6-4-yoshida - liquid motion loads in large-size lng carriers tank
TRANSCRIPT
6.4–1
LIQUID MOTION LOADS IN LARGE-SIZELNG CARRIERS TANK
CHARGEMENTS DUS AUX MOUVEMENTS DE LIQUIDESA L’INTERIEUR DE CUVES DE METHANIERS
DE GRANDE CAPACITE
Hisafumi Yoshida, Ph. D.Seijiro Miyake, M. Sc.
Structure & Fluid Engineering Research CenterHitachi Zosen Corporation
2-2-11, Funamachi, Taisho-kuOsaka 551-0022, Japan
Mituyasu Nagahama, B. Sc.Hydrodynamics Department
Maritec Corporation13-65, Nankoukita 1-chome, Suminoe-ku
Osaka, 559-0034, Japan
ABSTRACT
The liquid motion phenomenon in real sea is a complicated three-dimensional andirregular motion which is difficult to simulate by means of conventional 2-D regularmotion models. Furthermore, the bench test studies to correctly simulate and measuresuch motions require large scale models and experimental facilities, and are very muchtime consuming. Consequently today, reports on liquid motion studies in large size LNGcarriers are very scarce.
Recently, Hitachi Zosen has developed a three-dimensional simulation computerprogram called “3D-Slosh.” Comparative liquid motion studies have been carried outbetween 135,000 m3 type and 175,000 m3 type ships, by making use of this new software.
The liquid motions in the 94% full foremost tank of both ships are simulated andcompared in the four kinds of sea conditions; three cases of wave period (9, 7 and 5.5second) and two cases of incident wave angle (135 and 180 degree). Wave period of 9second is nearly corresponds to ships natural frequency and 5.5 second nearlycorresponds to the natural frequency of the tank liquid.
It was found that the maximum impact pressure to the tank ceiling by liquid motion islarge when the wave period is resonant with that of ships; in other words, ships oscillatelarge in resonance with wave, but small when the wave period is resonant with that oftank liquid; in other words, the ships oscillate small because the wave period is notresonant with that of the ships.
6.4–2
Comparing the two ships, generally 175, 000m3 type shows smaller impact pressurethan 135,000m3 type because the magnitude of ship motion of a large ship is smaller thanthat of a small ship. On the contrary, in the smaller wave period, however, the impactpressure of the larger ship is larger than smaller ships. But the magnitude of pressureitself is considerably small. The reason is supposed that, in this case, the effect of thelarger moving span of tank liquid exceeds that of the ship oscillating magnitude.
RESUME
Les Phénomènes de mouvements liquides de cargaison en mer réelle sont desmouvements en trois dimensions irréguliers et compliqués, qui sont difficiles à simuler aumoyen des modèles 2-D conventionnels aux mouvements réguliers. De plus, les étudessur modèles réduits dans le but de simuler et mesurer de manière satisfaisante de telsmouvements de liquide requièrent de lourdes installations expérimentales et sont trèscoûteuses en temps. En conséquence à ce jour, rares sont les rapports d'études réaliséessur les mouvements liquides de cargaison de méthaniers de grande capacité.
Récemment, HITACHI ZOSEN a dévelopé un logiciel de simulation en troisdimensions appelé “3-D Slosh”, et des études comparatives de mouvements de liquideont été réalisées sur des navires de 135,000 m3 et de 175,000 m3, en utilisant ce nouveaulogiciel.
Les phénomènes de mouvements de liquide ont donc été calculés sur la cuve avantdes deux navires remplie à 94% et pour 4 conditions de mer; 3 périodes de houle (9,7 et5.5 secondes) et deux angles d'incidence (135o et 180o) . La période de 9 secondes estcentrée sur la fréquence naturelle des navires, la période de 5.5 secondes correspondant àla fréquence naturelle du liquide dans les cuves.
Les pressions maximum d'impact sur le toit des cuves sont importantes quand lapériode de houle est en résonance avec celle du navire, mais faibles lorsque la période dehoule correspond à la résonance du liquide dans les cuves.
En comparent les résultats obtenus sur les deux navires, les pressions d'impact sur lenavire de 175000 m3 sont généralement plus faibles que celles obtenues sur le navire de135000 m3 simplement parce que les mouvements à la mer d'un gros navire sont plusfaibles que celles du navire de plus faible capacité. Au contraire pour des périodes pluspetites les pressions d'impact mesurées sur le navire de 175000 m3 sont plus élevées quesur le navire plus petit mais ces pressions d'impact sont considérablement plus faibles.
6.4–3
LIQUID MOTION LOADS IN LARGE-SIZELNG CARRIERS TANK
1. INTRODUCTION
The cost reduction for the sea born transportation of LNG is one of the relevant issuesfor the further development of LNG trade. In this regard, the cost effectiveness of thelarge size LNG carriers has been discussed and it seems generally accepted.
In the design of large LNG carriers, a membrane type ship has much merit comparingto a spherical tank type ship, because of the compactness in ship size and free choice ofship dimensions [1,2].
But at the same time, motions of larger moving spans of LNG cargo, and their loadson cargo containment systems, must be investigated in larger size LNG tanks, theirresonance conditions to ship motion and/or to sea waves being different from those ofcurrent size LNG carriers.
Although the computed result of “3D- Slosh” has been verified comparing with thebench test result, but regarding the calculated value of impact pressure, furtherverification may be necessary comparing with the actual damage data or actual shipmeasurement. Therefore, the study was made in comparison with the one actuallyoperating and the large one on design. Two prototype ships used for the simulation areshown in Table 1.1 and Fig. 1.1. Both ships are membrane type with four cargo tanks.Breadth of fore end of the No.1 tanks are narrowed to fit in the hull form.
Table 1.1 Prototype of Ships
135,000m3 type 175,000m3 typeLength betweenperpendiculars
260.0 m 286.0 m
Breadth moulded 44.3 m 48.8 mDraft moulded 11.75 m 12.0 m
Liquid motion of LNG cargo varies with cargo tank position, geometry and fillinglevel. In a high level filling condition, extremely high localized sharp impact pressureoccurs and also in a tapered tank in plan view such as foremost tank, dynamic pressurecan be magnified when compared with a tank of uniform section. Considering the above,the investigation were made for the No.1 cargo tank (foremost cargo tank) of 94% full.
The sea condition in which the ships will navigate, was determined as mentioned insection 2.2 under the realistically severest conditions. In addition to it, two cases ofshorter wave periods and one case of following sea condition, both at the same waveheight, were added to see the effects of resonance with tank liquid motion and the effectof trapezoidal tank shape.
6.4–4
In order to estimate the lifetime maximum of liquid motion pressure, statisticalanalysis accumulating sufficiently enough impact peak pressure data through theconsiderable length of ship motion data may be necessary [3]. But such lengthy motionsimulation is practically impossible due to the computation time restriction, and thereforethe simulation were made for the selected time span where the ship motion can beregarded as maximum as mentioned in Section 2.3.
Figure 1.1 Ship Arrangement
2. SIMULATION OF LIQUID MOTION LOADS IN LARGE SIZE LNGCARRIERS TANK
2.1 Outline of Approach
A general flow of simulation of liquid motion loads in large size LNG carriers tank isshown in Figure 2.1.
First of all, sea conditions ship will encounter must be examined to simulate liquidmotion loads. Significant wave heights, wave periods and wave encounter angles shouldbe determined to estimate liquid motion phenomenon by an adequate method. Somekinds of sea area information, that is, route, season and data of wave frequency arenecessary to set the sea conditions for a simulation.
Second, in order to simulate a model tank movement in irregular waves, timehistories of the ship motion in the sea conditions determined at the first stage must becomputed by means of ship response functions and wave spectra concerned. Thegeneration of time histories is carried out by an estimation program that is based on thestrip method.
6.4–5
Third, a series of numerical calculation of liquid motion loads are carried out bythree-dimensional simulation program called “3D-Slosh.” The simulation program canestimates impact pressures at a tank ceiling of LNG carriers. A procedure is introduced topick up the maximum impact pressure at the tank ceiling in limited computation time.
The details of the procedure mentioned above are shown as follows.
2. 2 Sea Condition and Random Motion
2.2.1 Setting of Sea Conditions
Figure 2.1 General Flow of Simulation of Liquid Motion Loads
In case that data of wave frequency on a ship’s route are available, the proceduresetting a sea condition is as follows.
Ship conditions
• Loading condition• Speed• Tank (dimension, position)
Sea area information
• Route• Season• Wave data
Set up sea conditions
• wave spectrum• H1/3, Tw
• Wave data
Generation of time history• ship motion in irregular waves
Generation of time history• tank motion in irregular waves
Response function of shipmotion in regular waves
Power spectrum of shipresponse in irregular waves
Simulation of liquid motionloads
Evaluation of the results
6.4–6
(1) If some tables of wave frequency are given by each segmental small sea area along aroute, label them with suffix k (k=1~Nk).
(2) Let the probability that the ship will goes into the area k be Rk.
(3) The time passing through the area k will be proportional to Lk, which is square root ofthe segment area.
(4) Pkij(Hi,Tj) is the wave occurrence probability at the area k. Where Hi is wave heightand Tj is wave period.(i=1~Ni), (j=1~Nj)
(5) From the definition mentioned above, the probability Qij that the ship will encounterthe wave of (Hi,Tj) is proportional to Σk{Pkij×Rκ×Lκ}.
where ΣiΣjQij=1.0.
(6) The expectation value of time that the ship will meet to sea conditions of (Hi,Tj) forher lifetime is expressed by the following equation (2.1).
Eij=Qij × (Y×365×24) × S (hour) (2.1)
where Y is the lifetime length of the ship and S is the rate of service.
(7) Generally, a ship may often changes the course in order to avoid an extreme stormyweather. Such extreme conditions, of which frequency is naturally small, are omittedby cutting off the Qij below a certain level.
(8) If an adequate value of ε is given for Qij according to the ship's lifetime length and thedivision's fineness of wave frequency tables of (Hi,Tj), then the maximum encounterwave height Hmj correspond to wave period Tj can be set.
Figure 2.2 shows a long-term distribution of ship motion (pitch angle and verticalacceleration at FP) for an actual ship. Figure 2.3 shows the wave frequency on NorthPacific Ocean in winter.
Figure 2.2 Long-Term Distributions of Ship Motions
Long-Term Distributions of Pitch Angle
0
2
4
6
8
10
12
0 5 10 15-LOG10(Q)
PIT
CH
AN
GL
E (
deg.
) Calculation
SR125 Experiment
Long-Term Distributions of Vert.Acc. at FP
0
0.20.4
0.60.8
11.21.4
1.61.8
2
0 5 10 15-LOG10(Q)
AC
CE
LE
RA
TIO
N (
g)
SR125 Experiment
Calculation
6.4–7
Figure 2.3 Wave Frequency in the North Pacific Ocean in Winter
The long-term distribution is calculated by using the table of wave frequency wherewave data of 0.4% is removed from the highest wave height. In case of North PacificOcean in winter, it will be sure that the ship keeps away from the sea area of the waveheight above 7.25m. This actual ship experiment had been carried out by a containercarrier (SR125; The 125 Regulation Research committee of Shipbuilding ResearchAssociation of Japan)[4]. This experiment is good agreements with the above mentionedcalculation. The result will become a reference for deciding ε. Thus, the wave height of10m is enough for the simulation of liquid motion loads on this route under the severeweather condition.
The procedure how to determine ship speed, encounter wave angle and wave period isstill remaining for the simulation of liquid motion phenomenon. The method is asfollows.
In case a ship is navigating in the severe weather condition, the ship speed will drop.But, the design speed is applied for this simulation because it is severe side for shipmotion prediction. The natural period of ship motion and that of liquid motion should betaken into account to determine the wave period and the wave encounter angle.
A standard should be laid down in order to select more severe wave conditions for theexciting forces of liquid in the tank. An index represent the magnitude of acceleration inirregular waves is defined by the following equation (2.2)
Fσ = {(Uσ)2+(Vσ)2+(Wσ)2+(g•θσ)2+(g•φσ)2+(lx•θσ)2
+(lz•θσv)2+(lx•φσv)
2+(lz•φσv)2+(lx•ψσv)
2 (2.2)
0.37
5
2.25
4.25
6.25
8.25
10.2
5
12.2
5
14.2
5
4. 5
7 . 5
10. 5
13. 5
0
102030
40
50
60
70
80
P(1/
1000
)
H( m)
T( s )
Wave Frequency in the NORTH PACIFIC
6.4–8
whereUσ,Vσ,Wσ : standard deviation of acceleration for surge, sway and heaveφσv, θσv, ψσv : standard deviation of angular acceleration for roll, pitch and yawφσ, θσ : standard deviation of angle for roll and pitchlx, lz : longitudinal and vertical distance from center of a ship’s gravity to that of a tankg : acceleration of gravity
That is to say, the meaning of this index Fσ is the cumulative acceleration causes theliquid motion. To set severe wave conditions is necessary to consider the combination ofFσ� and acceleration's encounter period, moreover the natural period of the tank.
Figure 2.4 shows a relationship between acceleration index Fσ and encounter periodsof the acceleration for 135,000m3 and 175,000m3 type of the LNG carriers. It can befinally seen from this figure that a severe wave condition is as follows.
• wave period ; 9 second (near to natural period of pitch motion of the ships)• encounter wave angle ; 135 degrees
(45 degrees from bow, describe head sea as 180 degrees.)
Wave height of 10m may be high enough for the route of North Pacific Ocean.
Figure 2.4 Relationship Between Fσσ and Encounter Periods of Acceleration
0
45 90
135
180
5
7
9
0
0. 005
0. 01
0. 015
F σ/H
^2
χ(deg.)
T( s )
135,000 m3 LNG Carrier0
45 90
135
180
5
7. 5
10
0
0. 005
0. 01
0. 015
Fσ/
H^2
χ(deg.)
T( s )
175,000 m3 LNG Carrier
0
45 90
135
180
5
7
9
0
5
10
15
20
Te(
s)
χ( d e g . )
T( s )
135,000 m3 LNG Carrier
0
45 90
135
180
5
7
9
0
5
10
15
20
Te(
s)
χ( d e g . )
T( s )
175,000 m3 LNG Carrier
6.4–9
2.2.2 The Generation Technique of Time Histories of Random Motion
In order to generate the time histories of ship motion, wave spectra is superimposedon the response function of ship motions. It is necessary for a calculation of ship motionsthat added mass and damping are estimated. Ursell-Tasai method is applied to calculatethe hydrodynamic forces. The response functions of ship motions are calculated by thestrip method. Then, the equation of motion is solved by putting the hydrodynamiccoefficients.
The wave spectra is used a type that I.S.S.C. advocated in 1964. The responsespectrum, which is made by the superimposing method, is used for generating the timehistories of the ship motions [5]. It is expressed by the following equation (2.3).
S(t)=ΣSQRT{2Sa(ωn)dωn}×cos{ωn•t+ε(ωn)+γs(ωn)}, n=1~N (2.3)
whereS(t) : time histories of ship motionSa(ωn) : response spectra, Sa(ωn)=As(ωn)
2×S(ωn)As(ωn), γs(ωn) : amplitude and phase of ship response functionS(ωn) : wave spectraε (ωn: random phaseωn : wave frequency
This equation (2.3) is used to generate the time histories in long-crested irregularwaves. In order to express ship response under the actual seas, the time histories in short-crested irregular waves are important. Those time histories are obtained bysuperimposing time histories on each motion in long-crested waves. In that case, thedirectional distribution's function is taken into account to generate the time histories. It isa consideration that the ship motions arise by each component wave distributing between±90 degrees around the average encounter wave angle. The function of COS2χ is appliedto the directional distribution.
The tank motions at any points are able to calculate from the ship motions around thecenter of gravity in accordance with coordinate system. That is to say, the time historiesof tank motions in short-crested waves can be obtained by coupling the ship motion'stime histories of six degrees of freedom.
2.3 Liquid Motion Simulation
2.3.1 Outline of Simulation Method
Liquid motions in the tank were simulated numerically by three-dimensionalsimulation program called “3D-Slosh” developed by Hitachi Zosen [6]. This program isbased on the MAC method and has following characteristics.
1) Fluid is assumed to be incompressible and inviscid.2) The governing equations are derived in a tank wall fitted coordinate system to
include the effects of inclined tank walls.3) Tank motions of six degree of freedom can be taken into account.
6.4–10
2.3.2 Estimation of Maximum Impact Pressure
Because of the time consuming property of liquid motion simulation, time histories ofship motion to simulate tank motion should be chosen carefully to reduce numericalsimulation time. In order to predict the maximum impact pressure at the tank top withpractical level of simulation time, assumption is introduced that maximum impactpressure occurs at the time near the acceleration of the tank takes maximum valuebecause acceleration of the tank motion mainly governs liquid motion. To determinewhen the acceleration of the tank motion at the center of the tank takes maximum value,an equation (2.4) similar to index Fσ introduced in section 2.2 are applied at the center ofthe tank on each time step and maximum value of it is searched,
Ft = (u + lz θ)2 + (v - lz φ + lx ψ) 2 + (w - lx θ)2 (2.4)
whereu, v, w: acceleration of surge, sway and heave motionφ, θ, ψ: angular acceleration of roll, pitch and yaw motion,lx, lz : longitudinal and vertical distance from center of gravitation of a ship to center of
the tankIf maximum of Ft value is found, input data of time history of ship motion is
determined as follows.
1) Compute time history of tank motion from ship motion data.2) Calculate value of function Ft defined in equation (2.2) at the center of the tank
and search the time t=Tmax when Ft takes maximum value.3) Pick up time range Tmax-30TW < t < Tmax+10TW from time history of tank
motion, where TW is mean wave period of incident waves.
2.3.3 Simulation Cases
Liquid motion simulation were perfomed at No.1 tank of both 175,000m3 type and135,000m3 type LNG carrier. Tank profile and cell arrangements for present calculationis shown in Figure 2.5 for 175,000m3 type and Figure 2.6 for 135,000m3 type. Twelvepoints to pick up pressure (5 points in fore part of the tank and 7 in aft part respectively)were chosen in present simulation and they are marked at the tank top in both Figure.Header TA and TF denote aft and fore part of the tank respectively. Number of cell usedfor both tank are shown in Table 2.1. Figure 2.7 denotes natural period of the tank withliquid motion in the tank for various filling ratio in surge and sway motion modes. It isobserved that natural period of 175,000m3 type is a little longer than that of 135,000m3
type in each mode. In this simulation case, filling ratio 94%, natural period for each tankare shown in Table 2.2.
Simulation conditions are shown in Table 2.3. Mean wave periods were determinedby following the procedure described in 2.2.
Table 2.1 Number of Cells for Liquid Motion Simulation
175,000m3 i•j • k=18 •22•15=5,940
135,000m3 i•j•k=16•20•15=4,800
6.4–11
Table 2.2 Natural Period of Each Tank (94% filling ratio)
Resonance Period [sec.]Mode of motion175,000m3 135,000m3
Surge 6.98 6.51Sway 7.54 7.14
Table 2.3 Wave Conditions for Liquid Motion Simulation
MeanWave Height
(m)
Mean WavePeriod Tw
(sec.)
Incident WaveAngle(deg.)
Case-1 9.0 135.0
Case-2 9.0 180.0
Case-3 7.0 135.0
Case-4
10.0
5.5 135.0
Figure 2.5 Tank Configuration and Cell Arrangement of175,000m3 Type LNG Carrier
42.6858.183
28.7
458.
783
6.40
3
6.193
24.3258.183
8.78
36.
403
28.7
45
6.19337.245
26.3
19
7.95
9
TA11
TA21
TA31
TA21'TA11' TA12'
TA12
TF11
TF21
TF11'
TF12
TF12'
6.4–12
Figure 2.6 Tank Configuration and Cell Arrangement of135,000m3 Type LNG Carrier
Figure 2.7 Natural Period of Each Tank for Various Filling Ratios
2.3.4 Results and Discussions
Time histories of ship motion in Case-1 are shown in Figure 3.8 for 175,000m3 typeLNG carrier and Figure 3.9 for 135,000m3 type . From these figures, it is observed that:
38.7758.635
28.2
158.
635
6.27
0
6.270
22.4408.635
8.63
56.
270
28.2
15
6.270
5.17
0
32.670
21.5
05
TA11TA12
TA31
TA21'
TA11'TA12'
TA21TF11
TF21
TF11'TF12'
TF12
4 6 8 10 12 140
0.2
0.4
0.6
0.8
1
Natural Period of tank [second]
Filli
ng R
atio
Surge mode 175,000m3
135,000m3
Sway mode 175,000m3
135,000m3
6.4–13
(1) Sway and pitch motion of 135,000m3 type is larger that of than 175,000m3 type.
(2) Roll motion of 175,000m3 type is larger than 135,000 m3 typeSimilar properties of ship motions are observed in other simulation cases.
It is expected that impact pressure at the fore end of the tank of 135,000m3 typebecomes large because pitch motion of ship affects on the liquid motion in longitudinaldirection and fore end breadth of the tank of 135,000m3 type is narrower than that of175,000m3 type.
Comparison of maximum impact pressure obtained by the liquid motion simulationfor Case-1, 2, 3 and 4 is shown in Figures 2.10, 2.11, 2.12 and 2.13. For the Case-1, 2 and3, maximum impact pressure at the aft part of the tank of 175,000m3 type is almost sameor a little smaller than that of 135,000m3 type, but as is expected above, maximum impactpressure of 135,000m3 type is much larger at the fore part.
On the contrary, for the Case-4, maximum impact pressure of 175,000m3 type ismuch larger than that of 135,000m3 type. As is seen in Figure 2.13, pressure values at aftpart are large compared with these at fore part for 175,000m3 type. The reason can beexplained that roll motion dominantly affects liquid motion severeness in aft part of thetank for trapezoidal configuration like under consideration. However, as the Sea Stateconsidered in Case-4 is actually very severe to encounter for ships in consideration of therelationship regarding wave height and period, maximum value of maximum impactpressure in this case must be smaller than that of other cases. This is explained by thereason that the ship motions in this case are small as compared with that in wave period,which is resonant with ship natural period.
Maximum impact pressure on the tank top for Case-1 are shown in Table 3.4 and plotof these value on the tank top is shown in Figure 2.14. In this figure, differences of thepressure distribution between two ships are clearly seen. Maximum pressure values areevenly distributed on the whole part of the tank top for 175, 000m3 type, but largepressure value concentrates at the fore part of the tank for 135,000m3 type.
6.4–14
Figure 2.8 Time Histories of Motions of 175,000m3 Type LNG Carrierin Waves (Case-1)
Figure 2.9 Time Histories of Motions Of 135,000m3 Type LNG Carrierin Waves (Case-1)
0 3 6-303
time [min.]Sway
[m
] Sway Motions
0 3 6-303
time [min.]Rol
l [de
g.] Roll Motions
0 3 6-303
time [min.]Pitc
h [d
eg.] Pitch Motions
0 3 6-303
time [min.]Surg
e [m
] Surge Motions
0 3 6-303
time [min.]Sway
[m
] Sway Motions
0 3 6-303
time [min.]Rol
l [de
g.] Roll Motions
0 3 6-303
time [min.]Pitc
h [d
eg.] Pitch Motions
0 3 6-303
time [min.]Surg
e [m
] Surge Motions
6.4–15
0
0.5
1
1.5
2
2.5
3
3.5
4
TA11
TA12
TA13
TA21'
TA11'
TA12
TA12'
TF12
TF12'
TF11
TF21
TF11'
Maximum Impact Pressure [kgf/cm2]
175,000
135,000
0
0.5
1
1.5
2
2.5
3
3.5
4
TA11
TA12
TA13
TA21'
TA11'
TA12
TA12'
TF12
TF12'
TF11
TF21
TF11'
Maximum Impact Pressure [kgf/cm2]
175,000
135,000
Figure 2.10 Comparison of Maximum Impact Pressure (Case-1)
Figure 2.11 Comparison of Maximum Impact Pressure (Case-2)
Figure 2.12 Comparison of Maximum Impact Ppressure (Case-3)
0
0.5
1
1.5
2
2.5
3
3.5
4
TA11
TA12
TA13
TA21'
TA11'
TA12
TA12'
TF12
TF12'
TF11
TF21
TF11'
Maximum Impact Pressure [kgf/cm2]
175,000
135,000
6.4–16
Figure 2.13 Comparison of Maximum Impact Pressure (Case-4)
Table 2.4 Maximum Impact Pressure (Case-1)
Maximum Impact Pressure(Kgf/cm2)
175,000m3 135,000m3
TA11 0.922 1.511TA12 0.836 1.082TA13 0.092 0.092TA21' 1.124 0.532TA11' 1.516 0.793TA12 1.249 0.971TA12' 1.330 0.768TF12 0.936 2.567TF12' 1.758 2.136TF11 1.547 1.667TF21 1.139 2.817TF11' 1.319 1.312
Time history of impact pressure at pressure picked up point in Case-1 is shown inFigure 2.15 for 175,000m3 type and in Figure 2.16 for 135,000m3 type. Pressure pickedup points (TA12’ for 175,000m3 type and TF12 for 135,000m3 type) is selected becausemaximum value of maximum impact pressure occur at these two points in Case-1.Difference of liquid impact phenomena between two tanks is clearly shown in thesefigures; Occurrence of liquid impact at tank top is limited in short time range for175,000m3 type. On the contrary impact phenomena occurs frequently for 135,000m3
type.
0
0.5
1
1.5
2
2.5
3
3.5
4
TA11
TA12
TA13
TA21'
TA11'
TA12
TA12'
TF12
TF12'
TF11
TF21
TF11'
Maximum Impact Pressure [kgf/cm2]
175,000
135,000
6.4–17
Figure 2.14 Comparison Of Maximum Impact Pressure (Case-1)
Figure 2.15 Typical Time History Of Impact Pressure of 175,000m3 TypeLNG Carrier (Case-1)
2
1
Unit : kgf/cm2175,000 m3 type 135,000 m3 type
0 3 60123
time [min.]
P [k
gf/
cm
2]
TF12'
0 3 60123
time [min.]
P [k
gf/
cm
2]
TF12
Figure 2.16 Typical Time History of Impact Pressure of 135,000m3 TypeLNG Carrier (Case-1)
6.4–18
Figure 2.17 Relationship Between Pressures and Wave Periods
Figure 2.17 shows the relationship between impact pressures of tank top and waveperiods. It is found from this figure that the maximum impact pressure at tank top is largewhen wave period is 9 second, which is nearly corresponds to natural period of ships. Onthe other side, the pressure for wave period 5.5 second which is nearly resonant withliquid motion in the tank is a little smaller than that of 9 second.
The estimated maximum wave height in the sea of which mean wave period is 5.5second is about 4.1m. 10m wave height applied in this calculation is very severe in termsof tank liquid motion analysis. Therefore the impact pressure in Figure 2.17 for the waveperiod of 5.5 second is to be taken with some discount.
4. CONCLUSIONS
Liquid motion simulation in No.1 Tank for two different types of LNG carrier inirregular sea were performed and following results are obtained.
(1) Simulation procedure to compute liquid motion and resultant impact pressure in realsea is established and evaluation of impact pressure in some Sea State is carried out.
(2) For the trapezoidal tank situated fore part of the ship, pitch motion of a ship governsimpact pressure at the fore end of the tank, and roll motion rules it at the aft end.
(3) To decrease maximum of maximum impact pressure, making ship size larger seems tobe effective.
In a regular motion , when a tank oscillates in its natural period, the liquid in the tankmovement gradually grows and violently moves within several number of oscillationeven under small oscillating amplitude . But in this study, we found that the impactpressures calculated at 5.5second irregular condition (natural period of the tank) arecomparatively small comparing to those at other mean wave periods and seemingly theyare mainly governed by the magnitude of ship motion.
We hope such study to compare the actual damage data or actual ship measurementwith such numerical simulation software would be made many other researchers andcould find clear understandings on this matter.
M ean of M axim um Im pact Pressure
0
0.5
1
1.5
2
9 7 5.5
W ave period [sec.]
Impact Pressure [kgf/cm2]
175,000m 3
135,000m 3
6.4–19
REFERENCES CITED
[1] M. Kawashima, T. Jono, et al: Up-sizing of LNG Carrier, LNG11
[2] T. Jono: Larger Capacity Membrane Ships, LNG Journal, Jan/Feb 1997
[3] T. Tanaka, S. Endo, S. Isozaki, T. Kobayashi, T. Imamura and M. Saito : Estimationof Impact Pressure and Hydrodynamic Force due to Sloshing in LNG carrier,NIPPON KOKAN TECHNICAL REPORT, Overseas No.42 (1984)
[4] SR125 : Study for Seakeeping Performance of High Speed Container Carrier(Japanese), Report of Shipbuilding Research Association of Japan(SR), 1975
[5] St. Dennis, M., and W.J.Pierson : On the Motions of Ships in Confused Seas,TSNAME, vol.61, 1953
[6] M. Nagahama, S. Nagahama, Y. Nekado, T. Yamamori and T. Hori : A 3-Dimensional Analysis of Sloshing by means of Tank Wall Fitted Coordinate System,Journal of the Society of Naval Architects of Japan, Vol.172 (1992).