This paper deals with the aeroelastic instabilities that have occurred and may still occur for modern commercial wind turbines: stall-induced vibrations for stall-turbines, and classical flutter for pitch-regulated turbines. A review of previous works is combined with derivations of analytical stability limits for typical blade sections that show the fundamental mechanisms of these instabilities. The risk of stall-induced vibrations is mainly related to blade airfoil characteristics, effective direction of blade vibrations and structural damping; whereas the blade tip speed, torsional blade stiffness and chordwise position of the center of gravity along the blades are the main parameters for flutter. These instability characteristics are exemplified by aeroelastic stability analyses of different wind turbines. The review of each aeroelastic instability ends with a list of current research issues that represent unsolved aeroelastic instability problems for wind turbines. Copyright © 2007 John Wiley & Sons, Ltd.

Aeroelastic instability problems for wind turbines

Nonlinearities in the aeroelastic system induce pathologies such as the observed store-induced limit cycle oscillations found with certain high-performance aircraft configurations. Many prior studies, including efforts by these authors, focus on the nonlinear behavior of the uncontrolled, nonlinear aeroelastic system. These studies are briefly reviewed. More importantly, there is limited study for the active control of these nonlinear aeroelastic systems. Although a linear controller may stabilize the nonlinear system under some circumstances, empirical evidence suggests that these control methods -will prove unreliable in strongly nonlinear regimes and that stability is not guaranteed. Herein, the authors describe the development of control strategies appropriate for these nonlinear systems. A nonlinear controller, and the resulting closed-loop stability, based on a partial feedback linearization are discussed. The approach depends upon the exact cancellation of the nonlinearity and, as a co_nsequence, the authors introduce an adaptive method in which guarantees of stability are evident. The authors present experimental results obtained using the adaptive controller.

Identification and Control of Limit Cycle Oscillations in Aeroelastic Systems

In this von Karman lecture, a subject is addressed whose foundations were significantly influenced by the work of Theodore von Karman. A classic paper by von Karman and Sears first considered the determination of aerodynamic forces on an airfoil undergoing general time-dependent motion. Also, early in his career, von Karman investigated fundamental issues in structural mechanics and derived the celebrated von Karman plate equations for determining the large (nonlinear) deflections of an elastic plate under a distributed force. Finally, he authored a widely cited paper on the importance of nonlinearities for engineers and engineering. In this lecture, these themes are recalled and the current state of the art in nonlinear aeroelasticity and unsteady aerodynamics is discussed. Several of the most significant nonlinearities arising in a structure or in an aerodynamic flow field are identified. Recent and relevant theoretical and experimental studies are reviewed and future developments are projected that are expected to have a significant impact on our ability to understand and beneficially use nonlinear dynamic aeroelastic behavior

Nonlinear Aeroelasticity and Unsteady Aerodynamics

Earlier results by the authors showed constructions of Lie algebraic, partial feedback linearizing control methods for pitch and plunge primary control utilizing a single trailing edge actuator. In addition, a globally stable nonlinear adaptive control method was derived for a structurally nonlinear wing section with both a leading and trailing edge actuator. However, the global stability result described in a previous paper by the authors, while highly desirable, relied on the fact that the leading and trailing edge actuators rendered the system exactly feedback linearizable via Lie algebraic methods. In this paper, the authors derive an adaptive, nonlinear feedback control methodology for a structurally nonlinear typical wing section. The technique is advantageous in that the adaptive control is derived utilizing an explicit parameterization of the structural nonlinearity and a partial feedback linearizing control that is parametrically dependent is defined via Lie algebraic methods. The closed loop stability of the system is guaranteed to be stable via application of La Salle's invariance principle.

Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity

The primary objective of this paper is to demonstrate that the field of aeroelasticity continues to play a critical role in the design of modern aerospace vehicles, and several important problems are still far from being well understood. Furthermore, the emergence of new technologies, such as the use of adaptive materials (sometimes denoted as smart structures technology), providing new actuator and sensor capabilities, has invigorated aeroelasticity, and generated a host of new and challenging research topics that can have a major impact on the design of a new generation of aerospace vehicles.

Renaissance of Aeroelasticity and Its Future

A two-dimensiona l airfoil with a free-play nonlinearity in pitch subject to incompressibl e flow has been analyzed. The aerodynamic forces on the airfoil were evaluated using Wagner's function and the resulting equations integrated numerically to give time histories of the airfoil motion. Regions of limit cycle oscillation are detected for velocities well below the linear flutter boundary, and the existence of these regions is strongly dependent on the initial conditions and properties of the airfoil. Furthermore, for small structural preloads, narrow regions of chaotic motion are obtained, as suggested by power spectral densities, phase-plane plots, and Poincare sections of the airfoil time histories. The existence of this chaotic motion is strongly dependent on a number of airfoil parameters, including, mass, frequency ratio, structural damping, and preload.

H. Alighanbari

Papers

Postinstability Behavior of a Two-Dimensional Airfoil with a Structural Nonlinearity

Postinstability behavior of a two-dimensional airfoil with a structural nonlinearity