A simple model for average kinetic energy flux within large wind turbine arrays

We propose a 1-D analytical model to investigate the kinetic energy distribution within an array of wind turbines, focusing on the interactions between large-scale wind farms and the atmospheric boundary layer (ABL). Wind farms harvest kinetic energy from atmospheric boundary layer winds, both at the leading edge and through vertical entrainment by turbulence from aloft. Based on our recent findings that turbulent flow in and above wind farms is similar to canopy-type flows, we use a new analytical model that can predict the development length of the wind farm flow as well as the vertical flux of kinetic energy to investigate this further. Within the region where the flow is developing, momentum is advected into the wind farm and wake turbulence draws excess momentum in from between turbines. This is characterized by significant dispersive fluxes of momentum. Once the flow within the wind farm is fully developed, the area-averaged velocity profile exhibits an inflection point, characteristic of canopy-type flows. The inflected velocity profile is linked to the existence of a dominant characteristic turbulence scale, which may be responsible for a significant portion of the vertical momentum and energy flux into the turbine array. Prediction of this scale is useful for estimating the amount energy captured by the turbine array versus energy lost to the surface. The amount of kinetic energy transported the ground or sea surface, when compared to the case without wind turbines can be used to assess environmental effects of wind farms. The new model is tested with results from wind tunnel experiments, which characterize the turbulent flow in and above model wind farms. The model can be used for optimizing wind turbine spacing and layout, and for assessing the impacts of wind farms on nearby wind resources and the environment.-2016-->