1

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 : k_suastika@na.its.ac.id

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

REFERENCES

[1] Artana, Ketut Buda dan Soegiono. (2006). Transportasi

LNG Indonesia. Surabaya: Airlangga University Press.

[2] Akyildiz H, Unal E. Experimental investigation of

pressure distribution on a rectangular tank due to the

liquid sloshing. Ocean Eng 2005;32:1503–16.

[3] A.Ibrohim,Rouf. (2005). Liquid Sloshing Dynamics

Theory and Applications. Cambridge; Cambridge

University Press.

[4] Azhar, Khoirul (2012). Tugas Akhir. Studi Gerakan

Sloshing Terhadap Tangki Kotak (Rectangular Tank)

Dengan Dan Tanpa Pelat Memanjang (Baffle) Akibat

Gerakan Rolling Kapal Dengan Metode Computational

Fluid Dynamics (CFD) .Surabaya; Institut Teknologi

Sepuluh Nopember

[5] Bhattacharrya, Rameswar. (1978). Dynamics Of Marine

Vehicles. New York; Wiley Publication.

[6] Cargo Operating Manual. Liquid Natural Gas Carrier

Disha (H2210).Petronet Pentatech.co.ltd.

[7] Gavory, T. (2009). Sloshing in Membrane LNG Carriers

and its Consequences from a Designer’s Perspective.

International Society of Offshore and Polar Engineer

[8] J. Glejin et al. ( 2012). Influence of winds on waves over

the near shore regions of eastern Arabian Sea. European

Geosciences Union; 9, 3021–3047, 2012

[9] Lee, S.J, dkk. (2005). The effects of LNG-tank sloshing on

The global motions of LNG carriers. USA: Texas A&M

University.

[10] Rowsen, K.J and Tupper, E.C. Basic Ship Theory Volume

I. Oxford: Longman group.

[11] Seung He-Lee et al. (2010). Numerical simulation of

three-dimensional sloshing phenomena using a finite

difference method with marker density scheme. 38 (2011)

206-225

[12] Septiansyah, Bahtiar Rifai. (2012).Tugas Akhir.Analisa

Sloshing Secara Memanjang Pada Tangki FLNG Dengan

Menggunakan Metode Computational Fluid Dynamic

(CFD).Surabaya: Institut Teknologi Sepuluh Nopember.

[13] Sloshing Assessment Guidance Document for Membrane

Tank LNG Operations (2009). London; Llyod Register.

[14] Sugiarso, Adin. (2010). Maxsurf Training 2010 Basic

Level. Surabaya

[15] Tautika, Firman. (2008). Dasar-Dasar CFD

Menggunakan Fluent. Bandung: Informatika.