Quantification of three-dimensional added turbulence intensity for the horizontal-axis wind turbine considering the wake anisotropy

The accurate evaluation of wake turbulence intensity (TI) is of great significance for the layout optimization of wind farms and research on control strategies. However, the existing engineering wake models still have many shortcomings in evaluating the TI in the wake of horizontal-axis wind turbines (HAWTs), especially in the near wake region. In response to this, this article proposed an analytical model based on the double-Gaussian ellipse function that can describe the three-dimensional added TI distribution in the entire wake region. Firstly, the anisotropy of wake expansion is taken into account in both the horizontal and vertical directions, assuming that the added TI distribution downstream of the HAWT is a double-Gaussian elliptical shape. Secondly, taking into account the self-similarity characteristics of flow TI, the maximum added TI and its position in the entire wake region are evaluated. In addition, considering the influence of the ground effect, the vertical turbulence distribution was corrected. Finally, the proposed added turbulence model was validated and relative error analysis was conducted using large eddy simulation (LES) data, wind field measurement data, and wind tunnel experimental data. The results show that the model had good prediction accuracy in the entire wake region, and its prediction performance was significantly improved compared to traditional models, especially in the near wake region, with the lowest even relative error of 3.66%. This model has significant advantages such as low computational cost, wide applicability, and high accuracy. It can reduce energy losses in wind farms, improve wind energy utilization efficiency, and has great potential for widespread application in large-scale wind farms.