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INNOVATIVE TOOLS OPEN UP NEW PROSPECTS FORLIQUID MOTION MODEL TESTS
THOMAS GAVORY
GAZTRANSPORT &TECHNIGAZ
THOMAS GAVORY graduated from the "Institut des Sciences del'Ingnieur de Toulon et du Var" in Marine Engineering and NavalHydrodynamics. After working on sea-state prediction in the "Bureau ofMeteorology" of Melbourne (Australia) and on ship stabilization bymeans of anti-rolling tanks in ACHE (Engineering office of Le HavreShipyard), he joined Gaztransport & Technigaz in 2002 where he hasbeen involved in liquid motion analysis and determination of sloshingloads on membrane-type insulation systems.
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INTRODUCTION
Membrane type Liquid Natural Gas carriers have been sailing for nearly 40 years, and the 120,000m 3ships of the early days are witnessing now the appearance of membrane LNG carriers with bigger andbigger capacities.
The "Pythagore", the first LNG carrier with tanks fitted inside the double hull and a membrane typeinsulation system, was built in 1964 and since then, the number of vessels of this kind has increasedsignificantly up to the present days. At the moment, more than 50% of the world fleet is Gaztransport& Technigaz (GTT) membrane type LNG carriers. Furthermore, more than 80% of the ships ordered in2004 are designed with GTT membrane type insulation systems.
As the number of innovative projects or designs goes up every year, the typical geometry ofmembrane tanks, due to their fitting in the double hull of the carrier, have put the liquid motionanalyses in the forefront. Alternative propulsion allowing more space to be dedicated to cargotransportation within the same hull, LNG ship projects with capacities of 215,000m3 and even more,the development of offshore LNG units, all these innovations lead to tank volumes sometimes close to50,000m3. As a consequence the LNG behaviour inside the tanks during a ship journey or in case of
offshore loading/unloading has to be assessed with care, and its consequences on the insulationsystem, if any, must be defined and understood as well as possible.
Usually, liquid motion is studied thanks to high technical tools, including Computational FluidDynamics(CFD) codes and small scale model tests. Unfortunately, liquid impact on a non-rigid wall(which is typically the case for an insulation panel, and even more for the several layers of insulationpanels and the various materials which constitute the membrane insulation systems) cannot yet beapprehended by way of numerical simulations, considering the huge size of the geometries to model(usual dimensions for LNG tanks are more than 50m in length, more than 40m in breadth andapproximately 30 meters in height) and the very small-size phenomena which would have to besimulated (entrapped gas, compressibility of the fluids, dynamic response of the insulation panels).During an impact, there is formation of bubbles, and this gas-liquid mixture is highly difficult tosimulate accurately enough to get sound results as far as the impact pressures are concerned. The
best way so far to obtain a good estimate of the impact pressures due to liquid motions still remainsthe model testing, but it is confronted with some strong issues, the major one being that noextrapolation law exists at the moment to scale model test impact pressures with water to full scaleimpact pressures with LNG.
Another of the main aspects of the liquid motion analyses is the feasibility study of partial fillingsinside membrane tanks. For filling ratios between 10%H (where H is the tank height) andapproximately 40%H, specific motions of the ship at some given frequencies can lead to the formationof progressive waves travelling from one side of the tank to the other, either in the longitudinal or inthe transverse direction, and sometimes breaking on the bulkheads. This phenomenon is quitedifferent from what appears at filling levels higher than 50%H where the liquid behaviour is the one ofa standing wave, with a smoother free surface and less chaotic motions, and its comprehension mayrequire a different approach than the ones that are usually taken.
An improvement of the tools that are used for the liquid motion studies, and especially for the modeltests, then becomes necessary to tackle all these fields of investigation and gain a betterunderstanding of the physics of the impact. The following paper will list first the tools which wereavailable up to now with their advantages and drawbacks, next it will detail the improved orinnovative tools which are used at GTT laboratory in order to overcome these obstacles and finallypresent some of the future prospects which are envisaged thanks to these tools.
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1. EXISTING ANALYSIS TOOLS AND THEIR LIMITATIONS
The main objective of the liquid motion studies is to produce evidence that the containment systemwill withstand the impact pressures caused by the liquid behaviour inside the tanks, or to advocatereinforcements of the insulation systems if needed. This was the case for example during the partialfilling study on a standard 138,000m3 LNG carrier, study that led to approval from one of the major
classification societies on the condition that reinforced GTT NO96 boxes were installed everywhereexcepted on the floor area of the tanks. Anyway these previous studies rested on a comparativeapproach between some well studied reference ships and the new projects to be studied, because noexisting scaling law is unanimously acknowledged as being valid for the very specific case of impactpressures due to sloshing.
1.1. Numerical simulations and model tests: two different tools for the sametarget
GTT uses two different methods to estimate the loads inside LNG tanks, which up to now haveworked in parallel, each with their respective advantages and drawbacks, but which could complementeach other in the future just by improving some of their weaknesses.
On the one hand, the numerical simulations are performed using DIVA3D software [ref 5]. This code
was developed by Principia Marine(ex IRCN) and CSSI, a French Software company. It simulates theliquid motions in partially filled moving tanks. Two viscous phases (liquid & gas) are taken intoaccount within the tank. The liquid phase is incompressible, while the gaseous phase is slightlycompressible and follows the equation of state p = g c
2, where p is the pressure, g the gas densityand c the speed of sound in the gas. It is assumed that there is no thermal phenomenon. ThereforeDIVA3D solves the Navier-Stokes equations (mass and momentum conservation) for both phases anda free surface equation derived from the rule of mixture and the Volume of Fluid (V.O.F.) technique.Different friction laws are available as boundary conditions on the bulkheads. Any six-degree-of-freedom motions can be imposed to the tank.
DIVA3D simulations are performed with aparallelepipedic meshing type, the origin ofwhich is the point where the ship motions have
been calculated (centre of gravity of the ship)by a 3D BEM sea-keeping code. A typical meshsize for a standard tank is approximately50,000 cells, with possibility to refine at thelocations where the impacts are more likely tooccur.
DIVA3D calculates a pressure in each cell ofthe meshing thanks to the momentumconservation equation. Actually this pressuredoes not deal with the impact pressure. Incase of quasi flat impacts, the impact pressureis strongly connected to both liquid and gas
compressibility and hydro-elasticity effects.None of these effects are taken into account byDIVA3D. Even if it were the case, the impactpressure peak is related to pressure wavepropagation through the fluid and stress wave
propagation through the containment system. Such phenomena could be numerically simulated byexplicit finite element software for instance but with much more refined meshing and much morerefined time step than those usually used by DIVA3D. Actually the state of the art allows simulatingfluid / structure quasi flat impacts only for ideal conditions: flat free surface and no gas entrapped.
Figure 1 : Diva 3D simulation of a 138,000m3 class
LNG carrier tank n2
For all these reasons it is preferred to quantify a liquid impact as simulated by DIVA3D only by theimpact velocity Vimp, which is totally intrinsic to the liquid motions.
In the worst conditions (flat impact without gas), the related impulsive pressure is givenby
impimp VCkP = , as explained in 1.1. The duration of such a pressure peak is lower than 1
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ms. As we dont know accurately the k characteristic, there is no relationship available to correlate thefluid velocity before the impact and the resulting impact pressure. Therefore, it is at the moment notpossible to calculate numerically the impact pressures due to liquid motions.
On the other hand, the model tests allow therecording of the impact pressures and loads
due to liquid motions, usually thanks toseveral small size pressure sensors (from 2mmdiameter to 8mm diameter) and force panels.The sampling rate has to be high enough toallow a correct recording of the whole impactpressure characteristics (pressure pulse,duration, rise time and decay time). Withpeak durations of the order of 10-4s, asampling rate at least equal to 20 kHz isrequired, which leads to a huge amount of
data to post-process during a test campaign.These data can then be classified according tothe pulse characteristics and statisticallyanalysed in order to define a statistical impactpressure with a given probability of occurrence, used as the design pressure for the study.
Figure 2: Model scale LNG tank with pressure
sensors locations
However, this kind of measurement does not give any sound information on the liquid flow and thevelocities before and during the impact. High-speed video recordings can be used, but they are limitedin picture size and they provide more qualitative than quantitative values. Model tests have otherlimitations, two of the major ones being the limited number of degrees of freedom available for thetesting and the scale of the model tank. Model tests are usually performed with neglecting heave andyaw motions because of the test rigs configurations, and the bigger the scale, the more restrictive therig limitations will be. It is then most difficult to simulate realistic motions of the tank, even more sowhen increasing the scale.
However, with small scale model tests, the main issue remains the extrapolation of the results (the
impact pressures) at full scale. As mentioned before, actually no scaling law is appropriate for thesloshing impact pressures, because of its specificities which make it quite different from the closesthydrodynamics topics (slamming impact, green water impact).
1.2. "Strong and weak points" of available scaling laws
It is not our purpose here to present a theoretical scaling law which could be applicable and to claimonce and for all that the other ones cannot and could never be used, but more likely to present theexisting scaling laws which are used in the closest naval or structural applications and look at theirtheoretical drawbacks.
Hydrodynamics model tests are usually performed according to Froudes scaling law. The motions ofthe free surface of the liquid are governed by the gravity wave behaviour and, as such, are wellapproximated by incompressible fluid equations. Froudes law ensures that the correct relationship is
maintained between inertial and gravitational forces, where the inertial force is:
aVFI = (1)
With
onacceleratifluida
volumefluidV
densityfluid
=
=
=
And the gravitational force is:
VgFG
= (2)
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Acceleration exists whenever there is a change in flow direction or normal acceleration i.e. rv2
, a
change in magnitude or tangential acceleration i.e. dtdv or turbulence fluctuations in velocity.
Density is the significant fluid property for inertial force. Surface flows, shape and depth areinfluenced by gravity.
The inertial force can be expressed as follows:
[ ] [ ] [ ][ ][ ]
[ ][ ][ ]
[ ] [ ] [ ] [ ]223
vLF
v
Lt
t
vLF
I
I
=
=
=
(3)
The Froude number is then defined by:
[ ][ ] Lg
v
Lg
vL
F
FFrnumberFroude
G
I
=
==3
22
(4)
Froudes law requires the Froude number to be the same at model and full scales. Geometrical scalingis normally employed throughout, in order to ensure that correct Froude number scaling is applied toall components of the structure. This means that all lengths involved in a particular model test arescaled by the same factor. The pressures can also be predicted this way as long as no impact occurs.By assuming that Froude scale applies for the impact pressures, the compressibility of the liquid is nottaken into account and the pressure is defined as follows:
[ ] [ ] [ ]2vP = (5)
Assuming that the Froude number is constant, the scaling factor of the recorded pressures is then:
m
mm
pp
p P
L
LP
=
(6)
Where Pp is the pressure at full scale (prototype) and Pm is the pressure at model scale.
When the liquid impacts the wall or ceiling of the tank, air entrapment and compressibility may alsoeffect the very short-duration acoustic shock pulse which is often recorded during sloshing modeltests, and is also sometimes seen in wave slamming or green water impact experiments. This pulse isusually, for these last two cases, of too short a duration to have any structural significance for thedesign. Nevertheless, in case of liquid impact inside LNG tanks, the containment system cannot beconsidered as a rigid wall, and its dynamic response makes it impossible to neglect this short durationpulse beforehand.
ms
97.5 100.0 102.5 105.0 107.5 110.0
ms47.5 50.0 52.5 55.0 57.5 60.0 62.5 65.0 67.5 70.0 72.5 75.0
1.25
1.00
0.75
0.50
0.25
0.00
-0.25
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
3. a 3. bDuration of the firstpulse: 0.65ms
Rising Time: 0.2ms
Pulse duration: 0.3msDuration of thepressure tail: 5ms
Figure 3: Examples of impact pressures recorded at 1/50
th
scale with water and air
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These very short duration pressures (see figure 3.a) are governed at least partly by impact velocityand compressibility of the liquid, the ullage gas and the tank wall dynamic response, so that theincompressible assumption doesn't hold when predicting pressures.
The initial conditions for the impact are the liquid velocity and shape of the free surface, which arecontrolled by the incompressible liquid behaviour on a time scale of seconds. Thus, the impact
pressure is influenced by both the compressible and incompressible aspects of the liquid behaviour. Tothe extent that compressibility governs the pressure, Froude scaling is inapplicable. Since liquidcompressibility is altered significantly by even small quantities of entrapped gas or vapour within theliquid, it is necessary to establish a relationship between the effective liquid compressibility and theimpact pressures in any sloshing test. If the pressures are totally dominated by compressibility, amajor change in scaling law away from the Froude scaling would be required [references 1, 2, 3, 4].
Bass & al. [ref 2] stated that for correct impact pressure scaling when the liquid compressibility isconsidered, the impact pressure is proportional to the liquid density, the speed of sound inside thefluid and the liquid velocity before the impact:
impimp vCkP = (7)
Where k accounts for real effects such as surface characteristics and entrapped gas bubbles, and canbe a maximum of 1.0. This boundary case is known as acoustic pressure.
For lower fillings, other types of impact pressures can be observed, as shown in figure 3.b, and then itis highly probable that the scaling law to be applied is not the same as for high fillings. In thisparticular case, the impact pressure can be separated into two parts: the pressure pulse, very sharp,with high magnitude and short duration and the pressure tail, of longer duration but also much lowermagnitude. The first part could be driven by a "compressible" scaling law, proportional to vthe impactvelocity, whereas the second part could be more a hydrodynamic pressure, driven by the"incompressible" theory and then proportional to v2.
To sum up, the actual scaling law may indeed be a combination of these two laws, taking into accountboth incompressible and compressible effects. Nevertheless, due to the many physical parameterswhich are thought to have a strong influence on the impact pressure but which do not appear in the
scaling laws (compressibility of the cushioning entrapped gas which is affected by gas pressure andcomposition, compressibility of the liquid which includes bubbles and entrapped gas, thermodynamiceffects), an experimental approach rather than a theoretical one could be contemplated in order tofind empirical scaling law, using new tools and different ways of measurements.
The following paragraphs will present some of the innovative tools that have been used in GTTlaboratory for some months in order to improve our understanding of the sloshing phenomena andgather more and more confidence in both the numerical simulations and the model tests results. Thefirst of these innovative tools is definitely the six degree-of-freedom test rig, allowing an extremelyrealistic excitation of the considered tank and its study at different scales, from 1/70 th to up to 1/25thfor some designs. These scale changes are the first and necessary step for the definition of empiricalscaling laws applicable for each filling ratio and each type of sloshing impact.
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2. THE SIX DEGREE-OF-FREEDOM TEST RIG, A GREAT STEP TOWARDS THESIMULATION OF HIGHLY REALISTIC SHIP MOTIONS.
The usual testing rigs often neglect heave and yaw motions, mainly because they are based on a 2-dimentional horizontal platform holding up the model tank and allowing the motions (translations androtations) with respect to its two perpendicular axes X and Y. Permitting the two last degrees of
freedom with respect to the Z axis requires a much more complicated test rig with external devicedriving the whole 2-D horizontal platform along Z-axis and with large amplitudes.
Heave motion is indeed the translation motion which is subject to the largest amplitudes, as shown infigure 4 on the left. Whatever thewave incidence is, the heaveamplitude is up to three timeslarger than the other translationmotions. Furthermore, whenstudying a cargo tank located atthe fore from the ship centre ofgravity, second order heave andsurge, induced by the pitch
motion, can have a significantinfluence on the liquid behaviourinside the tank.
As an example, for a 220,000m3class LNG carrier with 5 tanks, thetank n1 centre of gravity islocated approximately 97m at thefore from the ship centre ofgravity. This means (see figure 5below) that for head seas, with a
pitch angle closed to 6 degrees, the induced heave amplitude at the centre of gravity of tank n1 willbe higher than 10m! Such high
values cannot be neglectedwithout being confronted withstrong uncertainties in theconclusions when trying toextrapolate the test results atfull scale.
Figure 4: Translation motions for a 138,000m3 LNG Carrier,
loading case = 70%H in all tanks, ship speed = 19.5knts, 40-year
return period wav envelop in North Atlantic conditions
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
Tz motion [s]
Surge180 Sway 180 Heave180Surge195 Sway 195 Heave195Surge210 Sway 210 Heave210Surge225 Sway 225 Heave225Surge240 Sway 240 Heave240Surge255 Sway 255 Heave255Surge270 Sway 270 Heave270
To force out these uncertainties,it has been necessary to moveaway from existingconfigurations and find outanother way of exciting themodel tank.
2.1. Presentation of the GTT hexapod test rig
Already used in the entertainment industry or as part of the flight simulators for example, thehexapods (which might be named Stewart platforms or parallel robots as well) are closed-loopmechanisms with a moving plate connected to the ground by 6 independent kinematic chains.
Parallel manipulators are most usually used in the industry for accurate positioning and orientation ofspecific instrumentation, such as mirrors or optical features. Contrary to serial manipulators whereeach stage adds one degree of freedom and the combined movement is transmitted to the objectbeing manipulated, parallel manipulators consist of one moving element with more than one degree offreedom that is simultaneously driven by several motorized actuators. An hexapod (parallel robot with
6 legs allowing 6 d.o.f. motions) is inherently stronger than a serial mechanism because the load isdistributed among all legs, but also because the legs are only subjected to axial loads. Similarly,parallel manipulators are more precise since they are more rigid, and since the errors in the legs are
Figure 5: Scheme of the induced heave motion at tank n1
centre of for a standard 138,000m3 LNG carrier
Second order heave inducedb itch motion
gravity
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averaged instead of buit up. Finally, these robots are faster since they usually have their heavy motorsmounted on the base. On the other hand, parallel-link robots have a more limited and complex-shaped workspace. Moreover, the rotation and position capabilities are highly coupled whichcomplicates their control and calibration. Furthermore, parallel mechanisms generally havetreacherous singularities within their workspace [references 6 and 7, figure 6].
1/20
1/25
1/30
1/40
1/501/60
1/70
Figure 6: Example of (X,Y) workspaces for an hexapod at two different Z positions
For the specific application of wave simulator, the main difficulties are to perform high amplitudemotions with strong velocities and accelerations, moving elements heavier than a couple of tons andtaking into account the liquid unbalance.
Figure 7 shows the dimensions and total weight at different model scales of a conventional 138,000m3
LNG carrier tank n2. For a model tank at 1/30th scale, the needed volume of water is approximately1.5m3, so the total weight of the system (tank + water + acquisition system) will be over 2 tons. Atthe same time, the maximum motion's amplitudes could be as high as 500mm in heave and themaximum motion's accelerations could be greater than 0.5g, also for heave motion.
0.0
1.0
0
3.0
4.0
5.0
0
Model scale
Liquidvolum
einsidemodeltank[m3]
6.
138,000m3 220,000m3
Scale 1/70 1/40 1/20 1/70 1/40 1/20
L [mm] 625 1093 2186 617 1079 2159
B [mm] 541 947.5 1895 631 1105 2210
H [mm] 382 669 1338 384 671.5 1343
Total Weight [t] 0.150 0.890 >6 0.175 1.016 >7
2.
Figure 7: Main dimensions and weight of model tanks at different scales
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The hexapod which was developed for our application in collaboration with the French engineeringcompany Symtriehad to take up these challenges, and its workspace has been extended to thefollowing limitations:
Degree offreedom
Associatedship motion
Maximum amplitudewith 2.4tons weight
Maximum velocity with2.4tons weight
Maximum accelerationwith 2.4tons weight
X Surge 750mm
Y Sway 750mm
Z Heave 600mm
>1.6m.s-1 1g
Rx Roll 45
Ry Pitch 20
Rz Yaw 40
>70.s-1 >120.s-2
Table 1: Limitations of the GTT hexapod
Its dynamic precision (0.5mm in translation and 0.1 in rotation) is real-time checked through anindependent second hexapod located inside the first one, and measuring the exact position of 6different locations on the moving platform during the test (see picture???). These positions are thencombined together to calculate the real motion of the origin point during the test, which is thencompared with the time history of the motion given as input to the rig. As a consequence, the modeltank is now believed to move in the most realistic way and accurately enough to neglect all thepossible errors due to the test rig.
2.2. First results on the heave and yaw influence on the impact pressures
A few tests have been performed with a 1/50th scaled tank n2 of a standard 138,000m3 LNG carrierat various filling levels and with random sea motions in order to look at the influence of the heave and
yaw motions on the liquid behaviour and sloshing impacts. The tests were performed with water andair at ambient conditions (P = 1atm, T = 20C). We present hereafter the results we obtained for30%H and 92.5%H filling ratios and the associated worst cases in terms of liquid impact, casesselected from a 35 critical case test campaign (175h tests at full scale). The main parameters of thesetwo worst cases are summarized in the table below:
Test Case Filling ratio [%H] Wave Heading [] Ship Speed [knots] Wave Hs [m] Wave Period [s]
28 30 75 14.3 13.58 9.0
20 92.5 0 5.0 9.01 8.0
Table 2: Two worst test cases used for the heave and yaw influence preliminary study
Sixteen (16) piezo-electric pressure sensors of type PCB Piezotronicswith 5.54mm diameter pressuresensitive area were fitted at the most probable location of the impacts and the high samplingfrequency (20 kHz per channel) allowed the recording of the very narrow pulse (order of 10 -1msduration) which could otherwise be missed by the data acquisition system. A total of 152 holes weremade in the Plexiglas tank in order to fit the pressure sensors. The time duration of the simulationwas 5 hours at full scale, and a statistical post-processing was performed on the results in order tocalculate the maximum expected impact pressure for each sensor with a 3-hour return period.
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-150.0
-100.0
-50.0
0.0
50.0
100.0
150.0
510 520 530 540 550 560 570 580 590
Time [s]
Motionamplitude
[mo
rdeg]
Surge
Sway
Heave
Roll
Pitch
Yaw
-150.0
-100.0
-50.0
0.0
50.0
100.0
150.0
510 520 530 540 550 560 570 580 590
Time [s]
Motionamplitude
[mo
rdeg]
Surge
Sway
Roll
Pitch
Figure 8: Time histories of the test case n28 motions at 1/50th scale, with and without heave and yaw motions
A comparison between the statistical impact pressures with 4 and 6 degrees of freedom are presentedin the two graphs below:
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
71 91 90 92 57 64 72 73 74 93 94 106 107 108 105sensors locations
statisticalpressure3hrs(bar)
Test 28 - 4 dof
Test 28 - 6 dof
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
1 14 23 2 4 3 5 6 20 9 10 21 24 25 146 147sensors locations
statisticalpressure3hrs(bar)
Test 20 - 4 dof
Test 20 - 6 dof
Figure 9: Impact pressures for test case at 30%H filling Figure 10: Impact pressures for test case at 92.5%H filling
From these results, two inverse trends can be observed, i.e. the heave and yaw motions seem toincrease the statistical impact pressures at low fillings (+64% between the maximum expectedpressures recorded on the two worst sensors) whereas the pressures are lower for high fillings whenadding the 2 missing degrees of freedom (-25% between the maximum expected pressures recordedon the two worst sensors). If we look at the mean of the maximum expected pressures over all thesensors, then the trend is +42% for low fillings and -16% for high fillings, which confirms that thetrend is quite uniform over the whole number of pressure sensors. This is well assessed by the figures9 and 10 where we can observe that 13 sensors out of 15 recorded an increase of the impactpressures for the test 28 (30%H filling), and in the same time 13 sensors out of 16 recorded a
decrease of the impact pressures for the test 20 (92.5%H filling).These significant differences between the statistical pressures for tests with or without heave andyaw, as well as the fact that the trend is the same for the majority of the sensors, seem todemonstrate that the heave and yaw motions cannot be neglected when performing model testswithout risking to find a significant error on the statistical pressures at model scale when drawing theconclusions of a study.
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3. PARTICLE IMAGE VELOCIMETRY, A NON-INTRUSIVE MEASUREMENT OF THEEXPERIMENTAL LIQUID VELOCITIES
We have seen that one of the main limitations of the existing model tests is that they only allow therecording of pressures or loads on the walls, without giving any quantitative information on the flowbehaviour or liquid velocity during the test. This "velocity vector map" would also be of great interest
for a more accurate validation of the numerical tools which are used currently for the sloshing studies.Indeed, the CFD codes are usually validated in terms of free surface elevation, but a validation of thevelocity vector field along the whole liquid depth is missing. In order to improve confidence in thenumerical tools, it becomes necessary to look at this kind of validation, and as a consequence tosucceed to measure the liquid velocity vectors inside a model tank subjected to a range of excitationsand with various fillings.
Another interesting way of investigation is the possible existing correlation between the liquidvelocities when the liquid reaches the walls and the resulting impact pressure. Impact pressure isdriven not only by the liquid velocity magnitude but also by its incidence during the impact, theamount of gas entrapped and of course the wall flexibility, among others. Measuring the liquidvelocities vectors as close to the wall as possible for different impact configurations could lead to thedefinition of empirical correlation laws between impact velocities and pressures. These correlation
laws could then be used in the numerical simulations at full scale with LNG and methane vapour inorder to estimate more accurately the full scale impact pressures which are likely to occur inside realtanks.
The Particle Image Velocimetry is a non-intrusive optical method for measuring the fluid velocities in aconsidered planar field. A laser planar light sheet ispulsed twice during 4 to 6ns for each pulse, and imagesof fine particles lying in the light sheet are recorded on avideo-camera. The displacement of the particles ismeasured in the plane of the image as follows: astatistical approach is used based on a division of theimage plane into small spots, then we cross-correlate theimages for both time exposures.
The spatial displacement that produces the maximumcross-correlation statistically approximates the averagedisplacement of the particles in the interrogation cell.
Velocity associated with each interrogation spot is just
the displacement divided by the time between the laserpulses (see figure 12 below). It is then fullyunderstandable that the smaller the interrogation cells,the better the velocity field accuracy.
Figure 11: scheme of the PIV
measurement principle
Figure 12: calculation of the velocity vector from the cross-correlation approach
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The feasibility tests were performed on a 3 degree-of-freedom test rig, allowing respectively thesurge, roll and pitch motions with the pitchaxis of rotation off-centred with respect tothe tank centre of gravity (see figure 13).The aim of this first campaign being thefeasibility study of such measurements for
our applications, we focused on "simple" 2-D motions in transverse direction. The laserplane went through the longitudinalbulkheads and chamfers and the video-camera was located in front of the foretransverse bulkhead (see figure 13).
The tested tank was tank n2 of a standard138,000m3 LNG carrier, the scale was 1/70thand the tested configuration was water andair at ambient conditions (P=1atm,T=20C).
Figure 13: Configuration of PIV feasibility tests at
GTT laboratory
Pitch axis of rotation
Camera
Laser
Different filling ratios were studied, corresponding to both upper and intermediate fillings (90%H and40%H), and many roll amplitudes and frequencies were performed. The same tests were reproducednumerically with our CFD code DIVA 3D in order to compare the results coming from both approachesand try to explain the possible differences. The DIVA3D simulations were performed using a 2Dmeshing of 6930 cells (respectively 99 in the Y direction and 60 in the Z direction, with refinement ofthe meshing around the lower chamfers and vertical longitudinal bulkheads) and minimum size of thecells was 3mm x 3mm.
Table 3: Comparison between DIVA 3D simulations (above) and PIV measurements (below)
The PIV measurements presented in the bottom of Table 3 were obtained by averaging a total of 100picture doublets taken at the same location on the sinusoidal roll excitation. The 100 vector mapswere post-processed using moving average validation in a 3x3 pixels2 area around each velocityvector in the plane, and then a 3x3 average filter was applied on the vector field. Due to theinstallation set-up and to the PIV limitations, it was not possible at that time to get the velocityvectors on the whole transverse plane, and that is why contrary to the numerical simulations, the tank
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boundaries do not coincide with the vector field. The initial window size is 1248x1024 pixels2 and itwas decided to proceed iteratively from a 128x128 pixels2 to a 32x32 pixels2 interrogation area usingadaptive correlation, which leads to a total number of cells of 1248 (39 in the Y direction and 32 in theZ direction), with constant size.
The colour map shows that the similarity between the two velocity vector fields in Z direction is good
from a magnitude point of view. On the other hand the coloured areas do not perfectly match, thisbeing mainly due to the difference in mesh size and refinement. The bigger cell size for the PIVvisualization as well as the filtering used during the post-processing leads generally to a largerdiffusion of the velocities. The free surface is also quite difficult to define through PIV method,because of the fact that the final vector field is obtained by averaging 100 vector field snapshotswhich do not perfectly superimpose on one another in practice, and also because of the method initself (the PIV correlation is very difficult to perform at the boundaries of the flow).
Anyway it seems that PIV is a valuable way of estimating the liquid velocities inside the tanks atmodel scale, and the preliminary results, although wanting because of the lack of experience andfeedback in this specific sphere, are very encouraging and they open up new prospects for the liquidmotion model tests. In particular, the analysis at model scale of the liquid flow around the tripod mastis one of the topics which are studied currently at GTT laboratory with PIV and it is thought to be
really helpful for a more accurate estimate of the hydrodynamics loads applied to this structure.
4. TIME AND SPATIAL DISTRIBUTION OF IMPACT PRESSURES: THE ADVANTAGE OFUSING REFINED PRESSURE SENSOR GRIDS.
The sloshing impact is a very specific phenomenon which main parameters are not only the impactpressure magnitude but also its duration and the area impacted. Impact pressures are usually verysharp, with pulse duration of the order of 10 -4 to 10-3s and they affect a lesser or larger area,depending on the impact location (ceiling for high fillings, vertical walls for partial fillings ).
In each case it is of high importance to know where and over which area does the impact occur, andwhat is its spatial and time evolution. Usingpressure sensor grids instead of single sensorsat the locations where the impacts are morelikely to occur can help looking at this spatialand time evolution. Depending on the type ofsensors which are used, the studied areacovered by the grid is variable. For example,pressure sensors type PCBof 5.54mm diametercan be put at a distance as small as 10mmbetween axes, so when putting such grids inside1/40th scale model tank we are able to measurethe pressure applying to a 2.4m x 2.4m areathrough 36 different sensors. Interpolating thepressures in space enables us to calculate the
pressure applying over every area between400mm x 400mm (area corresponding to 1pressure sensor) and the whole sensors array.The interpolation defines a pressure surfacefrom a uniform grid, always passing through the data points. The method used is a triangle-basedcubic interpolation, based on a Delaunay triangulation of the data. This method produces smoothsurfaces with continuity in both the first and second derivates.
Figure 14: 6x6 sensor's array and corresponding
5.54mm PCB pressure sensor
The signals presented in figure 15 show pressure time histories of an impact recorded on a corner ofthe ceiling for a 138,000m3 LNG carrier tank n2, with 92.5%H filling ratio. The sampling frequencywas 20 kHz, and the duration of the presented recording is nearly 10ms.
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Figure 15: example of the pressure signal recorded during 10ms around a sloshing impact on a 6x6
sensors grid
From these 36 pressure signals, it is possible to interpolate at each time step a pressure surface overthe whole grid in order to look at the spatial distribution of the pressure during the impact.
Table 4 below shows 6 different pressure maps from the 200 which were extrapolated from the 10mstime histories of 25 pressure sensors (5 first rows x 5 first columns from the grid). The sensor gridwas located on a corner of the ceiling, and the tank vertical wall's location is the 0 coordinates alongboth longitudinal and transverse axes.
-3-3
Table 4: Time history of the corresponding integrated pressure pulse at model scale
We can see from table 4 visualizations that the recorded pressure on a given sensor has a very good
agreement with its neighbours; there is no strong discontinuity between two sensor's recordings atthe same time step, which explains why the pressure surface maps are so smooth. We mustremember here that the interpolated surface is passing through each data point, so the magnitudes
t = 0.00 x 10 s t = 0.10 x 10-3 t = 0.20 x 10 ss
-3t = 0.25 x 10 s t = 0.35 x 10
-3 -3s t = 0.40 x 10 s
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plotted at each node are the actual measurements from the model tests. The conclusion is that thesensors network is sufficiently dense to allow such an interpolation with a good accuracy.
In this example the impact affects a very small surface (10x10mm at the maximum at model scale)located on the very corner of the ceiling. Pressure sensors located a little further from the corner(more than 10mm in both directions) do not even notice the liquid impact. Another interesting point is
that the impact is moving along the walls, appearing at the junction between the ceiling and theupper chamfer and fading away at the junction between the ceiling and the transverse bulkhead.
Then, the mean pressure time histories on different sizes of loaded surfaces can be estimated directlyfrom this interpolated pressure surface history. For each zone representative of a given area, themean pressure is integrated from the interpolated surface defined above at each time step for eachevent. Once these pressure pulses have been calculated for each area, then a statistical analysis isperformed on the obtained sample, and by fitting a suitable distribution law (most usually a 3-parameter Log-Normal or 3-parameter Weibull law) to the sample we can calculate the extremeimpact pressure with a given return period for this area.
Figure 16: spatial repartition of the 3 hour statistical mean-pressure for the
loaded area 5x5 mm at model scale.
Figure 16 above shows the maximum expected impact pressure with a 3-hour return period over a5x5mm area. For this, we defined a 5x5mm square zone which we staggered by 2.5mm offsets inboth directions, in order to cover the 25x25mm array. The total number of integrated zones is 81 andthe figure 16 pressure surface is interpolated over these 81 points.
The red lines on the above figure represent the boundaries of the dihedron and trihedron areas,
whatever the type of insulation is.One can immediately notice that the load is higher in the corner than on the edges and on the edgesthan on the standard part of the insulation. As the insulation structure is not the same in the corner(trihedron) and on the edges (dihedron), it is interesting to sort the maximum load on the dihedronand trihedron areas, on the one hand, from the maximum load on the standard isolation, on the otherhand.
This post-processing gives us a curve representing the "impact load versus area" for the consideredlocation within the tank. It becomes then possible to compare it to a "resistance to static strengthversus area" curve for the insulation system which is studied. Figure 17 below shows such curves for aNO96 system (primary and secondary boxes) located on the junction between the ceiling and thetransverse bulkhead of a 138,000m3 LNG carrier tank n2.
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000 1.125 1.250
Area (m2)A
dim
entionednumber
Insulation strength
sloshing load
Figure 17: Comparison of the measured sloshing loads and calculated insulation resistance
versus area for NO96 insulation system
Figure 17 shows that the smaller the area over which the pressure is recorded, the higher thepressure. This indicates that the impacts are highly localized and that the maximum pressures arerecorded close to the vertical bulkhead. In the same time, due to special arrangement of theinsulation in these specific zones (dihedron or trihedron area), the insulation system resistance
increases largely, so that the ratio between the loads and the resistance is even smaller than for abigger area.
Such "impact loads versus area" curves can even be improved by taking into account the impactprofile and peak time duration. Classifying the peaks by their time duration or profile would improvethe statistics, making the samples become more homogeneous. It is also possible that theextrapolation laws were not the same for different pressure pulse time durations, because of thedifferent physical phenomena involved and the varying influence of the compressibility.
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5. CONCLUSION
The development of innovative tools like the hexapod or the utilisation of alternate measuringmethods like PIV or pressure grids during liquid motion model tests let us foresee a betterunderstanding of the physics of sloshing as well as more and more accuracy and confidence in themodel tests and numerical simulations results.
The in-depth validation of our CFD software is the major positive use of PIV measurements inthe short or medium term. The validation of the whole velocity vector field will be a strongimprovement compared to the free surface behaviour validation which is the common way ofvalidating existing CFD sloshing softwares.
Furthermore, the use in parallel of PIV measurements and pressure grids is expected to leadto the finding of empirical correlation laws between impact velocities and impact pressures for a wholerange of impact configurations and filling ratios. Once this correlation is defined at model scale, thecalculation through CFD simulations of impact velocities at full scale with LNG and methane could leadto a rather precise estimate of the impact pressures that are more likely to occur inside a real tankduring a ship journey.
Figure 18: Possible process for the estimation of empirical correlation law between impact velocities and
impact pressures
The appearance of giant-size LNG carriers on the market and the increasing demand for offshore LNG
terminals (Floating Production and Storage Offshore units or Floating Storage and RegasificationUnits) for which the membrane systems have a lot of advantages (high flexibility in tanks design andbuilding schedule, maximization of cargo and deck area for topside) make it necessary to use hightech, more reliable tools.
More than just improvements of the GTT former testing tools, the six degree-of-freedom test rig, theParticle Image Velocimetry measurements and the recording of impact pressure map-makings with ahigh time resolution constitute a big but necessary step forward for the global understanding of thesloshing phenomenon and its interaction with the membrane-type insulation systems.
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REFERENCES
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