A numerical study of the dynamic response of a...

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A numerical study of the dynamic response of a floating offshore

wind turbine system

Takeshi Ishihara

Department of Civil Engineering, The University of Tokyo

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土木学会第57回年次学術講演会　　 2002年9月27日

Introduction of this research project

Joint research project Tokyo Electric Power Companyand the University of TokyoTest the feasibility of two type of floating wind turbine systems

Cooperative companiesShimizu CooperationPenta-Ocean CooperationMitsubishi Heavy Industries

who are responsible for the design of the floaters and the wind turbine respectively.

A semi-submersible type

A spar type

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Outline of this presentation

Background and objectives

Experimental setup and results

A numerical study

Conclusions

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Floater concepts in Oil & Gas industry

Floating wind turbine technologies are derived from well known floater concepts in Oil&Gas Industry such as

Semi-submersibleSparTLP (Tension leg platform)

Some points are different from those in Oil & Gas industry, that is

Need to reduce cost for the mass productionNot need to consider the safety factor of human station

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Background

After FLOAT project (1991), several floating offshore wind turbine systems have been proposed based on the concepts in the oil and gas industry such as semi-submersible, spar and tension leg platform.

Some preliminary studies have been done to assess the platform using the numerical models, which were developed for the design of the platform used by the oil and gas industry.

NREL,U.S. 2004H. Suzuki, Japan. 2005TU Delft, ECN & Other,

Netherlands, 2001

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Previous study

Hederson (2000) used the Morison’s equation for the floating structures with large diameter sub-structures and ignored the hydrodynamic drag force and the elastic deformation of floating structures.

This simplification might lead to some loss in accuracy to predict the dynamic response of the floating structures with small diameter sub-structures, such as the floater proposed by Ishihara et al. (2007) for the economical design.

A. R. Henderson, UCL,London,2000

T. Ishihara,ICWE12, Australia 2007

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Objectives

A full nonlinear FEM code was developed in the time domain to investigate the effects of the hydrodynamic damping on the dynamic response of the floating structures.

A dynamic response analysis was also carried to clarify the effect of the elastic deformation and the nonlinear wave.

The performance of the code for the dynamic response analysis of the semi-submersible floating structures was verified by a model test.

Achieve the stability of floater for the reduction of the turbine and tower loading

Achieve the stability of floater for the reduction of the turbine and tower loading

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Experimental setup and results

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Wind tunnel with water tank

Upstream (wind)

(Wave generator)

Downstream (Absorbing beach)

Laminar wind speed:1~32m/sWind tunnel

Regular waveMax. wave height ： 0.3mPeriod ： 0.6～4.0sec

Wave generator

Absorbing beachWave absorption

L17.6m×W3m×H1.8m(Still water depth 1.5m）

Water tank

National Maritime Research Institute

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Model of the floaters

Wind

Wave generator Absorbing beachModel location

Operating case Survival case

The model is set at the 6.6m downstream of the wave generator.

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Measurement of displacement

3 CCD cameras

Optical target

LED

Six independent components of displacement of the floater were measured by means of three CCD cameras. The optical target with fourLEDs were mounted on the center floater and were used to measure the surge, heave and pitch motions of the floater.

Wave

Wind

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Video for the operating case

The pitch motion is limited to be very small. This implies that this floating system has little influence on the turbine loading.

ModelH=2cm, T=0.6s, U=1m/s

RealH=3m, T=7.3s, U=12.2m/s

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Video for the survival case

ModelH=8cm, T=1.0s, U=4m/s

The response of the floater shows larger amplitude, but the system is stable enough.

RealH=12m, T=12.2s, U=49m/s

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A numerical study

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A full nonlinear FEM code

1. Floater structure is constructed by beam elements to describe elastic behavior.

2. Interaction between wind turbine and floater is considered.

3. Equations are solved in the time domain to accurately simulate non-linearity of the hydrodynamic damping terms.

In this study, a full nonlinear FEM code was developed for the analysis of dynamic response of the floater and wind turbines, in which:

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Numerical model

[ ]{ } [ ]{ } [ ]{ } { } { } { } { }G R H AM X C X K X F F F F+ + = + + +

Where [M], [C], [K] is a mass, damping, stiffness matrix; {FG}, {FR}, {FH}, {FA} is a mooring force, hydrostatic force, hydrodynamic force and aerodynamic force, respectively; and {X} is unknown vectors containing translations．

H D w M aF F C Vu M Xρ= + −

• The equation of motion of the FOWTS is written as follows.

• The hydrodynamic force is described basically by Morison’s equation (Morison,1950).

Where ρw is water density; u is particle wave velocity; V,A is area, volume of element; CD and CM is hydrodynamic drag and inertia coefficient; Ma is the hydrodynamic added mass

( )0.5D w DF C A u X u Xρ= − −

• The vertical hydrodynamic force on the vertical column is described by using the added mass model by Haslum (2000) and drag force model by Srinivasan(2005).

( )3 3 3; 2 ; ( 20%)D ED ED aF C X C M Mζω ζ= − = + = (Srinivasan,2005)

(1)

(2)

(4)

( ) ( )31 2 3 2 ; 2.0a w M MM C D Cρ π= − =

( )1a w MM C Vρ= − (3)

(Haslum,2000) (5)

(6)

Where X3 is vertical motion, ω is the angular frequency of heave mode, M3 and Ma3 are the structure mass and hydrodynamic added mass of floater in the heave direction, respectively.

[ ]{ } [ ]{ } [ ]{ } { } { } { } { }G R H AM X C X K X F F F F+ + = + + +

Where [M], [C], [K] is a mass, damping, stiffness matrix; {FG}, {FR}, {FH}, {FA} is a mooring force, hydrostatic force, hydrodynamic force and aerodynamic force, respectively; and {X} is unknown vectors containing translations．

H D w M aF F C Vu M Xρ= + −

• The equation of motion of the FOWTS is written as follows.

• The hydrodynamic force is described basically by Morison’s equation (Morison,1950).

Where ρw is water density; u is particle wave velocity; V,A is area, volume of element; CD and CM is hydrodynamic drag and inertia coefficient; Ma is the hydrodynamic added mass

( )0.5D w DF C A u X u Xρ= − −

• The vertical hydrodynamic force on the vertical column is described by using the added mass model by Haslum (2000) and drag force model by Srinivasan(2005).

( )3 3 3; 2 ; ( 20%)D ED ED aF C X C M Mζω ζ= − = + = (Srinivasan,2005)

(1)

(2)

(4)

( ) ( )31 2 3 2 ; 2.0a w M MM C D Cρ π= − =

( )1a w MM C Vρ= − (3)

(Haslum,2000) (5)

(6)

Where X3 is vertical motion, ω is the angular frequency of heave mode, M3 and Ma3 are the structure mass and hydrodynamic added mass of floater in the heave direction, respectively.

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3D beam element model

4th mode: elastic mode

1st mode: heave mode 2nd mode: surge mode

3rd mode: pitch mode 4th mode: elastic mode

1st mode: heave mode 2nd mode: surge mode

3rd mode: pitch mode

The Floating wind turbine system was constructed by 188 beam elements, which was used in the dynamic response analysis. Each wind turbine with 46 elements. Floater with 50 elements.

The eigenperiods in the surge, heave and pitch direction show good agreement with experiment.

The higher mode corresponding to the elastic deformation was also obtained.

33.033.3

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7.334.036.0Eigen-period (s)-34.036.7Natural period (s)421Mode

33.033.3

3

7.334.036.0Eigen-period (s)-34.036.7Natural period (s)421Mode

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Hydrodynamic damping effect

The surge is overestimated when the drag force is ignored, whilethe Morison’s equation provides a good prediction.

surge

0

4

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Exp.(H=3m)Cal.(H=3m,F

D=0)

Cal.(H=3m,Morison)Exp.(H=12m)Cal.(H=12m,Morison)

2X/H

T(s)

6 12 18 24 32 36

This figure shows the predicted and measured amplitude of normalized surge for different wave period.

The dependencies of the peak response on the wave height can be simulated well by the proposed model,

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Predicted and measured heave

The heave is overestimated when the Morison’s equation is only applied, while the predicted heave shows a good agreement with experiments when the Srinivasan’s model was added.

0

2

4Exp.(H=3m)Cal.(H=3m,Morison)Cal.(H=3m,Srinivasan)Exp.(H=12m)Cal.(H=12m,Srinivasan)

2Z/H

T(s)

6 12 18 24 32 36

heave

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Elastic behavior

Exp.

Cal.(Transient response)

Cal.(Applied load)

M Z/H

(kN

)4e+4

2e+4

0e+0

T(s)

6 12 18 24 32 36Elastic mode

These bending moment are almost as same as the experiments in thenonresonant region. However, using the applied load as an excited transientload will underestimate the loads at the resonance region of the elastic modes.

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Nonlinear Wave Characteristics

• Waves at reference sites of water depth 50,100,200m with the maximum wave height H=22.23m and wave period T=15.5s were selected to investigate the dynamic response due to nonlinear waves.

• The wave at the water depth of 50m near water breaking limit requires to use the 9th order of the stream function.

• At 100-200m depth, 1st harmonic component of the wave elevation is dominant, while about 25% of the wave elevation is contributed by 2nd

harmonic component at 50m depth.

-25

0

25

80 90 100 110 120

d=50md=100md=200m

Water elevation(m)

Time(s)

Water elevation

0.0001

0.001

0.01

0.001 0.01 0.1

d=50m d=100m d=200mH/gT2

d/gT2

Shallow waterbreaking limitH/d=0.78

Hb

0.9Hb

Deep water breaking limitH/L=0.14

Stokes's 5th orstream function 3

Linear/Airy orstream function

Stream function

357911>11

Regular wave theory selection

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Dynamic response due to nonlinear wave

0

1 105

2 105

d=50md=100md=200m

MZ(kNm

)

15.5 7.8 5.2 3.9 3.1

Wave Period T(s)

Elastic mode’s period

-4 105

0

4 105

80 90 100 110 120

d=50md=100md=200m

MZ(kNm)

Time(s)

• Although the applied loads are almost same for any depths, the surge-exciting bending moment at 50m depth is 1.8 times larger than the other cases.

• The Fourier harmonic components of the surge-exciting bending moment indicate that the 2nd

harmonic component for 50m depth has a large contribution to the load acting on FOWTS.

• It is because the 2nd

harmonic component of wave (T=7.8s) resonates with the elastic mode(T=7.3s) of the FOWTS.

Surge-exciting bending moment

Fourier harmonics of the bending moment

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Conclusions

1. The response is strongly influenced by hydrodynamic damping in the resonance region. Morison’s equation provides satisfactory prediction of the surge motion, but overestimates the heave motion of the floating structure with vertical column. The hydrodynamic damping ratio proposed by Srinivasan et al. gives good predictions.

2. Elastic deformation plays an important role in dynamic response of the floating structure. The predicted response is underestimatedwhen the elastic deformation is ignored.

3. The nonlinearity of wave becomes dominant for the water depth less than 100m, and the elastic modes might be resonant with the higher order harmonic component of nonlinear wave, resulting in the increase of dynamic response of the floating structure.

A full nonlinear FEM code was developed in the time domain to investigate the effects of the hydrodynamic damping and the elastic deformation on the response of the floating structures.

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What we expect to see

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Thank you for your attention !

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