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Dynamics of floating structure and model testing

Day1AM 1

Current

Open ocean current at the sea surface The most common categories of current are:

• wind generated currents • tidal currents (associated with astronomical tides) • circulational currents (associated with oceanic circulation patterns) • loop and eddy currents • soliton currents

Total current = Vector sum of the above Speed and direction of the current at specified depths represented by a current profile. Steady Uniform Current Current is turbulent, but approximated by a mean flow. For the design value, a 100-year current is often chosen. Wind generated current velocity at water surface is

U = 0.015 UW UW = 1-hr mean wind speed at a 10m elevation Steady Shear Current ♦ Current may vary with water depth. ♦ Shear current is generally linear or bilinear with depth. ♦ In shallow water the current profile is logarithmic due to bottom shear.


Day1AM 2

Environmental conditions at several deep water sites [Moros and Fairhurst, Offshore,

April (1999), Courtesy BP]

Atlantic FrontierFaeroe - Shetland Channel

Brazil(Foz de Amazon)

West Africa(Girassol)

Wind 40.0m/s20 50

Wind 19.0m/s10 40

Wind 20.0m/s10 40

Surface Current 1.96m/sSurface Current 1.50m/sSurface Current 2.5m/s

Seabed Current 0.63m/s



Max Temp = 18.5°C

Min Temp = -1.5°C

Max Temp = 30.0°C

Min Temp = 4.0°C

Max Temp = 28.0°C

Min Temp = 3.0°C

WavesWavesWaves

Hmax 32.7m

Hs 18.0mHmax 7.5mHs 4.0m

3000m

2000m

1000m

0m

Water Depth1000m

Water Depth1350m

Water Depth3000m

Gulf of Mexico(Hurricane / Loop)

Wind 42.0m/s

20 50

Max Temp = 30.0°C

Min Temp = 4.0°C

Waves

Hmax 23.2mHs 12.5mHmax 9.0mHs 4.9m

Wind 30.9m/s

Surface Current 1.10 m/s / 2.57m/s

Seabed Current 0.1 m/s / 0.51 m/s

Submerged Current 1.1 m/s

Water Depth3000m

Hs 6.0mHmax 11.4m

Northern NorwayNyk High

Ormen LangeWind 38.5m/s

20 50

Surface Current 1.75m/s


Max Temp = 14.0°C

Min Temp = -1.5°C

Waves

Hmax 30.0m

Hs 15.7m

Water Depth1500m


Day1AM 3

Interaction of Current and Wave Current alters the shape and size of the waves. ♦ Wave kinematics are modified for waves on a superimposed steady current. ♦ The wave period is modified to an apparent period by the free-stream current

velocity. ♦ A current in the wave direction stretches the wavelength and opposing current

shortens it. ♦ This phenomenon is known as Doppler shift. ♦ The frequency is related to apparent frequency by the Doppler shift as

kUA += ωω The last term in the above equation is called the convective frequency.

where ω = wave frequency in the absence of current k = wave number, U = steady current speed, ωA = 2π/TA, where TA = apparent period seen by an observer moving with the current

Apparent wave period due to Doppler shift in steady current

0.8

0.9

1.0

1.1

1.2

1.3

-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020 0.025

U/gT

TA/T

0.010.020.04>=0.1


Day1AM 4

In deep water (tanh kd = 1) in uniform current, the wave number is related to the wave frequency by the relation

22/1

2

])/41(1[/4

gUgk

ωω

++=

Note that when U is positive (current in the same direction as the waves), the value of k is smaller so that the wavelength is larger (stretched wave). When U is negative (current opposing waves), k is larger and the wavelength is shorter.

Horizontal water particle velocity in waves plus current with and without interaction

wave amplitude, a = 0.25 in (6.3 mm), period T = 1.12 s

water depth = 0.37ft (114mm)


Day1AM 5

Wind & Wind Spectrum The wind effect on an offshore structure becomes important when the superstructure (portion above the MWL) is significant. Effects of wind: ♦ Mean speed and ♦ Fluctuation about the mean ♦ directionality of the wind Wind Speed Reference height = typically 30 feet (10 meters) above the mean (still) water level. Steady wind speed = average speed over one-hour duration Variation of wind speed at a given elevation z

125.0

),1(),1(

⋅=

RRww z

zzhrUzhrU

z = elevation of the wind center of pressure above SWL, zR = reference elevation taken as 10m, Uw(1hr, zR) = one hour mean wind speed at the reference elevation.


Day1AM 6

Wind Spectrum Wind has a random time-varying part over a mean speed. According to American Petroleum Institute guideline (API-RP2A, equation 3.3.2-5), the wind frequency spectrum is described by

3/5

2

5.11

))(()(

+

=

pp

w

fff

zfS σ

S(f) = spectral energy density, f = frequency, fp = peak frequency, and σw(z) = rms (standard deviation) wind speed.

Recommended range of fp is:

1001

010 .),(

coefff. p ≤⋅

=≤zhrU

zf

w

p

Generally, fpcoeff is taken as 0.025. The standard deviation of the wind speed is given by

SS

w

SS

w

w

zz if zzzhrU

zz if zzzhrU

z

>

≤

= −

−

275.0

125.0

15.0*),1(

15.0*),1()(σ

where zs is the thickness of the ‘surface layer’ and is taken as 20 m.


Day1AM 7

Power Spectral Density (PSD) of wind speed

0

50

100

150

200

250

0 0.02 0.04 0.06 0.08 0.1f

S(f)

f = frequency, Hz S(f) = spectral value at 10 m elevation, (m/s)2-s

For

fpcoeff = 0.025 Hz Uw(1hr, zR) = 20 m/s

Note above that the wind spectrum has low frequencies and is very wide-banded.


Day1AM 8

Construction process, launching and operations

Construction of a Fixed Open Bottom Piled Storage Tank

Towing by Tug with change in draft


Day1AM 9

Submergence of Tank by Ballasting

Running Pile from Derrick Barge


Day1AM 10

Submersible Drilling Rig for Gulf of Mexico

Model test for submergence


Day1AM 11

Construction of the Spar (Technip Offshore)

Offloading of Spar Hull for Transport (Dockwise)

Truss Spar in Dry Tow

Holstein Spar being towed out of site


Day1AM 12

Brutus TLP

Spar Upending Sequence (Kocaman et al, 1997)


Day1AM 13

Spar Mooring Line Hookup (Kocaman et al, 1997)


Day1AM 14

Derrick Barge Setting Deck on Spar Platform (Technip Offshore)

Holstein Spar in place being outfitted


Day1AM 15

ThunderHorse being launched

ThunderHorse being Towed to place


Day1AM 16

Seastar® fabrication, Louisiana (SBM Atlantia)


Day1AM 17

FPSO design

Installation of the lower turret on FPSO Balder

APL Buoy Turret System


Day1AM 18

Rendition of the new bridge left of the existing bridge

Final Drafts of Caisson Showing the Mooring Lines Attached


Day1AM 19

Current Flow past New Caisson behind the Roughened Pier

Location of the Immersed Tunnel of the Busan-Geoje Fixed Link

Immersion of TE into trench


Day1AM 20

Physical Testing of Rigs Moored above the Trench


Day1AM 21


Day1AM 22

Design tools and evaluation techniques

– Assessment of static and dynamic stability

Hydrostatic Loading and Stability Buoyancy Static equilibrium of a floating vessel influence of two forces: weight and buoyancy. Center of Gravity = Weight (mass) center of the body, about which the weight (mass)

distribution is balanced (zero weight moment). Weight = Product of mass and gravitational acceleration. It acts downwards

through the center of gravity. Buoyancy = Weight of the displaced volume of water )(∇ by the body generally,

at its equilibrium position. It acts upwards through the center of gravity.

When a vessel is floating freely, these two forces must act along the same vertical line and counteract each other.

BW

Stability

Ability of a system to return to its undisturbed position after external force is removed.

The higher the value of the righting capacity (moment), the higher is the stability of the vessel. Consider the following two examples: 1. Box barge


Day1AM 23

The displaced volume is given by LBT=∇

LB

T

Displacement of a prismatic structure

2. Ship shaped The displacement of a ship-shaped vessel is difficult to compute as the ship is contoured. Usually it is obtained by rigorous calculation from the ship contour charts. However, for additional computational purposes, each ship type is represented by an equivalent block coefficient with a prismatic box based on the ship width (beam) length between its perpendiculars and the floating draft.

BLBTC=∇ CB is the block coefficient of the vessel.

LT

B

Displacement of a ship

Transverse stability Stability is determined by the points of action of weight (the center of gravity) and buoyancy (center of buoyancy) and the horizontal distance and relative position between the two. Examine the two cases in the following figure.


Day1AM 24

Case 1 is stable --net moment tends to right the body Case 2 is unstable -- net moment tends to destabilize the body

Positive and negative stability

W B B

W

Case 1: Positively stable Case 2: Negatively stable or unstable

W

L

W L1G

B B

M

K

z

Righting Moment of the Vessel & Metacenter Defined

K = keel (bottom point/line) of the vessel, G = point of action of weight, i.e. center of gravity, B = point of action of buoyancy, i.e. center of buoyancy. Let us assume that the vessel heels by an angle given by θ. This amount of heel moves part of the body above water and a part that was above below the water. The result is that it shifts the center of buoyancy from B to B1. At this orientation the couple acting on the vessel is given by


Day1AM 25

GZWM ×= Metacenter M

The metacenter is the point of intersection between the line of action of buoyancy force (vertical) and the centerline of the vessel in its inclined position. Thus the metacenter changes its position with the angle of inclination of the vessel, hence the name metacenter.

M = Intersection point of buoyancy line and centerline, i.e. Metacenter. The metacenter can be likened to the center of oscillation of a suspended pendulum. Then GM becomes the length of the string, and for the pendulum to swing in a stable oscillation and return to its original position, the center must be above the pendulum. GM = Distance between G and M, i.e. metacentric height. Then the moment becomes

θsinGMWM ×= when M is above G the moment is righting. If it is below it is overturning and the vessel is unstable. Metacentric height follows from the above figure:

KGBMKBGM −+= where KB = distance from vessel keel to the centers of buoyancy KG = distance from vessel keel to the centers of gravity BM = the distance between the center of buoyancy and the metacenter: For an inclination of less than 15 deg,

∇= xxI

BM

Ixx = second moment (moment of inertia) of the waterplane cross-sectional area about the x-axis (middle line). GM > 0 -- floating system positively stable


Day1AM 26

For a submerged object to be stable, the center of gravity must be below the center of buoyancy. But since the point of action of buoyancy is fixed along the line of gravity and does not change, the metacenter is B itself. The criterion GM > 0 thus still holds well. Typical GM values for a semi-submersible is 6 m, and a FPSO in ballast around 3 m. Longitudinal stability

Longitudinal stability of a ship

GB

B

Ml

longitudinal metacentric height (similar to the transverse case,):

KGBMKBGM ll −+=

∇= yy

lI

BM

where Iyy = second moment of waterplane area about the y-axis For a typical vessel, since BMl is an order of magnitude larger than (KB – KG), we can assume ll BMGM ≈ Types of stability for a floating vessel:

♦ Stable in the static condition (e.g. due to a steady wind force), ♦ Stable in the dynamic condition (e.g. when a sudden gust blows along with a

steady wind),


Day1AM 27

♦ Reserve stability in case the vessel suffers a damaged condition, e.g., when one of its compartments is flooded.

A floating ship or a FPSO is very stable longitudinally compared to the transverse plane. On the other hand, the transverse stability of a ship is much less and the ships often capsize, if they are caught in a large transverse wave. The fishing vessels are particularly vulnerable in such waves in the sea. Example: compute righting moment versus heel angle Square cylinder of 50 ft side and 100 ft draft with a 50 ft freeboard CG of the cylinder = 60 ft below the waterline.

Rotated Geometry of a Simple Floating Structure for static stability

Assume vessel is rotating about the point of intersection of still water level as the pendulum point The line of action of the gravity force of the object as shown in Fig. Three separate sections

– the original volume, – inclined position at small angle with the top out of water and – inclined position at large angle with the top partly in water.

The calculation in two parts – a rectangular block and triangular section.


Day1AM 28

Figure 4.8 Locations of CG and CB

The stability curve for the floating circular cylinder is shown in Fig. Curve is continued until the moment becomes zero at an angle of 80 degrees. Note that the curve corresponding to the approximate formula matches the complete curve for an angle up to 15 deg well.

Arctic SPAR

-5.00E+080.00E+00

5.00E+08

1.00E+091.50E+09

2.00E+09

2.50E+09

3.00E+093.50E+09

4.00E+09

4.50E+09

5.00E+09

0 20 40 60 80 100

Angle of Tilt, deg

Rig

htin

g M

omen

t, ft-

lbs

Righting Moment - STAB

W*GM*theta

Comparison of Righting Moment

Righting Moment Curve for an Arctic Spar Concept


Day1AM 29

Dynamic stability Stability requirement to withstand a sudden environmental change, e.g. a gust of wind. Example of a 30,000 t displacement cargo vessel

righting moment distribution (product of buoyancy and righting arm). heeling moment caused by a steady 100-knot wind.

Dynamic stability curves for a 30,000t cargo vessel

0 15 30 45 60 75 90

A

BC

Righting Moment

Heeling Moment

2nd

Intercept

Mom

ent

Heel Angle

If A, B and C are the designated areas, such that (A+B) is the area under the righting moment curve up to the dotted line (called the second intercept) and (B+C) is similarly the area under the heeling moment curve up to the second intercept. Then the ABS rule requirement implies

)(4.1)( CBBA +>+ The 40% excess is a safety limit, and denotes the work required to be done by an external force (in addition to the heeling moment) to capsize the vessel. For semi-submersibles, the excess requirement is 30%.


Day1AM 30

Stability in damaged condition A vessel should be compartmentalized sufficiently to withstand flooding from the sea of any one main compartment. Further, in the damaged condition, the vessel should have sufficient stability to withstand a 50-knot wind (ABS MODU rules). The final waterline in the damaged condition is to be below the lower edge of any opening through which downflooding may occur. Flooding of a compartment results in sinkage as well as trim. There are two methods of assessing stability in this condition: Lost Buoyancy Method:

Flooded volume treated as lost underwater volume loss of water plane area calculated sinkage and trim estimated iterations carried out to get final position of vessel

Added weight method

flooded water treated as added weight new displacement and KG evaluated corrections for water plane area lost and displacement adjusted up to sinkage

condition repeat calculation to get convergent results

Both methods are equivalent. Other considerations Partially filled tanks affect stability. Half-filled tanks shift liquids when the vessel heels, thus moving G. This creates an adverse effect of decreasing stability. If the liquid cargo has density ρc, then the metacentric height is corrected to include effects of all partially filled tanks:

∑ ∇−= xxc iGMGM

ρρ)new(

For crane vessels operating offshore, when a load w is lifted from deck, the metacentric height changes by

∇−=

ρwhGMGM )new(


Day1AM 31

where h is the distance of the crane tip from the deck level. Effect of Flooded Column The stability rules are intended to prevent catastrophic loss of a vessel, even if a compartment floods. The semisubmersible P-36 was lost after an accidental flooding due to explosion in one of the columns Each maritime catastrophe leads to an investigation and rule review, which often results in new standards. As a result of the P-36 accident, a new rule have been proposed to have reserve buoyancy on the deck of semisubmersibles, and to prevent storage of hydrocarbons in columns meant for stability.

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