A two-dimensional model based on the expansion of physical wake boundary for wind-turbine wakes

Two-dimensional (2D) wake models with a self-similar Gaussian shape of velocity deficit are highly accurate in predicting wind-turbine wakes. To better leverage their advantages for large-scale engineering applications, an approximation of the physical wake boundary (r(w)) is proposed based on data from both numerical simulations and experiments, i.e. r(w) = 2 sigma, where sigma is the standard deviation of the Gaussian-like profile. In addition, instead of defining the wake expansion corresponding to a, a physically more intuitive expansion rate k that corresponds to the physical wake boundary is introduced. Then, a linear expansion law is employed to characterize the evolution of the wake behind the wind rotor, which leaves k as the only parameter to be determined in the 2D wake model. Data from large eddy simulation, physical experiments and field observations shows that the present analytical model can predict the wake of a wind turbine with high accuracy. The cases considered in the present study indicate that k = 0.075 recommended by the one-dimensional (1D) wake model (Jensen model) for onshore wind farms also works well in the present 2D model under moderate ground roughness for a turbine generally operating in regime II. Because of its simplicity, good accuracy and low cost, the present 2D model is appealing to large-scale engineering applications.