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Article

Parameter Variation Study of Two-Stroke Low-Speed Diesel Engine Using Multi-Zone Combustion Model

1
Faculty of Maritime Studies, University of Split, Rudjera Boskovica 36, 21000 Split, Croatia
2
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB), University of Split, Rudjera Boskovica 32, 21000 Split, Croatia
*
Author to whom correspondence should be addressed.
Energies 2022, 15(16), 5865; https://doi.org/10.3390/en15165865
Submission received: 26 June 2022 / Revised: 3 August 2022 / Accepted: 10 August 2022 / Published: 12 August 2022
(This article belongs to the Special Issue Combustion Performance, Thermal Conductivity and Efficiency)

Abstract

:
The latest electronically controlled marine engines have a control system that allows the operator to view all the essential parameters of the engine in real conditions during operation. The system is connected to the electronic control system (ECS) through the control network, thus controlling the engine. The operator has various management and monitoring options. The objective of this paper was to become familiar with the specific factors that affect engine operation and optimize engine operation. A model of a large marine engine was developed and calibrated with measured data. Simulations were performed, and the combustion process was analyzed. The parameter study was performed by varying the fuel injection and the gas exchange timing. Fuel consumption decreases by 6 g/kWh, and NOx emissions decrease by 0.5 g/kWh. The research conducted in this work will be used by engineers to understand the potential of new technologies to optimize combustion in real-world conditions during operation and for the future development of an expert system to continuously monitor, diagnose, and optimize engine health during operation.

1. Introduction

Internal combustion engines (ICEs) play an essential role in the power generation and transport sector. Therefore, modeling and optimal control of ICEs to improve engine performance and efficiency and reduce pollutant emissions is critical for the environment and air quality. Simulation of test engines using various simulation programs is the primary method for developing and optimizing new or existing engines. Simulation programs allow several different engine conditions to be tested simultaneously and several parameters to be changed to achieve the desired result [1]. The use of simulation software enables easier and faster engine optimization to reduce harmful emissions such as NOx and soot [2]. NOx emissions from marine diesel engines are responsible for 50% of the total NOx emissions in ports and coastal regions [3]. The use of biodiesel can reduce NOx emissions by up to 22% [4]. In order to meet current emission requirements, a combination of in-cylinder processes and aftertreatment technologies are proposed to reduce emissions. Emission reduction strategies can be broadly divided into indirect and direct emission reduction approaches [5]. Direct emission reduction (e.g., EGR, combustion optimization, use of alternative fuels) involves preventing the generation of pollutants during the combustion process, while the indirect approach (SCR, DPF) eliminates the combustion products before they are released from the exhaust gas into the atmosphere [6]. Selective catalytic reduction (SCR) technology is currently one of the most important technical options for eliminating excess NOx emissions from marine diesel engines and is the only IMO-approved NOx emission reduction technology that can be applied to various marine engines. The development of SCR technology for low-speed marine engines should be the compromise solution for the requirements of high-sulfur fuel, high thermal efficiency, and low pollutant emissions [7]. The effects of using other alternative fuels such as methanol [8] can also be simulated to study their effects on marine engine performance [9]. The dynamic behavior of the large marine engine is simulated and studied under different fuel types and environmental conditions [10]. Development of the model of a large marine engine using a multi-zone combustion model used for the analysis and simulation of performance, emissions, and combustion behavior [11]. The 0-dimensional model is used to analyze the operation of a large marine diesel engine with a two-stroke engine, including various cases with a turbocharger. A nonlinear mean-variance engine model (MVEM) of a large turbocharged marine engine is used as the engine model. The model can also be used for EGR and control system design and analysis. Raptotasios et al. [12] used the MZCM model to analyze NOx emissions. The multi-zone model is used to simulate the engine’s closed loop system and to analyze the fuel combustion rate using a fairly detailed chemical kinetics mechanism [13]. The method for modeling, simulation, and optimization of the two-stroke slow-rotation marine diesel engine in the AVL Boost program [14] was presented in this paper. The thermodynamic modeling was developed using AVL Boost software, which simulates a single-cylinder diesel engine [15]. AVL BOOST is a fully integrated IC engine simulation software. It provides advanced models for accurate prediction of engine performance, exhaust emissions, and acoustics [16]. It provides comprehensive species transport for a high degree of flexibility with respect to fuel composition and working gas. The main advantage of this software is that it can be coupled with 3D CFD software to accurately account for 3D flow and heat transfer effects in pipes, manifolds, and combustion chambers, allowing researchers greater flexibility in studying specific combustion phenomena. For aftertreatment systems, identical modelling of physics and chemistry allows easy switching between 1D and 3D models. This paper uses multi-zone combustion model on large two stroke marine engine to demonstrate the impact of the most influencing operating parameters on the performance of the existing engine and proposes how certain adjustments could achieve reduced consumption and less harmful emissions without using advanced aftertreatment solutions.

2. Large Marine Engine Modelling

The process of converting fuel into heat, which is then converted into mechanical operation, occurs in the cylinder of the engine, so it is also the most complex and important element of the simulation model. The calculation of the cylinder process is based on the first law of thermodynamics (energy conservation law), which states that the heat brought by combustion is spent on the change in energy in the cylinder, on the operation of the piston mechanism, on the heat that is handed over to the cylinder wall, on the flow of enthalpy due to flow between piston and cylinder and on the heat necessary for evaporation of fuel (Figure 1).
The following equation [15] is used to calculate the thermodynamic state in the cylinder:
d m c u d α = p c d V d α + d Q F d α d Q w d α h B B d m B B d α + + d m i d α h i d m e d α h e q e v f d m e v d t
where d m c u d α is the change in internal energy, p c d V d α is the work performed by the piston, d Q F d α is the rate at which heat is released by burning fuel, d Q w d α is the heat flow passing through the walls, h B B d m B B d α   is the flow of enthalpy due to flow between piston and cylinder, d m i d α h i is the amount of energy brought by the mass entering the cylinder, d m e d α h e is the amount of energy taken by the mass coming out of the cylinder, and q e v f d m e v d t is heat required for evaporation of fuel in the cylinder.
The change in mass in the cylinder can be calculated from the sum of the mass entering and the mass coming out of the cylinder [15]:
d m c d α = d m i d α d m e d α d m B B d α + d m e v d t
where m c is the cylinder mass, d m i d α is the mass flow entering the cylinder, d m e d α is the mass flow coming out of cylinder, d m B B d α is the mass flow flowing out due to blow by, and d m e v d t is the evaporating fuel mass.
This equation applies to engines with internal and external preparation of fuel and air mixtures, but terms that account for the change in gas composition due to combustion are treated differently for external and internal preparation of the fuel mixture.
In the internal preparation of the fuel mixture, it is assumed that:
  • The fuel injected into the cylinder is burned immediately;
  • The combustion products are mixed instantly with the rest of the cylinder charge and form a uniform mixture;
  • The air/fuel ratio is continuously reduced from a high value at the beginning of combustion to the final value at the end of combustion.

2.1. Calculation of Gas Properties

The properties of gases such as gas constant or thermal gas capacity depend on the pressure, temperature, and composition of the gas. In each working volume, properties of the gas are calculated with the current composition in each time step. Equations of mass preservation are used to calculate combustion products and fuel vapors. The air mass content is calculated through the expression [15]:
w a i r = 1 w F V w C P
where w a i r is air mass fraction, w F V is the fuel vapor fraction, and w C P is the combustion products fraction.

2.2. Energy Balance in-Cylinder with Closed Inlet Port and Exhaust Valve

The process with the inlet and outlet valves closed begins at the moment when the outlet valve is closed, and the inlet ports are covered. This process continues until the exhaust valve is opened. The mass of gases in the cylinder is constant during this time, but during the combustion process, the composition of the gases changes. It is calculated using a formula [15]:
d m c u d α = p c d V d α + d Q F d α d Q w d α h B B d m B B d α q e v f d m e v d t

2.3. Energy Balance in-Cylinder during Working Media Exchanging Process

The change in the working medium lasts from the moment the exhaust valve opens in the cylinder to the moment the exhaust valve closes. The equation for calculating the gas exchange process in a cylinder is also an equation of the first law of thermodynamics, only in a different form [15]:
d m c u d α = p c d V d α d Q w d α + d m i d α h i d m e d α h e

2.4. Mass Flow Calculation of Gases Entering and Leaving the Cylinder

Entering and exiting the cylinder mass flow is calculated from equations for isentropic flow through the opening, considering the flow efficiency through the opening. From the energy equation for flow through the opening in a stationary state, one can obtain an equation [15] for mass flow:
d m d t = A e f f p o 1 2 R 0 T o 1 Ψ
where A e f f is the effective flow area, p o 1 is the static gas pressure at the entrance, T o 1 is the static gas temperature at the entrance, R 0 is the gas constant, and Ψ is the pressure function. The pressure function is dependent on gas velocity. For velocities less than the speed of sound, gas type, and pressure differences affect the pressure function [15]:
Ψ = κ κ 1 p 2 p o 1 2 κ p 2 p o 1 κ + 1 κ
where p 2 is static gas pressure at the outlet, and κ is the ratio of specific heats.
While flowing at the speed of sound, the pressure function does not depend anymore on the pressure difference but only on the gas type [15]:
Ψ m a x = 2 κ + 1 1 κ 1 κ κ + 1
The effective flow area can be calculated through measured flow coefficients [15]:
A e f f = C v d v i 2 π 4
where C v is the flow coefficient and d v i is the inner diameter of the valve seat.

2.5. Combustion Model (Rate of Heat Release by Combustion)

2.5.1. Spray Model

This model was first introduced by Hiroyasu [17]. At each time step, the fuel injected into the combustion chamber according to the injection schedule forms a that moves in the spray axial direction. Each fuel parcel is further divided into small zones distributed in the radial direction. The mass of fuel in each parcel can either be predetermined or calculated using an empirical correlation based on the injection and chamber pressures and the geometry of the injector. No mixing or passing among zones is allowed. The individual zones have their own progression of temperature, pressure, and composition. The total number of zones in the direction of spraying corresponds to the number of spray parcels and is therefore determined by the injection duration and the size of the calculation time step.
Figure 2 shows the division of the spray into parcels at a certain instance. It is assumed that the fuel injected into the chamber first forms a liquid column moving at speed equal to the injection speed until the fuel breakup time has elapsed. Thereafter, the injected fuel is distributed within a spray angle that is unique to each spray zone and varies from one time step to another depending on conditions. The velocity of each zone is calculated by time-differentiating the correlation for spray tip penetration. After the breakup, the fuel spray is assumed to atomize into fine droplets, each with a diameter equal to the mean Sauter diameter (SMD). All calculations related to droplet evaporation are based on the SMD. The air entrainment rate depends on the physical position of each zone, with zones in the center receiving less air and zones at the edge receiving more. The amount of entrained air is calculated based on the law of conservation of momentum for each zone. It is assumed that the fuel droplets begin to evaporate immediately after the breakup. Both heat and mass transfer for a single evaporating droplet is considered to calculate the instantaneous droplet temperature, evaporation rate, and droplet diameter. Combustion is assumed to begin in each zone individually after the ignition delay time has elapsed.

2.5.2. Ignition Delay Model

Ignition delay is measured from the start of injection and calculated based on zone temperature and zone pressure. During the ignition delay, a portion of the injected fuel is evaporated and mixed with air, creating a combustible mixture. In the initial phase, combustion occurs under premixed conditions. Premixed combustion is assumed to occur until the amount of fuel evaporated at the end of the ignition delay period is consumed. When all of the initial fuel vapor has been consumed, combustion is assumed to be controlled by the diffusion of air into the zones. The chemical ignition delay depends on pressure and temperature, which is estimated by an Arrhenius-type correlation using the approach of Wolfer [18].
τ = C I g n D e l p 1.02 e C I g n E x p T I g n D e l  
where τ is characteristic late ignition time, T I g n D e l is the temperature for calculating the late ignition, C I g n D e l is the ignition delay parameter, and C I g n E x p is an exponent of the ignition overdue.

2.5.3. Combustion Model

The heat release rate in the zones is calculated according to the reaction kinetics of Jung [19]. Here, the concentrations of the reactants are represented by mass fractions of oxygen and fuel vapors. The expression for the reaction is an Arrhenius-type equation, which additionally takes density into account.
d x f b d t = K b ρ c h x f v x O 2 1.5 e 1200 T i
where d x f b d t is the fuel combustion rate; x f v is the mass content of fuel vapor; x O 2 is the mass content of oxygen; K b is the chemical reaction parameter; and a p , b O 2 ,   and   c a r r h are model constants.

3. Modeling and Calibration

In this work, the model of a large marine engine with a power of 8813 kW at 103 rpm and 100% load was created and calibrated. Since, in this work, mainly specific (independent of cylinder number) operating parameters of the engine were analyzed, an approximation was introduced, i.e., the operation of only one cylinder was simulated. Calibration of this model with the real engine parameters was performed, and the test was carried out on the hydrokinetic brake. After calibration, the effects of changing various parameters were analyzed to improve engine characteristics such as power, fuel consumption, pollutant emissions, etc.
Some of the main engine parameters are listed in Table 1.
A single cylinder model is created, consisting of the following elements:
  • Cylinder;
  • System boundary;
  • Pipe;
  • Engine interface;
  • Measuring point;
  • Engine.

3.1. Simulation Control

Convergence control was set for the indicated mean effective pressure parameter with a tolerance between the results of 500 Pa and with convergence after 3 established result values. Diesel fuel properties were set with a lower calorific value of 42,940 kJ/kg, a stochiometric ratio of 14.7 at an external pressure of 1 bar, and a temperature of 25 °C. The engine model parameters listed below refer to the case where the engine speed is 103 rpm at 100% load.
The engine friction was measured on the engine hydrokinetic brake as the difference between indicated and brake mean effective pressure and defined with a table where friction mean effective pressure (FMEP) is dependent on engine speed (Figure 3) and is required for the calculation of the brake mean effective pressure (BMEP) in the cylinder and the fuel consumption.
Geometrical characteristics of the engine are also defined, namely, the cylinder diameter is 500 mm, the piston length is 2214 mm, the compression ratio is 26, the piston rod length is 2214 mm, the piston shaft displacement is 0 mm, the tolerance between piston and cylinder liner is 0.0008 mm, and the mean pressure in the crankcase is 1.1 bar.
The scavenging parameters were set with an excess air ratio of 2.2 and a residual combustion ratio of 0.5. The amount of fuel per cycle was specified at 0.0395 kg/cycle. Preparation of the fuel–air mixture was performed internally, and the fuel temperature was 29 °C.
In order to calibrate the engine model, various physical characteristics such as the number of nozzles on the injector, the diameter of the nozzles, the discharge coefficient, and the injection pressure were entered (Table 2).
The burnt gas re-entrainment factor was used to control the recirculation of burned gas into the fuel jet. Setting a lower value results in faster combustion. The evaporative heat transfer affects the heat release rate in the initial stages of combustion and the peak values. A higher parameter value causes faster combustion. The ignition delay multiplier affects the delay of the ignition of the fuel–air mixture. Setting a higher value causes a delay in ignition. The combustion parameter factor affects the shape of the heat release rate curve. Setting a higher value results in higher temperatures and higher NOx emissions.
After setting the parameters of the MZCM combustion model, the parameters for the normalized injection pressure profile with an injection duration of 26° ATDC and an injection start angle of −2° ATDC were entered and gathered from official engine data (Figure 4).
The combustion parameters used for this model are listed in Table 3.

3.2. Emission Model of Harmful Gases

The emission model of harmful gases consists of various multipliers calibrating the emission of harmful gases obtained by simulation with the results of the actual engine (Table 4). It consists of a NOx multiplier for calibrating NOx production. The second multiplier is the CO multiplier used to calibrate CO gas production. Additionally, the last multiplier of soot production is used to calibrate the production of soot and the constant consumption of soot.

3.3. Heat Transfer Model

In order to define the surface over which heat transfer is carried out heat transfer model is used, such as the wall of the piston, cylinder head, liner, and surface temperature (Table 5). The heat transfer model used in this paper is Woschini 1978 [20]. DI was selected, which relates to engines without pre-chamber, and a swirling ratio in the cylinder was entered.

3.4. Valve Specification

Since the engine simulated in this work is a two-stroke engine, it is necessary to define the control of the intake using a piston and the control of the outlet by the exhaust valve, as well as the surface and temperature of the wall (Table 6).
After setting the intake and exhaust control, it is necessary to define the flow area depending on the angle of the crankshaft and to set the flow coefficient for the specified flow area (Figure 5).
After scavenging the port, the parameters of the exhaust valve must be defined (Figure 6). First, the opening and closing angle of the valve is defined, and the valve lift profile depends on the angle of the crankshaft.

3.5. Model Calibration

Model calibration is used to ensure that the engine model has the same characteristics as the actual engine. The characteristics that the model must have as well as the actual engine to be considered calibrated, are the exact geometric characteristics and the exact amount of fuel per cycle, mass airflow, and the pressures in the cylinders. The variables used to calibrate the model are listed in Table 7.
For the results of the model simulation, in this case, the pressure in the cylinder as a function of the angle of the crankshaft was compared with the results of the actual model and are shown in Figure 7.
The curves of the model and the actual model differ by 1%, and since the exact amount of air mass flow and fuel is present, the model can be said to be calibrated. Table 8 lists some of the main results and deviations from the actual engine measurements.

4. Parameter Variation Study

Parameter variation study of the calibrated model of the large marine engine is performed by changing certain parameters to the desired value. Various parameters can be selected, such as the physical parameters of the engine (cylinder diameter, piston stroke, etc.) or electronically controlled parameters (fuel injection timing and duration, exhaust valve opening and closing angle, etc.).
In this work, the influence of changes in electronically controlled parameters, i.e., changes in the exhaust valve opening angle and fuel injection timing, was studied with the aim of reducing fuel consumption and NOx emissions. In new electronically controlled engines, it is possible to adjust the fuel injection timing and the exhaust valve opening angle, which affects cylinder pressure, engine power, and NOx production.

4.1. Parameter Variation Study by Changing the Injection Timing

Changing the injection timing directly affects peak pressures in the engine cylinder, power output, fuel consumption, and exhaust emissions. Figure 8 shows a comparison of cylinder pressures at an injection timing of −2° ATDC and −4° ATDC.
Changing the injection timing to −4° ATDC results in a significant increase in peak pressures in the cylinder and an increase in pressures from 185 bar to 207 bar, which is above engine pressure allowance.
The injection timing of −4° ATDC increases the engine power from 1380 kW (by one cylinder) to 1390 kW, which is not of great significance, as shown in Figure 9.
The fuel consumption, shown in Figure 10, decreases from 171 g/kWh to 168 g/kWh with an injection timing of −4° ATDC.
Changing the angle from −2° ATDC to −4° ATDC increases engine power and reduces fuel consumption but has a negative effect on NOx emissions. Injecting the fuel earlier increases the pressure peaks and the temperature in the cylinder and thus also NOx emissions (Figure 11).

4.2. Parameter Variation Study by Changing the Opening Angle of the Exhaust Valve

Figure 12 shows the pressure changes in the cylinder when the opening angle of the exhaust valve is changed from 119° ATDC to 125° ATDC. The later opening of the exhaust valve prolongs the expansion of the gases.
The later opening of the exhaust valve extends the expansion stroke, resulting in a power increase of 63 kW per cylinder at 125° ATDC, as shown in Figure 13.
Fuel consumption decreases by 6 g/kWh and is shown in Figure 14. Opening the exhaust valve later and suitably changing the working fluids in the cylinder reduces NOx emissions by 0.5 g/kWh (Figure 15).

5. Conclusions

Simulation programs significantly accelerate the development of marine engine technology and shorten testing and production times for new engines. The entire process using simulation programs began with testing the engine on the test brake. The right choice of the test brake was very important to be able to test the engine under certain conditions and loads. The data from the test brake and the geometric characteristics of the engine were used to create models in the simulation program. The model was calibrated with the actual motor. The model was considered calibrated when it had the same geometric characteristics and mass flow rate, and the simulation results gave the cylinder pressures and NOx emissions corresponding to the tested engine. After the model was created and calibrated, a parameter variation study was performed. The objective of this work was achieved because the work of a large marine engine that used a multi-zone combustion model was simulated with full result validation. The parameter variation study was performed by changing the injection timing and the opening angle of the exhaust valve. Changing the injection timing from −2° ATDC to −4° ATDC increased the pressures in the cylinder, which increased NOx emissions, decreased fuel consumption, and slightly increased engine power. The later opening of the exhaust valve resulted in a longer duration of the expansion stroke. The longer duration of the expansion stroke increased engine power and reduced fuel consumption and NOx emissions, proving that improvements can still be made with optimized exhaust valve angle control without compromising performance or the use of aftertreatment systems.
The future goal of this research is to develop an expert system in the future that will allow continuous monitoring of the engine condition during operation at all loads and inform the operator of potential problems. An exhaust monitoring expert system will be developed that will provide the ability to analyze NOx, SOx, and CO2 emission levels in real time. The future expert system will provide the ability to continuously monitor the engine condition during operation and inform the operator of potential problems [21].

Author Contributions

Conceptualization, G.R.; Data curation, G.R.; Formal analysis, Z.J. and T.V.; Funding acquisition, G.R.; Investigation, Z.J., R.K. and T.V.; Methodology, Z.J., R.K. and T.V.; Project administration, G.R.; Software, R.K. and T.V.; Supervision, G.R.; Validation, R.K.; Visualization, T.V.; Writing—original draft, R.K.; Writing—review & editing, T.V. All authors have read and agreed to the published version of the manuscript.

Funding

This work has been fully supported by the Croatian Science Foundation under the project IP.2020-02-6249.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Energy balance in-cylinder [15].
Figure 1. Energy balance in-cylinder [15].
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Figure 2. MZCM Combustion Jet Discretization.
Figure 2. MZCM Combustion Jet Discretization.
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Figure 3. Friction mean effective pressure.
Figure 3. Friction mean effective pressure.
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Figure 4. Injection pressure profile.
Figure 4. Injection pressure profile.
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Figure 5. Flow surface profile of scavenging port depending on the crankshaft angle.
Figure 5. Flow surface profile of scavenging port depending on the crankshaft angle.
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Figure 6. Exhaust valve lift profile with respect to crankshaft angle.
Figure 6. Exhaust valve lift profile with respect to crankshaft angle.
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Figure 7. Comparison of pressures in the cylinder of the model and the actual engine.
Figure 7. Comparison of pressures in the cylinder of the model and the actual engine.
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Figure 8. Impact of injection timing change on cylinder pressures.
Figure 8. Impact of injection timing change on cylinder pressures.
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Figure 9. Impact of injection timing change on engine power.
Figure 9. Impact of injection timing change on engine power.
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Figure 10. Impact of changing the injection timing on fuel consumption.
Figure 10. Impact of changing the injection timing on fuel consumption.
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Figure 11. Impact of injection timing change on NOx emissions.
Figure 11. Impact of injection timing change on NOx emissions.
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Figure 12. Impact of change in the opening angle of the exhaust valve on cylinder pressures.
Figure 12. Impact of change in the opening angle of the exhaust valve on cylinder pressures.
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Figure 13. Impact of change in the opening angle of the exhaust valve on engine power.
Figure 13. Impact of change in the opening angle of the exhaust valve on engine power.
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Figure 14. Impact of changing opening angle of exhaust valve on fuel consumption.
Figure 14. Impact of changing opening angle of exhaust valve on fuel consumption.
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Figure 15. Impact of the change in the opening angle of the exhaust valve on NOx emissions.
Figure 15. Impact of the change in the opening angle of the exhaust valve on NOx emissions.
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Table 1. Main engine parameters.
Table 1. Main engine parameters.
Bore500 mm
Stroke2214 mm
Connecting rod length3321 mm
Compression ratio26
Maximum combustion pressure (at 100% load)186 bar
Scavenging air pressure (at 100% load)3.13 bar
Table 2. Combustion model MZCM.
Table 2. Combustion model MZCM.
Injector Holes Number8
Diameter of Hole1.15 mm
Discharge Coefficient1
Pressure in the rail1000 bar
Overall Air0.9
Burnt Gas Reentrainment Factor0.2
Evaporation Heat Transfer0.36
Ignition Delay Multiplier2.75
Table 3. Burnout model.
Table 3. Burnout model.
Package Number5
Delta Spray Angle
Heat Transfer Coefficient from Spray Zones to Charge Zone5000 W/(m2K)
Ignition Delay Exponent2600
Wall Distance490 mm
Evaporation Multiplier2
Table 4. Emission model of harmful exhaust gas parameters.
Table 4. Emission model of harmful exhaust gas parameters.
NOx Kinetic Multiplier3.25
NOx Postprocessing Multiplier1
CO Kinetic Multiplier0.00081
Soot Production Constant5000
Soot Consumption Constant10,000
Table 5. Heat transfer model.
Table 5. Heat transfer model.
Piston Surface Area202,137.5 mm2
Piston Wall Temperature350 °C
Piston Calibration Factor1
Cylinder Surface Area225,687.5 mm2
Cylinder Wall Temperature300 °C
Head Calibration Factor1
Surface Area (Piston at TDC)62,424.81 mm2
Wall Temp. (Piston at TDC)200 °C
Wall Temp. (Piston at BDC)130 °C
Liner Calibration Factor1
In-cylinder Swirl Ration nD/nM2
Table 6. Intake and exhaust control.
Table 6. Intake and exhaust control.
ControlFlow Area [mm2]Wall Temp. [°C]
PistonFigure 5N/A
Valve44,278.90550
Table 7. Variables used to calibrate models.
Table 7. Variables used to calibrate models.
Airflow correction factor on the intake0.188
Gas flow correction factor on exhaust0.6
Injection start angle−2° ATDC
Pressure profile and duration of injectionFigure 4
Fuel quantity per cycle0.0395 kg/cycle
Air supply correction factor to fuel jet1
Angle of exhaust valve closing283.25° ATDC
Angle of exhaust valve opening119° ATDC
Correction factor for return of burnt gas to fuel jet0.5
Fuel evaporation and heat transfer correction factor between jet zones3
Correction factor of ignition delay2.75
Combustion parameter correction factor0.015
Correction Factor of NOx3.25
Correction factor of CO0.00081
Table 8. Deviations and most important results.
Table 8. Deviations and most important results.
ResultsSimulationActual Engine ResultsVariance %
Mean indicated pressure (bar)19.17719.411.21
Effective Power (kW)8280.848813.426.05
Specific effective fuel consumption (g/kWh)171.21166.382.83
Maximum cylinder pressure (bar)185.31184.800.28
NOx emmisions (g/kWh)9.59.651.55
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Jurić, Z.; Kutija, R.; Vidović, T.; Radica, G. Parameter Variation Study of Two-Stroke Low-Speed Diesel Engine Using Multi-Zone Combustion Model. Energies 2022, 15, 5865. https://doi.org/10.3390/en15165865

AMA Style

Jurić Z, Kutija R, Vidović T, Radica G. Parameter Variation Study of Two-Stroke Low-Speed Diesel Engine Using Multi-Zone Combustion Model. Energies. 2022; 15(16):5865. https://doi.org/10.3390/en15165865

Chicago/Turabian Style

Jurić, Zdeslav, Roko Kutija, Tino Vidović, and Gojmir Radica. 2022. "Parameter Variation Study of Two-Stroke Low-Speed Diesel Engine Using Multi-Zone Combustion Model" Energies 15, no. 16: 5865. https://doi.org/10.3390/en15165865

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