1053
1 INTRODUCTION
The vessel is designed for the transport of the following
bulk cargoes: iron ore, grain, coal, phosphates and
similar. The vessel is built as a single propeller bulk-
carrier with machinery compartment and
superstructure at the stern. The ship has a continuous
deck with a deckhouse and stern rudder.
The vessel is powered by a supercharged diesel
engine, type MAN-B&W 6 S50MC-C reversible with
rated power 9480 kW at 127 rpm. The engine is a 6-
cylinder, 500 mm bore and 2300 mm stroke. At rated
power and with the supercharging system running, the
approximate fuel consumption is 173 g/kWh and the
oil consumption is 2.25 kg/h.
The main engine is designed to run on heavy fuel
(marine diesel) with a maximum viscosity of 3500
sec.Redwood at 380 Centigrade.
Satisfactory torsional vibration behaviour has been
found both under normal conditions and when a
cylinder is not operating properly. Maximum
crankshaft vibration stresses never exceed the limits of
the diesel crankshaft. Maximum vibration stresses in
the countershaft and propeller are below the guide
lines.
Modelling the Combustion Process of Marine Diesel
Engines to Reduce Pollutant Emissions and Influence
Vibrations at the Propeller Shaft for a Bulk Carrier
Vessel
L.C. Stan
Constanta Maritime University, Constanta, Romania
ABSTRACT: The modeling of the combustion process in internal combustion engines has always been a major
concern for experts in the field. The complex nature of the phenomena involved and their strong
interdependencies make the approach particularly challenging. The implementation of the provisions outlined in
the 1997 Protocol's Annex 6, which aimed at limiting pollutant emissions from ships, especially nitrogen oxides,
has been a significant focus for signatory countries since 2010. Coastal areas, particularly those frequented by port
technical vessels, have been identified as the most affected regions. From the technical documentation of the ship
received on board the ship in the design phase, the following values were calculated: actual diameter of the
intermediate shaft 387.2 mm adopting 420 mm, actual bore diameter of 472.4 mm adopting 500 mm, flange
thickness coupling 77.4 mm, adopted 100 mm, calculated radius of thread at the base of the 33.6 mm coupling
flanges adopted 70 mm, actual diameter of the 46.6 mm flange shaft flange bolts, adopted 64 mm. The ship's
propeller has four fixed-pitch blades and a weight of 31.42 tons. Furthermore, torsional vibrations, tree alignment
calculations, torsional vibration calculations, critical vibrations, propeller design calculations were calculated in
the project. As can be seen from the simulation results, the front-wheel resonance is 155% of the maximum engine
speed (127.0 rpm) and the critical resonance is 133% of the maximum engine speed. The result of the spin
calculation is therefore acceptable and is not expected to occur at the speed of the engine.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 3
September 2025
DOI: 10.12716/1001.19.03.40
1054
The indicated speed range (55~67 rpm) should be
achieved against I-6.0 under normal conditions and
with one cylinder running rough. In the case of
improperly operating one cylinder, engine speed
should not exceed 110 rpm (87% of MCR) to avoid
resonance of the order of 3.0 and thermal overload of
the working cylinders.
The second objective of this paper is to develop a
simulation program that can estimate nitrogen oxide
emissions produced by compression ignition engines.
This idea is based on an analysis of the methods used
to implement the regulations specified in Annex 6 of
the 1997 Protocol, which focuses on controlling
emissions from ships, specifically nitrogen oxides.
The combustion process is undoubtedly the most
crucial and complex process occurring in engines. It is
responsible for the energy flow used in the engine and
is directly linked to all pollutant emissions.
Furthermore, the combustion process significantly
influences engine efficiency. Despite considerable
advancements, the mechanisms of combustion,
particularly mixture formation and the chemistry
involved, remain complex and not fully understood
[1].
The technical characteristics of the ship are:
− IMO number: 9633422;
− Call sign: SVBV2;
− Gross tonnage: 85773;
− TDW: 70434;
− Ship type: Bulk carrier;
− Year of construction: 2014;
− Flag: Greece;
− Construction length: 294.2 meters;
− L between perpendicular: 289 meters;
− Maximum width: 46 meters;
− Construction: Daewoo SB & ME Co., KOR;
− Engine model : 6S50MC-C
− Power at MCR (Kw) : 9480.00
− Speed at MCR (rpm) : 127.00
− Crankshaft : FSB 242456
− Vibration damper : N/A
− Support bearing : M.O.I. = 12249.0 Kg
− Support bearing : M.O.I. = 3539.5 Kg
− Intermediate shaft : D 420.0 / 0.0, UTS = Min. 560
N/mm
2
− Carrier shaft : D 510.0 / 0.0, UTS = Min. 560 N/mm
2
− Propeller : 4-BLADE F.P.propeller
2 PROPULSION SYSTEM SHAFT LINE ANALYSIS
The analysis of the propulsion system's shaft line using
the Finite Element Method (FEM) starts with the
premise that calculating the exact parameters
(displacements, forces) for a continuous structure with
complex geometry and boundary conditions is either
infeasible or excessively demanding. If an approximate
solution that is easier to calculate and reasonably
accurate can be obtained, it is considered an acceptable
solution for the initial structure. In essence, FEM
replaces the structure under analysis with a simplified
model that facilitates the calculation of parameters. For
structures, FEM can be viewed as an extension of the
classical matrix statics method, which was developed
for studying assemblies with one-dimensional
structural elements (bar structures). FEM enables the
analysis of two-dimensional and three-dimensional
continuous structures [6].
The process involves discretizing the analyzed
structures (either naturally or artificially) and
establishing the equilibrium matrix equation for each
finite element using a direct formulation (typically
represented as a system of algebraic equations). The
discrete model's finite elements must be compatible
with the structure's spatial development and the
mathematical model used to simulate its behavior. For
instance, if the structure has a unidirectional
development, one-dimensional (1D) finite elements,
either straight or curved, are used. In the case of a flat
development, two-dimensional (2D) finite elements
with straight or curved sides are employed. Similarly,
for spatial developments, three-dimensional (3D) finite
elements with flat or curved faces are used. In this
study, the analysis focuses on the shaft line of a
reference ship, which has a total length of 15 m, and the
inner diameter is Dint = 0.4 ∙ Dext. The shaft
construction is simple, without flanges.
The shaft model is generated using specialized
software such as Ansys, which is designed for finite
element analysis. Subsequently, the following
operating scenarios are analyzed: operating the engine
at maximum power and locking the propeller in
situations such as landing on a sandbank, as well as the
normal operating mode of the propulsion system when
the ship reaches a maximum speed of 15 knots (Nd), a
speed corresponding to the maximum power of the
propulsion engine.
Additionally, the simulation considers the pushing
force at its maximum value. To initiate the simulation
process, the measurement units for the precise
determination of shaft line parameters are established.
Geometric parameters, such as length along the X, Y, Z
axes, volume, mass, scaling factor, number of bodies,
number of active bodies, and type of analysis (in this
case, three-dimensional), are introduced.
Subsequently, the Ansys program automatically
generates the geometric model of the shaft:
Figure 3. Generating the shaft geometric model [5]
The next step involves defining the coordinate
system and setting parameters for generating the
discretized model of the shaft. Once the model is
generated, the shaft's discretization is performed using
square finite elements [5].:
1055
Figure 4. Performing shaft discretization using square finite
elements [5]
The analyzes can then be performed on the defined
and discretized model of the shaft. As in the previous
steps, a series of parameters are redefined and then
loads related to the motor torque are applied:
Figure 5. Applying loads related to the motor torque on the
shaft [5]
The specified torque given by the engine depends
on the parameters for the analysis of total, directional,
stress deformations are defined below, as shown in the
figures below:
Figure 9. Diagram of total deformations expressed in [mm]
[5]
2.1 Natural frequencies and resonance modes
At the end of the analysis the program automatically
generates a series of tables in which data are presented
regarding the qualities of the material from which the
shaft line is produced and how it behaves during the
simulation.
Table 1.
Module no.
2
3
Frequency (Cpm)
1356.5
2775.3
Nr
1
- 0.7925
- 0.5072
2
- 0.5603
0.1150
3
- 0.2492
0.7282
4
0.0860
1.0000
5
0.4214
0.8062
6
0.7020
0.2448
7
0.8968
- 0.4022
8
0.9733
- 0.7613
9
1.0000
- 0.9211
10
0.2915
- 0.3440
11
- 0.0507
- 0.0126
Module no.
2
3
Frequency (Cpm)
1356.5
2775.3
Nr.
1
- 0.197 ∙ 10
6
- 0.529 ∙ 10
6
2
- 0.247 ∙ 10
6
- 0.487 ∙ 10
6
3
- 0.269 ∙ 10
6
- 0.218 ∙ 10
6
4
- 0.261 ∙ 10
6
0.151 ∙ 10
6
5
- 0.224 ∙ 10
6
0.448 ∙ 10
6
6
- 0.162 ∙ 10
6
0.539 ∙ 10
6
7
- 0.832 ∙ 10
5
0.390 ∙ 10
6
8
- 0.433 ∙ 10
5
0.260 ∙ 10
6
9
0.305 ∙ 10
5
- 0.248 ∙ 10
5
10
0.323 ∙ 10
5
- 0.336 ∙ 10
5
Table 2. Engine resonance speed and vector summation
Order
Natural frequency (Cpm)
362.9
1356.5
2775.3
1.0
363/ 0.035
1356/ 0.176
2775/ 1.817
2.0
181/ 0.155
678/ 1.084
1388/ 0.352
3.0
121/ 0.410
452/ 3.059
925/ 1.194
4.0
91/ 0.155
339/ 1.084
694/ 0.352
5.0
73/ 0.035
271/ 0.176
555/ 1.817
6.0
60/ 5.390
226/ 1.446
463/ 2.492
7.0
52/ 0.035
194/ 0.176
396/ 1.817
8.0
45/ 0.155
170/ 1.084
347/ 0.352
9.0
40/ 0.410
151/ 3.059
308/ 1.194
10.0
36/ 0.155
136/ 1.084
278/ 0.352
11.0
33/ 0.035
123/ 0.176
252/ 1.817
12.0
30/ 5.390
113/ 1.446
231/ 2.492
13.0
28/ 0.035
104/ 0.176
213/ 1.817
14.0
26/ 0.155
97/ 1.084
198/ 0.352
15.0
24/ 0.410
90/ 3.059
185/ 1.194
16.0
23/ 0.155
85/ 1.084
173/ 0.352
17.0
21/ 0.035
80/ 0.176
163/ 1.817
18.0
20/ 5.390
75/ 1.446
154/ 2.492
19.0
19/ 0.035
71/ 0.176
146/ 1.817
20.0
18/ 0.155
68/ 1.084
139/ 0.352
Stress value : 83.5 N/mm
2
Speed : 60.5 rpm
No. of shafts : 9
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Table 3. Table with maximum stress data (N/mm
2
)
RPM
1
2
3
4
5
6
7
8
9
10
82
3.8
7.9
8.9
6.6
10.6
9.9
2.6
2.9
10.5
5.9
84
4.3
9.0
9.9
7.2
11.4
10.4
2.8
3.0
10.3
5.7
86
5.0
9.6
10.0
8.0
11.9
10.2
3.1
3.2
10.6
5.9
88
5.4
10.0
10.3
8.8
12.6
10.4
3.5
3.5
11.7
6.5
90
7.5
12.2
13.4
12.2
15.3
11.8
5.0
4.6
13.3
7.5
82
6.3
12.0
12.3
10.3
13.5
10.1
4.2
4.0
12.1
6.8
94
5.2
11.0
11.7
8.9
12.2
9.3
3.2
3.2
11.1
6.2
96
5.6
11.0
12.6
9.2
11.9
10.0
3.0
2.9
9.9
5.5
98
5.5
11.0
12.1
8.7
12.1
10.9
2.7
2.7
9.2
5.1
100
4.8
11.0
11.4
8.1
12.4
11.1
2.2
2.5
8.8
4.9
102
4.7
11.3
11.5
7.9
12.8
11.1
2.0
2.3
8.6
4.8
104
4.8
11.7
11.9
8.0
13.1
11.4
2.0
2.3
8.4
4.7
106
5.1
12.7
12.9
8.6
14.0
12.3
2.1
2.3
8.6
4.8
108
5.1
12.7
12.9
8.6
14.0
12.3
2.1
2.3
8.6
4.8
110
5.3
12.8
13.3
8.9
14.6
13.0
2.3
2.4
8.8
4.9
112
6.4
14.7
15.6
10.5
16.3
14.4
3.0
2.8
9.8
5.5
114
6.5
14.3
15.4
11.1
17.3
15.2
3.6
3.1
10.7
6.0
116
5.9
13.7
14.8
10.3
16.9
14.8
4.0
3.7
15.2
6.8
118
5.9
14.4
15.4
10.4
16.9
14.8
4.9
4.7
15.4
8.6
120
6.5
15.2
16.5
10.8
16.4
14.8
5.4
5.5
18.7
10.4
122
6.7
15.3
16.9
10.0
15.9
14.9
4.9
5.2
18.7
10.4
124
6.5
15.0
16.6
9.2
16.1
15.4
4.4
4.6
15.9
8.9
126
6.2
15.3
16.6
9.2
16.4
15.9
4.0
4.1
14.2
7.9
128
6.2
15.6
16.9
9.7
16.9
16.1
3.6
3.5
12.7
7.1
130
6.6
15.9
17.5
10.3
17.2
16.4
3.4
3.1
11.2
6.3
132
7.5
16.6
18.5
11.3
17.7
17.0
3.3
2.8
10.2
5.7
134
9.0
18.6
20.5
13.2
18.3
18.1
3.7
2.8
9.7
5.5
136
10.8
20.8
21.6
14.8
20.6
18.0
3.9
2.6
10.0
5.7
138
10.1
18.9
18.5
13.0
19.8
16.4
3.2
2.2
9.0
5.1
140
9.6
18.0
17.6
12.3
20.3
16.4
3.1
2.0
8.3
4.7
The values with a negative sign are the vibratory
torques (kNm)
Engine type : 6S50MC-C
Tuning wheel : 12249.0 kgm
2
MCR rating : 9480 kW × 127 rpm
Turning wheel : 3539.5 kgm
2
Combustion conditions : Normal combustion
Gas harmonics : 242503
Speed range limit : 55 ~ 67 RPM
Limit : Diesel engine crankshaft limits
Crankshaft : FSB 242456 / SOLID CRANK PIN
Figure 10. Torsional vibration stress of crankshaft No.6 DIA.
= 600.0 mm UTS = 610.0 N/mm
2
Limit tau1 : Limit for continuous fuctioning with
factor 1.0 Ck
Limit tau2 : Limit for transient operation
Figure 11. Torsional vibration stress of intermediate shaft
No. 9. DIA. = 420.0 mm UTS = 560.0 N/mm
2
Figure 12. Maximum and minimum torque. Average torque
of the carrier shaft 10
Speed range limit : 55 ~ 67 RPM
Maximum speed : ~ 110 rpm (Misfiring only)
Limit : Diesel crankshaft limits
Crankshaft : FSB 242456 / SOLID CRANK PIN
Figure 13. Torsional vibration stress of crankshaft No. 7. DIA.
= 600.0 mm UTS = 610.0 N/mm
2
1057
The alignment calculation for the shaft system was
performed using the Nauticus Shaft Aligment
program. The shaft alignment procedure is followed
the standard shipyard procedure. Verification of the
shaft alignment results shall be carried out according
to standard shipyard methods. (Gap & SAG, jacking,
etc.)
The purpose of this shaft alignment calculation is to
find a set of vertical offsets for the intermediate shaft
bearings and engine bearings to ensure that the bearing
loads are kept within limits for all bearings.
Figure 14. Shaft alignment
Material data
Material data
Conditions
E-MOD (N/m
2
)
Density (kg/m
3
)
1
In the air
2.10 ∙ 1011
7 850
2
In the see water
2.10 ∙ 1011
6 850
3
In fresh water
2.10 ∙ 1011
7 000
4
Unweighability
2.10 ∙ 1011
0
Propeller weight:
50% submerged (half submerged) : 16.347 kg - 1.102 kg
= 15.245 kg
Propeller weight in air : 16,347 kg
Propeller weight half submerged : 1/2 × 16.347 kg /
7.600g/cm
3
× 1.025g/cm
3
= 1.102 kg
75% submerged : 16.347 kg - 1.653 kg = 14.694 kg
100% Immersed (Totally submerged) : 16,347 kg -
2,205 kg = 14,142 kg
Figure 15. Graphical results of the loading of the pens
The calculation is conducted at maximum speed
and power, with an engine speed of 2400 rpm, effective
power of 48 kW, specific consumption of
238.077 g/kWh, and an effective injection advance of β
= 5.5°RAC (rotation angle of the crankshaft). The
program performs an engine cycle starting at 120 °RAC
before the inner neutral point (INP). At this point, it is
assumed that turbulence in the cylinder ensures
uniform velocity gradients, resulting in approximately
uniform velocity within the cylinder. The program
utilizes 12 modes, and the fuel considered is saturated
pure hydrocarbon C10H20. The reactions are divided
into four slow kinetic reactions (fuel oxidation and the
extended Zel'dovich mechanism for nitrogen oxide
formation) and eight equilibrium reactions (element
dissociation reactions). The injection advance is set to
5.5 °RAC, and the injection duration is 17 degrees. The
average Sauter diameter (DSM) is set to 1x10
-3
cm. The
discretization network comprises 624 nodes and 583
cells. The size of the discretization network can be
adjusted using a set of parameters. Comparative values
of pressure and temperature, both calculated and
measured, are depicted in Figure 16 [2].
The simulation process requires 36 hours and 23
minutes of computation time for the given
discretization network, which includes 624 computing
cells and 1230 drop packets. The maximum amount of
working memory required is 425 MB. The output data
is stored in 2153 text files (one file for every 0.1°RAC),
occupying 682 MB of hard disk storage.
Figure 16. Indicated pressure
Figure 17. Cycle average temperature
The results obtained from the specific files are
processed using a program written in Matlab, and the
resulting graphs are presented below. Due to the large
dimensions of the tables with values, which lack
practical relevance, only the commentaries on each
chart are provided. Figure 16 shows a comparison
between calculated and experimentally measured
pressure values per cycle [3].
The calculated and measured pressures show good
agreement, with the exception of the combustion
period, during which the calculated pressure is
significantly higher than the measured one. This
disparity is expected to some extent, given the
combustion model used and the discretization scheme
employed. The scientific literature includes numerous
examples of simulations performed with similar
1058
models (e.g., KIVA I, Conchas-Spray), which have
highlighted similar issues. Due to this discrepancy, it is
anticipated that other quantities will be affected,
particularly the emissions of nitrogen oxides.
Some results are provided below to demonstrate the
program's capabilities.
The calculated average temperature within the
cylinder is presented, where the calculated
temperature represents the mass average of
temperatures in the computing cells for each time step.
The maximum pressure per cycle affects the
temperature, leading to a sharp increase in nitrogen
oxide concentrations [4].
Figure 18.Velocity distribution in the cylinder for
400°RAC[5]
Figure 19. Fuel jet at 357 °RAC and 2 °RAC, after injection
start[5]
Figure 20. Evolution of NOx concentration in the cylinder,
during one cycle
Figure 20 shows the evolution of the NOx
concentration in the cylinder over a cycle calculated
using the program and the experimentally measured
average value. As expected, there are big differences.
The maximum pressure per cycle influenced the
temperature, which caused a sharp increase in the
concentration of nitrogen oxides [6].
From the analysis of the results, it can be seen that,
for the combustion process, the obtained results have
only a qualitative character, these obtained values not
being in accordance with the measured values. Instead,
the evolution of the phenomena (as they are described
in the literature for similar cases) inside the cylinder is
captured with sufficient accuracy. Thus, one may
notice:
− vortices created by the fuel jet,
− the effect of the combustion chamber in the piston
head which:
− concentrates, in the first phase of the combustion
process, hot gases, having high concentrations of
fuel vapors and low concentrations of oxygen,
preventing the formation of NOx;
− in the second phase, the hot gases come out strongly
turbulent from the
− combustion chamber and mix with the air from the
upper dead sap, maintaining a high temperature
and pressure;
− the presence of flame at the periphery of the fuel jet
in the envelope, where the mixtures have
concentrations close to the stoichiometric ones;
− NOx formation in areas with high temperatures and
poor mixtures at the periphery of the jet;
− the presence of vortices at the exit of the rich
mixtures from the combustion chamber, from the
piston head, vortices that prevent the uniformity of
the mixtures;
− the presence of areas on the wall with low
temperatures and areas without mixing, where,
depending on the flow regime, unused air may
remain.
Apart from the limitations imposed by the adopted
models, presented in the theoretical substantiation,
there are other problems related to the numerical
solution of the system of differential equations, which
do not exactly meet all the requirements (as far as they
are known) of stability and convergence.
Some known problems in the literature, frequently
encountered in the case of internal combustion
engines, were also highlighted for the case under
consideration.
Due to the obtained high pressures, other results, as
expected, were altered, among them being the
emissions of nitrogen oxides, which had values much
higher than the measured ones.
As the proposed algorithm is based on the implicit
calculation of the pressure, its value being
used to update the other parameters, it goes
without saying that it is necessary to implement
algorithms designed to reduce it to acceptable and
realistic values.
This approach was also preferred due to the
experimental database, so that the pressure is the only
quantity for which the instantaneous values in the
cycle are known, and the other measured quantities
being averaged over several cycles [7].
3 CONCLUSIONS
The results obtained in this study have a qualitative
nature, as the values do not perfectly align with the
measured ones. However, the evolution of phenomena
inside the cylinder is captured with sufficient accuracy.
This includes the vortices created by the fuel jet, the
impact of the combustion chamber on the piston head,
1059
the presence of flame at the periphery of the fuel jet in
the tire, the formation of nitrogen oxides in high-
temperature areas and lean mixtures at the jet's
periphery, and the presence of vortices at the outlet of
rich mixtures from the combustion chamber into the
piston head. Furthermore, areas on the wall with low
temperatures and areas without a direct connection to
the combustion chamber are identified. These results
allow for an improved understanding of the
combustion process and the subsequent emission
formation mechanisms. Future studies should focus on
refining the combustion model, especially during the
combustion period, where the measured pressure
values differ from the calculated ones. Additionally, a
more detailed analysis of nitrogen oxide formation
should be performed to accurately predict emission
levels. To achieve this, additional mechanisms should
be included in the combustion model to account for
thermal and prompt mechanisms, as well as the impact
of turbulence on flame structure. The study is limited
by the available computational resources, which
restricted the resolution of the discretization network
and the simulation duration.
As can be seen from the results, the forward spin
resonance is 155% of the maximum engine speed (127.0
rpm) and the critical resonance is 133% of the
maximum engine speed. The result of the rotation
calculation is therefore acceptable and is not expected
to show engine speed.
Also, from the mathematical model that the
forward spin resonance is 155% of the maximum
engine speed (127.0 rpm) and the critical resonance is
133% of the maximum engine speed. The result of the
rotation calculation is therefore acceptable and no
engine speed variations are expected to occur.
REFERENCES
[1] SABĂU A., BUZBUCHI N., ŞOLOIU V. A., Combustion
Numerical Modelling in Diesel Engines, the 11th National
Conference for Thermotechnics, Galaţi, (2001).
[2] SABĂU A., BUZBUCHI N., ŞOLOIU V. A., Combustion
Processs Simulation, Analele Universităţii ”Ovidius”,
Constanța, (2000).
[3] SABĂU A., BUZBUCHI N., SABIE, S., Modelarea jetului
axisimetric, Analele Universităţii Maritime din
Constanța, Constanţa, (2003).
[4] FAITAR C., NEDELCU A.T., BUZBUCHI N., STAN L.,
DUMITRACHE L. M. Considerations of the energy
balance of an internal combustion engine and the
recovery of heat lost through the cooling water, IOP
Conference Series: Materials Science and Engineering,
ModTech 2019,
https://iopscience.iop.org/article/10.1088/1757-
899X/591/1/012088/meta , (2019)..
[5] ANSYS.
[6] WIESER K., VERSAEVEL P., MOTTE, P., A New 3D
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