5 - Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear Interaction

EARTH & SPACE 2010 – March 14-17 Honolulu HI 1/16

INTRODUCTION MODEL DESCRIPTION RESULTS CONCLUSIONS

Dynamic Analysis of an Offshore Wind Turbine:

Wind-Waves Nonlinear Interaction

S. Manenti, F. Petrini

[email protected]

University of Rome Sapienza

Faculty of Engineering

Department of Structural Engineering



PURPOSE AND CONTENTS OF THE WORK

In this work the dynamic analysis of a monopile supported offshore wind turbine forced

by a random wind a wave excitation in the frequency and time domain is carried out by

means of the ANSYS finite element model.

The effects of non-linear interaction is investigated for possible reduction of vibration

peaks in the structural response.

In the following:

1. an introduction to the problem and the analysis methodology adopted is given;

2. the main features of the finite element model and the analytical model for simulating

wind-wave random forcing are illustrated;

3. the results of the analyses carried out are discussed by pointing out the nonlinear effect

induced by wind-waves interaction;

4. final conclusions concerning the study are then illustrated.



INTRODUCTION

Offshore wind turbines represent rather complex structural systems.

ENVIRONMENT STRUCTURESTOCHASTIC

INTERACTING

TIME-VARYING

Though the major regularity and power of the offshore wind forcing, they could become

competitive if a proper design approach is established by taking into account the above

factors and assuring a good compromise between safety and costs related aspects.

STRUCTURAL BEHAVIOR

LOADS (wind, wave, current etc.)

CONSTRAINTS (soil etc.)

PROPERTIES (mechanical, geometrical etc.)

MULTI-SCALE (support, junctions etc.)



INTRODUCTION

To obtain such a goal, design method of an offshore wind turbine requires a critical revision

according to the systemic approach.

Systemic Decomposition

sub-problem sub-problem sub-problem

ENVIRONMENT

LOADS (wind, wave, current etc.)

CONSTRAINTS (soil etc.)

STRUCTURE

PROPERTIES (mechanical, geometrical etc.)

MULTI-SCALE (support, junctions etc.)

STOCHASTIC

INTERACTING

TIME-VARYING

STRUCTURAL BEHAVIOR

sub-problem sub-problem

com

ple

xity



INTRODUCTION

The natural frequency of a typical offshore wind turbine operating in intermediate-depth water

is wedged between the wind and wave excitation frequency; in this context simulation of

wind-wave nonlinear interaction become a crucial aspect as it can led to a beneficial

damping by selecting proper structural stiffness of the turbine’s support: this would lead to an

increase fatigue life and reduce the cost of the support.

WIND excit.

STRUCTURE

WAVE excit.

frequency

Nonlinear

Interaction

INTERNATIONAL CODES AND STANDARDS



F.E. MODEL DESCRIPTION

The In the present work a 5MW 3-bladed offshore wind turbine with monopile-type support

is considered as economically convenient for intermediate water depth purposes: it represents

a structure of interest for possible planning of an offshore wind farm in the Mediterranean Sea

near the south-eastern cost of Italy.

Monopile type support

Z

Y X

Aerodynamic

Fluid-

dynamic

Geotechnical

Foundation

Submerged

Emergent

d

lfound

H

mud line Z

Y X

Z

Y X

Aerodynamic

Fluid-

dynamic

Geotechnical

Foundation

Submerged

Emergent

d

lfound

H

mud line

H = 100m

d=35m

lfound=40m

D =5m

tw=0.05m

Dfound=6m

D = diameter of the tubular tower;

tw = thickness of the tower tubular

member;

FIXED

effects of foundation are neglected (the lower node is fixed at the sea bottom)

beam elements (BEAM4) for simulating the tower

blades and nacelle replaced by a concentrated mass (MASS21)



WIND-WAVE SPECTRA

A typical wind-wave forcing with relatively small recurrence period is assumed in the following

calculations (exercise load): this could be crucial for fatigue-induced long term damage.

4

5.19

4

4

5

2

74.0,

4

5,0081.0

exp2)(

===

−⋅

⋅=

mPM

pPMPM

p

PMPM

V

g

gS

βωβα

ω

ωβ

ω

απωηη

α

=

hub

hubmmz

zVzV )(

[ ] 6522 )(8701

)(

)(4

/

i

m

i

i

ijij

zf.

zV

zLf

σ

(f,z)Sf

+=

( )

+

−−=

)()(2

)(exp)()()(

22

kmjm

kjz

ikikijijijikzVzV

zzCffSfSfS

π

wvui ,,=

( )[ ] 2

0

2 751)log(arctan116 *i u.zg.-σ +=

Pierson-Moskowitz wave spectrum

Wind velocity: mean and turbulent spectrum

z

y

x,x’

z’

y’

Mean water level

Mud line

Waves

Mean

wind

Current

P

(t)v P

(t)w P

(t)u P

Turbulent

wind Vm(zP)P

Mean water level

Mud line

Hub level

R

H

h

vw(z’)

Vcur(z’)

z

y

z

y

x,x’

z’

y’

x,x’

z’

y’

Mean water level

Mud line

Waves

Mean

wind

Current

P

(t)v P

(t)w P

(t)u P

P

(t)v P

(t)w P

(t)u P

Turbulent

wind Vm(zP)P

Mean water level

Mud line

Hub level

R

H

h

vw(z’)

Vcur(z’)

normalized half-side von Karman



Assuming linear wave theory and performing the Fourier transform of the elementary force

experienced by a structural member, force spectra are obtained for both wind and wave.

WIND-WAVE FORCE SPECTRA

d

|z|

z

x

d+z

dF(z,t)dz

A A Sect. A-A

D

tw

d

z

x

dF(z,t)dz

A ASect AA

D

tw

),(),(8

),(),( tzxtzCtzxCtzdF xDI&&&

&σ

π+=

Linearized Morison equation

[ ]2),(

2

1),( tzxdACtzdF DD

&ρ=

Aerodynamic drag force

[ ]

)()()cosh(

8

)cosh(

)sinh(),(

2

2

2

ωσ

π

ωω

ω ηηSzkzC

kzC

kdzS

ixiD

iI

iFF

+

=

&

( ) ∫∫=A

ikijDmkjFiFi dAdASCVzzS2

),,( ρω

Wind force spectrum

Wave force spectrum



Assuming linear wave theory and performing the Fourier transform of the elementary force

experienced by a structural member, force spectra are obtained for both wind and wave.

WIND-WAVE FORCE SPECTRA

),(),(8

),(),( tzxtzCtzxCtzdF xDI&&&

&σ

π+=

Linearized Morison equation

[ ]2),(

2

1),( tzxdACtzdF DD

&ρ=

Aerodynamic drag force

[ ]

)()()cosh(

8

)cosh(

)sinh(),(

2

2

2

ωσ

π

ωω

ω ηηSzkzC

kzC

kdzS

ixiD

iI

iFF

+

=

&

( ) ∫∫=A

ikijDmkjFiFi dAdASCVzzS2

),,( ρω

Wind force spectrum

Wave force spectrum

Vm hub = 20m/s

1.E-01

1.E+01

1.E+03

1.E+05

1.E+07

1.E+09

1.E+11

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04

freq [Hz]

Force spectra [N2/Hz]

Wind

Wave



RESPONSE SPECTRA: WAVE ONLY

The frequency of the first relative maximum corresponds to the peak frequency of the wave

force spectrum (about 0.1Hz); the absolute maximum of the structural response occurs

however at about 0.2Hz which is very close to the first vibration mode of the structure.

1.E-01

1.E+01

1.E+03

1.E+05

1.E+07

1.E+09

1.E+11

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04

freq [Hz]


Wind

Wave

fp = 0.1 Hz

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

freq [Hz]

Response spectra [m2/Hz]

X direction

fp = 0.1 Hzfn = 0.2 Hz



A spectrum in the direction y orthogonal to the mean wind speed appears due to component

correlation. Two maxima occur for the peak frequency of the wind spectrum and close to

the first mode frequency of the structure.

RESPONSE SPECTRA: WIND ONLY

1.E-01

1.E+01

1.E+03

1.E+05

1.E+07

1.E+09

1.E+11

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04

freq [Hz]


Wind

Wave

fp = 0.1 Hz

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

freq [Hz]


X direction

Y direction

fn = 0.2 Hz



The increasing roughness length of the sea surface owing to the presence of the wave field

has been modeled (iterative procedure).

No contribution is present in y-axis due to the absence of wave directional spreading.

RESPONSE SPECTRA: COMBINED WIND-WAVE

The in x-direction wind-wave

combination produces the

appearance of a relative

maximum at the wave peak

frequency.

The resultant response spectrum

appears to be the superposition

of the wind-only and wave-only

response.

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

freq [Hz]


X direction

Y direction

fp = 0.1 Hz

fn = 0.2 Hz



The increasing roughness length of the sea surface owing to the presence of propagating

waves has been modeled (iterative procedure).

RESPONSE SPECTRA: COMBINED WIND-WAVE

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

freq [Hz]


X direction

Y direction

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

freq [Hz]


X direction

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

freq [Hz]


X direction

Y direction

WIND ONLY

WAVE ONLY WIND + WAVE



A load time history is generated in time domain

with Montecarlo method;

both wind and wave actions associated with 4

different wind mean speeds are considered;

corresponding peak displacements at the hub

height are evaluated.

TIME DOMAIN ANALYSIS: COMBINED WIND-WAVE

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

200 700 1200 1700 2200 2700 3200

time [s]

dalong hub [m]

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

15 20 25 30 35 40 45 50 55

Vm hub [m/s ]

dpeakalong hub [m]

Time domain

(* =samples)

Frequency domainComparison with results from spectral

analysis shows that nonlinear interaction

can be reasonably neglected for wind

speed lower than 20m/s;

Vm hub=20 [m/s]



A load time history is generated in time domain

with Montecarlo method;

both wind and wave actions associated with 4

different wind mean speeds are considered;

corresponding peak displacements at the hub

height are evaluated.

TIME DOMAIN ANALYSIS: COMBINED WIND-WAVE

Comparison with results from spectral

analysis shows that nonlinear interaction

can be neglected for wind speed lower

than 40m/s;

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

200 700 1200 1700 2200 2700 3200

time [s]

dacross hub [m]Vm hub=20 [m/s]

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

15 20 25 30 35 40 45 50 55

Vm hub [m/s ]

dpeakacross hub [m]

Time domain

(* =samples)

Frequency domain



CONCLUSIONS

In this work a finite element model for the dynamic analysis in both time and frequency domain

of a monopile-type support structure for offshore wind turbine has been presented.

Excitation wind and wave spectra are calculated for typical exercise conditions and nonlinear

interaction is evaluated concerning the structural response spectrum.

The obtained results have shown that wind-wave nonlinear interaction becomes important

for elevated wind speed and should be considered in the design phase of a safe and cost-

effective offshore wind turbine.

This can be done performing a time-domain analysis which is however computationally

cumbersome: in order to obtain analogous results from the frequency-domain analysis, which

is intrinsically linear, the wind-wave spectra correlation and geometrical nonlinearity

should be introduced; this is currently under development.

Design

5 - Dynamic Analysis of an Offshore Wind Turbine: Wind-Waves Nonlinear Interaction