Evaluation of the lifting line vortex model approximation for estimating the local blade flow fields in horizontal-axis wind turbines

Lifting line vortex models have been widely used to predict flow fields around wind turbine rotors. Such models are known to be deficient in modelling flow fields close to the blades due to the assumption that blade vorticity is concentrated on a line and consequently the influences of blade geometry are not well captured. The present study thoroughly assessed the errors arising from this approximation by prescribing the bound circulation as a boundary condition on the flow using a lifting line free-wake vortex approach. The bound circulation prescribed to free-wake vortex model was calculated from two independent sources using (1) experimental results from SPIV and (2) data generated from a 3D panel free-wake vortex approach, where the blade geometry is fully modelled. The axial and tangential flow fields around the blades from the lifting line vortex model were then compared with those directly produced by SPIV and the 3D panel model. The comparison was carried out for different radial locations across the blade span. The study revealed the cumulative probability error distributions in lifting line model estimations for the local aerofoil flow field under both 3D rotating and 2D non-rotating conditions. It was found that the errors in a 3D rotating environment are considerably larger than those for a wing of infinite span in 2D flow. Finally, a method based on the Cassini ovals theory is presented for defining regions around rotating blades for which the lifting line model is unreliable for estimating the flow fields.