Vortex model of the aerodynamic wake of airborne wind energy systems

Understanding and modeling the aerodynamic wake of airborne wind energy systems (AWESs) is crucial for estimating the performance and defining the design of such systems, as tight trajectories increase induced velocities and thus decrease the available power, while unnecessarily large trajectories increase power losses due to the gravitational potential energy exchange. The aerodynamic wake of crosswind AWESs flying circular trajectories is studied here with vortex methods. The velocities induced at the AWES from a generic helicoidal vortex filament, trailed by a position on the AWES wing, are modeled with an expression for the near vortex filament and one for the far vortex filament. The near vortex filament is modeled as the first half rotation of the helicoidal filament, with its axial component being neglected. The induced drag due to the near wake, built up from near vortex filaments, is found to be similar to the induced drag the AWES would have in forward flight. The far wake is modeled as two semi-infinite vortex ring cascades with opposite intensity. An approximate solution for the axial induced velocity at the AWES is given as a function of the radial (known) and axial (unknown) position of the vortex rings. An explicit and an implicit closure model are introduced to link the axial position of the vortex rings with the other quantities of the model. The aerodynamic model, using the implicit closure model for the far wake, is validated with the lifting-line free-vortex wake method implemented in QBlade. The model is suitable to be used in time-marching aero-servo-elastic simulations and in design and optimization studies.