Sloshing on The Inside Walls of Membrane Type Tank of LNG...
Transcript of Sloshing on The Inside Walls of Membrane Type Tank of LNG...
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Abstract - The development of an offshore LNG sector and the
increase demands for operational flexibility in LNG shipping
bring the new challenges for sloshing assessment on ship motion
of partially filled LNG inside tanks. The coupling motion and
interacting simulation between ship motion and inner-tank
sloshing are investigated by a time-domain simulation scheme.
Generally, the heaving and pitching motion will be affected to the
ship which is conducted to head for 180° heading angle on the
wave or called by head sea. Therefore the motion of LNG
membrane tank caused by ship motion that affected to the
sloshing in LNG membrane tank. Sloshing can be interpreted as
the free surface motion of fluid in a container. It also may
produce large pressures on the wall of tank structure. The
dimension of membrane tank had made in 3D for 266 m length of
ship .The LNG has been simulated for three variations in tank
no.4 for filled liquid level at 30%, 50%, and 80% of membrane
tank high. Simulation has been conducted by Computational
Fluid Dynamic (CFD). The simulation result is maximum
dynamic pressure occurred at 30% of LNG filling level equal to
5122.34 Pa on the aft wall node of the membrane tank at 10.92 m
from the base of the membrane tank.
Keywords: 3D, CFD, Heaving, LNG Carrier, Membrane tank,
Pitching , Sloshing.
I. INTRODUCTION
hip motion which is occurred to fluid motion in partially
filled tanks may cause large structural loads if the period of
tank motion is close to the natural period of fluid inside the
tank. The tank will produce a sloshing. Sloshing means any
motion of a free liquid surface inside a container. The
amplitude of the slosh, in general, depends on the nature,
amplitude and frequency of the tank motion, liquid-fill depth,
liquid properties and tank geometry. The dynamic behavior of
a free liquid surface depends on the type of excitation and its
frequency content. The excitation can be impulsive, sinusoidal,
periodic and random. Its orientation with respect to the tank
can be lateral, parametric, pitch/heave or roll and a
combination. Under low gravity field, the surface tension is
dominant and the liquid may be oriented randomly within the
tank depending essentially upon the wetting characteristics of
the tank wall (A Ibrohim Rouf, 2005) .
The basic problem of liquid sloshing involves the estimation
of hydrodynamic pressure distribution, forces, moments and
natural frequencies of the free-liquid surface. These
parameters have a direct effect on the dynamic stability and
performance of moving containers. Generally, the
hydrodynamic pressure of liquids in moving rigid containers
has two distinct components. One component is directly
proportional to the acceleration of the tank. This component is
caused by the part of the fluid moving with the same tank
velocity. The second is known as „„convective‟‟ pressure and
represents the free-surface-liquid motion. Mechanical models
such as mass-spring-dashpot or pendulum systems are usually
used to model the sloshing part. Most studies have therefore
concentrated on investigating forced harmonic oscillations
near the lowest natural frequencies, predicted by the fluid field
linear equations (A Ibrohim Rouf, 2005).
A lot of work has been done in the application of CFD to
liquid sloshing. For example, Sriram et al (2006) analyzed the
behavior of the sloshing waves in a tank subjected to
excitation in the horizontal and vertical directions using a
finite clement scheme. The research showed that the peaks
appear at the natural frequencies of the system and the peak
magnitude is close to the natural frequency for the sway
excitation regardless of peak excitation frequency.
Furthermore when the excitation frequency is equal to the first
mode of natural frequency for the resonance condition, its
consequence is a higher magnitude. In addition, for the heave
excitation, irrespective of whether peaks appear at the natural
frequencies, the magnitude of the spectral peak is the same for
different excitation frequencies. Some other relevant studies
also can he found in research literature (Armenio et al., 1996;
Rhee, 2005; Yu et at, 2008).
In this work, the CFD method is used to investigate the
Liquid sloshing behaviors in a membrane tank which is
subjected to coupled external excitations. The coupled external
excitations mean that different external excitations are
imposed on the tank at the same time. These excitations are
given through the CFD dynamic mesh technique, which was
implemented by FLUENT user-defined functions. The volume
of fluid (VOF) method is used to track the free surface of
sloshing. The external excitation is imposed through the
motion of the tank by using the dynamic mesh technique. The
paper is organized into the following sections. First, the
governing equations are briefly introduced followed by a
section on the parameter settings applied in the numerical
simulations. Subsequently, the modeling approach is validated
Sloshing on The Inside Walls of Membrane
Type Tank of LNG Carrier Due To Heaving and
Pitching Motion in Regular Waves Muhamad Syaiful Anwar, Ketut Suastika.
Department of Naval Architecture and Shipbuilding Engineering
Faculty of Marine Technology (FTK),
Sepuluh Nopember Institute of Technology (ITS)
Jl. Arief Rahman Hakim, Surabaya 60111 Indonesia
e-mail : [email protected]
S
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for a case with a single excitation source. Finally, the impulse
loads under excitations, pitch coupled with heave, are
analyzed.
The objective of this study is to analyst a simulation system
accounting for the effect of a large load inside membrane tank
NO.96 for LNGC voyage in order to predict LNG
characteristic within 4 tanks inside because it was the most
delivered tank of LNG carrier. One of the unique features of
membrane systems is that the insulation lines the inside of the
ship‟s tank. This allows the steel in the tank structure to
support the membrane and be part of the hull girder. Being in
direct contact with the liquid cargo, membrane systems must
have sufficient capacity to withstand all of the loads from
liquid sloshing from the motion of LNG carriers in waves. The
most common membrane systems in use are non-traditional
structures (i.e. insulated plywood boxes or polyurethane foam
panels). Considering the long history of successful experience
with these systems, minimizing the need for modifying the
membrane design certainly has merit.
II. OBJECTIVE AND FORMULATION
A. LNG Carrier Membrane Tank
The most commonly used plywood box type containment
system is known as the Gaz Transport NO.96 system designed
by GTT, see Figure 1. The system uses a thin sheet of high
nickel alloy, Invar, as the primary barrier. The secondary
barrier is of the same material and similar thickness to the
primary barrier. The insulation system consists of two layers of
plywood boxes, which are filled with a granular insulation
material, Perlite, or glass wool. The boxes have parallel
internal members (bulkheads), which are also made of
plywood sheet. Staples are used to fasten the plywood box
covers to the external and internal bulkheads. The secondary
barrier is located between a primary box and a secondary box.
As it is essential that the internal surface of the plywood boxes
are flat to support the Invar membrane, mastic “ropes” (also
known as resin ropes) are laid on the bottom surface of the
secondary boxes adjacent to the hull plating to remove any
undulations in the hull plating. The mastic cures against a thin
sheet of waxed paper which prevents fixed attachment to the
hull. The plywood boxes are held in place by an arrangement
of rods, tensioned by spring washers, which are secured via
sockets welded to the inner hull. The invar membranes are
held in place and made liquid tight by welding to "tongues"
which are retained in slots in the plywood boxes
Figure 1. Arrangement of GTT NO.96 containment system
Moreover, the most commonly used layered foam type
containment system is the Technigaz Mark III system designed
by GTT, see Figure 2 This system uses a corrugated membrane
of sheet austenitic stainless steel as the primary barrier. The
secondary barrier is a layer of Triplex which is a thin
aluminium foil with glass fiber cloth glued to each side. The
insulation for the primary and secondary barrier consists of
polyurethane foam reinforced with glass fiber (R-PUF). A
plywood sheet is glued to the top surface of the primary R-
PUF layer. The primary membrane is welded to stainless steel
"anchoring strips" which are recessed and riveted to the
plywood sheet. The Triplex barrier is glued directly to the R-
PUF layers. A plywood sheet is glued to the bottom of the
secondary R-PUF insulation to which mastic (resin) ropes are
applied. Unlike the NO.96 system, the mastic "ropes" adhere
to both surfaces and serve to glue the containment system
directly to the inner hull surface. The complete insulation
system including the R-PUF, secondary barrier and upper and
lower plywood sheets are manufactured as prefabricated
panels. The panels are positioned during installation by a
system of studs welded to the inner hull bolted through the
lower plywood, but the greater part of the strength of
attachment is provided by the mastic after it cures.
Figure 2. Arrangement of GTT Mark III containment system
B. Heaving Motion
In the case of free oscillation, the difference in displacement of
the ship to its upper extreme position from the equilibrium
position is the same magnitude as the difference in
displacement from the equilibrium position to its lower
extreme position. This magnitude is known as the amplitude of
the heaving motion. The time required for one complete cycle
of motion is termed the heaving period, since the free heaving
motion is a simple harmonic motion. The period of oscillation
is independent of the amplitude and is thus known as the
natural period. The frequency of motion likewise called the
natural frequency of the ship.
However, when damping is present, the amplitude of the
heaving motion gradually decreases until the ship finally stops
at its equilibrium position. The period will be slightly greater
in the case of damped oscillation. Now suppose that the ship
is being oscillated vertically up and down by a fluctuating
force that is periodic in nature. For a certain amount of time
the motion will be rather in irregular; such a motion is known
as transient oscillation. But because of damping, the
irregularities soon disappear and a steady-state oscillation
takes their place This is known as Three forced oscillation, in
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which the amplitude and frequency of motion are depend on
the amplitude and frequency of the exciting force. The
damping will also affect the amplitude of forced oscillation. In
this case of forced. However the forces must be in equilibrium;
thus the equation of motion can be written as
(1)
The inertial force which is present when the ship is in
oscillatory motion is
Where a is the virtual mass (ship mass plus added mass) and
is the vertical acceleration. The damping force
which always resists the motion is Fb=bz Where b is the
damping constant and is the velocity. The
restoring force, which always tends to bring the ship back to its
equilibrium position is Fc = cz where c is the restoring or
spring constant and z is the displacement of the centre of
grafity (CG) of the ship and cz = ρgAwpz.= ρgBCwp. The
exciting or encountering force which acts on the mass of the
ship is where F0 is the amplitude of the
encountering force, is the circular frequency of the
encountering force and t is the time.
Free, undamped heaving Motion (F0=0, b=0), from the condition of equilibrium, we have
and the solution for this differential equation is
(2)
Figure 3.Illustration of heaving motion
Where A and B are constant that can be determined from the
initial condition, is the natural frequency of the heaving
motion that is
= 2 π/Tz = (3)
Tz is the heaving period, and d is the phase angle. Note that the
natural heaving period Tz is considered to be a constant and
does not depend on the amplitude of motion. This may be true
for small and moderate motions. The natural period is an
important factor in determining a ships heaving motion in
seaway.
C. Pitching Motion
Ship may undergo a simple harmonic motion about 'either a
transverse axis or a longitudinal axis if it is displaced from its
equilibrium position and then released, or if it is given an
initial velocity away from its equilibrium position. It has also
been noted that we should always refer to the moments of
forces, rather than the forces, when we describe angular
motions like pitching and rolling. As in the case of heaving,
the following four moments act in pitching and rolling
motions:
Pitching motion is described in this section; rolling motion, the
equation of motion of pitching can be written as
(4)
Inertial moment = , Here d is the virtual mass moment of
inertia, and the angular acceleration. Damping moment =
Here e is the damping coefficient and is the angular
velocity. The damping moment is again considered to be
linearly proportional to the angular velocity for the sake of
simplicity, as in the ease of heaving. Restoring moment = .
Here f is the restoring moment coefficient, and is the angular
displacement in pitching. Again the restoring moment is
considered to be linearly proportional to the pitching
displacement. .This is true only for small angles of pitching.
The exciting moment, is considered to be
fluctuating with an encountering frequency of , If we can
determine the various values of d, e, f and M0, we shall be
able to determine the motion characteristics for pitching.
Therefore they should he determined separately for the
different kinds of motion. The virtual mass moment of inertia
for pitching d is the vessel moment of inertia for pitching plus
the added mass moment of inertia for pitching that is
(5)
Where is the added mass moment of inertia for pitching
and kyy is the radius of gyration for pitching. The virtual mass
moment of inertia for pitching d can also be defined as
(6)
Where the is the virtual mass. Here it is assumed that the
longitudinal distribution of mass is the same as of the
longitudinal distribution of displacement thus the vertical
distribution is neglected it. And it is also assumed that the CG
of the ship is at the midship section, Note that for the normal
ship form the radius of gyration for pitching motion is kyy =
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0.24L to 0.26L where L is the length of the ship. The added
mass moment of inertia for pitching can be determined by
experiment or by the method of strip theory, that is, the ship
considered to have different sections for each of which the
added mass is obtained. Then the added mass, as is the ship‟s
moment of inertia from the ship mass. Thus
(7)
Where dn is the added mass for each section and is the distance
of each section from the LCG. e is the damping force
coefficient of the pitching which is depending on increased of
beam, decrease of draft, decrease of vertical prismatic
coefficient (for example increase the V form) f is the restoring
moment can be expressed in the simple form as :
Where c is the restoring moment coefficient, and Iy is the
moment of inertia of load waterplane area, thus BML=Iy/V
For small angle of inclination, and therefore :
(8)
Figure 4.Illustration of pitching motion
D. Concept of Heaving and Pitching Motion in Coupled
The external perturbations of the tank include coupled heave
by which the tank translates vertically, pitch by which the tank
rotates around a fixed ordinate across the bottom center of the
tank, are periodic, they can be approximately represented as
shown:
(9)
(10)
Where z‟ is the vertical velocity of heaving motion, zo the
vertical displacement of heaving motion, θ‟ is the angular
velocity of pitching motion, θo is the amplitude of the angular
displacement in pitching motion and ωe is the frequency
.
Figure 5.Illustration of coupled heaving and pitching motion
E. Sloshing in Mathematical Model
The volume of fluid (VOF) method is adopted to capture the
free surface motion of sloshing in a liquid tank. The VOF
method uses a characteristic function F to capture the fluid
volume and identify the free surface position. F is defined as a
step function which represents the volume fraction of a ce11
fi11ed with liquid:
F=0 or F=1 means the cell away from the interface is fully
filled with air or liquid; while 0<F<1 means the cell is partly
filled with liquid and identifies the position of the free surface.
The advection equation for F is
(11)
Where u is the velocity, the normal direction of the free
surface can be obtained by calculating the gradient of F. the
free surface position can be determined approximately by the
piecewise linear scheme of geometric reconstruction.
The sloshing behavior in a liquid tank which can be
represented by an incompressible viscous fluid flow with a free
surface is governed by the Navier-Stokes equation and the
continuity equation.
(12)
Where u is the velocity, p the pressure, ρ the density, g the
accleration of gravity, F a body force and µ the viscosity of the
mixture. The trial CFD code Ansys-Fluent is used for all the
simulations presented in this work. The pressure-velocity
equations are decoupled by the "PRESTO!" algorithm the
transport equation for the volume fraction is solved by the
explicit time-marching scheme. The interface is constructed by
the piecewise linear scheme; thus, the convective flux across
the interface is computed. The convergence criterion is that the
residuals for all governing equations are below 1.0E-5. The
time step is 0.005 s. The boundaries of the tank are set as non-
slip walls, and the wave tank is initially static. Several user
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defined functions are plugged into the CFD code and work
with the CFD dynamic mesh model to implement the motions
of the tank under the periodic external excitations. The reader
can find more details about the dynamic mesh technology in
the Ansys-Fluent user's guide.
III. NUMERICAL IMPLEMENTATION
A. Object Characteristic
The object characteristics which were simulated for sloshing
taken from Disha LNG Carrier are; calculating the ship
hydrostatics, designing the dimension of membrane tank, and
analyzing the ship environment. These characteristics related
to predict the motion of membrane tank and fluid inside which
is filled by LNG.
1) Hull Form Parameters
The hull form parameters which are needed to design for
analyzing the ship motion by Computational Aided Design
(CAD) are Cb, Cm, Cp, Cwp, Lcb, KB, WSA, and ABT. The
design carried out on numerical results based on mathematical
implementation. Then numerical results carried out by maxsurf
trial software. The ship particulars have being taken from
Disha LNGC Cargo Manual to calculate hull form
characteristics are;
Table 1 Ship dimensions
Ship Dimensions
Loa 277 M 908.837 ft
LPP 266 M 872.746 ft
B 43.4 M 142.3954 ft
H 26 M 85.306 ft
TDesign 11.4 M 37.4034 ft
Tscantling 12.5 M 41.0125 ft
LWL 270.8 M 888.4948 ft
Displacement 100149 Ton 3450972.06 ft3
Deadweight 70151 Ton
Speed 19.5 Knot 10.0308 m/s
The ship particulars which are used for calculating the
hydrostatic characteristics of tanker ship can be implemented
based on the following formulation.
Cb = ∆ / L.B.T.ρ
Cm = 1,006- 0,0056.Cb-3.56
Cp = Cb/Cm
Cwp = (1+2.Cb)/3
Lcb = (-0.135+0,195.Cp).L
KB = T.(0,9-0,3.Cm-0,1.Cb)
WSA = 1,7.L.T+
ABT = CB(WSA-(Lwl.(2T+B) .(0.452+ 0.4425.CB-
0.2862.Cm-0.003467.B/T+0.369.Cwp)/2.36
Where Cb is block coefficient (Rawson K.J, 1926), Cp is
prismatic coefficient (Adrian Biran, 2002), Cm is merismatic
coefficient (Kerlen, 1970), Cwp is water plan coefficient ,KB
is distance keel to buoyancy (Schneekluth, 1921), Lcb is
longitudinal center of buoyancy (Kerlen, 1970), WSA is
wetted surface area and ABT is area of bulbous bow in
transverse-plan at draft (Holtrop and Mannen, 1982). All the
hull form characteristic for designing of ship hull using
maxsurf software has to be compared with the calculated
mathematical of hydrostatic. Besides, the comparison between
numeric and mathematic hydrostatic was difficult to be equal.
Than they must have a minimum interval value between
numeric and mathematic to obtain the precision of the design.
The interval which has implemented is between -0.5% and
0.5% of each characteristics of hull form parameters.
Table 2 Constrains of hull forms parameters
Mathematical Numerical Constrains Percent
Cb 0.729 0.73 0.001371 0.137%
Cm 0.986 0.98 -0.005085 -0.509%
Cp 0.738 0.74 0.002710 0.271%
Cwp 0.842 0.843 0.001187 0.119%
Lcb 133.101 m 133.918 m 0.000682 0.068%
KB 6.047 m 6.064 m 0.002811 0.281%
WSA 14622.96 m2
14745.3 m2 0.004367 0.437%
ABT 69.32 m2 70.012 m
2 0.0095303 0.953%
Disp. 100.194 tons 100.314,3 tons 0.00165 0.165%
The result of these is lines plan drawing of LNG Carrier which
has closed to hull form characteristics. This lines plan drawing
will be used for numerical ship motion in pitch and heave
motion. This motion will became the output from
Computational Aided Design (CAD) which will be defined of
membrane tank motion in CFD- Ansys Fluent.
Figure 6.Linesplan drawing as result of design
2) Membrane Tank Dimension
The design of membrane tank NO.96 in this vessel has adapted
to the need of the owner requirement. But for this case the
dimension of membrane tank has exists in general arrangement
drawing thus it can be measured directly from general
arrangement of Disha LNG Carrier (LNGC).
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Figure 7.General arrangement of LNGC
The membrane tank which will be simulated in this case is the
farthest from the center of gravity. Approximately the central
gravity was in same vertical axis with the center of buoyancy
therefore the center of gravity take on center of buoyancy for
the central rotation of the motion. Then the tank membrane
which will be simulated is tank membrane no.4 which is shown
in general arrangement drawing.
Table 3 Membrane tanks dimensions of LNGC Tank
No.
From
Ap (m)
Tank
Length
(m)
Tank
Breadth
(m)
Lower
Tank
Breadth
(m)
Upper
Tank
Breadth
(m)
Side Tank
Height
from Base
(m)
1 Aft 60.2 38 39.17 31.29 21.49 3.7
1 Fwd 98.2
2 Aft 102.1 43.78 39.17 31.29 21.49 3.7
2 Fwd 145.9
3 Aft 149.8 43.62 39.17 31.29 21.49 3.7
3 Fwd 193.4
4 Aft 197.3 32.46 39.17 31.29 21.49 3.7
4 Fwd 229.8 19.4 11.9 18.5
The geometric of membrane tank is about 32.46 m in length,
27.32 m high and 39.17 m width molded. But the aft lower
width is 31.29 m, aft upper width is 21.49 m and front width is
about 19.4 m, the front lower width is 11.9 m and front upper
width is 18.5 m within meshed 2195 nodes and 130286
elements uniform structured in CFD. During computation the
pressure is monitored at the eight points on the aft wall and the
fore wall of the tank which is divided into four parts in order to
record the sloshing loads.
Figure 8.Membrane tank geometry of LNGC
3) Ship Environment
The ship environment parameter is taken from wave statistic
for Disha LNGC voyage from India to Qatar through a year.
The several inputs of ship motion in numerical method using
CAD are taken from maximum mean period 10.2 second,
maximum wave height 7 m and seawater depth greater 800m.
This wave statistic recorded during January 2011 until
December 2011. [8]
Table 4 Wave parameters around Disha LNGC voyage
From these wave parameters, the encountering wave for ship
motion can be determined from calculating wave number in
circular frequency based on linear airy theory as ω2 =
g.k.tanh(kd) Where ω is wave frequency or 2π/T, g is
acceleration of gravity, d is seawater depth and k is wave
number. Then ω = 0,62 and the result of wave number k is
0.03211 rad/m. The wave velocity can be determined using k
as λ=2π/k= 111.28 m and the wave velocity c = λ/T = 10,91
m/s. from these results, the encounter frequency can be
determined as ωe=(c-u.cosµ).2π/λ = 0.67 rad/s. where u is ship
speed, and µ is heading angle of ship in this case 180o for
greater response of heaving and pitching in motion.
Figure 8.Disha LNGC voyage India - Qatar
B. Numerical Ship Motion
The ship motion of LNGC determined from numerical analysis
in regular waves has results the sinusoidal equation as show in
figure 9. The motions analysis which is using seakeeper trial
software are expressed for 90 second has 0.851 m of vertical
displacement in heaving motion and 1.29 degrees or 0.025
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radians of angular amplitude in pitching motion and encounter
frequency 0.67 rad/s.
Figure 9.Graphic of Pitching and Heaving Motion
The motion from ship motion results can be expressed in
vertical velocity equation on regular wave as z‟= -0,57 cos
(0.67.t) and angular velocity as θ‟= 0.0171cos(0,67.t). These
results of ship velocity equation will be added to CFD defined
formula for object coupled motion of the membrane tank.
C. Verification
The experimented sloshing under pitch excitation was resulted
which is depicted on the pressure history in figure bellow for
92x62x46 cm of rectangular tank on node 6 filled by fresh
water. These results compared the total pressure history
between experimental pressure and numerical pressure. The
node position in geometric experiment is shown in figure 10.
Where the experimental data (Hakan Akyildiz and Erdem
U‟nal., 2004) in figure 11-12 is expressed to solid line and
numerical result is expressed to dash line.
Figure 10.Node position on tank geometry for experiment
The experimental cases which are studied are simulating the
sloshing without baffle within 25%, 50% and 75% filling level
of the tank. The pitch amplitude is 4 degree and 8 degree with
2 rad/s of frequency. Velocity equation is based formulation
which will be arranged into CFD user defined formula. A total
of six cases simulated in this validation. The case parameters is
shown in table 5.
Table 5 Cases parameters from experimental studied
Case
No
Filling
Depth
(%)
Pitch
Angle
(degree)
Pitch Angle
(Radians)
Frequency
Pitch
User Defined
Velocity
1 25 4 0.06981317 2 0.13 .cos ( 2 t )
2 50 4 0.06981317 2.5 0.15 .cos ( 2.25 t )
3 75 4 0.06981317 3 0.17 .cos ( 2.5 t )
4 25 8 0.13962634 2 0.27 .cos ( 2 t )
5 50 8 0.13962634 2.5 0.31 .cos ( 2.25 t )
6 75 8 0.13962634 3 0.34 .cos ( 2.5 t )
Figure 11.Case no 1, 2, and 3 node 6 with 4 degree
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Figure 13.Case no 4, 5, and 6 node 6 with 8 degree
IV. SIMULATION RESULTS
The capture of fluid motion inside membrane tank which is
designed in 3D with 30% filling level can be depicted in figure
14 where the sloshing occurred on forewall and aftwall of the
membrane tank. The pressure on forewall was different from
aftwall within time domain scheme. The simulation was
carried out to 90 second of motion. The maximum pressure on
aftwall of membrane tank is higher than maximum pressure on
forewall of membrane tank because of different width of each
membrane tank.
Figure 14.Fluid motion for 80 second on aftwall
Figure 15.Node for 5.46 m height 30% filling level
Figure 16.Node for 10.92m height 30% filling level
The maximum pressure occured on aftwall for 5.46 m height
from base of the tank where the membrane tank was filled 30%
of LNG for LNGC coupled motion for pitch and heave is node
Z5 = 4291.24 Pa, Z6 = 5122.34 Pa and the maximum pressure
ocured on forewall for 5.46 m height is node Z1 = 3239.66 Pa,
Z2 = 1542.30 Pa. The comparison between each node in figure
17 with 30% filling level of LNG has depicted that the higher
load pressure occurred on aftwall unexpectedly.
Figure 17.Pressure history in each node at 30% filling level
In other case, fluid motion inside membrane tank which is
designed in 3D with 50% filling level can be depicted in figure
18 where the sloshing occurred on forewall and aftwall of the
membrane tank. The pressure on forewall was different from
aftwall within time domain scheme. The simulation also
carried out in 90 second of motion. The maximum pressure on
aftwall of membrane tank is higher than maximum pressure on
forewall of membrane tank because of different width of each
membrane tank. But the comparison of different load pressure
between aftwall in node Z1 in was close to node Z5. It can be
inferred that the local motion velocity close to free surface
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area higher than velocity on base of the tank because the
geometry of the tank.
Figure 18.Fluid motion for 12 second on fore wall
Figure19. Node for 5.46m height 50% filling level
Figure 20.Node for 10.92m height 50% filling level
The maximum pressure occured on aftwall for 5.46 m height
from base of the tank where the membrane tank was filled 50%
of LNG for LNGC coupled motion for pitch and heave is node
Z5 = 2569.64 Pa, Z6 = 3352.06 Pa and the maximum pressure
ocured on forewall for 5.46 m height is node Z1 = 2531.56 Pa,
Z2 = 2841.98 Pa. This case differ from 30% filling level which
is the comparison between each node in figure 17 with 50%
filling level of LNG has depicted that the higher load pressure
occurred on aftwall periodictly.
Figure 21. Pressure history in each node at 50% filling level
For the last case with 80% filling level has captured of fluid
motion inside membrane tank in figure 22 where the sloshing
occurred on forewall and aftwall of the membrane tank. The
pressure on forewall was different from aftwall within time
domain scheme. Same as two cases before, the simulation was
carried out to 90 second of motion. Maximum pressure on
aftwall of membrane tank is also higher than maximum
pressure on forewall of membrane tank because of different
width of each membrane tank. From figure 23 the pressure has
a same result as node 5.64m in 50% filling level but the
pressure in which close to free surface area still higher than
pressure around base of the tank.
Figure 22.Node position on tank geometry for experiment
Figure23. Node for 5.46m height 80% filling level
Figure24. Node for 10.92 m height 80% filling level
Figure25. Node for 16.93m height 80% filling level
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Figure26. Node for 21.85m height 80% filling level
Figure 27.Pressure history in each node at 80% filling level
In this case, the maximum pressure occured on aftwall for 5.46
m height from base of the tank where the membrane tank was
filled 80% of LNG for LNGC coupled motion for pitch and
heave is node Z5 = 2290.02 Pa, Z6 = 2658.08 Pa, Z7 = 3180.39
Pa, Z8 = 3842.90 Pa and the maximum pressure ocured on
forewall for 5.46 m height is node Z1 = 2409.64 Pa, Z2 =
2440.82 Pa, Z3 = 2594.83 Pa, Z4 = 2443.61 Pa. The
comparison between each node in figure 27 with 80% filling
level of LNG has depicted that the higher load pressure
occurred on aftwall close to free surface area periodictly or
more stable than maximum pressure which is closed to surface
area at 30% filling level.
Figure 28.Comparison the maximum pressure
The comparison between maximum pressures which was
occurred on each node at various fill level depicted the large
pressure has impacted on forewall at 30% filling level close to
free surface of LNG. Beside the deeper of filling level, the
stable load pressure will be occurred and the higher filling
level, the smaller pressure will be formed also in variation tank
form of membrane can occurred large pressure on aft wall of
the tank which is nearest from center of gravity or center
rotation (Seung He-Lee, 2011).
Table 6 Maximum pressure comparison of each node on
wall of membrane tank
Filling Level 30% Fore wall Filling Level 30% Aft wall
Node (m) Pressure (Pa) Node (m) Pressure (Pa)
5.46 3239.664 5.46 4291.244
10.92 1542.305 10.92 5122.342
16.93 0 16.93 0
21.85 0 21.85 0
Filling Level 50% Fore wall Filling Level 50% Aft wall
Node (m) Pressure (Pa) Node (m) Pressure (Pa)
5.46 2531.564 5.46 2569.641
10.92 2841.983 10.92 3352.06
16.93 26.13 16.93 88.72
21.85 0 21.85 0
Filling Level 80% Fore wall Filling Level 80% Aft wall
Node (m) Pressure (Pa) Node (m) Pressure (Pa)
5.46 2409.644 5.46 2290.023
10.92 2440.829 10.92 2658.083
16.93 2594.836 16.93 3180.393
21.85 2443.613 21.85 3842.907
V. CONCLUSIONS
From simulation above, it can be inferred that sloshing loads
will be increased around free surface area. Moreover liquid
sloshing will become violent and exhibit overturning, breaking
waves, and violent impact on the top wall if a tank is subjected
to coupled excitations and the excitation frequency is resonant.
It can be predicted that the larger the amplitude of sloshing,
the more complicated the coupled excitations, and the greater
the complexity of the mechanism of liquid sloshing. In
addition, the combined effect of the actual marine environment
and the mechanism of ship motion further complicate liquid
sloshing in the tank of a moving ship. So, it is particularly
necessary to study the mechanism of liquid sloshing of a tank
under multiple coupled excitations.
ACKNOWLEDGMENTS
This work has corried out with support from supervisor for his
advices, Assistant of Numeric Computation Laboratory,
Solikhan Arif, for using the facility and Indonesia Laboratory
Hydrodynamic ,Mr.Abdul Ghofur, for his advices and several
material. Their support is gratefully acknowledged.
11
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