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Ttitle: ROLL MORIONS OF FPSOs

Number:

Area: HYDRODYNAMICS

Authors: Daniel Cueva / Fernando Faria

PDF processed with CutePDF evaluation edition www.CutePDF.com

1 ROLL MOTIONS OF FPSOs

Summary 1. BACKGROUND ........................................................................................................................... 3

2. MOTION CAUSES ....................................................................................................................... 4

2.1. ENVIRONMENTAL ASPECTS ................................................................................................ 4

2.2. LOADING ASPECTS ............................................................................................................. 5

3. MOTION CONSEQUENCES .......................................................................................................... 7

3.1. COMFORT ON BOARD ........................................................................................................ 7

3.2. EFFECTS ON TOPSIDE ......................................................................................................... 7

3.3. GREEN WATER ................................................................................................................... 8

3.4. EFFECTS ON RISERS ............................................................................................................ 8

4. ROLL HYDRODYNAMICS ........................................................................................................... 10

5. DAMPING PROBLEM ................................................................................................................ 11

5.1. FREE OSCILLATION TESTS ................................................................................................. 12

5.2. Numerical Simulations of real FPSOs ................................................................................ 13

6. SECOND ORDER EFFECTS ......................................................................................................... 15

7. SUPPRESSION SYSTEMS ........................................................................................................... 18

7.1. ANTI-ROLL TANKS ............................................................................................................. 18

7.2. BILGE KEELS ..................................................................................................................... 20

8. REFERENCES ............................................................................................................................ 23

9. APPENDIX I - DEFINITIONS OF VARIABLES USED IN THE ANALYSIS OF THE STABILIZERS ............ 25


Table 1 - Wave conditions ................................................................................................................. 5

Table 2 - Confort criteria .................................................................................................................... 7

Table 3 - FPSO topside accelerations ................................................................................................. 8

Table 4 - Enlarged bilge keel effectiveness ....................................................................................... 21

Table 5 - Natural period variation due to enlarged bilge keel ........................................................... 21

Figure 1 – Bleo Holm FPSO (Cortesy of Bluewater) ............................................................................. 3

Figure 2 – Munin FPSO (Courtesy of StatoilHydro) ............................................................................. 3

Figure 3 - 2007 FPSO survey............................................................................................................... 3

Figure 4 - Spread Mooring System (DICAS) ......................................................................................... 4

Figure 5 - Single Point Mooring (Picture courtesy of Bluewater)......................................................... 5

Figure 6 - Roll of a FPSO ..................................................................................................................... 6

Figure 7 – Green water effects ........................................................................................................... 8

Figure 8 - Weld-on Threaded Connector (Courtesy of RTI Energy System) and Thread and Couple

Connector (Courtesy of Vallourec and Mannesman), for improved strength and fatigue performance

.......................................................................................................................................................... 9

Figure 9 - Hybrid Riser Tower Concept (Courtesy of Stolt Offshore) ................................................... 9

Figure 11 - Nonlinear roll ................................................................................................................. 11

Figure 10 - Decay test example ........................................................................................................ 12

Figure 12 - Model test and numerical test comparison .................................................................... 14

Figure 13 - Wave spectrum .............................................................................................................. 17

Figure 14 - Roll response spectrum .................................................................................................. 17

Figure 15 - Anti-roll tank .................................................................................................................. 18

Figure 16 - Comparison of the computed roll response of a typical ship with and without a good

passive roll tank............................................................................................................................... 19

Figure 17 - Comparison of passive and controlled-passive roll stabilizing tanks ................................ 19

Figure 18 - Bilge keel arrangement .................................................................................................. 20

Figure 19 - Bilge keel effectiveness .................................................................................................. 20


1. BACKGROUND

In the last decades, several new technologies were developed in order to fulfill the increasing

demand for deep-water offshore production units. As one of the most successful, the FPSOs

(Floating, Production, Storage and Offloading) were able to mix all the experience in ship operation

with a reliable vessel for oil production.

Figure 1 – Bleo Holm FPSO (Cortesy of Bluewater) Figure 2 – Munin FPSO (Courtesy of StatoilHydro)

The storage capacity and the safety of a big water plane area hull changed the scenario in the

offshore industry, and the concept becomes the standard solution for several applications all over

the world. According to a 2007 survey, there are 113 FPSOs currently in operation and 33 in

construction phase (ref. [26]).

Figure 3 - 2007 FPSO survey

However, the direct application of the technology also introduced new problems. Since most of the

current fleet of FPSOs are composed by converted units, several aspects that should be considered

in an offshore design are left behind, for instance motions in waves.

Excessive roll motions and accelerations are one of the key aspects in FPSO analysis, since they are

directly linked with downtime. The excessive motions of a FPSO are caused not only by severe

environmental conditions, but also due to mild combinations, that may lead the unit to unfavorable

beam seas conditions, in both SMS (Spread Mooring System) and SPM (Single Point Mooring).


2. MOTION CAUSES

2.1. ENVIRONMENTAL ASPECTS

The SMS system is defined by the presence of several mooring lines, which does not allow the unit

to “weathervane”. To weathervane means that the ship can rotate in the horizontal plane (yaw) into

the direction where environmental loading due to wind, waves and current are minimal.

Figure 4 - Spread Mooring System (DICAS)

As a result, SMS are usually applied where the weather conditions are moderate and the current

direction is relatively fixed. However, since the heading is almost permanent, the FPSO will not

encounter head waves all times, and deviations from 15 to 30 degrees are expected. Another

important issue is that, in most cases, the main driver to the heading definition is the mooring loads.

It means that the fixed heading of a SMS system will be specified by the optimum arrangement of

the lines, which is not necessarily the optimum for motion characteristics.

Besides that, the swell conditions are also present, and may result in long period waves hitting the

side of the unit.

In the SPM system a turret is usually used, and the system is able to weathervane about the mooring

point. As a consequence, the unit will be able to rotate and the final equilibrium position will result

in a minimum load in the mooring system, when exposed to waves, wind and current.


Figure 5 - Single Point Mooring (Picture courtesy of Bluewater)

However, even in SPM system critical sea conditions may appear, resulting in large roll motion

amplitudes. In Brazil, for example, simultaneous environmental conditions result in a difference of

wind and wave incidences up to 90 degrees, such as Wind from East and Swell from South. When

the wind speed is high enough to induce the unit’s heading, beam sea conditions will be faced by the

vessel.

Table 1 shows a summary of the sea states for Campos Basin for which the wind speeds were above

5 m/s in order to simulate the conditions for which the vessel’s heading starts to be affected by the

wind. Beam sea states are defined as conditions for which the angle between wind and wave is in

the vicinity of 90 degress.

Table 1 - Wave conditions

Return Period Peak Period (s) Sig. Wave Height (m)

1 month ~10.9 3.0 – 3.5

1 year ~13.0 4.5 – 5.0

10 years ~13.6 5.5 – 6.0

100 years ~14.2 6.0 – 6.5

2.2. LOADING ASPECTS

As a result of the storage capacity, the different loading conditions of a FPSO results in large

variations of draft and natural period. Conventional FPSOs may vary the draft from 8m to 27m, and

the natural roll period from 10s to 15s.

Figure 6 presents the roll RAO curves for different loading conditions of a conventional FPSO.


Figure 6 - Roll of a FPSO

Comparing the values presented above and the metocean information from Table 1, it is possible to

conclude that resonance will be induced, and high amplitudes will be achieved, especially for ballast

condition. Recent full scale monitoring showed that roll motion in FPSOs may achieve 15 degrees

(single-amplitude) in certain conditions (ref. [11]).

Loading and offloading operations are also critical for roll motions, since the ship’s cargo sequence

has direct influence on the metacentric height and the roll restoring moment. It is always desirable

to include intermediate loading and offloading situations on the motions analysis, in order to verify

possible problems.


3. MOTION CONSEQUENCES

The presence of excessive roll amplitudes is responsible for several aspects of the FPSO design and

operationability.

3.1. COMFORT ON BOARD

First point that should be evaluated is the crew performance due to comfort when subjected to low-

frequency vibrations, generally imposed by vessel motions. This oscillation may result in motion

sickness, body instability, fatigue, discomfort and increased health risk. A cumulative measure of

exposure to low-frequency oscillation may be used to provide an indication of the probable

incidence of motion sickness. ABS (ref. [1]) defines the vertical Motion Sickness Dose Value MSDVZ,

in m/s1.5, by the following expression:

𝑀𝑆𝐷𝑉𝑧 = 𝑎𝑧𝑤2

𝑇

0

𝑡 𝑑𝑡

Where azw(t) is the z-axis acceleration as a function of time in meters-per-second squared (m/s2),

weighted by the Wf frequency weighting as defined in BS 6841:1987 and ISO

8041:1990/Amd.1:1999, and T is the duration of the motion in seconds.

The measurements must be taken in 0.1 to 0.5Hz frequency range (2.0 to 10.0s period), and the

following criteria should apply.

Table 2 - Confort criteria

3.2. EFFECTS ON TOPSIDE

The reduction of roll amplitudes is important not only for improving the crew performance, but also

for the performance of installed equipments. Separation equipments, such as production separators,

glycol contractors and deaerator towers, are sensitive to motions. For other equipments such as

rotating equipment, heat exchangers and vessels (without separation function) motions and

accelerations have to be addressed but do not present large problems in the design. Motions have

adverse effects on the separatism performance, especially roll and pitch (ref. [15]). The accelerations

induce secondary flows in the liquid which create waves at the interfaces and dispersion of liquid

phases at the oil/water interface, and extreme motions can cause the shutdown of the production

plant. For optimum separation efficiency the separators are usually located approximately amidships

where accelerations due to pitch are lowest. However, there is no possible position that will reduce

roll induced accelerations.


Table 3 shows the expected accelerations for a process module in a converted FPSOs due to roll

motions in extreme sea states (100 years return period; Campos Basin), based on BV formulations

(ref. [25]).

Table 3 - FPSO topside accelerations

Longitudinal Transversal Vertical

(m/s2) (g) (m/s2) (g) (m/s2) (g)

Centenary Sea State ±0.985 ±0.100 ±4.457 ±0.457 -12.362 -1.260

3.3. GREEN WATER

Another issue that must be considered is the green water effect from the side of the FPSO. As

previously explained, the non-collinear directions of wind, current and waves may induce to green

water, with possible impacts of structure and equipment damage, as well as safety of the crew,

especially amidships and further aft. Additional information may be found in the “Green water from

the side of FPSOs” (ref. [3]).

Figure 7 – Green water effects

3.4. EFFECTS ON RISERS

The FPSOs are less riser friendly units compared to other types of offshore structures, like semi-

submersibles, SPARs, etc. Due to the composition of heave, roll and pitch, usually with natural

periods close to the wave peak period, the vertical motions at riser’s connections are relatively large.

In SPM system, the riser connections are usually located in the fore position, and the pitch motion

becomes the most important issue. In SMS systems, however, the risers are located at the FPSO’s

side, and the roll will induce high vertical motions at the connectors.

Due to the high motions, free hanged flexible risers are the available solution for FPSOs, especially

under harsh environmental conditions, but limitations in diameter, maximum water depth and high

costs may be faced.

Another option is the application of SCRs (Steel Centenary Risers), but the FPSO motions make the

riser design a challenging task. The most critical areas of SCRs directly connected to a FPSO through

flexible joints or stress joints are the strength of the hangoff and the sagbend region, as well as the

fatigue damage of the hangoff region and the touchdown region.


Some alternatives may be considered in order to allow the use of SCRs in FPSO, such as the

improvement of SCR fatigue and strength performance, the reduction of the FPSO motion or the

decoupling of riser and vessel motion, through the use of submerged intermediate structures (riser

towers, submerged buoys, etc) (ref. [18]).

Figure 8 - Weld-on Threaded Connector (Courtesy of RTI Energy System) and Thread and Couple

Connector (Courtesy of Vallourec and Mannesman), for improved strength and fatigue performance

Figure 9 - Hybrid Riser Tower Concept (Courtesy of Stolt Offshore)


4. ROLL HYDRODYNAMICS

First order motions of ships can be obtained by a simple dynamic equation that computes values of

inertia, damping, wave and restoring forces.

A typical roll motion with single degree of freedom can be described as (ref. [36]):

(1)

Where 𝜃 is the roll angle, 𝜃 and 𝜃 are the first and second differentiations with respect to time, i.e.,

angular velocity and angular acceleration. 𝐼 is the mass moment of inertia in roll (considering its

additional part), 𝐵𝜃 is the nonlinear damping moment, 𝐶𝜃 is the nonlinear restoring moment, and

M(t) is the exciting moment by waves.

Various expressions of damping and restoring terms were used to simulate the nonlinear

characteristics of roll motion. The most commonly used representations are:

(2)

where BL and BN are the linear and nonlinear damping coefficients, respectively, and C1 and C3 are

the linear and third-order restoring moment coefficients.

The usual procedure for calculation of the ship motions is the use of the so-called diffraction-

radiation software based on the potential flow theory. The damping calculated by this kind of codes

is linear and related to the wave making.

For linear assumption of the phenomena the expression (2) reduces to:

(3)

I B C M t

B BL BN

C C1 C 3

3

B BL

C C1


5. DAMPING PROBLEM

Linear damping coefficient, or potential damping coefficient, is the one obtained from potential flow

theory and depends on the hull geometry only. Other types of damping that are not evaluated by

this theory must be approximated or obtained from model tests.

These damping sources are identified as a dissipation of energy due to the drag, friction, flow

separation and some other effects.

Its influence is usually obtained from two common procedures (ref. 28):

Free oscillation model tests; Semi empirical methods;

Free oscillation model tests, or decay tests, provides the system natural period and the damping of

the unit. It is possible to say that these tests are the most reliable tool for predicting roll damping of

a unit. Several cares must be taken in order to correct evaluate damping from the time series

obtained from these model testing, as explained below.

Semi-empirical methods are based on an extensive series of model tests which results are fitted to

an empirical formula obtained after combining the model test results with some theoretical

considerations. The Ikeda-Himeno is the most popular method for evaluation of roll damping for

ship like bodies. This method decomposes the total roll damping in several components that

represent different physical phenomena occurring on the hull. The numerical implementation of this

method can be obtained from [13].

Unfortunately it is known that the roll motion is nonlinear. That means that the methods explained

above do not evaluate precisely the correct damping of the unit and other tests are often done in

order to enclose this wave amplitude influence. Regular wave tests, decay tests in waves or forced

roll motions tests in waves are some of the ones that comprises this behavior.

An example of nonlinear FPSO roll damping, due to different wave amplitudes, is shown below. The

hull was tested under regular and irregular waves, and its results were then compared to a

numerical calculation by a diffraction-radiation software.

Figure 10 - Nonlinear roll


Ones can see that different external values of damping were included in the numerical calculations

in order to correctly adjust the nonlinear damping that showed up for the several waves tested over

the body.

5.1. FREE OSCILLATION TESTS

The principles of the method are quite well known. An initial displacement in roll is given to the body

and the time history of the motion is registered.

Figure 11 - Decay test example

The following form of the motion equation is assumed:

(4)

Expression (4) can be re-written as:

(5)

where p1 = B1/I, p2 = B2/I and c = C/I.

i. Linear Damping

The assumption of linear damping considers only the linear damping coefficient. For this reason,

equation (5) is reduced to:

(6)

By assuming a solution of the form and knowing that:

(7)

I B C 0

p1 p2 c 0

p1 c 0

est

C c 2 I n

C

C c


where wn is the frequency natural period of motion.

It's possible to obtain the general solution to equation (6):

(8)

in which x is the magnitude of oscillation at t=0 and ε is the phase angle.

If two consecutive absolute values are given by and , then the logarithmic decrement

is defined as:

(9)

which gives:

(10)

ii. Nonlinear Damping

Since the equation (5) is nonlinear, it is difficult to solve it in a close form. Assuming the damping to

be constant with respect to the amplitude of oscillation, the linear and quadratic damping can be

determined from the relation:

(11)

where Tm is twice the period between and .

Plotting the points obtained and fitting a straight line to them, the values of p1 and p2 are found.

5.2. Numerical Simulations of real FPSOs

The importance of a correct adjust on the roll damping of a FPSO resides on the fact that most

numerical software are based on diffraction-radiation method and its calculus are rely on the

potential flow theory, which means that these do not evaluate nonlinear roll damping of a body.

Once the roll damping of a hull is known, one could simulate numerically the FPSOs behavior under

several mooring and environmental conditions.

Unfortunately, this kind of concordance cannot be achieved in a great number of situations. The

reason for this consists on the extreme difficulty for numerical software to predict some other

behaviors that often occur on a real FPSO, such as:

Green water effects. Slamming effects. Breaking waves effects.

x x0 exp n sin 12

n t

x k x k 1

ln xk ln x k 1

2 2

2

T m

lnxk 1

xk 1

p1

16

3

xk

T m

p2

xk xk 1


It is shown below two examples of simulations where good and bad results were obtained. The cases

were simulated for the same body with different irregular wave conditions. Each condition had its

damping adjusted properly.

Figure 12 - Model test and numerical test comparison

As displayed, the first numerical simulation adjusted well its numerical time series to a time series

obtained from the same wave on an ocean basin. The second time series, however, could not

achieve the same results.


6. SECOND ORDER EFFECTS

As we have already discussed, the presence of large roll motions is induced by the resonance

between the natural period and the sea state peak period. For the new built units, the optimization

of the hull geometry may result in better motion response, and in most cases the natural roll period

is shifted for high periods, outside the high linear wave energy range, usually over 20s.

Although several experiments were carried out around the world in order to confirm this strategy,

FPSOs with roll resonant periods larger than the maximum wave period demonstrated the presence

of roll response in their own wave periods, what is attributed to nonlinear mechanism (ref. [33]).

The second-order wave theory is considered when wave loads occurring at the difference of wave

frequencies must be evaluated, resulting in low-frequency wave loads, that are considered to be the

main source of large period roll motion.

Much work has been done in order to predict the horizontal components of second-order loads,

especially due to the influence in the mooring systems. Two main theories were developed: far field

formulation, based on the momentum principle, and near field formulation, based on the direct

integration of second-order pressure on the hull surface. However, just a few attempts were

developed in order to evaluate the vertical components of second-order loads.

The general formulation of second-order wave loads can be obtained by direct integration of the

second-order pressure on the hull surface of the body's mean position, the first-order pressure in

the intermittent zone around the waterline and the variation of the first-order loads due to the first-

order motions.

The second-order wave load is composed of one part dependent on the quadratic product of the

first-order quantities and another part contributed by the second-order potentials.

The first part forces can be decomposed in two other groups: one being the second-order variation

of the hydrostatic loads due to the first-order motions, dependent only on the hull geometry and

first-order motions; and the other, as given in Ogilvie (1983), being defined as

(12)

in which all involved quantities in the integrand are of the first order as η for the free-surface

elevation, Φ for the velocity potential, X − T + R ∧ r − ζ1 , ζ2, ζ3 for the displacement due to the

translation T − ξ1, ξ2, ξ3 and rotation R − θ1, θ2 , θ3 , and r − x − x0, y − y0, z − z0 for the

position vector with respect to the reference point x0, y0, z0 of rotation. In (12), Γ stands for the


intersection (waterline) of the hull H at its mean position with the mean free surface F z = 0 . The

normal vector n − n1, n2, n3 is positively oriented inwards to the fluid.

Another formulation based on the momentum theorem has been developed by Maruo (1960) and

extended to the moment around the vertical axis by Newman (1967). This formulation involving first

order wave field in the far field is often called far field formulation and it's preferred in practice as it

provides good convergence and stability.

The momentum formulation, equivalent to one given in Newman (1967), is given as:

(13)

written on a surface S∞ located at infinity and its upside boundary Γ∞touching vertically the mean

free surface.

Although both formulations presented above should give equivalent results, the near-field

formulation suffers from poor numerical convergence, as the singularities are present in the velocity

field around the hull area with a sharp variation of geometry like corners. On the other hand, the far-

field formulation is less sensitive to the hull mesh discretization and is numerically robust. However,

the far-field formulation only gives the three horizontal components of loads (ref. [33]).

Under the practical point of view, we may find roll second-order motion amplitudes higher than

first-order, especially when working in high natural period vessels. It is important to highlight that, in

many cases, all numerical analysis are carried out considering only first-order response and

horizontal second-order loads (for mooring and riser evaluation). As a result, the second-order

motions are only going to be verified during model tests, when the flexibility for major modifications

is smaller.

As an example, Figure 14 presents the experimental spectral roll response for a FPSO design with

high natural period. Ones can see that the unit’s response is located far away from the wave peak

period spectrum, which is attributed to nonlinear mechanisms. However, no linear response (first

order) is observed (ref. [12]).


Figure 13 - Wave spectrum

Figure 14 - Roll response spectrum


7. SUPPRESSION SYSTEMS

The non-dimensional roll RAO for a bare hull can be 10 times greater than the wave slope. For that

reason, a control of this roll motions is sometimes needed or desirable. The almost total lack of

inherent roll damping means that small additions to this damping can produce large reductions in

the response.

Since the most severe roll motions occur at resonance, the best way of reducing it is to increase

damping. The most common means of doing so is the installation of bilge keels or, if more control is

desired, the use of special anti-rolling devices.

7.1. ANTI-ROLL TANKS

The application of anti-roll tanks has been considered by a few FPSO projects.

The most common anti-rolling devices are the free surface tank, U-tube tank and external tank,

being the U-tube tank used in most vessels. The subsequent text will discuss the U-tube tank. More

information about these devices can be obtained in ref. [17].

This tank can be passive, controlled-passive or active. Passive ones do not require power or a control

system to operate. Controlled-passive tanks contains a servo-controlled valve system in the air duct

of the system. Active ones generally waste significant power for operating the system.

The liquid inside passive tanks, that are partly filled, flows from tank to tank in response of the roll

motion. The phasing of the roll moments acting on the ship as the result of the fluid motion are such

that they reduce the roll motion close to the natural period of the unit. This device cannot eliminate

the roll motion entirely, since it does not move until the ship moves.

The equations of motion are too complex to derive here, but details can be found in Vast, et al

(1961) or in Webster (1967). A careful analysis of the resulting coupled roll and stabilizer system

shows that the stabilization performance depends principally on five parameters. Additonal

information about these parameters may be found in Appendix I.

Figure 15 - Anti-roll tank


A RAO of a ship in beam seas with and without a stabilizer defined by the parameters is shown

below.

Figure 16 - Comparison of the computed roll response of a typical ship with and

without a good passive roll tank

UNSTABILIZED:

Represents a RAO for a

ship without anti-rolling

device, with a roll damping

ratio of 0.05;

STABILIZED:

For a ship with a good

passive roll tank, for the

parameters shown above;

Controlled-passive tanks are similar to passive tanks, with the exception that the area of the water

cross-over tube is larger in cross section than in the passive one and that it contains a valve that

controls the air flux through the air cross-over duct. In general, this kind of system controls natural

and low frequencies roll motions. Figure 17 shows the comparison between different types of

passive tanks.

Figure 17 - Comparison of passive and controlled-passive roll stabilizing tanks

VALVES OPEN:

Represents a RAO for a

ship stabilized with a

controlled-passive tank

that is not operating;

VALVES ACTIVE:

For a ship with a working

controlled-passive tanks;

PASSIVE TANK:

For a ship with a good

passive tank;


Active tanks generally imply that the system requires the use of machinery of significant power and

is designed to be much more effective in eliminating roll motions than passive systems. For that

reason it consists on a system that detects motions of the ship and predicts the roll moment that will

be applied on an immediate future. With that information, the system applies a roll moment that

will cancel this predicted moment. For U-tube tanks this kind of system usually provides a large lag in

the tank response and requires a great amount of efficiency and power from the pumps for the

system to work properly.

For FPSOs, however, the biggest problem is related to the draft variation. It makes the application of

any anti-roll stabilizing tank a very difficult task, since the natural period of the U-tank system would

have to be tuned all time, changing it from a passive system to an almost active system, with all its

disadvantages. Additionally, any mistake in the anti-roll tank tuning may lead even to an

amplification of the roll motion (ref. [11]).

7.2. BILGE KEELS

The magnitude of roll depends both on the relationship between the FPSO and wave dimension, as

well as the resonant effects. Since modifications on the geometry are usually complicated, especially

in converted units, the influence of damping becomes fundamental. However, the ship shape and

the length over breadth relation results in a small damping in transverse motions, with consequent

great sensitivity to resonant effects. Thus, the first attempt to reduce roll motion can be the

introduction of artificial damping, and bilge keels are the simplest way to do it.

These appendages are usually constructed from flat plates that form a sharp obstruction to the roll

motion. In ships, the height of a bilge keel is usually selected to be such that the tip of the bilge keel

lies within the maximum beam and above the baseline, in order to keep it protected during docking,

drydocking and shallow water sail. The size of the bilge keel also has to be restricted in ships, since it

can increase the forward resistance. Figure 19 presents a comparison of bilge keel effects with

forward speed.

Figure 18 - Bilge keel arrangement Figure 19 - Bilge keel effectiveness

Formulations for damping estimation, based on the model test regression analysis were developed.

Equation 14 presents the zero-speed damping ratio estimation, based on ship and bilge keel

characteristics.


(14)

Where:

ABK is the total area of the bilge keels (port and starboard).

bBK is the width of the bilge keel.

CB is the block coefficient.

d is the distance from the centerline at the load waterline to the turn of the bilge.

L is the length of the ship.

B is the beam of the ship.

T is the draft of the ship.

𝜂 4 is the roll amplitude in radians.

Although the bilge keel effectiveness increases as larger the structure is, there is a limitation due to

the increasing in the advance resistance. However, since FPSOs are stationary systems, there is no

limitation to bilge keel dimensions, which could be enlarged, resulting in two different hydrodynamic

effects: the increase of damping forces and the increase of added inertia.

Several studies had been carried out in order to evaluate the effectiveness of large bilge keels for

FPSO, mostly based on model tests, and results have shown that enlarged keels can produce more

than 100% increase on damping coefficients. Table 4 shows the damping, as a percentage of the

critical damping, for different sizes (widths) of bilge keel (ref. [11]).

Table 4 - Enlarged bilge keel effectiveness

Bilge Keel Width Damping

0.45m 2.46%

0.90m 3.90%

1.80m 6.51%

However, studies have shown that changes on the width are much more effective than modification

on the extension, in terms of extra damping. Some investigations have already discussed about

adverse pitch motions when large bilge keels are extended too far forward.

Attention must be paid for possible effects of added inertia when it comes to very large bilge keels,

which can result in higher natural periods. Table 5 shows the roll natural period variation on a new-

built FPDSO concept after the introduction of a 4m wide bilge keel (ref. [24]).

Table 5 - Natural period variation due to enlarged bilge keel

NATURAL PERIOD (s)

wo/ Enlarged Bilge Keel w/ Enlarged Bilge Keel

Roll 20.74 23.20


As previously highlighted, higher roll natural periods may be useful in terms of detuning the motion

response against the wave energy spectrum, but may lead to undesirable second-order effects.

However, since the motions cased by second-order effects are slow (and drag forces are related to

squared velocity), the effectiveness of bilge keels are smaller.

Additionally, extra-large bilge keels are subjected to high drag forces, which may induce to structural

and construction problems.


8. REFERENCES

[1] ABS; “Passenger Comfort on Ships”, 2001, Houston, USA.

[2] API RP 2SK; “Design and Analysis of Station Keeping Systems for Floating Structures”; Third

Edition.

[3] Buchner, B.; “Green Water on the Bow of FPSOs”, Hydrodynamics of Floating Structures Training

Course, 2007.

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9. APPENDIX I - DEFINITIONS OF VARIABLES USED IN THE ANALYSIS OF THE STABILIZERS

STABILIZER SIZE Effect of variations of stabilizer size on roll stabilization

: Loss of metacentric height caused by the stabilizer (free surface loss).

: Metacentric height with liquid in mid-position.

STABILIZER TUNING FACTOR Effect of variations of stabilizer tuning on roll stabilization

: Natural frequency of the stabilizer.

: Roll natural frequency.

NONDIMENSIONAL STABILIZER DAMPING Effect of variations of stabilizer damping on roll stabilization

Bt : Stabilizer's equivalent linear damping.

Bct :Stabilizer's critical damping.

GM T

GM T0

GM T

GM T0

t

t

n4

t

t

2 g

S'

; S'

0

L A0

Ad

n4

t

Bt

Bct


STABILIZER CAPACITY Effect of stabilizer capacity damping on roll stabilization in short crested random seas

ηs, maximum angle to which the stabilizer can heel the ship with all of the weight in the

stabilizer on one side (static heel angle induced when the fluid inside has moved to one side and completely fills one wing tank).Typical values of

capacity are 2 to 6 degrees.

STABILIZER HEIGHT PARAMETER Effect of variations of stabilizer height on roll stabilization

The following parameters represent a typical good design of a stabilizer:

t

S ' '

S'

S' '

0

Lq

Rd

0.20

t 1.08

t 0.30

S 0.05

t 0.00

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