Vortex model of the airborne wind energy systems aerodynamic wake

Abstract

Abstract. Understanding and modelling 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 is here studied with vortex methods, as momentum methods cannot be applied to AWESs in a physically consistent way. The velocities induced at the AWES from a generic helicoidal vortex filament, trailed by a position on the AWES wing, is modelled with an expression for the near vortex filament and one for the far vortex filament. The near vortex filament is modelled as the first half rotation of the helicoidal filament, where its axial component is 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 modelled as two semi-infinite vortex rings cascades with opposite intensity. An approximate solution for the induced axial velocity at the AWES is given as 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-dynamic-elastic simulations and in design and optimization studies.

Vortex model of the aerodynamic wake of airborne wind energy systems

“…Axial induced velocity at the wing center Data availability. All figures and the data used to generate them can be retrieved in MATLAB format via https://doi.org/10.5281/zenodo.8027915 (Trevisi et al, 2023) and opened with MATLAB or other open-source programming languages (e.g., Python, Octave).…”

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

“…Code and data availability. All figures and the MAT-LAB code developed to generate them can be retrieved via https://doi.org/10.5281/zenodo.8210953 (Trevisi et al, 2023a). The figures can be opened with MATLAB or other open-source programming languages (e.g., Python, Octave).…”

Modeling of separated flow over tailings storage facility

“…Research [6] proposed an approach to determine the "non-linear" aerodynamic wake configuration using the potential theory, where the influence of all induced velocity components on the aerodynamic wake configuration is taken into account in order to obtain a wake similar to the real one. In the article [7], the aerodynamic wake of the side wind is studied with the help of vortex methods, taking into account the different movement for the near and far wake. And in [8], a simplified analytical model is proposed, which combines the Gaussian wake model and the model of the induced cylindrical vortex to evaluate the interaction between the wake zones.…”