Nonlinear modeling of tuned liquid dampers (TLDs) in rotating wind turbine blades for damping edgewise vibrations

Tuned liquid dampers (TLDs) utilize the sloshing motion of the fluid to suppress structural vibrations and become a natural candidate for damping vibrations in rotating wind turbine blades. The centrifugal acceleration at the tip of a wind turbine blade can reach a magnitude of 7–8g. This facilitates the use of a TLD with a relatively small fluid mass and with feasible geometric dimensions to mitigate the lightly-damped edgewise vibrations effectively. In the present paper, modal expansions are carried out directly on the velocity field and the free surface of the sloshing liquid in the rotating coordinate system. A formulation has been proposed leading to coupled nonlinear ordinary differential equations, which have been obtained through the Galerkin variational approach together with the modal expansion technique. Two models, with one sloshing mode and three sloshing modes, have been studied in the numerical simulation. It is shown that the one-mode model is able to predict the sloshing force and the damped structural response accurately, since the primary damping effect on the structure is achieved by the first sloshing mode of the fluid. Although it is unable to predict the fluid free-surface elevation equally well, the one-mode model can still be utilized for the design of TLD. Parametric optimization of the TLD is carried out based on the one-mode model, and the optimized damper effectively improves the dynamic response of wind turbine blades.