Refining the airborne wind energy system power equations with a vortex wake model

The power equations of crosswind Ground-Gen and Fly-Gen airborne wind energy systems (AWESs) flying in circular trajectories are refined to include the contribution from the aerodynamic wake, modeled with vortex methods. This reveals the effect of changing the turning radius, the wing geometry and the aerodynamic coefficients on aerodynamic performances and power production. A novel power coefficient is defined by normalizing the aerodynamic power with the wind power passing through a disk with a radius equal to the AWES wingspan, enabling the comparison of different designs for a given wingspan. The aspect ratio which maximizes this power coefficient is finite, and its analytical expression for an infinite turning radius is derived. By considering the optimal wing aspect ratio, the maximum power coefficient is found, and its analytical expression for an infinite turning radius is derived. Ground-Gen and Fly-Gen AWESs, with the same idealized characteristics, are compared in terms of power production, and later three AWESs from the literature are analyzed. With this modeling framework, Ground-Gen systems are found to have a lower power potential than Fly-Gen AWESs with the same geometry because the reel-out velocity makes Ground-Gen AWESs fly closer to their own wake.