DYNAMIC TENSION ANALYSIS OF A SLACK MOORINGFOR A FLOATING OFFSHORE WIND TURBINE
Pham Van PHUC*, Takeshi ISHIHARA**, Kenji SHIMADA*, Tetsuji SHIROEDA**** Institute of Technology, Shimizu Corporation, 3-4-17 Etchujima, Koto, TOKYO 135-8530, JAPAN** Department of Civil Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, TOKYO 113-8656, JAPAN*** Engineering headquarters, Shimizu Corporation, 2-16-1 Kyobashi, Chuo, TOKYO 104-8370, JAPANObjective

Nonlinear FEM MethodConclusion

Mooring system plays an important role in the FloatingOffshore Wind Turbine System (FOWTS) to keep its position
from any critical weather conditions .

■ Equation of motion

・ This paper explained a nonlinear FEA using truss element which
accounts for a frictional contact with seabed to simulate the dynamic
response of the mooring line system.

Existing design and most previous studies are only basedon the linear mooring system without considering any slack
and snap tensions that may cause some errors on thedynamic responses of FOWTS and damage the mooring
system in storm conditions.

・ Several fundamental studies and comparisons with previousstudies are made to show the ability to simulate nonlinear behaviors
of mooring line system.

where M is the mass matrix, C is the damping matrix and K is the nonlinear
stiffness matrix of mooring cable system using truss element. The force F
includes the internal force Q which is the function of tension of mooring cable,
gravitational force Fg, buoyancy force Fb, hydrodynamic force Fh and seabedcontact force Fc.

This study has developed a fully nonlinear mooring systemusing FEM method1). Some fundamental studies of cable instate of slack and snap tension, mooring cable in contact
with the seabed in the experimental scale are described tounderstand the nonlinear behavior of mooring cable. Somecomparisons with the previous studies are also presented toshow the validity of the numerical method to evaluate
impact tension.

・ Propose method showed very good agreement with the previous
experimental results in comparison of the slack tension, snap tension
and bottom interaction of slack mooring system.

■ Hydrodynamic force

Reference
1. Phuc, P.V. and Ishihara, T., A study on the dynamic response of asemi-submersible floating offshore wind turbine system Part 2:
Numerical simulation, Proc. of 12th international conference onwind engineering (ICWE12), 2007.
2. Gobat, J.I. and Grosenbaugh, M.A., Dynamics in the Touchdown
Region of Catenary Moorings, Proc. of the Eleventh International
Offshore and Polar Engineering Conference, 239-247, 2001.
3. Ju, S.H. and Rowlands, R.E., A Three-dimensional frictional
contact element whose stiffness matrix is symmetric, J. of Applied
Mechanics, 66(2), 460-467, 1999.
4. Zhu, Z.H., Dynamic modeling of cable system using a new nodal
position finite element method, Communication in Numerical
Methods in Engineering, 2008.
5. Fried, I., Large deformation static and dynamic finite element
analysis of extensible cables, Computer & Structures, Vol.15, No.3,315-319, 1982.
6. Koh, C.G., Zhang, Y. and Quek, S.T., Low-tension cable dynamics:
Numerical and experimental studies, J. of Engineering Mechanics,
Vol. 125, No. 3, 347-354, 1999.

where Fhw is the Froude-Krylov force, FhM is the inertia force, FhD is thedrag force.

■ Seabed contact force
Frictional and normal force acting on the mooring elements in contact withthe seabed using are modeled by the symmetrical stiffness matrix3). It is
described in terms of a penalty constant stiffness k, and frictional coefficient
μ with relative displacement of mooring element in tangential and normaldirections.

A catenary mooring in FOWTS

Fundamental studies of Cable with Slack & Snap Tension
0 Free swinging cabley(m)Response tension
Cal.(Fried,1982)

L (m)

18.9

Cal. (this study, h=2%)y(m)CSlack tension

0.0112

EA (kN)

134.2

Exciting freq.
(Hz)0.807, 1.27

Exp. (Koh, 1999)

0x(m)

0.5

10-0.2

-0.2
1.8s
1.9s
2.0s1.7s
1.6s-0.4 1.1s
1.2s
-0.6
1.3s

1.5s

-0.4
-0.6

-1-0.5-10x(m)0.5

1Cal. (Koh, 1999)

-1

-0.5

0x(m)

1.3s

-1

-0.5

1.5s
1.4s
0x(m)

0.5

0

2.1s

2.4s

2.2s

-0.5

0x(m)

0.5

-1

1

2.9s

2.1s

2.5s
3.0s

-0.8
2.3s

-1

-0.4 2.7s
2.8s-0.6 2.6s

-1

2.4s

-0.5

2.2s

2.3s
0x(m)

0.5

 Seabed interaction

x/L
0.4

0.2

0.6

0.8

Force F
f=0.0

• Slack and large snap mooring tension was observedin previous
experimental studies (Gobat, 2001)• Simulated dynamic profiles of mooring chain is quite in good agreement withexperimental results by Gobat(2001) for upward and downward motion thechain mooring cable.
• The simulated tension of mooring chain is well agreed with the experimental
results both of in the slack and snap tension state.

f=0.2

Initial condition
y/L

f=0.4
f=0.6
f=0.8

Seabed-0.15

Smallfriction

f=1.0(a) Exp.(Gobat, 2001)
1.4

vertical coordinate z(m)Fixed point0Up1.2

Down

1.0

Initial condition

Initial condition

0.8
0.6
0.4
0.2
00.5
1
1.5
horizontal coordinate x(m)

20.5
1
1.5
horizontal coordinate x(m)2(b) Cal.(This study)
Mooring dynamic profiles (f=0.8Hz, Amp=0.25m)

LargefrictionSmallfrictionLargefriction

Exp. (Gobat,2001)
t=12.74s

Cal. (this study)t=12.87s(a) In slack tension state
Profiles of horizontally dragged cable with different seabed friction factors

0.15

0.2
t=0s
t=1s
t=2s
t=3s

0.4

0.6

0.8

2

1 x/LxC1.5

t=4s
t=5s
t=6s

B

y/LyC

Exciting
Force

F/F00.30

Snap tension

1

Snap tensionA

t=13.28s0.50

t=13.41s

Slack tension

BA-0.150Seabed

02

46Time(s)81012

Dynamic response and tension of vertically snapped cable (T=4s, f=1.0)

1(b) Damping ration h=10%

Mooring chain interaction with the Seabed• Horizontal dragging : profiles of the cable becomes asymmetricalwhen the friction forces from the seabed is large.
• Vertical snapping : Large snap tensions are found near the seabedby the dynamic response of cable in contact with the seabed

1Shapes of free fall cable with different structural damping ratio (this study)

Dynamic tension near fixed point Preliminary test

1

1.8s
1.9s
2.0s
1.7s
1.6s

1.1s
1.2s

(a) Damping ratio h=1%(b) Resonant state

0.4s
0.5

0.5s

-0.2

2.7s
-0.42.8s
2.6s
2.9s
-0.6
2.5s
3.0s
-0.8

-1

0.6s

-0.8

-0.2

Cal. (this study, h=6.2%)

mc (kg/m)

-0.5

-10-1

Snap tension
50.4s

0.3s

0.7s

-0.8

0Cal. (Zhu, 2008)

No of element-10.2s-0.4 1.0s
0.9s-0.6 0.8s

1.4s

Snap tension(a) Non-resonant state

0.3s

0.5s

-0.8Exp.(Fried,1982)

Cal.
I (This study)-0.6 0.8s
0.7s
-0.8
0.6s
-1

Initial condition

Exp. (Zhu, 2008)

1.0s
-0.4
0.9s

y(m)

• Simulated shapes of swinging cable are in good agreement withprevious experimental and calculated results (Fried, 1982).
• Near the free end of cable, tension drops and the cable coils up
into shape of high curvature that depended on the cablestructural damping ratio• Large snap tension occurred near the fixed point

0.1s

-0.2

0.2sy(m)Excited in a sinusoidal motion-0.2y(m)• An excited cable causes a large snap and slack tension in theresonant state.
• The simulated results show quite good agreement with previous
studies of Zhu(2008)

0.1sy(m) Submerged cable snapping in water0(b) In snap tension state
Experimental dynamics in the touchdown region of catenary mooring (Gobat, 2001)

Mooring tension time series (f=0.8Hz, Amp=0.25m)