WATER MOTION IN MOONPOOLS EMPIRICAL AND THEORETICAL APPROACH

par

Guilhem GAILLARDE Maritime Research Institute Netherlands MARIN

www.marin.nl

Anke COTTELEER HMC Heerema

SOMMAIRE

Les moonpools sont employees sur différents types de navires, cabliers, exploration et forage pétrolier, barge de production, recherche, ou support offshore. Elles servent a la mise a 1'eau d'équipements (pose de cable, pipeline, riser) ou de plongeurs dans un environnement protégé des vagues extérieures. Cette fonction est assurée tant que la colonne d'eau n'entre pas en résonance, excitée par 1'action des vagues et les mouvements de pilonhemerït du navire, provoquant des oscillations verticales pouvant aller jusqu'a trois a quatre fois la hauteur des vagues. Un autre phénomène d'oscillation peut aussi se produire en eau calme avec vitesse d'avance. Les oscillations provoquent une augmentation de la résistance a 1'avancement. Lorsque ces oscillations prennent une amplitude suffisante, Ie navire lui-même se met a pilonner et cavaler. Malgré 1'ensemble des recherches conduites sur Ie sujet, la plupart des solutions trouvées 1'ont été de maniere empirique. Ce mémoire présente des résultats d'essais oü de nouvelles solutions pour atténuer ces oscillations ont été étudiées. Des nouvelles approches numériques prometteuses sont aussi présentées, faisant appel aux methodes VOF.

SUMMARY

Moonpools are used on many types of vessels: cable-laying vessels, exploration and drilling vessels, production barges, research and offshore support vessels. They are used to launch and retrieve equipment, divers or diving bells, or lay cables or risers, in an environment protected from the waves. This use is valid as long as the column of water does not enter in resonant condition, excited by the waves and the heave motion of the vessel. In resonant condition, the oscillations can reach as much as three to four times the wave height. Another case of oscillation is observed in calm water with forward speed of the ship. The oscillations will cause a dramatic increase in calm water résistance. With large oscillations, the vessel will also start to heave and surge. Despite the research effort conducted on that subject, most of the solutions were found and are still found and validated experimentally. The present paper shows recent solutions applied to reduce the oscillations in the moonpool caused by the forward speed of the vessel. New numerical methods are also presented to solve the problem in transit and stationary conditions in waves, making using in particular of VOF models.

1 INTRODUCTION

A moonpool is a large wall-sided hole in the bottom of a ship through which, for instance, equipment can be lowered into the sea or through which pipes (riser, cables or drills) are going. When properly designed and located on the vessel, the outside horizontal forces as well as vertical motion of the water are suppressed to allow safe subsea operations. Vessels equipped with moonpools are drilling vessels, pipe-laying vessels, rock dumping ves­sels, survey vessels or diving support vessels.

The column of water inside the moonpool can, however, be excited at its own natural frequen-cy resulting in large vertical motions described in the literature as piston mode. Internal sloshing can also occur, resulting in transverse breaking waves that are added to the vertical motions. Water motions in the moonpool can be excited through different mechanisms, in waves or in calm water with forward speed of the vessel. This dynamic magnification can cause slamming on diving bells or ROVs that are launched, green water over the edge of the moonpool which can be dangerous for the crew, or can increase drastically the resistance of the vessel in transit conditions.

This paper presents the different conditions in which oscillations of the moonpool will hamper the operations of the vessel. Moonpool motions have been studied since a long time (see references [1] to [30]). Hereafter a summary is presented of the phenomenon, of the empirical solutions applied during model tests and on existing vessels, as well as new techniques to solve the problem numerically.

2 EXCITATION MECHANISM OF WATER IN MOONPOOL

2.1 General aspects

Moonpool oscillation can occur in two distinct situations:

• In calm water with forward speed. • In waves in stationary condition.

Of course, combined situations will also provide oscillations when the correct conditions are met as illustrated by the two situations in Figure 1.

ship speed

^£ flow separation at the moonpool bottom and induced ship motions

Excitation due to waves and ship motions

Figure 1: Conditions with motion of the water in the moonpool

The excitation mechanisms for the two situations in Figure 1 are quite different, which also explains why empirical solutions to damp the motions or simply alleviate the excitation differ.

2.2 Excitation in calm water at forward speed

Large oscillations can occur in calm water at certain threshold speeds. The excitation mecha-nism in that case is due to vortex shedding, formed by flow separation at the leading bottom edge of the moonpool. This was observed onboard several vessels as shown in Figure 2 and, of course, during model tests (prior to the start of construction, or after first trials in order to urgently find a solution).

Figure 2: Sloshing and pumping on a 6x6 m moonpool at 10 knots in calm water

Naudascher [27] wrote the following about flow-induced vibrations: "Exceptfor afew rare cases of extraneous excitation and self-excitation, most flow-induced vibrations can be traced to an instability of the flow. Whatever the nature of the instability, its effect in combination with disturbances will invariably be the development of fluctuations of velocity _ and pressure in an initially steady flow, unless viscous forces are large enough to damp this process. Depending on the presence and strength ofmechanisms by which:

1. the intensity of these fluctuations becomes amplified,

2. their correlation in space becomes increased, and

3. the distribution of their energy becomes concentrated around a dominant frequency,

an effective farce fluctuation along the flow boundaries may come about and possibly lead to (structuraï) vibration ".

Section 2.2.1 describes the growth of the disturbances (vortices). In section 2.2.2 the

- increased correlation in space is discussed. In section 2.2.3, phase locking and hysteresis are explained as they are important phenomena for the oscillation of the water in the moonpool.

2.2.1 Growth of vortices

The excitation leading to the water oscillations is due to an instability of the flow. Considering a flow without instabilities, the water level can only be expected to change, but not to oscillate. There must be some kind of flow-induced vibration, vortices shedding from the leading edge, introducing instabilities in the flow.

v ^-—v^

Figure3: Development of vorticity concentrations from a disturbed thin shear

layer (see [28])

Naudascher and Rockwell [28] describe the origination of these vortices. Figure 3 shows an idealized model of a shear layer: a surface of abrupt velocity discontinuity. A slight lateral perturbation of such a surface will produce a change in the velocity and pressure field, which

acts to modify the streamline pattern further in the direction of perturbation. As the disturbance is thus amplified, it becomes asymmetrie on account of the mean-velocity distribution and develops ultimately into a region of concen­trated vorticity. In a viscous fluid, this process of shear-layer roll-up is either damped or leads to the formation of discrete and gradually decaying vortices or eddies. In summary, then, flow instability initiates a transfer of energy from the flow to the disturbance, giving rise to flow fluctuations.

In 1977 Fukuda [12] made some photographs of the vortex in the opening of the moonpool when the water surface is moving up and down. Photographs taken from [28] are shown in Figure 4 and show vortices in a cavity which are similar to those observed by Fukuda for a moonpool.

Figure 4: Hydrogen bubble visualisation with approaching and clipping vortex

Cavity flow refers to air or water flow past a hole leading to a large pressure gradiënt in this hole. Both in the case of a cavity and in the case of a moonpool, flow separation occurs at the leading edge and a vortex arises from the forward side of the hole due to an abrupt velocity discontinuity.

2.2.2 Disturbance correlation in space

The feedback mechanism is the source that is of importance to the moonpool problem. This mechanism can be described as follows. The vortex that arises from the forward edge of the moonpool because of the abrupt velocity discontinuity comes into contact with the aft edge of the moonpool. This induces a pressure fluctuation that spreads over the surrounding flow field. A part of this influence will reach the forward edge of the moonpool, leading to the development of new vortices with the same frequency. In this way, a dominant frequency might arise and the energy at this dominant frequency will be large as shown in Figure 5. This condition is called phase locking.

5 0.80J

< <x

O IX

y O.-IÜ_

LU

LU

> o.oo.

T-PEAK CS>'

T02 CS)'

SIGN.VAL. -

6 .69

3.29

I .05

A -0 . 0 0

T T T ' n - T T -

2 . 0 0 FREQUENCY

4 . 0 0 CRAD/S>

Figure S: Energy of the wave rise in the forward part of a moonpool during

resistance tests

2.2.3 Hysteresis

The energy concentration that is required for flow induced vibration can by found in the combination of phase locking with hysteresis.

Hysteresis means that different frequencies and amplitudes are obtained when the velocity is increased than when it is decreased. Fukuda observed hysteresis effects when testing the models in a flow tank. It was possibte to increase the speed of the water and to decrease it after a while again.

Rockwell and Naudascher [29] mention that the hysteresis has to do with the peaks in energy concentration at certain frequencies. When increasing the velocity, one frequency is sus-tained longer and when decreasing the velocity again, the higher frequency is sustained.

Hysteresis is not observed for normal cavities, but maybe, some kind of self-controlled oscil-lation is needed for this phenomenon to appear. This self-control is absent in normal cavities, but is present in the moonpool.

When the volume of water oscillating in the moonpool is large enough, the moonpool oscillation in heave wiil yield excitation in heave for the vessel itself. Vertical motion of the vessel, when occurring at the same frequen­cy as the moonpool motions, will increase the flow separation at the leading edge and increase the piston motions.

This strong coupling between floater and moonpool heave motions seems to be of great importance in the mechanism. This coupling was clearly measured during model tests with a free-running model and was also observed onboard vessels.

In the same way as for heave, a coupling also exists with surge, most probably yielding slosh-ing motions in the moonpool that are then coupled with the piston mode. When the match of different parameters occurs, the relative motions in a moonpool in calm water can reach large amplitudes with water flowing over deck.

The coupling between heave and surge of the vessel in transit and moonpool motion yields a large resistance increase. This resistance increase is such that the vessel cannot exceed the threshold speed at which oscillations start. A slight increase in speed will increase the excitation and the motions and thus the resistance. Due to the apparent strong coupling effect between vessel and moonpool motions, only tests performed with a free-running and self-propelled model can correctly investigate the problem.

2.3 Wave excitation in stationary condition

In waves, large water motions in the moonpool originate from the match between vertical excitation and the natural frequency of the water column. The column of water can be seen as a single mass-spring system that can be excited at its natural frequency. The excitation mechanism is quite different from what is observed at forward speed in calm water. Excitations can be split in two main compo-nents, resulting from the ship motions and the waves:

• local vertical accelerations at the bottom of the moonpool;

• pressure differences at the bottom of the moonpool.

The equation of motion of the water column can be written, as shown by Albert Aalbers in [1].

3 OSCILLATION MECHANISM OF WATER IN MOONPOOL

Fukuda [12] has described different oscillation mechanisms that he observed during model tests. He gave a figure with the moving shape of the water surface for different values of l/d and b/d (1 = length of moonpool, d = draught, b = breadth of moonpool). This figure is given here as Figure 6.

heaving swaying surging

-1 -Wow Flow

Figure 6: Moving shapes of water

These different modes are shared by calm water and stationary in wave conditions. For the particular case of calm water in transit, the following sequence usually takes place. The letters (a) to (d) in the sequence correspond to those in Figure 7.

(<*)

\

(b)

(d)

K Figure 7: Pattern of water motion in the

moonpool during oscillation period

When the water in the moonpool is at the lowest point, the water starts to come up at the aft edge (a). This motion goes on, but the water at the surface starts to flow towards the forward edge (b). When the wave reaches this edge, it reflects and the water starts a backward flow (c). The point where the forward and backward flow meet each other, travels towards the aft edge (d), meanwhile, the flow coming up at the aft edge becomes smaller and the water level starts.to move down. When_the upward motion starts again, the meeting point mentioned in stage (c) and (et) disappears because it meets the new coming wave of the aft edge.

English [8] has drawn a figure of the water motion in the moonpool during the oscillation, which is shown in Figure 8. Please note that the ship velocity is to the left. The vortex, which arises from the forward edge, is shown in the side view, while the plan view shows the water coming up from the aft side and stagnating on the forward side.

ship direction of travel

E -—

back side of opening

swirlingboundar) layer fluid

under side of keel

Figure 8: Water motion in a rectangular moonpool (sec English [8])

The water in the moonpool of a ship in transit condition is not only oscillating; the mean water level also increases. This can be concluded from results of model tests. Figure 9 shows this increase.

I °2

J 0.15 s I 0.1 c (U

E 0.05

»- — « 6 8 10

Ship speed [XnJ

Figure 9: Increase of mean water level

4 REDUCTION OF WATER MOTIONS

There are two main ways to reduce the oscil-lations of the water in a moonpool: reduce the excitation or reduce the motions by damping devices. The first solution will in general be applied for transit conditions as the techniques make use of the flow vëlocity or obstrucf the moonpool opening. The second solution can be applied to both cases, with non-obstructive solution (in order to keep a "workable" moon­pool).

4.1 Rcduction of excitation

This section presents empirical solutions found during model tests or during trials. Merits and drawbacks of each solution are described through results of model tests. Even if this particular moonpool cannot be representative for al! kinds of situations, the trend obtained in the present set of model tests has been relatively similar to that in other configurations of dimensions and vessels.

The aim of the solutions presented hereafter is to alleviate the origin of the problem and reduce the excitation and not simply dampening the motions after the motions have starled.

4.1.1 Wedges and cut-out parts

Wedges are becoming a "classical" solution to avoid excitation in moonpool in transit condi­tion. This is a simple approach that can be retrofitted on the huil without obstructing the

moonpool opening, which probably explains its success. The idea behind wedges is to deflect the flow on the leading edge of the opening, in order to avoid that the vortex created by the separation enters the column of water. Cut-outs and wedges can also be applied on the trailing edge of the opening, as shown in Figure 10.

Heller and Bliss [19] performed airflow tests past a cavity. Franke and Carr [11] observed that the typical oscillation cycle and sequence of events found by water flow was the same as for air, so air flow past cavities can be inter-esting for the moonpool problem. Heller and Bliss have given explanations for the method they used to reduce the oscillation amplitude. The method that can be used for the moonpool is stabilization of the shear layer. This can be achieved by introduction of vorticity into the shear layer (upstream vortex-generators or by spoilers) or by providing a stabilizing trailing-edge geometry.

The optimum angle and length of the wedge are always obtained through model tests and by trials and errors, as no numerical tooi can support the decision so far. Angles usually vary between 5 to 15 degrees and the length is around 20% of the moonpool length. Intuitively, one can say that the opti­mum dimension of wedges most probably depends on the ship speed and moonpool length.

p moonpool length L

intitfenlutka DQÜCCI «hiüoo

Figure 10: Solution 1 - Wedges

4.1.2 Gridof flaps 4.1.3 Single flap

A new solution was tested on the same vessel as previously shown, consisting of a grid of flaps which aim is also to block the upwelling of vortices inside the moonpool, see Figure 11. This solution would, of course, impose the flaps to move on a rail, in order to open the moonpool during operations, just like a curtain.

Figure 11: Solution 2 - grid of flaps

The blocking of the upwelling is only necessary in the aft part of the moonpool, the forward flaps were removed during the tests, as shown in Figure 12. The results in terms of oscillation and added resistance were identical in the two cases and gave the advantage to leave more clearance in the moonpool opening.

According to the foregoing and based on the "understanding" of the physical phenomenon, a large single flap was also tested, consisting of. This solution is shown in Figure 13.

A flap of 30% and 50% of the moonpool length were tested, with different inclinations. The larger flap with the lowest inclination provided the best results. Overall, this solution proved to be the best one with nearly no oscillations in the moonpool, apart from the observation of a slight circula-tion of water inside the moonpool.

position used lo uiethe tuil opening in operalii

Figure 12: Solution 3 - Reduced grid of flaps

Figure 13: Solution 3 - Single flap

The system was mounted on an hinge, in order to rotate the flap for the different set-ups. The load on the flap was also measured by a two-component balance. A similar set-up should be used on a vessel in order, again, to open the moonpool during operations.

Performance increase in calm water Figure 14 shows the results obtained on calm water resistance for the solutions presented above.

The three curves in Figure 14 show the shaft power as a function of ship speed, for closed moonpool, open moonpool without devices and with the single flap solution.

moon,

ouvar • / e onfijn™ Bon / opUrrum

f f moonpool ^r f*f/na«

X f pull l inea mtnimum dellvrae

X

10 12 V nesse du nadre [noeud]

Figure 14: Required power for different co nfigu ratio ns

4.1.4 Vertical bulkhead

Other solutions for excitation reduction are also existing mainly based on the same principle, which is to obstruct the large vortex originating from flow separation. Change in the natural frequency of the column of water may also explain the result. Figure 15 shows a case where the vertical plate was fixed in the width of the moonpool, creating two moonpools. This solution was also tested successfully during model tests and adopted on a vessel.

Figure 15: Solution 4 - Vertical plate

4.1.5 Convergent openings

English [8] has given another way to reduce the oscillations in the moonpool caused by the vessel's forward speed. This method has to do with three-dimensional effect. He states that the

use of convergent openings will help. The flow pattern will change as is shown in Figure 16. He tested the two openings given in the same figure and found large reductions of oscilla­tions.

constant forcc 4 stifftow }— •

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0 - 3

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Figure 16: Effect of the opening geometry

4.1.6 Sucking away the boundary layer fluid

Finally, English gives another idea to reduce the excitation: "It is probable that the oscilla­tions in the opening could also be reduced by sucking away or re-energising the boundary layer fluid immediately upstream of the open­ing. However this would require machinery and expenditure of energy and from this point of view is not such an attraciive solution to the problem ".

4.1.7 Using hysteresis effects

It may be possible to use the hysteresis effect observed by Fukuda to reduce the vertical water motions in the moonpool. For situations where the required forward velocity is less than the maximum velocity, it can be possible to increase the velocity to a value over the hump and then reduce it to the required velocity.

4.2 Reduction of oscillations 4.2.2 Ciosing the top of the moonpool

Reduction of oscillations by damping devices is applied to both transient and working stationary vessels, because most of the solutions are non-obstructive.

4.2.1 Flanges

The first method to reduce the oscillation by increasing the damping is by placing flanges in the moonpool. Fukuda [12] tested the applica-tion of flanges at three places: at the opening of the moonpool, just below the water surface and on the water surface. The short flanges a little below the water surface proved to be very ef-fective (see Figure 17). This method to reduce the water oscillations is based on increasing the damping. Aalbers [1] has tested the effect of damping plates on the oscillations in the moon­pool for a ship lying still in waves. He also obtained better results for a higher placed damping plate than for plates placed at the opening of the moonpool.

Type A

?.—H

TypeB

:ü

&*.

I ! TypeC

0.2

2 h/l

0.1

0.0 0.0

» ty± TypeB

1.0

Figure 17: Effect of flanges on moonpool oscillations

That type C does not reduce the oscillations for a vessel in transit is strange, when looking at the excitation mechanism. In fact, the length of the opening is reduced. The excitation that is observed will probably occur at a different frequency, leading to a different vessel velocity at which the maximum amplitude occurs.

In fact, reducing the oscillations in the moonpool by ciosing tits top is also based on an increase of the damping as the air above the water surface creates damping. Assuming incompressibility of the air above the water, the moonpool can be seen as a real cavity where no vertical oscillation can occur. Fukuda has performed some resistance tests while a plate with air holes closed the top of the moonpool. The resistance increased by a constant amount compared with a ship without moonpool, but there was no peak increase for a certain velocity. Maybe, this way to reduce the oscillation can also be used for a fixed ship in waves.

4.2.3 Damping chambers

Spangenberg and Jacobsen [30] have investi-gated the effect of damping chambers on the reduction of the water motions in the moonpool of a ship in seaway, as shown in Figure 18. In order to reduce the water motion, the breadth of the moonpools has been increased approxi-mately from the water line to the main deck. When the water level rises, the water will run through perforated longitudinal bulkheads into damping chambers. When the water level decreases, the water will run from the damping chambers back into the moonpool. The effect of the damping chambers is that vertical wave motions are converted into horizontal wave motions and the wave energy, to a large extent, dissipated as heat energy by reflecting and conflicting currents from the holes of the perforated bulkheads.

Damping chambers

Choke decks

Perforated bulkheads

Figure 18: Damping chambers

4.2.4 Changing the draught

Reducing the oscillations by changing the draught of the ship must be possible because the natural frequency of the water column depends on the draught. On a ship in transit, the excitation frequency is dependent on the length of the moonpool and the forward velocity of the ship, so for different ship speed, different draughts can be preferred. On a ship in waves, the excitation frequency is dependent on the wave frequency, so for different wave frequencies, different draughts can be preferred as well.

4.2.5 Other applied solution

Adding air in the water inside the moonpool will decrease the impact load on the equipment passing through the moonpool but will not reduce the oscillations. This solution has been successfully applied in a number of vessels.

5 NUMERICAL APPROACHES

5.1 Existing semi-empirical and numerical methods

This section will not present all existing methods in detail, it will only give the overall results of available methods and the references.

Frequency Faltinsen [9] regards the water column in the moonpool as a mass-spring system without damping. He gives the following formula for the calculation of the natural period T„ of the moonpool:

where d is the draught of the ship in m.

Fukuda [12] uses the same formula, but he makes use of an increased length, to take account of the added mass and the increased draught. This 'added draught' is an empirical estimation and is given by the following formula: t/'=0.4lVs where S is the water sur-face area in m2.

r>=2Jrf+o.4Wt7

where d is the draught of the ship in m, b and / are respectively the breadth and length of the moonpool in m. This equation seems to give a good estimation of the natural frequency when comparing with model test results.

Molin ([24], [25] and [26]) provides a method to obtain the piston and sloshing modes of moonpools.

Amplitude in calm water in transit Fukuda [ 12] has given a method to calculate the amplitude of the heaving mode of the water column using a measured value of the ship speed where the oscillation starts. Whether the amplitude Fukuda uses is the maximum value or the significant value is not mentioned. The final form of the equation gives the dimension-less amplitude:

where: h = amplitude of oscillation [m] l = length of moonpool [m] V = ship velocity [m/s] U' = ship speed where oscillation starts (mea­

sured) [m/s] 6h = natural frequency of oscillation of water

column [rad/s].

This equation is only valid for co <cOo-

Figure 19 shows the model test results from which the semi-empirical formulation was de-rived.

The ship speed where the oscillation starts may be calculated by the method given by Covert [3], otherwise obtained from model tests.

Even if the results cannot be applied to all moonpool geometries, this graph can be used in a design stage to check if a potential oscillation problem may occur, given the ship speed, the main dimensions of the moonpool and the draught of the vessel.

For a square moonpool, this leads to the following equation for the natural period:

2h/l

-> 2.0

2U/lüJo

Figure 19: Calculated and mcasured amplitude of water motion in a rectangular

moonpool (Fukuda [12])

Amplitude in waves in stationary condition Aalbers [1] has given a method to calculate the water motions in a moonpool for a ship on a fixed position in waves. The final equation of Aalbers' method is almost the same as the equation of Fukuda, with which the approxima-tions are started. In the equation of Aalbers, the heave motion of the ship is also taken into account. The vertical displacement of the water in the moonpool can be modelled in the same way for a ship fixed in waves and for a ship in transit condition. The exciting force, however, is different. In waves, two main components can be identtfied in the excitation mechanism:

• vertical acceleration, due to floater motions; • pressure at the bottom of the moonpool, due

to ship motions and waves.

The excitation forces can be calculated thanks to any 3D diffraction code, in order to be used as input for the equations of motions. They are solved in the time domain, as non-linear terms do not allow to find a simple solution in the frequency domain. Results were very encour-aging, but are highly dependent on the choice (or evaluation) or added mass and damping (linear and quadratic). Added mass estimation, even crude, is usually quite well described. Damp ing terms, however, are much more difficult to obtain.

5.2 Introduction of VOF model

5.2.1 Introduction

Recent developments in numerical techniques, such as volume of fluid, may open a new approach for the moonpool problem. The following presents first results obtained with the software ComFLOW available at MARIN.

ComFLOW is an improved 3D Volume Of Fluid (iVOF) Navier-Stokes solver. The pro­gram has been developed initially by the University of Groningen/RuG (Prof. Dr. Arthur Veldman) to study the sloshing of liquid fuel in satellites. This micro-gravity environment requires a very accurate and robust descnption of the free surface. Coupled dynamics between the sloshing fluid and the satellite were inves-tigated as well (Gerrits, [16] and [17]). In close co-operation with MARIN, this methodology was later extended to the calculation of green water loading on a fixed bow deck (Fekken [10]; Buchner [2]). Also anti-roll tanks, in-cluding the coupling with ship motions (van Daalen [5]), were investigated.

The Volume Of Fluid (VOF) algorithm as developed by Hirt and Nichols [20] is used as a basis for the fluid advection. The method solves the incompressible Navier-Stokes equations with a free-surface condition on the free boundary. In the VOF method a VOF function F (with values between 0 and 1) is used, indicating which part of the cell is filled with fluid. The VOF method reconstructs the free surface in each computational cell. This makes it suitable for the prediction of all phases of the local free-surface problem.

5.2.2 First results

VOF techniques have been used recently to reproduce model tests and moonpool behaviour observed during sea trials. The simplest ap­proach is the one in calm water, with the vessel sailing at constant speed. The domain around the moonpool is modelled as shown in Figure 20. The real domain taken into account is much larger than shown in order to avoid bottom interaction. A constant inflow condition was given in order to simulate constant ship speed.

First results showed a relatively good reproduc-tion of the physical phenomenon, with flow separation at the leading edge and a clipping vortex entering the back side of the moonpool. The flow separation on the sharp edge can only occur when a disturbance is present, such as a strong velocity gradiënt that occurred at the start of the simulation. When starting in an uniform velocity field (except inside the moonpool), no separation occurred leading to a nice laminar flow over the full domain.

ship direction <

Figure 20: VOF simulation of calm water moonpool oscillation

Flow separation would not occur within the boundary layer within the VOF simulation, as the latter is not correctly modelled. It seems quite important to model the full interaction of the vessel and the moonpool itself. Recent sea trials confirmed that the moonpool oscillations in calm water would increase gradually while the vessel was already at its maximum clam water speed. Increasing moonpool motions would be accompanied by surge and heave motions of the vessel, at about the same frequency of piston oscillations in the moonpool. When repeating simulation with forced heave or surge oscillation, clear flow separation was maintained at the leading edge, while magnifi­cation of water motion was calculated.

The technique seems to model correctly the global physics underlying moonpool behaviour. Recent study [22] confirms the fact that VOF models are suited to solve moonpool problems.

5.2.3 Further developments

Several clear developments must be done to turn these first simulations into proven tech-niques that will probably end up in a useful design tooi.

This effort is proposed to be conducted in an upcoming Joint Industry Project initiated by MARIN.

For the calm water oscillation, the following developments should be made:

• coupled version of VOF and ship motion in time domain, in order to obtain the correct heave and surge motions of the vessel;

• update of ComFLOW program to take into account moving body and inflow condi-tions;

• validation of simulation for different moon­pool shapes and speed ranges;

• investigation of 3D effects on moonpool behaviour;

• comparison of existing semi-empirical formulation and advanced time domain VOF techniques;

• development of a general design tooi.

For the stationary case in waves, the following developments should be made:

• introduction of the excitation forces into VOF simulations (excitation being calcu­lated, for example, in the frequency domain thanks to existing codes);

• update of ComFLOW program to take into account moving body and inflow condi-tions;

• validation of simulations; comparison with existing techniques and development of a design tooi.

6 CONCLUSIONS

For many years moonpool motions have been studied. These studies have allowed to identify the excitation mechanism both in calm water and in waves. Despite these efforts, solutions are still found in an empirical way thanks to model testing, intuition and trials and errors.

New numerical developments using VOF techniques may yield improvements in the numerical prediction of potential problems and in a better design of the moonpool at an early stage of the project. Early identification of the problems could allow an early detailed design of efficiënt solutions thanks to advanced numerical techniques.

LITERATURE

[1] Aalbers, A.B.; "The water motions in a moonpool", Ocean Engineering, Vol. 11, No. 6, pp. 557-579, 1984.

[2] Buchner, B., Bunnik, T.H.J., Fekken, G. and Veldman, A.E.P.; "A numerical study on wave run up on an FPSO Bow", OMAE200I, Rio de Janeiro, 2001.

[3] Covert, E.E.; "An approximate calculation for the onset of cavity oscillations", A1AA Journal, Vol. 8, No. 12, pp. 2189-2194, 1970.

[4] Cotteleer, A.; "Experimental study on water motion in a moonpool caused by forward speed of the ship", Master Thesis, Delft University of Technology, The Netherlands, 2000.

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