A new three-dimensional entrainment model for wind-turbine wakes

Abstract

A linear entrainment (LE) wake model can maintain both mass conservation and momentum conservation, improving wake prediction accuracy. However, its key parameter entrainment coefficient E determines the exchange of fluids inside and outside the wake region, which significantly affects its prediction accuracy and requires further testing and correction. Also, its assumed top-hat shape can cause large errors. This work first establishes the best value of E (E = 0.12) based on experimental data and numerical simulation. Then we construct the three-dimensional cosine-shaped wake model by correcting the radial velocity distribution of the LE model with the cosine function and considering the wind shear effect. In addition, different from the two-parameter turbulence intensity model used in the previous models, the recently proposed three-parameter turbulence-intensity model is used to correct the E value in order to integrate the effects on downstream distance, thrust coefficient, and ambient turbulence intensity. Comparisons with two field measurements and three wind tunnel test cases demonstrate the accuracy of this model, which provides predictions of wake velocity loss in both the lateral and vertical directions that are more accurate than those of the conventional models.