st h ti d i l i fstochastic dynamic analysis of offshore ... gao.pdf · 1 st h ti d i l i...

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St h ti d i l i fStochastic dynamic analysis of offshore wind turbines

– with emphasis on fatigue

Zhen GaoCeSOS, NTNU

CeSOS Highlights and AMOS Visions ConferenceTrondheim, Norwayy

May 27, 2013

www.cesos.ntnu.no Author – Centre for Ships and Ocean Structureswww.cesos.ntnu.no Gao – Centre for Ships and Ocean Structureswww.cesos.ntnu.no CeSOS – Centre for Ships and Ocean Structures

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Contents

• Personal information

Co te ts

• Overview of offshore wind technology• Modelling of environmental conditions• Dynamic analysis of offshore bottom-fixed wind turbines• Modelling and dynamic analysis of floating wind turbines• Frequency-domain fatigue analysis• Main conclusions

R d ti f f t k• Recommendations for future work

www.cesos.ntnu.no Author – Centre for Ships and Ocean Structureswww.cesos.ntnu.no Gao – Centre for Ships and Ocean Structures

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Personal information• 2000.9 – 2003.3,

– MSc; SJTU; Prof. Yongning Gu

e so a o at o

– Numerical Simulation of Ship Collision

• 2003.8 – 2008.2, – PhD; CeSOS, NTNU; Prof. Torgeir Moan– Stochastic Response Analysis of Mooring Systems with Emphasis on Frequency-

domain Analysis of Fatigue due to Wide-band Response Processes

• 2008.3 – 2010.7,– Post-doc; CeSOS, NTNU; Prof. Torgeir Moan– Stochastic dynamic analysis of offshore wind turbines; mooring system for wave

energy converters

• 2010 8 –• 2010.8 –– Researcher / adj. assoc. prof.; CeSOS, NTNU– Co-supervisor for some PhD candidates with Prof. Torgeir Moan as main supervisor– Stochastic dynamic analysis, extreme response prediction, fatigue analysis as well as y y , p p , g y

structural reliability assessment of offshore wind turbines and combined wind and wave energy devices


4

Overview of offshore wind technology (1/2)gy ( )

Rated power 2-3 MW 2-3 MW 3-5 MW 5 MW + (?)

Support structure Monopile, gravity- Tri-pod Jacket FloatingSupport structure Monopile, gravitybased

Tri pod Jacket Floating

Water depth (m) 0-30 10-40 30-80 >100 (?)

Industry Large commercial wind farms Demonstration wind Prototype (HywindIndustrydevelopment

Large commercial wind farms already exist (Denmark, UK, the Netherlands, Germany, Sweden, etc.)

Demonstration windfarms (Beatrice, Alpha Ventus)

Prototype (Hywind, WindFloat, BlueH,Sway, etc.)

I t ti l IEC 61400 3 GL DNV BV d R f t ff h U d d l tInternational standard

IEC 61400-3, GL, DNV, BV and ABS; an extension of design code for onshore wind turbines

Refer to offshoredesign rules for support structures

Under development

Software International Energy Agency (IEA), code-to-code comparison, OC3 (monopile, tri-pod and


developmentgy g y ( ), p , ( p , p

spar, coordinated by NREL), OC4 (jacket and semi-submersible, coordinated by Fraunhofer IWES and NREL)

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Overview of offshore wind technology (1/2)gy ( )• Design of offshore wind turbine

– Power production– Structural integrity, wrt ULS, FLS, ALS

• Integrated analysis of offshore wind turbine system– Environmental conditionsEnvironmental conditions

• Turbulent wind • Random waves

– Load analysis:y• Aerodynamics • Hydrodynamics

– Response analysis:• Structural dynamics• Mooring analysis for floating WT

– Control theory• To maximize power prod. (<Uw_rated)• To keep constant power and reduce loads (>Uw_rated)• Applied in time domain

D i f t


• Design of components– Hierarchical system of analysis (global / local)

Load source on a floating wind turbine(Butterfield et al., 2007)

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Modelling of environmental conditions (1/3)• Short-term condition:

– Wind: turbulent wind field (profile spectrum coherence)

g ( )

Wind: turbulent wind field (profile, spectrum, coherence)– Waves: random irregular waves (lin./nonlin., spectrum)– Stationarity: wind (10 min) vs. waves (1-3 h) ?

Directionality– Directionality

• Long-term condition:g– Joint env. data

• Wind: mean wind speed Uw, (wind turbulence intensity?)• Waves: significant wave height Hs, spectral peak period Tp ‘Wind speed box’ in the• Analytical joint distribution• Extrapolation of 50-year extreme conditions

– Measurement vs. hindcast data

Wind speed box in the aerodynamic code HAWC2

– Directional distribution

Wind turbine design rules require a significant number of simulations considering various load conditions and load cases and fast sim lation tools are needed


conditions and load cases, and fast simulation tools are needed.

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Modelling of environmental conditions (2/3)• Long-term env. data of European offshore sites

(Li et al., 2013)

g ( )Representative sites

(Li et al., 2013)– EU FP7 MARINA Platform project (combined wind and

wave or tidal energy technology)– Hindcast data (hourly, 2001-2010), National and

K d t i U i it f AthKapodestrian University of Athens– Joint distribution model (Johannessen et al., 2001)

( ) ( ) ( ) ( )hutfuhfufthuf HsUwTpUwHsUwTpHsUw ,,, ,,, ⋅⋅=Uw: - Mean wind speed at 10m height, Weibull distributionHs conditional on Uw: - Weibull distribution with parameters as function of uTp conditional on Uw and Hs:

Site Area Name Geo coordinates Water depth Distance to Average wind power at 80m

Average wave

Tp conditional on Uw and Hs: - Lognormal distribution with parameters as function of u and h

Information of the five selected European offshore sites

No. Area Name Geo-coordinates (m) shore (km) power at 80m height (kW/m^2)

power (kW/m)

1 Atlantic Sem Rev 47.24N, -2.77E 33 15 0.53 16.51

3 Atlantic Buoy Cabo Silleiro 42.13N, -9.40E 449 40 0.65 42.72

5 Atlantic Wave Hub 50.36N, -5.61E 43 20 0.62 31.79


,

14 North Sea Norway 5 61.85N, 4.23E 202 30 1.09 46.43

15 North Sea Denmark, North Sea Center 55.13N, 3.43E 29 300 0.87 14.29

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Modelling of environmental conditions (3/3)• Long-term extreme response

analysis based on the

g ( )

yenvironmental contour method

• Extrapolated 50-year contourExtrapolated 50 year contour surface of Uw, Hs and Tp

Condition on the 50-year contour surface with maximum Uw or maximum Hs

Uw (m/s) Hs (m) Tp (s)

Condition with maximum Uw 33.6 13.4 13.1maximum Uw

Condition with maximum Hs 31.2 15.6 14.5


Fifty-year contour surface at Site No. 14 (Northern North Sea, Norway)

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Dynamic analysis of offshore bottom-fixed wind turbines (1/3) – Modellingturbines (1/3) – Modelling

Jacket wind turbine analysis(Gao et al., 2010)( , )

• Jacket structure• Aker Solutions’ design• Water depth: 70mp

• Wind turbine• 5MW NREL wind turbine• Variable speed/ variable pitch

• Decoupled analysis method

p p• Controller: Risø Nat. Lab.

Decoupled analysis method for jacket wind turbine– Wind- and wave-induced responses calculated separately

– Quasi-static responses induced by wave loads

• Replacement of the jacket by an equivalent monopile

wind turbine

– Equivalent mass, stiffness and hydrodynamic properties– When the global responses (e.g. the bending moment at the sea bed) are of interest.

• Software: HAWC2 and USFOS


Now, there exist integrated tools for dynamic analysis of jacket wind turbine! (IEA OC4 benchmark)

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Dynamic analysis of offshore bottom-fixed wind turbines (2/3) – Response characteristics

• Main observations:- Wind turbine loads excite responses at various frequencies (low freq rotational freq natural freq of 1st and

turbines (2/3) – Response characteristics

- Wind turbine loads excite responses at various frequencies (low freq., rotational freq., natural freq. of 1 and 2nd global bending modes), while wave loads mainly induce quasi-static responses at wave freq.

- Jacket responses, dominated by wind loads in operational condition, while by wave loads in extreme condition- Second global bending mode, excited in operational condition, but not in extreme condition (rotor parked)

Mainly wind-induced, first bending mode

Wave-induced, quasi-static

Wind-induced, quasi-staticWide-band process!

Wind-induced, second bending mode

Wind-induced, rotational frequency (blade, 3P effect)

The first and second global bending modes (scale factor of 1000) with a natural frequency

Spectral density function of global bending moment at jacket bottom in operational condition

Imply high fatigue damage!


(scale factor of 1000) with a natural frequency of 2.2 and 10.5 rad/s, respectively

at jacket bottom in operational condition (Uw=15m/s, Hs=4m, Tp=8s)

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Dynamic analysis of offshore bottom-fixed wind turbines (3/3) – Fatigue analysis of tubular jointsturbines (3/3) – Fatigue analysis of tubular joints

• Long-term fatigue analysis of tubular joints (Dong et al., 2010)– Methods available from offshore oil & gas industry (e.g. SN-curve approach)– Time-domain global response analysis for member forces/moments– Hot-spot stress calculation for fatigue analysis– Rainflow cycle counting method Due to the effect of a

wide-band processMember forces/moments from global response analysis

wide-band process

Hot-spot stress calculation pbased on a linear combination of members forces/moments

Contribution of wind and wave induced


Typical joints analyzedContribution of wind- and wave-induced

fatigue damage to the total fatigue damage

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Modelling and dynamic analysis of floating i d t bi (1/3)

• Wind turbine aerodynamic modelBEM (Bl d l t t th d) A t t di t t li d l CFD

wind turbines (1/3)

– BEM (Blade element momentum method), Actuator disc or actuator line model, CFD– Simplified thrust force model (TDHMILL)

• Velocity-dependent thrust force acting on the nacelle• Validation against refined model with BEM: Simo/Riflex/TDHMILL against HAWC2 for spar floating

wind turbine (Karimirad & Moan, 2012)

• Hydrodynamic model– Morison’s formulae, Potential theory (rigid-body hydrodynamics)– Combined panel and Morison model

• Global responses of braces in semi-submersible wind turbines (Luan et al., 2013)

• Structural model– Aero-elasticity is important for large-size wind turbines (blades, tower), considered in BEM

and Actuator disc or actuator line model– Beam and rigid-body model typically used– Mooring system: nonlinear spring, full dynamic model (coupled mooring analysis)Mooring system: nonlinear spring, full dynamic model (coupled mooring analysis)

• Software development


– Integrated tools in the OC3 and OC4 benchmark study: HAWC2, FAST, Simo/Riflex/AeroDyn, etc.

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Modelling and dynamic analysis of floating wind t bi (2/3)

• Comparison of three concepts (Gao et al., 2011)

turbines (2/3)

(Gao et al., 2011) – Analysis methods:

• Simplified thrust force model• Potential theory for hydrodynamicsy y y• Rigid-body motion analysis• Coupled mooring analysis

Spar (OC3-Hywind)

Semi-sub(WindFloat)

TLP(MIT/NREL)

80S WT

25

func

tion

of

^2*s

/rad)

50

60

70

Spar WTSemi-submersible WTTension-leg WT (*1000)

Pitch resonant motion

unct

ion

of

^2*s

/rad)

15

20

Spar WTSemi-submersible WTTension-leg WT (*100)

Pitch resonant motion

Spec

tral d

ensi

ty f

pitc

h m

otio

n (d

eg

20

30

40

Wave-freq. motion

Spec

tral d

ensi

ty fu

pitc

h m

otio

n (d

eg^

5

10Wave-freq. motion

Frequency (rad/s)

0.0 0.5 1.0 1.5 2.00

10

Frequency (rad/s)

0.0 0.5 1.0 1.5 2.00

5


Spectra of pitch motion for operational condition(Uw=11.4m/s, Hs=3.1m, Tp=10.1s)

Spectra of pitch motion for parked condition(Uw=50m/s, Hs=12.7m, Tp=14.1s)

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Modelling and dynamic analysis of floating i d t bi (3/3) F ti l iwind turbines (3/3) – Fatigue analysis

• Global analysisM d lli i Si /Rifl /TDHMILL– Modelling in Simo/Riflex/TDHMILL

• Columns – rigid-body, potential theory (multi-body hydrodynamics)• Braces – beam, Morison’s formulae

Responses:– Responses:• Rigid-body motions• Member forces in braces

Global analysis model (Luan et al., 2013)• Local analysis– Linear refined structural model– Hot-spot stress calculation

F ti d t

Local model for fatigue analysis (Fredheim, 2012)

• Fatigue damage assessment– Stress time series– Rainflow cycle counting


Local model for fatigue analysis (Fredheim, 2012)(left: column-brace joints, right: refined FE model)

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Frequency-domain fatigue analysis (1/5)q y g y ( )• Fatigue assessment based on the SN-curve approach

– Cycle counting for effective stress rangesCycle counting for effective stress ranges– Fatigue damage accumulation law (e.g. Palmgren-Miner)

• Cycle counting method for wide-band Gaussian processes– Reference method: the time-domain rainflow counting method– Frequency-domain methods:

• The narrow-band approximationBi d l G i• Bimodal Gaussian process

– Jiao & Moan (1990) – approx. analytical formula– etc.

• Multi-modal Gaussian process Multi modal Gaussian process– Gao & Moan (2008) – approx. semi-analytical formula

• Empirical formulae for general wide-band Gaussian process– Dirlik (1985)– Benasciutti & Tovo (2005)– etc.


Illustration of the rainflow cycle counting method

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Frequency-domain fatigue analysis (2/5)• The narrow-band approximation is always conservative, but

– Maximum 30% for% f

q y g y ( )

0.5δ ≤0* *(2 2 ) * (1 2)mD T v K mσ= Γ +

– Maximum 10% for– Too conservative for

FC 10

11

12

13NB

1.4

1.5N B1δ →

0.3δ ≤

( )G ω ( )G ω

0

Gao & Moan

e da

mag

e to

RF

7

8

9

10

1.2

1.3

21σ 2

2σ2

1σ23σ2

2σ

Gao & Moan (2007)

Rat

io o

f fat

igue

3

4

5

6

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.601.0

1.12ω1ω 2ω1ω 3ω

Vanmarcke's bandwidth parameter0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

R0

1

2NB

RFC

DD

Vanmarcke s bandwidth parameter

Accuracy of the narrow-band approximation for wide-band fatigue analysis (based on the comparison with the rainflow counting methods for over 4000 spectra)Benasciutti

& Tovo (2005)


Spectra considered21 0 21 / /m m mδ = −

Vanmarcke’s bandwidth parameter

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Frequency-domain fatigue analysis (3/5)• Bimodal Gaussian process

Ji & M (1990)( ) ( ) ( )HF LFX t X t X t= + ( )HF LF True RFC NBD D D D D+ < = <

q y g y ( )

• Jiao & Moan (1990)* NB fatigue damage

* P d l (NB)

0 max 00

(2 ) ( )m mX

T TD x f x dx SK Kν ν

+∞

= =∫* Pseudo-envelope (NB)

* A lit d f

( ) ( ) ( )HF LFP t R t X t= +

( )P t( )G ω

* Amplitude of ( ) ( ) ( )HF LFQ t R t R t= +

( )P t2

1σ 22σ

* Mean zero up-crossing rateThe Rice formula

0, (0, )P PPpf p dpν+∞

= ∫

2ω1ω

Example of a bimodal process, its pseudo-envelope and amplitude

processes

Spectral density function of a bimodal process

* Fatigue damage

JM HF PD D D= +

0∫ processes

• Gao & Moan (2007)* Extension to non-Gaussian processes


* Applied in DNV-OS-E301 Extension to non Gaussian processes (fatigue analysis of mooring line)

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Frequency-domain fatigue analysis (4/5)q y g y ( )

• Generalization (Gao & Moan, 2008)– Assume the NB components with decreasing central

frequencies as – Define the equivalent processes as

1 2( ), ( ),..., ( )iX t X t X t( ) ( ) ( )P t P t P tDefine the equivalent processes as

– Approximate the fatigue damage as the sum of– Semi-analytical solution can be obtained

1 2( ), ( ),..., ( )iP t P t P t

1 2, ,...,P P PiD D D


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Frequency-domain fatigue analysis (5/5)• Results for trimodal Gaussian processes

q y g y ( )

RFC

1 5

2.0

var1

FD

RFC

DD

dam

age

to R

1 0

1.5var1

var2 var3

Spectral density funciton1ω 2ω 3ω

o of

fatig

ue d

0 5

1.0

SSNB

Spectral density funcitonSS – Summation of components

NB – Narrow-band approximationR

atio

0 0

0.5 NBDKBTProposedVIV and WF+LF

DK – Dirlik’s formula

BT – Benasciutti & Tovo’s formula

Proposed – Gao & Moan

Vanmarcke's bandwidth parameter0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0p

VIV and WF+LF – Summation of the VIV fatigue and the combined WF and LF fatigue

Accuracy of the frequency-domain methods for trimodal fatigue analysis


Accuracy of the frequency domain methods for trimodal fatigue analysis

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Main conclusions• The long-term joint env. model developed can be used for both power estimation

and fatigue assessment. Extrapolated extreme conditions might be used for extreme response prediction using the environmental contour method.e e e espo se p ed c o us g e e o e a co ou e od

• For the jacket wind turbine considered, a decoupled analysis method can be applied since the wave-induced responses are mainly quasi-static. However, there pp p y qare available integrated tools now. Fatigue in the jacket foundation is dominated by wind turbine loads.

• Simplified aerodynamic model can be used for rigid-body motion analysis of floating wind turbines in a preliminary design. Further validation is needed.

• In line with the development of integrated tools for floating wind turbines, various modelling techniques for floaters have also been applied with an aim of obtaining structural responses directly from time-domain global analysis and then for local analysisanalysis.

• Frequency-domain cycle counting methods in particular for multi-modal processes are developed and might be used for fatigue analysis of offshore wind turbines.


are developed and might be used for fatigue analysis of offshore wind turbines.

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Recommendations for future work• Develop joint environmental model including wind turbulence intensity

• Further validate hindcast data with long-term measurements

• Further develop and validate modelling techniques that can predict responses p g q p pin structural components directly from time-domain global analysis

• Develop software that can integrate global and local analysis of offshore bottom-fixed and floating wind turbines for structural design

• Validate numerical tools by comparison with experiment and/or field measurements

• For preliminary design, develop frequency-domain methods for load and l i f ff h i d t bi d l f d iresponse analysis of offshore wind turbines and apply frequency-domain

fatigue assessment methods


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References• Dynamic analysis of offshore wind turbines:• Dong, W.B., Moan, T. and Gao, Z. (2011) Long-term Fatigue Analysis of Multi-planar Tubular Joints for Jacket-type Offshore

Wind Turbine in Time Domain. Engineering Structures; Vol. 33, No. 6, pp. 2002-2014.• Fredheim Ø (2012) Fatigue Analysis of Column Brace Connection in a Semi submersible Wind Turbine Master Thesis NTNU• Fredheim, Ø. (2012) Fatigue Analysis of Column-Brace Connection in a Semi-submersible Wind Turbine. Master Thesis, NTNU.• Gao, Z., Luan, C.Y., Moan, T., Skaare, B., Solberg, T. and Lygren, J.E. (2011) Comparative Study of Wind- and Wave-induced

Dynamic Responses of Three Floating Wind Turbines Supported by Spar, Semi-submersible and Tension-leg Floaters. In:Proceedings of the 2011 International Conference on Offshore Wind Energy and Ocean Energy, October 31-November 2, Beijing,China.

• Gao Z Saha N Moan T and Amdahl J (2010) Dynamic Analysis of Offshore Fixed Wind Turbines under Wind and WaveGao, Z., Saha, N., Moan, T. and Amdahl, J. (2010) Dynamic Analysis of Offshore Fixed Wind Turbines under Wind and WaveLoads Using Alternative Computer Codes. In: Proceedings of the 3rd Conference on the Science of making Torque from Wind(TORQUE), June 28-30, Heraklion, Greece.

• Karimirad, M. & Moan, T. (2012) A simplified method for coupled analysis of floating offshore wind turbines. Marine Structures,Vol. 27, No. 1, pp. 45-63.

• Luan, C.Y., Gao, Z. and Moan, T. (2013) Modelling and Analysis of a Semi-Submersible Wind Turbine with a Central Tower with, , , , ( ) g yEmphasis on the Brace System. In: Proceedings of the 32nd International Conference on Ocean, Offshore and ArcticEngineering, OMAE2013-10408, June 9-14, Nantes, France.

• Joint distribution of environmental conditions:• Li, L., Gao, Z. and Moan, T. (2013) Joint Environmental Data At Five European Offshore Sites For Design Of Combined Wind

And Wave Energy Devices. In: Proceedings of the 32nd International Conference on Ocean, Offshore and Arctic Engineering,gy g , g g,OMAE2013-10156, June 9-14, Nantes, France.

• Frequency-domain cycle counting methods:• Benasciutti, D. & Tovo, R. (2005) Spectral methods for lifetime prediction under wide-band stationary random processes.

International Journal of Fatigue; Vol. 27, pp. 867-877.• Dirlik T (1985) Application of computers in fatigue Ph D Thesis University of WarwickDirlik, T. (1985) Application of computers in fatigue. Ph.D. Thesis, University of Warwick.• Gao, Z. and Moan, T. (2007) Fatigue Damage Induced by NonGaussian Bimodal Wave Loading in Mooring Lines. Applied Ocean

Research; Vol. 29, pp. 45-54.• Gao, Z. and Moan, T. (2008) Frequency-domain Fatigue Analysis of Wide-band Stationary Gaussian Processes Using a Trimodal

Spectral Formulation. International Journal of Fatigue; Vol. 30, No. 10-11, pp. 1944-1955.• Jiao G & Moan T (1990) Probabilistic analysis of fatigue due to Gaussian load processes Probabilistic Engineering Mechanics;


Jiao, G. & Moan, T. (1990) Probabilistic analysis of fatigue due to Gaussian load processes. Probabilistic Engineering Mechanics;Vol. 5, No. 2, pp. 76-83.

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Thank you!


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