13_plate close to bottom
DESCRIPTION
13_Plate Close to BottomTRANSCRIPT
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FGN Date: 2005-03-11 Page: 1 Hydro Oil & Energy
Problem: Intermediate phase of jacket installation
Four legs with mudmats, (circular plates).Platform stable before piling?
Fwave
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FGN Date: 2005-03-11 Page: 2 Hydro Oil & Energy
Plate close to bottom
R: Radius of plate.h : Gap.V: Vertical velocity.
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FGN Date: 2005-03-11 Page: 3 Hydro Oil & Energy
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
= + =
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FGN Date: 2005-03-11 Page: 4 Hydro Oil & Energy
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:
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FGN Date: 2005-03-11 Page: 5 Hydro Oil & Energy
State space formulation
[ ]
33
33
i 1 i
x = Ax + bFwith :
Vx
h
dA1 B kV(h)A 2M dh M M
1 0
1b M m AM
0
Forward Euler :x x dt Ax + bF+
= = = = +
= +
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FGN Date: 2005-03-11 Page: 6 Hydro Oil & Energy
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 (s ec)
F
(
N
)
Wave period 13.3sec, Fa = 22MN
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 (s ec)
d
V
/
d
t
(
m
/
s
e
c
2
)
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FGN Date: 2005-03-11 Page: 7 Hydro Oil & Energy
Installation of gravity anchor. Use of method Molin & Nielsen(2004)
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FGN Date: 2005-03-11 Page: 8 Hydro Oil & Energy
Model. Solid top, open top.
H = 3.42mR = 3.77m
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FGN Date: 2005-03-11 Page: 9 Hydro Oil & Energy
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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FGN Date: 2005-03-11 Page: 10 Hydro Oil & Energy
Added mass from panel program
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
X: 0.05Y: 0.4853
wall thicknes s (m)
A
3
3
/
(
V
)
Added mas s (A33) and volume of s uction anchor (VSA), 20m s ubmergence, 12m2
X: 0.05Y: 0.5482
A33 + VSAA33VSA
Results from WAMIT analysis. Added mass in heave as function of wall thickness. With and without inclusion of wall volume. Closed lid (left) and 12m2 openings (right).
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.5
1
1.5
2
2.5
X: 0.05Y: 2.05
wall thicknes s (m)
A
3
3
/
(
V
)
Added mas s (A33) and volume of s uction anchor (VSA), 20m s ubmergence, clos ed s urface
X: 0.05Y: 1.984
A33 + VSAA33VSA
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FGN Date: 2005-03-11 Page: 11 Hydro Oil & Energy
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
P erforation ratio %
C
A
KC= 1.2KC= 1.2KC= 0.6KC= 0.6KC= 0.1KC= 0.1
A2XH
KC =
Red: MeasuredBlue: Computed
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FGN Date: 2005-03-11 Page: 12 Hydro Oil & Energy
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/H
B
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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FGN Date: 2005-03-11 Page: 13 Hydro Oil & Energy
Effect of bottom proximity (1.0 and 0.25m from bottom)
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
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
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FGN Date: 2005-03-11 Page: 14 Hydro Oil & Energy
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