Transonic Buffet Suppression by Airfoil Optimization

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

The quality of the English Language must be improved. There are too many typos, and a few repetitions.

Author Response

Dear Tracy and Reviewers:

Thank you for your letter and for the reviewers' comments on our manuscript entitled " Transonic buffet suppression by airfoil optimization"[aerospace-2774048]. Those comments are all valuable and very helpful for revising and improving our paper. We have studied the comments carefully and have accordingly made correction which we hope can meet your requirements. Revised parts are marked in red in the paper.

Responses to Editor:

 Major issues

1. Please provide the accurate mail of [email protected] as our email could not be delivered successfully.

Reply: Thanks for your advise. Chen Yong has been removed from the author column.

2. We have did a pre-layout for your paper, please make you will make revision based on the version downloaded from the link in this mail.

 Reply: Thanks for your advise. The modification has been completed based on the version downloaded from the link in this mail.

3. Please note the author self-citation should be decreased.

Reply: Thanks for your advise. The author self-citation has been decreased. Hope to meet your requirements.

The main corrections in the paper and the responses to the reviewer's comments are as follows.

Responses to Reviewer1:

 Major issues

1. In the introduction, I recommend discussing at length the differences with the paper [1] recently published by the same research team, and whose content is quite similar.

[1] H. Chen et al., Study on Optimization Design of Airfoil Transonic Buffet with Reinforcement Learning Method, Aerospace, 10, 486 (2023).

Reply: Thanks for your advise. I have read this paper, and add it to the Reference. In this paper, the buffet amplitude is used to represent the characteristics of the flow instability and reinforcement learning method is used. But it is only effective when buffet occurs in the design state. Meanwhile, it is computationally costly to get the buffet amplitude. The optimization objective is to suppress buffet without decreasing aerodynamic performance. So, the aerodynamic performance of the optimized airfoil has not been significantly improved at a lower angle of attack.

2. I strongly recommend defining the design variables X = [x1, x2, ..., xn] before the introduction of surrogate models in section 3.2. The CST parameterization should be presented with more details, like in [1] for instance. The range of each parameter should also be precised.

Reply: Thanks for your advise. The range of each parameter is 35%, which is given in Chapter 4.1.

3. When LHS is introduced, the prior probability distribution of the parameters should be given (I guess the distributions are uniform).

Reply: Thanks for your advise. The prior probability distribution of the parameters is uniform, which is given in Chapter 4.1.

4. The notation r in the RBF subsection is unnecessary and should be replaced by x .

Reply: Thanks for your advise. The modification has been completed, which is in Chapter 3.2.

5. Many references appear larger the body text. The equations are generally misaligned when included in the body text, and are also printed too large.

Reply: Thanks for your advise. The format modification has been completed.

6. The expression “radial basis function” should be used consistently instead of “radius-based function”. Please use the expression conservative variables instead of “conservative values” for describing U.

Reply: Thanks for your advise. The modification has been completed.

7. The paragraph including the sentence “But the time-domain simulation method needs large computational costs and cannot directly obtain the flow field characteristics such as aerodynamic damping and fluid modes” is too negative regarding the time-domain simulations (URANS/DES/LES/DNS). Admittedly, these simulations cannot provide unstable fluid modes. However, they can predict the buffet onset, i.e. the transient flow leading to a fully developed buffet, from which a damping-rate could be post-processed if needed. These predictions contain arguably more information than a global stability analysis. Moreover, only the time-domain simulations can predict the buffet amplitude, which is a crucial information. Please rephrase this paragraph, and include recent references to accurate time-domain buffet simulations.

Reply: Thanks for your advise. The recent references to accurate time-domian buffet simulations have been added to the introduction. The sentence is modified as “The time-domain simulation method can predict the buffet onset and buffet amplitude. However, it needs large computational costs and cannot directly provide the flow field stability characteristics such as aerodynamic damping and fluid modes.”

8. The spatial discretization methods (finite volume) should be mentioned before introducing a matrix version of the governing equations.

Reply: Thanks for your advise. The modification has been completed, which is in Chapter 3.1.

9. I do not understand why the ROM results are also compared to URANS and Bi-Global predictions (Figure 3). I am perhaps missing something here... Please justify their presence or remove them completely.

Reply: Thanks for your advise. The ROM results are meaningless in this paper. So they are removed completely, which is shown in Fig.3.

10. Most of the time, the horizontal velocity flow mode is shown instead of a pressure mode (Figure 5). The pressure mode does not exhibit an energetic post-shock shear layer, which is usually a feature associated with an unstable velocity mode. Could the authors explain why?

Reply: Thanks for your advise. The pressure mode is corresponding to the pressure field. In order to express it more accurately, the horizontal velocity flow mode is shown in Fig.5.

11. “The flow damping is -0.0173 and the frequency is 0.173 computed by the Biglobal analysis which agrees well with the results of numerical simulation. The error of the two methods is not over 4%.” The agreement is overstated. The PSD is rather flat around ω = 0.172, and there is no clear peak at that frequency. An error over the reading of ω should be provided.

Reply: Thanks for your advise. The peak value of PSD is , which is shown as follows. The frequency of numerical simulation is about . The Bi-Global result is . The error is not over 1%.

12. Similarly, the comments describing the figure 8 should be nuanced. Both Biglobal analysis and URANS are poorly accurate at Ma = 0.8.

Reply: Thanks for your advise. The sentence is modified as “the computational results correspond well with the results of the experimental results except for the case ”.

13. Similarly, the comments of Figure 10 hide the fact that the URANS tends to over-predict the pressure in the attached boundary layer.

Reply: Thanks for your advise. The sentence is modified as”The pressure coefficients computed by the CFD solver agree well with the experimental results, which are shown in Fig. 10. The CFD solver tends to over-predict the pressure in the attached boundary layer. The buffet onsets computed by the BiGlobal analysis are close to the reference results”.

14. It is a very high-level description of the TLBO algorithm. Either in section 3.3 or 4.1, there should be a brief description of how the optimization constraints are managed by the algorithm (penalization of the cost function ?).

Reply: Thanks for your advise. The brief description of TLBO optimization is added in section 3.3.

15. Please format the references in Table 3, such that they look similar to the ones in the body text. The optimized value 0.0143 given in the main text is different from the one given in Table 3.

Reply: Thanks for your advise. The modification has been completed.

16. The authors should use extensively an advanced spell check.

Reply: Thanks for your advise. The mistake sentences have been modified.

17. The perturbation of conservatives values should be denoted .

Reply: Thanks for your advise. The modification has been completed. Hope to meet your requirements.

Yours sincerely,

Corresponding author:

Chuanqiang Gao

Email: [email protected]

Reviewer 2 Report

It's an interesting paper that addresses an important issue of aircraft buffet. 

There are a lot of style/grammar glitches that need to be fixed; see the file attached with my proposed (marked in red) corrections. 

Also, you need to carefully check the numbers stated in the tables and mentioned in the text, as sometimes they do not match.

Comments for author File: Comments.pdf

The quality of the English Language is generally good. However, some style/grammar issues still need to be fixed; see above.

Author Response

Dear Tracy and Reviewers:

Thank you for your letter and for the reviewers' comments on our manuscript entitled " Transonic buffet suppression by airfoil optimization"[aerospace-2774048]. Those comments are all valuable and very helpful for revising and improving our paper. We have studied the comments carefully and have accordingly made correction which we hope can meet your requirements. Revised parts are marked in red in the paper.

Responses to Editor:

 Major issues

1. Please provide the accurate mail of [email protected] as our email could not be delivered successfully.

Reply: Thanks for your advise. Chen Yong has been removed from the author column.

2. We have did a pre-layout for your paper, please make you will make revision based on the version downloaded from the link in this mail.

 Reply: Thanks for your advise. The modification has been completed based on the version downloaded from the link in this mail.

3. Please note the author self-citation should be decreased.

Reply: Thanks for your advise. The author self-citation has been decreased. Hope to meet your requirements.

The main corrections in the paper and the responses to the reviewer's comments are as follows.

Responses to Reviewer2:

 Major issues

There are a lot of style/grammar glitches that need to be fixed; see the file attached with my proposed corrections. Also, you need to carefully check the numbers stated in the tables and mentioned in the text, as sometimes they do not match.

Reply: Thanks for your advise. The modification has been completed. Hope to meet your requirements.

Yours sincerely,

Corresponding author:

Chuanqiang Gao

Email: [email protected]

Reviewer 3 Report

The subject of research presented by the authors is of interest to the community. Overall, the methodology and results presented provide an interesting method for the optimization airfoils while taking into account buffet onset. However, a more detailed introduction and thorough description of prior work would improve the paper. Other aspects that need to be improved or clarified are as follows:

-On page 10 of the paper, a comparison of the BiGlobal results, ROM results and URANS simulation are given. Are the ROM results based on an RBF surrogate of the URANS results? If so, please provide more details.

-In Table 3, the delta Cd for the RAE2822 airfoil should be zero, and the for the other airfoils it should be negative (as a delta from the baseline).

-The assessment of the accuracy of the RBF surrogate is incomplete. The design objective of the airfoil is the drag coefficient, yet no assessment is given of the accuracy of the drag coefficient output by the surrogate. This must be added.

-The chosen optimization algorithm is TLBO, but very little justification is given for this choice. What are the main reasons for choosing TLBO? Why not choose a gradient-based algorithm? Explain.

-Description of the airfoil meshes: what is the y+ of the cell height along the  airfoil boundary?

-In figure 14, the green dashed line does not have the same lift-curve slope as the linear part of the CL-alpha curve, therefore the CL curve has a degree of non-linearity, which implies some flow separation. How was this slope chosen? Why not do a linear extrapolation to CL=1.07 (1.3x0.824), which would result in an alpha of about 4.5 degs. at that condition?

English must be improved significantly before publication.

Also, typesetting and alignment of the equations embedded in the text must be corrected. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Congratulations to this interesting and thorough numerical investigation.

The article addresses the buffet alleviation in the design stage of transonic airflow by means of airfoil shape optimization. The obtained results are of significant interest.

The paper is clear, well presented and structured.

The work done in the past is clearly introduced with good references to it.

Are the Optimized airfoil 1 and 2 been verified/re-validated by Unsteady CFD? It is not clear from the article. If not, they should in order to provide more robustness to the framework, particularly for the Surrogate model adopted.

Figures are clear and showing properly the data, but all the tables and figures need to be centred.

Be sure that the figures in which the flow field is shown the legend is correct. Is P or Cp?

Units should be added in the Nomenclature.

A few comments on the text are as follows:

In the abstract the authors mentioned that: The buffet suppression is not always considered in the aerodynamic optimization in the state of airfoil design, because it is difficult to extract an appropriate key design variable to indicate the flow stability.

It should be a key objective variable (output of the analysis) and not a design variable.

In the Introduction:

The flow around the wing in transonic flow can easily become unstable at certain combinations of Mach number and angle of attack because of the interaction between the shock wave and the boundary “layer” is missing.

Correct table 3: 2nd row RAE2022 Delt Cd should be =0, and Opt_cd for Optimize_2 airfoil 0.01423 according to what written in the text, therefore also the value of Cl/Cd needs to be changed or vice versa.

Some references in the text have a different font:

For example in pag 6:

stall at high angle of attack (Iorio M C 2015; Iorio M C 2016), and transonic buffet (Crouch J D 2007; Crouch J D 2009; Sartor F 2015) effectively.

Overall the English language is good

Author Response

Please see the attachment.

Author Response File: Author Response.pdf