This paper presents the development of a computational aeroelastic tool for the analysis of performance, response and stability of horizontal-axis wind turbines. A nonlinear beam model for blades structural dynamics is coupled with a state-space model for unsteady sectional aerodynamic loads, including dynamic stall effects. Several computational fluid dynamics structural dynamics coupling approaches are investigated to take into account rotor wake inflow influence on downwash, all based on a Boundary Element Method for the solution of incompressible, potential, attached flows. Sectional steady aerodynamic coefficients are extended to high angles of attack in order to characterize wind turbine operations in deep stall regimes. The Galerkin method is applied to the resulting aeroelastic differential system. In this context, a novel approach for the spatial integration of additional aerodynamic states, related to wake vorticity and dynamic stall, is introduced and assessed. Steady-periodic blade responses are evaluated by a harmonic balance approach, whilst a standard eigenproblem is solved for aeroelastic stability analyses. Drawbacks and potentialities of the proposed model are investigated through numerical and experimental comparisons, with particular attention to rotor blades unsteady aerodynamic modelling issues.
This paper presents an aeroelastic formulation based on the Finite Element Method (FEM) for performance and stability predictions of isolated horizontal axis wind turbines. Hamilton’s principle is applied to derive the equations of blade aeroelasticity, by coupling a nonlinear beam model with Beddoes-Leishman sectional unsteady aerodynamics. A devoted fifteen-degrees-of-freedom finite element to model kinematics and elastic behaviour of rotating blades is introduced. 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. The proposed formulation may be enhanced to face the analysis of advanced-shape blades, as well as the inclusion of the presence of the tower, and represents the first step of an ongoing activity on wind energy based on a FEM approach; as a consequence, results have to be considered as preliminary. Due to similarities between wind turbine and helicopter rotor blades aeroelasticity, validation results firstly concern with the aeroelastic response of helicopter rotors in hovering. Next, the performance of a wind turbine in terms of blade elastic response and delivered thrust and power is predicted and compared to that provided by a validated aeroelastic solver based on a modal approach as well as with experimental data.
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