Aeroelastic stability of idling wind turbines

Wind turbine rotors in idling operation mode can experience high angles of attack within the post-stall region that are capable of triggering stall-induced vibrations. The aim of the present paper is to extend the existing knowledge on the dynamics and aerodynamics of an idling wind turbine and characterize its stability. Rotor stability in slow idling operation is assessed on the basis of nonlinear time domain and linear eigenvalue analyses. The aim is to establish when linear analysis is reliable and identify cases for which nonlinear effects are significant. Analysis is performed for a 10 MW conceptual wind turbine designed by DTU. First, the flow conditions that are likely to favor stall-induced instabilities are identified through nonlinear time domain aeroelastic simulations. Next, for the above specified conditions, eigenvalue stability analysis is performed to identify the low damped modes of the turbine. The eigenvalue stability results are evaluated through computations of the work done by the aerodynamic forces under imposed harmonic motion following the shape and frequency of the various modes. Nonlinear work characteristics predicted by the ONERA and Beddoes–Leishman (BL) dynamic stall models are compared. Both the eigenvalue and work analyses indicate that the asymmetric and symmetric out-of-plane modes have the lowest damping. The results of the eigenvalue analysis agree well with those of the nonlinear work analysis and the time domain simulations.

Aeroelastic Stability of Idling Wind Turbines

Wind turbine rotors in idling operation mode can experience high angles of attack, within the post stall region that are capable of triggering stall-induced vibrations. In the present paper, rotor stability in slow idling operation is assessed on the basis of non-linear time domain and linear eigenvalue analyses. Analysis is performed for a 10 MW conceptual wind turbine designed by DTU. First, the flow conditions that are likely to favour stall induced instabilities are identified through non-linear time domain aeroelastic simulations. Next, for the above specified conditions, eigenvalue stability simulations are performed aiming at identifying the low damped modes of the turbine. The eigenvalue stability results are evaluated through computations of the work of the aerodynamic forces under imposed harmonic motion following the shape and frequency of the various modes. Eigenvalue analysis indicates that the asymmetric and symmetric out-of-plane modes have the lowest damping. The results of the eigenvalue analysis agree well with those of the non-linear work analysis and the time domain analysis.

Sources of Error in Eigenvalue Spectra for Pipe-Poiseuille Flows

An operational Chebyshev Tau approach was used to establish temporal eigenvalue stability spectra for pipe-Poiseuille flows, using the Sexl equation which was transformed to remove the singularity at the origin. Substantial deviations were noted between the long-standing results of Davey and Drazin (1969) which are scattered and display branching patterns, and those of the present work which manifest a more orderly progression of the stable high-order eigenvalues. Formal distinctions are made between errors arising from round-off, basis truncation, and poor choice of basis function: the inaccuracies in Davey and Drazin’s data are thought to have arisen from the latter two effects.