm3s	Calculated NO Concentration, mol/rpm	Calculated NOx Concentration, g/kWh	Measured NOx Concentration, g/kWh
$k_{1,f}=6.68\cdot {10}^{12}\cdot T^{0.4}\cdot \exp \left(-\frac{37707}{T}\right)$	0.370183	36.0828	14.47
$k_{1,f}=7.6\cdot {10}^{13}\cdot \exp \left(-\frac{38000}{T}\right)$	8.623153	337.0949
$k_{1,f}=1.82\cdot {10}^{14}\cdot \exp \left(-\frac{76241}{R\cdot T}\right)$	15.974068	624.4557
$k_{1,f}=1.473\cdot {10}^{13}\cdot \exp \left(-\frac{315000}{R\cdot T}\right)$	1.803006	70.4828
$k_{1,f}=3.0\cdot {10}^{-10}\cdot \exp \left(-\frac{38400}{T}\right)$	2.3341·10−11	8.7068·10−10

and

Table 4. Nitric oxide emission formation using different kinetic coefficients k₁, _f at 75% MCR [22].

First Chemical Reaction Forward Rate Constants, mol/cm3s	Calculated NO Concentration, mol/rpm	Calculated NOx Concentration, g/kWh	Measured NOx Concentration, g/kWh
$k_{1,f}=6.68\cdot {10}^{12}\cdot T^{0.4}\cdot \exp \left(-\frac{37707}{T}\right)$	0.231957	6.9402	10.37
$k_{1,f}=7.6\cdot {10}^{13}\cdot \exp \left(-\frac{38000}{T}\right)$	2.134097	63.8531
$k_{1,f}=1.82\cdot {10}^{14}\cdot \exp \left(-\frac{76241}{R\cdot T}\right)$	3.878566	116.0483
$k_{1,f}=1.473\cdot {10}^{13}\cdot \exp \left(-\frac{315000}{R\cdot T}\right)$	0.448852	13.4298
$k_{1,f}=3.0\cdot {10}^{-10}\cdot \exp \left(-\frac{38400}{T}\right)$	1.415·10−11	4.036·10−10

show the formation of nitrogen oxides using the values of k₁ according to Table 2 at 50% and 75% of MCR. Load analysis at 25% and 100% of MCR have been analyzed but not included in this paper because ships very rarely sail at a load of 25% MCR, and hardly ever with 100% MCR. Sources [33,34,35] use the same k₁ and are not repeated in the following tables. Analyzing the data from Table 3 and

Table 5. Fuel oil specification.

Characteristic Values	Unit	ISO-F-DMA
Kinematic viscosity @ 50 °C	mm2/s	2.913
Density	kg/m3	834.3
Net specific energy	kJ/kg	42940
Carbon	m/m	85.86
Hydrogen	m/m	13.78
Sulfur	m/m	0.033
Nitrogen	m/m	0.0019
Oxygen	m/m	0.32
Water	m/m	0.0

, it is necessary to use different rates of the first chemical reaction for the low-pressure and high-pressure combustion part in the engine cylinder. Due to the constant change of pressure and temperature in the cylinder of a two-stroke low-speed diesel engine, it is almost impossible to accurately determine the resulting NO concentration. Therefore, it is necessary to introduce the slow-down coefficient for the kinetic coefficient rate k₁ at 50% and 75% MCR loads, in order to obtain the measured NO_x values from testing engine protocol data. The introduction of the slow-down coefficient would make it possible to predict the change in NO_x emissions due to the changes in the injection timing and the compression ratio. Therefore, the reaction rate change coefficients for k₁ are introduced: 0.894313967 and 0.908851884.

3.1.2. Prompt NO

Nitrogen oxides can be produced very quickly in the flame front, in the presence of hydrocarbon radicals (CH), whereas intermediates are formed in the flame front at a relatively low temperature. Nitrogen oxides formed in this way are called prompt nitrogen oxides, as proposed by Fenimore [26]. Hydrocarbon radicals (CH) react with nitrogen molecules according to the following reaction step:

$$CH+N_2\to HCN+N,$$

(37)

The nitrogen (N) atom obtained from Equation (37) can react with an oxygen molecule (O₂) to form nitrogen monoxide (NO), according to the reaction

$$N+O_2\to NO+N,$$

(38)

Nitrogen (N) reacts with hydrocarbon (CH) radicals to form hydrogen cyanide (HCN), and further hydrogen cyanide (HCN) reacts with nitrogen (N) to eventually form nitrogen monoxide (NO), via a series of steps.

$$HCN+N\to \hspace{0.17em}\cdot \cdot \cdot \to NO,$$

(39)

The activation temperature for Equation (37) is about 9020 K. Unlike thermal mechanisms that have an activation temperature of about 38,000 K (39), the formation of prompt nitrogen monoxide (NO) can be formed at low temperatures of about 1000 K.

3.1.3. N₂O Route

Nitrogen monoxide (NO) produced by the combustion process is unstable and easily converted into nitrogen dioxide (NO₂). With sunlight, where the wavelength of light is λs < 429 nm, nitrogen dioxide (NO₂) is photo-electrically converted back to nitrogen monoxide (NO) and the oxygen radical (O) [28,39,40].

$$N{O}_2\stackrel{h\cdot v}{\to }\hspace{0.17em}\hspace{0.17em}NO+O,$$

(40)

Additionally, the oxygen (O₂) molecule is in partial equilibrium with oxygen radicals at high temperatures, as follows:

$$O_2\leftrightarrow 2O,$$

(41)

Under high pressure, nitrogen (I) oxide (N₂O) formation can occur through the coupling reaction of the three reactants

$$N_2+O+M\to N_{2}O+M,$$

(42)

where M can be any inert molecule.

Due to the nature of the three reactants, the importance of Equation (42) increases with increasing pressure. As soon as nitrous oxide (N₂O) is formed, it reacts with oxygen (O) according to the reaction

$$N_{2}O+O\to NO+NO,$$

(43)

Reaction (43) has an activation temperature of about 11,670 K; therefore, nitric oxide (NO) can be formed at low combustion temperatures of about 1200 K.

3.1.4. Fuel-Bound Nitrogen (FBN)

Nitric oxide (NO) can be produced from fuels, most commonly from solid fuels, and is formed by the oxidation of nitrogen which is chemically bound in a fuel molecule. If such a fuel molecule reaches the flame front, it is converted into cyanide radical compounds, which are partially oxidized to nitrogen monoxide in the part of the flame front (NO) [26].

4. Influential Parameters of the Diesel Engine on the Formation of Nitric Oxide

The concept of reducing the concentration of nitrogen monoxide, and thus nitrogen oxides (NO_x) in order to optimize engine performance, involves changing one or more parameters, such as the fuel injection timing, compression ratio, fuel injection sequence, exhaust valve opening timing, fuel injector design and its nozzles, scavenging air temperature, fuel oil injection pressure, and scavenging air pressure.

Modern electronically controlled diesel engines allow high flexibility to optimize the combustion process in the entire mode of their operation. Some features of electronically controlled diesel engines are also available with conventional engines, but electronically controlled engines allow very high operational flexibility. Electronically controlled engines have several characteristic features such as the control of variable injection timing (VIT), control of the variable exhaust valve closing (VEC), and control of the injection pressure and injection patterns. By controlling the closing of the exhaust valve, it is possible to change the compression pressure, which can also be achieved by changing the thickness of the compression shim below the piston rod. VIT and VEC control enable the interaction of injection timing displacement and compression pressure along the entire engine mode, with maximum combustion pressures at low loads and the avoidance of high combustion pressures at high engine loads [40,41]. Electronically controlled engines enable high injection pressures and thus high-quality fuel injection, even at low engine loads.

These parameters are subject to change in all major licensees to produce marine two-stroke low-speed diesel engines, such as MAN Energy Solutions, Wärtsilä Services Switzerland Ltd. and Mitsubishi Heavy Industries Ltd., in order to meet the provisions of the statutory regulations. In this article, the influence of fuel injection timing and compression ratio on the formation of nitrogen oxides in the two-stroke low-speed diesel engines are considered.

4.1. Influence of Change of Injection Timing on Formation of Nitrogen Oxides

Changing the fuel injection timing can be performed in two ways to adjust the VIT mechanism [41]:

• Individual adjustment on each fuel oil high-pressure pump is enabled separately to equalize the maximum combustion pressures on each engine cylinder (±3 bar), which can be conducted in two ways:
  • By physically moving the position of the servo on each fuel oil high-pressure pump VIT lever;
  • By adjusting the screw connection of the VIT lever between the servo positioner and the lever of the VIT control (such as adjusting the indicated combustion pressure by acting on the lever to regulate the amount of fuel at each high-pressure pump).
• Common adjustment: for the whole engine, this is performed on the pneumatic position sensor unit located on the emergency control panel. Commonly, adjustments are performed if:
  • There is a deviation of fuel quality from the prescribed quality;
  • In case of wear of the high-pressure pump or if there has been a significant change in the fuel net specific energy.

Both methods of regulating the maximum combustion pressure can be applied during engine operation. Figure 5 shows the dependence of pressure and combustion temperature change due fuel injection timing changes.

Before reaching the maximum combustion pressure, the exhaust gases generated by combustion are “compressed” due to the increase in combustion pressure. This lasts until the combustion pressure rises to the maximum value. The combustion gases remain under the influence of the peak combustion temperatures for a relatively long time compared to the total combustion time, which increases the time for the formation of NO_x. At the same time, delaying fuel injection will shorten the combustion duration and consequently decrease maximum pressures and temperatures of most combustion processes. At the same time, delaying fuel injection will shorten the combustion duration and consequently decrease maximum pressures and temperatures of most combustion processes. Due to the later combustion ending and higher heat losses, the specific fuel consumption (BSFC) will be increased in the delayed injection. Soot content will also increase due to poorer combustion and lower combustion temperatures.

4.2. Influence of Change of Compression Ratio on the Formation of Nitrogen Oxides

In marine two-stroke low-speed diesel engines, the compression ratio ε is brought to the desired value by selecting the thickness of the shim below the piston rod, and its value can be calculated according to the expression

$$\epsilon =\frac{V}{V_k}=\frac{V_s+V_k}{V_k},$$

(44)

where V_S is the cylinder displacement volume, m³; V_K is the clearance volume, m³; and V is the cylinder total volume, m³.

Its value is calculated according to the expression depending on the thickness of the shim below the piston rod

$$\epsilon =\frac{V}{V_k\pm \Delta l\cdot {\left(\frac{d}{2}\right)}^2\cdot \pi },$$

(45)

where ε is the compression ratio; Δl is the change in compression shim thickness, mm; and d is the cylinder diameter, m.

Increasing the engine compression ratio improves thermal efficiency because higher power output is achieved. The ideal cycle has a thermal efficiency that increases with increasing compression ratio according to the expression

$${\eta }_t=1-\frac{1}{{\epsilon }^{\gamma -1}},$$

(46)

where γ is the ratio of specific heat capacities at constant pressure c_p and volume c_v, and can be determined by approximation according to Equation (5).

Figure 6 shows the dependence of combustion temperature on the change of compression ratio.

5. Testing, Verification and Validation of the Simulation Model

For the application of the simulation model, a two-stroke slow-speed diesel engine with the following characteristics was selected:

• Process: two-stroke, direct injection;
• Number and engine design: 6, in line;
• Cylinder diameter: 500 mm;
• Stroke: 2214 mm;
• Ignition sequence: 1-5-3-4-2-6;
• Maximum continuous rating MCR: 8680 kW;
• Maximum continuous engine speed: 103 rpm;
• Highest mean effective pressure: 19.4 bar;
• Highest combustion pressure: 184.8 bar;
• Brake-specific fuel consumption BSFC: 170.57 g/kWh @ 100% MCR;
• Compression ratio: 14.3;
• Ratio of crank radius to the connecting rod length: 0.5;
• Exhaust manifold volume: 6.13 m³;
• Scavenging air manifold volume: 7.14 m³;
• Scavenging ports opening angle: 40° before BDC;
• Scavenging ports closing angle: 40° after BDC;
• Exhaust valve opening angle: 60 to 65° before BDC;
• Exhaust valve closing angle: 95 to 100° after BDC.

Engine parameters were measured on an engine test bed, and the engine was tested using ISO-F-DMA diesel fuel, the properties of which are shown in Table 5 [42].

The tests were performed under the following conditions:

• Environmental temperature: 30 °C;
• Atmospheric pressure: 758 mmHg/1011 mbar;
• Relative humidity: 45%.

Table 6. Engine acceptance test data.

Engine Load (MCR)	Unit	50%	75%
Engine indicated power	kW	4759.98	6856.19
Engine effective power	kW	4358.08	6505.20
Mechanical efficiency	-	0.9155	0.9488
Engine speed	rpm	81.90	93.60
Compression pressure	bar	127.10	139.86
Max. combustion pressure	bar	150.32	162.76
Mean indicated pressure	bar	13.37	16.85
Fuel oil consumption	g/kWh	163.45	164.21
NOx (as NO2)	g/kWh	14.47	10.37

shows the measured values for the selected engine at stationary load at 50% and 75% of MCR [42].

According to the results of measurements of nitrogen oxides NO_x, the engine met the IMO regulations on NO_x emissions, tier II, 14.4 g/kWh.

Table 7. Simulation model data [22].

Engine Load (MCR)	Unit	50%	75%
Engine indicated power	kW	4747.29	6851.72
Engine effective power	kW	4347.95	6500.95
Mechanical efficiency	-	81.90	93.60
Engine speed	rpm	81.90	93.60
Compression pressure	bar	127.10	139.86
Max. combustion pressure	bar	150.32	162.76
Mean indicated pressure	bar	13.34	16.84
Fuel oil consumption	g/kWh	163.44	164.21
NOx (as NO2)	g/kWh	14.47	10.37

shows the parameters obtained on the simulation model.

Engine acceptance test data provided by the manufacturer were compared to simulation model data, and the deviations are shown in

Table 8. Model data deviations from engine acceptance test data [22].

Engine Load (MCR)	Unit	50%	75%
Engine indicated power	kW	−0.266	−0.065
Engine effective power	kW	−0.232	−0.065
Mechanical efficiency	-	0	0
Engine speed	rpm	0	0
Compression pressure	bar	0	0
Max. combustion pressure	bar	−0.224	−0.059
Mean indicated pressure	bar	0	0
Fuel oil consumption	g/kWh	0	0
NOx (as NO2)	g/kWh	0	0

.

The validity of the model was tested for stationary load at 50% and 75% of MCR. Table 8 and

Table 9. Parameters and NO_x emission changes due to changes in fuel injection timing at 50% MCR [22].

Δφ [°CA]	ΔφID [°CA]	pinj [bar]	Tinj [K]	Pi [kW]	pmax [bar]	Tmax [K]	BSFC [g/kWh]	NOx [g/kWh]
−2.0	1.9641	125.28	1095.62	5145.28	152.82	1562.93	150.86	17.82
−1.5	1.9606	126.06	1099.54	5008.06	151.72	1552.44	154.99	16.98
−1.0	1.9578	126.68	1102.79	4915.43	151.27	1546.68	157.92	16.18
−0.5	1.9564	127.01	1104.35	4818.40	150.86	1540.47	161.10	15.33
0.0	1.9560	127.10	1104.76	4749.27	150.32	1537.13	163.44	14.47
+0.5	1.9563	127.01	1104.35	4637.06	149.27	1535.87	167.39	13.92
+1.0	1.9578	126.68	1102.78	4494.04	147.62	1535.24	172.72	13.12
+1.5	1.9606	126.06	1099.53	4332.25	145.33	1534.76	179.17	12.42
+2.0	1.9641	125.28	1095.62	4157.95	142.98	1533.81	186.68	11.85

show minimal deviations between the measured values and those obtained by simulation on the model at 50% and 75% load, which indicates the usability of the model.

6. Analysis of the Influence of the Injection Timing Change on the Formation of Nitrogen Oxides

The formation of NOx largely depends on the combustion temperature, the duration of the peak combustion temperatures and the mass of the excess air. Fuel injection timing is a function of the angle of the crankshaft at which combustion starts. The change in the state of the air in the engine cylinder, into which the fuel is injected, changes because the starting point of the fuel injection also changes, and thus the ignition delay of the mixture also changes. If the fuel injection starts earlier, the initial temperature and air pressure in the cylinder are lower; thus, the ignition delay of the mixture will be prolonged. If the fuel injection starts later, the temperature and air pressure in the cylinder are initially higher; thus, the ignition delay of the mixture will be reduced. If the injection time is delayed until beyond the top dead center, the ignition delay time is extended again, due to the reductions in pressure and temperature in the engine cylinder. This means that changing the starting point of fuel injection has a strong effect on the ignition delay, and thus on the fuel combustion process in the engine cylinder and on NO_x emissions due to the changes in maximum pressure and temperature in the engine cylinder. Table 9 and

Table 10. Parameters and NO_x emission changes due to changes in fuel injection timing at 75% MCR [22].

Δφ [°CA]	ΔφID [°CA]	pinj [bar]	Tinj [K]	Pi [kW]	pmax [bar]	Tmax [K]	BSFC [g/kWh]	NOx [g/kWh]
−2.0	2.2272	137.14	1001.18	7126.25	167.93	1469.54	157.88	13.63
−1.5	2.2226	137.99	1005.38	7056.66	166.72	1468.57	159.44	12.46
−1.0	2.2178	138.80	1009.98	6978.96	165.45	1467.68	161.22	11.67
−0.5	2.2163	139.57	1010.12	6902.66	164.08	1466.86	163.00	10.97
0.0	2.2148	139.61	1012.06	6851.72	162.76	1466.11	164.21	10.37
+0.5	2.2163	139.57	1010.12	6731.02	161.23	1465.37	167.15	9.61
+1.0	2.2178	138.80	1009.98	6655.61	159.56	1464.68	169.05	8.68
+1.5	2.2226	137.99	1005.38	6612.81	157.79	1463.69	170.14	7.84
+2.0	2.2272	137.14	1001.18	6565.15	155.58	1462.75	171.38	7.12

and Figure 7, Figure 8, Figure 9 and Figure 10 show the firm dependence of the change of the fuel injection timing on the duration of the ignition delay and the values of the parameters of peak pressures, temperatures and heat released, and thus on nitrogen oxide emission concentrations.

Table 9 and Table 10 present the following values: Δφ—start of injection, °α; Δφ_ID—ignition delay, °α; p_inj—pressure at the time of injection, bar; T_inj—temperature at the time of fuel injection, K; P_i—indicated engine power, kW; p_max—maximum combustion pressure, bar; T_max—maximum combustion temperature, K; BSFC—brake specific fuel consumption, g/kWh; and NO_x—nitrogen oxide emission concentration, g/kWh.

Analyzing the change in the fuel injection timing at 50% and 75% of the MCR, a change in the indicated power, brake-specific fuel consumption and nitrogen oxide emissions is observed, in relation to the actual injection timing, i.e., 0° CA. If the fuel injection timing changes by a negative value (earlier injection), an increase in the indicated power and increases in nitrogen oxide emissions are observed.

Figure 7 and Figure 8 shows that at the maximum change of the injection timing of −2.0° CA at 50% of the MCR, there is an increase in the indicated power by 8.3%, and in the emission of nitrogen oxides by 23.1%. In contrast, if the timing of fuel injection is changed by a positive value (later injection), the indicated power is reduced, and the emission of nitrogen oxides is reduced. At the maximum change of +2.0° CA, the indicated power is reduced by 12.5% and the emission of nitrogen oxides is reduced by 18.1%.

Figure 9 and Figure 10 show that at the maximum change of the injection timing of −2.0° CA at 75% of the MCR, there is an increase in the indicated power by 3.9%, and in the emission of nitrogen oxides by 23.9%. In contrast, if the injection timing is changed by a positive value (later injection), the indicated power is reduced, and the emission of nitrogen oxides is reduced. At the maximum change of +2.0° CA, there is a reduction in the indicated power by 4.2% and in the emission of nitrogen oxides by 31.3%.

7. Analysis of the Influence of the Change in the Compression Rate on the Formation of Nitrogen Oxides

The effect of changing the compression ratio has a great impact on engine performance, NO_x emissions and combustion parameters. Analysis of the change of compression ratio from 13.55 to 15.15 was performed by changing the thickness of the compression shim from −10 mm to +10 mm in steps of 2 mm at engine loads of 50% and 75% of MCR. The results presented in

Table 11. Engine parameters and NO_x emission changes due to changes in the compression ratio at 50% MCR [22].

Δl [mm]	ε [[–]	ΔφID [°CA]	pinj [bar]	Tinj [K]	Pi [kW]	pmax [bar]	Tmax [K]	BSFC [g/kWh]	NOx [g/kWh]
−10.0	13.55	1.9968	116.01	1069.76	4421.50	138.66	1484.65	175.57	5.93
−8.0	13.69	1.9874	118.23	1077.68	4487.26	141.00	1496.02	173.00	7.23
−6.0	13.84	1.9786	120.45	1085.14	4552.95	143.33	1507.03	170.50	8.72
−4.0	13.99	1.9705	122.67	1092.14	4618.57	145.66	1517.55	168.08	10.42
−2.0	14.14	1.9630	124.88	1098.68	4684.12	147.99	1527.58	165.73	12.34
0.0	14.30	1.9560	127.10	1104.76	4749.61	150.32	1537.13	163.44	14.47
+2.0	14.46	1.9495	129.32	1110.38	4815.01	152.64	1546.21	161.22	16.82
+4.0	14.63	1.9434	131.54	1115.54	4880.36	154.96	1554.80	159.06	19.39
+6.0	14.80	1.9379	133.76	1120.24	4945.63	157.28	1562.91	156.96	22.17
+8.0	14.97	1.9327	135.97	1124.49	5010.84	159.59	1570.55	154.92	25.15
+10.0	15.15	1.9279	138.19	1128.27	5075.99	161.90	1577.71	152.93	28.53

and

Table 12. Engine parameters and NO_x emission changes due to changes in the compression ratio at 75% MCR [22].

Δl [mm]	ε [[–]	ΔφID [°KV]	pinj [bar]	Tinj [K]	Pi [kW]	pmax [bar]	Tmax [K]	BSFC [g/kWh]	NOx [g/kWh]
−10.0	13.55	2.3141	122.14	937.92	6444.91	151.61	1426.18	169.38	4.62
−8.0	13.69	2.2902	125.68	953.97	6485.63	153.84	1434.88	168.32	5.52
−6.0	13.84	2.2685	129.23	969.41	6526.28	156.08	1443.23	167.27	6.54
−4.0	13.99	2.2488	132.77	984.24	6566.86	158.31	1451.21	166.23	7.69
−2.0	14.14	2.2308	136.31	998.45	6607.37	160.53	1458.84	165.21	8.96
0.0	14.30	2.2143	139.86	1012.06	6647.80	162.76	1466.11	164.21	10.37
+2.0	14.46	2.1993	143.40	1025.05	6688.17	164.98	1473.01	163.22	11.91
+4.0	14.63	2.1856	146.95	1037.43	6728.46	167.21	1479.55	162.24	13.58
+6.0	14.80	2.1729	150.49	1049.20	6768.69	169.42	1485.74	161.28	15.39
+8.0	14.97	2.1614	154.03	1060.36	6808.85	171.64	1491.57	160.33	17.31
+10.0	15.15	2.1507	157.58	1070.90	6848.95	173.86	1497.20	159.39	19.36

show changes in the compression ratio due to change in compression shim thickness, and increasing the compression ratio improves performance characteristics such as indicated power, thermal efficiency, and specific fuel consumption at all engine operating loads. The tables show the following values: Δl—change in the thickness of the compression shim, mm; ε—compression ratio; Δφ_ID—ignition delay, °α; p_inj—pressure at the time of injection, bar; T_inj - temperature at the time of fuel injection, K; P_i—indicated engine power, kW; p_max—maximum combustion pressure, bar; T_max—maximum combustion temperature, K; BSFC—brake-specific fuel consumption, g/Wh; and NO_x—nitrogen oxide emission concentration, g/kWh.

However, an increase in the compression ratio causes an increase in NO_x emissions. In contrast, reducing the compression ratio worsens performance in all engine loads but causes a reduction in NO_x emissions. Analyzing the change in the thickness of the compression shim at 50% of the MCR, changes in the indicated power, ignition delay, combustion pressures, combustion temperature, specific fuel consumption, and nitrogen oxide emissions are observed, compared to the installed compression shim of 20 mm thickness.

Changes in motor parameters at a load of 50% MCR are presented in Table 11. To maximize the thickness of the compression shim at 50% of the MCR, the indicated power is reduced by 6.9% and the emission of nitrogen oxides by 59.0%. In contrast, the maximum increase in the thickness of the compression shim leads to an increase in the indicated power by 6.9%, and in the emission of nitrogen oxides by 97.2%.

Figure 11 and Figure 12 graphically present the dependences of the compression pressure, combustion pressure and emission of nitrogen oxides due to changes in the compression ratio and thickness of the compression shim at an engine load at 50% of MCR.

Changing the thickness of the compression shim at an engine load of 75% MCR, the indicated power, ignition delay, combustion pressures, combustion temperatures, specific fuel consumption, and nitrogen oxide emissions change in relation to the installed 20 mm thick compression shim. Engine parameter changes at a load of 75% MCR are presented in Table 12. For the maximum reduction in the thickness of the compression shim at 75% of the MCR, there is a reduction in the indicated power by 3.1%, and in the emission of nitrogen oxides by 55.4%. In contrast, the maximum increase in the thickness of the compression shim leads to an increase in the indicated power by 3.1%, and the emission of nitrogen oxides by 86.7%.

Figure 13 and Figure 14 graphically present the dependences of the compression pressure, combustion and emission of nitrogen oxides on changes in the compression ratio and in the thickness of the compression shim at an engine load of 75% MCR. The conducted research shows that the examined engine meets the Tier II IMO emission regulations, which is 14.4 g/kWh of nitrogen oxides. At certain loads, we could meet the regulations by reducing fuel consumption, by changing the angle of injection and changing the thickness of the compression shim. Values for Tier III IMO emission regulations were not achieved with a change in the injection timing or a change in the compression ratio.

8. Conclusions

To model the process of two-stroke low-speed marine diesel engines for the purpose of predicting the NOx content in exhaust gases, a zero-dimensional model was developed in this paper. With the necessary changes in the geometric dimensions of the engine, the type of fuel and the introduction of appropriate parameters, the simulation model can be applied to any propulsion system with a turbocharged two-stroke slow-speed diesel engine. Using this application for modeling the working process of a two-stroke slow-speed diesel engine, by analyzing the indicator diagram of a marine two-stroke internal combustion engine, it is possible to obtain values of the working process of the engine that are otherwise difficult to measure.

In the usage of the developed application for modeling the process of slow-speed marine diesel engines in order to predict the share of NO_x in exhaust emissions, features relevant to the diagnosis of engine operation and analysis of the causes of increases or decreases in NO_x formation were obtained. Relevant features are the combustion pressure, engine cylinder temperature, engine cylinder pressure rise rate, heat used, heat losses, combustion rate, excess air ratio and type of fuel used.

Model validation was performed for stationary loads of 50% and 75% of the MCR.

The simulation model shows that the greatest influences on the nitrogen oxides, NOx, are the peak combustion temperatures and the duration of combustion, either caused by a change in the angle of fuel injection or a change in the compression ratio.

When changing the fuel injection timing at 75% of the MCR, the engine load, which is closest to the optimal engine load point of 67% of the MCR, there is a change in the indicated power, specific fuel consumption and nitrogen oxide emissions relative to the actual injection timing, corresponding to 0° CA. Changing the injection timing of −2.0° CA, an increase in the indicated power by 3.9%, and an increase in nitrogen oxide emissions by 23.9%, with a decrease in specific fuel consumption by 3.9% are observed. When changing the injection timing for +2.0° CA, a decrease in the indicated power by 4.2%, and a decrease in the emission of nitrogen oxides by 31.3%, an increase in the specific fuel consumption by 4.7% are noticed.

Analysis of the change in compression ratio from 13.55 to 15.15 was performed. It has been shown that if the thickness of the compression shim changes by −2 mm, the indicated power decreases by 0.6%, increasing the ignition delay by 0.7%. Maximum combustion pressures are reduced by 1.4%, and combustion temperature by 0.5%. Nitrogen oxide emissions are reduced by 13.6%. Due to the reduction in the indicated power, the specific fuel consumption also increases by 0.6%. If the thickness of the compression shim is changed by +2 mm, the indicated power is increased by 0.6% and the ignition delay is reduced by 0.7%. Maximum combustion pressures increase by 1.6% and combustion temperatures increase by 0.5%, resulting in nitrogen oxide emissions increasing by 14.8%. The specific fuel consumption decreases by 0.6%. From this research, it can be concluded that the thickness of the compression shim has to be changed by +0.5 mm, and changing the injection time by +1.0° CA will reduce fuel consumption and decrease NO_x.

The presented methodology provides a suitable basis for further, more complex research, and a proposal for further research would be to extend the model to the simultaneous impact of changing the injection timing and compression ratio, exhaust valve opening and closing times, as well as the impact of multiple fuel injection to reduce consumption and maintain exhaust emissions within the permissible limits. The determination of NO formation based on the adiabatic flame temperature and the approach presented in this paper could also be compared. The model may include other harmful emissions (carbon monoxide, particular meters, and sulfur oxides) in further phases of development.