Comparison of time and frequency domain simulations of an offshore floating wind turbineMaxime PHILIPPE, Aurélien BABARIT and Pierre FERRANT

Laboratoire de Mécanique des Fluides CNRS UMR 6598Ecole Centrale Nantes

The authors would like to acknowledge ADEME (the French environment agency) and région Pays de la Loire for funding the PhD

program in which this study has been done.

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Presentation summary

� Introduction and model properties

� Simulation capabilities

� Results comparison

• Freq. dom. model and simple time dom. aerodynamic models

• Linear hydrodynamic + FAST : frequency and time domain

• Effect of hydrodynamic non-linearity� Quadratic damping� Non linear hydrostatic and Froude-Krylov

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Introduction

Source : Jonkman J., Dynamics Modeling and load Analysis of an Offshore Floating Wind Turbine, PhD Thesis, 2007

Wind power : fast growing energy source

Offshore wind advantages :

� Wind tends to blow more strongly � Size and power of turbines is not limited

� Visual and noise annoyance can be avoid

� Vast sea areas are available

Current offshore wind technology, fixed bottom substructures, is water depth limited

In deeper water floating wind turbines may become economical

Different support floating structures are availableThese concepts are derived of those used by O&G industry

O&G industry has demonstrated the viability of such structures

The challenge is to find an economical solution

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Floating platform model properties

MIT/NREL Shallow Drafted Barge :• Concept developed by E. Wayman under the direction of P. Sclavounos

at M.I.T [Wayman,2006]• The design is thought to be stable without mooring• Mooring Stiffness only in surge and sway Steel

Concrete

Summary of MIT/NREL SDB Properties

Source : Wayman E.N., Sclavounos P.D., Butterfield S., Jonkman J., and Musial W., Coupled Dynamic Modeling of Floating Win d Turbine Systems, 2006 Offshore Technology Conference, 1-4 May 2006

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Floating wind turbine model properties

NREL offshore 5-MW baseline wind turbine :• Concept developed at National Renewable Energy Laboratory (US)• Reference turbine for offshore system development

Nominal rating for 11.2 m/s wind speed

Maximum thrust on rotor

Source : Jonkman J., Butterfield S., Musial W., and Scott G., Definition of a 5-MW Reference Wind Turbine for Offshore System Developpement, NREL/TP-500-39060, Golden, CO: NREL, 2009.

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Coordinate system and modes of motion

� System is assumed to undergo rigid body motion

� Tower base coincides with surface water line

� Base case : � Wind speed : 11.2 m.s-1

� Water depth :200 m

� 1 – Surge� 2 – Sway� 3 – Heave

� 4 – Roll � 5 – Pitch� 6 – Yaw

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Simulation capabilities

Time domain :

Hydrodynamic :

� Linear diffraction/radiation

� Quadratic damping

� Non linear Froude-Krylov loads on instantaneous wetted surface

Wind turbine :

� Simple wind load model

� FAST time domain model

Frequency domain :

Hydrodynamic : Linear diffraction/radiation

Wind turbine : aerodynamic damping

+ gyroscopic stiffness

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Simulation capabilities

RAOs from freq. dom. are compared with pseudo-RAOs from steady-state time dom. :

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FAST Linearization and RAOs calculation

The equation of motion solved by FAST in case of a floating wind turbine moored on the seabed, without incident wave reads:

q: vector of DOFs

Me: turbine mass matrix

Mp: platform mass matrix

f: forcing function excepting Frad, Fb and Fa

Fa: mooring loads

Fb: buoyancy

Frad: radiation loads calculated with Aquaplus

FAST numerically linearizes this equation by perturbing each value from his value at operating point

*

System oscillating motion can be written by linearizing eq. * :

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FAST Linearization and RAOs calculation

(1): mass matrix

(2): added mass matrix

(3): aerodynamic damping

(4): wave damping

FAST gives access to resulting matrices Mres, Lres and Kres

Equation of oscillating motions of the system around operating point due to an harmonic excitation Fex of incident wave, using complex notation is:

(5): gyroscopic stiffness

(6): hydrostatic stiffness

(7): mooring stiffness

( )² ( ) ( ) ( )res res res exM i L K q Fω ω ω ω ω− + + ∆ =

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Simple Time domain models

Aerodynamic force on the system is modeled as:

Simple model 1 : Constant Thrust and Torque

Simple model 2 : Relative wind speed thrust and constant torque

Hydrodynamic is taken into account with linear theory

0

( ) ( ) ( ) ( ) ( ( ) ( )) ( )t

e p rad h a ex dif aeroM M X K t X d K K X K t K t d Fµ τ τ τ τ τ η τ τ+∞

∞−∞

+ + + − + + = − + − +∫ ∫&& &

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Frequency model and simple time domain model

Damping in pitch has to be fitted

Transverse motions are different

Taking into account gyroscopic effect could resolve this issue

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Time domain model : Achil3D+FAST

� Impulse responses are calculated with Achil3D, in house code

� FAST computes at each time step hydrodynamic loads on the platform in a user defined routine

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Time domain : linear hydrodynamic

Hydrostatic loads:

Radiation loads:

Wave excitation loads:

In linear hydrodynamic theory, hydrodynamic loads expression is

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Linear hydrodynamic : frequency and time domain

Good agreement between time and frequency domain results

Damping in pitch is the same in the two simulations

Non linear effect around 0.3 rad/s

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Effect of quadratic damping

with

Damping of the motions around natural frequency

Quadratic roll and pitch damping :

Motion in a 1 m amplitude wave height

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Effect of quadratic damping

Important non linear effect

Motion in a 4 m amplitude wave height

with

Quadratic roll and pitch damping :

Unrealistic response without quadratic damping

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Effect of non linear Froude-Krylov loads

Froude-Krylov and hydrostatic load on instantaneous wetted surface

avec avec

• Yaw instability appears

• Mooring stiffness in yaw stabilize the system

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Effect of non linear Froude-Krylov loads

Important effect on roll motion even for 1m incident wave

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Conclusion

� Simple aerodynamic time domain model are not in good agreement

� Good agreement for time and frequency domain for

� Natural frequency

� Small amplitude motions

� Hydrodynamic non linearity are not negligible for:

� high amplitude motions

� rotational degrees of freedom

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Thank you for your attention