Verification of BModes: Rotary Beam and Tower Modal Analysis Code

This paper describes verification of BModes, a finite-element code developed to provide coupled modes for the blades and tower of a wind turbine. The blades, which may be rotating or non-rotating, and the towers, whether onshore or offshore, are modeled using specialized 15-dof beam finite elements. Both blade and tower models allow a tip attachment, which is assumed to be rigid body with six moments of inertia, and a mass centroid that may be offset from the blade or tower axis. Examples of tip attachments are aerodynamic brakes for blades and nacelle-rotor subassembly for towers. BModes modeling allows for tower supports including tension wires, floating platforms, and monopiles on elastic foundations. Coupled modes (implying coupling of flap, lag, axial, and torsional motions) are required for modeling major flexible components in a modal-based, aeroelastic code such as FAST 1 . These are also required for validation of turbine models using experimental data, modal-based fatigue analysis, controls design, and understanding aeroelastic-stability behavior of turbines. Verification studies began with uniform tower models, with and without tip inertia, and progressed to realistic towers. For the floating turbine, we accounted for the effects of hydrodynamic inertia, hydrostatic restoring, and mooring lines stiffness. For the monopole-supported tower, we accounted for distributed hydrodynamic mass on the submerged part of the tower and for distributed foundation stiffness. Finally, we verified a model of a blade carrying tip mass and rotating at different speeds (verifications of other blade models, rotating or non-rotating, have been reported in another paper 2 ). Verifications ® results. All results in general show excellent agreement. I. Introduction BModes is a finite-element code developed for high-fidelity modal analysis of a wind turbine’s blade or tower, whether offshore or onshore. Both the blade, rotating or non-rotating, and the tower may have an arbitrary distribution of structural properties. Both blade and tower models allow a tip attachment, which is assumed to be rigid body with six moments of inertia, and a mass centroid that may be offset from the blade or tower axis. Examples of tip attachments are aerodynamic brakes for blades and nacelle-rotor subassemblies for towers. In addition, the blade may have a precone and an arbitrary pitch-control setting. For the tower, BModes allows five configurations: a land-based tower, an offshore monopile-supported tower, an offshore floating-barge-supported tower, an offshore tension-leg-supported tower, and an offshore spar-buoy-supported tower. Figure 1 shows the three floating turbine configurations. Optionally, the land-based tower may have tension support wires. The modes of a blade or a tower are generally coupled, which implies the presence of flexural, axial, and torsional motions in a natural mode of vibration. For the blade, flexural motion means flap and lag bending, whereas for the tower it means fore-aft and side-to-side bending. Coupled modes are crucial to several applications: