the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Refining the airborne wind energy systems power equations with a vortex wake model
Filippo Trevisi
Carlo Emanuele Dionigi Riboldi
Alessandro Croce
Abstract. The power equations of crosswind Ground-Gen and Fly-Gen airborne wind energy systems (AWESs) flying circular trajectories are refined to include the contribution from the aerodynamic wake, modelled with vortex methods. This allows to understand the effect of changing turning radius, wing geometry and aerodynamic coefficients on the aerodynamic power production. A novel power coefficient is defined by normalizing the aerodynamic power with the wind power passing through a disc with radius equal to the AWES wing span. The aspect ratio which maximizes this power coefficient (i.e. which maximizes the aerodynamic power for a given wing span) 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 geometry, are compared in terms of power production and three AWESs from literature are analyzed. Ground-Gen have lower power potential than the same geometry Fly-Gen AWESs because the reel-out velocity makes them to fly closer to their own wake.
Filippo Trevisi et al.
Status: open (until 30 Jun 2023)
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RC1: 'Comment on wes-2023-52', Anonymous Referee #1, 23 May 2023
reply
The work presented in this article is interesting. I only have minor comments.
1. The authors have done an extensive review of the literature. However, the purpose of paragraph 2 in the introduction is unclear. This arrangement makes it harder to identify the motivation of the article, which is only mentioned later in the third paragraph (momentum theory – as it is applied to wind turbines – is not suitable for investigating wake induction in AWES). The authors should consider either making the purpose of paragraph 2 clearer, or introducing the motivation of the article earlier.
2. The authors does mention that the new power coefficient can identify an optimal aspect ratio that is not infinite. I believe that this advantage over the previous definition (which would result in an infinite aspect ratio) should be highlighted in the abstract and the introduction. Similarly, the ability to compare different AWES using the new power coefficient deserves mentioning.
3. In figure 1:
- Are the axes e1, e2, and e3 fixed to the aircraft?
- The frame of reference in the figure is unclear to me. The descending trajectory of the AWES would suggest that the viewpoint of figure 1 is fixed to the wind. This should be mentioned if true. And if the viewpoint is indeed fixed to the wind, then the wind vector vw can be moved closer to the aircraft to highlight that this wind vector is applied locally to the aircraft.
4. Equation 5 and the paragraph below it are very hard to follow. Instead of a long paragraph, I suggest the authors deconstruct equation 5 into smaller equations. For example, eq 5 will be
CD = CL / (CD + CT,t)
Followed by (along with the accompanying explanation text)
CD = CD0 + CnD + CfD
CD0 = CD,v + CD,t
Etc.
5. The graphs should be bigger (figures 5, 6, … ,14). They look small when printed.
6. Finally, the authors are invited to consider the suggested grammatical and editorial changes found in the attached pdf.
I recommend publication of this article once the above queries are addressed.
Filippo Trevisi et al.
Filippo Trevisi et al.
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