Preprints
https://doi.org/10.5194/wes-2021-163
https://doi.org/10.5194/wes-2021-163
 
07 Jan 2022
07 Jan 2022
Status: a revised version of this preprint was accepted for the journal WES and is expected to appear here in due course.

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

Ang Li, Mac Gaunaa, Georg Raimund Pirrung, Alexander Meyer Forsting, and Sergio González Horcas Ang Li et al.
  • 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.

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on wes-2021-163', Anonymous Referee #1, 04 Feb 2022
  • RC2: 'Comment on wes-2021-163', Vasilis A. Riziotis, 06 Mar 2022
  • AC1: 'Comment on wes-2021-163', Ang Li, 12 Apr 2022

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on wes-2021-163', Anonymous Referee #1, 04 Feb 2022
  • RC2: 'Comment on wes-2021-163', Vasilis A. Riziotis, 06 Mar 2022
  • AC1: 'Comment on wes-2021-163', Ang Li, 12 Apr 2022

Ang Li et al.

Ang Li et al.

Viewed

Total article views: 503 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
347 145 11 503 11 3
  • HTML: 347
  • PDF: 145
  • XML: 11
  • Total: 503
  • BibTeX: 11
  • EndNote: 3
Views and downloads (calculated since 07 Jan 2022)
Cumulative views and downloads (calculated since 07 Jan 2022)

Viewed (geographical distribution)

Total article views: 498 (including HTML, PDF, and XML) Thereof 498 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
1
 
 
 
 
Latest update: 01 Jul 2022
Download
Short summary
A consistent method of using two-dimensional airfoil data when using generalized lifting-line methods for the aerodynamic load calculation of non-planar horizontal-axis wind turbines is described. The important conclusions from the unsteady two-dimensional airfoil aerodynamics are highlighted. The impact of using a simplified approach instead of using the full model on the prediction of the aerodynamic performance of non-planar rotors is shown numerically for different aerodynamic models.