Aeroelastic formulations for performance and stability predictions of horizontal axis wind turbines

Abstract

Today wind turbines are assuming great importance in the generation of electrical power worldwide. Due to the increased dimensions of the rotor blades, design of a wind turbine is a very complex and multidisciplinary task in which aeroelasticity plays a crucial role. In this context, the present thesis proposes the development of numerical aeroelastic tools for the analysis of performance, response and aeroelastic stability of horizontal-axis wind turbines. The objective of the present work is the formulation of numerical solvers combining accuracy and numerical e ciency that can be useful in the preliminary phase of the design process. A nonlinear beam model for blades structural dynamics is coupled with di erent aerodynamic models of increasing complexity able to predict unsteady effects due to wake vorticity, flow separations and dynamic stall. Several computational fluid dynamics and structural dynamics coupling approaches are investigated to take into account rotor wake inflow influence on downwash. Sectional steady aerodynamic coefficients are extended to high angles of attack in order to characterize wind turbine operations in deep stall regimes. The first aeroelastic tool proposed is based on a spectral approach in which the Galerkin method is applied to the aeroelastic differential system; to improve the efficiency of the proposed solver, a novel approach for the spatial integration of additional aerodynamic states, related to wake vorticity and dynamic stall, is introduced and assessed. The second aeroelastic formulation is based on the Finite Element Method (FEM); Hamilton's principle is applied to derive blade equations of motion on which a devoted fifteen-degrees-of-freedom finite element is introduced to model kinematics and elastic behavior of rotating blades. Spatial discretization of the aeroelastic equations is carried-out to derive a set of coupled nonlinear ordinary differential equations solved by a time marching algorithm. Different time marching schemes are discussed and compared. Due to the aeroelastic similarity between wind turbine and helicopter rotor blades, validation of the FEM-based solver firstly deals with the response and performance of helicopter rotors in hovering and forward flight. Then, the performance of a wind turbine examined in terms of blade elastic response and delivered thrust and power is predicted and the results are compared with those provided by the solver based on modal approach, as well as with experimental data.