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

Transcription

1 NONLINEAR BEHAVIOR OF A SINGLE- POINT MOORING SYSTEM FOR FLOATING OFFSHORE WIND TURBINE Ma Chong, Iijima Kazuhiro, Masahiko Fujikubo Dept. of Naval Architecture and Ocean Engineering OSAKA UNIVERSITY

2 RESEARCH BACKGROUND As 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

3 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

4 RESEARCH OBJECTIVES Advantage: Easy to install Simplify the design of platform (the mechanism of the yaw controlled) Low cost for mooring system Disadvantage: Relevant research is few For the mooring part, nonlinear phenomenon may happen due to the large deflection and large rotation. The research objective is: To clarified the nonlinear behavior of SPM for wind platform. To find out the response of platform and mooring when aerodynamic force and hydrodynamic force are acting on, the model experiment is conducted. Prototype

5 EXPERIMENT PHOTO

6 DIMENSION OF MODEL Design Power Generation Mass Metacentric Height 5 Mw Ton 71.3 m

7 EXPERIMENT ARRANGEMENT Wind & Wave Generator

8 EXPERIMENT ARRANGEMENT Wind Wave

9 THE VIDEO OF THE EXPERIMENT-TRACING Front View Side View Back View

10 THE VIDEO OF THE EXPERIMENT -NORMAL DOWNWIND Front View Wind Tunnel Rotational Wave Height Wave Period 155 rpm 4 cm 0.8 s Side View Back View

11 EXPERIMENT RESULT-TIME DOMAIN The following figures show the six degree of motion for platform:

12 EXPERIMENT RESULT-FREQUENCY DOMAIN It 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

13 EXPERIMENT RESULT Linear response Linear response Linear response v

14 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.

15 THEORETICAL ANALYSIS ABOUT THE NONLINEARITY OF SPM Linear equation of motion: MU U Uft 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. A j s x z y z y x 0 x y z ( X X ) ( Y Y ) ( Z Z ) j j j j j j u 0 u 0 u 0 x, y, z L0 L0 L0, L ( X X ) ( Y Y ) ( Z Z ) 2 2 j j 2 j j 2 j j 2 x y 0 u 0 u 0 u 0

16 THEORETICAL ANALYSIS ABOUT THE NONLINEARITY OF SPM 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 AU U U ft M AU U Uft U U Uf t where: 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.

17 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

18 THANK YOU!

19 LONG TIME PERIOD VIBRATION To observe the long period vibration in FFT analysis, the time duration is enlarged for 15s to 36s: Surge: 11.36s 1.83cm Roll: ~ Sway: 34.09s 4.66cm Pitch: 11.36s 0.42deg Heave: 34s-11s 0.17cm Yaw: 34.09s 1.84 deg

20 NONLINEAR DISPLACEMENT-STRAIN RELATIONSHIP Discretization of model: Hermite cubics interpolation function Ux () u() xu () x 1 2 x 1 x 2 Vx () u() xu () xt () xt () x y 3 y 4 z 5 z 6 Wx () u() xu () xt () xt () x z 3 z 4 y 5 y 6 () x t () x t () x 1 2 x 1 x 2 x 1 ( x ) 1 L x 2 ( x ) L 3 x 2 x 3 ( x ) L L x 2 x 4 ( x ) 2 3 L L x x 5 ( x ) x 2 L L 2 3 x x 6 ( x ) 2 L L 2 3 Euler-Bernoulli assumption dv ( x) dw ( x) ux ( x, y, z) U( x) y z dx dx u ( x, y, z) V( x) z( x) y u ( x, y, z) W( x) y( x) z T ux uy uz C u,, [ ]

21 NONLINEAR DISPLACEMENT-STRAIN RELATIONSHIP geometric nonlinear: Green-Lagrange strain: T ux uy uz C u,, [ ] u u x y u z x x x T u [ Bn ] According to the principle of virtual work nonlinear strain g x u 1 u u u x ( ) ( ) ( ) x 2 x x x x x 2 y 2 z 2 1 T T gx u [ Bn] [ Bn] u 2 u T F ( g ) dxdydz u T ( [ B ] T [ B ]) dxdydzu n x x x n n F ( [ B ] T [ B ]) dxdydzu n x n n T [ Kn] ( x[ Bn] [ Bn]) dxdydz

22 MORISON EQUATION f pnds Ka dz K u u dz * j * j * j * j * j * j * j v a rn d rn rn Coordinate System: o* j -x* j y* j z* j Froude- Krylov Force (linear) Hydrodynami c Mass Force (linear) Viscous Drag Force (nonlinear) m p n z ds K a z dz K u u z dz * j * j * j * j * j * j * j * j * j * j v (0,0, ) a rn (0,0, ) d rn rn (0,0, ) Where, 2 D Ka Ca, 4 D Kb Cd 2 C a : added mass coefficient C d : drag coefficient transient wave elevation