# A Dynamic Wake Model based on Vortex Rings for Airborne Wind Energy Systems

### Bachelor Thesis Defense

Antonia Mühleck

University of Freiburg

Monday, December 11, 2023, 15:00 - 16:00

online via Zoom

As with conventional wind turbines, the energy yield of Airborne Wind Energy Systems (AWES) is reduced by wake effects. Due to the dynamic trajectories of AWES, steady-state assumptions do not apply. A dynamic model is therefore required to better understand the aerodynamic wake of AWES and to minimise losses caused by it.

The aim of this thesis is to derive a dynamic but numerically inexpensive model for the wake of single and dual kite crosswind AWES flying on circular trajectories. As angular velocities are very high in crosswind flight, gravitational forces are assumed to be negligible compared to centrifugal and aerodynamic forces. If wind shear is neglected as well, the problem becomes axisymmetric about the free-stream wind direction. The wake can then be represented in a simplified form by a sequence of vortex rings. Using the Biot-Savart-Law, the induced velocities of these rings at the kite’s position are evaluated. The resulting integrals are replaced by an expression with elliptic integrals. These can be evaluated via power series, thus reducing the computational time of the model. For each full revolution of a kite, a new ring is added to the wake. The induction is then calculated and the propagation speed of the rings is modified accordingly. The model developed in the following can be used to describe the induction at different stages of the wake development. It is therefore used to analyse induction at the beginning of the reel-out phase. Furthermore, the power production during this stage is considered, specifically addressing the optimal length of the reel-out phase in terms of induction. It was found that shorter reel-out times lead to overall higher power production. The model also takes into account that the tether length of a single-kite AWES increases during the reel-out phase. This results in a larger radius of rotation and increased tether drag, which also affects power production. For dual kites, a significantly higher induction was found for otherwise identical kite parameters.

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