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Abstract

A computational fluid dynamics model of the marine diesel engine was established and validated, and the simulation studies were carried out using this model. Different gravity conditions were set in the computational fluid dynamics model to investigate their effect on marine diesel emissions and performance. By comparing the simulation results under different basic grid sizes, 1.2 mm was selected as the basic grid size of the computational fluid dynamics model. The model uses the experimental data including cylinder pressure, heat release rate, and nitrogen oxides (NO _x ) emissions to calibrate and validate the model. The simulation results are very close to the experimental data, and slight errors are also within the allowable range. In particular, when considering the heat transfer of the combustion chamber wall, the simulation results of the heat release rate are closer to the experimental data. The simulation results show that gravity has a slight effect on cylinder pressure and heat release rate, and has a certain degree of effect on fuel spray and atomization. The penetration length of the fuel is proportional to the gravity, and the maximum deviation of the Sauter mean diameter of the droplet is 25.74%. The spray and atomization process of fuel directly affects combustion and emissions. The maximum deviation of NO _x emissions is 6.03%, which is reduced from 7.46 to 7.01 g/kW·h. Finally, the three-dimensional simulation results of temperature, equivalence ratio, and NO _x emission of different crank angles under different gravity conditions are compared.

Keywords

Gravity Sauter mean diameter marine diesel engine computational fluid dynamics

Handling Editor: James Baldwin

Introduction

As the quality of atmospheric environment continues to deteriorate, people continue to have concern about environmental issues. Pollutant emissions from marine diesel engines, especially NO _x and soot, have drawn increasing attention. The International Maritime Organization (IMO) imposes limits on the NO _x emissions from marine diesel engines by developing and publishing Tier-III regulations.^1,2 The introduction of the Tier-III standard has caused a considerable impact on plenty of shipping countries and shipping companies. The Tier-III standard is reduced by 76% compared to the Tier-II standard, which means more stringent regulations are enforced to reduce marine diesel NO _x emissions. At present, the mainstream NO _x emission reduction technologies include exhaust gas recirculation (EGR), selective catalytic reduction (SCR), natural gas engines, and so on, all of which have made breakthrough in the reduction of NO _x emissions.³^–⁵

Gravity condition

Ocean-bound vessels are significantly affected by marine meteorological conditions. Not only does the harsh and constant-changing marine meteorological environment affect the comfort level of personnel, it also causes disruption to the operation of the equipment. The hull caused by the waves is in a state of being overweight or weightless for a short time. People have long been aware of the effects that gravity has on the combustion process.⁶ However, due to the complexity of the combustion process, the classical combustion theory described by mathematical formulas tends to overlook gravity as an influencing factor.⁷ Such experimental facilities as drop towers and weightless aircraft can obtain weightlessness for a short period. Through these devices, many countries have conducted weightless combustion experiments on various combustible materials.⁸^–¹¹ The establishment of the International Space Station has promoted the weightless combustion experiment based on which many positive results have been obtained.¹²^–¹⁶ Gravity can have effect on heat transfer, mass transfer, flame propagation, and flame stability during the process of combustion.^7,17 Under normal gravity conditions, the flame shows a “droplet” shape with a center of gravity, while the flame is of “circular” shape under weightless conditions. Besides, gravity could affect chemical reaction, thus resulting in different combustion products.¹⁸ In general, combustion exhibits the following characteristics under weightless conditions.^7,19^–²¹ First, it is more conducive to the study of stationary and low-speed flow combustion under circumstance where natural convection almost disappears. Second, gravity sedimentation is almost non-existent, which facilitates the study of combustion under stable and free-suspension conditions. Third, the disappearance of buoyancy leads to an increase in combustion in time and space scales, which will be conducive to the observation of combustion.

A range of physical and chemical changes experienced by a droplet before burning play an important role in engine combustion. Combustion is directly associated with to emissions.²² There is a possibility that ignition would not occur until several crank angles after the start of injection. Once ignition occurs, the fuel that has been injected and mixed with air undergoes the premixed combustion process. When the combustible mixture as prepared in advance has been consumed, mixing-controlled combustion occurs. As the name suggests, burning in this combustion process is subject to control by the fuel–air mixing process.²³ Droplet combustion is commonly found in diesel engines. Despite plenty of studies focusing on diesel spray combustion,²⁴^–²⁷ none of them takes into account the effect of gravity. The University of Tokyo, Japan, took the lead in conducting research into the combustion of n-heptane droplets under the context of microgravity.⁸

Simulation software

Due to the rapid development of computer technology, it is made increasingly convenient to study engine performance and emissions by means of numerical simulation. Traditional experimental methods are faced with the difficulty in observing the effects that gravity has on the performance and emissions of combustion plants. Engine numerical simulation technology is capable to simulate a variety of different engine operating conditions, especially those that are difficult to simulate in traditional experiments.²⁸ As an engine computational fluid dynamics (CFD) simulation software, CONVERGE shows massive advantages that make it most commonly in practice.²⁹^–³⁸

In order to calculate the spray in a simulation, CONVERGE introduces drop parcels into the domain at the injector location at a user-specified rate. Parcels represent a group of identical drops (e.g. same radius, velocity, temperature, etc.) and are used to statistically represent the entire spray field. With the concept of drop parcels applied, CONVERGE leads to a significant reduction of the computational time required by a simulation involving spray.³⁹

In CONVERGE,³⁹ a drop’s velocity, $v_{i}$ , is obtained using its equation of motion

ρ_{l} V_{d} \frac{d v_{i}}{d t} = F_{d, i}

where

ρ_{l}

indicates the liquid density,

V_{d}

denotes the drop volume, and

F_{d, i}

is determined by the sum of the drag force and the gravitational body force as

F_{d, i} = F_{d r a g, i} + F_{g, i} = C_{D} A_{f} \frac{ρ_{g} | U_{i} |}{2} U_{i} + ρ_{l} V_{d} g_{i}

A_{f} = π r^{2}

represents the drop’s frontal area,

ρ_{g}

indicates the gas density, and

U_{i}

refers to the drop-gas relative velocity expressed as

U_{i} = u_{i} + {u^{'}}_{i} - v_{i}

where

u_{i}

and

{u^{'}}_{i}

represent the local mean and turbulent fluctuating gas velocities, respectively, and

g_{i}

indicates the gravitational acceleration. Therefore, the equation of motion can be rewritten as

\frac{d v_{i}}{d t} = \frac{3}{8} \frac{ρ_{g}}{ρ_{l}} C_{D} \frac{| U_{i} |}{r} U_{i} + g_{i}

which is used in CONVERGE to update drop velocities at any given time-step.

In summary, the velocity of the fuel droplets subject to impact from gravity. The difference in droplet velocity causes change to the statistics and distribution of parcel in CONVERGE. In this article, a validated model is applied to explore the effect of different gravity conditions on the performance and emissions of marine diesel engines.

Simulation model

Brief description of the CFD model

The CFD model of Perkins Rolls-Royce marine four-stroke engine (2306C-E14TAG3) was constructed and validated with experimental data. Based on this model, research is conducted. The main technical parameters of the engine are presented in Table 1

Table 1.

Main technical parameters of the engine.

Technical parameters
Cylinder number	6
Bore (mm)	137
Stroke (mm)	165
Power (kW·h)	396
Speed (r/min)	1500
Displacement (L)	14.6

CONVERGE 2.4, commercial CFD software, is applied to facilitate simulation. The CFD model geometry is drawn according to the shape of the engine combustion chamber. Figures 1

Figure 1.

Geometric models at BDC.

and 2

Figure 2.

Geometric models at TDC.

illustrate the geometry corresponding to the top dead center (TDC) and bottom dead center (BDC), respectively. The characteristics of the CFD model are as follows. First, the combustion chamber consists of the piston, the cylinder head, and the cylinder wall only. Second, with the symmetry of the combustion chamber, the model is calculated using the engine sector (60°). Third, the cylinder head is simplified to a flat surface. Fourth, the moment is taken when the intake valve and the exhaust valve are closed altogether as the starting point of the simulation. Fifth, the exhaust valve opening time is taken as the end point of the simulation. Finally, only the compression, combustion, and expansion strokes are calculated. Not only does this setting reduce the time required for, it also reduces the need for computing resources. Moreover, a smaller grid size can be used to improve simulation accuracy.

Various turbulence models are available in CONVERGE (e.g.

S t a n d a r d k - ε

, Rapid Distortion

R N G k - ε

R N G k - ε

R e a l i z a b l e k - ε

k - ω S S T

). In order for a better simulation of the gas motion in the cylinder under high Reynolds number, the Renormalization Group (RNG) model is applied as the Reynolds-averaged Navier–Stokes (RANS) turbulence model.⁴⁰ The fuel atomization and spray process have a considerable impact on engine performance and the final combustion products.²² Fuel atomization and spray involves a complex process where gas–liquid two-phase flows are coupled to each other. Spray droplets are subject to multiple processes from injection burning. Table 2

Table 2.

Atomization and spray model used in simulation CONVERGE.³⁹

Spray model physical process	Model options
Spray breakup	Kelvin–Helmholtz and Rayleigh–Taylor model
Drop drag	Dynamic drag models
Collision model	NTC model
Collision outcomes model	O’Rourke, Post
Drop turbulent dispersion	O’Rourke model
Drop/wall interaction	Rebound/slide model
Evaporation model	Multi-component vaporization

below shows the fuel atomization and spray models applied in this article. As for the numerical simulation of marine diesel engines, n-heptane⁴¹^–⁴⁵ and n-tetradcane⁴⁶^–⁴⁸ are commonly taken as surrogate fuels for heavy fuel oil. In this article, n-heptane is taken as surrogate fuel. The n-heptane reaction mechanism (42 species and 168 reactions) provided by CONVERGE is utilized. The detailed chemical kinetics model SAGE was selected to construct the combustion model. An extended Zeldovich mechanism and Hiroyasu soot model were applied to predict NO _x and soot emissions, respectively.^49,50 The diesel engine speed is 1500 r/min, and the power is 396 kW under 100% load. The fuel consumption rate measured by the experiment is 204.8 g/kW·h.

Best base grid size

The governing equations used in CFD simulation are partial differential equations. The solution to the partial differential equation is to discretize the solution region into a mesh in the first place. Then, the physical parameters at the mesh node are solved. Finally, the physical parameters between the nodes are obtained by interpolation. CONVERGE is also reliant on the same method to solve partial differential equations, for which the number of meshes is closely related to the simulation results. The grid control methods in CONVERGE include base grid, adaptive mesh refinement, and fixed embedding. Both adaptive mesh refinement and fixed embedding are performed to further refine the mesh based on the base grid. Therefore, the size of the base grid determines the total number of meshes required for the CONVERGE simulation. Despite the theoretical proportionality that the number of meshes has to the accuracy of the simulation, the number of grids determines not only the computational time but also the need for computational resources. In addition, the iteration error caused in the solution process increases as the number of meshes is on the rise increases. Therefore, it is essential to determine how to choose an appropriate grid number in calculation accuracy and calculation cost for CFD simulation. Figures 3

Figure 3.

Comparison of cylinder pressures of different base grid.

and 4

Figure 4.

Comparison of HRR of different base grid.

present the comparison of the simulation results of cylinder pressure and heat release rate (HRR) in the absence of adaptive mesh refinement and fixed embedding, respectively. Figure 5

Figure 5.

Comparison of result under different BG: (a) pressure, (b) calculation time, (c) P_max, and (d) NO _x .

shows a more intuitive comparison of maximum combustion pressure (P_max), P_max position, NO _x emissions, and computational time consumption for different base grid sizes.

As shown in Figures 3–5, when the base grid size reaches 1 mm, the cylinder pressure, the HRR, and the NO _x emission approach the experimental data. When the basic mesh size is further set to 0.9 mm, the simulation results barely change. The trend of the compression and expansion strokes shows basically no changes, which suggests that they are irrelevant to the choice over the base grid. Close to TDC, the most complex stage of physical and chemical processes, however, the result is affected significantly by base grid size. Therefore, in order to ensure accuracy of calculation and reduce the time for calculation. In this article, the base grid is set to 1.2 mm, while adaptive mesh refinement and fixed embedding are conducted to refine the grid near TDC. Throughout the calculation process, the 2-scales adaptive mesh refinement based on velocity and temperature gradient was performed in the solution region. Fixed embedding is applied to nozzle, piston, and cylinder head. Not only does such grid control approach ensure sufficient calculation accuracy and less computational time for the compression and expansion stroke, it also facilitated the capture of in-cylinder details during the spray and combustion process. With no consideration given to other factors like the combustion model, atomization model, and mechanism, such a grid strategy can achieve an excellent trade-off between simulation accuracy and calculation time.

Model calibration verification

Figures 6

Figure 6.

The comparison of experiment and simulation pressure data.

and 7

Figure 7.

The comparison between calculation and measured HRR.

present the comparison performed between simulation results and experimental data. As shown in Figure 6, the trend of cylinder pressure and HRR is consistent with the experimental data. The errors of critical data are indicated in Table 3

Table 3.

The comparison of critical parameters.

	Experiment	Simulation	Error (100%)
Specific fuel consumption (g/kW·h)	204.8	204.55	0.122
P_max (MPa)	11.57	11.6	−0.26
The time of P_max (°CA)	11.71	11.83	−1.02
NO _x emissions (g/kW·h)	7.6	7.46	1.84
NO _x emission (mg)	5.573	5.47	1.84

. As shown Figures 6 and 7, though the cylinder pressure error is 4.4% when the expansion process is complete, it remains within the acceptable limits.

Correction of HRR

There is a significant difference between the simulation results and the experimental data of HRR, especially the maximum value of the simulation results that is considerably higher compared to the experimental value, which is due to that the HRR obtained by the experimental method is affected by the heat transfer loss of the combustion chamber wall surface, and that this part of the heat transfer loss is neglected at the time of conventional CONVERGE simulation. The HRR of the combustion chamber wall as output of CONVERGE is shown in Figure 8

Figure 8.

HRR of combustion chamber wall.

, while Figure 9

Figure 9.

Comparison of correction of HRR.

presents the comparison between the simulation HRR and the experimental data after subtraction the wall HRR. As revealed by Figure 9, after consideration given to the wall HRR, the simulated HRR peak value approaches the experimental data more. In summary, the errors of cylinder pressure, NO _x emission, and HRR are validated as acceptable, which verifies the model.

Results and discussion

A marine four-stroke diesel CFD model was applied to investigate the effect of different gravity on engine performance and emissions. When the engine worked, the state of the fluid in the cylinder showed a rapid change. It is difficult to observe the effect of gravity on engine performance and emission using the conventional experimental methods. CFD models can be applied to observe the details that are difficult to capture in traditional experiment, and to gain understanding as to the process of combustion and formation of emissions.⁵¹

Figure 10

Figure 10.

The comparison of cylinder pressure and HRR under different gravity.

presents the comparison of cylinder pressure and HRR under different gravity conditions (0, +9.8, and −9.8 m/s²). As shown in Figure 10, gravity has barely any effect on the cylinder pressure but a certain impact on the HRR. The difference of HRR at −3°CA reaches its maximum. The difference is that 0 m/s² is roughly 10.3% higher than +9.8 and −9.8 m/s². The different in NO _x and soot emission is shown in Figure 11

Figure 11.

NO _x emission under different gravity: (a and b) NO _x emission and (c and d) soot emission.

, which reveals that the NO _x emission of 0 m/s² is approximately 6% higher than +9.8 and −9.8 m/s², with the rate of NO _x formation being the highest. The production of soot was maximized at 13°CA. The peak value position of −9.8 m/s² lags 0.2°CA with respect to +9.8 and 0 m/s², and the amount of emission is roughly 1.1% higher. Nevertheless, the soot emissions at 0 m/s² by the end of the expansion stroke were minimized. The parameters of performance and emission are compared under different gravity conditions, as shown in Table 4

Table 4.

Comparison of parameters under different gravity.

	0 m/s²	−9.8 m/s²	+9.8 m/s²
HRR at −3°CA (J/S)	263.56	250.63	263.37
Soot emission at 13°CA (mg)	3.68	3.70	3.66
Soot emission at 13°CA (g/kW·h)	5.02	5.05	4.99
NO _x emission at 50°CA (mg)	5.47	5.14	5.17
NO _x emission at 50°CA (g/kW·h)	7.46	7.01	7.05

HRR: heat release rate.

The penetration length (PL) and Sauter mean diameter (SMD)⁵² of the fuel are shown in Figures 12

Figure 12.

The comparison of SMD under different gravity.

and 13

Figure 13.

The comparison of penetration length under different gravity.

, respectively. Different gravity conditions tend to impact on SMD and PL during the process of atomization and breakup. The same Blob injection model was applied under different condition of gravity simulation (the initial droplet diameter defaults to the same nozzle diameter). As shown in Figure 13, PL shows a declining trend as gravity is reduced. This trend is made more noticeable in the middle and late process of atomization. SMD is the most used indicator to evaluate the quality of fuel atomization. It refers to the ratio of the volume to the surface area of the atomized oil droplets. The smaller the SMD, the faster the evaporation rate of the droplets, and the better the atomization quality of the oil droplets.^52,53 As shown in Figure 12, the SMD prior to burning is consistent with the diameter of the nozzle. SMD will lead to significant fluctuations after the start of combustion (10°CA). The SMD in the absence of gravity is shown to be the minimum.

Equivalent ratio, temperature, and NO _x distribution cloud maps provide more support for the analysis of two-dimensional results. The equivalent ratios, temperatures, and NO _x of contours at different crank angles (11–17°CA) are shown in Figures 14

Figure 14.

The equivalent ratio in different crank angle under different gravity.

–16. The marine diesel engine is fitted with a six-nozzle injector, and the CFD model is 1/6 of the combustion chamber. The turbulence causes the fuel to be distributed clockwise after hitting the cylinder wall in the injection direction. As shown in Figure 15

Figure 16.

The NO _x in different crank angle under gravity.

Figure 15.

The temperature in different crank angle under different gravity.

, the temperature in the combustion chamber rises at a fast pace when combustion occurs. A sharp increase in temperature causes the evaporation rate of the droplets to exceed burning rate. The difference between the evaporation rate and the burning rate results in the formation of a substantial amount of oil and gas mixture. Therefore, as shown in Figure 14, the equivalence ratio is high at the front surface of the spray, particularly near the wall surface. According to Figures 14 and 15, the equivalence ratio on the flame surface of the diffusion combustion shows a gradual decline as the combustion rate is on the rise. NO _x production is directly associated with oxygen concentration and temperature.^3,50 NO _x is mainly produced in the areas with high temperature and abundant oxygen. It is easy to observe that the amount of NO _x produced is high in a region with appropriate equivalent ratio and temperature.

As shown in Figures 14–16, the difference in equivalence ratio, temperature, and NO _x under different gravity conditions is self-evident. Figure 12 shows the effect of gravity on SMD. SMD bears an inverse proportionality to the evaporation rate of the fuel droplets. The effect of gravity on SMD is the root cause of the difference in equivalence ratio, temperature, and NO _x distribution. Except for 0 m/s², regardless of whether it is +9.8 or −9.8 m/s², the existence of gravity causes the temperature in the core region of the cylinder to be higher, the distribution to be wider, and the NO _x formation area to be expanded significantly.

Conclusion

In this article, experimental data are used to calibrate and validate the CFD model. Cylinder pressure, HRR, and NO _x emissions are well consistent with experimental data. Based on this CFD model, the simulation results of three gravity models are analyzed. The effects of performance and emissions on four-stroke marine diesel engines are investigated, which leads to the following results:

The validity of the model has been confirmed. There is almost no error in the cylinder pressure, and the NO _x emission error is 1.84%. The HRR in the absence of wall heat transfer is different from the experimental value by −10.58%, and the difference of HRR after consideration given to the wall heat dissipation value is 5.82% compared to the experimental value. In the process of CFD simulation, the correction of HRR is vitally important.

Gravity conditions have little effect on HRR, and soot production is basically irrelevant to gravity. The effect of gravity on the NO _x emissions of marine diesel engines can be maximized to 6.03%. The contours of temperature and NO _x emission are different for different gravity. This can explain the different results for marine diesel engine emission characteristics under different gravity.

Under three gravity models, there are differences observed in fuel atomization and spray. SMD fluctuates considerably after the process of combustion starts. This tends to be affected by the evaporation rate of the fuel droplets and in-cylinder temperature. PL is proportional to the gravity, which is because the natural convection almost disappears with the disappearance of gravity. Moreover, turbulence intensity in the cylinder will be reduced.

Due to the difference in fuel spray and atomization, the equivalence ratio distribution is different which is the range of equivalence ratio distribution under non-gravity conditions is smaller. The temperature field remains distributed in line with the contour of the equivalence ratio. NO _x is generated in high temperature and oxygen-rich regions, and the difference in temperature and equivalence ratio is also contributory to the difference in NO _x distribution in the absence of gravity conditions.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors thank Natural Science Foundation Committee of China (No. 51709163), China Postdoctoral Science Foundation (No. 2018T110382), Shanghai Sailing Program (No. 17YF1407500), for the financial support.

ORCID iD

Xiuwei Lu

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Numerical simulation of performance and emission of marine diesel engine under different gravity conditions

Abstract

Keywords

Introduction

Gravity condition

Simulation software

Simulation model

Brief description of the CFD model

Best base grid size

Model calibration verification

Correction of HRR

Results and discussion

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References