NONLINEAR BEHAVIOR OF A SINGLE-POINT MOORING SYSTEM FORFLOATING OFFSHORE WIND TURBINE

Ma Chong, Iijima Kazuhiro, Masahiko FujikuboDept. of Naval Architecture and Ocean Engineering

OSAKA UNIVERSITY

RESEARCH BACKGROUNDAs a effective renewable-energy, wind-power is developed rapidly. At the present, the EU has already started huge offshore wind power expansion, with China not far behind.

• Enormous wind energy• Saving land source• Smaller negative impact on

aesthetics of the landscape

WHY WE SELECT THE SINGLE POINT MOORING (SPM)?

Most design of platform for offshore wind turbine is based on the experience of drilling platform. However, there is a essentially difference between wind platform and drilling platform. For wind platform, even though enough stability is still indispensable, it isn’t required that platform must be kept in a fixed position. Instead, it will be better if the position of wind platform can be optimized automatically according to the wind and wave direction.

SPM System

RESEARCH OBJECTIVES

Prototype

The research objective is:To clarified the nonlinear behavior of SPM for wind platform.

Advantage: Easy to install Simplify the design of platform (the mechanism of the yaw

controlled) Low cost for mooring systemDisadvantage: Relevant research is few For the mooring part, nonlinear phenomenon may happen

due to the large deflection and large rotation.

To find out the response of platform and mooring when aerodynamic force and hydrodynamic force are acting on, the model experiment is conducted.

EXPERIMENT PHOTO

DIMENSION OF MODEL

Design PowerGeneration

5 Mw

Mass 12924 Ton

Metacentric Height 71.3 m

EXPERIMENT ARRANGEMENT

Wind & Wave Generator

EXPERIMENT ARRANGEMENT

Wind

Wave

THE VIDEO OF THE EXPERIMENT-TRACINGFront View

Back ViewSide View

THE VIDEO OF THE EXPERIMENT-NORMAL DOWNWIND

Wind TunnelRotational

155 rpm

Wave Height 4 cmWave Period 0.8 s

Front View

Back ViewSide View

EXPERIMENT RESULT-TIME DOMAIN

The following figures show the six degree of motion for platform:

EXPERIMENT RESULT-FREQUENCY DOMAINIt’s very difficult to judge if the response of motion is linear or nonlinear. Therefore, after selecting the analysis time duration, the Discrete Fourier Transform is conducted. The results in frequency domain is shown:

All the responses (except roll) have the same main component in freq (1.23 s-1) corresponding to the wave period 0.8 s

EXPERIMENT RESULT

Linear response

Linear response

Linear response

v

EXPERIMENT RESULT

Linear response

Nonlinear response

For the tension, excepting the linear response in frequency 1.24 s-1, there is quadratic response in 2.5 s-1 which is resulted from nonlinear property of the SPM system. Besides, the third order and fourth order response also exist although they are relatively small.

THEORETICAL ANALYSIS ABOUT THE NONLINEARITY OF SPM

Linear equation of motion:M U U U f t

Where the mass matrix, damping matrix and stiffness matrix is constant and all of them can be calculated when the displacement U equal to zero.

However, when the rotation is large enough, the transformation matrix between local coordinate system and global coordinate system should be taken into account.

0

y zx z

yj xs

x y z

A

0 0 0

0 0 0

2 2 2 2 20 0 0 0

( ) ( ) ( ), ,

, ( ) ( ) ( )

j j j j j ju u u

x y z

j j j j j jx y u u u

X X Y Y Z ZL L L

L X X Y Y Z Z

　　

To utilize the same mass, damp and stiffness matrix, all the external force, displacement, velocity and acceleration should be transferred to the local coordinate system.

M A U U U f t

M A U U U f t

U U U f twhere: M A , ,

Therefore, when the rotation angle isn’t small, the influence of transformation matrix should be considered and the mass, damping, and stiffness matrix will become a function of displacement. As the consequence, the equation of motion will become nonlinear.

THEORETICAL ANALYSIS ABOUT THE NONLINEARITY OF SPM

CONCLUSION

Nonlinearity of single point mooring system is observed apparently and it should be carefully taken account into during design process

The response of platform seems rather linear so that the conventional experience of platform can be referred.

For platform, besides the normal linear response, due to the rotation around the mooring system, an additional low frequency component exists.

The numerical simulation is on the way…

THANK YOU!

LONG TIME PERIOD VIBRATION

Surge: 11.36s 1.83cm Roll: ~

Sway: 34.09s 4.66cmPitch: 11.36s 0.42deg

Heave: 34s-11s 0.17cm Yaw: 34.09s 1.84 deg

To observe the long period vibration in FFT analysis, the time duration is enlarged for 15s to 36s:

NONLINEAR DISPLACEMENT-STRAIN RELATIONSHIP

Discretization of model:

( ) ( )( , , ) ( )

( , , ) ( ) ( )

( , , ) ( ) ( )

x

y

z

dV x dW xu x y z U x y zdx dx

u x y z V x z x

u x y z W x y x

Euler-Bernoulli assumption

1 21 2

1 2 1 23 4 5 6

1 2 1 23 4 5 6

1 21 2

( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

x x

y y z z

z z y y

x x

U x u x u x

V x u x u x t x t x

W x u x u x t x t x

x t x t x

Hermite cubics interpolation function1

2

2 3

3 2 3

2 3

4 2 3

2 3

5 2

2 3

6 2

( ) 1

( )

3 2( ) 1

3 2( )

2( )

( )

xxL

xxL

x xxL L

x xxL L

x xx xL L

x xxL L

3 12 12 1, , [ ]

T

x y zu u u C u

geometric nonlinear:NONLINEAR DISPLACEMENT-STRAIN RELATIONSHIP

Green-Lagrange strain:

nonlinear strain gx

1 [ ] [ ]2

T Tx n ng u B B u

2 2 21 ( ) ( ) ( )2

yx x zx

uu u ux x x x

3 12 12 1[ ]

Tyx z

n

uu u B ux x x

( ) ( [ ] [ ])T T Tn x x x n nu F g dxdydz u B B dxdydz u

( [ ] [ ])Tn x n nF B B dxdydz u

[ ] ( [ ] [ ])Tn x n nK B B dxdydz

According to the principle of virtual work

3 12 12 1, , [ ]

T

x y zu u u C u

Viscous Drag Force

(nonlinear)

Froude-Krylov Force

(linear)

Hydrodynamic Mass Force

(linear)

MORISON EQUATION

* * ** * * *j j jj j j jrn rn rnv a df p nds K a dz K u u dz

* * ** * * * * * *(0,0, ) (0,0, ) (0,0, )j j jj j j j j j j

rn rn rnv a dm p n z ds K a z dz K u u z dz

Coordinate System: o*j-x*jy*jz*j

Where,

Ca: added mass coefficientCd: drag coefficient

2

,4

2

a a

b d

DK C

DK C

transient wave elevation