Study on Amplitude and Flatness Characteristics of Elastic Thin Strip under Fluid–Structure Interaction Vibration Excited by Unsteady Airflow

Round 1

Reviewer 1 Report

The paper presents the results of research on the impact amplitude and flatness characteristics of elastic thin strip under fluid-structure interaction vibration excited by unsteady airflow. It was found that with the alternating aerodynamic loads increasing, the strip amplitude increased in the form of quadratic polynomial, however, with the tensions decreasing, the strip amplitude decreased exponentially. The strip dimensions also influenced the amplitude of vibration, the wider and the thinner the strip, the larger the amplitude.

Although the work deals with a rather complex problem regarding the interaction of the dimensions and shape of the sheet and the pressure of the fluid flowing on vibration amplitude, there is no specific purpose, which needs to be completed.

Comments

1. Figure 6 needs improvement

2. The conclusions should be specified in the present form as observations.

Author Response

Dear editors and reviewers,

Thanks for your letter and for the reviewers’ comments concerning our manuscript entitled “Study on amplitude and flatness characteristics of elastic thin strip under fluid-structure interaction vibration excited by unsteady airflow” (metals-479556).

We thank the editors and reviewers for the positive and constructive comments on the previous manuscript. These comments are all valuable and very helpful for improving our paper, as well as guiding our researches. We have studied comments carefully and have made correction and explanation which we hope meet with approval. The main corrections in the revised paper are made in red and the responses to the reviewer 1 comments are as following:

Response to Reviewer 1 Comments:

Point 1: Although the work deals with a rather complex problem regarding the interaction of the dimensions and shape of the sheet and the pressure of the fluid flowing on vibration amplitude, there is no specific purpose, which needs to be completed.

Response 1: At the second paragraph of Introduction, please see Line 63-66, the paper points out“Therefore, it is necessary to accurately grasp the amplitude distribution characteristics of the elastic thin plate excited by the unsteady airflow, and the flatness characteristics under this amplitude can be further calculated, which would be a basis for the deviation compensation of the flatness meter.” This is the main question to be solved of the paper. And the end of Introduction has been modified (Line 79-83), which emphasizes the purpose much clearly.

Point 2: Figure 6 needs improvement.

Response 2: Thanks for your suggestions. The figure has been improved in the new version.

Point 3: The conclusions should be specified in the present form as observations.

Response 3: The conclusions have been explained in more detail and modified with the correct tenses in the new version. Please see Line 378-394.

We try our best to improve the manuscript and make some corrections in the revised paper. And here we do not list all the corrections but mark in the revised paper. We appreciate for editors’ and reviewers’ warm work earnestly, and hope that the corrections and responses can meet with approval. Once again, thank you very much for the comments and suggestions.

Best regards!

Yours sincerely,

                                                                           Hongbo Li

Address: School of Mechanical Engineering,

        University of Science and Technology Beijing,

No. 30 Xueyuan Road, Haidian District, Beijing, 100083 P.R.China

E-mail: lihongbo@ustb.edu.cn

Tel: +86-10-62334723

Reviewer 2 Report

My main criticism concerns the framework and methodology followed. The paper doesn't present function and test spaces, the framework of the FSI problem (e.g. if it is in Eulerian or in ALE framework, etc., if yes, why?) (including novel contribution), and so on. Furthermore, there is not any single example/validation problem comparable to. Comparisons in the improvement of the solution error or computation performance to other methods are not given. Authors must provide/solve any benchmark problem in order to compare their methodology.

Authors must provide Convergence tests in time, space, and different time schemes in order to validate their methodology. This would add value to the admirable work presented in the present manuscript. If the author does not answer this question convincingly, I advise the Editor to definitively reject this article.

It seems that the font size is bigger on the figure compared to the text (cf. Figure-6). The authors should be aware of the fact that the font size should be adjusted. Furthermore, The authors should be aware of the aspect ratio of the figure so that they have a similar legend and readable. Please check all figures. The authors could change colour and figure size to improve the readability. Additionally, it would be helpful if the authors improve the Conclusions and make a better explanation. And please don't use bullet point or anything similar. 

Last but not least, the overall ‘English’ of the complete paper (e.g. writing mechanics and grammar) needs to be checked and revised carefully. I have mentioned a few grammatical corrections below, but the authors should check the complete paper for similar grammatical mistakes.

There are too many mistakes to list them all here, but are few:

Author Response

Dear editors and reviewers,

Thanks for your letter and for the reviewers’ comments concerning our manuscript entitled “Study on amplitude and flatness characteristics of elastic thin strip under fluid-structure interaction vibration excited by unsteady airflow” (metals-479556).

We thank the editors and reviewers for the positive and constructive comments on the previous manuscript. These comments are all valuable and very helpful for improving our paper, as well as guiding our researches. We have studied comments carefully and have made correction and explanation which we hope meet with approval. The main corrections in the revised paper are made in red and the responses to the reviewer 2 comments are as following:

Response to Reviewer 2 Comments:

Point 1: My main criticism concerns the framework and methodology followed. The paper doesn't present function and test spaces, the framework of the FSI problem (e.g. if it is in Eulerian or in ALE framework, etc., if yes, why?) (including novel contribution), and so on. Furthermore, there is not any single example/validation problem comparable to. Comparisons in the improvement of the solution error or computation performance to other methods are not given. Authors must provide/solve any benchmark problem in order to compare their methodology.

Response 1: The emphasis of this paper is using the finite element model to qualitatively analyze the influences of aerodynamic load, tension and flatness defects on the strip midpoint amplitude and the flatness calculation deviation, the innovation of this paper is the amplitude characteristic calculation of the elastic thin plate with initial residual stress (i.e. initial tensile stress) under the application of alternating aerodynamic loads, which may be very helpful for the further research and scientific application of SI-FLAT flatness meter. The FEM model is just a tool to do the research, so there is not much discussion and analysis on the framework and methodology in the modeling process. But the basic modeling process of the fluid-structure interaction model with ANSYS software has been elaborated in detail in this paper, and the basic settings of fluid-structure interaction in ANSYS have been introduced at the end of Section 2.1, please see Line 116-125, namely, “By using the bidirectional coupling method of ANSYS and CFX in ANSYS workbench [10,11], the characteristics of the fluid-structure interaction of the strip with different parameters under the aerodynamic loads in a large space are calculated. The strip vibration calculation uses the transient dynamics method in ANSYS, the aerodynamic loads uses the ideal air module in CFX, the control equation uses the unsteady Reynolds average Navier-Stokes equation, the space uses the second-order upwind scheme, the time uses the second-order Euler backward-difference scheme, the time step is set as 0.2s, and the coupling machine is calculated by the dynamic mesh. By setting the consistent fluid-structure interaction interface and reasonably simplifying the boundary conditions, the model is stably convergent and the calculation time of each simulation condition is about 50 minutes.”

    As for the verification of the model, since the actual amplitude measurement values cannot be obtained in industrial production field, so it can only be qualitatively verified in combination with the flatness target curve in field. And this part is reflected in Section 3.1, that is, the simulation results with interaction in Figure 5 have a corresponding relation with the actual flatness target curve in Figure 6.

Point 2: Authors must provide Convergence tests in time, space, and different time schemes in order to validate their methodology. This would add value to the admirable work presented in the present manuscript.

Response 2: Thanks very much for your comments and suggestions. It is true that for some very complex dynamic finite element calculation problems, the mesh generation, the calculation time and other factors need to be emphatically considered in the finite element calculation and analysis process. But in this paper, similar to the Point 1, the emphasis of this paper is using the finite element model to qualitatively analyze the influences of aerodynamic load, tension and flatness defects on the strip midpoint amplitude and the flatness calculation deviation. So there is not much discussion and comparison on the grid size, the calculation time and other factors in the research process. Moreover, the finite element model does not take a long time in the calculation process and it is easy to converge. Some important settings about the model has been further supplemented in Section 2.1, including the grid size, the time step and so on, namely, “The strip is divided into grids of 0.02m in the width direction, compared to the smaller grids, these grids occupy less resource and need shorter calculation time.” (Line 112-114) and “The strip vibration calculation uses the transient dynamics method in ANSYS, the aerodynamic loads uses the ideal air module in CFX, the control equation uses the unsteady Reynolds average Navier-Stokes equation, the space uses the second-order upwind scheme, the time uses the second-order Euler backward-difference scheme, the time step is set as 0.2s, and the coupling machine is calculated by the dynamic mesh. By setting the consistent fluid-structure interaction interface and reasonably simplifying the boundary conditions, the model is stably convergent and the calculation time of each simulation condition is about 50 minutes.” (Line 118-125)

Point 3: It seems that the font size is bigger on the figure compared to the text (cf. Figure-6). The authors should be aware of the fact that the font size should be adjusted. Furthermore, The authors should be aware of the aspect ratio of the figure so that they have a similar legend and readable. Please check all figures. The authors could change colour and figure size to improve the readability.

Response 3: Thanks for your comments and it is our negligence, we have checked all the figures and modified them in the revised paper according to unified standards.

Point 4: Additionally, it would be helpful if the authors improve the Conclusions and make a better explanation. And please don't use bullet point or anything similar.

Response 4: The conclusions have been explained in more detail and we have rewritten them in the revised paper, please see Line 378-394.

Point 5: Last but not least, the overall ‘English’ of the complete paper (e.g. writing mechanics and grammar) needs to be checked and revised carefully. I have mentioned a few grammatical corrections below, but the authors should check the complete paper for similar grammatical mistakes.

There are too many mistakes to list them all here, but are few:

1. Line 81: Figure 1 shows/illustrates the schematic

2. Line 82: an/the airflow channel

3. Line 85: distance range from 0.1 mm - 0.2 mm

4. Line 89: Related study [9] showed

Response 5: Thanks for your suggestions. We have checked the overall ‘English’ in the complete paper and the corrections in the revised paper are made in red.

We try our best to improve the manuscript and make some corrections in the revised paper. And here we do not list all the corrections but mark in the revised paper. We appreciate for editors’ and reviewers’ warm work earnestly, and hope that the corrections and responses can meet with approval. Once again, thank you very much for the comments and suggestions.

Best regards!

Yours sincerely,

                                                                           Hongbo Li

Address: School of Mechanical Engineering,

        University of Science and Technology Beijing,

No. 30 Xueyuan Road, Haidian District, Beijing, 100083 P.R.China

E-mail: lihongbo@ustb.edu.cn

Tel: +86-10-62334723

Round 2

Reviewer 2 Report

Thank you for submitting yet another revision of your manuscript with a clearer indication of the changes made. I am essentially happy to accept the paper for publication, but I am somewhat frustrated by your refusal to address the final, very sensible (and easy-to-do) requests for clarification raised by my last reviews:

(1) Please define (briefly, in parenthesis, if necessary) the framework of the solid and fluid part in the FSI problem. Software name such as ANSYS, or Comsol or anything else not going to help the reader about the framework or methodology. If authors use the default setup from ANSYS, then there will be a question about nobility of this paper. Please comment about the algorithm that have been used in this paper, e.g. monolithic or particulation approach or anything else. Please define what you mean or rephrase it in an unambiguous way.

(2) Authors must provide Convergence tests in time, space, and different time schemes in order to validate their methodology. Here Authors must provide or comment or compare the simulation result of different time step such as 0.2s, 0.1s, 0.05s etc., as well as for the global remeshing (e.g. r=1,2,3,...) with different time schemes such as Crank-Nicolson, shifted Crank-Nicolson, and fractional-step-theta scheme. Obviously backward Euler time scheme is not an ideal for Multiphysics problem like the FSI problem.

None of this should take more than 30 minutes, so I hope to receive a final version of the manuscript in the very near future - at which point we'll all breathe a big sigh of relief!
Looking forward to hearing from you in due course.

Author Response

Dear editors and reviewer,

Thanks for your letter and for the reviewers’ comments concerning our manuscript entitled “Study on amplitude and flatness characteristics of elastic thin strip under fluid-structure interaction vibration excited by unsteady airflow” (metals-479556).

We thank the editors and reviewer for the encouragement and constructive comments on the revised manuscript again. We have studied comments carefully and have made correction and explanation on the basis of major revised manuscript. The main corrections are made in red and the responses to the reviewer 2 comments are as following:

Response to Reviewer 2 Comments:

Point 1: Please define (briefly, in parenthesis, if necessary) the framework of the solid and fluid part in the FSI problem. Software name such as ANSYS, or Comsol or anything else not going to help the reader about the framework or methodology. If authors use the default setup from ANSYS, then there will be a question about nobility of this paper. Please comment about the algorithm that have been used in this paper, e.g. monolithic or particulation approach or anything else. Please define what you mean or rephrase it in an unambiguous way.

Point 2: Authors must provide Convergence tests in time, space, and different time schemes in order to validate their methodology. Here Authors must provide or comment or compare the simulation result of different time step such as 0.2s, 0.1s, 0.05s etc., as well as for the global remeshing (e.g. r=1,2,3,...) with different time schemes such as Crank-Nicolson, shifted Crank-Nicolson, and fractional-step-theta scheme. Obviously backward Euler time scheme is not an ideal for Multiphysics problem like the FSI problem.

Response: The two comments mainly concentrate on the modeling process and the convergence tests in this paper.

    At First, we have carefully studied the modeling process of the model, and there are supplements and modifications in detail in this paper, please see Section 2.1 Line 112-140. And the grid generations of the strip and fluid are separately supplemented. Namely, the descriptions of strip are: “In the grid generation of strip, when the grid size is larger than 0.03mm, there are big deviations in the calculation results of amplitude, and the model exhibits a poor convergence; when the grid size is 0.01mm or 0.02mm, the difference between the two amplitude calculation results can be neglected, furthermore, the calculation time of 0.02mm is much shorter than that of 0.01mm. So, after comprehensive consideration, the strip is meshed in hexahedral grids with the size of 0.02mm.” (Line 112-117) The descriptions of fluid are: “The mesh size of fluid in the contact area above and under the strip is the same as that of the strip, this is mainly because in the case of dynamic mesh technology, the larger the deviation between the mesh size of fluid above and under the strip and that of the strip, the worse the convergence. And the grid size of other fluid has little effect on the convergence of the model, so the automatic grid generation in ANSYS workbench is used considering the time cost.” (Line 122-126)

    The descriptions of time step are also supplemented in this paper. Namely, “The same physical time step is used in the transient dynamic calculation of structure as well as the unsteady calculation of flow field. According to the frequency of aerodynamic load during the analysis, each pulsation period is 0.1~0.2s, and the calculation time is set as 0.8s, so the time step is set as 0.01s, and this time step can guarantee the calculation accuracy and efficiency at the same time.” (Line 135-138) On the other hand, we are sorry that the time step of 0.2s in the major revision is incorrect. Actually, 0.2s is the pulsation period during analysis, and the time step is set by considering the pulsation period. When the pulsation period is 0.2s, the calculation time is 0.8s, that is, there are 4 pulsation periods. And 0.01s is set as the time step, so a total of 80 time steps are calculated. Because the above time step is already small, therefore, different time steps are not explored and compared in the modeling process, we hope you can understand.

The time uses the second-order Euler backward-difference scheme in the CFX model, while “the backward Euler time scheme is not an ideal for Multiphysics problem like the FSI problem” is proposed in the comments. We are very grateful for your suggestion, which will be a improvement for our simulation research of fluid-structure interaction in the future.

We try our best to improve the manuscript and make some corrections in the revised paper. Moreover, we appreciate for editors’ and reviewers’ considerate work and help honestly, and hope that the corrections and responses can meet with approval. Once again, thank you very much for the comments and suggestions.

Best regards!

Yours sincerely,

                                                                           Hongbo Li

Address: School of Mechanical Engineering,

        University of Science and Technology Beijing,

No. 30 Xueyuan Road, Haidian District, Beijing, 100083 P.R.China

E-mail: lihongbo@ustb.edu.cn

Tel: +86-10-62334723