Accuracy of the aerodynamic performance of wind turbines using vortex core models in the free vortex wake method

Abstract

The size of the vortex core of the vortex model is very important for the accurate prediction of the aerodynamic characteristics of wind turbines in the free vortex wake (FVW) method. The size of the vortex core includes its initial radius and the variation in the wake due to the dissipation effect. In the FVW method, the governing equation of the vortex line is discretized by the three-step and third-order predictor-corrector difference scheme. The classical Lamb-Oseen model and the Scully model are adopted for the vortex core model, and the vortex dissipation effect and stretching effect are taken into account. First, the value range of the initial radius of the vortex core is obtained through the analysis of the aerodynamic load and the mean value of the tip vorticity. Then, based on the tip vortex dissipation characteristics, the empirical constants reflecting the increase in the vortex core radius are determined. Finally, the effect of the vortex core size on the shape of the tip vortex line is analyzed. The results demonstrate that in both vortex core models when the radius of the initial vortex core is greater than 50% of the chord length, the FVW method converges stably and can accurately predict the aerodynamic load of the wind turbine. Considering the aerodynamic load of the wind turbine and the dissipation characteristics of the tip vorticity, it is advisable to use a chord length from 60% to 70% as the initial radius of the vortex core. In addition, the corresponding empirical constant of vortex-viscous dissipation is also different; the aerodynamic load of the wind turbine which is related to the mean value of the tip vorticity and the shape of the tip vortex is mainly affected by the radius of the initial vortex core, and the empirical constant has little influence on it, while it mainly affects the dissipation characteristics of the tip vorticity in the downstream wake field.