innovation for our energy futurenational renewable energy laboratory 1 gunjit bir national renewable...

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Innovation for Our Energy Future National Renewable Energy Laboratory

Gunjit BirGunjit Bir

National Renewable Energy LaboratoryNational Renewable Energy Laboratory

4747thth AIAA Aerospace Meetings AIAA Aerospace Meetings

Orlando, FloridaOrlando, Florida

January 5-8, 2009January 5-8, 2009

BModesBModes (Blades and Towers Modal Analysis Code) (Blades and Towers Modal Analysis Code)

Verification of Blade Modal AnalysisVerification of Blade Modal Analysis

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BackgroundMotivation for development of BModes

• Modal-based codes, such as FAST, need modes of main flexible components (towers and blades) to build wind turbine models.

• BModes developed to provide such modes.

FAST

BModes Post-process modal data

Blade modes

Tower modes

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Background Other Applications of BModes

• Experimental validation or code-to-code verification of blade & tower components

• Parameters identification (model updating)• Modal reduction• Physical interpretation of dynamic couplings• Aiding stability analysis• Modal-based fatigue analysis

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• Given:– Blade distributed geometric & structural properties– Rotational speed– Pitch control setting, precone– Tip mass inertia properties

• Computes:– Modal frequencies*– Coupled mode shapes

* BModes provides up to 9*(Number_elements) of modes

BModes Usage: for Blades

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• Each natural mode has coupled flap + lag + twist + axial motion

• Types of coupling:– Dynamic couplings, caused by

• Geometric offsets of section c.m., tension center, and shear center from the pitch axis

• Blade twist and precone• Blade rotation• Blade curving (built-in or induced by deformation)

– Material couplings, caused by material cross-stiffness.

• Sophisticated modeling required to capture these couplings and rotational effects.

Coupled Modes

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• Tower configurations that BModes can model:– Land-based tower

• with tower head inertia

• with or without tension-wires support

– Offshore tower: supported by• floating-platform

– Barge + mooring lines– spar-buoy + mooring lines– TLP (tension-legs platform)

• monopile (no multi-pod supports)

BModes Usage: for Towers

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• Given:– Elastic tower distributed geometric & structural properties– Tower-head inertias and c.m. offsets from tower top– Tension-wires stiffness and geometric layout– Floating-platform hydrodynamic & hydrostatic properties + mooring

lines 6x6 stiffness matrix– Monopile foundation elastic properties– Hydrodynamic added mass on submerged part of the elastic tower

• Computes:– Modal frequencies & coupled modes

(coupled fore-aft + side-side + twist + axial motion + platform motions)

BModes Usage for Towers (cont’d)

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Technical Approach

Structural Idealization:Elastic Beam + Rigid Bodies

Nonlinear CoupledIntegro-PDEs

Spatial Discretization using FEs

ODEs in TimeAnalytical

Linearization

Coupled Mode Shapes& Frequencies

Eigensolver

Hamilton’s Principle

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• Uses 15-dof finite element with two external and three internal nodes

Salient Features of BModes

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1

1

1

1

1

u

v

v

w

w

4

2

2

2

2

3

u

v

v

w

w

2u 3u2

Distributed stiffness

Distributed hydrodynamic mass

1

1

1

1

1

1

u

v

v

w

w

4

2

2

2

2

3

u

v

v

w

w

2u 3u2

Distributed stiffness

Distributed hydrodynamic mass

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• Accurately handles rotational effects (centrifugal, Coriolis, tennis-racket, etc)

• Uses quasi-coordinates: give rise to spatial-integral terms• Uses specialized finite-element assembly • Provides for precone & pitch control setting• Allows arbitrary distributed beam properties• Has potential to handle a complex range of boundary

conditions• Uses analytically linearized equations accurate and

computationally fast

Salient Features of BModes (cont’d)

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• Straight Euler-Bernoulli beam

• Isotropic properties (no cross-stiffnesses)

• Rotary inertia effects included, but shear deformation effects ignored.

• Moderate deformations, but small strains.

• For tower modal analysis, tower head (nacelle+rotor) and platform are modeled as 6-dof rigid-body inertias.

• Foundation (soil) is modeled as a distributed spring.

Assumptions & Limitations

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BModes Verification

• For blades:BModes verified extensively using models ranging from a rotating string to realistic blades.

• For towers:Verification in progress.

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Sample Verification Resultsfor

Blades

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Cantilevered Uniform Blade (Nonrotating)Comparison of Modal Frequencies

Mode Number

Flap Frequencies (Hz)

Lag Frequencies(Hz)

Torsion Frequencies (Hz)

Analytical BModes Analytical BModes Analytical BModes

1 0.560 0.560 1.119 1.119 2.572 2.572

2 3.507 3.507 7.014 7.014 7.717 7.717

3 9.819 9.819 19.639 19.639 12.862 12.862

4 19.242 19.242 38.484 38.484 18.007 18.007

5 31.809 31.809 63.617 63.618 23.152 23.152

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Spinning Uniform CableComparison of Flap Modal Frequencies

CableSpin Rate

(rad/sec)

First Flap Frequency (rad/sec)

Second Flap Frequency (rad/sec)

Third Flap Frequency (rad/sec)


0 0.0 0.00 0.00 0.00 0.00 0.00

2 2.0 2.00 4.90 4.91 7.75 7.76

6 6.0 6.01 14.70 14.72 23.24 23.27

10 10.0 10.02 24.49 24.53 38.73 38.79

15 15.0 15.03 36.74 36.80 58.09 58.18

20 20.0 20.04 48.99 49.07 77.46 77.58

25 25.0 25.04 61.24 61.33 96.82 96.97

30 30.0 30.05 73.48 73.60 116.19 116.37

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Spinning Uniform CableComparison of Lag Modal Frequencies

Cable Spin Rate,

(rad/sec)

First Lag Frequency (rad/sec)

Second Lag Frequency (rad/sec)

Third Lag Frequency (rad/sec)


0 0.0 0.00 0.00 0.00 0.00 0.00

2 0.0 0.02 4.47 4.48 7.48 7.50

6 0.0 0.04 13.42 13.44 22.45 22.49

10 0.0 0.06 22.36 22.40 37.42 37.48

15 0.0 0.09 33.54 33.60 56.12 56.22

20 0.0 0.12 44.72 44.80 74.83 74.96

25 0.0 0.15 55.90 56.01 93.54 93.69

30 0.0 0.18 67.08 67.21 112.25 112.43

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Spinning Uniform CableComparison of Bending Mode Shapes

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Span Locaion (x/L)

Mo

da

l D

isp

lac

em

en

t(F

lap

or

La

g)

Mode 1

Mode 3

Mode 2

= 6 rad/sec

BModes Analytical

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Rotating Uniform Blade Comparison of Flap Frequencies

Blade Spin Rate,

(rad/sec)

First Flap Frequency (rad/sec)

Second Flap Frequency (rad/sec)

Third Flap Frequency (rad/sec)


0 3.516 3.516 22.035 22.034 61.697 61.696

1 3.682 3.682 22.181 22.181 61.842 61.841

2 4.137 4.137 22.615 22.615 62.273 62.272

3 4.797 4.797 23.320 23.320 62.985 62.984

4 5.585 5.585 24.273 24.273 63.967 63.966

5 6.450 6.450 25.446 25.446 65.205 65.204

6 7.360 7.360 26.809 26.809 66.684 66.683

7 8.300 8.300 28.334 28.334 68.386 68.385

8 9.257 9.257 29.995 29.995 70.293 70.293

9 10.226 10.226 31.771 31.770 72.387 72.386

10 11.202 11.202 33.640 33.640 74.649 74.649

11 12.184 12.184 35.589 35.589 77.064 77.063

12 13.170 13.170 37.603 37.603 79.615 79.614

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Rotating Uniform Blade Comparison of Lag Frequencies

Blade Spin Rate,

(rad/sec)

First Lag Frequency (rad/sec)

Second Lag Frequency (rad/sec)

Third Lag Frequency (rad/sec)

Analysis BModes Analysis BModes Analysis BModes

0 11.118 11.118 69.529 69.678 194.455 195.101

2 11.153 11.153 69.685 69.835 194.624 195.274

4 11.255 11.255 70.153 70.304 195.143 195.791

6 11.421 11.421 70.927 71.079 196.000 196.650

8 11.642 11.642 71.996 72.150 197.187 197.845

10 11.911 11.911 73.348 73.505 198.712 199.370

12 12.219 12.219 74.967 75.127 200.547 201.216

15 12.735 12.735 77.858 78.025 203.887 204.565

21 13.877 13.877 85.083 85.266 212.501 213.210

25 14.668 14.668 90.774 90.968 219.539 220.275

30 15.652 15.652 98.648 98.859 229.609 230.379

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WindPact 1.5 MW Turbine Blade Comparison of Modal Frequencies

Blade Spin Rate,

(rad/sec)

First Modal Frequency (Hz)

Second Modal Frequency (Hz)

Third Modal Frequency (Hz)

RCAS BModes RCAS BModes RCAS BModes

0 1.229 1.228 1.875 1.873 3.662 3.657

2 1.300 1.298 1.889 1.887 3.736 3.732

5 1.608 1.606 1.959 1.957 4.104 4.100

10 2.146 2.144 2.384 2.381 5.159 5.154

15 2.429 2.426 3.209 3.205 6.366 6.359

20 2.732 2.730 4.055 4.051 7.237 7.229

25 3.044 3.041 4.905 4.900 7.339 7.331

35 3.669 3.665 4.546 4.541 6.612 6.605

50 4.591 4.586 9.150 9.140 12.389 12.375

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WindPact 1.5 MW Turbine Blade Comparison of 1st Modes

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.2 0.4 0.6 0.8 1

Span Locaion (x/L)

FlapTorsion

Lag

1st Coupled Mode= 50 rad/sec

BModes RCAS

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.2 0.4 0.6 0.8 1

Span Locaion (x/L)

Mo

dal

Dis

pla

cem

ent

Flap

Torsion

Lag

1st Coupled Mode= 2 rad/sec

BModes RCAS

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WindPact 1.5 MW Turbine Blade Comparison of 2nd Modes

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

Span Locaion (x/L)

Flap

Torsion

Lag

2nd Coupled Mode= 50 rad/sec

BModes RCAS

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

Span Locaion (x/L)

Mo

dal

Dis

pla

cem

ent

Flap

Torsion

Lag

2nd Coupled Mode= 2 rad/sec

BModes RCAS

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WindPact 1.5 MW Turbine Blade Comparison of 3rd Modes

-0.05

-0.025

0

0.025

0.05

0.075

0.1

0 0.2 0.4 0.6 0.8 1

Span Locaion (x/L)

Mo

dal

Dis

pla

cem

ent

FlapTorsion

Lag

3rd Coupled Mode= 2 rad/sec

BModes RCAS

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

Span Locaion (x/L)

Flap

Torsion

Lag

3rd Coupled Mode= 50 rad/sec

BModes RCAS

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• Complete verification of tower modal analysis.

• Release BModes-3 along with new user’s manual.

• Integrate BModes with CFD (collaboration with NASA).

• Provide for composites.

• Integrate with FAST.

• Extend formulation for curved blades

• Introduce Timoshenko beam element.

Future Plans

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Operated for the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy by Midwest Research Institute • Battelle

Questions?

innovation for our energy futurenational renewable energy laboratory 1 gunjit bir national renewable...

Documents

bmodes blades

tower modal analysis

bmodes verificationfor

modal frequencies

tower head nacelle rotor

tension center

deformation effects

realistic blades