module 1 : hydrostatics constant flows surfacewaves · november 2007 1 offshorehydromechanics...

November 2007

1

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