167
1 INTRODUCTION
The sloshing phenomenon is a natural event for LNG
carrier ships caused by external excitation force during
ship operation in wave conditions, and energetic
sloshing during this condition could lead to excessive
motions. These motions could endanger the ship not
only the stability but also structural damage as a result
of impact pressure caused by violent flows of the
volatile fluid with the side wall of the tank. Many
studies have been performed to overcome sloshing
problems with baffles that efficiently reduce the
sloshing phenomenon. Both numerical and
experimental studies were carried out to capture the
effect of sloshing inside the tank with and without
baffle. One of the numerical methods that are
commonly used in computational fluid dynamics
(CFD), which is in the present study a meshfree CFD,
i.e., was used to simulate sloshing with perforated
baffles. Smoothed particle hydrodynamics (SPH) is one
of the major meshfree CFDs that is commonly used for
large deformation and violent flows such as sloshing.
The study of sloshing for a prismatic tank using a
large number of particles was first performed in GPU
to accelerate the computation time by Trimulyono et al
[1] showed the static and dynamic pressure was well
reproduced by SPH. Later on, the studies extended to
application sloshing with vertical and T-shaped baffles
with low filling ratios [2]–[4] that showed SPH could
capture the effect of sloshing with different shapes
reduced the wave elevation and dynamic pressure. The
studies of sloshing with long duration in a dimension
LNG tank were successfully performed and validated
with experiment [5], a similar study was performed in
both two and three-dimensional using rectangular
Effect of Perforated Baffle Shapes on Sloshing
Reduction in Prismatic Tanks Using SPH Analysis
A. Trimulyono, N.A. Riadi, I.P. Mulyatno, D. Chrismianto, M. Iqbal & A. Firdhaus
Diponegoro University, Semarang, Java, Indonesia
ABSTRACT: Sloshing is a phenomenon that is nonlinear in a liquid carrier, such as LNG or a tanker ship. One
type of LNG carrier is the membrane-type carrier. The membrane type is similar to a prismatic tank, whose shape
is suitable for a ship. This paper investigates the mitigation of sloshing in a prismatic tank by implementing a
perforated baffle. There are four models of perforated baffle circles, rectangular, long ellipsoid, and short
ellipsoid. The baffle position is at the midpoint of the tank, with a longitudinal position to suppress fluid in rolling
motion. The filling ratios of the tank are 25% and 50%, mimicking experimental conditions with the excitation
force rolling. The pressure sensor located near the free surface in 25% filling ratio was used to validate and verify
the numerical approach of smoothed particle hydrodynamics (SPH). SPH is one of the numerical approaches for
computational fluid dynamics (CFD) based on the particle method, which is suitable for large deformations and
nonlinear free surface flows, such as sloshing. The dynamic pressure and free surface deformation after
installation of the perforated baffle significantly decreased and proved the perforated baffle design suitable for
the prismatic tank.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 20
Number 1
March 2026
DOI: 10.12716/1001.20.01.18
168
tanks[6], [7]. The findings indicated that SPH is well-
reproduced sloshing in long-duration periods with
consistent diffusion terms for the continuity equation.
The study of SPH with an elastic baffle using a couple
of SPH-SPIM was carried out then it was found that
both the shape of the free surface and the large
deformation of the elastic baffle can be well captured
[8], [9], the study of elastic baffles also performed with
open-source SPH solver SPHinXsys which showed
SPH also well captured the fluid-structure interaction
cases [10]. Recently model of floating baffles was used
to supress the fluid inside in tank [11], [12]. It showed
that the perforated baffle study is still few conducted
to mitigate sloshing, and in this paper, we carried out
a study to suppress sloshing in the prismatic tank by
employing smoothed particle hydrodynamics (SPH).
The present study aims to design a perforated baffle
for sloshing in an LNG tank using a fixed perforated
baffle. There are four models of perforated baffle
circles, rectangular, long ellipsoid, and short ellipsoid.
The position of the baffles is in mid of tank to supress
the fluid in rolling motion. The roll excitation motion
with two ratios used, i.e., 25% and 50% filling ratios.
The pressure sensor located near the free surface in
25% filling ratio was used to validate and verify SPH
results.The study employed open-source SPH solver
DualSPHysics [13], [14] which has been widely used
for real-life engineering problems.
2 METHODOLOGY
The present study was perfomed in numerical
approach with SPH that developed for free surface
problems by Monaghan [15] then it widely used for
real engineering problems such as dam break and
water wave progations. The SPH method discretized
the computational domain into points or particles
weighted by distance or smoothed length. To reduce
the contribution, range from close particles, the
quantities are calculated as a weighted sum from those
particles within the smoothing length (h). The particle
properties such as mass, velocity, and position are
calculated with the weighting or kernel functions. The
essential elements of the SPH technique, which is based
on integral interpolants, are detailed explain in
References [16]. In SPH particle a has distance rab with
particle b with smoothing length (h) to calculate
particle contribution in the kernel function (Wab). The
integral approximation field function A(r) in the
domain (Ω) showed in the equation (1) then equations
(2) indicated in particle approximation form. In this
study the Wendland kernel function was used where
αD is equal to 21/164πh3 in 3D, and q is the
nondimensional distance between particles a and b
represented as r/h (see equation 3). Equations (4)
indicated the continuity equation in SPH form and
equation (5) is momentum equation in Lagrangian
form. The equation of state for calculating the pressure
field indicated by equations (6) which the delta-SPH
was used to reduce the spurious pressure
( ) ( ) ( )
Ω
,A A W h d=−
r r r r r
(1)
( ) ( ) ( )
,
b
a b a b
b
b
m
A A W h
−
r r r r
(2)
( ) ( )
4
1 2 1 0 2
2
D
q
W q q q
= − +
(3)
( )
0
2
2
a ab a ab b
b ab a ab b a
b
ab
bb
d W m
m W hc
dt
−
= +
r
v
r
(4)
b
aP
a
b ab a ab
ab
b
P
d
mW
dt
+
= − + +
g
v
(5)
0
0 0
ab ab
ab ab
ab
ab
ab ab
c
where
−
=
vr
vr
2
00
0
1
c
P
=−
The sloshing condition of this study was based on
the Trimulyono et al. [1], which in this study two filling
ratios was used, i.e., 25% and 50% with rolling motion.
Table 1 indicated the dimension of prismatic tank
based on Trimulyono et al. [1]. Figure 1 illustrated the
prismatic tank based experimental condition [1], which
the setup of SPH computation was based on
Trimulyono et al. [2] that well proven for sloshing cases
with baffles, then the baffles in present studies
illustrated in Figure 2. The variation of perforated
baffles are circle (B1), rectangular (B2), long ellipsoid
(B3) and short ellipsoid shape (B4), this shape is
commonly used in the fabrication of ship in the
construction of bulkhead. The location of perforated
baffles was in middle of tank in longitudional
positions, Figure 3 illustrated the exact location of
baffles in tank.
Table 1. Principal particular of prismatic tank
Dimension of prismatic tank
Heigh(h)
0.21 meter
width (l)
0.30 meter
length (L)
0.36 meter
Water depth(d)
0.0525m (25%)
0.1050m (50%)
Figure 1. Prismatic tank with fix baffle in mid of tank (a) and
location of pressure sensor (b)
169
Figure 2. Perforated baffle with shape of circle (a),
rectangular (b), long ellipsoid (c) and short ellipsoid (d).
Figure 3. Location of perforated baffle in mid of tank circle
(a), rectangular (b), long ellipsoid (c) and short ellipsoid (d).
3 RESULTS AND DISCUSSION
Firstly the analysis of pressure performed by
comparing the hydrostatic pressure in calm conditions
as the findings of previous study the static pressure
showed good agreement with analytical solution as
mentioned in references [1] as well as in present study
indicated in Figure 4. The pressure field showed the
correct phenomenon which the highest pressure
located in the bottom of tank. It showed the setup of
SPH computation was could be use for general
sloshing problem and the setup is consistent for current
cases. Figure 5 indicated the dynamic pressure without
baflles (a) and with perforated baffles (b). The red
colour indicating the dynamic pressure of SPH and
blue colour experiment results, it showed that SPH in
trasient motions has small discrepancy especially in
time 15-20 seconds, finally in steady state condition the
discrepancy of pressure become decreased. The
perforated baffle indicated effectively reduce the
dynamic pressure in side wall of tank that it illustrated
in Figure 5 (b) dynamic pressure become decreased as
the fluid inside tank is calm compared without
perforated baffles. The variations showed similar trend
for all configurations of baffles, it can be caused by the
hole in the baffles location is based on previous study
[2] that effectively to reduce the wave on free surface
caused by tank movement. It indicating the location of
holes in baffles is essentials to reduce sloshing
phenomena by reduce the wave in the near free
surface. Table 2 showed the comparison of mean peak
of dynamic pressure in filling ratio 25% dan 50%, it
indicated that dynamic pressure is reduce by
perforated baffle. The dynamic pressure decreased
caused by fluid inside tank become calm as results of
impact pressure vanish or reduce by baffle.
Figure 6 illustrated the dynamic pressure in 50%
filling ratio with and without baffles. The similar
phenomena was captured as in the 25% filling ratio
which baffles effectively reduce the dynamic pressure.
Figure 6 (a) indicated the pressure without baffle that
it showed the accuracy of SPH slightly decreased
compared to 25 % filling ratio. The locations of pressure
sensor is the same as 25% filling ratio but the dynamic
pressure more influenced by hydrostatic pressure as
pressure sensor located in mid of fluid. The dynamic
pressure by installation of perforated baffles decreased
the wave of free surface as consequence the dynamic
pressure also decreased. The reason similar
phenomena in filling ratio 50% caused by the position
of holes in perforated located in the near of free surface,
as mentioned before that position of holes has
significant effect to reduce wave caused by movement
of fluid inside tank by external excitation force.
Figure 4. Static pressure of filling ratio 25% and 50%
Figure 5. Dynamic pressure for filling ratio 25% without (a)
and with perforated baffles (b)
170
Figure 6. Dynamic pressure for filling ratio 50% without (a)
and with perforated baffles (b).
Table 2. Mean of peak pressure in two filling ratios
No
Model of Baffle
Filling ratio 25% (Pa)
Filling ratio 50% (Pa)
1
Without Baffle
408,4
826,95
2
B1
52,74
174,26
3
B2
52,29
166,30
4
B3
53,8
177,32
5
B4
52,53
188,77
The Free surface deformation illustrated in Figure 8
and Figure 9 which in present study advanced post
processing was performed in VisualSPHysics [17] that
add on in Blender. The free surface deformation in the
Figure 7 illustrated the fluid without perforated baffle
more violent compared to perforated baffles. The
dynamic pressure inside tank was caused by the
movement of fluid accelerate by movement of tank
then it hit the wall which caused peak dynamic
pressure very high then the fluid deaccelerate then
pressure decreased as showed in Figure 5 and 6. By
installing the perforated baffle inside the tank, it was
dampened the movement of fluid inside tank by
decreasing the wave created by displacement of fluid
caused by movement of tank. The fluid inside tank
become calm after perforated baffles installed to tank,
the reason is the fluid dampen by perforated baffle by
reducing the wave created as results the fluid it calmer
compared without perforated baffle. The advanced
post processing SPH performed to provide the realistic
fluid by VisualSPhysics.
Figure 7. Free surface deformation of without and with
perforated baffles
Figure 8. Free surface deformation of without and with
perforated baffles with advanced texturing for filing ratio
25%
171
Figure 9. Free surface deformation of without and with
perforated baffles with advanced texturing for filing ratio
50%
4 CONCLUSIONS
It demonstrated the SPH was able to replicate the
sloshing in the prismatic tank with and without baffles,
then the hydrostatic pressure as mentioned in previous
study shows agreement well with analytical solution.
According to the results of present studies, the
perforated baffles all shape is proven to reduce the
sloshing effect as result the dynamic pressure
decreased and the fluid inside tank become calm for
both filling ratios 25% and 50% Future works of
multiphase sloshing using perforated baffles is
undergoing reasearchto complete present study. To
achieve realistic fluid visualisation, a complex post-
processing technique using VisualSPHysics was also
applied.
ACKNOWLEDGMENTS
This research was funded by the Institute for Research and
Community Services of Universitas Diponegoro (LPPM
UNDIP) under the scheme International Publication Grant
(RPI) 2024, grant number 225-39/UN7.D2/PP/VII/2024.
REFERENCES
[1] A. Trimulyono, H. Hashimoto, and A. Matsuda,
“Experimental validation of single- and two-phase
smoothed particle hydrodynamics on sloshing in a
prismatic tank,” J. Mar. Sci. Eng., vol. 7, no. 8, 2019.
[2] A. Trimulyono, A. Haikal, C. Deddy, and S. Samuel,
“Investigation of Sloshing in The Prismatic Tank With
Vertical And T-Shape Baffles,” Brodogradnja, vol. 73, no.
2, pp. 43–58, 2022.
[3] A. Trimulyono, S. T. M. Owhaamsorrc Gultom, E. S. Hadi,
and D. B. Purwanto, “Investigation of Sloshing with
Vertical and Horizontal Baffle in the Prismatic Tank using
Meshfree CFD,” CFD Lett., vol. 15, no. 6, pp. 115–129,
2023.
[4] A. Trimulyono, D. Chrismianto, H. Atthariq, and Samuel,
“Numerical Simulation Low Filling Ratio of Sway
Sloshing in the Prismatic Tank Using Smoothed Particle
Hydrodynamics,” CFD Lett., vol. 14, no. 7, pp. 113–123,
2022.
[5] C. Pilloton, A. Bardazzi, A. Colagrossi, and S. Marrone,
“SPH method for long-time simulations of sloshing flows
in LNG tanks,” Eur. J. Mech. - B/Fluids, vol. 93, pp. 65–92,
2022.
[6] M. D. Green and J. Peiró, “Long duration SPH simulations
of sloshing in tanks with a low fill ratio and high
stretching,” Comput. Fluids, vol. 174, pp. 179–199, Sep.
2018.
[7] M. D. Green, R. Vacondio, and J. Peiró, “A smoothed
particle hydrodynamics numerical scheme with a
consistent diffusion term for the continuity equation,”
Comput. Fluids, vol. 179, pp. 632–644, 2019.
[8] T. Hu, S. Wang, G. Zhang, Z. Sun, and B. Zhou,
“Numerical simulations of sloshing flows with an elastic
baffle using a SPH-SPIM coupled method,” Appl. Ocean
Res., vol. 93, p. 101950, 2019.
[9] G. Zhang, X. Yang, G. Liang, K. Zheng, and Z. Zhang,
“Numerical simulation of sloshing flows with elastic
structure by coupling δ+-SPH and SPIM,” Eng. Anal.
Bound. Elem., vol. 165, p. 105764, 2024.
[10] Y. Ren, A. Khayyer, P. Lin, and X. Hu, “Numerical
modeling of sloshing flow interaction with an elastic
baffle using SPHinXsys,” Ocean Eng., vol. 267, p. 113110,
2023.
[11] R. Abdullah, A. Trimulyono, Samuel, and B. A. Adietya,
“Numerical simulation of sloshing with floating baffles
using smoothed particle hydrodynamics,” IOP Conf. Ser.
Earth Environ. Sci., vol. 1461, no. 1, 2025.
[12] C. G. Koh, M. Luo, M. Gao, and W. Bai, “Modelling of
liquid sloshing with constrained floating baffle,”
Comput. Struct., vol. 122, pp. 270–279, 2013.
[13] J. M. Domínguez et al., “DualSPHysics: from fluid
dynamics to multiphysics problems,” Comput. Part.
Mech., vol. 9, no. 5, pp. 867–895, 2022.
[14] A. J. C. Crespo et al., “DualSPHysics: Open-source
parallel CFD solver based on Smoothed Particle
Hydrodynamics (SPH),” Comput. Phys. Commun., vol.
187, pp. 204–216, 2015.
[15] J. J. Monaghan, “Simulating Free Surface Flows with
SPH,” J. Comput. Phys., vol. 110, pp. 399–406, 1994.
[16] Liu, G. R and M. B. Liu, Smoothed Particle
Hydrodynamics: A Meshfree Particle Method. World
Scientific Publishing Company, 2003.
[17] O. García-Feal, A. J. C. Crespo, and M. Gómez-Gesteira,
“VisualSPHysics: advanced fluid visualization for SPH
models,” Comput. Part. Mech., 2021.
