Entrainment model for wind turbine wakes considering blockage effect

Abstract

The entrainment model applied firstly by P. Luzzatto-Fegiz can predict the streamwise velocity of the far-wake more accurately than the traditional models (e.g., Jensen model, Frandsen model). The current model, however, neglects the wind speed drop approaching the rotor caused by the blockage effect, the phenomenon of which cannot be considered in the velocity recovery of the far-wake region, further affecting the precision of wake prediction. Hence, this paper proposes an entrainment model considering the blockage effect. We adopt several numerical simulation results to analyze the performance with the vortex cylinder model for the rotor vicinity. The initial entrainment parameter Einitial calculates, according to the formula of the breakdown position of tip vortices proposed by J.N. Sørensen. The Enear-wake can obtain with the length of the near-wake region, defined by P. E. J. Vermeulen. The linearized entrainment-parameterized expression we develop combines the linearization hypothesis with the above two positions and their entrainment values. The proposed model consists of two main components: the modified entrainment model and the vortex cylinder model, validated against the advanced Gaussian model of Bastankhah and Porté-Agel (BPA) and several LES cases. The results demonstrate that the proposed model significantly improves the streamwise wake distribution.