#
Low-Speed Marine Diesel Engine Modeling for NO_{x} Prediction in Exhaust Gases

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## Abstract

**:**

_{2}) 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

_{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.

_{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).

_{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, NO

_{2}. 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 (NO

_{2}) makes up 5 to 10% of the volume; and nitrous oxide (N

_{2}O), dinitrogen trioxide (N

_{2}O

_{3}) and dinitrogen pentoxide (N

_{2}O

_{5}) 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.

_{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. 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%.

_{x}emissions.

_{x}emissions during the diagnosis and optimization of two-stroke low-speed marine engines.

## 2. Description of the Simulation Model

_{S}is the cylinder volume, m

^{3}; ε is the compression ratio; and λ

_{m}is the ratio of crank radius to the connecting rod length.

_{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

^{3}; dV is the cylinder volume change, m

^{3}/°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.

_{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}.

_{air}supplied to the engine for complete combustion and cylinder scavenging. The mass of delivered air is adopted from test bed records.

_{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.

_{1}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.

_{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

_{wall, i}is the combustion chamber surface, m

^{2}; 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:

_{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, m

^{3}.

_{1}and C

_{2}refer to the change in the velocity of the gas mixture during the cycle, and are expressed in m/sK, where the coefficient c

_{0}according to the original expression for the Woschni coefficient for the mean value of heat transfer is c

_{0}= 130. Considering only the coefficient c

_{0}, 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 C

_{1}and C

_{2}, the following values apply [15,19] during the working fluid exchange

_{v}

_{r}/c

_{m}is the ratio of the mean vortex flow of a mixture of gases and mean piston speed.

_{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.

_{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].

_{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.

_{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]:

_{air}is the excess air ratio.

_{i}, and the mean piston speed, v

_{m}, according to the equation

_{i}is the mean indicated pressure, bar; and c

_{m}is the mean piston speed, m/s.

_{m}according to the equation

## 3. Marine Diesel Engines Exhaust Emissions

#### 3.1. Nitrogen Oxides

_{2}or H

_{2}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].

_{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 (O

_{3}). Nitrogen monoxide (NO) produced by combustion in an engine cylinder is unstable and easily converted to nitrogen dioxide (NO

_{2}). When measuring the content of nitrogen compounds in exhaust emissions, usually only the content of nitrogen dioxide (NO

_{2}) 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;
- N
_{2}O route; - Fuel-bound nitrogen (FBN).

#### 3.1.1. Thermal NO

_{2}] is the molecular nitrogen concentration; [N] is the atomic nitrogen concentration; [O

_{2}] is the molecular oxygen concentration; [O] is the atomic oxygen concentration; and [OH] is the hydroxyl radical concentration.

_{2}] is the molecular nitrogen concentration; [O] is the atomic oxygen concentration; and k

_{1}is the rate constant of Equation (25).

_{2}). 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 (O

_{2}).

_{P}depends only on temperature and is determined by the equation

_{2}is the mole fraction of nitrogen.

_{2}Gibbs potential mol fraction of oxygen.

_{1}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.

_{1}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.

_{1}is either constant, or a value that depends on the temperature prevailing within the observed volume. Table 2 presents the expressions for calculating the first chemical reaction forward rate constants, k

_{1}, of the first chemical reaction of the Zeldovich mechanism by different authors.

_{1}, for use in the model, Table 3 and Table 4 show the formation of nitrogen oxides using the values of k

_{1}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 k

_{1}and are not repeated in the following tables. Analyzing the data from Table 3 and Table 5, 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 k

_{1}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 k

_{1}are introduced: 0.894313967 and 0.908851884.

#### 3.1.2. Prompt NO

_{2}) to form nitrogen monoxide (NO), according to the reaction

#### 3.1.3. N_{2}O Route

_{2}). With sunlight, where the wavelength of light is λs < 429 nm, nitrogen dioxide (NO

_{2}) is photo-electrically converted back to nitrogen monoxide (NO) and the oxygen radical (O) [28,39,40].

_{2}) molecule is in partial equilibrium with oxygen radicals at high temperatures, as follows:

_{2}O) formation can occur through the coupling reaction of the three reactants

_{2}O) is formed, it reacts with oxygen (O) according to the reaction

#### 3.1.4. Fuel-Bound Nitrogen (FBN)

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

_{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.

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

- 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.

_{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

_{S}is the cylinder displacement volume, m

^{3}; V

_{K}is the clearance volume, m

^{3}; and V is the cylinder total volume, m

^{3}.

_{p}and volume c

_{v}, and can be determined by approximation according to Equation (5).

## 5. Testing, Verification and Validation of the Simulation Model

- 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 m
^{3}; - Scavenging air manifold volume: 7.14 m
^{3}; - 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.

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

_{x}, the engine met the IMO regulations on NO

_{x}emissions, tier II, 14.4 g/kWh.

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

_{x}emissions due to the changes in maximum pressure and temperature in the engine cylinder. Table 9 and Table 10 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.

_{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.

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

_{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 and Table 12 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.

_{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.

## 8. Conclusions

_{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.

_{x}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BDCCFD | Bottom Dead leftComputational Fluid Dynamics |

DMAEGR | Distillate Marine Fuel, Grade AExhaust Gases Recirculation |

EU | European Union |

F | Fuel |

FBN | Fuel-Bound Nitrogen |

IMO | International Maritime Organization |

ISO | International Organization for Standardization |

MAN | Maschinenfabrik Augsburg Nürnberg |

MARPOL | International Convention for the Prevention of Pollution from |

MCR | Maximum Continuous Rating |

MEPC | Marine Environment Protection Committee |

MSSCR | MicrosoftSelective Catalytic Reactor |

SEU27 | Emissions from land-based sources (incl. domestic shipping) |

TSAP | Target in line with the EU’s Thematic Strategy on Air Pollution |

VBA | Visual Basic for Application |

VEC | Variable Exhaust Valve Closing |

VIT | Variable Injection Timing |

Latin Symbols | |

A | Frequency of collisions of molecules |

A_{0} | Stoichiometric amount of air, kg_{air}/kg_{fuel} |

A_{wall} | Total combustion chamber surface, m^{2} |

BSFC | Brake Specific Fuel Consumption, g/kWh |

C_{1} | Constant in Equation (11), m/sK |

C_{2} | Constant in Equation (11), m/sK |

CA | Crank Angle, ° |

c_{m} | Mean piston speed, m/s |

CN | Fuel cetane number |

c_{vm} | Mean piston speed, m/s |

c_{vr} | Mean gases speed, m/s |

d_{c} | Cylinder diameter, m |

dp | Cylinder pressure change, bar/°α |

dQ | Heat transferred to the gas, J/°α |

dQ_{ch} | Amount of chemical energy, J/°α |

dQ_{wall} | Heat transferred to the chamber surface, J/°α |

dV | Cylinder volume change, m^{3}/°α |

E_{a} | Activation energy, J/kmolK |

G | Gibbs potential at standard pressure, kJ/kmol |

h | Amount of hydrogen, kg_{h}/kg_{fuel} |

h_{k} | Height from the piston crown and the first compression ring, m |

k | Arrhenius rate constant |

k_{1} | Rate constant of the first Zeldovich reaction |

k_{2} | Rate constant of the second Zeldovich reaction |

k_{3} | Rate constant of the third Zeldovich reaction |

K_{p} | Equilibrium constant |

m | Vibe function form factor |

m_{air, d} | Mass of delivered air, kg/kWh |

m_{air, stoich} | Mass of air required for stoichiometric combustion, kg/kWh |

N_{2}O | Nitrous oxide |

N_{2}O_{3} | Dinitrogen trioxide |

N_{2}O_{5} | Dinitrogen pentoxide |

NO | Nitrogen monoxide |

NO_{2} | Nitrogen dioxide |

NO_{x} | Nitrogen oxide emission concentration, g/kWh |

o | Amount of oxygen, kg_{o}/kg_{fuel} |

O_{3} | Ozone |

p | Combustion pressures, bar |

p_{c,UZ} | Pressure at the time of closing the exhaust valve, bar |

P_{e} | Effective engine power, kW |

p_{e} | Mean effective pressure, bar |

P_{i} | Indicated engine power, kW |

p_{i} | Mean indicated pressure, bar |

p_{inj} | Pressure at the time of injection, bar |

p_{max} | Maximum combustion pressure, bar |

p_{mot} | Motoring pressure (cylinder pressure without combustion), bar |

R | Universal gas constant, J/kmolK |

R_{cp} | Gas constant of combustion products |

ROHR | Rate of Heat Release, MJ |

rpm | Revolution Per Minutes, min^{−1} |

s | Amount of sulfur, kg_{s}/kg_{fuel} |

T | Temperature, K |

T_{c,UZ} | Temperature at the time of closing the exhaust valve, K |

T_{in}j | Temperature at the time of fuel injection, K |

T_{max} | Maximum combustion temperature, K |

V | Cylinder volume, m^{3} |

v | Rate of reaction progress |

V_{c,UZ} | Cylinder volume at the time of closing the exhaust valve, m^{3} |

V_{K} | Cylinder clearance volume, m^{3} |

V_{s} | Clearance volume, m^{3} |

V_{S} | Cylinder displacement volume, m^{3} |

xN_{2} | Mole fraction of nitrogen |

xO_{2} | Mole fraction of oxygen |

Greek symbols | |

α_{wall} | Heat transfer coefficient |

γ | Ratio of specific heat capacities at constant pressure and volume |

Δl | Change in compression shim thickness, mm |

ε | Compression ratio |

η_{m} | Mechanical efficiency |

λ_{ai} | Excess air ratio |

λ_{m} | Ratio of crank radius to the connecting rod length |

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**Figure 1.**Emissions of NO

_{x}from 2000 to 2030 (tons) [1]. SEU27 = Emissions from land-based sources (incl. domestic shipping): Sea—emissions from international shipping in European sea areas; TSAP—target in line with the EU’s Thematic Strategy on Air Pollution; IMO—expected outcome from implementing the revised IMO MARPOL Annex VI.

**Figure 5.**Dependence of pressure and combustion temperature changes due fuel injection timing changes [22].

**Figure 6.**Dependence of combustion temperature on the change of compression ratio [22].

**Figure 7.**Pressure and heat release changes due injection timing changes at 50% MCR [22].

**Figure 9.**Pressure and heat release changes due injection timing changes at 75% MCR [22].

**Figure 11.**Dependence of combustion and compression pressure on the change in compression ratio at 50% MCR [22].

**Figure 13.**Dependence of combustion and compression pressure on the change in compression ratio at 75% MCR [22].

**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 |

First Chemical Reaction Forward Rate Constants, mol/cm^{3}s | First Chemical Reaction Backward Rate Constants, mol/cm^{3}s | Reference |
---|---|---|

${k}_{1,f}=6.68\cdot {10}^{12}\cdot {T}^{0.4}\cdot \mathrm{exp}\left(-\frac{37707}{T}\right)$ | ${k}_{1,b}=3.3\cdot {10}^{12}\cdot {T}^{0.3}$ | [31] |

${k}_{1,f}=7.6\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{38000}{T}\right)$ | ${k}_{1,b}=3.3\cdot {10}^{12}\cdot {T}^{0.3}$ | [32] |

${k}_{1,f}=7.6\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{38000}{T}\right)$ | ${k}_{1,b}=3.2\cdot {10}^{7}$ | [33] |

${k}_{1,f}=7.6\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{38000}{T}\right)$ | ${k}_{1,b}=1.6\cdot {10}^{7}$ | [34] |

${k}_{1,f}=3.8\cdot {10}^{9}\cdot {T}^{1.0}\cdot \mathrm{exp}\left(-\frac{20820}{T}\right)$ | ${k}_{1,b}=3.8\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{844}{R\cdot T}\right)$ | [35] |

${k}_{1,f}=1.473\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{315000}{R\cdot T}\right)$ | ${k}_{1,b}=3.3\cdot {10}^{12}\cdot {T}^{0.3}$ | [36] |

${k}_{1,f}=3.0\cdot {10}^{-10}\cdot \mathrm{exp}\left(-\frac{38400}{T}\right)$ | / | [37,38] |

**Table 3.**Nitric oxide emission formation using different kinetic coefficients k

_{1},

_{f}at 50% MCR [22].

First Chemical Reaction Forward Rate Constants, mol/cm ^{3}s | Calculated NO Concentration, mol/rpm | Calculated NO_{x} Concentration,g/kWh | Measured NO_{x} Concentration,g/kWh |
---|---|---|---|

${k}_{1,f}=6.68\cdot {10}^{12}\cdot {T}^{0.4}\cdot \mathrm{exp}\left(-\frac{37707}{T}\right)$ | 0.370183 | 36.0828 | 14.47 |

${k}_{1,f}=7.6\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{38000}{T}\right)$ | 8.623153 | 337.0949 | |

${k}_{1,f}=1.82\cdot {10}^{14}\cdot \mathrm{exp}\left(-\frac{76241}{R\cdot T}\right)$ | 15.974068 | 624.4557 | |

${k}_{1,f}=1.473\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{315000}{R\cdot T}\right)$ | 1.803006 | 70.4828 | |

${k}_{1,f}=3.0\cdot {10}^{-10}\cdot \mathrm{exp}\left(-\frac{38400}{T}\right)$ | 2.3341·10^{−11} | 8.7068·10^{−10} |

**Table 4.**Nitric oxide emission formation using different kinetic coefficients k

_{1},

_{f}at 75% MCR [22].

First Chemical Reaction Forward Rate Constants, mol/cm ^{3}s | Calculated NO Concentration, mol/rpm | Calculated NO_{x} Concentration,g/kWh | Measured NO_{x} Concentration,g/kWh |
---|---|---|---|

${k}_{1,f}=6.68\cdot {10}^{12}\cdot {T}^{0.4}\cdot \mathrm{exp}\left(-\frac{37707}{T}\right)$ | 0.231957 | 6.9402 | 10.37 |

${k}_{1,f}=7.6\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{38000}{T}\right)$ | 2.134097 | 63.8531 | |

${k}_{1,f}=1.82\cdot {10}^{14}\cdot \mathrm{exp}\left(-\frac{76241}{R\cdot T}\right)$ | 3.878566 | 116.0483 | |

${k}_{1,f}=1.473\cdot {10}^{13}\cdot \mathrm{exp}\left(-\frac{315000}{R\cdot T}\right)$ | 0.448852 | 13.4298 | |

${k}_{1,f}=3.0\cdot {10}^{-10}\cdot \mathrm{exp}\left(-\frac{38400}{T}\right)$ | 1.415·10^{−11} | 4.036·10^{−10} |

Characteristic Values | Unit | ISO-F-DMA |
---|---|---|

Kinematic viscosity @ 50 °C | mm^{2}/s | 2.913 |

Density | kg/m^{3} | 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 |

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 |

NO_{x} (as NO_{2}) | g/kWh | 14.47 | 10.37 |

**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 |

NO_{x} (as NO_{2}) | g/kWh | 14.47 | 10.37 |

**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 |

NO_{x} (as NO_{2}) | g/kWh | 0 | 0 |

**Table 9.**Parameters and NO

_{x}emission changes due to changes in fuel injection timing at 50% MCR [22].

Δφ [°CA] | Δφ_{ID} [°CA] | p_{inj} [bar] | T_{inj} [K] | P_{i} [kW] | p_{max} [bar] | T_{max} [K] | BSFC [g/kWh] | NO_{x} [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 |

**Table 10.**Parameters and NO

_{x}emission changes due to changes in fuel injection timing at 75% MCR [22].

Δφ [°CA] | Δφ_{ID} [°CA] | p_{inj} [bar] | T_{inj} [K] | P_{i} [kW] | p_{max} [bar] | T_{max} [K] | BSFC [g/kWh] | NO_{x} [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 |

**Table 11.**Engine parameters and NO

_{x}emission changes due to changes in the compression ratio at 50% MCR [22].

Δl [mm] | ε [[–] | Δφ_{ID} [°CA] | p_{inj} [bar] | T_{inj} [K] | P_{i} [kW] | p_{max} [bar] | T_{max} [K] | BSFC [g/kWh] | NO_{x} [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 |

**Table 12.**Engine parameters and NO

_{x}emission changes due to changes in the compression ratio at 75% MCR [22].

Δl [mm] | ε [[–] | Δφ_{ID} [°KV] | p_{inj} [bar] | T_{inj} [K] | P_{i} [kW] | p_{max} [bar] | T_{max} [K] | BSFC [g/kWh] | NO_{x} [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 |

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**MDPI and ACS Style**

Lalić, B.; Poljak, A.; Radica, G.; Mišura, A.
Low-Speed Marine Diesel Engine Modeling for *NO*_{x} Prediction in Exhaust Gases. *Energies* **2021**, *14*, 4442.
https://doi.org/10.3390/en14154442

**AMA Style**

Lalić B, Poljak A, Radica G, Mišura A.
Low-Speed Marine Diesel Engine Modeling for *NO*_{x} Prediction in Exhaust Gases. *Energies*. 2021; 14(15):4442.
https://doi.org/10.3390/en14154442

**Chicago/Turabian Style**

Lalić, Branko, Andrijana Poljak, Gojmir Radica, and Antonija Mišura.
2021. "Low-Speed Marine Diesel Engine Modeling for *NO*_{x} Prediction in Exhaust Gases" *Energies* 14, no. 15: 4442.
https://doi.org/10.3390/en14154442