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Ocean Engineering 255 (2022) 111486
Available online 8 May 2022
0029-8018/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
COVID-19 transmission inside a small passenger vessel: Risks
and mitigation
Luofeng Huang
a
,
b
,
*
, Soegeng Riyadi
c
, I.K.A.P. Utama
c
, Minghao Li
d
, Peiyign Sun
e
,
Giles Thomas
b
a
School of Water, Energy and Environment, Craneld University, UK
b
Department of Mechanical Engineering, University College London, UK
c
Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Indonesia
d
Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Sweden
e
School of Engineering and Informatics, University of Sussex, UK
ARTICLE INFO
Keywords:
COVID-19
Passenger vessel
Virus
Airborne transmission
Computational uid dynamics
Particle modelling
ABSTRACT
The global shipping industry has been severely inuenced by the COVID-19 pandemic; in particular, a signicant
amount of passenger transportation has been suspended due to the concern of COVID-19 outbreak, as such
voyages conne a dense crowd in a compact space. In order to accelerate the recovery of the maritime business
and minimise passengers’ risk of being infected, this work has developed a computational model to study the
airborne transmission of COVID-19 viruses in the superstructure of a full-scale passenger vessel. Considering the
vessel advancing in open water, simulations were conducted to study the particulate ow due to an infected
person coughing and speaking, with the forward door open and closed. The results suggest that keeping the
forward door closed will help prevent the external wind ow spreading the virus. When the forward door is
closed, virus particles’ coverage is shown to be limited to a radius of half a metre, less than a seat’s width. Thus,
an alternate seat arrangement is suggested. Furthermore, investigations were conducted on the inuence of wall-
mounted Air Conditioner (AC) on the virus transmission, and it was found that controlling the AC outlet direction
at less than 15◦downward can effectively limit the virus spread. Meanwhile, it was demonstrated that an AC’s
backow tends to gather virus particles in a nearby area, thus sitting farther from an opening AC may reduce the
risk of being infected. Overall, this work is expected to inform hygienic guidelines for operators to counter
COVID-19 and potentially similar viruses in the future.
1. Introduction
The maritime industry has been severely affected by the COVID-19
pandemic. Ships are currently operating with reduced capacity or
restricted from leaving port. In particular, the operation of passenger
vessels has been reduced by up to 42.77% (Milleori et al., 2021). Crew
and passengers can be exposed to a serious risk of contagion, since the
compact and crowded space of ships implies a high likelihood of
COVID-19 outbreak. In this context, there is an urgent need to research
the best technical solutions to ensure COVID-19 safety for ships (Thomas
et al., 2021).
COVID-19 infection has been found to be primarily induced by
inhalation (Jin et al., 2020). The virus can be transmitted via air,
existing in a form of aerosols and droplets injected by humans coughing,
speaking, breathing, singing and sneezing (Vuorinen et al., 2020).
Coughing and speaking are the most likely scenarios, as coughing is one
of the primary COVID-19 symptoms whilst speaking is almost inevitable
in daily contacts and can actually output a signicant amount of the
virus (Chao et al., 2009). The transmission mechanism of the COVID-19
virus may be referred to in previous work that studied u, as it has a
similar mechanism to SARS (Gao and Niu, 2007).
To investigate the airborne transmission of COVID-19 virus,
Computational Fluid Dynamics (CFD) has the capability to understand
the virus’s movement and coverage, which is essential for developing
effective mitigation strategies for infection control. To date, computa-
tional studies of COVID-19 transmission have been conducted for certain
high-risk areas. For example, Zhang et al. (2021a) performed a CFD
analysis for virus transmission inside a bus. A simple air-spray
* Corresponding author. School of Water, Energy and Environment, Craneld University, UK.
E-mail address: luofeng.huang@craneld.ac.uk (L. Huang).
Contents lists available at ScienceDirect
Ocean Engineering
journal homepage: www.elsevier.com/locate/oceaneng
https://doi.org/10.1016/j.oceaneng.2022.111486
Received 10 February 2022; Received in revised form 26 April 2022; Accepted 4 May 2022
Ocean Engineering 255 (2022) 111486
2
experiment was also conducted to validate the CFD model (Zhang et al.,
2021b). They compared the validated CFD results with the prediction
from an analytical approach that was previously widely used. The
comparison indicates that the analytical approach produces signicant
inaccuracies due to a lack of consideration of complex velocity and
particle concentration elds. Thus they suggest that CFD should be used
in future studies. Abuhegazy et al. (2020) and Talaat et al. (2021) used
CFD to investigate the virus transmission in, respectively, a classroom
and a passenger aeroplane; both papers suggest placing lateral
shields/barriers between people sitting side-by-side, with simulations
used to demonstrate their effectiveness. Guo et al. (2021) used CFD to
study the virus transmission in hospital rooms. As the central AC system
in hospitals may cause extensive spreading of the virus, they suggested
placing portable air puriers for mitigation and used simulations to
identify the ideal locations for air puriers. Welch et al. (2022) used CFD
to demonstrate the effectiveness of using ultraviolet lights to limit the
virus’ airborne transmission.
Based on the above review, CFD has become a standard approach to
studying COVID-19’s airborne transmission in various scenarios. How-
ever, relevant research has not been seen for scenarios on board ships.
During ship operations, natural winds, ACs and ventilation systems can
induce airborne transmission of virus particles inside a vessel. The
airow environment on ships is unique due to its forward motion and
the location of a doorway facing forward at the front of the passenger
area which can be open. This open door may allow a signicant wind
ow in the passenger area when the ship is moving. In addition, rela-
tively small ships usually use wall-mounted ACs instead of a central AC
system. The airow direction of the wall-mounted ACs can be adjusted,
and the inuence on COVID-19 transmission should be studied.
In this context, the present work develops a CFD-based model to
analyse the potential transmission of the COVID-19 virus inside a ship.
The paper starts by introducing the theories and practicalities of the
model, followed by validating the model against experimental mea-
surements of velocity eld and particle diffusion inside an idealised
room. Subsequently, the room geometry was replaced by the super-
structure of a small passenger ship. Analyses were presented on the virus
distribution in different scenarios, concerning a passenger coughing or
speaking when the vessel’s forward door is open or closed, and inves-
tigating the inuence of AC winds on the virus spread. The obtained
results were used to discuss measures that may minimise the spread and
contagion risk of COVID-19 virus.
2. Computational approach
CFD is used to model airow whilst the transmission of virus parti-
cles is tracked by a Lagrangian approach. The simulations were
Fig. 1. Experimental setup of Chen et al. (2006).
Fig. 2. Computational model to repeat the experiment of Chen et al. (2006).
L. Huang et al.
Ocean Engineering 255 (2022) 111486
3
Fig. 3. Experimental and computational results of velocity eld.
Fig. 4. Experimental and computational results of particle concentration.
L. Huang et al.
Ocean Engineering 255 (2022) 111486
4
performed using the commercial software STAR-CCM+.
2.1. Governing equations
In this work, Lagrangian particles are applied to model the COVID-19
virus aerosols/droplets, by which the particle movement is subjected to
its gravity (G) and a drag force from its surrounding airow (F
d
):
mdVP
dt =G+Fd(1)
where m denotes the particle’s mass, VP is the particle’s velocity, G =mg
and g is set at 9.81 m/s
2
. The uid drag force is calculated through the
Schiller-Naumann Correlation (Liu et al., 1993):
Fd=1
2Cd
ρ
PAP|Vs|Vs(2)
where
ρ
P is the particle density, AP is the particle project area and Vs is
the relative velocity between the particle and the air. Cd is an empirical
coefcient calculated based on the particle’s Reynolds number (ReP),
which is dened as follows.
Cd=
24
ReP1+0.15Re0.687
P,if ReP≤1000
0 44 ,if ReP>1000
(3)
The surrounding uid ow is solved by the standard Reynolds-
Averaged Navier-Stokes (RANS) equations:
∇⋅v=0(4)
∂
(
ρ
v)
∂
t+ ∇ ⋅(
ρ
vv) = − ∇p+ ∇ ⋅(
τ
−
ρ
v′v′) +
ρ
g(5)
where v is the time-averaged velocity, v
′is the velocity uctuation,
ρ
is
the uid density (
ρ
air
=1 kg/m
3
), p denotes the time-averaged pressure,
τ
=
μ
[∇v+(∇v)
T
] is the viscous stress term,
μ
is the dynamic viscosity
(
μ
air
=1.48 ×10
−5
N s/m
2
). Since the RANS equations have considered
the turbulent uid, the Shear Stress Transport (SST) k −
ω
model was
adopted to close the equations (Menter, 1993; Pena and Huang, 2021).
In particular, a sufciently-small particle in turbulent ow reveals a
randomly-varying velocity eld, which induces the microscopic parti-
cles to perform constant stochastic motions thus diffusing. This behav-
iour is modelled by including the effect of instantaneous velocity
uctuations on the particle (Gosman and Loannides, 1983):
v=v+v
′(6)
Fig. 5. Quantitive comparison of velocity measured at certain locations of the central plane: experiment (red crosses) and CFD ne mesh (black circles). (For
interpretation of the references to colour in this gure legend, the reader is referred to the Web version of this article.)
Fig. 6. A passenger ship operated by PT. Pelayaran Nasional Ekalya Purna-
masari (PNEP).
L. Huang et al.
Ocean Engineering 255 (2022) 111486
5
To be more specic, the applied uid velocity in calculations is v,
which is different from a usual RANS approach for macroscopic prob-
lems where v is directly used to simplify the calculation, e.g. (Huang
et al., 2020).
2.2. Validation
Based on the above governing equations, a validation study was
conducted to reproduce the experiment of Chen et al. (2006). The
experiment used articial particles to mimic a u virus, which has very
similar particle dimensions, airborne transmission mechanism, and
infection mechanism to COVID-19 virus. The experiment was conducted
in a cubic chamber, with a size of 0.8 m ×0.4 m ×0.4 m, as shown in
Fig. 1. The chamber has an air inlet near the left top side and an outlet
near the right bottom side. The inlet and outlet sections are of the same
size, 0.04 m ×0.04 m. The centers of them are located at x =0, y =0.2
m, z =0.36 m and x =0.8 m, y =0.2 m, z =0.04 m. Particles were
injected from the inlet with airow and diffused in the entire room. The
velocity prole and particle distribution were measured across the
centre plane of the chamber (the centre plane is marked in Fig. 1).
To reproduce the experiment, a computational domain of the same
size, inlet and outlet was established, as shown in Fig. 2(a). The inlet was
set as “xed-velocity inlet” with a constant airow velocity of (0.225, 0,
0) m/s, and the outlet was set as “xed-pressure outlet” with a reference
pressure of 0 Pa. This value is insignicant since the CFD calculation is
based on relative pressure. Other boundaries are “non-slip walls”.
Spherical Particles of a diameter of 1 ×10
−5
m and a density of 1.4 ×
10
−3
kg/m
3
were injected with the inlet ow, at a rate of 1000 particles
per second. The particle concentration at the inlet was used as a non-
dimensional standard, denoted as C
inlet
=1. Initially there is no parti-
cle in the domain, i.e. C
t =0
=0. The particles were set to attach to walls
upon contact and can leave the domain from the outlet. The above pa-
rameters were set to be consistent with the validation experiment.
The computational domain was then discretised into a hexahedral
Fig. 7. Prole and plan views of the ship’s external and internal design.
Table 1
The details of virus import due to coughing and speaking (Chao et al., 2009).
Virus source Coughing Speaking
Injection duration 0.3 s, short event 60 s, long event
Inject speed 11.7 m/s 3.1 m/s
Particle diameter 13.5
μ
m 16
μ
m
Inject particle number 6950 per second 443 per second
Fig. 8. Computational model of the vessel’s internal space.
L. Huang et al.
Ocean Engineering 255 (2022) 111486
6
mesh, as shown in Fig. 2(b). A mesh sensitivity test is presented with
three different cell sizes, respectively 0.05 m (coarse), 0.04 m (ne) and
0.03 m (very ne). The three mesh sizes were tested with a maximum
Courant number of 1 to determine the corresponding timestep size.
Simulations using the three sets of meshes were run for 60 s, and the
same measurements as per the experiment were taken for comparison, i.
e. the velocity prole and particle distribution were measured across the
centre plane of the box. To assess the numerical uncertainty from spatial
discretisation, an estimation was conducted as reported in Appendix A.
The Grid Convergence Index (GCI) method (Celik et al., 2008) was used
and the numerical uncertainty in the ne-grid solution for the ne mesh
turned out to be 3.68%.
Figs. 3 and 4 show a qualitative comparison between the experi-
mental measurements and simulations performed with the three mesh
densities. Overall there is good consistency between the experiment,
CFD with ne mesh, and CFD with very ne mesh. This can be seen in
both the velocity and concentration results. However, there are certain
inaccuracies in the coarse mesh results, as circled in the gures.
Therefore, the ne mesh density was chosen for the following in-
vestigations, as it requires less computational recourses than the very
ne mesh whilst maintaining the required accuracy.
Furthermore, a quantitive comparison was performed between the
experiment and CFD with ne mesh. Specic velocity data measured in
the experiment are compared with corresponding CFD results, as plotted
in Fig. 5. Good agreement can be seen for all the data points, which
conrms the accuracy of the CFD model. Based on the results presented
in this section, the present computational approach is deemed suitable
to study the airborne transmission of COVID-19 virus.
3. Ship model and COVID-19 risks
Upon validation of the computational approach, a small passenger
ship operating in Indonesia was selected as the research object of this
paper. The vessel’s photo and geometry drawings are shown in Figs. 6
Fig. 9. Velocity eld across the centre plane, when V =6 knots and the forward door is open: the difference between t =3 s and t =5 s is negligible, so the ow at t
=5 s is deemed converged.
Fig. 10. Coughing with the forward door open.
L. Huang et al.
Ocean Engineering 255 (2022) 111486
7
and 7. It is 19.5 m long and 4.5 m wide, with an internal space of
approximately 7 m long that contains 25 seats. This vessel is used to
transport workers to and from offshore installations such as drilling
platforms. There are two primary reasons for choosing this ship for the
present study:
(1) The operation of this vessel type in Indonesia has been signi-
cantly impacted ships by COVID-19. The country, heavily reliant
Fig. 11. Coughing with the forward door closed.
Fig. 12. Speaking with the forward door open.
L. Huang et al.
Ocean Engineering 255 (2022) 111486
8
on sea transportation, is looking to recover its crew and passenger
operations to aid the economic situation.
(2) The ship’s superstructure is compact, and the average voyage
time is 12 h, which gives a high-risky environment of COVID-19
transmission where people stay in a crowded space for a fairly
long time.
There are two types of virus import mechanisms considered in this
work: a passenger coughing and speaking. Both are the most possible
initiations of how COVID-19 starts to transmit in such a ship. The virus
particle details of coughing and speaking used in this work were set
according to the measurements of Chao et al. (2009), as given in Table 1.
Coughing is a short event whose duration is considered to be 0.3 s, and
speaking is modelled to last 60 s. The viruses injected through coughing
have a higher concentration and initial speed than those from speaking,
while overall speaking produces more oating viruses as its duration is
much longer.
As long as viruses are imported, their transmission relies on airows.
There can be two typical types of airow in the present case: (a) external
airow comes from the vessel’s forward door; (b) internal airow from
ACs. For modelling both the external and internal airows, the vessel’s
superstructure was imported into the CFD software at full scale, estab-
lishing a computational domain as shown in Fig. 8. The domain was
discretised using the ne mesh density as per the reported mesh sensi-
tivity test. CFD investigations were then performed using the approach
introduced in Section 2. The COVID-19 transmission due to the two
types of airows was analysed respectively in Sections 4 and 5.
4. External airow entering the vessel
To study the impact of external airow entering the vessel on the
COVID-19 transmission, the vessel was assumed to advance at a constant
speed (V). Four case studies were conducted for V =6 knots, as a
combination of the situations when a passenger sitting in the rst row is
Fig. 13. Speaking with the forward door closed.
Fig. 14. Comparison of virus distribution for different ship speeds (a front passenger speaking 60 s with the forward door open).
L. Huang et al.
Ocean Engineering 255 (2022) 111486
9
coughing or speaking, and when the forward door is open or closed.
When the forward door is open, the forward door was set as “xed-ve-
locity inlet” with a constant velocity of (-V, 0, 0), and the back door was
set as “xed-pressure outlet”. Other boundaries were set as “non-slip
walls”. When the forward door is closed, all boundaries were set as “non-
slip walls” and there is no wind ow in the domain.
For the open-door cases, a signicant airow forms inside the vessel.
As shown in Fig. 9, this ow takes around 5 s of simulation to converge,
thus each of the following simulations was rst run for 10 s without
particles to ensure the ow convergence. After 10 s, virus particles were
injected, assuming from an infected passenger sitting in the rst row.
For the simulation of a passenger coughing with the forward door
open, it can be seen in Fig. 10 that viruses were coughed out and scat-
tered. Along with the airow, the viruses moved rapidly towards the
back door. For around 5 s, the passengers behind the coughing person
were extensively contacted by the viruses, after which the viruses were
mostly blown out from the vessel.
For the simulation of a passenger coughing with the forward door
closed, it can be seen in Fig. 11 that viruses were coughed out and then
only stayed in the area where the passenger sits. The virus movement
was mainly a slow sinking due to gravity, alongside a small diffusion due
to stochastic motions. Although the viruses stayed in the air for around
100 s, the contagion risk appears to be minimal, based on the assump-
tion that coughing is usually not made directly towards other people.
For the simulation of a passenger speaking with the forward door
open, it can be seen in Fig. 12 that a wake of viruses was created and
severely affected the passengers behind the speaking person, especially
the next two rows. When the speaking stopped, the viruses were carried
away from the ship in 10 s.
For the simulation of a passenger speaking with the forward door
closed, it can be seen in Fig. 13 that a signicant number of viruses were
outputted and remained in a small area in front of the speaking person.
However, since speaking usually occurs as one person facing another, a
Fig. 15. Social distancing for the seat arrangement of the passenger ship –
black crosses indicate the seats that should not be used.
Fig. 16. Illustration of two Air Conditioners (AC1 and AC2) and their corresponding virus import as a nearby speaking person (SP1 and SP2).
Fig. 17. The air outlet (blue) and return air inlet (red) of the AC. (For inter-
pretation of the references to colour in this gure legend, the reader is referred
to the Web version of this article.)
L. Huang et al.
Ocean Engineering 255 (2022) 111486
10
contagion risk exists if the conversating people are sufciently close to
each other. It is suggested that a safe distance should be half a metre,
according to the virus coverage shown in Fig. 13(a). This conrms that it
is necessary to keep social distancing in the installed seats.
Combining the results from the four cases, it is shown that: when the
ship’s forward door is open, a signicant airow forms in the ship,
which carries the viruses to make extensive contacts with the passengers
in the back seat rows; when the forward door is closed, the viruses
mainly sink due to gravity and the diffusion is limited to a small area.
These two behaviours are also observed by relevant experimental and
computational COVID-19 studies for other environments, as summarised
in the review of Katre et al. (2021). More ship speed conditions (V =12
and 18 knots) have also been tested for the open-door scenario, con-
cerning an infected passenger speaking. It is found that the virus dis-
tribution is similar to that of V =6 knots, despite that the virus spread is
smaller when V is higher, as shown in Fig. 14. Overall, it is recom-
mended to keep the forward door closed to minimise the virus’s diffu-
sion, although this might be counter-intuitive.
Fig. 18. AC1 wind streamlines and the induced virus distribution.
L. Huang et al.
Ocean Engineering 255 (2022) 111486
11
It is also found that speaking generally creates a higher risk than
coughing, as speaking usually lasts a much longer duration, thereby
more viruses are introduced to the air. Whilst speaking may have been
less altered than coughing which is more likely to be treated as a red
ag, the present research suggests that more attention should be paid to
the COVID-19 risk in daily conversations.
When there is no external airow, the modelling indicated that a
conversation between two people should keep a distance of at least half
a metre (less than a seat’s width). Based on this, Fig. 15 presents two
potential seat arrangements for the ship. The aligned arrangement
shown in Fig. 15(a) reduces the capacity by 33%, and the crossed
arrangement shown in Fig. 15(b) reduces the capacity by 50%. How-
ever, as the setting in Fig. 15(a) may not avoid the risk from a front
passenger who turns around and speaks with the passenger behind, the
social distancing setting in Fig. 15(b) is recommended.
Fig. 19. AC2 wind streamlines and the induced virus distribution.
L. Huang et al.
Ocean Engineering 255 (2022) 111486
12
5. Internal air conditioner ow
There are two wall-mounted ACs installed inside the ship, respec-
tively in the front and back as shown in Fig. 16 (AC1 and AC2). Each AC
has a size of approximately 0.25 m ×1.1 m ×0.45 m, but it is not cubic,
as shown in Fig. 17. The AC has an air outlet near the bottom and a
return air inlet at the top. The air outlet area is 1.1 m ×0.05 m, and the
return air inlet is 0.7 m ×0.25 m. In the CFD model, the AC’s outlet was
set as “xed-velocity inlet” with a constant speed of 2 m/s, which was
measured on-site when the AC was operating at its middle power. The
return air inlet was set as “xed-velocity outlet” with a constant speed of
0.63 m/s, which was calculated based on volume conservation, i.e. the
air amount that exits from the air outlet equals that enters the return air
inlet (2 m/s ×1.1 m ×0.05 m ≈0.63 m/s ×0.7 m ×0.25).
This study investigates the inuence of each AC’s airow direction
on the transmission of COVID-19. The airow direction from the air
outlet was varied between 0◦and 60◦(relative to horizontal, θ), with
four cases studied respectively for AC1 and AC2, where θ =0◦, 15◦, 30◦
and 60◦. The virus source is assumed as an infected passenger sitting on a
seat nearby the opening AC (as marked in Fig. 16), and the person is
considered to speak for 60 s.
Figs. 18 and 19 show the velocity eld and virus distribution inside
the ship, when AC1 or AC2 is operating. It is found that a wall-mounted
AC can generate a ow circle that is highly dependent on θ. When θ is
0◦or 15◦, the AC ow was conned in the top part of the room and
within a relatively small region, so did the virus transmission. When θ is
30◦or 60◦, the virus spread was evidently expanded by the AC ow,
which is particularly true for AC2, as shown in Fig. 19(c)&(d). It is also
found that an AC tends to accumulate the virus particles, as in both
Figs. 18 and 19 where the virus particles gathered near the opening AC.
This is because an AC’s backow attracts virus particles to move toward
the device.
Based on the ndings above, two suggestions are given for the AC
operation on such a passenger vessel: (a) control the AC outlet direction
at less than 15◦downward, and (b) arrange passengers to not sit nearby
an operating AC. The second suggestion can be adapted to other AC
types whose inlet and outlet are at separate locations in a room (such as
the setup in Fig. 1), and the suggestion is to not sit downstream of the AC
ow.
6. Conclusions
To provide effective measures that can minimise COVID-19 trans-
mission for passenger vessels, a computational model has been estab-
lished to investigate the airborne transmission of the virus in the
superstructure of a small passenger vessel. The model was validated
against experimental results to prove the capability of accurately pre-
dicting the velocity eld and virus distribution inside a room. Based on
the validated model, a series of simulations were conducted to study the
inuence on the virus transmission from both external wind ow and
internal AC ow. The simulation results have helped identify opera-
tional improvements as summarised below.
When the forward door is open, ship advancement generates an
extensive wind ow across the passenger area, which fosters the spread
of virus. Therefore, it is suggested to keep the ship’s forward door shut.
When there is no wind ow in the vessel’s superstructure, the virus
spread from coughing or speaking is limited to a radius of half a metre.
Based on the radius, a crossed seat arrangement plan has been proposed
in the present paper.
Although wall-mounted ACs could also foster the spread of virus in a
vessel, this study has demonstrated that this effect can be suppressed by
controlling the AC outlet direction to be less than 15◦downward. In
addition, it is found that virus particles can follow an AC’s backow to
accumulate. Hence, sitting far from an opening wall-mounted AC can
minimise the associated risk.
In future work, the computational approach can be applied to study
the COVID-19 airborne transmission in other environments. Many
maritime environments are still at COVID-19 risk which requires more
research, such as a large cruise ship, an open-air nishing vessel and an
offshore platform.
CRediT authorship contribution statement
Luofeng Huang: Conceptualization, Methodology, Software, Vali-
dation, Visualization, Investigation, Writing – original draft. Soegeng
Riyadi: ConceptualizationConceptualisation, Investigation, Resources.
I.K.A.P. Utama: Supervision, Project administration, Funding acquisi-
tion, Writing – review & editing. Minghao Li: Methodology, Software,
Visualization. Peiyign Sun: Software, Investigation. Giles Thomas:
Supervision, Project administration, Funding acquisition, Writing – re-
view & editing.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgements
This work is part of a project that has received funding from the
British Council under the Newton Institutional Links Grants - Ensuring
the safety of Indonesian seafarers and shers in the time of COVID-19
and beyond (agreement No. 623457938), in conjunction with the
Indonesian Governmental Funding from the Ministry of Education,
Culture, and Higher Education (agreement No. 2242/PKS/ITS/2021).
The authors appreciate PT. Pelayaran Nasional Ekalya Purnamasari
(PNEP) for sharing the studied vessel’s geometry and information.
Appendix A. Numerical uncertainty analysis
The approximation of a physical problem via CFD requires the solution of a set of partial differential equations, as introduced in Section 2. Due to a
lack of closed-form solutions for the RANS equations, the present work discretised the governing equations in space and obtained approximate results.
Thus the discretisation resolution, i.e. mesh density, has a signicant impact on the prediction. In order to assess the associated uncertainty, here
applies the GCI method (Celik et al., 2008).
Step 1 :
Dened three mesh densities h
1
=0.03 m, h
2
=0.04 m, h
5
=0.05 m.
Step 2 :
Calculated r
21
=h
2
/h
1
=1.33, and r
32
=h
3
/h
2
=1.25.
L. Huang et al.
Ocean Engineering 255 (2022) 111486
13
A variable critical φ was dened as velocity magnitude at the central point of the room (Fig. 2).
Calculated:
P=1
ln(r21)|ln|
ε
32/
ε
21| + q(P)|
q(P) = lnrP
21 −S
rP
32 −S
S=1⋅sgn(
ε
32 /
ε
21)
where
ε
32 =φ
3
– φ
2
,
ε
21 =φ
2
– φ
1
.
Step 4 :
Calculated the extrapolated value:
φ21
ext =
rP
21 φ1−φ2
rP
21 −1
Step 5 :
Calculated the approximate relative error:
e21
a=
φ1−φ2
φ1
Calculated extrapolated relative error:
e21
ext =
φ21
ext −φ1
φ21
ext
Calculated the ne-grid convergence index:
GCI21
fine =1.25e21
a
rP
21 −1
The results are summarised in Table A1, in which the numerical uncertainty in the ne-mesh solution for the velocity magnitude is 3.68%
Table A1
calculations of spatial discretisation
uncertainty
Parameter Value
r
21
1.33
r
32
1.25
φ
1
0.0163
φ
2
0.0175
φ
3
0.0203
P 4.3967
φ21
ext 0.0158
e21
a 7.36%
e21
ext 2.94%
GCI21
fine 3.68%
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