Abstract
Abstract. In this work, a computationally efficient engineering model for the aerodynamics of swept wind turbine blades is proposed for the extended blade element momentum (BEM) formulation. The model is modified based on a coupled near- and far-wake model, in which the near wake is assumed to be the first quarter revolution of the non-expanding helical wake of the own blade. For the special case of in-plane trailed vorticity, the original empirical equations determining the steady-state value of the near-wake induction are replaced by the analytical results, which are in the form of incomplete elliptic integrals. For the general condition of helical trailed vorticities, the steady-state near-wake induction is approximated based on the results of the special conditions and a correction factor. The factor is calculated using empirical equations with influence coefficient tensors, to minimize the computational effort. These influence coefficient tensors are pre-calculated and are fitted to the results from the numerical integration of the Biot–Savart law. With the indicial function approach, it is not necessary to explicitly save the information of the vorticities that were trailed in the previous time steps. This engineering approach is a combination of analytical results and numerical approximations, with low and constant computational effort for each time step. The proposed model is practically applicable to time-marching aero-servo-elastic simulations. The results of the swept blades with uniform inflow perpendicular to the rotor calculated from the proposed model are compared with the results from a BEM code, a lifting-line solver and a Navier–Stokes solver. The significantly improved agreement with the higher-fidelity models compared to the BEM method highlights the performance of the proposed method.
Highlights
With the technological advancements in the design optimization and manufacturing of horizontal-axis wind turbines, the turbine blades are becoming increasingly flexible
In the previous work of Li et al (2018), the aerodynamic loads calculated from the blade element momentum (BEM) method and an early version of the coupled model are compared with the results from CFD
The CFD computations using EllipSys3D were performed on the Jess high-performance computing (HPC) cluster, in which each node has 20 cores running at 2.8 GHz
Summary
With the technological advancements in the design optimization and manufacturing of horizontal-axis wind turbines, the turbine blades are becoming increasingly flexible. Li et al.: A computationally efficient engineering aerodynamic model for swept wind turbine blades This led to the formulation of the coupled model (usually referred to as the near-wake model) by Madsen and Rasmussen (2004), which is a hybrid model of a liftingline method and the BEM method. In that work, the near-wake induction is calculated by directly integrating the Biot–Savart law numerically This approach is computationally expensive and is not suitable for the application to aeroelastic simulations. The aerodynamic loads of the swept blades under the special condition of uniform inflow perpendicular to the rotor plane predicted by the proposed model are compared with the results from a BEM code, a lifting-line solver and a CFD Reynoldsaveraged Navier–Stokes (RANS) solver
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