A Gaussian wake model for Airborne Wind Energy Systems

Modeling the aerodynamic interactions between Airborne Wind Energy Systems (AWES) is an open and challenging problem. To this end, a new Gaussian wake model is introduced for fly-gen AWES, also called windplanes here. The engineering wake models of windplanes can be split in induction models, used to find the induced velocities at the wing, and wake models, used to account for the wind deficit downwind. The proposed model combines an improved induction model, starting from one available in the literature, with a novel wake model that assumes that the wake velocity has a Gaussian shape and imposes momentum conservation. The variance of the Gaussian wake is assumed to vary with the downstream distance from the windplane. The model entails just one tuning parameter that is estimated using CFD results from the literature, showing high accuracy. The new model is then used to study the influence of an upwind system on a downwind one. A sensitivity analysis is carried out by moving the downwind system in the direction transverse to the wind speed or by yawing it with respect to the wind direction. A maximum in power production of the downwind system is found when the projections of the two trajectories are partially overlapping. The extremely low computational cost of the model and the physical insights provided by this paper contribute to clear the way for simulation, planning and control of large scale airborne wind farms.