ATMA 2012

SLOSHING LOADS DETERMINATION APPLICATION TO FLOATING GAS STORAGE

AND LIQUEFACTION UNITS (FLNG, FSRU)

Louis DIEBOLD, Nicolas MOIROD

Thomas GAZZOLA, Eric BAUDIN Bureau Veritas – Research Department – Neuilly-Sur-Seine (France)

(Presented at the ATMA 110th session - Translated from French by Michel HUTHER)

SOMMAIRE

De nombreux projets d’unités flottantes d’opération et de liquéfaction de gaz (FLNG, FSRU, LNG FPSO) sont actuellement dans leur phase finale de développement à l’image du SHELL-FLNG qui constituera la plus grande unité flottante jamais construite. Ces unités flottantes (FLNG, FSRU…) devront pouvoir opérer à tout remplissage contrairement aux méthaniers classiques pour lesquels seuls les remplissages bas et hauts sont autorisés en navigation. En particulier, les parois des cuves de ces unités devront pouvoir résister aux fortes pressions de sloshing associées aux remplissages partiels. Ce mémoire présente tout d’abord les différents paramètres influençant le phénomène de sloshing. Ensuite est présentée la méthodologie utilisée par le Bureau Veritas (BV) permettant de quantifier les chargements dus au sloshing (ballottement du gaz liquéfié dans les cuves) afin de pouvoir échantillonner les cuves de ces unités flottantes en conséquence. Chaque étape de cette méthodologie fait l’objet de recherches au BV et sera illustrée par des validations reposant sur des comparaisons entre calculs et expériences.

SUMMARY

Nowadays, the offshore LNG (Liquefied Natural Gas) terminals (FLNG, FSRU, LNG FPSO) have become a reality, and the initial feasibility studies evolved to the actual project achievements like the SHELL-FLNG which will hold the title of the world’s largest floating object ever constructed. These floating LNG terminals (FLNG, FSRU…) shall operate at all filling levels unlike standard LNGC which operate only at low or high filling levels during navigation. Especially, tanks’ walls shall withstand the possible high sloshing pressures caused by violent LNG flows at low partial fillings. First, this paper will present the different parameters that influence sloshing phenomenon. Then Bureau Veritas sloshing assessment which enables to determine sloshing loads in order to evaluate the hull scantling will be presented. Each step of this methodology will be illustrated with some validations relying on comparisons between calculations and experiments.

1. INTRODUCTION

1.1. Liquefied Natural Gas transportation (LNG)

In this paper we shall only consider the Liquefied Natural Gas (LNG) mainly composed of methane. The LNG transportation can be done either by underground pipelines or by sea by methane carriers.

The transportation by pipeline is costly as it requires compression stations installed all along the way. Crossing oceans and large seas can so only be done by specialised ships called methane carriers or LNGC (Liquefied Natural Gas Carriers). The LNG is carried inside these methane carriers at liquid phase at very low temperature (-162°C) which allows a density 600 times greater than at gas phase. The capacity of the methane carriers varies from 130,000 m3 to 260,000 m3.

Today it exists 3 types of methane carriers, each of them corresponding to a different tank building technique: membrane, spherical and IHI prismatic LNG ships. This paper only considers LNG carriers and floating gas terminals with membrane technology. As illustrated by figure 1, the membrane technology is from afar the largest applied technique both for existing and under order LNG ships (1st October 2011).

Fig. 1 : Membrane LNG ships (blue): 68% of in-service ships (left), 95% of ships

in order (right)

1.2. LNG operation and liquefaction floating units

Based on a very good return experience of the navigating LNG ships (no major incident during 50 years), floating LNG terminal projects have appeared in the 2000s and are

actually in their final development phase. Two types of floating terminals are existing: the storage and regasification floating units such as FSRU (Floating Storage and Regasification Unit) or LNGRV (Liquefied Natural Gas & Regasification Unit) and the production units such as the FLNG (Floating Liquefied Natural Gas)

Fig. 2 : Excelsior, EXMAR LNGRV

Fig. 3 : FLNG project (Prelude – SHELL).

The figures 2 and 3 illustrate these 2 types of floating terminals: a LNGRV (Excelsior from EXMAR) and a FLNG (projet Prelude project from SHELL). These units present the economical and environmental advantage of not needing long pipelines with their compression units between the gas field and the coast, nor the coastal arrangement that requires any onshore installation. Also these units can be towed and so transferred from a production zone to another. In counterpart, all the production installation has to resist to the floater motions and environmental conditions (wind for on deck installations, currents for subsea).

Whatever is the unit type (LNGRV, FSRU or FLNG), these terminals have to be able to operate with any filling and in particular with partial filling. The floater motions induce a flow in each tank with risk of generating important impacts on the tank walls. This LNG motion induced by the floater motions is called sloshing. This phenomenon is particularly important for intermediate filling denominated partial.

The paper presents the adopted methodology by BV to determine the sloshing pressures in view to verify that the tank walls, i.e., the insulation system of the membrane tanks, can resist to these loads.

1.3. Membrane tank

It exists mainly two membrane types, each developed by GTT. First Mark type composed

of reinforced PUF blocks covered by a 1.2 mm corrugated stainless steel membrane. The corrugations allow to absorb the loads due to thermal shrinkage of the stainless steel during the LNG transportation (-162°C). The second type is composed of a invar membrane. The insulation is done by means of plywood boxes filled with perlite or glass fibre covered with a invar membrane (alloy with very low expansion coefficient).

These systems are presented in more detail in the BV guidance note ([2]).

Fig. 4 : NO96 and Mark III insulation systems (GTT)

2. SLOSHING PHENOMENON

The sloshing phenomenon in LNG carriers corresponds to LNG motions in the tanks induced by the ship motions during navigation or at fixed point. The sloshing is a multi-scale phenomenon, strongly non linear and can be violent, i.e., induce damages in the LNG carriers, FLNG or FSRU tanks.

2.1. Gobal flow

First, sloshing is a large scale phenomenon. The LNG flow in the tanks depends of the ship motions, tank geometry and filling ratio.

2.2. Local effects

Secondly, the sloshing is also a small scale phenomenon. The sloshing impact pressures are deeply influenced by the tank wall local geometry (raised edges) and the liquid/gas mixture properties (density ratio, compressibility, superficial tension). These local effects have a great incidence on the sloshing impact pressures and explain the large variations in amplitude and space distribution. This large variations and non regular space distribution of the sloshing impact pressures are observed as well during

small scale tests than during tank inspections after incidents ([5]). Finally, the sloshing is a complex thermodynamic phenomenon due to the LNG vapour partial condensation during the impact.

In conclusion, the sloshing phenomenon is still too complex to be modelled as a whole making impossible any direct approach. It is the reason why Bureau Veritas proposes a comparative approach which consists to compare the studied floating unit to a reference ship having navigated without incident.

3. AT SEA BEHAVIOUR STUDY

3.1. Objective

The at sea behaviour study objective is to determine as precisely as possible the considered floating unit motions. These motions will be used both for the numerical calculations and for the sloshing model tests.

3.2. Hydrodynamic analysis

The hydrodynamic analysis allows to determine the considered floating unit motions by means of model basin tests or hydrodynamic calculations. Generally, during the project development stage, no model basin test are available. The hydrodynamic calculations are then necessary and performed by means of a at sea behaviour software.

At BV, the in-house developed HydroSTAR software is used. HydroSTAR is a power software to calculate the at sea behaviour (diffraction/radiation calculations) which allows the computation of the considered

floating unit, 1st order (motions for sloshing studies) and 2nd order (for relative incidence between wave and LNG terminal). This HydroSTAR software presents also the following advance options:

• Multi body calculations, particularly adapted for studies of side by side unloading

• Liquid free surface dynamical effects on the floating unit at sea behaviour

These advanced options can also be combined. HydroSTAR allows to compute the FLNG and LNGC motions during the side by side transfer operation (or in tandem) taking into account the dynamic effects of the liquid free surfaces in the tanks of the two ships.

3.3. At sea behaviour/sloshing coupling

3.3.1. Coupling phenomenon

Generally the sloshing study state of the art neglects the influence of the liquid motions inside the tanks on the at sea behaviour of the LNG floating units. In reality this interaction has a large influence on the LNG terminal motions and has to be taken into account.

The motions which are influenced by this coupling are the surging, the swaying, the rolling and the pitching. The rolling is the more strongly influenced motions by this coupling as illustrated by the figure 6 where the RAOs without (black curve) and with coupling (red) are presented.

Fig. 5 : Sloshing / at sea behaviour coupling Fig. 6 : Rolling RAO without / with coupling.

The rolling RAO which takes into account the coupling presents the 2 characteristic peaks of a coupled system (ship + tank) at the opposite of the classical rolling RAO (without coupling) which presents only one peak. On the figure 6, the first peak is associated to the ship natural rolling period when the second peak is associated to the resonant period associated to the considered filling.

3.3.2. Coupling modelling in HydroSTAR

This coupling is taken into account in HydroSTAR as follows. The at sea behaviour and sloshing (dynamic free surface effects) problems are solved separately. The same way than for the at sea behaviour problem, the sloshing is treated as a limits partial derivative problem (internal) for each degree of freedom. When solved (added mass, damping and hydrostatic stiffness calculations) the results of these two problems are combined for the final solution of the coupled motions equation. But, from the theory, the calculated damping by the solution of the internal (sloshing) problem is

zero. To solve this non physical state (infinite free surface elevation in the tank), the limits problem is slightly modified (modification of the limits conditions at the level of the walls in each tank) and an artificial dissipation is introduced aiming to represent the energy dissipation due to viscous effects. This artificial dissipation parameter has to be calibrated by tests or CFD calculations.

3.3.3. Validation

This artificial dissipation parameter has been calibrated during model basin tests performed within the scope of the JIP SALT ([4]). During the tests two LNG tanks were installed at the fore and aft part of a standard LNGC model. Within all the tested filling combinations, the hereafter presented case corresponds to a same filling in both tank (R=30%H). The used hydrodynamic mesh and the measured and calculated by HydroSTAR rolling RAO are given in figures 7 and 8.

Fig. 7 : LNGC hydrodynamic mesh with 2 tanks (R=30%H).

Fig. 8 : Rolling RAO comparison, test / calculations (HydroSTAR).

The figure 8 corresponds to rolling RAO (transverse sea) and two artificial dissipation values (ε=0.02 et ε=0.1). The best results are obtained for the following values of the artificial dissipation parameter [0.02° : 0.07°] which is coherent with the obtained test values for the global forces (see 4.3.2). For the considered example the agreement between test and calculation is excellent. So the linear model in frequency domain is considered satisfactory for the calculation of the coupled motions at sea.

3.3.4. Environmental conditions

At the opposite of the LNG carriers during navigation for which the North Atlantic height-period diagram is selected (IACS Rec.34, Rev 1 June 2000), the sloshing study for a floating LNG terminal is performed for the specific location where this terminal will operate. The necessary environmental data are the height-period diagram, the wave component number and their associated spectra (type, Hs, Tp, γ, spreading or not). In

addition the wind and current data are required as well as the water depth.

3.3.5. Orientation FLNG / waves analysis

Versus the selected mooring arrangement (spread or turret), the LNG terminal will not have the same orientation versus waves. In the case of spread mooring the ship will point to a constant direction. The relative incidence between waves and the floating LNG terminal is so easy to determine.

At the opposite, when the ship is moored by a turret, it will change direction versus the conditions (swell, wind waves, wind and current). The equilibrium can only be determined by a low time step frequency calculation. The additional damping due to the mooring system can be evaluated following the BV rules recommendations. The aerodynamic properties (necessary to evaluate the wind forces) are linked to the ship surface exposed to wind and wind force coefficients. This type of calculation is performed by the in-house developed BV software Ariane.

The result of such calculation are shown in figure 9.

Hs function ofthe FLNG/wave relative incidence

FLNG/wave relative incidence

Fig. 9 : FLNG relative incidence with respect to waves.

This figure 9 presents the relative incidence between the ship and the coming waves for ten years of environmental data. Each cross represents a sea state. The incidences 0° and 180° represent respectively head and following sea. It can be noted that the ship has tendency to go to head seas for the highest sea states.

This result is very important because the more critical conditions for the sloshing loads appear for transverse seas and lowest partial fillings ([10%H : 40%H]). So to neglect the results of this incidence wave/LNG terminal analysis may lead to consider non realistic critical transverse sea conditions. It is why BV recommend such study for all LNG terminal with turret.

3.4. Spectral calculations

The spectral calculations and the motion histories determination are detailed in the BV guidance ([1]).

4. CFD CALCULATIONS

4.1. Objective

The objective of the CFD calculations (Computational Fluid Dynamics)is to evaluate the flow cinematic and the loads applied to the structure behind the insulation system.

The evaluation of the flow kinematic allows firstly to evaluate the loads acting on the tripod mast using Morison formula and secondly to provide an independent (from the sloshing model tests) evaluation of the loads which apply on the insulation system (fluid normal velocities before the wall).

4.2. OpenFOAM

OpenFOAM is a parallel software and « open source » ([7]) which can simulate complex flows (large scale simulations, RANSE model, compressible flows, ...). OpenFOAM uses a finite volume method to solve the partial derivative equation systems with any non structured 3D meshing, composed of polyhedric volumes.

4.3. Validation : Global loads

The first type of validation of the CFD tool for sloshing phenomenon concerns the global flow evaluation inside the tanks. Two quantities allow to verify that the calculation predicts correctly the global flow: the free surface elevation and the global loads generated by the fluid on the tank walls. The used testing arrangement is described hereafter (4.3.2).

4.3.1. Validations 2D

Within the scope of the European project Marstruct, a series of tests have been performed on a quasi-2D tank. The geometry and the characteristics are given on figure 10 hereafter.

The agreement between the test and OpenFOAM (CFD calculations) is excellent for the free surface elevation, the applied moment by the fluid to the tank walls and the pressure, as illustrated on the figures 11.

However it must be stated that the sampling frequency(f=100 Hz) used for the signal measurement was too small. As it will be demonstrated later, a minimum sampling frequency of 20 kHz is necessary to measure the pressure peaks.

Fig. 10 : Test arrangement description and 2D cases.

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Fig. 11 : Comparison of tests (left) and CFD calculations (right) for the free surface elevation, for the pressure (left) and the global moment (right) applied by the fluid to the tank

4.3.2. 2D validations – harmonic motions

Within a cooperation with Ecole Centrale de Nantes, BV performs its own sloshing test campaigns. The testing disposition (hexapod + tank � GTT courtesy) is illustrated on figures 12 and 13.

During the 3D test campaign, the free surface elevation (video) and the global loads generated by the fluid on the tank walls were measured.

Fig. 12 : Motion platform for motions simulation (hexapod)

Fig. 13 : Global loads balance

More details referring the technical characteristics of the testing system can be found in ([3]). The aim of this test campaign was to validate the CFD tool with respect to the global flow versus all the filling types and motion amplitudes. Therefore the adopted testing plan has been the following:

• 7 filling ratios were analysed (7.5%H – 10%H – 20%H – 30%H – 50%H – 70%H – 95%H)

• 4 sway motion amplitudes were analysed (0.5m; 1.0m; 1.5m ; 2.0m at full scale)

• for association (filling, amplitude) a minimum of 15 tests (i.e., 15 motion periods) were analysed

• each test duration is at least equal to 150s

• a video is recorded for each test

• 530 tests were so performed with the hexapod

The sway harmonic motion periods (simulated for 4 different amplitudes) versus the filling level are illustrated on figure 14.

All here described tests have been simulated using OpenFOAM and Flow3D (CFD sofware also used by BV during this study).

Period Range by filling level&

Transversal Tank resonance curve (Theoretical)

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Fig. 14 : Tested periods versus filling level

4.3.2.1. Free surface elevation

Comparisons of free surface elevation corresponding to the same instant are presented in figures 15 and 16.

The presented filling is R=20%H. This filling has been selected because this low filling is critical for sloshing loads. The agreement

between tests and CFD calculation is excellent.

Similar comparisons between test ant CFD calculations have been performed for all other tests, i.e., all fillings, all sway amplitudes and periods. The agreement between test and CFD calculations are each time excellent.

Fig. 15 : Free surface elevation calculated with OpenFOAM – 20%H – 1m – T=1.41s.

Fig. 16 : Free surface elevation obtained from the test video – 20%H – 1m – T=1.41s.

4.3.2.2. Global loads

Comparisons between measured and calculated by Flow3D and OpenFOAM global loads are presented in figures 17 and 18.

As previously, the presented filling ratio is R=20%H (critical for sloshing loads). The agreement between rest and CFD calculations is excellent.

Similar comparisons between test ant CFD calculations have been performed for all other tests, i.e., all fillings, all sway amplitudes and periods. The agreement between test and CFD calculations are each time excellent.

4.3.2.3. Added mass and damping

By a Fourier series decomposition of the global loads the added masses (1st component in phase with the motion) and the damping coefficients (1st component in quadrature) of the free surface liquids are extracted. So the added masses and damping coefficients obtained from tests can be compared to those obtained by the CFD calculation. Also these values are compared to the values obtained by HydroSTAR (frequency domain linear theory) as illustrated in figures 19 and 20.

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Fig. 17 : Global loads comparison between test and CFD calculations (Flow3D & OpenFOAM)

20%H – 1m – f=0.854Hz.

Fig. 18 : Global loads comparison between test and CFD calculations (Flow3D & OpenFOAM)

20%H – 2m – f=0.854Hz

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Fig. 19 : Test measured, CFD calculated (Flow3D & OpenFOAM) and HydroSTAR

added masses (20%H – 1m – ε=0.05)

Fig. 20 : Test measured, CFD calculated (Flow3D & OpenFOAM) and HydroSTAR

added masses (20%H – 2m – ε=0.07)

The agreement between test and CFD calculation of the added masses is excellent, which is logical as the agreement between the global load signals was excellent.

Also the agreement between test and HydroSTAR 'frequency domain linear theory) is highly satisfactory for correctly selected values of the artificial dissipation.

Finally, the artificial dissipation parameter value interval [0.02 , 0.07] corresponds well to the interval identified during the JIP SALT ([4]) based on a totally different test. These two types of test provide the same calibration values for the artificial dissipation coefficient. Considering that the CFD calculation provides results in excellent agreement with tests, the calibration of this artificial dissipation coefficient can be done only by CFD calculation without need of tests.

4.4. Validation : drop tests with and without raised bended

In the previous chapter the validation concerns the global flow (free surface elevation and global loads). Now we propose to validate the CFD tool for impact peak pressures and for the influence of the raised edges. To do so, we use the drop test ([6]) of a dihedral with and without raised edges. These raised edges correspond to those existing on the NO96 insulation system.

4.4.1. Drop tests without raised edges

The drop test is performed dropping a dihedral on a still liquid free surface. For the considered opening angle (10°), the pressure peak is correctly approximated by the Wagner formula ([6]). The testing arrangement is shown on figure 21.

Fig .21 : Testing arrangement scheme.

Various scales and drop height are tested ([6]). The used mesh for CFD calculation, which represents half dihedral (condition of symmetry with respect to the dihedral central axis) is shown in figure 22.

Fig .22 : OpenFOAM mesh

For the largest scale (1/6) and drop height (0.6m), the pressure peaks obtained by the Wagner formula (very good approximation of the tests) and the OpenFOAM calculations are compared for different pressure gauges installed along the dihedral ([6]) as indicated in the following table:

1/6, h=0.8m OpenFOAM Wagner (OF/Wagner)

Capteur 10 623481 622000 1.002

Capteur 11 623824 622000 1.003

Capteur 12 628800 622000 1.011

Capteur 13 632826 622000 1.017

Capteur 14 642751 622000 1.033

Capteur 15 643088 622000 1.034

Capteur 16 638552 622000 1.027

Capteur 17 640465 622000 1.030

Capteur 18 642697 622000 1.033

The agreement between the Wagner formula (very good approximation of the tests) and the OpenFOAM calculations is excellent as the difference does not exceed 3%. The figure 23 illustrates the pressure time history for one of the pressure gauges, Wagner formula and CFD calculation.

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Fig. 23 : Pressure time histories comparaison, Wagner formula and OpenFOAM (CFD).

Therefore the CFD calculation allows to compute precisely the large impact pressures, at least for academic cases (still free surface � no bubble at surface, α=10° � no air cushioning effect, no raised edges).

4.4.2. Drop tests with raised edges

The same test (same dihedral opening, same scales and same drop heights) has been performed with a dihedral equipped with raised edges similar to those of the NO96 insulation system. These raised edges were scaled. The testing arrangement is shown in figure 24.

Fig. 24 : Test arrangement scheme for the dihedral with raised edges.

The used mesh for the CFD calculations is shown in figures 25 and 26.

The pressure time histories obtained from test and by CFD calculations are given on figures 27 and 28.

Fig .25 : OpenFOAM mesh for the dihedral with raised edges.

Fig. 26 : Zoom at the level of one of the two raised edges

Fig. 27 : Measured pressure time history for pressure gauges #1- #18 during test

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Fig. 28 : Calculated by OpenFOAM pressure time history for pressure gauges #1- #18

Qualitatively the comparison between the time histories between test and CFD calculations is satisfactory and can be explained as follows:

• For the first pressure gauges (#1, #2, #3, #4 & #5) before the first raised edge, the pressure peak is similar to the observed peak for the dihedral without raised edge.

• Overpressure (with respect to the pressure without raised edge) due to the first raised edge on pressure gauge #9

• Depression (with respect to the pressure peak without raised edge) after the first raised edge 'pressures gauges #10, #11 & #12)

• Overpressure on the pressure gauges #17 & #18 due to the second raised edge.

This comparison between the cases with and without raised edges and between tests and CFD calculations is also illustrated in the figure 29.

Fig .29 : Pressure peak ratio comparison (with / without raised edges) for tests and OpenFOAM calculations

Quantitatively, the agreement between test and CFD calculation is satisfactory. However, to obtain better results the physical model may be improved by taking into account the gas compressibility.

4.5. Post-processing : dynamic probes

One of the major inconvenient of the sloshing test is the impossibility to cover the whole tank surface with pressure gauges. The State of the Art in sloshing tests is the use (for the best) of pressure gauge sets which can be located only on given areas. It is therefore impossible to obtain a total representation of the sloshing pressures.

In principle the CFD calculations, by recording all data at each time step in all cells, may provide this total representation of the sloshing impacts on all the tank walls. Unfortunately the classical CFD studies are concentrated only on predefined areas (as with the sloshing model tests) because the recording of all data at each time step requires too much space on disks.

To solve this problem a specific post-treatment called "Dynamic gauge) has been, in-house, developed by BV.

A each time step the flow is analysed and eventual sloshing impacts are detected and recorded if the pressure or the normal fluid velocity with respect to the wall exceed a given level fixed by the user. In case where the impact is detected (pressure or normal velocity greater than the threshold), "dynamic gauges" are instantaneously created at the impact location. Each impact is then recorded during a time interval also fixed by the user in view to later verification. Finally, this specific post-treatment tool developed by BV allows to obtain a total knowledge of all sloshing impacts everywhere on the tank walls and during all the simulation duration.

The figure 30 presents all the detected sloshing impacts on the tank ceiling during a simulation of a real sea state (i.e., irregular motions and simulation duration corresponding to 5 hours).

As we shall see later, this tool is particularly adapted to optimize on board insulation systems of gas terminals (FLNG, FSRU…).

Fig. 30 : Ceiling impact map for a simulated sea state during 5 hours at real scale

with OpenFOAM.

4.6. Application

One the CFD calculations target is to provide an independent evaluation – of the model tests – of the sloshing loads applied to the tripod mast., the insulation system and the double hull. Effectively, even if the insulation system designer has to provide to the classification society the model test results, it is fundamental for the classification society to have an independent, from these model tests, analysis tool. The CFD calculation represents this independent analysis tool.

4.6.1. Tripod mast

The loads to be applied for the tripod mast structure verification include the hydrodynamic loads. An illustration of a tripod mast is given by figure 31.

Fig .31 : Tripod mast (GTT).

This hydrodynamic load is calculated by the Morison formula ([2]). by using the flow cinematic (at the tripod mast location) extracted from the sloshing simulations. The CFD (OpenFOAM) calculated flow cinematic has been validated on 2D and 3D tanks for harmonics but also irregular excitations. The hydrodynamic load can be so considered validated. To be noted that the gas terminals operating with all fillings, the partial fillings induce a necessary re-enforcement of the tripod mast with respect of the classical LNGC.

4.6.2. Insulation system

4.6.2.1. Normal velocity criteria

In view to evaluate the severity of sloshing loads which may be occurred on a gas terminal insulation system, BV uses the normal fluid velocity to the tank wall criteria. As indicated for the tripod mast study, the global flow is well predicted by the CFD calculation and this criteria is considered validated.

4.6.2.2. Critical fillings identification

During the development phase of some projects, the model tests are not always available. A model test campaign for a particular project being relatively (about 1 month), it is important to be able to predict what critical fillings will have to be tested. The CFD tool allows to determine these critical fillings.

The figure 32 presents the envelope curve of the maximum normal to the wall velocity (non dimensional) versus filling level for a particular FSRU terminal.

The critical filling given by the CFD study corresponds to the low filling R=20%H. This result has been confirmed by model tests which have indentified the same filling level.

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Fig. 32 : Normal to the wall fluid velocity versus filling level for a FSRU project

4.6.3. Insulation system optimisation for Boil-Off Gas (BOG) reduction

As mentioned previously, BV has developed in-house a CFD post treatment tool called "dynamic gauge". This tool allows to obtain a total knowledge of all sloshing impacts on all the tank walls during the whole simulation duration.

This tool was used within the scope of the optimization of the tank ceiling insulation system in view to reduce the Gas Boil-Off (LNG evaporation). For that, a sea state identified as critical for high filling ratios has been simulated (random motions during 5 hours) for all tanks of a classical LNGC. A map of the impacts identified during the simulation of this sea state is given in figure 33.

This map is in agreement with the return experience of ships equipped as well with NO or MarkIII insulation systems. The observed incidents for high fillings remained located in the 4 tank ceiling corners, on the Larbi Ben M'Hidi (NO) and on the MarkIII (corrugation deformations). The presented map is so totally coherent with this return experience.

4.6.4. Double hull scantling

In view to verify the double hull scantling proposed by the shipyard the CFD "dynamic gauge" post-treatment tool (4.5) extracts the quasi-static loads.

Fig. 33 : Ceiling impacts map in the 4 tanks of a classical LNGC. Random motions of a 5 hours sea state.

For the yet presented particular FSRU project, the envelope curve of the maximum quasi-static loads (without dimension) versus filling level are given On the figure 34.

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1

Filli

ng R

atio

- R

(%H

)

Adim. Quasi-Static Pressure (kN/m2)

Adim. Quasi-Static Pressure (kN/m2) = fct ( R(%H) ) Side Wall

Adim. Quasi-Static Pressure Side Wall

Fig. 34 : Maximum quasi-static loads versus filling level for a FSRU project

As for the normal to wall maximum fluid velocity, the identified critical filling for the quasi-static loads corresponds to a low partial filling of R=20%H. This result is well correlated with model tests which have identified the same critical filling.

When these loads are determined, the scantling can be verified following the BV rules ([2]).

5. SLOSHING MODEL TESTS

5.1. Objective

The objective of the sloshing model tests (small scale) is to determine the sloshing loads in view to select the insulation system.

The sloshing loads evaluation methodology is the following:

1. the measured sloshing pressure peaks are extracted from the pressure time signal for various gauge dispositions (corresponding to different load areas) and for each tested navigation condition

2. a statistical law is adjusted to these empirical pressure peak distributions

3. this adjusted law is used to predict the sloshing loads applying a long term approach.

For all model test Froude scaling is applied to allow a similar global flow between model scale and real size.

5.2. Required equipment

The required equipment for sloshing tests is described in the BV guidance note ([1]). The characteristics of the required equipment (shortly summarized here) are the following:

• The motion platform must reproduce precisely the random motions for the 6 degrees of freedom.

• The tank model must be geometrically similar to the studied tank. The minimum scale is 1/70

• The tank walls are sufficiently stiff with respect to the measured loads. The model must be equipped of locations able to receive the pressure gauge modules. The tank walls must be transparent to allow the internal flow observation.

• The sloshing phenomenon being a very fast dynamic phenomenon, the gauge sampling frequency is at the minimum equal to 20kHz

• Generally the model tests use water as liquid. It is recommended the use of an ullage gas respecting the density ratio between LNG and its vapour.

5.3. Empirical sloshing pressure peaks distribution

Following the model tests, the BV methodology ([1]) only consider the pressure peaks exceeding a given level (« Peak Over Threshold » ou POT method). Then the applied method is summarized as given in the graph of figure 35.

This graph shows clearly a great dispersion of the sloshing pressure peaks. Therefore there is a great sensibility of the pressures with respect to the considered return period. (here 10 hours and 1 year). The proposed adjustment law by BV is Pareto distribution as discussed hereafter.

Then a statistical law is adjusted to the empirical distribution of the pressure peaks. An example of adjustment obtained from model tests is given in figure 36.

Pressure peaks(Peak Over Threshold)

Density of probability

Cumulativeprobabilties

Exceedingprobabilties

Fig. 35 : Sloshing peaks post-treatment scheme

Adjustment example on an

empirical sloshing distribution ����

large pressure peaks variability

Adjusted statiscal law

pressure

Fig. 36 : Statistical law adjustment to an empirical sloshing pressure peaks distribution

5.4. Sloshing test (480h) statistical post-treatment – Pareto distribution

Weibull distribution is generally used in industry as statistical adjustment law. In view to determine if this Weibull law is the adapted adjustment law for sloshing peak distribution, BV performed a specific test series to obtain a sample of 480 hours (96 tests of 5 hours) instead of the maximum 30 hours in general

considered. Each test duration was 5 hour at full scale.

5.4.1.1. Studied case

The tests were performed with the following conditions:

• the considered LNGC is the reference LNGC (i.e. 138,000m3)

• the studied tank is the nb 2 tank of this reference LNGC

• the considered filling is R=20%H (low partial filling) which is critical in terms of sloshing loads

• the considered sea state is represented by a Jonswap spectrum with the following characteristics: Hs=8.0m, Tz=8.5s, β=195°, γ=2 (Jonswap parameter) and spreading coefficient (N=3)

• the ship (LNGRV for example is considered at a fixed point (turret), so V=0knt. The water depth is considered infinite.

Each test (5 hours at full scale) was generated from different initial conditions. The motion time histories are so different for each test even if the statistical characteristics are identical.

5.4.1.2. Model tests

The used tank (GTT tank) is in plexiglass at 1/70 scale. The pressure gauge locations are given in the figure 37.

5.4.1.3. Statistical post-treatment

The following 3 adjustment statistical laws are compared: Weibull, Pareto and Generalized Extreme Value (GEV)

The greatest pressure are recorded on channel 9, so only this channel is represented. The reference distribution (test of 480 hours) of the channel 9 is given in figure 38.

This empirical distribution of 480 hours is composed of 96 empirical distributions of 5 hours tests. The reference empirical pressure corresponding to a return period of 400 hours is also given.

Fig. 37 : Pressure gauge locations in tank nb 2 (GTT) of a classical LNGC. Scale 1/70.

Fig. 38 : Empirical pressure peak distribution for the total test of 480 hour at full scale

Each 5 hours (full scale) test distribution is adjusted by the 3 analysed statistical distribution laws. These adjustment laws are extrapolated to the considered return period (400 hours) and the obtained statistical pressure (black points on figure 39) is then

compared with the empirical reference pressure (orange line). These comparisons (with the confidence intervals at 95%, min = purple points and max green points) are illustrated on figure 39.

Test number

Pre

ssur

e (m

B)

Test number

Pre

ssur

e (m

B)

Test number

Pre

ssur

e (m

B)

Fig. 39 : Extrapolated pressures at 400 hours for the 96 test of 5 hours (full scale) using Weibull, Pareto & Gev laws. The confidence intervals at 95%, min and max are also represented

For studied case the Weibull distribution (underestimation) and GeV (overestimation) do not allow a good estimation of the sloshing pressures. At the opposite, the Pareto distribution provides a satisfactory estimation of the sloshing pressure. In addition, the

confidence intervals of the Pareto distribution cover clearly better than the two other distributions the empirical reference pressure.

To improve the sloshing pressure estimation it is recommended to increase the test duration as shown in the figure 40.

Test duration (hours)

Pre

ssur

e (m

B)

Fig. 40 : Convergence of the estimation of the pressure versus test duration

So the increase of the test duration improves the sloshing pressure estimation and also decreases the confidence interval range. Therefore BV recommends to repeat tests for the navigation conditions more participating to the long term pressure (see following) and to control the adjustment by confidence interval calculations.

5.5. Sloshing pressure dispersion – Long term approach

As yet mentioned, the observed incidents during navigation ([5]) and the model tests demonstrate a large dispersion of the sloshing pressures. The estimated pressure associated to a navigation condition is so sensitive to the return period of this condition. To take into account the stochastic character of the sloshing phenomena a long term approach is considered.

The main idea of the long term approach is to associate to each navigation condition the two following characteristics: its probability of exceeding (part 5-3) and its probability of occurrence. Then the contribution of all the navigation conditions encountered by the floating terminal are summed to provide the long term exceeding probability. By

comparing this long term exceeding probability with the insulation system strength, it is finally possible to determine the damage probability.

This method is illustrated in the following paragraph through a school case application.

5.5.1. Application to a given scenario

As explained previously, the long term approach requires the knowledge of the operational profile of the considered floating unit, i.e., the ship loading cases, the operational fillings, the encountered navigation conditions (sea state, speed, wave incidence) and their occurrence probabilities.

To simplify the considered study case, we shall consider one loading condition, one low partial filling (the more critical for sloshing loads) and 3 navigation conditions (Hs=4m, 6m & 8m). The occurrence probabilities of these navigation conditions are the following:

• the condition Hs=4m appears 1000 hours each 10 years

• the condition Hs=6m appears 100 hours each 10 years

• the condition Hs=8m appears 10 hours each 10 years

The considered return period RP is 10 years. For the remaining time we assume (school case) that the Hs is sufficiently small to not

generate any sloshing impacts (Hs<1m). The model tests provide then the empirical distributions adjusted by a Pareto law given in figure 41 (part 5-3).

Using the following formula we determine the long term exceeding probability:

( )SL

SLiSL

i

TTNTzT

STiLT pQTpQ/

1

/)(11),(

−−= ∑α (1)

with the following definitions: • QLT (p, T) : long term exceeding

probability (per hour) • p : sloshing pressure • T : return period in hours • NSL : number of navigation conditions • αi : occurrence probability of the ith

navigation condition • QSTi (p) : short term exceeding

probability of the ith navigation condition

• TSL : duration of the condition navigation in hours

• Tzi : mean tile between two impacts

Applying this formula we obtain the exceeding long term probability given in figure 42.

It can be easily determined the respective contribution of each navigation conditions given in figure 43.

Pressure

Exc

eedi

ngpr

obab

ility

–m

ean

even

trat

e

Fig. 41 : Empirical law adjustments (4m, 6m & 8m) by a Pareto law

Pressure

Exc

eedi

ngpr

obab

ility

–m

ean

even

trat

e

Fig. 42 : Long term exceeding probability

Pressure

Nav

igat

ion

cond

ition

con

trib

utio

n (%

)

Hs=6m is the more contributing for

RP, 10 RP, 100RP

Post-treatment must be on Hs=6m and not

Hs=8m

Fig. 43 : Contribution of each navigation condition to the long term pressure

The conclusion of this school case is that the condition with maximum contribution is not the highest Hs but an intermediate Hs level. This conclusion is only valid for the here considered scenario (very simple).

It with this target to identify what are the navigation conditions with greater contribution that the sloshing model tests have to be performed.

6. CONCLUSION

This paper first presented the parameters which have influence on the sloshing phenomenon. Then the methodology used by Bureau Veritas (BV) which allows to quantify the loads due to sloshing in view to determine consequently the floating unit tank scantlings have been presented. Each step of the method being the subject of R&D in BV has been illustrated by validations based on comparisons between calculations and tests.

7. REFERENCES

[1] « Design Sloshing Loads for LNG Membrane Tanks », NI554 DT R00 E, Guidance Note, May 2011

[2] « Strength Assessment of LNG Membrane Tanks under Sloshing Loads », NI564 DT R00 E, Guidance Note, May 2011

[3] N. Moirod, L. Diebold & al. – Experimental & Numerical Investigations of the Global Forces exerted by fluid motions on LNGC prismatic tank boundaries - ISOPE 2011

[4] G. Gaillarde & al. – Coupling between Liquefied Gas and Vessel’s Motion for Partially Filled Tanks: Effects on Seakeeping – RINA – 2004

[5] E. Gervaise & al. – Reliability-based Methodology for Sloshing Assessment of LNG Membrane Vessels – ISOPE 2009

[6] J. F. Kuo & al. – Influence of Raised Invar Edges on Sloshing Impact Pressures – ISOPE 2009

[7] www.openfoam.com