How to Estimate Hydrodynamic Coefficients Applicable for Lifting
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Transcript of How to Estimate Hydrodynamic Coefficients Applicable for Lifting
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Classification: Internal Status: Draft
Finn Gunnar Nielsen, Chief Researcher StatoilHydro Research Centre, Bergen
How to estimate hydrodynamic coefficients applicable for lifting from the sea bed.
Subsea Lifting OperationsKranteknisk ForeningTekniske foreningers servicekontorStavanger, 27. 28. november 2007
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2Hydrodynamic coefficients for subsea structuresContent Hydrodynamic mass and damping
Crossing of the splash-zone.
Deeply submerged.
Landing on bottom.
Estimating hydrodynamic coefficients Tabulated values
Simple estimates
Advanced methods
Simulation challenge during lift-off. Example
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3Phases of the installation process1. Lift-off from deck.2. Lift in air3. Crossing splash zone.4. Lowering through the water column5. Landing the structure.
12
3
4
5
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4Subsea template Ormen Lange
L * B * H =
44m *33m *15m
M=1150*103 kg
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5Added mass for simple 2Dforms
Challenge:How to relate such values to real structures?
Key issues:InteractionShieldingPerforationFinite lengthViscous effectsFree surface proximityBottom proximity
Source: DNV RP C205
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6Natural periods (Lightly damped)
Pendulum in air:
Pendulum in water:
( )111 2
m A LT
mg gV
+= ( )22
2 2m A L
Tmg gV
+=
( )333 2
Em A LTEA
+=
1,2 2LTg
=
3 2 EmLTEA
=
1, 2
3
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7Added mass versus damping ? Oscillation of a body in calm water: Added mass:
Force on body in phase with acceleration
Damping: Force on body in phase with velocity ( ) 1 2F m A x B x B x x= + + +
0 5 10 15 20 25 30 35 40 45 50-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
F
t
o
t
PositionForce
Position and total force
0 5 10 15 20 25 30 35 40 45 50-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
F
o
r
c
e
ForceAdded mass force
Total force and added mass contribution
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8Added mass versus damping ?
( ) 1 2F m A x B x B x x= + + +
0 5 10 15 20 25 30 35 40 45 50-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
F
t
o
t
PositionForce
Position and total force Total force and linear damping force
0 5 10 15 20 25 30 35 40 45 50-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
F
o
r
c
e
ForceLinear damping
Oscillation of a body in calm water: Added mass:
Force on body in phase with acceleration
Damping: Force on body in phase with velocity
-
9Added mass versus damping ?
( ) 1 2F m A x B x B x x= + + +
0 5 10 15 20 25 30 35 40 45 50-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
F
t
o
t
PositionForce
Position and total force Total force and quadratic damping force
0 5 10 15 20 25 30 35 40 45 50-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (sec)
F
o
r
c
e
ForceDrag force
Oscillation of a body in calm water: Added mass:
Force on body in phase with acceleration
Damping: Force on body in phase with velocity
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10
Water entry of TOGP template (2000)
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11
Water entry forces, calm water
Vertical hydrodynamic force (positive upwards):
Note: A33 from high frequency limit
V
2333 33h z z
dAF gV A U Udh
= + +
z
xz = 0
h
Uz
Hydrostatic Added mass SlammingWater entry
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12
Water entry forces, including waves
Vertical hydrodynamic force:
z
x
V
z = 0 h
( ) ( )( ) ( )
2333 33
1 2
hdAF gV V Adh
B B
= + + + + +
Water entry termPosition dependent added mass
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13
Added mass for simple structures.Horizontal circular cylinder
-1 -0.5 0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 Added mass for horizontal 2D cylinder. = 0 at z = 0
Submergence h/r
A
3
3
/
r
2
Analytical expressionsAsymptotic values
-1 -0.5 0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Derivative of A33 for horizontal 2D cylinder.
= 0 at z = 0
Submergence, h/r
(
d
A
3
3
/
d
h
)
r Numerical differentiationAsymptotic value
h
2R
=0
3
-
14
Close to bottom No action from waves Modified water entry / slamming term Added mass for body close to fixed wall (Zero frequency limit)
-
15
Vertical force close to bottom
2333 33 3 3
1 3 2 3 3
0.5=
hdAF gV Adh
B B
h
2R
3
33 0dAdh
-
16
A33 2D cylinder close to bottom
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30
0.5
1
1.5
2
2.5Added mass for horizontal 2D cylinder. d/dz = 0 at z = 0
Centre distance from wall h/r
A
3
3
/
r
2
2/3-1
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17
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51
1.5
2
2.5
3
3.5
4
4.5
5
h/R
A
3
3
/
R
3
WAMIT results for t/R=0.05Asymptotic results for h/R1
Circular disc close to bottom
Far from bottom h/R >>1:
Close to wall (Vinje 2001):
333
83
A R=
33 as h 0A
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18
Perforated plate, circular hollows, potential theory Plate L*B = 15m*10m
(0) 233 0.625A LB=
-
19
Suction anchor Fully submerged, no ventilation (a=0):
2R
2a
H2
11
233
, = 0.6 - 1(plus enclosed water)
413
A R H
RA R HH
=
+
-
20
Suction anchor Fully submerged, with ventilation, a > 0:
2R
2a
H
A2XH
KC =
-
21
Partly submerged, with ventilation Free air flow
Restricted airflow?
Suction anchor
2R
2a
H
33 0A
-
22
Templates with cover and mudmats.Range of experimental results
-
23
Protection cover made from tubular members. (approx 14 * 19m) (perforation ratio 0.27)
-
24
Computed and measured (forced oscillations) added mass. Protection cover
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5KC
C
a
Measured
Perforated plate
Sum of cylinders w/ interaction
2 AXKCB
=
-
25
Theoretical method. Horizontal circular disk
z R
a
z = d
z = h 3.
2.
1.
Disk
Circular disk, perforation ratio,
Restricted flow through disk
Pressure drop proportional to velocity squared.
Porous KC number:
2
1porKC KC
=
-
26
Estimated and measured damping including estimate on the effect of the edge vortex. Hatch 18 (perforation 0.25).
0 1 2 3 4 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
KCpor
C
b
Hatch 18
TotalMeasuredMeasuredMeasuredperforationEdge effect
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27
Total force on hatch 18
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
KCpor
F
t
/
2
R
4
Hatch 18
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28
Installation of gravity anchor. Use of method Molin & Nielsen(2004)
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29
Model. Solid top, open top.
H = 3.42mR = 3.77m
-
30
Comparison with model tests. Suction anchor with central hole in top plate.
0 2 4 6 8 10 120
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Perforation ratio %
C
A
KC= 1.2KC= 1.2KC= 0.6KC= 0.6KC= 0.1KC= 0.1
A2XH
KC =
Red: MeasuredBlue: Computed
2R
2a
H
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31
Added mass and linearized damping
332Rm
ACH
= 332RbBC
H=
( ) ( ) 12 2 22 33 331
2 2 2 22
Rb
tot A
a A
F A B X
C C X H
= + = +
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32
Added mass and damping, fully submerged, 12.2% open area.
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
KC = 2XA/H
A
3
3
/
(
R
2
H
)
Linearized A33, R=3.949 m, d/H=5.8548, R/H=1.156
T=8 sec
Asymptotic value: CA0 = 1.99
0 0.5 1 1.5 2 2.5 3 3.5 40.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
KC = 2XA/HB
3
3
/
(
R
2
H
)
Linearized B33, R=3.949 m, d/H=5.8548, R/H=1.156
T=8 sec
-
33
Added mass and damping, fully submerged, 12.2% open area.
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
KC = 2XA/H
A
3
3
/
(
R
2
H
)
Linearized A33, R=3.949 m, d/H=5.8548, R/H=1.156
T=8 sec
Asymptotic value: CA0 = 1.99
0 0.5 1 1.5 2 2.5 3 3.5 40.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
KC = 2XA/HB
3
3
/
(
R
2
H
)
Linearized B33, R=3.949 m, d/H=5.8548, R/H=1.156
T=8 sec
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34
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
2.5
KC = 2XA/H
A
3
3
/
(
R
2
H
)
Linearized A33, R=3.949 m, d/H=10.4169, R/H=1.156
T=8 sec
Effect of bottom proximity (1.0 and 0.25m from bottom)
0 0.5 1 1.5 2 2.5 3 3.5 40.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
KC = 2XA/H
B
3
3
/
(
R
2
H
)
Linearized B33, R=3.949 m, d/H=10.4169, R/H=1.156
T=8 sec
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
2.5
3
KC = 2XA/H
A
3
3
/
(
R
2
H
)
Linearized A33, R=3.949 m, d/H=10.6364, R/H=1.156
T=8 sec
0 0.5 1 1.5 2 2.5 3 3.5 40.2
0.4
0.6
0.8
1
1.2
1.4
1.6
KC = 2XA/H
B
3
3
/
(
R
2
H
)
Linearized B33, R=3.949 m, d/H=10.6364, R/H=1.156
T=8 sec
Added mass Damping
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35
Effect of free surface proximity (2.5 and 1.25m from free surface)
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
KC = 2XA/H
A
3
3
/
(
R
2
H
)
Linearized A33, R=3.949 m, d/H=0.73185, R/H=1.156
T=5 secT=8 secT=12 sec
0 0.5 1 1.5 2 2.5 3 3.5 40.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
KC = 2XA/H
B
3
3
/
(
R
2
H
)
Linearized B33, R=3.949 m, d/H=0.73185, R/H=1.156
T=5 secT=8 secT=12 sec
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
2.5
KC = 2XA/H
A
3
3
/
(
R
2
H
)
Linearized A33, R=3.949 m, d/H=0.36593, R/H=1.156
T=5 secT=8 secT=12 sec
0 0.5 1 1.5 2 2.5 3 3.5 40.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
KC = 2XA/H
B
3
3
/
(
R
2
H
)
Linearized B33, R=3.949 m, d/H=0.36593, R/H=1.156
T=5 secT=8 secT=12 sec
Added mass Damping
-
36
Lift and drag force close to bottom (DNV RP C205)
-
37
Example: Intermediate phase of jacket installation
Four legs with mudmats, (circular plates).Platform stable before piling?
Fwave
-
38
Plate close to bottom
R: Radius of plate.h : Gap.V: Vertical velocity.
-
39
Added mass. Circular plate close to bottom
4 3
33
333
R 8 R 5 R hA log for 18 h h 3 2 R8 hA R for 13 R
= + =
-
40
Dynamic equation.
( ) ( )23333 B 3dA1m A V V F kh F g mg2 dh+ + + + = +
Inertia Slamming damping Spring External Netforce buoyancy
B D
B
1F C V V2
F BV
= =
Damping:
Quadratic:
Linear: Details:Nielsen 2007: Lecture notes in Marine operations, NTNU,
-
41
0 1 2 3 4 5 6 7 8 9 100
5x 106
R= 4 h0= 0.05
A
3
3
(
k
g
)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0
x 107
d
A
/
d
h
(
k
g
/
m
)
0 1 2 3 4 5 6 7 8 9 10-5
0
5x 107
t (sec)
F
(
N
)
Wave period 13.3sec, Fa = 22MNInitial clearance 0.05m
Lift force >0
0 1 2 3 4 5 6 7 8 9 10-2
0
2R= 4 h0= 0.05
V
(
m
/
s
e
c
)
0 1 2 3 4 5 6 7 8 9 100
5
10
h
(
m
)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0
1
t (sec)
d
V
/
d
t
(
m
/
s
e
c
2
)
-
42
CFD is coming. Example ComFLOW. Courtesy: DNV /Tormod Be
Developed by University of Groningen, The Netherlands, in EU project SafeFlow(2001-04)
Based on Volume of Fluid method. Solves Navier Stokes equations for fluid and free surface.
Application areas: Wave in deck, slamming, green water, sloshing
Comflow is being further developed in project JIP Comflow-2 (2005-07) to account for
two-phase flow
arbitrary body motions
irregular wave inflow
Inflow boundary,Airy or Stokes5th wave
Structure
Fluid domain
-
43
Summary Proper added mass values crucial to find wave loads during installation. Water entry equations contain a slamming term. In splash zone: Added mass sensitive to submergence and frequency. By landing on bottom an increased added mass may contribute to softer landing. Coefficients very sensitive to inclination. The derivative of added mass versus distance from bottom pushes the object
upward.
Numerical and experimental tools available to find rough estimates on added mass and damping.
Viscous effects important. Theoretical expressions exist for several simple shapes. Real shapes very difficult to handle. CFD is being introduced. The future tool for load assessment
Still several pitfalls Requires very skilled users and proper codes.
How to estimate hydrodynamic coefficients applicable for lifting from the sea bed.Hydrodynamic coefficients for subsea structuresContentPhases of the installation processSubsea template Ormen LangeAdded mass for simple 2DformsNatural periods (Lightly damped) Added mass versus damping ?Added mass versus damping ?Added mass versus damping ?Water entry of TOGP template (2000)Water entry forces, calm waterWater entry forces, including wavesAdded mass for simple structures.Horizontal circular cylinder Close to bottomVertical force close to bottomA33 2D cylinder close to bottomCircular disc close to bottomPerforated plate, circular hollows, potential theorySuction anchorSuction anchorSuction anchorTemplates with cover and mudmats.Range of experimental resultsProtection cover made from tubular members. (approx 14 * 19m) (perforation ratio 0.27)Computed and measured (forced oscillations) added mass. Protection coverTheoretical method. Horizontal circular diskEstimated and measured damping including estimate on the effect of the edge vortex. Hatch 18 (perforation 0.25).Total force on hatch 18Installation of gravity anchor. Use of method Molin & Nielsen(2004)Model. Solid top, open top.Comparison with model tests. Suction anchor with central hole in top plate.Added mass and linearized dampingAdded mass and damping, fully submerged, 12.2% open area.Added mass and damping, fully submerged, 12.2% open area.Effect of bottom proximity (1.0 and 0.25m from bottom)Effect of free surface proximity (2.5 and 1.25m from free surface)Lift and drag force close to bottom (DNV RP C205)Example: Intermediate phase of jacket installationPlate close to bottomAdded mass. Circular plate close to bottomDynamic equation.Wave period 13.3sec, Fa = 22MNInitial clearance 0.05mCFD is coming. Example ComFLOW. Courtesy: DNV /Tormod BeSummary