An Entrainment-Based Wake Model for Airborne Wind Energy and Annular Wind Turbines

Several novel wind energy systems have annular wakes instead of the disc-shaped wakes common to conventional horizontal-axis wind turbines (HAWT). Systems with annular wakes include airborne wind energy (AWE) devices, which harvest power from tethered kites flying in a circular path (such as the Makani energy kite), as well as rim-drive wind turbines. Since wind farms use arrays of hundreds of turbines, good analytical wake models are essential for efficient wind farm planning. Several models already exist for HAWTs, such as the Park, Frandsen, and Entrainment models. However, none have yet been proposed for turbines with annular wakes, making it impossible to estimate their array performance. We use the entrainment hypothesis to develop an analytical model for the shape and flow velocity of an annular wake. Our model is in good agreement with Large Eddy Simulation results from Haas \& Meyers ({\it J. Phys.: Conf. Ser.} 2017), especially in the far wake region, and enables the prediction of AWE kite array performance.