Muhammad Arif Budiyanto, Fadhil Naufal, Gerry Liston Putra, Achmad Riadi, Dedy Triawan Suprayogi, Muhammad Iqbal, Triwilaswandio Wuruk Pribadi

Corresponding email: ma.budiyanto@ui.ac.id

Corresponding email: ma.budiyanto@ui.ac.id

**Published at : ** 05 Feb 2024

**Volume :** **IJtech**
Vol 15, No 2 (2024)

**DOI :** https://doi.org/10.14716/ijtech.v15i2.6661

Budiyanto, M.A., Naufal, F., Putra, G.L., Riadi, A., Suprayogi, D.T., Iqbal, M., Pribadi, T.W., 2024. Performance Analysis of Duct Vane Application on Patrol Boats Using Computational Fluid Dynamics.

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Muhammad Arif Budiyanto | Naval Architecture and Marine Engineering, Department of Mechanical Engineering, Universitas Indonesia, Depok, West Java, 16424, Indonesia |

Fadhil Naufal | Naval Architecture and Marine Engineering, Department of Mechanical Engineering, Universitas Indonesia, Depok, West Java, 16424, Indonesia |

Gerry Liston Putra | Naval Architecture and Marine Engineering, Department of Mechanical Engineering, Universitas Indonesia, Depok, West Java, 16424, Indonesia |

Achmad Riadi | Department of Mechanical Engineering, Universitas Sultan Ageng Tirtayasa, 42435, Indonesia |

Dedy Triawan Suprayogi | Department of Mechanical Engineering, Universitas Sultan Ageng Tirtayasa, 42435, Indonesia |

Muhammad Iqbal | Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow, Scotland, SC015263 |

Triwilaswandio Wuruk Pribadi | Department of Naval Architecture and Marine Engineering, Institut Teknologi Sepuluh Nopember, 60111, Indonesia |

Abstract

Fast patrol boats are designed for high
performance in surveillance and warfare missions. In terms of hull technology
development, the fast patrol boat commonly uses a V-type hull with hard chine.
A duct vane is an innovation developed to improve the performance of patrol
boats by combining the principles of wake-equalizing duct and hydrofoil. The
objective of this paper is to investigate the hydrodynamic effect of the
application of duct vane on the patrol boat hull design. The investigation was
carried out using computational fluid dynamics that was validated using
experiment data. The result of the duct vane application can improve the ship
speed performance and reduce the total resistance by 40% at Fn 0.6. The results
of this study also provide an overview of the influence of the duct vane on the
lift force of a hard chine hull-type.

Duct vane; Hydrodynamics; Patrol boat

Introduction

The wake equalizing duct (WED) is
a component that can improve the ship's propulsion system and the economic
performance of the ship (Furcas *et al.,*
2020). WED component consists of two semicircular duct airfoil nozzles,
which are mounted in two sections at the rear of the ship and in front of the
propeller (Korkut, 2006). In that section,
the duct accelerates the flow to the top of the propeller while slightly
slowing it down to the bottom of the propeller, thereby generating a more
homogeneous wakefield. WED can make the flow through the duct accelerate faster
towards the top of the propeller while maintaining a relatively slower flow at
the bottom of the propeller (Go, Yoon, and Jung, 2017). WED is able to make the flow
more uniform so that there is no separation at the rear of the ship (Seo, Yoon, and Kim, 2022). The incorporation of WED has
the capability to enhance propeller thrust and minimize excitation vibrations.
This is achieved by ensuring a uniform and homogeneous flow to the propeller,
consequently reducing propeller excitation vibrations (Rezaei, Bamdadinejad, and Ghassemi, 2022). In addition to increasing the

Based on
experiments regarding the effect of using WED on ship resistance, propulsion
performance, and visualization of flow at the rear of the ship, it is
illustrated that the flow that occurs in ships that have been optimized with
WED has a more homogeneous flow compared to the original ship shape (Tacar *et al.,* 2020). Flow characteristics
pass through the rear of the original ship shape, with the rear being optimized
with WED (Tacar *et al.,* 2020). The
results show that the shape of the ship that has been optimized using WED can
reduce resistance compared to the original shape of the ship. This reduction in
resistance occurs due to a reduction in the separation of the boundary layer (Wu, Chang, and Huang, 2022).

Several
researchers use computational fluid dynamics for ship resistance investigation.
The excellent agreement between model testing and CFD predictions for total
ship resistance in calm water has resulted in a high confidence level in the
CFD results (Riyadi, Aryawan, and Utama, 2022). The total resistance and
increased resistance caused by the hydroelastic body were explored, as well as
the hydroelastic body's influence on the magnitude of resistance and added
resistance (Baso *et al.,* 2022). Actively reducing ship
resistance can have an effect when considering the ship energy efficiency
management plan (Dawangi and
Budiyanto, 2021).

The increase
in ship propulsion performance is also due to the reduced number of flow
separations at the rear (Kim and Kinnas, 2022).
The flow at the back tends to be more homogeneous, resulting in a reduction in
required power. However, a significant challenge in high-speed propellers
remains cavitation (Duy *et al.,* 2022; Köksal
*et al.,* 2021). Cavitation is defined as the process of forming a
liquid vapor phase due to reduced pressure at a constant room temperature (Yusvika *et al.,* 2020). The process occurs
more because of the decrease in pressure than the addition of heat. Cavitation
in the propeller occurs in the part of the propeller that has low pressure
which is at the top of the propeller. At this time, the fluid phase change
began to occur from liquid fluid to vapor fluid. This form of cavitation is in
the form of air bubbles (Köksal *et al.,*
2021).

Duct vane is
an innovation that can be used for fast patrol boats. This innovation combines
the principle of a wake equalizing duct with a hydrofoil (Budiyanto, Syahrudin *a*nd
Murdianto,
2020). The wake
equalizing duct is a component that can increase the propulsion performance of
the ship (Syahrudin, Budiyanto, and
Murdianto,
2020). This component consists of two duct foil nozzles in the shape of
a semicircle which are installed in two parts behind the ship and in front of
the propeller (Budiyanto, Murdianto, and Syahrudin*,*
2020a). This
component works by directing the fluid flow to the top of the propeller to
increase the speed of the thrust force on the ship using the hydrofoil concept (Budiyanto, Murdianto, and Syahrudin*,** *2020a). The hydrofoil works by
utilizing the speed of the ship so that it can lift the hull out above the
water surface where the hull is not subject to frictional resistance by the
water fluid (Daskovsky, 2000).

The
objective of this paper is to investigate the application of duct vane on
patrol boats by the simulation model. The investigation includes the
hydrodynamic parameters, such as a comparison of drag coefficient and lift
force analysis. The originality of this study is the use of a hard-chine hull
for the basic design of patrol boats. The contribution of this study is twofold: first, to offer an
overview of the effect of duct vane on hydrodynamic parameters, and second, to
present the advantages associated with the application of duct vane on patrol
boats. The hydrodynamic characteristics of the duct vane used by patrol boats
are investigated to find the resistance of the ship using a computational fluid
dynamics simulation method so that it becomes the basis for considering the use
of duct vanes on fast patrol boats. The independent variable in this study is the
speed of the water flow. The examination of these variables allows us to
understand the impact of water flow speed on the resulting hydrodynamic
parameters.

Experimental Methods

*2.1. Design and the Principal
Dimension of **t**he Patrol Boat*

A fast
patrol boat using a hard-chine hull with a duct vane is designed using linear
algebra to determine the meeting points of the plates so that the coordinates
are in one flat plane on each plate. The line plan is made into a 3D model
using Maxsurf UK

**Figure 1** Fast patrol boat design with
flat plate hull with duct vane

In
calculating the need for Hydrofoil on the Duct Vane, the Hydrofoil lift
calculation formula is used on the ship by using Equation 1 ^{2}), V = speed (m/s), C_{L}
= coefficient of lift, and F_{AR} = factor correction for aspect ratio.

Each profile of the hydrofoil
section has its own coefficient of displacement depending on the characteristics
of the profile shape. After determining the profile used, the next step is to
calculate the lift using Equation 1. Through the results of the calculation of
the lift from the hydrofoil, the area of the duct vane is obtained, as well as
the shape of the hydrofoil used in the duct vane. The profile used for the duct
vane is NACA 4412 ^{2},
F_{AR} 0.67, CL 0.4 and Lift 19.76 N.

**Figure
2** Cross
section of NACA 4412 used as hydrofoil

*2.2. Simulation Setting and
Parameter Inputs*

In the
simulation geometry settings, the design geometry of the draft ship must be in
the form of solid bodies. The design geometry and boundary conditions used as
space boundaries in the simulation process are shown in Figure 3. The
geometrical model of simulation is based on the practical guidelines for ship
CFD applications recommended by ITTC (The International Towing Tank
Conference). The dimensions used in this geometric model are the overall
length, which is twice the length of the ship model, the height of the inlet
and outlet is three times the height of the ship model, the width of the inlet
and outlet is three times the width of the ship model.

The
simulation has 45778 mesh quality nodes and 199131 elements. The free surface
is modeled using the volume of fluid (VoF) method, which involves two phases -
water and air. The water conditions are characterized by incompressible flow,
as well as steady and multiphase flow. The turbulence model used when water and
air fluids are flowing is the k-epsilon standard wall function, which has the
simplest turbulence equation. The type of solver chosen is pressure-based
because the simulated fluid flow has incompressible flow characteristics.
Setting the setup menu in the simulation model includes determining multiphase
and turbulence equation models, defining boundary conditions, cell zone
conditions, and solution methods.

**Figure
3** Boundary
conditions on a fast patrol boat simulation

In
determining the multiphase model, there are three types of multiphase modeling
in Ansys US software

Turbulent
fluid flow will tend to occur when a ship passes through the fluid. However, in
this case, the flowing fluid is considered a steady flow, and the ship speed is
constant so turbulence is predicted to occur, which is not too complicated.
Therefore, the K-Epsilon turbulence model is used. In this study, the fluid
flow is assumed to be incompressible, viscous, turbulent, and two-phase. Such
flow is governed by the incompressible ReynoldAverage Navier Stokes (RANS)
equation. The RANS equation has the same general form as the Navier-Stokes
equation with velocity and other solutions

The initial
state of the geometry and boundary conditions that have been determined will
affect the completion of the Navier-Stokes equation and the continuity equation
in the simulation process. Boundary conditions are used to model a phenomenon
to direct flow in the domain. For flow simulation, boundary conditions are
defined as inlet velocity and outlet pressure. There are several different
types for certain conditions. In incompressible fluid flow conditions, velocity
inlet and outflow are usually used, whereas incompressible fluid flow
conditions, mass flow inlet and pressure far-field are used. However, the
selection of boundary conditions can be adjusted to a particular problem model.

In the flow
simulation that will be carried out, the model ship, which is called the
Hard-chine hull is considered as a static object flowing fluid with the speed
variations determined in this study. The inlet of the fluid flow is defined as
the velocity-inlet, and the exit area is defined as the pressure-outlet. At the
inlet side of the fluid flow, a constant velocity in one direction with a
turbulence intensity of 0.5% is considered based on wind tunnel experiments
where the inlet turbulent intensity is around 0.5% - 1%. The open channel
method, particularly suitable for these conditions, is designated as
velocity-inlet. Meanwhile, on the exit side, where the fluid flow maintains a
constant static pressure, it is deemed appropriate to define it as a pressure
outlet, allowing for the distribution of radial equilibrium pressure. In
addition, the bottom side, top side, right side and left side of the domain are
defined as walls without friction as a symmetry so that they are considered
infinitely wide free surfaces.

The
following are the settings used for the boundary inlet and outlet. The inlet is
defined as a velocity inlet because, in this simulation, the air and water flow
from the inlet at a constant velocity. The input speed for the hard-chine hull
model without duct vane is 0.8 m/s, 1.2 m/s, 1.6 m/s, 2.0 m/s, 2.4 m/s, 2.8 m/s
and 3.2 m/s. As for the hard-chine hull model with duct vane are 1.6 m/s, 1.9
m/s, 2.2 m/s, 2.4 m/s, 2.7 m/s, 2.9 m/s and 3.2 m/s. The speed variation is
considered the Froude number for high-speed patrol boats, and the value is
higher than 0.5. The intensity and viscosity of the turbulence are given a
small value, namely 0.5%. This aims to minimize the turbulent flow that occurs
at the inlet to model calm waters. In the multiphase menu, the flowing fluids
are defined as water and air. The free surface level setting is adjusted to the
modelling of water depth and ship draft, which is 0.049 m (ship draft).
Detailed settings at the inlet and outlet are described in Table 1.

**Table 1** Detail setting of inlet and
outlet of the simulation model

Inlet Setting |
Outlet Setting | ||

Reference Frame |
Absolute |
Backflow Direction Method |
Normal to Boundary |

Averaged Flow (m/s) |
0.8 |
Backflow Pressure Spec. |
Total Pressure |

Turbulent Intensity (%) |
0.5 |
Turbulent Intensity (%) |
0.5 |

Turbulent Viscosity |
0.5 |
Backflow Turbulent Ratio |
0.5 |

Multiphase |
Open Channel |
Multiphase |
Open Channel |

Secondary Phase |
Water |
Pressure Specification |
Free Surface Level |

Free Surface Level (m) |
0.049 |
Bottom Level (m) |
0 |

The Solution
Method used in this study was determined based on the validation results. In
the validation stage, the least square cell-based method is used. According to
the validation results, it was found that the arrangement using the least
square cell-based method approached the experimental results with an error
percentage of around 1.8%. Pressure velocity coupling is an equation derived
from the continuity equation to reduce unexpected pressure conditions. Some of
the types are Simple, Simplec, Piso, Coupled, and Fractional Step. In this
research, the SIMPLE scheme is used because this scheme considers pressure and
speed in its calculations

*2.3. Validation of Simulation
Results*

Validation
at this stage aims to prove that the results of research data from CFD
simulations resemble the results of observational data in experimental tests.
It is hoped that the results of the CFD simulation in the form of a graph of
velocity against total resistance will have a curve that resembles the graph of
velocity against total resistance as the result of the experiment. Table 4 and
Table 5 provide a comparison of the results and graphs obtained from
experimental testing and CFD simulation for the patrol boat. The results for
the patrol boat without a duct vane are shown in Figure 4, while the results
for the patrol boat with a duct vane can be found in Figure 5. Validation is
carried out by comparing the simulation results with the results of experiments
that have been carried out previously. The experiments use the same model
dimension as the simulations carried out in the experimental basin. Experiments
were carried out with towing tests with the same load and speed variations. The
accuracy of the experiment was evaluated using uncertainty analysis. Based on
the calculation results of the average deviation error. Obtained error
validation results of 2.38%. Because the error obtained is below 10%, it is
assumed to be in good agreement. The geometry, mesh, and set-up settings can be
used to simulate the Hard-chine hull Ship model. Based on the calculation
results of the average deviation error. The obtained error validation results
of 3.5%. Because the error obtained is below 10%, the geometry, mesh, and
set-up settings can be used to simulate a Hard-chine hull model with duct vane
(Duct vane).

Results and Discussion

*3.1. Comparison of Drag
Coefficient*

The analysis
was carried out to determine the value of the drag coefficient found in
Hard-chine hulls without duct vane. The components contained in the total
resistance coefficient are the pressure resistance coefficient (Cp), the
viscous resistance coefficient (Cv) and the air resistance coefficient (Ca).
Figure 6 illustrates the coefficient of viscous resistance, represented by the
blue dots, which tends not to experience a significant decrease in the velocity
range of 1.6 m/s to 2.2 m/s. In contrast to the coefficient of pressure
resistance, which is depicted with red dots, there is a drastic decrease in the
velocity range. In this case, it is suspected that the resistance found on
Hard-chine hulls without duct vane is dominated by pressure resistance. This is
also evidenced by the value of the drag coefficient. In addition, at a velocity
range above 3 m/s, the values of the three drag coefficients are getting
smaller, and the values of the three are getting closer. This result consistent
with the experiment results *et al.,* 2021)

Figure 7
shows the value of the drag coefficient found on a hard-chine hull with a duct
vane (Ductship). The main components contained in the total resistance
coefficient (Ct) are the pressure resistance coefficient (Cp), the viscous
resistance coefficient (Cv), and the air resistance coefficient (Ca). As can be
seen from the graph below, the pressure resistance coefficient (Cp) has the
greatest value compared to the viscous resistance coefficient (Cv) and air
resistance coefficient (Ca). In Ductship, the increase in velocity does not
significantly affect the magnitude of the viscous drag coefficient (Cv).
However, the pressure resistance coefficient (Cp) value decreases as the
velocity value increases.

In comparing the velocity graph
to the total resistance (Rt) and the velocity graph to the total resistance
coefficient (Ct), two curves are used, which are the results of the CFD
simulation that has been carried out. Figure 8 illustrates the total resistance
results for the two model ships. Both curves share a similar shape, indicating
that the ship's resistance value increases as the ship's speed rises. The total
resistance curve for a flat plate vessel with a duct vane, which is illustrated
with a black line, is shown below the total resistance curve for a flat plate
vessel without a duct vane of the hard-chine hull, which is colored in red.
This proves that the addition of a duct vane on a hard-chine hull can reduce
the value of the total resistance on a hard-chine hull. This result is
consistence with the previous result

**Figure 6** Drag coefficient value of
hard-chine hull

**Figure 7** Drag coefficient value of
application of duct vane

**Figure 8** Comparison of the total
resistance of the application of the duct vane

From the
results of the comparison of the total resistance, it can be seen that a
hard-chine hull with duct vane has a smaller resistance compared to a
hard-chine hull without using duct vane (hard-chine hull). At the
Froude number (Fn) of 0.6, there was a 40% reduction in total resistance (RT).
Similarly, at Fn 0.8, there was a 38% reduction, at Fn 0.96, a 30% reduction,
and at Fn 1.1, a 20% reduction in total resistance. Observing the calculations of
total resistance reduction, it becomes evident that the percentage reduction in
total resistance tends to decrease with an increase in speed and Froude number.
This proves that the use of duct vane on a hard-chine hull has a percentage
reduction in the largest total resistance value at the range of range Froude
number of 0.6 to 0.8. In addition to the value of the total resistance of the
ship, the coefficient value of the total resistance of the ship is also
compared to obtaining a multiplier factor that can be used as a reference to
ship design.

*3.2. Duct Vane Lift Force
Analysis*

In the
previous discussion it was found that the addition of Duct Vane can reduce the
total resistance of Hard-chine hulls. This reduction in total resistance is
thought to be due to the lift force exerted by the Duct Vane on the stern of
the ship. Duct vane is an additional device at the stern of the ship that
utilizes the shape of the hydrofoil to generate lift force at the stern of the
ship. Based on research conducted through experimental methods, it is known
that the shape of the hard-chine hull model tends to experience trim by stern
when sailing at high speed. Trim by stern is the condition of the ship when
sailing where the stern draft is greater than the bow draft. The addition of a
duct vane at the stern of a hard-chine hull can solve the trim problem with the
lift force provided by the hydrofoil. As stated in the discussion chapter on
the hydrofoil, the lift force exerted by the hydrofoil is due to the difference
in pressure on the hydrofoil cross-section. So at a certain speed, the ship's
hull will rise above sea level due to the lift force provided by the hydrofoil *et al.,* 2011)

The
phenomena obtained from the experiments were also proven by the results of the
CFD simulations that had been carried out. Figure 9 is the result of a CFD
simulation in the form of volume rendering in the form of a pressure contour on
the fluid around the simulated model ship. Volume rendering is done when the
ship is flowing with fluid at a speed of 1.6 m/s on both ship models. This
speed is used because the speed of the model is a speed value that has a
significant effect on the difference in resistance. From the results of this
volume rendering, it can be seen that the pressure distribution in the fluid
around the model ship. Thus, the effect of the addition of Duct Vane on the
pressure distribution around the model ship can be analyzed.

**Figure
9** CFD
simulation of a pressure contour on the fluid around the stern hull

**Figure
10** Fluid flow
passes through the stern of the hard-chine hull and duct vane

Figure 10
shows the fluid flow passing through the stern of the hard-chine hull and duct
vane. Based on the figure, it can be seen that the flow passing through the
stern of a Hard-chine hull without a duct vane has an irregular and
inhomogeneous flow direction. It can be seen that several flow lines have
different directions. Meanwhile, at the stern of a hard-chine hull with a duct
vane, it can be seen that the direction of fluid flow is more homogeneous. The
more homogeneous flow is thought to be due to the addition of a Duct Vane at
the stern of the hard-chine hull. With a more homogeneous form of fluid flow,
the flow separation that occurs at the stern of the ship can be reduced by
adding duct vanes to Hard-chine hulls. The shape of the water fluid flow, which
is more regular and homogeneous, also affects the value of the pressure
resistance and frictional resistance of flat plate vessels. The results of the
flow contours show that the addition of a duct vane can reduce the value of the
pressure resistance on hard-chine hulls. One of the additional components of
pressure resistance is eddy-making resistance. Eddy-making resistance is an
obstacle caused by the separation of shapes on the ship, in this case, on the
stern of a hard-chine hull where there are fractures that cause the flow to
break away and then form eddies. The addition of duct vane makes the flow at
the stern of hard-chine hulls more regular, has a homogeneous direction, and
fewer eddies occur compared to the hard-chine hull model, where more eddies
occur *et al.,* 2019)

Conclusion

CFD
simulations have been carried out on hard-chine hulls with duct vanes to
calculate ship resistance and are validated by experimental test results. The
simulation method uses the multiphase volume of fluid equation and k-epsilon as
the turbulence equation. Data validation of the simulation results was carried
out on experimental results regarding hard-chine hulls with duct vanes. The
average deviation error obtained in the validation is around 2-3% for both ship
models. From the two simulated ship models, namely hard-chine hulls without
duct vanes and hard-chine hulls with duct vanes (ductship), it can be concluded
that adding duct vanes to hard-chine hulls can reduce the total drag on
hard-chine hulls. The addition of a duct vane on a hard-chine hull can reduce
the total resistance of the ship by 40% at Fn 0.6. Suggestions that can be
considered for further research development are the collection of experimental
data at high speeds to obtain the physical effects due to the lift force from
the duct vane.

Acknowledgement

The authors express their gratitude to the
Faculty Engineering Universitas Indonesia for the Seed Funding Program 2023
number NKB-2563/UN2.F4.D/PPM.00.00/2023.

References

AirfoilTools.com. (n.d.). NACA 4412. http://airfoiltools.com/airfoil/naca4digit?MNaca4DigitForm%5Bcamber%5D=4&MNaca4D. Accessed on 22^{nd}
January 2024

Ansys, 2020. Ansys Fluent: Fluid Simulation Software. © ANSYS, Inc. All rights reserved

Baso, S., Ardianti, A., Anggriani, A.D.E., Rosmani, R.,
Bochary, L., 2022. Experimental Investigation of Added Resistance of a Ship
using a Hydroelastic Body in Waves. *International Journal of
Technology.* Volume 13(2), pp. 332–344

Budiyanto, M.A., Syahrudin, M.F., Murdianto, M.A., 2020. Investigation of the Effectiveness of a Stern Foil on a Patrol Boat by Experiment and Simulation. *Cogent
Engineering*, Volume 7(1), p. 1716925

Budiyanto, M.A., Murdianto, M.A., Syahrudin, M.F., 2020a. Study on the Resistance Reduction on High-Speed Vessel by
Application of Stern Foil Using CFD Simulation. *CFD Letters*, Volume 12(4), pp. 35–42

Budiyanto, M.A., Wibowo, H.T., Naufal, F., Obindias, R., 2021. Study on the Effectiveness
of a Stern-Foil on a Multi-Chine Hulls. *In: *IOP Conference Series: Materials Science and Engineering,
Volume 1034, 2nd International Conference on Mechanical Engineering Research
and Application, Malang, Indonesia

Çelik, F., 2007. A Numerical
Study for Effectiveness of a Wake Equalizing Duct. *Ocean
Engineering*, Volume 34(16), pp. 2138–2145

Daskovsky, M., 2000. The Hydrofoil in
Surface Proximity, Theory and Experiment. *Ocean Engineering*, Volume 27(10), pp. 1129–1159

Dawangi, I.D., Budiyanto, M.A., 2021. Ship Energy Efficiency Management Plan Development
Using Machine Learning: Case Study of CO2 Emissions of Ship Activities at
Container Port. *International Journal of Technology*. Volume 12(5), pp.
1048–1057

Duy, T.N., Nguyen, V.T., Phan, T.H., Hwang, H.S., Park, W.G., 2022.
Numerical Analysis of Ventilated Cavitating Flow Around an Axisymmetric Object with
Different Discharged Temperature Conditions. *International
Journal of Heat and Mass Transfer*, Volume 197, p. 123338

Furcas, F., Vernengo, G., Villa, D., Gaggero, S., 2020. Design
of Wake Equalizing Ducts using RANSE-based SBDO. *Applied Ocean
Research*, Volume 97, p.
102087

Go, J.S., Yoon, H.S., Jung,
J.H., 2017. Effects of a Duct Before a Propeller on Propulsion Performance. *Ocean Engineering*, Volume 136, pp. 54–66

Harwood, C.M., Felli, M., Falchi, M., Ceccio, S.L., Young, Y.L., 2019. The Hydroelastic
Response of a Surface-Piercing Hydrofoil in
Multiphase Flows. *Journal of Fluid Mechanics*, Volume 881, pp. 313–364

Kandasamy, M., Ooi, S.K., Carrica, P., Stern, F., Campana,
E.F., Peri, D., Osborne, P., Cote, J., Macdonald, N., Waal, N.d., 2011. CFD Validation Studies for a
High-Speed Foil-Assisted Semi-Planing Catamaran. *Journal of Marine Science
and Technology**, *Volume 16(2), pp. 157–167

Khazaee, R., Rahmansetayesh, M.A., Hajizadeh, S., 2019. Hydrodynamic Evaluation of a Planing Hull in Calm Water
Using RANS and Savitsky’s Method. *Ocean
Engineering*, Volume 187, p. 106221

Kim, S., Kinnas, S.A., 2022. A Panel Method for the Prediction of Unsteady Performance of Ducted Propellers in Ship
Behind Condition. *Ocean Engineering*, Volume 246, p. 110582

Köksal, Ç.S., Usta, O., Aktas, B., Atlar, M., Korkut, E., 2021a.
Numerical Prediction of Cavitation Erosion to Investigate
the Effect of Wake on Marine Propellers. *Ocean
Engineering*, Volume 239, p. 109820

Korkut, E., 2006. A Case
Study for the Effect of a Flow Improvement Device (A Partial Wake
Equalizing Duct) On Ship Powering Characteristics. *Ocean
Engineering*, Volume 33(2), pp. 205–218

Maxsurf. (n.d.)., Intact
and Damage Stability Analysis. https://maxsurf.net/stability Accessed on 22^{nd} January 2024

Murdianto, M.A., Budiyanto, M.A., Syahrudin, M.F., 2020. Application Of Stern Foil on Full Draft Patrol Vessel at High Speed Condition Using Computational Fluid Dynamics (CFD)
Method. *AIP Conference Proceedings*, Volume 2255, p. 020023

Patankar, S.v., 2018. *Numerical Heat Transfer and Fluid Flow*. CRC Press

Rezaei, S., Bamdadinejad, M., Ghassemi,
H., 2022. Numerical Simulations of the
Hydrodynamic Performance of the Propeller with Wake Equalizing Duct Behind the Ship. *Scientia
Iranica*, Volume 29(5), pp. 2332–2348

Riyadi, S., Aryawan, W.D., Utama, I.K.A.P., 2022.
Experimental and Computational Fluid Dynamics Investigations into the Effect of
Loading Condition on Resistance of Hard-Chine Semi Planning Crew Boat. *International
Journal of Technology*. Volume 13(3), pp. 518–532

Seo, J., Yoon, H.S., Kim,
M.il., 2022. Flow Characteristics and Performance of the Propulsion
System with Wavy Duct. *Ocean Engineering*, Volume 257, p. 111727

Syahrudin, M.F., Budiyanto, M.A. and Murdianto, M.A., 2020. Analysis of the Use of Stern Foil on the High-Speed Patrol
Boat on Full Draft Condition. *Evergreen*, Volume 7(2), pp. 262–267

Tacar, Z., Sasaki, N., Atlar, M., Korkut, E., 2020. An Investigation
into Effects of Gate Rudder® System on Ship
Performance as a Novel Energy-Saving and Manoeuvring Device. *Ocean Engineering*, Volume 218, p. 108250

Vellinga, R., 2009. *Hydrofoils
Design Built Fly**.* Peacock Hill Publishing

Wu, P.C., Chang, C.W., Huang,
Y.C., 2022. Design of Energy-Saving Duct for JBC to Reduce Ship
Resistance by CFD Method. *Energies**, *Volume 15(17), p. 6484

Yusvika, M., Prabowo, A.R., Tjahjana, D.D.D.P., Sohn, J.M. 2020.
Cavitation Prediction of Ship Propeller Based on Temperature and Fluid Properties
of Water. *Journal of Marine Science and Engineerin**g**, *Volume 8, p. 465