AN EFFICIENT METHOD FOR SOLVING THREE-DIMENSIONAL TIME-VARYING AERODYNAMIC DAMPING OF WIND TURBINE BLADES BASED ON NESTED BEM-GEBT-HBM FRAMEWORK

During the wind-induced vibration of wind turbine blades, aerodynamic damping exhibits significant temporal and spatial variations. However, due to limitations in current computational methods and the demand for engineering efficiency, the three-dimensional time-varying characteristics of aerodynamic damping are often simplified in practical applications using empirical approximations. To address this issue, this study develops a nonlinear dynamic model of wind turbine blades by coupling an improved Blade Element Momentum (BEM) theory with the Geometrically Exact Beam Theory (GEBT), and discretizes it using the Legendre spectral finite element method. Based on the variational principle, the nonlinear aeroelastic system is linearized. Subsequently, the Harmonic Balance Method (HBM) is embedded to achieve periodic model order reduction in the frequency domain, enabling decoupled solutions of the vibration and flow fields. Accordingly, an efficient computational method for three-dimensional time-varying aerodynamic damping is proposed. The method's accuracy and robustness are validated through comparisons with aeroelastic wind tunnel test data, and the primary error sources are analyzed. Furthermore, the IEA 15MW reference blade is used as a case study, and the three-dimensional time-varying aerodynamic damping characteristics under rotating conditions are investigated at a specific tip-speed ratio. Numerical results demonstrate that the proposed BEM-GEBT-HBM framework effectively captures the spatiotemporal evolution of aerodynamic damping, significantly improving both computational accuracy and efficiency. Moreover, it reveals the coupling effects between damping distribution and structural vibration modes. The study shows that aerodynamic damping in wind turbine blades exhibits pronounced three-dimensional time-varying characteristics along the spanwise, chordwise, and azimuthal directions, primarily driven by mode coupling-induced phase differences and the dynamic evolution of local vortex structures in unsteady flows.