Numerical Study on the Influence of Installation Height and Operating Frequency of Biomimetic Pumps on the Incipient Motion of Riverbed Sediment

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors present a numerical analysis of changing height and operating frequency of a biomimetic pump on maximum near-bed velocity. The manuscript is well-written and provides sufficient argument however, some points need to be addressed.

1) Why 2D model was used as we know that these pumps create a motion in 3D? Will a 3D model provide more description of the motion of this pump?

2) The major findings of the literature given in literature review section are not provided.

3) What is J in equation 6? No description of J is provided.

4) How can vertical velocity reach zero when there might be some convection currents present or the riverbed might not actually be completely horizontal?

5) In mesh generation you can write urban rivers in the southern regions of China because your statement might not be true for all southern regions of the world

6) In Figure 4, you have written beforeground mesh whereas in my understanding it should be foreground mesh.

7) Which type of meshing was used in the simulation? Description is needed. In my opinion, a tetrahedral mesh was employed.

8) What will be the effect of using a cubic mesh?

9) Why heights and operating frequencies are changed at fixed intervals? Can we perform a 2d sweep on operating frequency and height so that more better operating points can be obtained?

Comments on the Quality of English Language

The points relating to English correction are also given in the comments to the authors section.

Author Response

Comments 1: Why 2D model was used as we know that these pumps create a motion in 3D? Will a 3D model provide more description of the motion of this pump?

Response 1: Thank you for your question! A large body of existing research has demonstrated that hydrofoils yield essentially identical results in three-dimensional and two-dimensional simulations. (Please refer to this reference: https://doi.org/10.47176/jafm.15.03.32911). Therefore, to avoid the unnecessary waste of computational resources, this paper adopts a two-dimensional simulation model. In light of the issue you raised, it may be necessary for us to provide further clarification in our article, so we have supplemented this section in the original text (at the beginning of Section 2.1).

Comments 2: The major findings of the literature given in literature review section are not provided.

Response 2: Thank you for pointing that out! The literature review section lacked necessary conclusions for some of the literature mentioned, which we have supplemented in the revised version.

Comments 3: What is J in equation 6? No description of J is provided.

Response 3: Thank you for pointing that out! The article lacked necessary explanations for variable J, which was an oversight in our paper review. We have now supplemented the description of variable J. (In the second paragraph of section 3.2 of the article)

Comments 4: How can vertical velocity reach zero when there might be some convection currents present or the riverbed might not actually be completely horizontal?

Response 4: We also considered your question regarding this issue, which is explained in the literature [24]. The literature points out that when the research object is a river channel or open channel bed slope and the main direction of water flow is in the x-direction, the water velocities in the y and z directions are not significantly different from the velocity of sediment particles and can be ignored. Meanwhile, this relative velocity will not differ due to convection phenomena or the riverbed not being completely horizontal. Therefore, it is reasonably explained that the velocity in the z-direction (i.e., vertical velocity) is zero in the text. Based on this, we have supplemented the explanation for your question in the text. (In the last paragraph of section 3.2)

Comments 5: In mesh generation you can write urban rivers in the southern regions of China because your statement might not be true for all southern regions of the world

Response 5: Previously, the description of the region in this part was somewhat vague. According to your suggestions, we have made corresponding modifications in this section. (In section 3.3, paragraph 1)

Comments 6: In Figure 4, you have written beforeground mesh whereas in my understanding it should be foreground mesh.

Response 6: Thanks for the correction! Here is the spelling error, we ignored the revision of some figures during the review process, and have corrected the wrong part.

Comments 7: Which type of meshing was used in the simulation? Description is needed. In my opinion, a tetrahedral mesh was employed.

Response 7: You are right that the use of the grid does need to be described, and we have added to this section of the article (in the second paragraph of section 3.3).

Comments 8: What will be the effect of using a cubic mesh?

Response 8: Thank you for your careful review and feedback. In our two-dimensional fluid simulation study, we use the quadrilateral mesh with the corresponding dimension, but do not use the cubic mesh. Misuse of the three-dimensional cubic grid in the two-dimensional problem will introduce additional dimensions, which will complicate the problem itself and the post-processing analysis. In addition, three-dimensional grids contain more degrees of freedom than two-dimensional grids, which unnecessarily increases computation time and memory requirements, resulting in extremely inefficient resource use.

Comments 9: Why heights and operating frequencies are changed at fixed intervals? Can we perform a 2d sweep on operating frequency and height so that more better operating points can be obtained?

Response 9: Thank you very much for your valuable advice. In the research design phase, we chose to change the height and operating frequency at fixed intervals, mainly considering that by setting fixed parameter intervals, we can systematically compare the performance differences under different configurations, which is convenient to identify the trend and law of the impact of parameter changes on the system. In addition, given that simulation research often involves a large amount of computational resources and time costs, specific parameter intervals can effectively ensure that the research is completed within limited resources. We have added explanations about this part in the revised draft (paragraphs 1 and 2 of Section 4.1).

Reviewer 2 Report

Comments and Suggestions for Authors

 

Review for water 3039412v1 – Water

 

The authors present a useful numerical study of the impact of the installation height and operating frequency of biomimetic pumps on the motion of riverbed sediment. There are a few minor language errors to be corrected, and some technical deficiencies to be addressed. Improving suggestion are listed below:

01. Page 1: It would be better to write “Numerical study of” instead of “Research on” in the title.

02. P1 Abstract: Be specific by writing “a commercial CFD package was employed” instead of “a numerical simulation was employed”.

03. P1 Abstract: Define the parameters “installation height” and “c” before using them, as it is done in p.3.

04. P1: Add the Keyword “riverbed sediment”.  Also, write “CFD” instead of “numerical simulation”.

05. P2: Write “Lin et al. [8]” instead of “Tianlong Lin et al. [8]”. Do similarly for all other citations, i.e., [9-11, 17-20]. Also, write “Mei et al. [16] instead of “MEI et al. [16]”.

06. P3: In Fig. 2, indicate the coordinates x1 and x2 which are used in equations (3) and (4).

07. P4: Correct the definition of the eddy viscosity in Eqn. (4) by writing “γi = cμk2/ε” instead of “γi = cμk2ε”.

08. P5: Provide a justification of the choice “7.06” for the constant “η” in Eqn. (5).

09. P5: After Eqn. (6), write “D stands for the sediment diameter” instead of “H stands for….”

10. P5: In Table 1, indicate the formula used for the entries of column “Results from Formula Calculations”.

11. P7: Better to write “with total number of cells” instead of “with their total numbers”. Also, it would have been better to try 20000, 40000, 100000 and 150000 cells in order to see if there be a difference.

12. P8: Provide an explanation for the phase shift in the results of Fig. 6.

13. P8: Simplify the section title “4. Results and Discussion”.

14. P8: Better to write “A numerical study” instead of “A numerical simulation analysis”.

15. P8: Better to write “interest range” instead of “measurement range”.

16. P9: In Table 2, are the results corresponding to height of 1.2m (column 5) correct? Is there enough vertical space to apply the “pressure” boundary condition on the free surface? Is this the reason for the non-asymptotic behavior of the results?

17. P12: The definition of the “location of the maximum near-bed velocity point” is not clear. Rephase the sentence to improve its clarity. When writing “horizontal”, do the authors mean “axial” (x1) direction?

18. P15: Section 4.3 is rather unclear. The authors should rephrase the text in order to improve its clarity.

19. P15-16: Rephrase the Conclusions in order to improve their narrative and clarity.

20. P16-17: Make sure that references are listed complete, consistently and according to the standards of the Journal.

 

Comments on the Quality of English Language

Only minor errors to be corrected.

Author Response

Comments 1: Page 1: It would be better to write “Numerical study of” instead of “Research on” in the title.

Response 1: Thanks for your suggestion, we have revised the title according to your suggestion.

Comments 2: P1 Abstract: Be specific by writing “a commercial CFD package was employed” instead of “a numerical simulation was employed”.

Response 2: Thank you for your suggestion, we have made modifications to the abstract section according to your advice.

Comments 3: P1 Abstract: Define the parameters “installation height” and “c” before using them, as it is done in p.3.

Response 3: Thank you for your correction! The previous abstract lacked explanations for the parameters "c" and "installation height," which we have supplemented in the revised version.

Comments 4: P1: Add the Keyword “riverbed sediment”.  Also, write “CFD” instead of “numerical simulation”.

Response 4: Thanks for your suggestion, we have added "riverbed sediment" as the keyword in the revised version, and changed "numerical simulation" to "CFD".

Comments 5: P2: Write “Lin et al. [8]” instead of “Tianlong Lin et al. [8]”. Do similarly for all other citations, i.e., [9-11, 17-20]. Also, write “Mei et al. [16] instead of “MEI et al. [16]”.

Response 5: Thank you for your correction! We have revised the citation section according to your suggestion and re-proofread the citation format throughout the article.

Comments 6: P3: In Fig. 2, indicate the coordinates x1 and x2 which are used in equations (3) and (4).

Response 6: Thank you for your correction! We have updated figure 2 in the revised version.

Comments 7: P4: Correct the definition of the eddy viscosity in Eqn. (4) by writing “γi = cμk2/ε” instead of “γi = cμk2ε”.

Response 7: Thank you for your correction! We have changed the definition of γi in the revised manuscript.

Comments 8: P5: Provide a justification of the choice “7.06” for the constant “η” in Eqn. (5).

Response 8: Thank you for your reminder! Previously, we did not provide a sufficient explanation for the choice of variable η. To enhance the applicability of our research results, we set the value of η to the mean of 7.06. As referenced in literature [22], it is known that at this point, the calculated values align closely with the measured values. We have now supplemented this explanation in the original text. (In the first paragraph of section 3.2)

Comments 9: P5: After Eqn. (6), write “D stands for the sediment diameter” instead of “H stands for….”

Response 9: Thank you for your correction! We did not notice that the meaning of D was misstated during the review process, and we have made modifications in the revised manuscript as per your reminder.

Comments 10: P5: In Table 1, indicate the formula used for the entries of column “Results from Formula Calculations”.

Response 10: In Table 1, "Results from Formula Calculations" used the results obtained from formula 6, which were explained in the paper. The third column, "The Friction Velocity from the Literature", is the result of reference [23]. Previously, there was confusion about the unclear expression of this part, we have made changes to this part to avoid readers' misunderstanding. (In paragraph 4 of section 3.2)

Comments 11: P7: Better to write “with total number of cells” instead of “with their total numbers”. Also, it would have been better to try 20000, 40000, 100000 and 150000 cells in order to see if there be a difference.

Response 11: Thank you for your suggestion! In the revised manuscript, we have changed "with their total numbers" to "with total number of cells." Additionally, you mentioned that using 20,000, 40,000, 100,000, and 150,000 cells might make the results clearer. Following this strategy, we revalidated the grid independency and modified the corresponding figures. We found that the revised cell counts indeed demonstrated grid independence more clearly than the previous cell counts of 50,000, 100,000, 150,000, and 200,000. We have updated the relevant figures and descriptions in the revised version. (In the second paragraph of Section 3.4)

Comments 12: P8: Provide an explanation for the phase shift in the results of Fig. 6.

Response 12: Thank you for your suggestion! Since the numerical simulation in this paper adopts a steady velocity incoming flow, whereas the experimental paper cited used a towing tank experiment, where the incoming flow velocity is passively generated by towing the hydrofoil. This method of generating incoming flow can result in certain delay errors. We have added an explanation for the cause of phase error in the revised manuscript. (In the last paragraph of section 3.5)

Comments 13: P8: Simplify the section title “4. Results and Discussion”.

Response 13: Thank you for your suggestion! We have made changes to title four in the revised manuscript.

Comments 14: P8: Better to write “A numerical study” instead of “A numerical simulation analysis”.

Response 14: Thank you for your suggestion! We have changed "A numerical simulation analysis" to "A numerical study" in the revised manuscript. (In the third paragraph of section 4.1)

Comments 15: P8: Better to write “interest range” instead of “measurement range”.

Response 15: Thank you for your suggestion! We have changed "measurement range" to "interest range" in the revised manuscript. (In the third paragraph of section 4.1)

Comments 16: P9: In Table 2, are the results corresponding to height of 1.2m (column 5) correct? Is there enough vertical space to apply the “pressure” boundary condition on the free surface? Is this the reason for the non-asymptotic behavior of the results?

Response 16: Thank you for pointing out this possible error. We have rechecked and verified the calculation results, and the results in the fifth column of Table 2 are correct. The content mentioned in the first paragraph of Section 3.3 is sufficient to explain that the vertical space required for the "pressure" boundary condition to act on the free surface is sufficient. The reason for the non-asymptotic behavior of the results is that when the installation height is too high, the movement of the hydrofoil cannot form a multiple pairs of reverse von Kármán vortex streets. It can be seen from Figs. 8(d) and 9 that there will be an obliquely downward jet is produced between the water vortices below the hydrofoils and the counterclockwise-rotating trailing vortices generated by the hydrofoils. which causes the high-velocity region in the flow field to act obliquely downward on the riverbed, leading to an increase in the maximum near-bed velocity.

Comments 17: P12: The definition of the “location of the maximum near-bed velocity point” is not clear. Rephase the sentence to improve its clarity. When writing “horizontal”, do the authors mean “axial” (x1) direction?

Response 17: Thank you for your suggestion! We have supplemented the definition of "location of the maximum near-bed velocity point" in the revised manuscript. (In the second paragraph of section 4.2)

Comments 18: P15: Section 4.3 is rather unclear. The authors should rephrase the text in order to improve its clarity.

Response 18: Thank you for your suggestion! We have rewritten parts of Section 4.3 in the revised manuscript to make the content of this section clearer and easier to understand. (In the first paragraph of Section 4.3)

Comments 19: P15-16: Rephrase the Conclusions in order to improve their narrative and clarity.

Response 19: Thank you for your suggestion! We have re-edited the conclusion section of the revised manuscript to make it clearer and easier to understand.

Comments 20: P16-17: Make sure that references are listed complete, consistently and according to the standards of the Journal.

Response 20: Thank you for your suggestion! We have carefully reviewed the references in the revised manuscript to ensure they conform to the journal's standards.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have given satisfactory responses to almost all the comments.

However, since the authors pointed out the limitations of computational resources I strongly believe that in the "mesh generation and computational setup" section, a paragraph should be added that states the computational resources available to the authors and how much time did it take to run a single simulation, and what can be done to mitigate the limitation of computational resources? This will help other researchers working on similar topics.