Numerical Study of Fluid–Solid Interaction in Elastic Sluice Based on SPH Method

Round 1

Reviewer 1 Report

General Comments:

The article presents the SPH simulation of an elastic sluice where both solid and liquid have been modeled by the SPH approach. To validate the proposed models, the SPH method is compared with the finite element method under the same simulation conditions and with experimental results from the literature. The validation focused on a qualitative comparison for the flow regime, changes in the free surface or reservoir liquid level (experiment, FEM and SPH) and the fluid-solid force (SPH-based).

Introduction:

-        The approach of the described method needs to be further clarified and the advantage of this method over those described in the literature/existing methods needs to be highlighted.

-        36: “With the progress and development of science” is too general.

-        45: “Increase in computational efficiency”, do you have a reference to this statement?

-    54: do you mean “et al.” or other authors/researches? In that case you should add references.

-        55-56: Some abbreviations should be explained, SPHS-BEM, MLS …

-        80-84: do you have a reference for this statement?

-        108: What do you mean by few studies? this is contradictory to the several papers you already mentioned that use the SPH method.

1.      Numerical Model:

-        120: You should rephrase this sentence to reduce confusion.

-        136-138: can you add a reference for this statement.

-        139: you should briefly explain the Jaumann time derivative or add some reference for clarification.

-        167:  you may add the name of the QuinticSpline kernel and reference it, have you tried other kernels?

-        177: can you explain based on any criteria or reference, why the viscous stress is neglected?

-        195: please note that usually c is a numerical value use to express the speed of sound in a material. Therefore, the c value you used should be also documented.

-        197: can you provide a reference when alpha can be set to 1, is it also suitable for solid applications?

-        Eq 16: Please check whether all suffixes are correct.

-        208: this sentence is incomplete.

-        Equations in the dynamic domain conditions part need a better explanation of the terms.

-        217-219: This needs further explanation. What do you mean by inhomogeneity of the particle distribution? Since in SPH all particles usually have the same size, or have you used adaptive resolution?

2.      Model validation:

-        308:  moment of 0 time: do you mean at the first simulation frame (t=0)?

-        Table 2 and 3:

o   are basically the same since the parameter values are the same, maybe you could combine both?

o   on 8 are non-English symbols.

o   Is the time step in your simulations a fixed value or adjustable perhaps on the CFL? Can you comment on this?

o   You might add that the real time was selected to be 0.4 according to the experimental data, if that was the case.

-        334: can you explain where exactly the water jump happens and why?

-        Figure 6: A color scale should be added to the simulation results, otherwise it is not possible to compare the values. Why is the fluid so much red in FEM than in SPH? can you comment on these differences?

-        Figure 7:

o   make sure to define the x and y displacement properly. is not clear if longitudinal or transversal.

o   Can you explain to which part of the simulation correspond the displacement showed, is this only for a point on the solid? This is not clear.

-        376: can you comment on why the corresponding values for the first and last time step are not displayed?

-        400: can you comment why there is a minimum at point C regarding the pressure?

Recommendations:

Please note that full SPH Models for both Fluid and elastic structure interaction already exist. You should describe more how your model has advantages over the existing models, specially the differences. There are even further existing benchmarks for the SPH-FSI problems, did you also consider them?

Han, L., Hu, X. SPH modeling of fluid-structure interaction. J Hydrodyn 30, 62–69 (2018). https://doi.org/10.1007/s42241-018-0006-9

JosephO’Connor;Benedict D. Rogers: https://doi.org/10.1016/j.jfluidstructs.2021.103312

PersionSPH: they have also integrated Fluid-Flexible structure interaction in SPH. Maybe you can take a look in their work. www.m2clab.com/persiansph

In general, the writing level should be improved as many of the ideas are very difficult to understand because they are not well formulated. 

Author Response

Thank you for taking the time to review this article. We have revised and responded to your feedback. Please refer to the attachment for the response to the comments. The revised manuscript and comments have been sent to the editor. We will use MDPI's polishing service to comprehensively adjust the language quality issues you mentioned in the final manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper concerns with a numerical study of the fluid-structure interaction caused by the opening of an elastic sluice gate. The adopted numerical scheme is based on the Smooth Particle Hydrodynamics (SPH) methodology.  

Main comments

-        The numerical method adopted in the paper is based on a well-known numerical methodology (SPH) and does not present any original numerical contribution. The main element of originality of the proposed numerical study is the application of that methodology to a challenging problem related to the pressure variation and deformation of a sluice gate during its opening.

The authors should better clarify which are the numerical expedience adopted to avoid the onset of numerical instabilities and where do these numerical corrections come from.

-        In Section 2.1 “governing equations”, many sentences are written in an unclear way, that make it difficult to understand.

-        In Section 2.2 “SPH methodology”, the equations used to express the main ingredients of the adopted numerical model are not explained: there is no explanation why Eq.s  (16), (17) and (18) are able to prevent the onset of numerical instabilities in the numerical solution.

-        In Section 2.3 “Particle velocity correction”, the equation used to correct the particle velocities (Eq. 19) is not explained. The authors should specify why it is used to correct the velocity and which is the role of the denominator of the second term on the right-hand side (the authors should refer to the correction of the kernel).

-        In Section 2.4 “Dynamic interface conditions”, there is no explanation of Eq. (20) and its discretization. The authors should refer to the problem of the representation of the first term on the right-hand side of the equation in the case of kernel support domain that is only partially contained inside the domain occupied by particles of the same type (liquid or solid).  

-        In Section 2.4.2. (Similarly to Section 2.3), Eq. (30) is not explained. The authors should clarify the role of the denominator in limiting the discretization errors introduced by the numerator.

                                                                           Minor comments

In Section 1, “Introduction”

Many references to the cited papers are written in an unusual way that seems not correct:

-        “Zhang [3] and others”, “Wu [4] and others”, “Raymond [5] et al.”, “Liu [6] et al.” etc…

The usual way should be “Zhang et al. [3]”, “Wu et al. [4]” …. etc …

-        Some terms have been never defined in the text: MLS, ISPH, GSPH, as well as “stretching instability”, “stress instability”.

-        The last sentence of the introduction is not clear: “Based on this, by …….. SPH program”.

The sentence is made up of many sub-phrases without a main one. Please rephrase.

In Section 2, “Numerical model”

-        on line 129, the sentence “the stress tensor is composed of both positive and partial stresses” is not correct. What does the authors mean with “positive and partial stresses” ?

-        on line 137-138, the sentence starting with “That is, assuming that the fluid ,” is incomplete and unclear.

-        on line 138-139, the sentence starting with “This leads to …” is incomplete and unclear.

-        On line 140-145 is made up by only one sentence, without any full stop. The paragraph is too long and not clear.

-        on line 148: “Among them” is not clear. Please clarify.

-        on line 208 some symbols are missing. Throughout the whole paper, several comma “,” are placed at the end of the sentence or before a blank space. It is not clear whether it is due to some editing errors in building the pdf file. 

-        In Section 2.1 “governing equations”, many sentences are written in an unclear way, that make it difficult to understand.

Many references to the cited papers are written in an unusual way that seems not correct:

-        “Zhang [3] and others”, “Wu [4] and others”, “Raymond [5] et al.”, “Liu [6] et al.” etc…

The usual way should be “Zhang et al. [3]”, “Wu et al. [4]” …. etc …

In Section 2, “Numerical model”

-        on line 129, the sentence “the stress tensor is composed of both positive and partial stresses” is not correct. What does the authors mean with “positive and partial stresses” ?

-        on line 137-138, the sentence starting with “That is, assuming that the fluid ,” is incomplete and unclear.

-        on line 138-139, the sentence starting with “This leads to …” is incomplete and unclear.

-        On line 140-145 is made up by only one sentence, without any full stop. The paragraph is too long and not clear.

-        on line 148: “Among them” is not clear. Please clarify.

-        on line 208 some symbols are missing. Throughout the whole paper, several comma “,” are placed at the end of the sentence or before a blank space. It is not clear whether it is due to some editing errors in building the pdf file. 

Author Response

Thank you for taking the time to review this article. We have revised and responded to your feedback. Please refer to the attachment for the response to the comments. The revised manuscript and comments have been sent to the editor. We will use MDPI's polishing service to comprehensively adjust the language quality issues you mentioned in the final manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

The aim of this paper is to study the fluid-solid interaction in elastic sluices using a SPH-based scheme. Specifically, the authors show the superiority of a full Lagrangian and particle scheme in the above class of problems. Remarkable is not only the comparison between the SPH and mesh-based schemes, but also the use of a physical experiment as a benchmark. Therefore, I think that this paper is worthy of publication in the journal WATER after addressing the following issues:

There is a misinterpretation of the concept of ALE scheme and particle based scheme. Note that a mesh-based scheme can also be an ALE scheme. See for example: "A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D". Please clarify this in the Introduction.

Line 48, please support the sentence with the following works: "Application of a SPH-DEM coupled model for elastic fluid-structure interaction" and "Towards a high order convergent ALE-SPH scheme with efficient WENO spatial reconstruction".

Line 80, please support the sentence with the following works: the following works: "Smooth particle hydrodynamics (SPH): an overview and recent developments" and "An alternative smooth particle hydrodynamics formulation to simulate chemotaxis in porous media".

Support the sentences from line 120 to line 152 with some appropriate references.

Eq(8): there are different ways of discretising the density in the SPH framework, could the authors justify their choice?

Line 171 - Where should be where. Please check all papers for indentation after equations. Points and semicolons are also missing.

Author Response

Thank you for taking the time to review this article. We have revised and responded to your feedback. Please refer to the attachment for the response to the comments. The revised manuscript and comments have been sent to the editor. We will use MDPI's polishing service to comprehensively adjust the language quality issues you mentioned in the final manuscript.

Author Response File: Author Response.pdf

Reviewer 4 Report

The paper is interesting and concerns fluid-structure interaction using particle methods. The paper worth’s publication. However, the authors should perform several amendments to the manuscript.

1)      Since the authors mention SPH literature they could include for completeness reasons the following papers for completeness reasons

For general introduction

https://doi.org/10.1016/j.oceaneng.2022.112026

https://doi.org/10.30955/gnj.003052

as well as

https://doi.org/10.1016/j.oceaneng.2021.108870 for specific comparison with their results

2)      Line 59: architectural fracture is the term correct?

3)      Line 137: the phrase is not clear; I think there is something missing.

4)      In figure 2 the behavior for λ=0.93 and λ=0.97 seems visually very close to experiments, could the authors also provide the numerical errors they mention?

5)      In the same figure it appears that the shapes of the curves are similar to the experimental up to X=0.7. Could the authors discuss any ideas why the differences are larger above this value?

6)      In the conclusion section the authors should stress the novelty of their work and its advantages

7)      Not directly related to the quality of the paper. The authors employ figures form paper [10] if I understand well. Do they have obtained permission?

Languge is in general fine. Some minor points are mentioned in the comments

Author Response

Thank you for taking the time to review this article. We have revised and responded to your feedback. Please refer to the attachment for the response to the comments. The revised manuscript and comments have been sent to the editor. We will use MDPI's polishing service to comprehensively adjust the language quality issues you mentioned in the final manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Main comments

From a scientific point of view, the level of the paper is only slightly improved because, in the revised version of the paper, the authors made only a minimum effort to comply with the reviewer’s requests. The authors have given some more exhaustive explanations in the “Response to Reviewer 2” letter, while in the revised version of the paper, the requested scientific clarifications and insights were carried out only in minimal form.

I suggest the authors expand the paper by using the clarifications provided in the “Response to Reviewer 2” letter.

From the point of view of readability of the paper, several problems still remain: every new sentence contains some errors and misprints. Furthermore, the authors should carefully read all the manuscript to correct some repetitions and typing errors (they should have the English text checked by a native English speaker).

Minor comments

-        on line 35, “mechanical engineering” is repeated twice. Please correct.

-        on line 85, the sentence “Currently…….  [20],[21]” is too long, difficult to understand and written with the wrong punctuation. Please rewrite it, subdividing the sentence in shorter sub-sentences and correcting some error (on line 88, the authors really mean “Lagrangian” coordinate system or they mean “Eulerian”?).

-        on line 98, the sentence “For example, SPH method, SPH method …”  is not clear. Please rewrite it with the correct punctuation.

-        on line 105, in the sentence “The above studies ….” the punctuation is not correct. The authors should use a period not a comma to separate two main sentences.

-        on line 109, the sentence “Based on this …. ….. program.” is made up of subsentences only; a main sentence is missing.

-        From line 122 to line 149, the equations are written with wrong format of the symbols (some symbols are deformed or too small).

-        on line 135, the sentence “This leads to ……, Use the rotation ….” Is not clear and is not correctly written. Please rewrite, by using the correct punctuation (why the authors use a capital letter after a comma?).

-        on line 137, the sentence “This formulation ……[32]” is too long and is written with too many commas, without any period. Please rewrite it.

-        on line 237, the sentence “In calculating the pressure gradient ….” Is written twice. Please correct.

-        From line 332 to line 363, the sentences are so long that are difficult to understand. The authors should rewrite the paragraph by using shorter sentences and a correct punctuation.

-        The same error affects the Conclusions (See, for example, the paragraph from line 427 to line 436 and the one from line 447 to 453). Please rewrite it with shorter sentences and using a correct punctuation.

From the point of view of readability of the paper, several problems still remain: every new sentence contains some errors and misprints. Furthermore, the authors should carefully read all the manuscript to correct some repetitions and typing errors (they should have the English text checked by a native English speaker).

Author Response

Thank you again for your review. We have made modifications based on your suggestions and made language changes to the entire text. As we are also new to the SPH field, we may not have a deep understanding of your suggestions and will continue to strengthen our theoretical learning in future studies. Thank you for your review!!!

Author Response File: Author Response.pdf