How should the lift and drag forces be calculated from 2-D airfoil data for dihedral or coned wind turbine blades?
- Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde, Denmark
Abstract. In the present work, a consistent method for calculating the lift and drag forces from the 2-D airfoil data for the dihedral or coned horizontal-axis wind turbines when using generalized lifting-line methods is described. The generalized lifting-line methods include, for example, lifting-line (LL), actuator line (AL), blade element momentum (BEM) and blade element vortex cylinder (BEVC) methods. A consistent interpretation of classic unsteady 2-D thin airfoil theory results for use in a generally moving frame of reference within a linearly varying onset velocity field reveals that it is necessary to use not only the relative flow magnitude and direction at one point along the chord line (for instance three-quarter-chord), but also the gradient of the flow direction in the chordwise direction (or, equivalently, the flow direction at the quarter-chord) to correctly determine the magnitude and direction of the resulting 2-D aerodynamic forces and moment. However, this aspect is generally overlooked and most implementations in generalized lifting-line methods use only the flow information at one calculation point per section for simplicity. This simplification will not change the performance prediction of planar rotors, but will cause an error when applied to non-planar rotors. The present work proposes a generalized method to correct the error introduced by this simplified single-point calculation method. In this work this effect is investigated using the special case, where the wind turbine blade has only dihedral and no sweep, operating at steady-state conditions with uniform inflow applied perpendicular to the rotor plane. We investigate the impact of the effect by comparing the predictions of the steady-state performance of non-planar rotors from the consistent approach with the simplified one-point approach of the LL method. The results are verified using blade geometry resolving Reynolds-averaged Navier-Stokes (RANS) simulations. The numerical investigations confirmed that the correction derived from thin airfoil theory is needed for the calculations to correctly determine the magnitude and direction of the sectional aerodynamic forces for non-planar rotors. The aerodynamic loads of upwind and downwind coned blades that are calculated using the LL method, the BEM method, the BEVC method and the AL method are compared for the simplified and the full method. Results using the full method, including different specific implementation schemes, are shown to agree significantly better with fully-resolved RANS than the often used simplified one-point approaches.
Ang Li et al.
Ang Li et al.
Ang Li et al.
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