How should the lift and drag forces be calculated from 2-D airfoil data for dihedral or coned wind turbine blades?

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.

Laminar separation bubble dynamics and its effects on thin airfoil performance during pitching-up motion

This article reports an investigation into dynamic characteristics of the laminar separation bubbles (LSBs) associated with aerodynamic loads unsteadiness of a cambered thin airfoil in pitching-up motions at low Reynolds number flows. Unsteady Reynolds-averaged Navier–Stokes (URANS) simulations were conducted for a 4%c cambered thin airfoil at Reynolds number of 30,000 and 60,000. The airfoil pitches up from 0° to 25°angles of attack at dimensionless pitch rate [Formula: see text] of 0.0398 and 0.0199. The [Formula: see text] SST [Formula: see text] turbulence transition model was used to account for the effect of transition on LSBs’ development. The LSBs are shown to evolve in their shape and size during the pitching motion. The influence of the LSBs on the airfoil upper surface during pitching motion continues to a higher incidence in comparison with that under static conditions before developing into a fully detached flow. Vortex merging is observed in the rear part of the LSBs in the turbulent portion for a Reynolds number of 30,000. At Reynolds number 60,000, the changing of the LSB length during pitching-up motion is similar to that of steady cases, except a delayed transition is observed as incidence increases. The results show further insight into the dynamic characteristics of the LSBs and their relation to the aerodynamic performance of the airfoil.