A novel three-dimensional wake model based on anisotropic Gaussian distribution for wind turbine wakes. (15th August 2021) - He, Ruiyang; Yang, Hongxing; Sun, Haiying; Gao, Xiaoxia
Highlights: A novel analytical three-dimensional elliptical Gaussian wake model is developed. Multivariate Gaussian function is adopted from the beginning of model derivation. The wind shear effect and the anisotropy of the wake radius are taken into account. The accuracy of the proposed mode is validated by both experimental and CFD data. The model is highly concise with a little requirement of computing resources. Abstract: The development of a more advanced three-dimensional wake model for wind power generation is presented based on a multivariate Gaussian distribution. The newly-presented model is closer to reality as it truly depends on two independent dimensions (namely horizontal and vertical directions) rather than the radius of a circle. For this reason, the general expression of wake expansion rate in each dimension is specifically developed. In addition, by taking into account the inflow wind shear effect, this current model is able to accurately capture the asymmetric distribution of the vertical wake profile. Four cases including experimental data from wind tunnels and field observations as well as high-fidelity numerical simulation are used to validate the present model. Compared with conventional models, this new model is capable of predicting the wake distribution of a single wind turbine reasonably well. The proposed model is highly simple with a low computational cost. Before applying this model, no additional numerical calculation or trial calculation is required. Wake velocity at any given spatial position can be calculated in an accurate and fast manner. Because of its accuracy, universality and low cost, the present three-dimensional wake model is able to make contributions to farm-level applications such as layout optimization and control strategies and therefore benefit the power output of wind farms.