Module 1 : Hydrostatics Constant Flows SurfaceWaves · November 2007 1 OffshoreHydromechanics...
Transcript of Module 1 : Hydrostatics Constant Flows SurfaceWaves · November 2007 1 OffshoreHydromechanics...
November 2007
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Offshore Hydromechanics
Module 1 : HydrostaticsConstant FlowsSurface Waves
OE4620 Offshore Hydromechanics
Ir. W.E. de Vries
Offshore Engineering
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1. INTRODUCTION
• Some definitions
• Floater types
• Relevance of hydromechanics
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Floater motions
static dynamic symbol
X : surge x
Y : sway y
Z : heave z
Around X : heel, list roll φAround Y : trim pitch θAround Z : course angle yaw ψ
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Axes convention
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Application
Nearly every offshore design or problem
• DP vessel design
• Semi submersible optimization
• Jacket launch
• FPSO mooring
• Etc. etc.
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2. HYDROSTATICS
• Equilibrium situations
or
• Quasi-static situations
Law of Archimedes : Ευρεκα !!
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Archimedes Law
The weight of a floating body is equal to the weight of the displaced fluid.
The term “displacement” of a floater refers to its weight.
D = ρ g ∇ [N]
∇ = submerged volume [m³]
ρ = specific density of the fluid
seawater : ρ = 1025 kg/m³
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Static internal forces, stresses
Consider external (and internal) pressures and the local loads or weights.
Archimedes applies to complete bodies, not to internal forces.
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Example : drillstring in mud
Effective tension versus
real tension
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Example : drillstring in mud
s mgA L gALρ ρ∆ =
Effective tension versus = 0 when Fz= Fb
Fb
Fz
Fint
m
s
L Lρρ
∆ =
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Floating Stability
The property of floating bodies that keeps them upright.
Offshore : quiet motion behaviour, in particular in roll.
These two definitions are to some extent contradictory !
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Floating Stability
Applications:
• Determine angle of heel due to heeling moment
• Determine shift of center of gravity due to additional mass
• Find center of gravity (inclining experiment)
• Determine static stability curve
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Floating Stability
A floating structure at rest is in:
• Horizontal equilibrium
• Vertical equilibrium
• Rotational equilibrium (!)
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Weight and buoyancy
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Heeling Moment
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Shifting loads
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Shifting buoyancy
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Stabilizing Moment
MS = ρ g ∇ GNφ sin φ= D.GZ
Equilibrium :
MS = MH
Small angle of heel :
sin φ ≈ φGZ = GNφ.φ = GM.φ
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Stabilizing Moment
MS = ρ g ∇ GNφ sin φ= D.GZ
Equilibrium :
MS = MH
Small angle of heel :
sin φ ≈ φGZ = GNφ.φ = GM.φ
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Rectangular barge
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Arbitrarily shaped floater
•At very small angles of heel :
•If side walls are vertical when the unit is floating upright :
(Scribanti Formula)
•Otherwise : compute the position of B in every heeled position
( )2121 tanTI
BNφ φ= +∇
TIBM =
∇
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Static Stability Curve
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Static Stability Curve
Characteristics
• Slope at origin = GM
• Maximum GZ value
• Range of stability
• Angle of deck immersion
• Area under the curve
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Shifting a load
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Liquid loads with free surface