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Dynamics of floating structure and model testing

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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.

  • Dynamics of floating structure and model testing

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    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

    Seabed Current 0.50m/s

    Seabed Current 0.30m/s

    Max Temp = 18.5C

    Min Temp = -1.5C

    Max Temp = 30.0C

    Min Temp = 4.0C

    Max Temp = 28.0C

    Min Temp = 3.0C

    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 = 30.0C

    Min Temp = 4.0C

    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

    Seabed Current 0.49m/s

    Max Temp = 14.0C

    Min Temp = -1.5C

    Waves

    Hmax 30.0m

    Hs 15.7m

    Water Depth1500m

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

    where = wave frequency in the absence of current k = wave number, U = steady current speed, A = 2/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

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    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

    ++=

    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)

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    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.

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    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

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

    Recommended range of fp is:

    1001

    010 .),(

    coefff. p = zhrUzf

    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()(

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

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    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.

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    Construction process, launching and operations

    Construction of a Fixed Open Bottom Piled Storage Tank

    Towing by Tug with change in draft

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    Submergence of Tank by Ballasting

    Running Pile from Derrick Barge

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    Submersible Drilling Rig for Gulf of Mexico

    Model test for submergence

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    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

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    Brutus TLP

    Spar Upending Sequence (Kocaman et al, 1997)

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    Spar Mooring Line Hookup (Kocaman et al, 1997)

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    Derrick Barge Setting Deck on Spar Platform (Technip Offshore)

    Holstein Spar in place being outfitted

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    ThunderHorse being launched

    ThunderHorse being Towed to place

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    Seastar fabrication, Louisiana (SBM Atlantia)

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    FPSO design

    Installation of the lower turret on FPSO Balder

    APL Buoy Turret System

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    Rendition of the new bridge left of the existing bridge

    Final Drafts of Caisson Showing the Mooring Lines Attached

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    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

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    Physical Testing of Rigs Moored above the Trench

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  • Dynamics of floating structure and model testing

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    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

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    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.

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    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 . 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

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    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

    sinGMWM = 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,

    =xxIBM

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

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    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),

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    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.

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    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

  • Dynamics of floating structure and model testing

    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

    2ndIntercept

    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%.

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    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 c, then the metacentric height is corrected to include effects of all partially filled tanks:

    = xxciGMGM

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

    = whGMGM )new(

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    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.