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OTC 8073

The Influence of the Bow Shape of FPSOs on Drift Forces and Green Water Bas Buchner, Maritime Research Institute Netherlands (MARIN)

Copyright 1996. OFFSHORE TECHNOLOGY CONFERENCE

This paper was prepared for presentation at the Offshore Technology Confwane* held In Houston Texas, 6-9 May 1996.

This paper was selected for presentation by the OTC Program Committee foBowfng review of information contained in an abstract submitted by the author. Contents ot the paper, as presented, have not been reviewed by BIB Offshore Technology Conference and are subject to correction by the author. The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference or Its officers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgement of where and by whom the paper was presented.

Abstract In this paper the influence of the bow shape of FPSOs on drift forces and green water loading is studied. Use is made of the results of model tests and diffraction calculations for three different bow shapes: a traditional tanker bow, a sharp alternative bow without flare and the same alternative bow with a significant flare above the still waterline. For the sharper alternative bows the mean wave drift forces and low frequency drift forces seem to be smaller than for a traditional bow. Due to the fact that the wave frequency motions with the alternative bows are larger, it is not clear yet whether the total mooring line loads for this type of vessels will be lower. For the alternative bows the relative motions around the bow are larger. This results in more water on the deck with the alternative bows than with a traditional bow. Also the impact pressures are significantly higher. The results presented in this paper make clear that it is not sensible to optimize a bow of an FPSO on one aspect only.

Introduction With the trend to bring FPSOs to increasingly harsh environments, the problem of solid green water on the bow becomes an important design aspect • . This green water can cause serious damage to the sensitive equipment or superstructure at the bow, as was experienced with operating FPSOs at the North Sea. There are two ways to cope with this problem: protecting critical structures against green water loading or minimizing the occurrence of green water occurrence and its loading. The achieve the last, the bow shape and bow height of the FPSO can be optimized. Especially for new build

FPSOs this is an option, but also for existing tankers optimizations are possible1.

The effect of the bow shape on the occurrence of green water has been a point of discussion for Naval Architects over a large number of years. Some authors report a decrease in deck wetness when a significant flare is applied3 for traditional ships, whereas others find an increase in deck wetness4 with flare. In Ref. 1 the author presented tests with a traditional FPSO tanker with and without bow flare. It was found that for this particular bow the relative motions increase when flare is applied, whereas the water height on the deck decreases slightly. However, it was concluded at that time that this is not per definition a general trend.

It should also be noted that it is not sensible to optimize the bow shape of FPSOs solely on green water loading. The bow shape can also effect other aspects of the design, like the (low frequency) drift forces on the ship and the related mooring forces. A bow optimized on green water loading, can may be increase the mooring forces and vice versa. The effect of the bow shape on the added resistance of sailing ships in waves has been studied by Blok . Detailed published studies on the subject of drift force dependency on the bow shape of moored FPSOs are not known to the author at present.

The purpose of the paper is to . show trends and sensitivities, not to present an optimum bow design.

Study program The purpose of the project was to study the sensitivity of the drift forces and green water occurrence or loading for the shape of the bow of an FPSO. For this purpose model tests were carried out with three different bow shapes of an FPSO with the same main dimensions and stem shape. The different bow shapes are shown in Fig. 1. The first bow shape is a traditional tanker hull with only a small flare in the bow region. The first alternative bow has a triangular shape from ordinate 15 towards to forward perpendicular. This bow shape does not have any flare and has vertical sides from the bilges up to the main deck. The second alternative bow is equal to the first triangular alternative, but from the waterline it has a significant flare.

Of course this variation in bow shape can be considered as relatively large, but it is not unrealistic. It should be noted that

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THE INFLUENCE OF THE BOW SHAPE OF FPSOs ON DRIFT FORCES AND GREEN WATER OTC 8073

this paper does not discuss the stern shape of the FPSO. The stern shape can! in combination with the bow shape, be an important aspect in drift forces on the ship.

During the tests the following signals were measured:

- Translations of the vessel with an optical system - Roll and pitch of the model with a gyroscope - The relative wave motion in front of the bow (Rl) with a

wave probe - The water height on the deck 28.6 m aft of the forward

perpendicular (HI) with a wave probe - The position/velocity of the waterfront over the deck (HV1)

with a horizontal wave probe along the axis of the deck. - The mean pressure on a force panel in a box type structure

33.6 m from the fore perpendicular (Fl) - The forces between the ship and the linear soft mooring

system (FXTOT)

The mooring system consisted of 4 linear springs, which gave the mooring system a stiffness of 224 kN/m in the x-direction. This is a realistic stiffness for a mooring system in the applied water depth of 150 m.

The model tests were carried out in both regular and irregular head waves. The regular wave tests were carried out in wave frequencies of 0.418, 0.483, 0.571 and 0.698 rad/s. As a check of the (non)linearity in the motions or drift forces generally three different wave amplitudes were tested for each wave frequency: 100%, 75%, 25% of the maximum amplitude. The 100% wave amplitude was chosen to investigate green water loading. The 75% and 25% wave amplitudes were chosen to have a good comparison of the motions and drift forces in high and low waves. The irregular wave tests were carried out in a JONSWAP wave spectrum with a significant wave height of 13.2 m and a peak period of 12.9 s. The tests in irregular waves lasted for a period of 3 hours prototype.

The results of these model tests were compared with calculations with a linear diffraction program . In linear diffraction theory the hull shape is only taken into account up to the still waterline. This means that the flare of the second alternative bow is neglected in this type of linear analysis. For linear diffraction analysis both alternative bows are identical. The element distribution for the diffraction analysis is shown in Fig. 2.

Vessel motions and relative wave motions The vessel motions and relative wave motions around the bow are very important parameters in both greenwater phenomena and drift forces.

Although it is not true that every exceedance of the freeboard results in the same height of water on the deck ' , the relative wave motions around the bow can be seen as the input to the green water problem. The relative wave motions are calculated by subtracting the local vertical vessel motion from the local absolute wave motions according to:

u ~ 'x,t ^x.t (1)

For an accurate prediction of the relative wave motions both the ship motions and wave motions should be predicted accurately. The complicated flow of the water onto the deck determines finally the relation between the relative motions and the green water on the deck.

The relative motions are also one of the main contributions to the wave drift forces, as was shown by Pinkster. An accurate prediction of the relative wave motions and their phases is of vital importance to the determination of the drift forces.

Tanker motions and relative motions are nowadays generally calculated based upon linear diffraction analysis. In a diffraction program the exciting forces on the ship due to the undisturbed waves and due to the waves reflected (diffracted) by the vessel are determined. Also the added mass and damping due to the wave generation as a result of the motions of the ship are calculated. A diffraction program is based on the following main assumptions: - The wave input is considered to be sinusoidal - The waves and vessel motions are assumed to be small - The interaction between the structure and die fluid is only

taken into account up to the still waterline. This implies that the bow shape above the waterline is considered to be 'wall sided'

Based upon these assumptions it is possible to linearize the problem. Therefore the relation between the ship or relative motion amplitude and the incoming wave amplitude can for each .frequency be expressed in the frequency domain as a linear Response Amplitude Operator H((u). This RAO can be determined for regular waves as the ratio between the output signal amplitude ua and the input wave amplitude £a, or for irregular waves as the square root of their spectral densities:

Hu(co) = ua(w)

•N

Suu<w) (2) S;;(co)

It is the question whether these linear assumptions hold true for FPSOsin survival conditions. In Figs. 3 through 5 the calculated and measured RAOs of the pitch motions and relative wave motions in front of the bow are therefore given for the traditional bow and the alternative bows with and without bow flare. From the model tests both the irregular wave test results as well as the regular wave test results are shown. For most of the regular wave tests three wave amplitudes were tested (100%, 75%, 25%). The results for these different heights are connected in the figures to indicate the non-linearity in the results.

Observations. If we look to these figures, the following observations can be made: - For the traditional bow shape the diffraction analysis results are in a good comparison with the model test results for the

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OTC 8073 BAS BUCHNER

RAO and phase of both the pitch motions and relative motions in smaller wave amplitudes. - If the wave height increases, as is the case in the irregular survival waves, the calculations seem to overpredict the motions. Especially around wave frequencies with a wave length approximately equal to the ship length {0.5 rad/s), a significant non-linearity is present. From 25% to 100% of the wave amplitude the pitch motion RAO decreases 25%. This non-linearity is also present in the relative wave motions, resulting in the curved Rayleigh distribution plots of the crests in Fig. 6.

- In shorter waves there is a tendency in the measurements of somewhat larger pitch motions than predicted. - For the alternative bows the measured RAOs are also closer to the calculated RAOs for the smaller wave heights. With the wave length equal to the ship length the pitch decreases 30% if the wave height increases. - Although the bow flare of the alternative bow is not taken into account in the diffraction analysis, it is clear from the model . tests that it is affecting the ship motions and relative wave motions. For the alternative bow with flare the differences in the measured and calculated RAOs are larger than without flare. The motions and relative motions are smaller with the bow flare.

- For the alternative bows the difference in measured and calculated phase angles is much larger than for the traditional bow. For the wave frequency of 0.571 rad/s the difference in pitch phase angle with large waves is even 65 degrees. This can have a significant effect on the drift forces and green water loading.

Explanation. Taking into account the behaviour of an FPSO in large waves, the following reasons for the observed differences can be found: - Green water on the deck of the FPSO can influence the vessel motions. In Ref. 2 the author showed that the pitch motions can be influenced significantly by the moment induced by the water at the most forward part of the ship. In short waves (>0.5 rad/s) this green water moment is almost equal to the wave pitching moment. Taking into account the amount of water on the deck, it was shown in Ref. 2 that in short waves the pitch motions can increase as a result of the green water. In longer waves the effect of the green water is smaller and seems to decrease the motions slightly.

- The alternative bow has a very small buoyancy in the bow region. This makes the vessel's pitch motions and relative wave motions very sensitive to variations in loads and non-linearities. This type of variations are for instance caused by the flare which is pushed into the waves, a variation of buoyancy in the stem region and the fact that the bow is coming out of the water in high waves.

In Fig. 7 a direct comparison is made between the measured RAOs for the three different bow shapes. From this figure it becomes clear that the pitch motions and relative wave motions are generally larger for the alternative bow. When flare is

applied for the alternative bow, the motions decrease significantly. The additional buoyancy in the bow region decreases the pitch motions.

The observed non-linearities question the use of linear transfer functions for FPSOs in survival conditions.

Drift forces The linear ship motions, relative wave motions and water velocities in the diffraction analysis are the input for the calculation of the wave drift forces. The wave drift forces are in this way based on the same linear assumptions as the calculation of the wave and vessel motions. The wave drift force is a mean force on the structure in regular waves due to second order (quadratic) effects. In irregular waves the wave drift forces have the low frequency of the wave groups. These low frequency forces determine the low frequency motions of the FPSO in its mooring system. Drift forces are therefore an important aspect in FPSO design.

The mean drift forces are assumed to be quadratic with the wave amplitude. This implies that, when die wave amplitude increases with a certain factor, the wave drift forces increase with the square of that factor. This makes it possible to present the drift forces in a Quadratic Transfer Function Q((u):

Q(co) - 5 * (3)

The calculated drift force QTFs for the traditional tanker and the alternative bow shape are shown in Fig. 8. From this figure it becomes clear that the calculated drift forces are almost the same for the longer wave periods. However, in shorter waves the drift forces for the alternative bow are significantly smaller. The fact that the drift forces in the longer periods are almost equal does not say that the origin of the forces is equal. If we take into account that the major component in the drift forces is dependent on the square of the relative motions, it should be noted that for the alternative bow these relative motions are almost purely due to the vessel motions. Wave reflection and wave radiation do not play an important role in the drift forces for this very thin bow. The bow hardly disturbs the wave field. For the traditional bow the relative motions are not only related to the ship motions. The disturbance of the wave field by die bow due to wave radiation and diffraction also plays a role. In Table 1 the calculated hull pressure contributions (wave frequency pressure) on a point at the bow of the tanker are shown for the two different bow shapes.

In short waves the vessel motions are almost zero and the drift forces are only related to the wave diffraction. The traditional full bow will reflect the waves into the wave direction again, whereas the alternative bow without flare is hardly reflecting in this direction. The resulting drift forces are therefore much smaller for the alternative bow without flare than for the traditional bow.

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4 THE INFLUENCE OF THE BOW SHAPE OF FPSOs ON DRIFT FORCES AND GREEN WATER OTC 8073

Assuming linear ship motions and quadratic drift forces, the drift forces measured during the tests in regular waves can be presented in QTFs as well. In Fig. 9 this is done for the three different bow shapes. The results are shown at four wave frequencies for the three different wave amplitudes used.

If we look to the drift forces on the traditional tanker, it is clear that there is some dependency on the wave amplitude. But in general the measured drift forces are close to the calculated values. This justifies the use of QTFs to determine the drift forces in numerical simulations of mooring behaviour in the preliminary design.

For the alternative bow shapes the situation is different. Fig. 9 shows that the measured drift forces deviate much from the calculations. In the longer wave region the drift forces are lower than predicted. In the shorter waves the forces are, however, significantly larger and also very dependent on the wave height. In fact they increase with increasing wave height.

The reasons for this difference are not investigated in detail at present. However, it is clear that the following aspects play a role: - The pitch motions and relative wave motions of the alternative bows are very dependent on the wave height. With the larger wave heights the pitch motions decrease rapidly. As was mentioned before, the relative motions for the alternative bows are determined by the vessel motions only, diffraction effects are negligible. Taking into account the relation between drift forces and relative motions, this will be an important aspect in the difference.

- Not only the RAO, but also the phase of the calculated pitch motions and relative wave motions is clearly different than measured values. This will influence the balance between the different components in the drift forces significantly6. - The amount of green water is larger for the alternative bow than for the traditional bow. This will in the first place influence the ship motions. In the second place it will effect the relation between the relative motions and the drift forces. Because the deck is lower than the level of the relative motions, a cut-off effect on the drift forces can occur when the water flows on the deck instead of backwards.

This difference between measured and calculated drift forces should be investigated further in the future. The differences make in any case clear that the use of wave drift force' coefficients for the determination of the drift forces in numerical simulations is questionable for this type of bows. Even in relatively low waves the calculated drift forces are different from the measured values. The vessel also seems to react differently on low than high waves (not quadratic with the wave amplitude).

Still it is clear that in the long waves the measured drift forces will be smaller with the alternative bow than with the traditional bow. This is confirmed by the results of the model tests in the irregular waves shown in Table 2. In this condition the vessel starts to oscillate in the soft spring mooring system at its natural frequency. The total force in the longitudinal direction

of the soft spring system can be associated with the total force on the turret in a real mooring system.

The results make clear that the'mean mooring force is the lowest with the alternative bow with flare. The same applies for low frequency oscillations in the mooring system, indicated by the standard deviation. It is, however, not clear yet what the effect of the flare is in shorter waves. The drift forces in this region are a result of the wave diffraction, which is small for a bow with a thin waterline. However, the flare above the still waterline for the alternative bow with flare can on the other hand result in additional wave diffraction. The tests at a wave frequency of 0.698 rad/s show that the drift forces for this bow increase when the wave height increases.

Another point is the effect of the wave frequency motions on the mooring forces. The mooring line loads and turret loads are determined by the combination of the low frequency motions and wave frequency motions of the vessel. It is clear from the presented RAOs that the wave frequency motions are larger for the alternative bows. The relative importance of the wave frequency motions is very dependent on the water depth, environmental conditions and mooring system. Depending on the phase of the wave frequency motions also chain dynamics can play a role . This makes clear that lower drift forces do not imply per definition that the mooring forces will be lower. This should be evaluated for each field specifically.

Green water loading In Refs. 1 and 2 green water loading and its phenomena are studied in detail. Also design aspects, like the breakwater design, were investigated. In Table 3 a number of parameters of a typical impact are shown from that study. The observed loading level needs careful consideration in the design. The present study focuses on the question whether is possible to optimize the bow shape so that the green water occurrence and loading on FPSOs is minimized.

The greenwater occurrence and loading were determined during the present model tests measuring, the relative wave motion in front of the bow (Rl), the water height on the deck 28.6 m aft of die forward perpendicular (HI), the position/velocity of the waterfront over the deck (HV1) and the mean pressure on a force panel in a box type structure 33.6 m from the fore perpendicular (Fl). Due to space limitations the velocity of the waterfront over the deck could not be measured for the alternative bow without flare.

In Table 4 the results are shown of regular wave tests with a period of 11.0 s for the three different bow shapes. In Fig. 6 the relative wave motions in front of the bow are given for the tests in the irregular wave spectrum. The following observations can be made after study of these results.

Relative motions. The relative wave motions for the alternative bows are significantly (20%) larger than for the traditional bow. The relative motions for the bow without flare are only slightly larger than the relative motions for the alternative bow with flare. The last thing is surprising because the pitch motions

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OTC 8073 BAS BUCHNER 5

without the flare are almost 25% higher. This indicates that for the alternative bow with flare there is a significant contribution of the radiating and reflecting waves due to the flare above the still waterline. The flare pushes the water up around the bow when the bow is falling in the waves. With a smaller pitch motion it is therefore still possible to have approximately the same relative wave motions.

Although the relative motions are important, they are not the only aspect in the amount of green water on the deck. In the past it was sometimes assumed that the height of the water on the deck was equal to the exceedance of the freeboard8. If we subtract the freeboard (11.2 m) from the relative motions, we see in the first place that the height of water on the deck is much lower than the exceedance of the freeboard. If we take the ratio between the water height on the deck and the exceedance of the freeboard for the traditional bow, alternative bow with flare and alternative bow without flare we find ratios of 0.47, 0.37 and 0.53 respectively. This makes clear that although the relative motions for the alternative bow with flare are larger, the relative amount of water on the deck itself is lower. This is due to the fact that the flare does not only push the water up, but also away from the bow. This explains the difference between the results for the alternative bow with and without flare.

Impact loads. The impact loads at the structure on the deck are almost three times larger for the alternative bows than for the traditional bow. This is surprising, because the water height on the deck is only slightly different for the traditional bow and die alternative bow with flare (21%). This difference can be explained if we consider the formulations found in Ref. 2 for die relation between the impact forces on one side and the water height on the deck and the velocity of the water front over the deck on the other side. If we consider die typical green water impact at a vertical structure, we can observe that the flow direction is rapidly deflected 90 degrees . This results in a peak pressure at the structure, which has a typical rise time between 0.15 and 0.35 s. The described phenomenon shows considerable resemblance with a jet impinging perpendicularly at a plate. The load of the water at the structure is not due to a solid impact, but due to a jet with an increasing height. The load may therefore be developed as a sequence of quasi-stationary loads due to an impinging jet of an increasing height h. This is a case of classical fluid dynamics. For each time step dt in the initial stage of the impact the incoming momentum of the water flow is destroyed by the impulse of die structure on the fluid according to:

F dt = m U <4>

Based upon the assumption of a constant velocity U of the incoming water flow in the initial stage of .the impact and the shallow water assumption of a constant velocity over the full height h, the impulse will be linear with water height (characterizing the mass) and the velocity at some distance from the structure. Based upon these considerations it is assumed that

die peak force per metre breadth can now be expressed as the rate of change of linear momentum at the moment that the maximum water height at the deck reaches the structure. This can be expressed as:

Fpcak = P "max U 2 (5)

If we now go back to the results in Table 4, we see that the water velocity over the deck is a factor 1.46 higher for the bow with flare (which can be associated with the higher exceedance of the freeboard). The water height on the deck is a factor 1.21 higher. Following expression (5), it may be expected that me load on die structure per unit breadth is 1.462.1.21=2.6 times larger, which comes very close to the actual factor of 2.8.

Deck loading. Another aspect in the green water loading is the load of the water on deck itself. During model tests widi sailing ships much higher deck loads were observed than the static water pressure . Until now it was assumed that the pressure of die water at the deck is equal to the static water pressure , to the static pressure corrected for die vertical acceleration of the deck9

or to the impulsive pressure of a falling breaking wave . In Ref. 2 it was shown mat the first two aspects play a role in the loading on the deck. Falling breaking waves are not observed in green water loading, the flow of the water onto the deck is more related to the dam breaking problem. In Ref.2 it was shown that for sailing ships, like frigates, the impulsive loading on the deck is mainly due to the rate of change of water height on the deck. When the water height at a certain point increases rapidly at the moment that the deck has a vertical velocity, large pressure peaks can occur. This will be explained below.

Basis for this analysis is a cylindrical control volume above the deck. For a control volume, which makes vertical motions, the following relation applies according to Newton's law:

_ d(m.w) , 3 m . ^ , 3w. ,#> dt dt dt

The mass m in control volume is equal to phA. Implementing mis in equation (6), dividing by the area A and taking into account the acceleration of gravity with a pitch inclination angle 8, gives die pressure at the deck:

p = p ( ^ ) w + p(g cos9 + ^ ) h (7)

For sailing ships the first term is very important and die main cause of die dynamic amplification in die deck loads. For sailing ships pressures of even 15 times die static water pressure are found. For moored FPSOs this dynamic amplification will be smaller, but still it is interesting to investigate the pressure on the deck. Using die measured water height on the deck and die ship motions the water pressure on the deck was therefore

393


calculated. In Fig. 10 the time traces are presented, showing: - the .water height on the deck (HI) L - the pitch motion (PITCH) - the static pressure component (FSTATIC) - the pressure due to the vertical acceleration of the deck

' (FACC) - the pressure as a results of the rate of change of water height

on the deck (FHDHDT) - the sum of the static and acceleration pressure (FSTAT+A) - the total calculated force according to expression 7 (FTOT

C)

From this figure it becomes clear that: - For the traditional bow the maximum pressure on the deck is almost equal to the static pressure. The vertical accelerations and velocities are relatively small. Also the velocity of the waterfront over the deck and the related rate of change of water height on each point on the deck are small. - For the alternative bow with flare a dynamic amplification is observed due to the rate of change of water height on the deck. - For the alternative bow without flare the dynamic amplification is both due to the vertical acceleration of the deck and the rate of change of water height on the deck. Due to the fact that the water comes on the deck in an earlier stage, there still is a vertical acceleration of the deck, which is zero or negative for the other bow shapes.

Evaluation The purpose of the project was to study the sensitivity of the drift forces and green water loading for the shape of the bow of an FPSO. This implies that it was not tried to propose the most ideal solution of the lowest green water loading combined with favourite mooring loads. .

If we look to the sensitivities of the drift forces and green water for the bow shape of FPSOs found in this study, the following general conclusions seem justified: - Ship motions, relative wave motions and drift forces are considerable non-linear in wave heights associated with the survival conditions of FPSOs in harsh environments. This type of effects is mainly due the non-linear buoyancy, radiation and diffraction in larger waves (as a result of the bow or stern shape) and the effect of green water on ship motions. The alternative bow seems to be more sensitive to these non-linearities than the traditional bow. Linear diffraction theory can therefore be used in the preliminary design, but the final mooring loads should be determined in the realistic environment during a model test.

- The phenomena in the occurrence and loading of greenwater are even more complex ' . The flow onto the deck and the impact loading can only be described with simple models. More complex models are being developed , but they need considerable further validation and development.

If we look to the behaviour of the three different bow shapes in this study, the following observations can be made with respect

to their motion behaviour, drift forces and green water loading: - For the sharper alternative bows the mean wave drift forces and low frequency drift forces seem to be smaller than for a traditional bow. This can result in lower low frequency mooring loads for this type of vessels. - Due to the fact that the wave frequency motions of the alternative bows are larger, it is still the question whether the total mooring line loads for this type of vessels is lower. Wave frequency motions and possible chain dynamics can be an important part of the total mooring lines force on top of the low frequency motions. This depends on the water depth and the environmental conditions. This needs further study in the future. - For the alternative bows the relative motions around the bow are larger as a result of large pitch motions. This results in more water on the deck than for a traditional bow. - The green water impact forces are the largest for the alternative bow with flare. This is due to the larger .velocity of the green water over the deck for this bow. This makes clear that a bow should not be optimized on the water height on the deck only, but also on the velocity of this water over the deck and the related impact pressures. - As a result of the ship motions and their phase the pressures at the deck are significantly larger than the static water pressure for the alternative bows. For the traditional bow the pressure is almost equal to the static pressure.

The observations above make clear that it is not possible to optimize a bow of an FPSO on one aspect only. A bow optimized on green water loading, can may be increase the mooring forces and vice versa. Further study on the subject is needed to come to tools which are able to predict the studied phenomena. Numerical tools are being developed at present, but they still have significant drawbacks. Their capability to give reliable predictions is not clear yet, they are sometimes very sensitive to small changes in the input and time stepping, they are very time consuming and finally rather costly.

To have reliable information for the design of FPSOs, it is therefore recommended to perform model tests in regular and irregular survival waves with models with different bow (and stern) shapes. Combining these results with the simulation of the wave frequency mooring line loads for different water depths will give valuable input for the design of optimum FPSOs. The optimum design will be different for each combination of environmental conditions, functional requirements and given boundary conditions.

Nomenclature rx t = relative wave motion as function of time and

position in m £x t = undisturbed wave motion as function of time

and position in m zx t = absolute vertical ship motion as function of time

and position in m £a = wave amplitude in m HU(G>) = Response Amplitude Operator at frequency o)

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ua Suu(co)

S K ( Ü »

F((ü) Q(co)

F t

m

U

P h

P w

g e

amplitude of output signal u spectral density of output signal u spectral density of the wave m s

mean wave drift force in regular waves in kN Quadratic Transfer Function at frequency (0

force in kN (or kN per meter breadth) time in s

mass in t velocity of waterfront over deck in m/s density of seawater in t/m

water height on deck pressure in kN/m vertical velocity in m/s gravity acceleration (9.81 m/s ) pitch angle in degrees

References 1. Buchner, B.: "The Impact of Green Water on FPSO Design",

OTC paper 7698, Offshore Technology Conference 95 (OTC'95), Houston, May 1995.

2. Buchner, B. "On the Impact of Green Water Loading on Ship and Offshore Unit Design": PRADS'95, Seoul, September 1995

3. O'Dea, J.F. and Walden, D.A., "The Effect of Bow Shape and Non-linearities on the Prediction of Large Amplitude Motions

4.

6.

9.

10.

11.

and Deck Wetness", 15th Symposium on Naval Hydromechanics, 1984 Lloyd, A.J.R.M., Salsich, J.O. and Zseleczky, J.J., "The Effect of Bow Shape on Deck Wetness in Head Seas", RINA, 1985 Biok, J.J., The Resistance Increase of a Ship in Waves", PhD-thesis Delft University of Technology, 1993 Pinkster, J.A., "Low Frequency Second Order Wave Exciting Forces on Floating Structures, PhD-thesis, MARIN publication No. 600, 1980 De Kat, O.J. and Dercksen, A. "Investigations of the Effect of Spectral Wave Characteristics on the Dynamics of a Turret Mooring System", Proceedings OMAE'93, June 1993 Ochi, M.K., "Extreme Behaviour of a Ship in Rough Seas -Slamming and Shipping of Green Water", Annual Meeting SNAME, November 1964. Hansen, H.J., "Über die Vorhersage von Decksbelastungen durch Grilnes Wasser", Schijf & Hafen 24, 1972. Takezawa, S., Kobayashi, K. and Sawada, K-, "On Deck Wetness and Impulsive Water Pressure Acting on the Deck in Head Seas (in Japanese)", Journal ofZosen Kiokai, SNAJ, Vol. 141,1977. Van Daalen, E.F.G., "Numerical and Theoretical Studies of Water Waves and Floating Bodies", PhD-thesis, University of Twente, 1993.

TABLE 1 - AMPLITUDES OF CALCULATED HARMONIC PRESSURE COMPONENTS AT BOW IN T/M2 FOR A WAVE AMPLITUDE OF 1.0 M

Traditional o=0.483 rad/s

Alternative (0=0.483 rad/s

Traditional co=0.571 rad/s ,

Alternative (u=0.571 rad/s

Undisturbed wave pressure 1.025 1.025 1.025 1.025

Diffracted wave pressure 0.380 0.157 0.84 0.138

Static wave pressure as a result of ship motions

1.487 2.11 0.73 1.257

Radiated wave pressure 0.337 0.332 0.234 0.186

TABLE 2 - TOTAL FORCES IN X-DIRECTION IN THE IRREGULAR WAVE SPECTRUM

Traditional bow Alternative bow with flare Alternative bow without flare

Mean FX force in kN 1571 1200 1261

Standard deviation FX force in kN 3415 3036 3188

TABLE 3 • PARAMETERS OF A TYPICAL GREEN WATER IMPACT

Velocity of water front 17.0 m/s

Maximum water height on deck 5.0 m

Mean pressure on panel 200 kPa

Maximum local pressure 375 kPa

FX global load on structure 10000 kN

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TABLE 4- GREEN WATER OCCURRENCE AND LOADING FOR REGULAR WAVES WITH A PERIOD OF 11.0 S

Traditional bow Alternative bow with flare Alternative bow without flare

Pitch motion 6 in degrees 2.39 2.95 3.49

Relative motion R1 in m 17.5 20.9 21.1

Exceedance of freeboard in m 6.34 9.74 9.94

Water height on deck H1 in m 2.98 3.62 5.23

Water velocity over deck HV1 in m/s 16.0 23.3 -

Mean pressure on panel F1 in kPa 54 151 137

Fig. 1 - The'different bow shapes used during the present study: the traditional tanker bow (left), the alternative bow without flare (middle) and the alternative bow with flare (right)

Fig. 2 - Element distribution for diffraction analysis of the traditional and alternative bows

396


RESPONSE OF PITCH RESPONSE OF R1

IRREGULAR WAVES o CALCULATED • REGULAR WAVES

IRREGULAR WAVES CALCULATED REGULAR WAVES

/** r

• h 0 — i \

\

0 \

v,I

0

T 7^ • ; > ^

° 0 T fi I.

; •

E FREQUENCY IN RAO'S Er4EOUCNC'KnAD4

Fig. 3 - Calculated and measured RAO and phase for pitch and relative motions of the traditional bow

RESPONSE OF PITCH

IRHEOULAH WAVES o CALCULATED * REGULAR WAVES

RESPONSE OF R1


:r*~r

T

a-' I

6

i \

\

\ \

: ° 0

- Ï

y ^ o . - ^

' \ ' h /

1

\

- '.I

WAVE FWOUCNCV • ! UOiS W.Vt fttOJtHCI H «OS

Fig. 4 - Calculated and measured RAO and phase for pitch and relative motions of the alternative bow without flare

397


RESPONSE OF PITCH RESPONSE OF RI



J "^O * o

** ft* o c'

°

0 I

0

•N

\

\ I\

\ .

' I . e e

_yi y

.X--"

' H

/ » \

< l \

•

l

« A r t m t o u t N C » « FAfOUCNCrrHMDiS

Fig. 5 - Calculated and measured RAO and phase for pitch and relative motions of the alternative bow with flare

TRADITIONAL BOW ALTERNATIVE BOW WITH FLARE ALTERNATIVE BOW WITHOUT FLARE

100 99

i -2 95 Ö 90

UJ 60

Z ™ Ü 60

O 50 < 40 a X 20 LU

U.

O 10 >-5 5

-T^-.^ 573401 19.3902 575801 22.7243 577901 22.9002

"~~^-. "--y ̂ 573401 19.3902 575801 22.7243 577901 22.9002

^N ~<>^ 573401 19.3902 575801 22.7243 577901 22.9002 \ <N

573401 19.3902 575801 22.7243 577901 22.9002

\ s^ \ X

\ \ \ V

\ \

\ \ v ^\

\ v* \

\ \ \

Fig. 6 - Rayleigh distribution plot of maximum relative motions in front of the bow

398


RESPONSE OF PITCH

TRAOmONAL BOW ALTERNATIVE SOW WITH FLARE ALTERNATIVE BOW WITHOUT FLARE

RESPONSE OFR1

TRADITIONAL BOW ALTERNATIVE BOW WITH FLARE ALTERNATIVE BOW WITHOUT FLARE

y-! ^ 1 i

I 1 i

\ Vi Vi

I 1 i 1

\ i

i i

V

G

i

i 1 1

i WAVE •BFQUENCV IN KA&S

- ^ s

1 i,

a if

\ „ I

s J I

r V "I

1

»VE f B(OUtNC' K M U S

Fig. 7 - Measured RAO and phase for pitch and relative motions for the three different bow shapes

SO-

•MTTVE BOV t

•

0-

~?"<r-

/ 1 1

1 / / 1

\

1 1

/ /^

~ ' V' /

\ t /

~

—' ...

Fig. 8 - Calculated mean wave drift forces in x-direction for the traditional bow and the alternative bows in head waves

399


0-0-0-

s \ I

0-

\ / ^

1 -I / *

Vt I

\) 11

ISO-

•

r

WBVI *B*i*ncv «n rfed/i i hMViwcr n rev»

Fig. 9 - Measured and calculated mean wave drift forces for the traditional tanker bow (left), the alternative bow without flare (middle) and the alternative bow with flare (right)

'TL ^ ^ fV A^ f

• J V * X ^ X ^ - U , ^ - ^ ,-A o V *

kPa O-O !^KhK:

-jt̂ L*- t^-i

'!tvj

Fig. 10 - Time traces of the different components in the pressure on the deck for the traditional tanker bow (left), the alternative bow without flare (middle) and the alternative bow with flare (right).

400

otc 8073 the influence of the bow shape of fpsos on drift ... · the influence of the bow shape of...

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