Free-vortex-wake dynamics of airborne wind energy kites in crosswind flight

Abstract

The wake of an airborne wind energy kite is shaped by its crosswind path and, for on-board generation, by the slipstreams of its rotors, and in farms it reaches downstream units. It is computed here by a vortex step method with a time-marching free vortex wake, implemented by the authors in their open-source code OpenFAWE with a lumped-mass tether, actuator-disc rotors releasing vortex rings and several kites. It reproduces an independent vortex step code to 10^-9 on the rigid-wing Makani M600 and within 0.3% in lift and 0.9% in drag on the TU Delft V3 leading-edge inflatable kite, matching its Reynolds-averaged Navier-Stokes lift within 3.1%. For fixed kites the lift deficit of a finite wake is the far field of its starting vortex, which fixes the wake length before a run, and the vortex core must stay below the narrowest panel width. With these settings the helical tip-vortex pair of the M600 on its loop lowers its lift by about 0.5% from 5 to 13 m/s. Free rotor rings do not converge with the time step, whereas an undeformed slipstream tube converges once its rings are refined at the wing and raises the lift by 1.9%. A slipstream deflected by the wing lowers it by 3.5%, so the treatment near the wing sets the sign of the rotor effect. A second unit one loop diameter downstream loses 0.5% of its lift and 2.2% of its aerodynamic power, with or without rotors.