Self-sustained shock oscillations on airfoils at transonic speeds

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

▪ Abstract Interaction of a vortex, or combinations of them, with a cylinder, blade, or foil may involve both rapid distortion of the incident vorticity field and shedding of vorticity from the surface of the body. This review focuses on the underlying flow physics, with the aim of clarifying the origin of the induced loading. In the case of near or direct encounter of the incident vortex, the relation between three-dimensional features of the flow structure and the local loading poses interesting challenges for further research. With recently developed simulation and laboratory techniques, opportunities now exist to determine the instantaneous quantitative structure of these complex distortions and to interpret them within a theoretical, vorticity-based framework. Effective control of vortex interactions appears to be attainable. It will be necessary, however, to develop creative strategies, distinct from those traditionally employed for control of unstable shear flows.

Vortex-body interactions

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

The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities

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.

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

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

Wind-tunnel studies of F/A-18 tail buffet

The describing function method is used to analyze the flutter characteristics of the CF-18 aircraft with structural nonlinearities. The first nonlinearity studied is located at the CF-18 wing-fold hinge. From ground test data, this hinge can be represented by a bilinear spring. A flutter sensitivity study is carried out, which shows that when the hinge stiffness is reduced, divergent flutter involving the wing bending and torsion modes is replaced by limit-cycle flutter of the wing torsion and outer wing rotation modes. Another form of nonlinearity at the outboard leading-edge flap is also studied by treating it as a spring with free-play. Limit-cycle oscillations are possible only within a small range of velocities in the vicinity of its linear flutter velocity. The flutter modes remain unchanged and their frequencies are practically constant for hinge-stiffness values ranging from a few percent to its nominal value. Positive aileron angles are found to be more effective in alleviating limit-cycle flutter at the wing-fold than negative angles. Similar observations are made at the outboard leading-edge flap hinge where downward deflection of the aileron gives larger values of the preload and, hence, the equivalent stiffness than upward deflection.

B. H. K. Lee

Papers

The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities

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

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

Wind-tunnel studies of F/A-18 tail buffet

Effects of structural nonlinearities on flutter characteristics of the CF-18 aircraft