A new coupled model for the equivalent roughness heights of wind farms. (June 2021) - Zhang, Huan; Ge, Mingwei; Liu, Yongqian; Yang, Xiang I.A.
Abstract: Accurate parameterization of wind farms' equivalent roughness heights is critical to meso-scale climate simulations as well as power predictions of wind turbines. A notable inadequacy of the existing models is that the results sensitively depend on s x / s y, where s x and s y are the dimensionless streamwise and spanwise spacing of the turbines. To understand the issue, we conduct large-eddy simulations (LESs) for three types of quasi-infinite wind farms with moderate, large, and small s x / s y . We find that the wind speed at the rotor is different from the horizontally averaged wind speed at the hub height, and this is particularly true for wind farms with small s x / s y . This flow inhomogeneity at the hub height plays an important role in determining wind farms' equivalent roughness height but is often neglected in the existing models. Accounting for the flow inhomogeneity at the hub height, we propose a new coupled top-down/bottom-up model for the equivalent roughness heights of wind farms. Our model is compared with the existing models and our LESs. The results show that the proposed model is able to predict the equivalent roughness height of all types of wind farms irrespective of s x / s y 's value. Highlights: The mean profile of wind farm boundary layer shows a three-layer structure. Flow inhomogeneity at the hub height is important for the model of wind farm. A new model is proposed for the equivalent roughness heights of wind farms. The model is validated via LES and works better than the existing models.