the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 May 2025
Aero-servo simulations of an airborne wind energy system using geometry-resolved computational fluid dynamics
Abstract. Airborne wind energy (AWE) is an innovative technology to harness wind energy, often through the use of tethered aircraft flying in crosswind patterns. A comprehensive understanding of the unsteady interactions between the wind and the aircraft is required for developing efficient, reliable, and safe AWE systems. High-fidelity simulation tools are essential for accurately predicting these interactions. To provide meaningful insights into crosswind flight maneuvers they must incorporate the coupled nature of aerodynamics, dynamics, and control systems. Therefore, this work presents a geometry-resolved computational fluid dynamics (CFD) framework of an AWE system, encompassing all lifting surfaces and integrating movable control surfaces, referred to as the virtual wind environment (VWE). Unlike existing models that only consider linear combinations of individual aerodynamic effects, the VWE addresses the challenge of combining the relevant aerodynamic interactions specific to crosswind flight motion. This VWE is coupled to the dynamics and control framework of an AWE system, enabling the first geometry-resolved aero-servo simulations. We demonstrate the coupling by tracking a pre-optimized 1-loop power cycle in the VWE coupled to model predictive control (MPC), achieving 96 % of the reference power.
- Preprint
(3390 KB) - Metadata XML
- BibTeX
- EndNote
Status: final response (author comments only)
-
RC1: 'Comment on wes-2025-73', Anonymous Referee #1, 30 May 2025
Technical Review for WES-2025-73
Summary:
This paper addresses the limitations of current airborne wind energy (AWE) simulations, which often rely on simplified aerodynamic models that cannot capture unsteady effects, flow separation, or the interaction between control surfaces and aircraft dynamics. To overcome this, the authors develop a geometry-resolved CFD framework—called the Virtual Wind Environment (VWE)—and couple it with the AWEbox simulation and control toolbox using an explicit aero-servo approach. They simulate a 1-loop power cycle of the MegAWES aircraft under realistic wind conditions and demonstrate accurate trajectory tracking and power output, achieving 96% of the reference performance. The study reveals aerodynamic effects missed by low-fidelity models and offers a high-fidelity tool for improving AWE design and control.
nomenclature:
It is better to add this section before the introduction to ease tracking the paper content.
Introduction:
Make this section right after adding a nomenclature section.
In the Introduction, the authors point out that most AWE simulations use simple aerodynamic models that miss unsteady flows and how moving control surfaces really work together. They give a fair overview of past studies, but don’t show how big the errors usually are or explain in detail why earlier coupled methods fall short. They make a good case for using full-geometry CFD to see things like flow separation, but don’t warn readers that this requires a lot more computing power. The term “Virtual Wind Environment” is a helpful name, but it isn’t defined until after its first mentioned.
CFD
The authors use a linear aerodynamic model (AAM) for a fixed-wing aircraft, where the key aerodynamic effects are captured with matrix-based derivatives. They calculate those derivatives by running CFD simulations on an overset (Chimera) mesh, which is great for handling complex shapes and moving parts without having to remake the grid each time.
Still, the paper misses a few practical details. First, there’s no information on how much computer time or memory these CFD runs need when you add more moving surfaces. Second, the authors never check their results against a known aircraft or wind-tunnel data, which would help prove their model really works under different flight conditions. Third, they don’t show a mesh-independence study—refining the grid until the results stop changing—to confirm their CFD setup is reliable. Because their model is linear, it may lose accuracy when control surfaces move a lot or during strong unsteady effects; discussing where that approach breaks down would round out the paper. The methods are solid, but adding notes on run-time, a basic validation case, a mesh-sensitivity check, and the limits of linearization would make the work much stronger.
AWE system dynamics and control
The presented work is clear that describes the six-degree-of-freedom dynamics, tether modeling, and MPC framework. To help readers fully understand and trust your approach, could you please elaborate on a few points? For instance, a brief explanation of how you selected the Baumgarte stabilization parameter and the MPC horizon length would be very insightful, as would a discussion of the controller’s sensitivity to errors in the analytical aerodynamic model—have you tested how deviations in those coefficients affect tracking performance? It would also be helpful to know the computational effort required to solve the MPC every 5 ms (for example, whether it runs in real time on standard hardware or needs a high-performance cluster). Additionally, could you comment on the straight-tether assumption under strong crosswinds or slack conditions and whether you plan to extend the model to include tether sag or bending? Since the tether’s mass grows continuously as it reels out, some discussion of how that changing mass and inertia influence the dynamics and controller performance over a full power cycle would greatly clarify the robustness and applicability of your framework.
Aero-servo coupling
The aero-servo coupling you’ve implemented is very elegant in how it links the high-fidelity CFD solver with the AWEbox dynamics and MPC in a single explicit time-stepping loop, and using CoCoNuT to shuttle motion and force data keeps the workflow organized. To help readers appreciate and trust this approach, could you expand on a few aspects? For example, you mention that no coupling iterations are performed within each 5 ms timestep—have you observed any drift or stability issues over longer simulations, and how did you decide that single-step coupling was sufficient? It would also be useful to know the additional runtime cost and data-transfer overhead introduced by the CoCoNuT interface, especially when moving multiple overset zones each step. In the transition period where you blend AAM and VWE forces, what guided your choice of n₁ and n₂, and how sensitive are your results to that weighting schedule? Could you briefly describe any tests you ran to verify that the explicit coupling preserves energy consistency or avoids unphysical oscillations? A few sentences on these points would greatly strengthen confidence in the robustness and practicality of your aero-servo coupling.
Results
The Results section presents a clear demonstration of your coupled framework, showing both the trajectory tracking—where you achieve a close match within 4 m of the reference path—and the power output, with 96 % of the target average power captured. The side-by-side plots of aerodynamic forces and moments from the VWE and the analytical model effectively highlight model agreement and key discrepancies. To deepen the reader’s understanding, it would be helpful to include quantitative error metrics (e.g., root-mean-square deviation over the cycle) for trajectory, power, and force comparisons
-
RC2: 'Comment on wes-2025-73', Anonymous Referee #2, 02 Jun 2025
Thanks for your hard work and for writing this up for the world to read!
I have summarized my remarks per section and most of the style points separately.
I was wondering if it is correct that you are making no data or any code available?
Style Points
- Descriptive subscripts should not be italic, and should be in straight font instead. (see #7 https://physics.nist.gov/cuu/Units/checklist.html: "Superscripts and subscripts are in italic type if they represent variables, quantities, or running numbers. They are in roman type if they are descriptive.")
- Minimize the number of brackets, e.g. Figure 5 caption could be "...(a) xz-plane at y = 1.3m and in the (c).." or in line 322.
- WES style guide mandates that you use acronyms for Eqs. and Fig. etc. except when at the beginning of the sentence, see the WES style guide and adjust accordingly. (eq. line 322)
- You should include all numbers in mathmode, now you are including some and others not, which is not consistent and is not following style guides.
- Units should be (m) and not [m]
- WES demands colorblind readable plots, yours are not. (e.g. Fig 12)
- Units should be m s^-1 and not m/s, e.g. line 383 deg/s
- You could move author contributions, competing interests and acknowledgements in front of the appendices
Abstract
"To provide meaningful insights into crosswind flight maneuvers they must incorporate.." I would write instead, should incorporate as it is not the case that one can not get meaningful insights at all without incorporating the additional effects. It is just that the insights get more accurate/more useful.
As you can never be 100% certain that your work is a first of its kind, it's better to use the word "novel" in the abstract.
Introduction
Paragraph on lines 34--46 or so, there you could add a reference to D. Eijkelhof's work, as you are discussing fixed-wing simulation works.
You also don't discuss in the introduction that you are neglecting deformation, why you are doing it, why that is okay, and what the effect is.
Sentence 51: "Specifically, they fail to account for unsteady aerodynamic phenomena and omit the interaction of various aerodynamic effects - such as the influence of the rotational speed on aileron effectiveness." -- rephrase, into something like: "they fail to account for various aerodynamic effects, including unsteady and .."
2. Virtual Wind Environment
line 100--105: Explain briefly what the overset technique is and how it works, could be 1 sentence.
Earlier, you talked about resolving local flow phenomena accurately, and in line 110, you state using a y+ value of 100. This means that boundary layer properties (which are local flow phenomena) are not captured accurately. This is not to say that y+ of 100 you can't meaningfully resolve any local flow phenomena, but then you should be more open and clear about the limitations, and what you are resolving and what not. Also, at current, there is no mention of why y+ is 100, would be good or bad, or why it is chosen.
You mention the z_0 value twice (line 139)
Line 145, if this is in the local frame, please add this.
4. AWE system dynamics
Skew operator is in the wrong order, line 190
Add some space between Fig. 6 and eq. 5 and 6
Why don't you use the terminology kite rather than aircraft? Kite is defined as anything from the bridle point up, which in your configuration is identical to the aircraft itself.
You talk about 3D forces, then you should use capital subscripts: C_L, C_M, C_N, etc.
Line 257 could leave the "of 1" out. The sentence is smoother without.
5. Aero-servo coupling
An itemized list in lines 275--282, rather than having the steps described in a line, would be much easier to follow as a reader.
Equations around line 325, you can't add text to the equations like you are doing there.
6. Results
Fig 10. Use LaTeX font, or even generated labels, and make them non-overlapping.
Line 365, rewrite, the use of - here is not so clear.
Line 369, could remove VWE from brackets and add in text.
Line 373 rewrite
Line 365- 378: You leave the reader with some questions here. Make it more explicit that the 'minimal model mismatch' is only visible here, and later, the differences are clearer. From this part of the analysis, one thinks from the intro that large differences will be seen, and then suddenly argues that one anticipates small differences, which is strange.
Figure 12: Why is blue not shown on the left? What is the consequence of the LARGE deviation in sideslip?
Figure 13 (b): Why is there this difference? And can you make the legend external? The overlap with lines is not so nice.
Line 388, do you mean C_M instead of C_l?
Line 418, you could combine sentences and leave out "finally"
7. Conclusion and outlook
Line 430, mention which effects are not captured and which deviations are found.
Appendices
Formatting of equations A4, A5, A6. should be improved
Avoid double subscripts at all costs, could use, to separate, e.g. ,line 481 C_i,jCitation: https://doi.org/10.5194/wes-2025-73-RC2
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 81 | 16 | 9 | 106 | 6 | 9 |
- HTML: 81
- PDF: 16
- XML: 9
- Total: 106
- BibTeX: 6
- EndNote: 9
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1