1. Innovation for Our Energy FutureNational Renewable Energy Laboratory 1 Gunjit Bir National Renewable Energy Laboratory 47 th AIAA Aerospace Meetings Orlando, Florida January 5-8, 2009 BModes (Blades and Towers Modal Analysis Code) Verification of Blade Modal Analysis

2. Innovation for Our Energy FutureNational Renewable Energy Laboratory 2 Background Motivation 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

3. Innovation for Our Energy FutureNational Renewable Energy Laboratory 3 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

4. Innovation for Our Energy FutureNational Renewable Energy Laboratory 4 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

5. Innovation for Our Energy FutureNational Renewable Energy Laboratory 5 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

6. Innovation for Our Energy FutureNational Renewable Energy Laboratory 6 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

7. Innovation for Our Energy FutureNational Renewable Energy Laboratory 7 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)

8. Innovation for Our Energy FutureNational Renewable Energy Laboratory 8 Technical Approach Structural Idealization: Elastic Beam + Rigid Bodies Nonlinear Coupled Integro-PDEs Spatial Discretization using FEs ODEs in Time Analytical Linearization Coupled Mode Shapes & Frequencies Eigensolver Hamilton’s Principle

9. Innovation for Our Energy FutureNational Renewable Energy Laboratory 9 Uses 15-dof finite element with two external and three internal nodes Salient Features of BModes

10. Innovation for Our Energy FutureNational Renewable Energy Laboratory 10 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)

11. Innovation for Our Energy FutureNational Renewable Energy Laboratory 11 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

12. Innovation for Our Energy FutureNational Renewable Energy Laboratory 12 BModes Verification For blades: BModes verified extensively using models ranging from a rotating string to realistic blades. For towers: Verification in progress.

13. Innovation for Our Energy FutureNational Renewable Energy Laboratory 13 Sample Verification Results for Blades

14. Innovation for Our Energy FutureNational Renewable Energy Laboratory 14 Cantilevered Uniform Blade (Nonrotating) Comparison of Modal Frequencies Mode Number Flap Frequencies (Hz) Lag Frequencies (Hz) Torsion Frequencies (Hz) AnalyticalBModesAnalyticalBModesAnalyticalBModes 1 0.560 1.119 2.572 2 3.507 7.014 7.717 3 9.819 19.639 12.862 4 19.242 38.484 18.007 5 31.809 63.61763.61823.152

15. Innovation for Our Energy FutureNational Renewable Energy Laboratory 15 Spinning Uniform Cable Comparison of Flap Modal Frequencies Cable Spin Rate  (rad/sec) First Flap Frequency (rad/sec) Second Flap Frequency (rad/sec) Third Flap Frequency (rad/sec) AnalyticalBModesAnalyticalBModesAnalyticalBModes 00.00.00 22.02.004.904.917.757.76 66.06.0114.7014.7223.2423.27 1010.010.0224.4924.5338.7338.79 1515.015.0336.7436.8058.0958.18 2020.020.0448.9949.0777.4677.58 2525.025.0461.2461.3396.8296.97 3030.030.0573.4873.60116.19116.37

16. Innovation for Our Energy FutureNational Renewable Energy Laboratory 16 Spinning Uniform Cable Comparison of Lag Modal Frequencies Cable Spin Rate,  (rad/sec) First Lag Frequency (rad/sec) Second Lag Frequency (rad/sec) Third Lag Frequency (rad/sec) AnalyticalBModesAnalyticalBModesAnalyticalBModes 00.00.00 20.00.024.474.487.487.50 60.00.0413.4213.4422.4522.49 100.00.0622.3622.4037.4237.48 150.00.0933.5433.6056.1256.22 200.00.1244.7244.8074.8374.96 250.00.1555.9056.0193.5493.69 300.00.1867.0867.21112.25112.43

17. Innovation for Our Energy FutureNational Renewable Energy Laboratory 17 Spinning Uniform Cable Comparison of Bending Mode Shapes

18. Innovation for Our Energy FutureNational Renewable Energy Laboratory 18 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) AnalyticalBModesAnalyticalBModesAnalyticalBModes 03.516 22.03522.03461.69761.696 13.682 22.181 61.84261.841 24.137 22.615 62.27362.272 34.797 23.320 62.98562.984 45.585 24.273 63.96763.966 56.450 25.446 65.20565.204 67.360 26.809 66.68466.683 78.300 28.334 68.38668.385 89.257 29.995 70.293 910.226 31.77131.77072.38772.386 1011.202 33.640 74.649 1112.184 35.589 77.06477.063 1213.170 37.603 79.61579.614

19. Innovation for Our Energy FutureNational Renewable Energy Laboratory 19 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) AnalysisBModesAnalysisBModesAnalysisBModes 011.118 69.52969.678194.455195.101 211.153 69.68569.835194.624195.274 411.255 70.15370.304195.143195.791 611.421 70.92771.079196.000196.650 811.642 71.99672.150197.187197.845 1011.911 73.34873.505198.712199.370 1212.219 74.96775.127200.547201.216 1512.735 77.85878.025203.887204.565 2113.877 85.08385.266212.501213.210 2514.668 90.77490.968219.539220.275 3015.652 98.64898.859229.609230.379

20. Innovation for Our Energy FutureNational Renewable Energy Laboratory 20 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) RCASBModesRCASBModesRCASBModes 01.2291.2281.8751.8733.6623.657 21.3001.2981.8891.8873.7363.732 51.6081.6061.9591.9574.1044.100 102.1462.1442.3842.3815.1595.154 152.4292.4263.2093.2056.3666.359 202.7322.7304.0554.0517.2377.229 253.0443.0414.9054.9007.3397.331 353.6693.6654.5464.5416.6126.605 504.5914.5869.1509.14012.38912.375

21. Innovation for Our Energy FutureNational Renewable Energy Laboratory 21 WindPact 1.5 MW Turbine Blade Comparison of 1 st Modes

22. Innovation for Our Energy FutureNational Renewable Energy Laboratory 22 WindPact 1.5 MW Turbine Blade Comparison of 2 nd Modes

23. Innovation for Our Energy FutureNational Renewable Energy Laboratory 23 WindPact 1.5 MW Turbine Blade Comparison of 3 rd Modes

24. Innovation for Our Energy FutureNational Renewable Energy Laboratory 24 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

25. Operated for the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy by Midwest Research Institute Battelle 25 Questions?