Structural Dynamic Behavior of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 652

Classical Aeroelastic Flutter Analysis for HAWTs and VAWTs
Background
Flutter is a self-starting and potentially destructive vibration where aerodynamic forces
on an object couple with a structure's natural mode of vibration to produce rapid periodic
motion . Flutter can occur in any object within a strong fluid flow, under the conditions that
a positive feedback occurs between the structure's natural vibration and the aerodynamic
forces. That is, when the vibrational movement of an object like a flexible airfoil increases an
aerodynamic load which in turn drives the object to move further. If the energy during the
period of aerodynamic excitation is larger than the natural damping of the system, the level of
vibration will increase. The vibration levels can thus build up and are only limited when the
aerodynamic or mechanical damping of the object match the energy input. This often results
in large amplitudes and can lead to rapid failure.
Although classical aeroelastic flutter has generally not been a driving issue in utility-
scale wind turbine design, one case in which classical flutter was observed involved a vertical-
axis wind turbine (VAWT) turning in still air [Popelka 1982]. The rotor was purposefully
motored at ever-increasing speeds until the flutter boundary was breached and dramatic clas-
sical flutter oscillations were observed. Flutter occurred at approximately twice the design
operating speed of the rotor.
For very large horizontal-axis wind turbines (HAWTs) fitted with relatively soft (flex-
ible) blades, classical flutter becomes a more important design consideration. Innovative
blade designs involving the use of aeroelastic tailoring , wherein the blade twists as it bends
under the action of aerodynamic loads to shed loads resulting from wind turbulence, increase
the blades proclivity for flutter.
Analytical Model of Flutter
The analysis of classical flutter in wind turbines necessitates the use of unsteady aerody-
namics. As pointed out by Leishman [2002], for horizontal axis wind turbines there are two
interconnected sources of unsteady aerodynamics. The first is a result of the trailing wake of
the rotor and is addressed by investigating the interactions between the rotor motion and the
inflow. The second, which will be the focus here, is due to the shed wake of the individual
blades and can be addressed using techniques developed for analyzing flutter in fixed-wing
aircraft.
To simplify the analysis, the rotor is assumed to be turning in still air on a hub fixed in
space. Because there is no wind inflow, unsteady aerodynamics caused by the trailing wake
can be neglected. Consequently, the aerodynamic behavior of a single blade is similar to that
of a fixed wing with a free stream velocity that varies linearly from the root to the tip, assum-
ing that the shed wake of the preceding blade dies out sufficiently fast so that the oncoming
blade will encounter essentially still air. Focusing on aeroelastic stability associated with the
shed wake from an individual HAWT blade, the technique developed by Theodorsen [The-
odorsen 1935, Fung 1969, Dowell 1995] for fixed wing aircraft has been adapted for use with
HAWT blade flutter [Lobitz 2004].
The Theodorsen technique specifically addresses classical flutter in an infinite (i.e. two
dimensional with no end effects) airfoil undergoing oscillatory pitching and plunging motion
in an incompressible flow, as illustrated in Figure 11-14. The airfoil's pitching motion is rep-
resented by the angle a and its plunging motion by the vertical translation h . L represents the
lift force vector positioned at the quarter-chord, M is the pitching moment about the elastic