Prediction and suppression of chaos following flutter in wind turbines

Abstract

Chaotic motion in a fluttering wind turbine blade is investigated by the development of an efficient analytical predictive model that is then used to suppress the phenomenon. Flutter is a dynamic instability of an elastic structure in a fluid, such as an airfoil section of a wind turbine blade. It is presently modelled using generalised two degree of freedom coupled modes of a blade airfoil section (pitch and plunge) combined with local unsteady aerodynamics, based on flutter derivatives and a continuous bilinear lift curve under damping. The mode coupling causes instability and limit cycle flutter due to a Hopf bifurcation. Following the critical flutter speed, the response can transition to chaos through successive other bifurcations like period doubling. New closed-form conservative analytical conditions for chaos following blade flutter are identified and discussed for the wind turbine section taking into account the blade geometry and optimal design of the wind turbine. These predictions are numerically verified for a range of conditions including stall slope and damping. The results confirm that chaos following blade flutter can occur due to nonlinearities in the aerodynamics, i.e. due to a bilinear lift law. This phenomenon is then suppressed to unrealistically high wind speeds and/or eliminated by quantified variation of system parameters using the predictive model. The results show that small changes in tip speed ratio (−15%), and stall slope factor (−17%) can eliminate or suppress chaos following flutter, while, in general, larger magnitude changes in dynamic parameters (i.e. mass, inertia > 81%, stiffness > 97%, damping > 100%) are required to achieve the same, by detuning the coupled plunge and pitch natural frequencies or damping out overlapping parametric resonances. These results also highlight that the analytical predictions can remarkably be generalized to any parameter set and provide almost instantaneous calculations representing many thousands of numerical simulations from many bifurcation diagrams (computational acceleration factor of 107 times). General insight is also provided into the occurrence and suppression of airfoil chaos following flutter in aeroelastic structures like wind turbines.