Damping of Wind Turbine Tower Vibrations by a stroke ...

Damping of WindTurbine Tower

Vibrations

Mark L. Brodersen

MotivationOffshore wind turbine towervibrations

Implementation ofdampersCriteria for effectivedamping

Tower modes

Brace concepts

Numerical modelsBeam model and HAWC2model

ResultsDamper stroke

Attainable damping

Damper force

Free decay

Outlook

Damping of Wind Turbine Tower Vibrationsby a stroke amplifying brace concept

Mark L. Brodersen & Jan Høgsberg

Department of Mechanical EngineeringTechnical University of Denmark

[email protected]

EERA DeepwindJanuary 22-24 2014


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Outline

Motivation

Implementation of dampers

Numerical models

Results


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Offshore wind turbine tower vibrations

• Wind-wave misalignment– Larger wind turbine and deeper waters

• Resonant dampers• Dampers inside the tower


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook



• Resonant dampers

• Dampers inside the tower


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook



• Resonant dampers• Dampers inside the tower


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Criteria for effective damping• Damper stroke

– Activation of damper– Damper force

Ed = u̇d fd

udfd

• Attainable damping

– Given by the change in frequency

ζmax 'ω∞ − ω0

ω∞ + ω0


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Criteria for effective damping• Damper stroke

– Activation of damper– Damper force

Ed = u̇d fd

udfd

• Attainable damping– Given by the change in frequency

ζmax 'ω∞ − ω0

ω∞ + ω0ω0 ω∞


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Criteria for effective damping

• Tuning of dampers– Viscous dampers with damping parameter c

fd = cu̇d

– Tuning for maximum damping

copt ' 2ω∞ − ω0∑N

k γ2k

γ is the damper stroke with respect to mode u0 forunit modal mass uT

0 Mu0 = 1

u0


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Tower modes

For-aft mode Side-to-side mode


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Brace concepts

θ3

z

x y

Curvature-brace Curvature-toggle-brace


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Brace concepts

θ3

z

x y

l

lθ3

z

x y



Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Brace concepts

60◦ 60◦



Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Numerical models

• Linear beam model– Wind turbine at standstill– Linear Winkler type spring model– Lumped inertia– Stiffness matrix derived from complementary energy

• HAWC2

– Blade element momentum theory– Multi-body formulation– Control via Dynamic Link Library (dll) interface– External system

• Offshore Code Comparison Collaboration

– NREL reference turbine + monopile in 20 m water


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Numerical models


• HAWC2– Blade element momentum theory– Multi-body formulation– Control via Dynamic Link Library (dll) interface– External system

• Offshore Code Comparison Collaboration

– NREL reference turbine + monopile in 20 m water


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Numerical models


• HAWC2– Blade element momentum theory– Multi-body formulation– Control via Dynamic Link Library (dll) interface– External system

• Offshore Code Comparison Collaboration– NREL reference turbine + monopile in 20 m water


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Displacement of damper

0 50 100 150 200 250 300 350−6

−4

−2

0

2

4

6

θ3

ud[m

m]

ud for the curvature brace with respect to the fore-aft mode (dotted) and the side-to-sidemode (dash-dotted) and ud for the curvature-toggle-brace with respect to the fore-aft

mode (dashed) and the side-to-side mode (solid)


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Displacement of damper

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Position of rotor

∑kγ2 k[m

m2]

γ2 for the curvature brace with respect to the fore-aft mode (dotted) and the side-to-sidemode (dash-dotted) and γ2 for the curvature-toggle-brace with respect to the fore-aft

mode (dashed) and the side-to-side mode (solid)


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Attainable damping

1 1.005 1.01 1.015 1.02 1.025 1.030

0.005

0.01

0.015

1

ωd/ω0

ζ


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Attainable damping

1 1.005 1.01 1.015 1.02 1.025 1.030

0.005

0.01

0.015

2

3

4

5

6

7

89 10

1

ωd/ω0

ζ


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Attainable damping

1 1.005 1.01 1.015 1.02 1.025 1.030

0.005

0.01

0.015

2

3

4

5

6

7

89 10 11

12

13

14

15

16

17

18

1 19

ωd/ω0

ζ


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Attainable damping

Curvature-brace

1 1.005 1.01 1.015 1.02 1.025 1.030

0.005

0.01

0.015

2345

67

89 10 11

1213

1415161718

1 19

ωd/ω0

ζ

1 1.005 1.01 1.015 1.02 1.025 1.030

0.005

0.01

0.015

2345

67

89 10 11

1213

1415161718

1 19

ωd/ω0

ζ

Fore-aft mode Side-to-side mode

Curvature-toogle-brace

1 1.005 1.01 1.015 1.02 1.025 1.030

0.005

0.01

0.015

2345

67

89 10 11

1213

1415161718

1 19

ωd/ω0

ζ

1 1.005 1.01 1.015 1.02 1.025 1.030

0.005

0.01

0.015

2345

67

89 10 11

1213

1415161718

1 19

ωd/ω0

ζ

Fore-aft mode Side-to-side mode


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Damper force

0 50 100 150 200 250 300 350−1500

−1000

−500

0

500

1000

1500

θ3

fd[kN]

fd for the curvature brace (dash-dotted)and fd for the curvature-toggle-brace (solid)


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Free decay

0 50 100 150 200 250−0.4

−0.2

0

0.2

0.4

t [s]

ut[m

]


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Free decay

0 50 100 150 200 250−0.4

−0.2

0

0.2

0.4

ζ = 0.0065

t [s]

ut[m

]


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Free decay

0 50 100 150 200 250−0.4

−0.2

0

0.2

0.4

ζ = 0.0065

t [s]

ut[m

]

0 50 100 150 200 250−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

t [s]

ut[m

]


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Free decay

0 50 100 150 200 250−0.4

−0.2

0

0.2

0.4

ζ = 0.0065

t [s]

ut[m

]

0 50 100 150 200 250−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

ζ = 0.0198

t [s]

ut[m

]


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Outlook

Summary• Maximize attainable damping and damper stroke

– Installation at the bottom of the tower– Stroke amplifying toggle brace– Attainable damping: 1.3 % critical– Optimum tuning independent of the orientation of the rotor– The same tuning can be used for both critical modes

Ongoing work

• Physical implementation• Experimental validation


Vibrations

Mark L. Brodersen



Tower modes

Brace concepts



Attainable damping

Damper force

Free decay

Outlook

Outlook

Summary• Maximize attainable damping and damper stroke

– Installation at the bottom of the tower– Stroke amplifying toggle brace– Attainable damping: 1.3 % critical– Optimum tuning independent of the orientation of the rotor– The same tuning can be used for both critical modes

Ongoing work• Physical implementation• Experimental validation

Damping of Wind Turbine Tower Vibrations by a stroke ...

Documents

Transcript of Damping of Wind Turbine Tower Vibrations by a stroke ...