Dynamic Analysis of Floating Offshore Wind Turbine System
Considering Combined Hydrodynamic Loadings

PO.ID133

Takeshi IHIHARA, Ken KAGAYA, Yuka KIKUCHI
Department of Civil Engineering, School of Engineering, The University of Tokyo

Introduction

Nonlinear damping effectInteraction of wave and current

Fukushima Floating Offshore Wind
Farm Demonstration Project has
started in 2013. The nonlinear effectof hydrodynamic force and elastic
motions are significant for dynamic
analysis of Floating Offshore Wind
Turbine System due to the slendermembers.
A nonlinear finite element model has been developed
considering coupling between wind turbine, floater andmooring[1],[2] and used in this study to investigate thefollowing issues.

Surge, heave and pitch motions were predicted bynonlinear model in regular waves. Predictions agree
well with experiments. Wave nonlinearity effect wasreproduced at resonant region in heave. The model
underestimated heave before resonance period andoverestimated pitch around natural period.

Conventionally, combined loading of wave and current
is estimated by superposing of wave and current
response, assuming no interaction. This study
investigated the interaction between wave and current
by comparing predictions by linear superposition modeland nonlinear model with experiments.

1Surge2.5

exp H=2cm
exp H=6cm
exp H=10cm
cal H=2cm
cal H=6cm
cal H=10cm

21.5

Phase ()1■ Analysis in current only
In current, mean displacement of floater motion wasobserved in surge. Predictions showed good agreementwith experiments for all current speeds.

0.5
0-0.5

0.5
0.05

-1

1

1.5

2

2.5

13

Water tank experiment
Water tank experiment was conducted to verify the FEMmodel. The scale was 1:50 following Froude similitude.
The model was semi-sub floater used at Fukushima
project and the wind turbine was simplified by a
distributed mass. Water tank had 55m long and 8mwide. Water depth was set to 2.5m. Four catenary
moorings were attached to keep the position and used
to reproduce major motions in surge, heave and pitch.

2.5

301

Heave

Phase ()

2.5
2
1.5
1
0.5

0.5
0-0.15

-0.5

-0.2
00.05

-1

1.5

2

2.5

31

Wave period (sec)

1.5

2

2.5

1Pitch0.15

0.2

Phase ()2.5
21.510.5
0-0.5

0.5
-1

1

1.5

2

2.5

31

Wave period (sec)

1.5

2

2.5

3

Wave period (sec)

Response of the floater in regular waves

The comparison of heave motions measured andpredicted by linear and nonlinear damping model wasconducted with different wave heights. Linear model
underestimated the experiment in 2cm andoverestimated in 10cm of wave height. Nonlinear modelshows good agreement for all wave heights.

■ Analysis in wave and current
To investigate the interaction between wave andcurrent, experiment and prediction were performed inwave and current. Responses predicted by linear
superposition and nonlinear model were compared withexperiments. For mean displacement, predictions bylinear and nonlinear model agreed well withexperiments. For variance of displacement, predictions
by linear model overestimated experiments and thoseby nonlinear model agreed well for surge and pitch.
Heave response was still overestimated by nonlinear
model. That means hydrodynamic damping decreased
due to the current effect.
0.5

Natural periods of floater(Real scales in parentheses)

Average (m) (rad)Amplitude Za/a3.0Surge
HeavePitch0.1

Response of the floater in current

3

Wave period (sec)3Natural period
7.6 sec (53.7sec)
2.4 sec(17.0sec)
3.0 sec(21.2sec)-0.1

Current speed (m/s)
10-0.05

expcal0

Amplitude aa3) Estimation of the interaction of wave and current andcomparison of the prediction by nonlinear model withthat by superposing of wave and current response.

Amplitude Za/a32) Clarification of the mechanism of low-frequency
motion (oscillatory) for semi-sub floater.

2

Wave period (sec)Wave period (sec)1) Prediction of floater response in heave direction
considering wave nonlinearity effect and comparisonof it with that by conventional linear model.

1.5

exp
cal_linear damping
cal_nonlinear damping

2.5
2.0
1.5
1.0
0.5
0.0

1
exp
cal_linear
cal_nonlinear

0-0.5

2cm

0.8
0.6
0.4
0.2
0

Surge

6cm
10cm
Wave heightStandard diviation

0Surge (m)AmplitudeXa/a3

Heave

Pitch

Surge

Heave

Pitch

Numerical modelLow-frequency motion

Conclusions

In this study, nonlinear finite element scheme was used.
The nonlinear damping model was introduced for dragforce in vertical direction.

To investigate the low-frequency motion, experimentand prediction were performed in irregular waves.
The low-frequency motions were observed in thefrequencies according to the floater natural periods
especially in surge and pitch. However, low-frequency
energy is not significant in wave spectrum. This meansthat forces were excited by nonlinearity of drag force.
The prediction underestimated heave response in highfrequencies, which agreed with the prediction
underestimated heave response before resonant region
in regular waves.

Dynamic analysis of floating offshore wind turbine
system has been improved by introducing nonlinear
damping model. By employing the model, lowfrequency motion and interaction of wave and current
has been investigated. Conclusions are summarized asfollows.
1) By introducing nonlinear damping model, theamplitude-dependency of heave response wasreproduced and prediction accuracy was improved.
2) The low-frequency motion is erected since irregularwaves excite the low-frequency loadings through thedrag force.
3) The interaction of wave and current leads to reducehydrodynamic damping. Nonlinear analysis predictwell experiment, while linear superposition model
overestimated the variance of displacement.

FR is restoring force, FE is hydrodynamic force, FG isgravitational force and Fw is aerodynamic force.
■ Hydrodynamic forces are estimated as acombination of Froude-Krilov force FEM, diffraction force
FEW and drag force FED.

FE   FEM   FEW   FED FEM   w AuFEW   CM  1 wV  u  x FED  0.5wCD Au  X  u  X Drag and inertia coefficients CD, CM were identified withtest and CD of mooring was obtained from DNV[4].
Drag and inertia force coefficients, CD and CM
Floater Horizontal

VerticalMooring

CD
1.5

2.0
1.3[4]

CM
2.2

3.0
2.2

In this study, a linear damping ratio, 15 %[3] was used forcomparison with the nonlinear model.

10-210-310-4

10-510-610-710-810-90Wave

expcal
0.5

1

1.5

210-2

10-310-410-510-610-710-810-90-2

10-310Heave-410-510-61010-7-810-9

10 00.5

11.5

Frequency [Hz]Surge0.5

11.5

2Frequency [Hz]Frequency [Hz]2Power Spectrum [rad 2s] M x  C x   K x  FR   FE   FG   FW 

Power Spectrum [m2s]■ The equation of motion can be written as:

Power Spectrum [m2s]Comparison of prediction by linear and nonlinear model(Current speed:0.2m/s Wave height:60mm Wave period:2.8s)

Power Spectrum [m2s]Comparison of heave responses measured and predictedby linear and nonlinear damping modelReferences-210-31010-410-510-610-710-810-90Pitch

0.5

11.52

Frequency [Hz]Response of the floater in irregular waves(Significant wave height: 10cm, Peak wave period: 1.41s)

EWEA OFFSHORE 2013

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floating offshore wind turbine system Part2: Numrical simulation, ICWE12,
2007.
2. M. B. Waris, T. Ishihara, Dynamic response analysis of floating offshore windturbine with different types of heave plates and mooring systems by using afully nonlinear model, Coupled Systems Mechanics, Vol.1, No.3, 2012.
3. N. Srinivasan, et al., Damping controlled response of a truss pontoon
semisubmersible with heave plates, Proceeding of the 24th international
conference of OMAE, 2005.
4. Det Norske Veritas, Offshore Standard，DNV-OS-J101，2010．