A computationally efficient engineering aerodynamic model for swept wind turbine blades

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.