Two-dimensional entrainment model for wind turbine wakes based on expansion effects

To address the unclear physical relationship and low accuracy between wake radius and wake half-width in existing two-dimensional entrainment models, this study presents a two-dimensional entrainment model for wind turbines based on wake expansion effects, built upon the conventional two-dimensional entrainment framework. First, by introducing the initial wake width of the plume model based on Taylor dispersion theory and integrating the relationship betweenxth in the plume model and the rigorou physical mechanisms of mass-momentum streamwise distancex, the standard deviation coefficient of wake distribution in the entrainment model is modified to be a function of the streamwise distance from the wind turbine. Second, combining the two-dimensional treatment results of existing entrainment models, the influences of ambient turbulence, mechanical turbulence, and downstream distance on entrainment parameters are further considered to establish a parameterized expression for the entrainment coefficient that evolves with multiple variables. Finally, the model is validated using observational data from the Sexberium wind farm and field measurement results from lidar in Jiuquan, Gansu. Results show that the proposed model significantly improves the calculation accuracy of wake center velocity deficits and non-uniform distribution. This work will provide an efficient and reliable theoretical tool for wind farm micro-siting and power production assessment.