An Aero-Structural Model for Ram-Air Kite Simulations

Round 1

Reviewer 1 Report

The authors coupled a panel method with a membrane solver to represent a steady flight of a ram-air kite. Simultaneously, the authors performed measurements on a kite during the quasi-steady part of the flight path. The results are compared in a scaled way and show good agreement.

Remarks:

·         Line 140: A wrinkling model is used in the membrane structure solver, but to what extent does wrinkling occur in the simulations? Are the locations with wrinkling matching those in the experiments?

·         Line 151: How can either explicit or implicit coupling methods be used if only a single pseudo time step is performed? Isn’t explicit then just a single iteration of the implicit coupling methods? Furthermore, Algorithm 1 also indicates that always implicit coupling is used. How many of these iterations are used in the simulations? How often do you get divergence and how is this remedied in a next attempt?

·         Algorithm 1: The scaling of u_i on line 13 is not explained.

·         Line 282: Multiple possible reasons for the difference are given, but can’t the most important one be determined by performing simulations where only one item from the list is changed?

·         Why no max L_t in Figures 11 (a) and (c)? The difference between max and min L_t is similar to that between max and min V_a.

 

Minor comments:

·         Line above Eq (6): the the => the

·         Line 321: Equation (8)is => Equation (8) is

·         Line 366: abd => and

Author Response

Dear reviewer,

Thank you very much for providing feedback. Below we list your remarks and our answers.

Best regards,
The authors

Remarks:

1. Line 140: A wrinkling model is used in the membrane structure solver, but to what extent does wrinkling occur in the simulations? Are the locations with wrinkling matching those in the experiments?

2. Line 151: How can either explicit or implicit coupling methods be used if only a single pseudo time step is performed? Isn’t explicit then just a single iteration of the implicit coupling methods? Furthermore, Algorithm 1 also indicates that always implicit coupling is used. How many of these iterations are used in the simulations? How often do you get divergence and how is this remedied in a next attempt?

3. Algorithm 1: The scaling of u_i on line 13 is not explained.

4. Line 282: Multiple possible reasons for the difference are given, but can’t the most important one be determined by performing simulations where only one item from the list is changed?

5. Why no max L_t in Figures 11 (a) and (c)? The difference between max and min L_t is similar to that between max and min V_a.

Answers by the authors:

1. A wrinkling model is used in the numerical FEM simulation to correct the stress state in the membrane. An underlying assumption in the FEM model is that the membrane has neither compressive nor bending resistance. By simply setting the stiffness to zero in case of compressive or bending loads, the solver will diverge. To prevent numerical instability, a non-compressive or wrinkling model is utilized that rotates the stiffness tensor for a given load so that the second principal stress is co-linear with the direction of compression. The advantage of such a model is that individual wrinkles (their geometry) are not simulated but rather the stress state. It is comparable to a turbulence model in CFD, where individual eddies are not modelled.
   
   In the kite simulation, wrinkling occurs in the ribs and the canopy where the load in one direction is approximately 5-10 times larger than in the direction perpendicular to it. In that case, the membrane considerably changes its stiffness properties, and the principal stress shows the direction of the wrinkle. In this work, we did not compare the wrinkling direction to experiments but verified the validity of the FEM code implementation (Thedens, 2022 - https://edu.nl/ceetm) with analytical and numerical solutions found in the literature. The wrinkling model used in this work has been validated with experimental data (Jrusjrungkiat, 2009 - https://edu.nl/4mcer).

2. The coupling is done using the FSI library preCICE which provides several implicit and explicit coupling options. In the case of explicit coupling, no information about the previous solution (neither from the previous time step nor from the previous iteration within a time step) is used, the pressure is given to the FEM, and the displacements are handed back to the panel code until convergence in the displacement is reached.
   In the case of implicit coupling, the IQN-ILS approach proved to perform better for some kite geometries than the explicit method. In the implicit approach, an implicit least-squares method (ILS) approximates the relation between pressure and displacement within a single timestep. Information from previous time steps can accelerate the convergence but is not required. The difference between the implicit and explicit coupling is that for the implicit approach, the displacement vector is scaled by the least-squares method, whereas for the explicit method, no scaling is applied, and the first iteration of both approaches is equivalent.
   We added information about the number of iterations required for convergence in Section 2.3. A more detailed description of the coupling approach and the divergent behaviour can be found in the dissertation (Thedens, 2022 - https://edu.nl/ceetm).

3. A description of the displacement scaling u_i was added to Algorithm 1.

4. This is a valid question. In our experience with the FSI solver, it is very difficult to isolate a single behaviour, such as the local increase in the angle of attack or profile change due to deformation, because of the internal coupling between fluid and structure. For example: If the local angle of attack is increasing because of strain in the bridle lines and twist in the canopy, it will cause feedback on the pressure distribution, which in return increases the load on the canopy that might deform the profile considerably. Even small deformations can lead to drastic changes in the geometry. In the dissertation (Thedens, 2022 - https://edu.nl/ceetm) an example is shown where the wing’s trailing edge bends in the first coupling iteration that eventually causes the wing to collapse.

5. This is indeed an error in the legend. It should read “FSI – no tether” because the tether does not influence the belt force. A corrected figure was added to the manuscript.

Reviewer 2 Report

"An Aero-Structural Model for Ram-Air Kite Simulations":

1. The abstract should briefly display the results of the research.

2. In Introduction, the authors must state clearly the novelty and contribution of this research.

3. It is better to make a more comprehensive literature review in the form of a table (matrix) so that the reader is more confident with the contribution of this research. Literature review section can be added after the introduction.

4. Need to add a Methodology section before the Results section.

5. In the Methodology section, the authors should present the complete research steps in the form of a complete flowchart accompanied by descriptions.

6. In the Results section, the authors should present an in-depth analysis of the research results. There has not been seen an adequate analysis for a journal article.

7. In conclusion, it is better to disclose opportunities for further research from the research that has been done.

 

Author Response

We agreed with the editor to not reply to this review.

Reviewer 3 Report

This paper provides a staggering aerodynamic/structural coupling method to simulate the performance of a ram-air kite. The proposed method adopts the panel method for aerodynamic analysis and FEM for structural analysis, and the simulation results are validated by flight data. The developed simulation scheme can be used in the early stage of the ram-air kite. Some problems still exist in this paper:

 

1. ‘the’, ‘a’, singular and plural forms. Like lines 9, 87, …

2. lift-drag ratio is important during the whole analysis process, while the panel method cannot take the viscous into consideration. How to mitigate this impact in the early design stage and give a reasonable design scheme?

3. In Figure 2(a), the symbols are not unique and the expression of spherical coordinates is hard to understand. Some modifications are needed.

4. Some simple quantitative analyses from airborne wind energy force to electric energy are suggested to supplement.

 

5. There are 11 self-citations in the total 22 references. Add some papers of other researchers.

Author Response

Dear reviewer,

Thank you very much for providing feedback. Below we list your remarks and our answers.

Best regards,
The authors

Remarks:

This paper provides a staggering aerodynamic/structural coupling method to simulate the performance of a ram-air kite. The proposed method adopts the panel method for aerodynamic analysis and FEM for structural analysis, and the simulation results are validated by flight data. The developed simulation scheme can be used in the early stage of the ram-air kite. Some problems still exist in this paper:

1. ‘the’, ‘a’, singular and plural forms. Like lines 9, 87, …

2. lift-drag ratio is important during the whole analysis process, while the panel method cannot take the viscous into consideration. How to mitigate this impact in the early design stage and give a reasonable design scheme?

3. In Figure 2(a), the symbols are not unique and the expression of spherical coordinates is hard to understand. Some modifications are needed.

4. Some simple quantitative analyses from airborne wind energy force to electric energy are suggested to supplement.

5. There are 11 self-citations in the total 22 references. Add some papers of other researchers.

Answers by the authors:

1. It is not clear what you mean. We have checked the use of singular and plural forms and can not find any mistakes.

2. It is true that the panel method based on the potential flow assumption is not good at capturing the aerodynamic drag of a wing compared to CFD or experimental measurements. In our experience, the lift-to-drag ratio of the wing is typically overestimated by a factor of 10-30, depending on the wing geometry. These results are not usable in the design stage because the wing’s performance is drastically overestimated.
   
   However, we found that the added bridle drag corrects this to some degree. For paragliders or ram-air kites used by Skysails the aerodynamic drag of the bridles is approximately a third of the total drag of the entire wing-bridle system. By approximating the bridle drag with a cylinder drag model, the system lift-to-drag ratio is decreased and reaches more realistic values (15% overestimation compared to measured field data), which is sufficiently accurate for the initial design stage.

3. We do not see any symbols in Figure 2(a) that are not unique. We improved the illustration of the spherical coordinates θ and φ in the figure and in the text.

4. A subsection in the introduction was added that cites two publications about the electric energy production of airborne wind energy systems.

5. The second author of this paper is one of the pioneers of the emerging field of airborne wind energy and has not only coauthored many publications but also edited the two textbooks that were published on the topic. We have added six citations where the second author was neither co-author nor editor.