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Gunjit Bir National Renewable Energy Laboratory 47 th AIAA Aerospace Meetings Orlando, Florida

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

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Gunjit Bir National Renewable Energy Laboratory 47 th AIAA Aerospace Meetings Orlando, Florida

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

  2. 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. Blade modes Post-process modal data BModes Tower modes FAST

  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. BModes Usage: for Blades • 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

  5. Coupled Modes • 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.

  6. BModes Usage: for Towers • 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)

  7. BModes Usage for Towers (cont’d) • 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)

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

  9. Salient Features of BModes • Uses 15-dof finite element with two external and three internal nodes

  10. Salient Features of BModes (cont’d) • 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

  11. Assumptions & Limitations • 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.

  12. BModes Verification • For blades:BModes verified extensively using models ranging from a rotating string to realistic blades. • For towers:Verification in progress.

  13. Sample Verification Results for Blades

  14. Cantilevered Uniform Blade (Nonrotating)Comparison of Modal Frequencies

  15. Spinning Uniform CableComparison of Flap Modal Frequencies

  16. Spinning Uniform CableComparison of Lag Modal Frequencies

  17. Spinning Uniform CableComparison of Bending Mode Shapes

  18. Rotating Uniform Blade Comparison of Flap Frequencies

  19. Rotating Uniform Blade Comparison of Lag Frequencies

  20. WindPact 1.5 MW Turbine Blade Comparison of Modal Frequencies

  21. WindPact 1.5 MW Turbine Blade Comparison of 1st Modes

  22. WindPact 1.5 MW Turbine Blade Comparison of 2nd Modes

  23. WindPact 1.5 MW Turbine Blade Comparison of 3rd Modes

  24. Future Plans • 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.

  25. Questions?

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