An efficient reduced-order modeling framework for spatiotemporal aerodynamic damping in flexible wind turbine blades

Wind turbine blades experience significant spatial and temporal variations in aerodynamic damping during aeroelastic responses. However, these three-dimensional, time-varying effects are often neglected in practice due to computational constraints and engineering efficiency requirements, leading to a reliance on simplified empirical models. This study presents an efficient computational framework for modeling the three-dimensional time-varying aerodynamic damping of wind turbine blades, achieve by integrating an improved blade element momentum (BEM) theory and geometrically exact beam theory (GEBT) with the harmonic balance method (HBM). The nonlinear dynamic model of the blade is formulated using Legendre spectral finite elements, and the resulting nonlinear aeroelastic system matrix is linearized via the variational principles. The linearized model undergoes periodic order reduction and aeroelastic-flow decoupling via the HBM through Fourier series truncation and algebraic transformation. The method's accuracy and reliability are validated against aeroelastic wind tunnel experimental data, with errors identified and analyzed. The International Energy Agency 15 MW reference blade is then used, and the three-dimensional time-varying aerodynamic damping characteristics are analyzed at a specified tip-speed ratio, along with the corresponding flow field features around the blade surface. The results show that the proposed BEM-GEBT-HBM method efficiently captures the spatiotemporal evolution of aerodynamic damping, while maintaining high computational accuracy. Additionally, it reveals the spanwise distribution patterns and modal coupling characteristics, highlighting significant negative and positive work alternations and vortex evolution in typical operating conditions.