Ứng dụng phương pháp tính toán động lực học lưu chất (CFD) trong tối ưu hóa hình dạng mũi tàu quả lê ttta

MINISTRY OF TRANSPORT

MINISTRY OF EDUCATION AND TRAINING

HOCHIMINH CITY UNIVERSITY OF TRANSPORT

HUYNH VAN CHINH

APPLICATION OF COMPUTATIONAL FLUID
DYNAMICS (CFD) TO OPTIMIZE BULBOUS
BOW SHAPE

SUMMARY OF DOCTORRAL THESIS

MAJOR:
SECTOR CODE:

MECHANICAL ENGINEERING
9520116

Supervisors 1:

Assoc Prof. Dr. TRAN GIA THAI

Supervisors 2:

Dr. BUI HONG DUONG

HO CHI MINH CITY – 2022

1
PREAMBLE
1. REASONALE
Using the bulbous bow is not only an effective solution to reduce the total
resistance but also improves most important performances of the ships, and thus to
enhance safety and economic-techno efficiency for seagoing ships such as
increasing speed, decreasing fuel consumption, improving stability and
seakeeping, etc. However, due to the complexity of the interactions between the
wave systems above and the bulb also not being efficient at all ship speeds, the
design and prediction of the capacity of a bulbous bow ship has always been
complicated and controversial. Under favorable circumstances, a bulb will produce
the bow waves that interfere positively with the waves generated by a hull,
resulting in a reduction in total resistance (12 -15%). Conversely, a negative
interference between these two wave systems can occur and greatly increase the
resistance. In the past, the bulbous bow and position were determined through
model testing, but such tests took a lot of time, effort, and expense. Along with the
development of computers is the appearance of the CFD (Computational Fluid
Dynamics) method which effectively solves many practical problems in general
and the bulbous bow optimization problem in particular. In recent times, along
with the strong development of the fishery industry and the support of the State
through Decree No.67/2014/NĐ-CP, a series of steel fishing vessels under 30 m
have been built to serve offshore fishing operations. These ships are built
according to domestic designs, most of which have not been model tested, so, in
fact, there are some models that are not really suitable for the fishing industry,
leading to low maritime features and efficiency. Due to the lack of data on the
operation of the bulbous bow, most fishing vessels in our country are designed
with a straight bow, not equipped with a bulb. This also affects the ship’s
performance when traveling in waves, especially with resistance and shaking
properties, which are essential maritime features for fishing vessels. With the
policy of modernizing the fishing fleets, the State is very eager to develop the

design of modern steel fishing vessels with a length of over 40m to reach offshore
fishing grounds and protect national maritime security. From the practice of the
fishing fleets, we have proposed to develop small and medium-sized steel fishing
vessels that have been tested by the United Nations Food and Agriculture
Organization (FAO) in famous test tanks with the desire to use these models as a
basis for designing fishing vessels that ensure features and are suitable for fishing
activities in our country today.
That is the reason for the implementation of the thesis entitled “Application of
Computational Fluid Dynamics (CFD) to optimize bulbous bow shape” to develop
a method to design and optimize the bulbous bow for ships in general and for steel
fishing vessels in particular to serve the current database of steel fishing vessel
designs in our country.


2
2. OBJECTIVE, OBJECT, AND SCOPE OF STUDY
2.1. Objective of study
The objective of study is to apply CFD in optimizing the bulbous bow based
on ensuring the maximum reduction in the total resistance of the ship and
satisfying the constraints set forth in terms of geometry and marine features.
2.2. Object and scope of study
The objects of study are the FAO’s small and medium-sized steel fishing
vessels with and without bulbs that were model tested to determine resistance.
With such objects of study, the scope of study is as follows:
- The ships move in a straight line in still water, not affected by the wave
system and air resistance, with unlimited depth.
- The fluid used for simulation is homogeneous, viscous, and incompressible.
- Resistance test data in the test tank for comparison is considered accurate
and is the basis for evaluating and correcting simulation parameters when
calculating resistance of ships by CFD method.

3. RESEARCH METHOD AND STRUCTURE OF THE THESIS
The method used is theoretical research combined with the use of available
experimental data of calculated ship samples to test and correct the theoretical
research results to match the calculated ship types.
The thesis is structured into four chapters as follows:
Chapter 1. Literature review
Presenting an overview of studies related to the topic of the thesis and, based
on that, analyzing and choosing a research direction to solve the goals and contents
set out in the thesis.
Chapter 2. Calculation of ship resistance by CFD
Presenting an overview of CFD theory and research results on the application
of the CFD method in calculation of resistance of ship models.
Chapter 3. Optimal design of fishing vessel's bulbous bow
Presenting the geometrical features of the bulbous bow and the research
results on building a model and a method to solve the problem of optimizing the
bulbous bow form for ships in general and fishing vessels in particular.
Chapter 4. Conclusions and recommendations
Presenting new findings, conclusions, and recommendations drawn from the
research results and future research directions.


3
4. SCIENTIFIC AND PRACTICAL SIGNIFICANCE OF THE THESIS
In terms of scientific significance, the thesis contributes the following specific
results:
- Building a theoretical basis and practical application of CFD to accurately
calculate the resistance of a specific type of ship, particularly medium and large
steel fishing vessels, slow running, short body length, with or without bulbous
bow, including the following contents: building and examining the accuracy of the
3D ship model, determining the simulation parameters (input parameters for the

CFD solution) suitable for the type of ship being calculated to ensure the
differences between the results calculated from the CFD and the model experiment
within the allowable limit (less than 5%).
- Proposing a method to optimize the form of the bulbous bow, including
building an optimal model, analyzing and selecting the calculation modes suitable
for fishing vessels, building plans for calculating the bulb, and building and
calibrating the surrogate model to determine the optimal bulb alternative.
- Serving as the basis for solving many hydrodynamic problems of ships in
general and fishing vessels in particular, especially the problem of optimizing ship
form.
In terms of practical significance, the thesis contributes the following specific
results:
- Supporting the design and manufacture of bulbous bows for ships in general
and large steel fishing vessels in general.
- Providing teaching and research materials in the field of ships in general and
fishing vessels in particular.
5. SUMMARY OF NEW CONTRIBUTIONS OF THE THESIS
(1) Applying the CFD method to accurately calculate the resistance of a
specific type of ship, in this case FAO steel hull fishing vessel models, based on
ensuring accuracy when building 3D geometric models and determining the
reasonable values of the simulation parameters, including the dimensions of the
computational domain and the parameters of the entanglement model, which are
turbulent kinetic energy k and turbulent kinetic energy diffusion rate ω.
(2) Proposing the use of Kracht graph to design bulbous bows for ships with
block coefficients that are not within the scope of application of this graph and
applying it in the design of bulbs for calculated ships with block coefficients out of
range of graph application and integrating bulb form into design ship line to ensure
even smoothness between two surfaces, not changing defined form and bulb
parameters.
(3) Proposing models and methods to optimize the form of the bulbous bow of

fishing vessels, including: Building of a multi-objective function according to the
typical working modes of a fishing vessel; Analysis and selection of changing
ranges of design variables and constraints; and method of solving bulbous bow
optimization problem based on the alternative option and model methods.


4
CHAPTER 1. LITERATURE REVIEW
1.1. OVERVIEW OF RELATED RESEARCHES
The bulbous bow was created in the early twentieth century, but it was not
until 1910 that Taylor (USA) incorporated it into the design of the USS Delaware.
However, it was still not widely accepted. Formal studies of this bow type began
in the late 1950, and it was not until 1960 that civil and military ships were
equipped with many of these bows. In general, researches could be divided into
two main directions:
1.1.1. Traditional researches
Traditional researches often conduct model tests in test tanks to determine the
forms and sizes of bulbs suitable for the ships. There have been many
experimental researches of Kim (1961), Inui (1962)… but the most effective are
the experimental graphs of Kract (1978).
1.1.2. Modern researches
Current bulb researches usually calculate the ship's resistance then change the
form of the bulb to find the most favorable option in terms of resistance. The
overview of related studies can be divided into two main directions as follows.
1.1.2.1. Bulbous bow optimization based on CFD and option method
Studies in this direction often use CFD to calculate resistance for ships with
bulbous bows, and then resize the bulbs by certain increments to select the optimal
bulb form with a reduction in total resistance compared to the largest initial. The
representatives in this direction include a study by D.A.Cominetti, University of
Genoa (Italy) and that of Grzegorz Filip at the University of Michigan, who

performed the bulb optimization for KCS ship. This method often combines the
use of a surrogate model to find the optimal option based on the original set of
discrete resistance data.
1.1.2.2. Bulbous bow optimization based on parametric method
This research direction uses the parametric model built from a set of basic
curves that are used to represent the hull and bulb lines. Then, the lines and faces
forming the surface of the ship and the bulb are interpolated from the above basic
lines, so it is possible to change the form of the hull and the bulb effectively.
The relationship between the ship's geometrical parameters and the model
parameters is established to select the optimal geometrical parameters that are the
design variables of the optimization problem to determine the optimal form of the
hull or bulbous bow. Gradient or genetic algorithms are often combined to find the
optimal option. A typical representative of this research direction is Weilin Luo
(China) who used control parameters to create basic lines to describe the bulb
form.


5
1.2. ANALYSIS AND SELECTION OF RESEARCH DIRECTION
1.2.1. Analysis of related research directions
From the overview of related researches, PhD candidate (NCS) draw some
comments as a basis for choosing my research direction, specifically as follows:
(1) Optimization researches are usually carried out for ships that already have
bulbous bows. Ship models also have geometrical and hydrodynamic
characteristics different from fishing vessels.
(2) The optimal objective function is the total resistance of the ship calculated
by the CFD method, but there is no solution to guarantee the accuracy of the
resistance calculation result.
(3) Kracht's graphs are used to design bulbs but only for ships with block
coefficients within the range CB = 0.56 - 0.82.

4) The bulb optimization model is not suitable for fishing vessel working
characteristics with single objective function of resistance. The design variables
are bulb sizes, while constraints related to ship features are rarely mentioned.
1.2.2. Selection of research direction
(1) Selecting the research object as a steel fishing vessel with a bulbous bow
(FAO 72) and without a bulbous bow (FAO 75) that are used as design models for
some recent Vietnamese fishing vessels, and there are sufficient data of model
testing implemented by the United Nations Food and Agriculture Organization
(FAO).
(2) Researching solutions to ensure the accuracy of the ship resistance
calculation results by CFD based on ensuring the accuracy of the CFD solution
input, including the 3D model and the simulation parameters suitable for the
calculated ships.
(3) Researching the use of Kracht graphs to design bulbs for ships with block
coefficients that are not within the scope of application of these graphs.
(4) Building models and optimization methods for bulb forms, including
determining design variables, multi-objective functions, constraints, and solutions
suitable to the working characteristics of fishing vessels to ensure the best
efficiency of the bulbs, without affecting the ship performance.


6
Conclusion of Chapter 1
The Chapter presents an overview of related studies and analyzes and develop
the research direction, including the following contents:






Analyzing and selecting calculated ships based on the objectives and
contents of the thesis.
Researching and applying CFD to accurately calculate the calculated
ship's resistance.
Researching the use of Kracht graphs to design bulbs for fishing vessels
with block coefficients that are not within the scope of application of
these graphs.
Building models and methods to optimize bulbous bows of fishing
vessels.


7
CHAPTER 2. SHIP RESISTANCE CALCULATION USING CFD
2.1. CFD AND APPLICATION IN SHIP RESISTANCE CALCULATION
2.1.1. Overview of CFD theory
CFD was formed in 70, starting from the combination of sciences such as
mathematics, physics, numerical methods... to simulate fluid flows, and it has
created a new development in computational science in several technical areas.
The theoretical basis of CFD is the system of major equations referring to the
physical process and is a mathematical statement of the basic physical principles
when calculating the fluid flow, also known as the Navier-Stock system of
equations:
.U  0

(1.4)
 dU
  p   2 U  g
 dt


There are many methods of solving the above system of equations in which
the most effective one is Reynolds Average Navier-Stokes Equations (RANSE)
where the system of equations is transformed as follows.

.U  0

 dU
   p   2 U  g

 dt

(1.13)

Symbols of quantities in the formulas are explained in the thesis.
To simulate complex fluid flows such as the fluid around the ship hull, it is
necessary to use a turbulent model. The most effective is the SST k-ω turbulent
model.
2.1.2. Application of CFD in calculating ship resistance
When studying the effect of bulbs on the components of resistance, the total
resistance RT is divided into the following components:
RT = RF + RPV + RWF + RWB
Of which:
RF: the frictional resistance;
RPV: the viscous pressure resistance;
RWF: the wave generation resistance; and
RWB: the breaking wave resistance.

(1.18)

8
With the development of computers, the application of CFD in
hydrodynamics in general and ship resistance in particular has had a very strong
development. The most effective is the RANSE method with the k SST k-ω
turbulent model as mentioned above. Current studies often use available CFD
software to solve, in which the most effective is Xflow due to its advantages as
analyzed in the thesis.
2.2. APPLICATION OF CFD IN SHIP RESISTANCE CALCULATION
The purpose of optimizing the bulb geometry is to minimize the overall
resistance of the ship. Therefore, to achieve the thesis research goal, it is necessary
to study the application of CFD in solving the problem of accurately calculating
the resistance for calculated ships. Theoretically, when applying CFD in general or
CFD software in particular with the given input parameter values, it is possible to
get calculation results, but their accuracy and reliability cannot be assessed. In fact,
the results of calculating ship resistance by CFD depend greatly on the accuracy of
the 3D input model and the values of simulation parameters such as the spatial
dimensions of the computed domain, boundary conditions, and parameters of the
3D model. Therefore, to ensure the accuracy and reliability when calculating the
resistance of a specific type of ship, the author will build and test the accuracy of
the 3D ship model and determine the CFD simulation parameters that are relevant
to the types of calculated ships. On that basis, a method is proposed to accurately
calculate resistance by CFD for a specific type of ship by the sequence as follows:
(1) Analyzing and selecting ship models suitable for calculation and model
testing data;
(2) Building 3D models of the selected ships for resistance calculation using
CFD;
(3) Determining the simulation parameters when estimating the ship's
resistance using CFD, in this case Xflow, suitable for the type of calculated ships,
specifically:
- Determining the appropriate calculation domain dimensions for the

calculated ships, ensuring that the resistance calculation results using CFD are
stable and unchanged.
- Determining the parameters of the turbulent model suitable for a specific
ship type, ensuring that the difference between the resistance calculation results
and the testing data is within the allowable limit of less than 5%.
(4) Calculating the resistance for the ship models similar to the calculated
simulation parameters and comparing with the testing data to check the reliability
of the calculation results.
2.2.1. Analysis and selection of ship models for calculation
The calculated ship models selected from the FAO steel hull fishing vessel
samples are the ship models with the symbols of FAO 72 and FAO 75 for the
following reasons.


9
 Having the characteristics of the form line and the range of changes of
geometric parameters suitable for the group of wooden and steel fishing
vessels in our country today as shown in Tables 2.1, 2.2, and 2.3 of the thesis.
 Having sufficient experimental data on resistance as shown in Figures 2.5
and 2.6 of the thesis.
In addition, the two ships have the same size and form, only the bow is
different. Of which FAO 75 has a V-shaped bow and FAO 72 has a bulbous bow,
so it is convenient to deal with the research objectives and contents of the thesis.
2.2.2. Building of 3D model and preliminary calculation of the calculated
ship's resistance
The results of building and checking the accuracy of the 3D model of the
calculated ship FAO 75 in AutoShip software are presented in Figure 2.9 and
Table 2.4, showing the deviation between the parameters of the built 3D model
and the real ships within 2% that is allowable for conventional engineering
problems.

Fig 2.9. 3D model and form parameters of FAO 75 vessel exported
from AutoShip software.

No
1
2
3
4
5
6
7
8

Table 2.4. Comparative the geometric parameters of the 3D model in
AutoShip and the actual vessel.
3D hull Deviation
FAO 75
Hull form parameters Notation Units
model in
(%)
vessel
AutoShip
Length of waterline
LWL
m
44.200
44.146
0.12
Breadth of waterline

BWL
m
10.400
10.400
0.00
Depth
Ttb
m
4.57
4.57
0.00
Displacement
tons
1130.0 1127.20
0.25

Longitudinal center of
LCB
m
1.223
1.218
0.41
buoyancy
Block coefficient
CB
0.524
0.524
0.00
Prismatic coefficient
CP

0.581
0.590
-1.55
Wetted surface area
m2
598.00
590.26
-1.29



10
Import the 3D ship model built and checked in AutoShip into the CFD
software as Xflow, then preliminarily set up simulation parameters such as
calculation domain dimensions, boundary conditions, turbulent model... to
calculate the ship resistance. As simulation parameters greatly affect the results of
resistance calculation, if the values that are suitable for the ship model cannot be
determined, the resistance calculation results have low accuracy and are often
different from the experiment data. Therefore, to ensure the accuracy of the
calculation results of the of ship resistance, it is necessary to determine the main
simulation parameters suitable for the calculated ships, including the dimensions
of the calculation domain, boundary conditions and other parameters of the
turbulent model.
2.2.3. Determination of simulation parameters suitable for a particular ship
2.2.3.1. Determination the spatial dimensions of calculation domain suitable for
the calculated ship
The appropriate calculation domain will be the domain with the smallest
dimensions, and the resistance calculation results are stable and do not change
when increasing the dimensions. Therefore, it is possible to determine the
appropriate domain for the calculated ship through the following steps.

 Preliminary selection of domain dimensions based on existing
recommendations.
 Building of the calculation domain options by changing one dimension and
keeping the others the same.
 Calculation of the resistance for each dimension of the calculation domain
and selection of the appropriate domain corresponding to the smallest domain
dimensions and the results of the calculation of the stable resistance.
The results of determination of the calculation domain dimensions suitable for
the FAO 75 ship are shown in Figure 2.13.

Fig 2.13. The computational domain size suitable for the FAO 75 vessel


11
2.2.3.2. Determination of parameters of turbulent model suitable for calculated
ship
When simulating with the SST k-ω turbulent model, it is necessary to
determine the model parameters, including the turbulent kinetic energy coefficient
k and the turbulent kinetic energy diffusion rate ω. The order of determining the
parameters of the turbulent model suitable for the calculated ship is as follows.
 Taking the value of turbulent intensity I for preliminary calculation of
turbulent kinetic energy k and turbulent kinetic energy dissipation rate ω
according to known empirical formulas.
 Using the domain dimensions and boundary conditions defined above, and
the options for the values of the coefficients k and ω already available to
calculate the ship resistance.
 Determining a suitable turbulent model parameter option that is the one
with the deviation between the resistance calculation results from XFlow and
the model test within the allowable limits.
The research results have determined that the parameter values of the

turbulent model suitable for the calculated FAO 75 ship are I = 0.052, k = 0.241,
and ω = 0.046.
2.2.4. Calculation of resistance of calculated ship models
With the simulation parameters determined, calculating and comparing the
results of resistance calculation for FAO 75 ship from Xflow and from the ship
model testing. The comparison results and resistance graphs shown in Table 2.12
and Fig. 2.17 have shown that the accuracy of the resistance calculation results
when the deviation is less than 5%.
Table 2.12. The comparison results of the total resistance values of FAO 75
from Xflow and from model testing.
Ship Total resistance values of FAO 75
Froude
Deviation
No
speeds
XFlow
Model test
Fn
(%)
U (m/s) RXF (N) RXF (KG)
Rt (KG)
1 0.150
3.12
14727.90 1501.31
1501.50
-0.01
2 0.175
3.64
16093.20 1640.49
1606.18

2.09
3 0.200
4.16
22508.53 2294.45
2252.25
1.84
4 0.225
4.69
30476.65 3106.69
3003.00
3.34
5 0.250
5.21
45317.85 4619.56
4504.51
2.49
6 0.275
5.73
56965.70 5806.90
5733.01
1.27
7 0.300
6.25
62461.79 6367.15
6381.38
-0.22
8 0.325
6.77
74245.68 7568.37
7623.01

-0.72
9 0.350
7.29 101250.06 10321.11
10617.76
-2.87
10 0.375
7.81 169586.65 17287.12
16816.82
2.72
11 0.390
8.12 225106.50 22946.64
23244.17
-1.30


12

Fig. 2.17. The comparison on resistance curves of FAO 75
from Xflow and from model testing.
To check the reliability of the research results, using XFlow with the values of
simulation parameters determined to calculate the resistance of FAO 72 ship and
compare the corresponding model testing data shown in Table 2.13 and Fig. 2.18.
Conclusion of Chapter 2.
Chapter 2 presents the new research results of the thesis in applying CFD to
accurately calculate specific ship resistance based on accurate construction of 3D
ship models and determination of simulation parameters, including domain
dimensions and turbulent model parameters such as turbulent kinetic energy k and
turbulent kinetic energy diffusion rate ω suitable for the geometrical and
hydrodynamic characteristics of the types of calculated ships. The results show
that the accuracy and reliability of the proposed method when the difference

between the calculated and experimental resistance values of FAO 75 ship
(Table 2.12) and FAO 72 ship (Table 2.13) are less than 3%, especially at the
values of design speeds.


13
CHAPTER 3. OPTIMIZATION OF BULBOUS BOW
3.1. GEOLOGICAL CHARACTERISTICS OF BULBOUS BOW
According to Kracht (1978), the bulbous bow form is characterized by the
following six geometrical parameters:
(1) Three linear bulb parameters
 Length parameter (CLPR): the ratio of the protruding length (LPR) and the
ship's length between perpendiculars (LPP), CLPR = LPR/LPP (Fig. 3.3a).
 Breadth parameter (CBB): the ratio of the maximum breadth (BB) of the
cross-sectional area of the bulbous bow (ABT) at the forward perpendicular
and the ship's beam (BMS) at amidship, CBB = BB/BMS (Fig. 3.3b).
 Depth parameter (CZB): the ratio of the height (ZB) of the foremost point of
the bulb over the baseline and the draft (T FP) at the forward perpendicular,
CZB = ZB/TFP (Fig. 3.3c).

(a) Length parameter C LPR

(b) Breadth parameter CBB

(c)Depth parameter C ZB

Fig.3.3. Determine three linear bulb parameters
(2) Three non-linear bulb parameters
 Cross-section parameter (CABT): the ratio of the cross-sectional area of the
bulbous bow at the forward perpendicular (ABT) and the ship's midship section

area (AMS) (see Fig. 3.5a).
 Lateral parameter (CABL): the ratio of the area of the protruding bulb in the
longitudinal plane (ABL) and the ship's midship-section area (AMS) (Fig. 3.5b).
 Volumetric parameter (CPR): the ratio of the volume of the protruding
bulb (VPR) and ship's volume (VWL) excluding the volume of the transition
part (VF) for fitting the bulb to the hull (see Fig. 3.5c).

(a) Cross-sectsion parameter CABT (b) Lateral parameter CABL

(c) Volumetric parameter CPR

Fig. 3.5. Determine three non-linear parameters of the bulb.
Linear parameters have the greatest influence on the phase relationship and
interference effects between the hull and bulb wave systems, while the nonlinear
parameters usually only affect the bulbous bow wave amplitudes.


14
3.2. DESIGN OF BULBOUS BOW FOR CALCULATED SHIPS
Currently, in addition to the Taylor method, which is considered to be not
strong enough, only the Kracht (1978) method of bulb design is the most effective.
However, it has the limitation that it only applies to ships with block coefficients
CB = (0.56 - 0.82), the calculated bulb is only suboptimal and does not mention the
connection of the bulb to the hull. Therefore, the thesis has proposed a bulb design
method including the following two contents:
(i) Using the Kracht graph to design a bulb to ensure the highest efficiency for
ships with a block coefficient that is not within the applicable scope of the graph.
(ii) Building the profile and integrating the bulb into the hull surface to ensure
even smoothness between the two surfaces and keep the determined parameters.
3.2.1. Determination of geometric coefficients of bulb for calculated ships

Kracht graphs are the lines showing the relationship between residual power
reduction coefficient (CPR) and 6 bulb coefficients set up for ships with specific
CB and Froude Fn number. Therefore, the bulb design is to choose 6 Kracht graphs
suitable for the CB and Fn of the ship and determine on the graphs of 6 bulb
parameters so that the coefficient CPR is the largest. Mathematically, it can be
seen that all Kracht graphs show the relationship between quantities, including
coefficients CPR, 6 bulb geometric coefficients, CB, and Froude number (Fn).
Therefore, if the maximum value (CPR)max is taken in advance to ensure the
highest bulb efficiency and the Froude number value is suitable for the calculated
ship, by interpolating between the values of the lines on all Kracht graphs will
calculate the curves showing the relationship between the remaining quantities of 6
bulb coefficients and CB coefficient. As FAO 75 ship with CB = 0.524 is outside
the scope of application of Kracht graphs, it is possible to determine interpolation
curves showing the relationship between the 6 bulb coefficients and the block
coefficient at the value Fn = 0.337 corresponding to the design speed of the ship
U=15knots and the maximum residual power reduction coefficient as shown in
Fig.3.8.

Fig. 3.8. Interpolation curves show the relationships between the six bulb
parameters and the block coefficient at Fn =0.377.


15
The observation of Fig. 3.8 shows that the bulb geometric coefficients, except
CABL coefficient, change very little when CB changes in the range (0.56-0.82), so
these lines can be used to determine 6 bulb coefficients for CB = 0.524 of FAO 75
ship. Corresponding to the values of these bulb coefficients, using the Krach graph
with CB = 0.56, i.e. the closest graph to CB = 0.524 of the calculated ship to
determine the value of the maximum residual power reduction coefficient
(CPR)max corresponding to each determined bulb coefficient. Research results

using interpolation and extrapolation curves calculate the bulb parameters for the
calculated ship with CB = 0.524 as shown in Table 3.4.
Table 3.4. Bulb sizes and hull parameters of the FAO 75 vessel.
Notations and values of LPP, m B, m Tm, m
AMS, m2
, m3
hull parameters of the
44.2 10.36 4.57
43.80
1111.0
FAO 75 vessel
Notations and values of CLPR CBB CZB
CABL
CABT
CPR
bulb parameters
0.0337 1.709 0.460 0.1733 0.0862 0.0028
Notations and values of LPR, m BB, m ZB, m ABL, m2 ABT, m2 VPR, m3
bulb sizes
1.490 1.709 2.102 3.21
3.78
3.11
3.2.2. Construction of profile line and integration of bulb into hull
With the values of the bulb geometric parameters in Table 3.4, proceeding to
build a bulbous profile line to ensure smoothness and meet the calculated
parameters. The process of building the profile line and integrating the bulb into
the hull of FAO 75 is done in AutoShip software to control and ensure the
smoothness (Fig. 3.15) and the deviation between the geometric parameters of the
calculated bulb and the model does not exceed 3% as shown in Table 3.6.

Fig. 3.15. 3D model of the FAO 75 hull after integrating the bulb designed
Table 3.6. Comparison of the computed and actual values of the six bulb
parameters of the model vessel by AutoShip.
Notations
Units Computed values Actual values Deviation (%)
LPR
m
1.490
1.500
-0.671
BB
m
1.709
1.700
0.527
ZB
m
2.102
2.100
0.095
2
ABL
m
3.210
3.220
-0.312
2
ABT
m
3.780

3.740
1.058
VPR
m3
3.110
3.170
-1.929


16
3.3. MODEL AND METHOD FOR OPTIMIZATION OF BULBOUS BOW
FOR FISHING VESSEL
3.3.1. Model of optimization problem of bulbous bow for fishing vessel
3.3.1.1. Design variables
The correct selection of the design variables is very important in the
optimization problem. Since the bulb sizes have a great influence on the phase and
strength of the wave system caused by itself, the bulb sizes should be selected as
the design variables of the optimization problem and change them to have the
optimal bulb with the smallest ship resistance (Figure 3.18).
(i) The length of the bulb LPR is determined at the front end of the bulb along
the ship. This parameter is important because it affects both the phase and the
volume of the bulb, leading to the effect of the wave intensity generated by the
bulb.
(ii) The depth of the bulb ZB determines the position of the top of the bulb in
the direction of the z-axis, affecting the ability of the bulb to flood at different
drafts.
(iii) The maximum breadth BB mainly affects the volume of the bulb, so it
usually only affects the wave strength generated by the bulb.

Fig. 3.18. Bulb sizes as variables of the optimal model.

In fact, if the design variables are the dimensions of the bulb as stated, and the
options for calculating the bulb are built by changing these dimensions, the
number of calculation options is very large. So, it is necessary to find the limited
range of changes of the bulb sizes. The analysis results show that on the Kracht’s
design graphs, there is always an area that ensures the bulb to work most
effectively, corresponding to the maximum value of the residual power reduction
coefficient (CPR)max, so determining the limited extent of this area has allowed
us to propose a limited range of changes of the size coefficients to ensure effective
bulb as follows:
0.03  CLPR = LPR/LPP  0.04
0.18  CBB = BB/B

 0.20

0.26  CZB = ZB/T

 0.55

0.03LPP ≤ LPR ≤ 0.04LPP


0.15B ≤ BB ≤ 0.20B
0.40T

≤ ZB ≤ 0.50T

(3.16)


17

3.3.1.2. Objective function
The purpose of using a bulbous bow is to reduce the ship total resistance, so
optimizing the bulb geometry means finding its sizes to maximize the reduction in
total resistance RT (%) of the ship after fitting a bulb..
RT = (RT – RTb)/RT = f(LPRi, BBi, ZBi)  max

(3.17)

where RT and RTb are the total resistance of the ship before and after fitting a
bulb computed at only one speed U.
As fishing vessels work at different speed modes, the bulb optimization
problem becomes a multi-objective problem, consisting of single objective
functions of resistance reduction RTi after fitting a bulb in working mode (i)
corresponding to the ship speed Ui.
RT = [(RT1, U1),…, (RTi, Ui), …, (RTn, Un)]  max
(3.18)
where RTi is the total resistance reduction of the ship after retrofitting a
bulbous bow under operating mode (i) corresponding to ship speed U i
RTi = (RTi – RTbi)/RTi

(3.19)

where RTi, RTbi are the total resistance of the ship before and after fitting the
bulb calculated at each speed Ui.
In this case, it is most appropriate to convert a multi-objective function (3.18)
into a multi-objective function of required power reduction Pe (%) after
retrofitting a bulb at a same ship speed Ui (m/s) by the following equation:
Pe = (Pe1, Pe2, …, Pei, …, Pen)  max

(3.20)

where Pei (%) is the change in effective power of the ship after mounting the
bow in working mode (i) corresponding to the ship speed Ui calculated by the
following equation:
Pei = (Pei – Pebi)/Pei = (RTiUi – RTbiUi)/RTiUi = RTi

(3.21)

where Pei, Pebi are the effective power (HP) of the ship before and after fitting
a bulb in working mode (i), corresponding to the ship speed U i.
Regarding the solution method, it is possible to calculate the conversion of the
multi-objective function (3.20) to a single-objective by adding the weighted singleobjective functions wi calculated according to the typical working modes of fishing
vessels, including (i) Running to the fishing ground, returning to the wharf, and
finding the fish at speed U1 equal to the design speed U and the time up about 60%
of the trip time; (ii) Towing the net at a speed of U 2 = 0.8U and about 10% of the
trip time; and (iii) Dragging or dropping the net at a speed of U 3 = 0.3U and the


18
time up about 30% of the trip time. Therefore, it is possible to determine the
objective function of the fishing vessel bulb optimization problem as follows:
n

Pe =  w i R Ti U i = 0.6RT1 + 0.1RT2 + 0.3RT3  max
i 1

(3.24)

where RT1, RT2, RT3 are the change in total resistance of the ship
calculated at speeds U1, U2 and U3 in running, towing, and towing and dragging

modes.
Statistics show that the time of fishing vessels operating at draft T and 0.8T at
speeds 0.3U, 0.8U, U accounts for 85.5% of the trip time, so the speeds 0.3U,
0.8U, U and two drafts T, 0.8T are chosen for calculation.
3.3.1.3. Constraint conditions of the optimization problem
Current bulb optimization studies generally do not introduce constraints. The
thesis proposes the constraint conditions for the change of parameters that greatly
affect the working conditions of fishing vessels, longitudinal center of buoyancy
LCB, initial metacentric height MG, block coefficient CB, displacement , the main
dimensions of the ship are within the allowable range of 1%, which is expressed
in expressions from (3.25) to (3.29) in the thesis.
3.3.2. Method to solve the bulbous bow optimization problem
After using the Kracht graphs to design a preliminary bulb, called the original
bulb, building the calculation options by changing the initial bulb size and using a
combination of the CFD method with the surrogate models to solve the bulb
optimization problem according to the following specific calculation steps.
Step 1: Calculation of value of objective function
Using CFD software to calculate resistance at different bulb size options and
subtracting the corresponding experimental data of the ship to calculate the
reduction in total resistance RT (%) according to equation (3.19), then
substituting to equation (3.24) to calculate the value of objective function of
effective power reduction Pe (%).
Step 2: Initialization of surrogate models
Initializing 3 Kriging surrogate models from the data calculated in Step 1,
including (i) Model 1: first-order polynomial regression function and Gaussian
correlation coefficient.; (ii) Model 2: second-order polynomial regression function
and Gauss correlation coefficient; and (iii) Model 3: second-order polynomial
regression function and second power correlation coefficient.
Step 3: Preliminary determination of optimal bulb option
Finding the extreme points of the 3 surrogate models created in Step 2,

corresponding to the optimal bulb option with the largest reduction in effective
power of the ship Pemax. In this calculation, as the surrogate models are created


19
from only a few discrete values, the optimal bulb options found may not be
accurate, so it is necessary to evaluate and improve the accuracy of these models.
Step 4: Evaluation and improvement of accuracy of surrogate models
Comparing the value Pemax in optimal bulb options when calculating the
accuracy according to Xflow and approximating the built surrogate models. If the
deviation is within the allowed limit, it is the optimal option, otherwise, updating
the optimal bulb option with the value Pemax calculated from XFlow into the
original data set to reconstruct the surrogate models more accurate.
Step 5: Determination of optimal bulb option
Repeat steps 3 and 4 until the deviations between the results calculated
according to the surrogate model and XFlow is within the limit (less than 3%),
then stop, and that is the optimal bulb option to be found.
3.4. OPTIMIZATION OF BULBOUS BOW FOR CALCULATED SHIP
3.4.1. Establishment of matrix of options for bulb calculation
FAO 75 ship has parameters LPP = 44.2 m, B = 10.36 m and T = 4.57 m,
applying (3.16) to determine the limit of variation in the size of the ship's bulb as
follows:
1.33 m ≤ LPR ≤ 1.77 m ; 1.55 m ≤ BB ≤ 2.07 m ; 1.83m ≤ ZB ≤ 2.29 m
The original bulb of FAO 75 ship has LPRo = 1.50 m, BBo = 1.70 m, ZBo = 2.10
m, thus determining the limit for the change in the dimensions of the original bulb
as follows:
-0.17m ≤ LPR ≤

0.27m ; -0.15m ≤ BB ≤ 0.37m ; -0.27m ≤ ZB ≤0.19m

From the stated value of the variable limit for the bulb size variables,
establishing a matrix of options for the size of the calculated bulb by varying the
dimensions of the original bulb in increments of  = 0.1 m as shown in Table 3.8.
Table 3.8. Matrix of initial bulb size variants of the FAO 75 fishing vessel.
Matrix of initial bulb size
Bulb size variants
Notation Units
variants
Variants to change in length
m
-0.2 -0.1 0.1 0.2 0.3
LPR
Variants to change in breadth BB
m
-0.1 0.1 0.2 0.3 0.4
Variants to change in depth
m
-0.3 -0.2 -0.1 0.1 0.2
ZB
To ensure that variations in bulb size do not affect ship performance, checking
the constraints on variation of ship design parameters for bulb-limited size options
have been established by moving the points lying on the original bulb profile to the
following limit sizes.


20
Minimum variant
LPRmin = LPRo – 0.2 = 1.3 m
BBmin = BBo – 0.1 = 1.6 m
ZBmin = ZBo – 0.3 = 1.8 m

Maximum variant
LPRmax = LPRo + 0.3 = 1.8 m
BBmax = BBo + 0.4 = 2.1 m
ZBmax = ZBo + 0.2 = 2.3 m

The results in Table 3.9 show that all the constraints are satisfied.
Table 3.9. Checking constraints at extreme bulb sizes.
Bulb size variants
Vessel
LPR = -0.20 m LPR = 0.30 m
with
BB = -0.10 m BB = 0.40 m
Hull form parameter
Units initial
ZB = -0.30 m ZB = 0.20 m
bul
Value
(%) Value (%)
Block coefficient CB
0.525
0.524
0.19 0.526 -0.19
tons
1134.6 1134.3
0.03 1134.7 -0.01
Displacement 
Longitudinal
center
of %

-0.184 -0.181
1.63 -0.185 -0.54
buoyancy LCB
Initial metacentric height MG
m
2.204
2.201
0.14 2.211 -0.32
3.4.2. Determination of optimal bulb option
Building the calculation options by changing the two bulb sizes at the same
time, namely length - breadth, length - depth, breadth - depth, and finding the
optimal bulb option based on the calculation steps presented in section 3.2.3.
Specifically, building the calculation options when changing the length and
breadth of the original bulb at the same time according to the matrix of options in
Table 3.8 as follows:
- Moving the initial tip of the bulbous bow vertically from the position of
-0.2m to +0.3m in increments of LPR = 0.1m (Fig. 3.23a).
- Moving the two extreme points at the position of the largest breadth of the
original bulb to the sides horizontally from the position of -0.1m to +0.4m in
increments of BB = 0.1 (Fig. 3.23b).
The results form 25 options of bulb size as shown in Fig.3.23.

(a) Change in bulb length
(b) Change in bulb breadth
Fig. 3.23. Variants to change of bulb length and breadth


21
Regarding the method, in order to calculate the ship resistance in the bulb
options built by CFD in general and Xflow in particular, it is necessary to calibrate

the 3D ship models from the original bulb to the bulb corresponding to the change
in dimensions. The process of simultaneously changing the length and breadth of
the bulb of FAO 75 ship to the calculation options is done in AutoShip as shown in
Fig. 3.23. Changing other bulb dimensions is done in the same way.

Fig. 3.24. Simultaneous change in length and breadth of the initial bulb
of the FAO 75 fishing vessel.
Calculating the total resistance of the ship using the CFD software Xflow and
substituting the calculated values into the equations (3.19) and (3.22) to calculate
the change in the effective power of the ship Pe (%) in all bulb options (step 1).
All calculations are performed in typical modes defined for fishing vessels,
including modes for speeds 0.3U, 0.8U, and U, and drafts T, 0.8 T. Running the
initialization program for surrogate models based on the data (step 2) and
performing calculations from step 3 to step 5 to update and gradually calibrate the
surrogate models until the accuracy is ensured as shown in Fig.3.26.
The results show that the accuracy and efficiency of bulbs calculated
according to model 2 is the highest, so the optimal bulb size option has the
parameters LPRop = 0.11 m, BBop = 0.21 m, Pemax  13.931%, i.e. the
dimensions of bulb
- Optimal bulb length

LPRop = LPRo + LProp

- Optimal bulb breadth

BBop

= BBo + BBop = 1.7 + 0.21 = 1.91 m

- Optimal bulb depth

ZBop

= ZBo = 2.10 m

= 1.5 + 0.11 = 1.65 m


22

Fig. 3.26. The surrogate models represent Pe = f (LPRi, ZBi) of the FAO 75
at 4.57 m draft
Proceeding in the same way as above and having the results of calculating the
optimal bulb options in the case of changing the length - breadth at the same time
(Fig. 3.27) and width - depth (Fig. 3.30) according to the matrix of options in
Table 3.8.

(a) Change in bulb length

(b) Change in bulb depth

LPR = 0.214 m, ZB = 0.097 m, Pemax = 13.678%.
Fig. 3.27. Simultaneous change in length and breadth of the initial bulb


23

(a) Change in bulb depth

(b) Change in bulb breadth

BB = 0.193 m, ZB= -0.128 m, Pemax = 13.578%.
Fig. 3.30. Simultaneous change in breadth and depth of the initial bulb
From the optimization results, it is possible to draw specific comments as
follows:
 The optimal bulb option is less dependent on the calculated draft, in which
the efficiency of the bulb at the design draft is usually the highest. The reason
is that the bulb is quite deep under the water surface, so the small change of
the survey water does not affect the calculation results.
 The efficiency of the bulb, expressed in terms of the maximum effective
power reduction Pemax or the maximum total resistance reduction RTmax of
the calculated ship in the case of simultaneous changes in the length and
breadth of the bulb is the highest, approximately 13.678%, while the
simultaneous change of length and depth is 13.678%, and the change of
breadth - depth is 13.578%. The reason is that the length and breadth greatly
affect the intensity and phase of the bulbous bow wave system, so it is easy to
affect its efficiency, while the increase in height mainly affects the bulb depth
but has little effect on the bulbous wave system as well as the amplitude and
phase of the bulb wave. However, the elongation of the bulb is limited to a
certain extent because it is constrained by the constant maximum length of the
ship, which significantly increases the wet surface area and affects other
design elements.
 Calculation results show that the optimal bulb option determined by the
three Kriging models is different, but in all cases, model 2 always has the
highest accuracy compared with the remaining ones. This can be explained as
model 2 with the quadratic polynomial regression and Gaussian correlation
function has the highest nonlinearity compared to the remaining models, so it
responds well to the known complex changes in the total resistance of the ship
when simultaneously varying the bulb dimensions.

24
 Calculation results show that the bulbous bow in the most optimal case has
allowed to reduce the useful power Pe or the total resistance of the ship RT
by about 14%, which is consistent with the published experimental data of
(12) -15)%,
Fig. 3.33 and 3.34 are the results from Xflow, a graph of the distribution of
velocity and pressure fields in the fluid around the FAO 75 hull without and with
the optimal bulb equipped at U = 15 knots and draft T = 4.57 m. A qualitative
comparison of the images clearly shows that the ship's waveform edge height is
significantly reduced after the optimal bulb fitting, resulting in a significant
reduction in the wave-generating resistance component, and thus, the total ship
resistance is also significantly reduced. In addition, the clear appearance of waves
in the aft area of the hull without the bulbous bow (Fig. 3.33) indicates that the
waves in the aft area of the bulb hull have been largely suppressed (Fig. 3.34)
thanks to the active interference between the hull wave system and the wave
system generated by the optimal bulbous bow.

(a) Velocity distribution
(b) Pressure distribution
Fig. 3.33. Velocity and pressure distributions in the flow around of the FAO
75 hull without the bulbous bow

(a) Velocity distribution
(b) Pressure distribution
Fig. 19. Velocity and pressure distributions in the flow around of the
FAO 75 hull with an optimal bulbous bow
Fig. 3.33 is a line drawing of FAO 75 ship with the initial bulbous bow having
the dimensions LPRo = 1.50 m, BBo = 1.70 m, ZBo = 2.10 m (black line) and the
optimal bulb (red line) with the dimensions LPRop = 1.65 m, BBop = 1.91 m,