Two Three-Dimensional Super-Gaussian Wake Models for Wind Turbine Wakes

Abstract

This study develops and verifies two advanced wake models based on super-Gaussian distribution: three-dimensional (3D) super-Gaussian (3DSG) and 3D anisotropic super-Gaussian (3DASG) models. They have a smooth Gaussian–top-hat shape (a combination of Gaussian and top-hat shapes) in the near-wake region that gradually transitions to a Gaussian shape in the far-wake region. These models are based on the law of mass conservation and considers wind shear effect; hence, they can accurately describe asymmetric wind distribution in the vertical direction. Because of this Gaussian–top-hat shape, the model is more accurate in simulating the wake in the near-wake region. The anisotropic model also considers different wake expansion rates in various dimensions, rendering the model more realistic. The accuracy and generality of the two models are verified using four wake data sets obtained from wind tunnel tests and wind field measurements. The validation includes the prediction of the wake profile and relative error of the models. The results show that the two models can well predict the wake distribution of various sizes of turbines at any spatial location in the full-wake region.