Development and validation of a three-dimensional wind-turbine wake model based on high-order Gaussian function

Under natural conditions, the wake velocity distribution approximates top-hat shape in the near wake center, and a Gaussian shape in the far wake. To improve the prediction accuracy of the wake distribution, this paper proposes a three-dimensional high-order Gaussian linear entrainment wake model by modifying the wake velocity distribution with high-order Gaussian function. Field tests and wind tunnel tests are then conducted. The obtained results show that the proposed model can accurately describe the radial and vertical spatial distributions of the wake flow. Under different wind speeds, the maximum and minimum radial relative errors are respectively 7.29% and 1.4%, while the maximum and minimum vertical relative errors are respectively 7.64% and 3.87%. This demonstrates that the proposed model can accurately predict the velocity distribution in the whole wake region. The proposed model is simple, has low cost, and exhibits high accuracy. Thus, it can be used in wind farm layout optimization and wake control.