Offshore Hydrogen Infrastructure: Insights from CFD Simulations of Wave–Cylinder Interactions at Various Cross-Sections

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. It is suggested to further enrich the literature review section and provide a detailed review of previous research on the interaction between waves and structures, especially the interaction with cylinders of different shapes, in order to highlight the innovation and contribution of this study.

2. It is recommended to add a model validation section to verify the accuracy and reliability of the numerical model by comparing it with actual experimental data or existing literature results. At the same time, conduct uncertainty analysis and discuss the impact of model parameters, grid resolution, and other factors on the results.

3. Ensure that the chart is clear, the annotations are complete, and the key data and trends in the chart are appropriately explained.

4. In the results discussion section, in addition to describing the discovered phenomena, it is also necessary to delve into the underlying physical mechanisms, such as how the angle ratio affects the nonlinear behavior of waves.

5. It is suggested to add comparative analysis between different cylindrical cross-sectional shapes, as well as the similarities and differences in wave response under different wavelength conditions, in order to more comprehensively reveal the influencing factors.

6. Considering the small vibrations or dynamic responses of a cylinder under wave action, what impact do these dynamic boundary conditions have on the nonlinear amplification of waves, the formation of edge waves, and harmonic structures?

7. the assumption of non breaking waves was adopted, but in practical applications, wave breaking is a common phenomenon. How to extend the model to include wave breaking effects and explore their impact on structural response?

8. Three-dimensional effects such as diffraction, reflection, and refraction of waves may have a significant impact on the results. How to conduct 3D simulation and compare the differences between 2D and 3D models?

9. multiple structures are often subjected to wave action simultaneously. How do the interactions between these structures affect their respective wave responses and dynamic behaviors?

10. Is there any experimental data available to validate the simulation results of this study? If not, how can the CFD model be calibrated and validated?

11. During the simulation process, there are multiple sources of uncertainty (such as model parameters, initial conditions, boundary conditions, etc.). How to quantify these uncertainties and evaluate their impact on the final results?

Comments on the Quality of English Language

Moderate editing of English language required.

Author Response

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Response to Reviewer 1
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Dear Reviewer 1

    Thank you very much for taking the time to review this manuscript thoroughly. I also appreciate your detailed and insightful comments, which have been very helpful in improving the manuscript. Below, you will find responses to each of your comments, with your remarks repeated in italics followed by my responses.

Best regards on behalf of the authors
Mohammad Mohseni

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Comments 1: It is suggested to further enrich the literature review section and provide a detailed review of previous research on the interaction between waves and structures, especially the interaction with cylinders of different shapes, to highlight the innovation and contribution of this study. 

Response 1: Thank you for your suggestion. We have significantly expanded the literature review section to include a more detailed analysis of previous research on the interaction between waves and structures, with a particular focus on cylinders of various shapes. This addition aims to highlight the innovation and contribution of our study more clearly.

Comments 2: It is recommended to add a model validation section to verify the accuracy and reliability of the numerical model by comparing it with actual experimental data or existing literature results. At the same time, conduct uncertainty analysis and discuss the impact of model parameters, grid resolution, and other factors on the results.

Response 2: Thank you for your comment. regarding section 2.4 of the manuscript, the first author in the previous work (Mohseni and Guedes Soares (2022b)) conducted a comprehensive verification and validation of the numerical model.  This section details the comparison of the model results with experimental data and includes an uncertainty analysis, as well.

Comments 3: Ensure that the chart is clear, the annotations are complete, and the key data and trends in the chart are appropriately explained.

 

Response 3: Thank you for your comment. We have revised the chart to improve clarity and ensure that all annotations are complete. Key data and trends are now clearly explained in the updated chart.

Comments 4: In the results discussion section, in addition to describing the discovered phenomena, it is also necessary to delve into the underlying physical mechanisms, such as how the angle ratio affects the nonlinear behavior of waves.

Response 4: Thank you for your valuable suggestion. We have expanded the Results and Discussion section to include a detailed analysis of the underlying physical mechanisms, including how the corner ratio affects the nonlinear behavior of waves. This addition aims to provide a deeper understanding of the phenomena observed in our study. Additionally, these insights have been highlighted in the Conclusion section to reinforce their significance.

Comments 5: It is suggested to add comparative analysis between different cylindrical cross-sectional shapes, as well as the similarities and differences in wave response under different wavelength conditions, to more comprehensively reveal the influencing factors.

 Response 5: Thank you for your suggestion. We have added a comparative analysis of different cylindrical cross-sectional shapes, including an examination of how these corner ratios influence wave response under varying wavelength conditions (T=7s, T=15s). This analysis aims to reveal the similarities and differences in wave behavior more comprehensively.

Comments 6: Considering the small vibrations or dynamic responses of a cylinder under wave action, what impact do these dynamic boundary conditions have on the nonlinear amplification of waves, the formation of edge waves, and harmonic structures?

Response 6:  Thank you for your insightful question. In this study, we have assumed a fixed cylinder to simplify the analysis and maintain consistency with the benchmark established by ITTC (OEC, 2013). Consequently, investigating the impact of small vibrations and dynamic responses of the cylinder on the nonlinear amplification of waves, formation of edge waves, and harmonic structures is beyond the scope of this paper. However, we recognize that these factors could be important in other contexts and suggest that future research might explore these dynamics in greater detail.

 

Comments 7: the assumption of non-breaking waves was adopted, but in practical applications, wave breaking is a common phenomenon. How to extend the model to include wave-breaking effects and explore their impact on structural response?

 Response 7:  Thank you for raising this important point. In our study, we have assumed non-breaking waves to simplify the analysis and focus on the fundamental interactions between waves and the structure. Incorporating wave-breaking effects into the model would indeed be valuable for practical applications. To extend the model to include wave breaking, one would need to integrate additional physical processes, such as turbulence and energy dissipation, which typically require more complex modeling approaches. Exploring these effects would involve incorporating advanced numerical methods or experimental data that account for wave-breaking dynamics. We acknowledge the relevance of this extension and suggest that future research could investigate how wave breaking influences structural responses in more detail.

Comments 8: Three-dimensional effects such as diffraction, reflection, and refraction of waves may have a significant impact on the results. How to conduct 3D simulations and compare the differences between 2D and 3D models?

Response 8:  Thank you for your valuable comment. The basic assumption of this study is to model the three-dimensional phenomenon of wave amplification around a given cylinder using the three-dimensional Unsteady Reynolds-averaged Navier–Stokes equations. Given the assumption of deep water, the nature of the wave amplification around the cylinder remains inherently three-dimensional. Thus, investigating two-dimensional effects would not be applicable in this context.

Comments 9: multiple structures are often subjected to wave action simultaneously. How do the interactions between these structures affect their respective wave responses and dynamic behaviors?

Response 9:  Thank you for your comment. This study builds upon previous research by the first author, Mohseni and Guedes Soares (2021b), which investigated the wave interaction with a pair of fixed large tandem cylinders subjected to regular, non-breaking waves. Their work, titled "Numerical Simulation of Wave Interaction with a Pair of Fixed Large Tandem Cylinders Subjected to Regular Non-Breaking Waves," explored how the presence of tandem cylinders affects their individual wave responses and dynamic behaviors. For further details, please refer to the paper. “Mohseni, M., and Guedes Soares, C. (2021b). "Numerical simulation of wave interaction with a pair of fixed large tandem cylinders subjected to regular non-breaking waves." ASME. J. Offshore Mech. Arct. Eng. DOI: https://doi.org/10.1115/1.4053254.”

 

Comments 10: Is there any experimental data available to validate the simulation results of this study? If not, how can the CFD model be calibrated and validated?

Response 10:  Thank you for your comment. As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) conducted a comprehensive verification and validation of the numerical model. This section includes comparisons of the model results with experimental data from established benchmarks, such as those provided by ITTC (OEC, 2013) and Swan et al. (2015). These comparisons help ensure the accuracy and reliability of the CFD model.

Comments 11: During the simulation process, there are multiple sources of uncertainty (such as model parameters, initial conditions, boundary conditions, etc.). How to quantify these uncertainties and evaluate their impact on the final results?

Response 11: Thank you for your comment.  As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) and Mohseni, M., Soares, C.G., 2024., conducted a comprehensive verification and validation of the numerical model.

 

Reviewer 2 Report

Comments and Suggestions for Authors

Perhaps by mistake, an absolutely unfinished, “raw” version of an article was uploaded. The first thing that catches one’s eye is the pieces highlighted with a yellow marker. The reason of highlighting is unclear. The introduction begins with a large piece of raw text that is only vaguely related to the topic of this article. The following are two paragraphs that mention the papers of one of the authors of the article. They look like they have been copied from a dissertation or a report. Further, there are also inconsistent phrases that were clearly not re-read or corrected by the authors.

Section 2.1.1. provides the basic Navier-Stokes equations and the volume fraction transport equation for the vof model, but does not say anything about how these equations are closed (RANS,LES?). Instead, there is a reference to the work Rusche (2002), where the reader is presumably supposed to find all the missing information.

Approximately the same picture is observed in the next section 2.1.2. Instead of describing the boundary conditions and the wave generation model used, the references are provided to works where this can be found.

I did not read further, since, in my deep conviction, at first the article must be brought to some acceptable form, and then it can be accepted for the adequate scientific review.

Comments on the Quality of English Language

Since the article is obviously unfinished, checking the quality of the English language does not make sense. In the current version, some phrases are inconsistent, which will probably be corrected in the final version

Author Response

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Response to Reviewer 2
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Dear Reviewer 2

    Thank you very much for taking the time to review this manuscript thoroughly. I also appreciate your detailed and insightful comments, which have been very helpful in improving the manuscript. Below, you will find responses to each of your comments, with your remarks repeated in italics followed by my responses.

Best regards on behalf of the authors
Mohammad Mohseni

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Perhaps by mistake, an unfinished, “raw” version of an article was uploaded.

Comments 1: The first thing that catches one’s eye is the pieces highlighted with a yellow marker. The reason for highlighting this is unclear

Response 1: Thank you for your observation. The yellow highlights were used to draw attention to specific revisions and additions made in response to the Journal secretary. These highlights were intended to make it easier to identify the changes and updates in the manuscript. We apologize for any confusion this may have caused. In the final version of the manuscript, we will remove the highlights to ensure a cleaner presentation.

Comments 2: The introduction begins with a large piece of raw text that is only vaguely related to the topic of this article. The following are two paragraphs that mention the papers of one of the authors of the article. They look like they have been copied from a dissertation or a report. Further, there are also inconsistent phrases that were not re-read or corrected by the authors.

Response 2: Thank you for your detailed feedback. We have reviewed and revised the manuscript to correct any inconsistent phrases and improve overall readability.

Comments 3: Section 2.1.1. provides the basic Navier-Stokes equations and the volume fraction transport equation for the vof model, but does not say anything about how these equations are closed (RANS, LES?). Instead, there is a reference to the work by Rusche (2002), where the reader is presumably supposed to find all the missing information.

Response 3: Thank you for your feedback. In Section 2.1, it is stated that “InterFoam solves the three-dimensional Unsteady Navier–Stokes Equations using the finite-volume method (FVM) for two incompressible phases, assuming a static mesh and utilizing a VOF-based (Volume of Fluid) interface-capturing approach.” For this study, we assumed laminar flow, therefore, in this study, the turbulent viscosity is set to , for all simulations.

Comments 4: Approximately the same picture is observed in the next section 2.1.2. Instead of describing the boundary conditions and the wave generation model used, the references are provided to works where this can be found.

Response 4: Thank you for your comment.  As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) and Mohseni, M., Soares, C.G., 2024., conducted a comprehensive verification and validation of the numerical model, which addresses the boundary conditions used.

Comments 5: I did not read further, since, in my deep conviction, at first the article must be brought to some acceptable form, and then it can be accepted for adequate scientific review.

Response 5: We appreciate your feedback and the opportunity to enhance the quality of our work.

Reviewer 3 Report

Comments and Suggestions for Authors

This paper provides valuable insights into the interactions between waves and cylindrical structures, which are important for designing offshore hydrogen infrastructure. The methodologies and analyses are solid and thorough, forming a strong foundation for future research. I recommend this manuscript for publication after the authors address the suggested revisions to improve clarity and detail in certain sections.

 

1.      The abstract is clear and should include some quantitative results for better context.

2.      Boundary conditions are well-chosen and need more justification related to specific case studies.

3.      The literature review could be improved by including a more general discussion about hydrogen's future role, referencing articles such as doi.org/10.1039/D3CS00723E and doi.org/10.1021/acsenergylett.1c00845.

4.      Mesh independence studies are reliable and need a more detailed explanation of the criteria used.

5.      The choice of wave conditions is logical and could use further justification related to real-world scenarios.

6.      Assumptions are clearly stated and need clearer justification to ensure they do not compromise the study's validity.

7.      Harmonic analysis is well-done and could use more detailed explanations of the underlying physical phenomena.

8.      Surface tension effects are mentioned and modeled, though not deeply discussed in terms of their real-world implications.

9.      The limitations of the model are not thoroughly discussed, which is important for understanding the scope of the findings.

10.  Figure captions are descriptive and could be more detailed to explain the figures without needing to refer back to the text.

Author Response

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Response to Reviewer 3
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Dear Reviewer 3

    Thank you very much for taking the time to review this manuscript thoroughly. I also appreciate your detailed and insightful comments, which have been very helpful in improving the manuscript. Below, you will find responses to each of your comments, with your remarks repeated in italics followed by my responses.

Best regards on behalf of the authors
Mohammad Mohseni

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This paper provides valuable insights into the interactions between waves and cylindrical structures, which are important for designing offshore hydrogen infrastructure. The methodologies and analyses are solid and thorough, forming a strong foundation for future research. I recommend this manuscript for publication after the authors address the suggested revisions to improve clarity and detail in certain sections.

 

Comments 1: The abstract is clear and should include some quantitative results for better context.

Response 1: Thank you for your suggestion. I have revised the abstract to incorporate key numerical findings from the study, ensuring that the reader gains a clearer understanding of the outcomes and significance of the research.

 

Comments 2: Boundary conditions are well-chosen and need more justification related to specific case studies.

Response 2: Thank you for your comment. As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) conducted a comprehensive verification and validation of the numerical model.

 

 

Comments 3: The literature review could be improved by including a more general discussion about hydrogen's future role, referencing articles such  as doi.org/10.1039/D3CS00723E and doi.org/10.1021/acsenergylett.1c00845

Response 3: Thank you for this valuable suggestion. I agree that including a broader discussion on the future role of hydrogen would enhance the literature review. I will incorporate references to the suggested articles, to provide a more comprehensive overview of hydrogen's potential and its relevance to the context of this study.

 

 

Comments 4: Mesh independence studies are reliable and need a more detailed explanation of the criteria used.

Response 4: Thank you for your comment. I acknowledge the need for a more detailed explanation of the criteria used in the mesh independence studies. As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) conducted a comprehensive verification and validation of the numerical model.

 

 

Comments 5: The choice of wave conditions is logical and could use further justification related to real-world scenarios.

Response 5: Thank you for your comment. I recognize the importance of further justifying the selected wave conditions concerning real-world scenarios. Section 2.4 of the manuscript provides a detailed account of the verification and validation of the numerical model by the first author, Mohseni, and Guedes Soares (2022b),

 

 

Comments 6: Assumptions are clearly stated and need clearer justification to ensure they do not compromise the study's validity.

Response 6: Thank you for your comment, corrected

 

Comments 7: Harmonic analysis is well done and could use more detailed explanations of the underlying physical phenomena.

Response 7: Thank you for your comment. The authors provided a more detailed explanation of the underlying physical phenomena related to the harmonic analysis to enhance understanding of the observed results.

 

Comments 8: Surface tension effects are mentioned and modeled, though not deeply discussed in terms of their real-world implications.

Response 8: Thank you for your comment. In offshore applications, surface tension effects are generally minimal and often disregarded in simulations. To avoid any potential confusion, the authors have removed the related sentence from the manuscript. This ensures that the focus remains on more significant factors relevant to the study.

Comments 9: The limitations of the model are not thoroughly discussed, which is important for understanding the scope of the findings.

Response 9: Thank you for your comment. The current CFD model is well-suited for analyzing wave interactions with fixed offshore structures. However, it does have limitations when it comes to modeling wave-breaking or floating structures. To address this, the model would require modifications for those scenarios.

 

Comments 10:  Figure captions are descriptive and could be more detailed to explain the figures without needing to refer back to the text.

Response 10: Thank you for your comment. the authors revised the figure captions to provide more detailed explanations.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Please find attached my comments/questions related to the paper Offshore Hydrogen Infrastructure: Insights from CFD Simulations of Wave-Cylinder Interactions at Various Cross-Sections.

Comments for author File: Comments.pdf

Author Response

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Response to Reviewer 4
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Dear Reviewer 4

    Thank you very much for taking the time to review this manuscript thoroughly. I also appreciate your detailed and insightful comments, which have been very helpful in improving the manuscript. Below, you will find responses to each of your comments, with your remarks repeated in italics followed by my responses.

Best regards on behalf of the authors
Mohammad Mohseni

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Overall, the paper Offshore Hydrogen Infrastructure: Insights from CFD Simulations of Wave Cylinder Interactions at Various Cross-Sections investigates the interaction between waves and cylindrical structures with various cross-sections using CFD simulations. This reviewer's impression is that it presents a thorough CFD analysis of wave-cylinder interactions, highlighting the importance of cross-sectional variations. However, the lack of experimental validation and practical implications needs to be discussed. Please find below some comments and questions regarding my review of the paper.

Comments 1: The abstract should be improved by including the major findings of the work quantitatively

Response 1: Thank you for your suggestion. The authors have revised the abstract to include key quantitative results, which highlight the major findings and enhance the context and impact of the research

Comments 2: Could the authors improve the resolution/quality of the figures

Response 2:   

Comments 3: How do the different cross-sectional variations specifically impact the lateral edge waves?

Response 3: Thank you for your question. The corner ratio of the cylinder is a key factor affecting the dissipation of lateral edge wave propagation around the cylinder. Variations in cross-sectional shape influence how these waves are scattered and dissipated. Cylinders with sharper corners tend to affect the propagation speed and circulation of lateral edge waves more significantly compared to those with smoother or more rounded shapes. A more detailed explanation of these effects can be found in the Conclusion section of the manuscript.

Comments 4: Based on my review, the authors used specific parameters for the OpenFOAM modeling and simulations. Could the authors justify the choice of these parameters and discuss how variations in these parameters might affect the results?

Response 4: Thank you for your comment.  As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) and Mohseni, M., Soares, C.G., 2024., conducted a comprehensive verification and validation of the numerical model.

Comments 5: What boundary conditions were applied in the simulations? I believe the authors could discuss how these conditions affect the accuracy and reliability of the results.

Response 5: Thank you for your comment.  As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) and Mohseni, M., Soares, C.G., 2024., conducted a comprehensive verification and validation of the numerical model, which addresses the boundary conditions used.

Comments 6: The paper mentions limited experimental data for validation which is also covered in section 2.4. Verification and validation of the numerical model (pg. 6-7). Could the authors discuss any efforts made to validate the CFD results against available experimental or field data, even if limited?

Response 6: Thank you for your comment. As detailed in Section 2.4 of the manuscript, the first author, Mohseni, and Guedes Soares (2022b) and Mohseni. et.al (2018) conducted a comprehensive verification and validation of the numerical model. This section includes comparisons of the model results with experimental data from established benchmarks, such as those provided by ITTC (OEC, 2013) and Swan et al. (2015). These comparisons help ensure the accuracy and reliability of the CFD model.

Comments 7: I believe that the comparison of the findings with traditional wave interaction studies involving cylindrical structures could be extended, with a focus on the key differences and similarities.

Response 7: Thank you for your suggestion. We agree that comparing our findings with traditional wave interaction studies involving cylindrical structures could provide valuable insights. In the papers by Mohseni and Guedes Soares (2022b) and Mohseni et al. (2018), the first author performed a comparison of the results with the analytical solutions for circular cylinders provided by McCamy and Fuchs (1954).

Comments 8: In real-world scenarios, sediment transport can affect the performance of offshore structures. How does the proposed model account for sediment transport, and what are the expected impacts on wave-cylinder interactions? If not in the scope of the discussion, please comment.  

Response 8: Thank you for raising this important point. In our study, we have focused on non-breaking waves in deep water to simplify the analysis and concentrate on the fundamental interactions between waves and the cylinder. Incorporating sediment transport would indeed involve additional physical processes and more complex modeling approaches. As such, this aspect is beyond the scope of our current study.

Comments 9: Please consider providing more detailed recommendations for future research based on the findings of this work.  

Response 9: Thank you for your suggestion. Based on the findings of our study, we recommend several areas for future research:

1. Inclusion of Dynamic Effects: Investigate the impact of small vibrations and dynamic responses of cylindrical structures on wave interactions, including nonlinear wave amplification and harmonic structures.
2. Wave Breaking Phenomena: Extend the model to incorporate wave-breaking effects and explore their influence on wave-cylinder interactions, particularly in practical scenarios where wave breaking is common.

These recommendations have been incorporated into the revised manuscript to provide a clearer direction for future research. Please refer to the updated sections for detailed insights into these suggestions.

Comments 10: Could the authors discuss the long-term stability and durability of the cylindrical structures under continuous wave interaction?

Response 10: Thank you for this important consideration. The current study focuses on the immediate interactions between waves and cylindrical structures, and thus, it does not directly address long-term stability and durability. However, discussing these aspects could be valuable. For long-term stability and durability, factors such as material degradation, fatigue due to continuous wave interaction, and the cumulative effects of wave forces over time should be considered. Future research could explore these aspects by:

1. Material Degradation: Investigating how continuous wave action affects the material properties of cylindrical structures, including corrosion and wear.
2. Fatigue Analysis: Examining how repeated wave forces contribute to fatigue and potential structural failure over time.
3. Cumulative Impact: Assessing the long-term impact of wave interactions on the structural integrity of cylinders, including possible adaptations and reinforcements.

These considerations would provide a comprehensive understanding of the performance and longevity of cylindrical structures in real-world conditions.

Comments 11: Also, how do the different cross-sectional designs influence these aspects mentioned in my previous question? Again, if not in the original scope of the paper, please comment.  

Response 11: Thank you for this important consideration. The current study focuses on the immediate interactions between waves and cylindrical structures, and thus, it does not directly address long-term stability and durability.

Comments 12: Please consider including a table with abbreviations/nomenclature and the main terms used.

Response 12: Thank you for your suggestion. We have included a table of abbreviations and nomenclature in the revised manuscript to provide clarity on the main terms and symbols used throughout the study.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Solved most of the issues and could now be published.

Author Response

Thank you for your constructive feedback. Your insights are invaluable to us and play a crucial role in enhancing the quality and effectiveness of our work. We truly appreciate your thoughtful comments and are committed to incorporating your suggestions better to meet our community's expectations.

Reviewer 2 Report

Comments and Suggestions for Authors

My remark from the previous review that the work does not show a calculation scheme with boundary and initial conditions was completely ignored by the authors.

Please explain why the calculation method ignores the additional "turbulent" viscosity (present according to the Boussinesq hypothesis)? What prevents it from being included and how it can change the results?

Please remove the repeated paragraph (lines 159-161)

I recommend (but not insist) that the results section be significantly reworked. It should be drastically shortened, and most of the numerous repeated figures should be sent to the appendix.

And the main concern: Please explain what is the scientific novelty of this article? More specifically: How does this article differ from [Mohseni and Guedes Soares (2022b)] in the following parameters:

- Object of study

- Methodology used

- Considered computational cases 

- Obtained results 

- General structure of the article

 

Author Response

Reviewer 2:

Second round:

My remark from the previous review that the work does not show a calculation scheme with boundary and initial conditions was completely ignored by the authors.

Response: We acknowledge the reviewer’s remark regarding the calculation scheme with boundary and initial conditions. However, much of this information is extensively covered in the existing literature, and including it in full detail here would lead to unnecessary duplication, detracting from the main objective of the study. Additionally, incorporating these details, along with figures and tables, would significantly lengthen the paper, which is not aligned with the scope of this work. To maintain the focus on the novel aspects of our research, we have provided proper references to key sources where interested readers can find detailed information about the calculation schemes, boundary conditions, and initial setups. We believe this approach maintains clarity and conciseness while ensuring that all necessary information is accessible to those who require it.

Please explain why the calculation method ignores the additional "turbulent" viscosity (present according to the Boussinesq hypothesis). What prevents it from being included and how it can change the results?

Response: The decision to exclude additional "turbulent" viscosity, is based on the characteristics of the specific flow regime studied in this paper. The main focus is on the interaction of non-breaking, regular waves with a surface-piercing cylinder, where the Keulegan-Carpenter (KC) number is relatively low. According to well-established research, such as that of Sumer and Fredsøe (2006), when the KC number is below 4, the flow is primarily governed by inertia-dominated forces rather than viscous or turbulent forces. In such cases, the contribution of turbulence is minimal, and the inclusion of turbulent viscosity does not significantly affect the accuracy of the results.

Additionally, this choice is supported by previous studies that utilized similar numerical setups, such as Mohseni et al. (2018) and Mohseni and Guedes Soares (2022b), where the model without turbulent viscosity was validated against experimental data and showed good agreement. In those cases, the exclusion of turbulent viscosity did not detract from the accuracy of the hydrodynamic forces and wave amplification predictions. Including turbulent viscosity in the current study would introduce unnecessary complexity and computational cost, without yielding significant improvements in the accuracy of the results for this wave regime.

The decision not to incorporate turbulent viscosity in our simulations is also based on practical considerations. When turbulent viscosity is added to the model, it primarily affects the behavior of the boundary layer near the cylinder’s surface, particularly in flows with high shear or higher KC numbers (typically above 7), where viscous effects play a more dominant role. In such cases, turbulence modeling becomes crucial to capturing the detailed shear layer dynamics, wake formation, and separation, which could influence wave amplification, force distribution, and energy dissipation.

However, in the flow regime studied here, where inertia dominates and the KC number is below 4, the impact of turbulent viscosity is minimal. Introducing it could potentially lead to minor adjustments in the drag force predictions and slight changes in the boundary layer, but these effects would be negligible in terms of overall wave-structure interaction results, especially for the types of forces and wave patterns of interest in this study. If turbulent viscosity were to be included, it could slightly modify the dynamics of wave scattering and boundary layer development, particularly in regions close to the surface of the cylinder. This might slightly alter the distribution of forces along the cylinder or modify the wave amplification patterns, particularly for high-frequency components or in situations where localized turbulence might develop. However, in the specific wave and flow conditions of this study, these potential changes would be minimal, and the overall accuracy of the model, particularly for large-scale hydrodynamic forces, would remain largely unchanged.

As a result, the inclusion of turbulent viscosity could provide more detailed insight into small-scale turbulence effects in different flow regimes, it is not necessary for the accuracy or objectives of the current study. The choice to exclude it allows for a more efficient and focused analysis and given the nature of the waves and flow studied, it does not compromise the reliability of the results.

Please remove the repeated paragraph (lines 159-161)

Response: It is completed in the revised version of the manuscript.

I recommend (but do not insist) that the results section be significantly reworked. It should be drastically shortened, and most of the numerous repeated figures should be sent to the Appendix.

Response: Thank you for your detailed feedback and the recommendations concerning the results section of our manuscript. We appreciate your suggestion to streamline this section by shortening it and relocating most of the repeated figures to the appendix. We agree that this approach could enhance the readability and clarity of the results, focusing the reader's attention on the most critical data.

In response, we will carefully review the section to identify and eliminate redundancies and ensure that only essential figures are presented in the main text. The remaining figures, which support but do not directly contribute to the key findings, have already been moved to Appendix B. This will declutter the results section and allow interested readers to access supplementary data without overwhelming them.

And the main concern: Please explain what is the scientific novelty of this article. More specifically: How does this article differ from [Mohseni and Guedes Soares (2022b)] in the following parameters:

- Object of study: different

- Methodology used: same

- Considered computational cases: same

- Obtained results: different, structure different

- General structure of the article: Harmonic pattern details in cylinder explained in detail.

Response: To address the concern regarding the scientific novelty of the article and how it differs from [Mohseni and Guedes Soares (2022b)], as mentioned in the revised version, we classified the following:

1. Object of Study:

Current Article: The object of study in this article is the offshore hydrogen infrastructure and the CFD-based analysis of how various cross-sections of cylinders (e.g., circular, square, rounded corners) interact with regular waves and present a comprehensive harmonic analysis of the wave field around the structure. The study focuses on hydrogen production, storage, and transportation, emphasizing structural integrity under marine conditions.

[Mohseni and Guedes Soares (2022b)]: The object of study in the previous work was also wave-cylinder interaction, but it focused primarily on understanding wave loads and amplification in the context of regular head waves. The previous study was more generic and did not address hydrogen infrastructure or offshore renewable energy systems.

Novelty: The current article expands the scope to hydrogen infrastructure with direct implications for safety and design under hydrogen production and storage scenarios, addressing renewable energy challenges.

2. Methodology Used:

Current Article: This article uses CFD simulations through OpenFOAM, employing a VOF approach. It focuses on understanding nonlinear wave interactions, harmonic amplifications, and the effects of corner geometries on dynamic wave behaviour, particularly how these affect offshore hydrogen systems.

[Mohseni and Guedes Soares (2022b)]: The previous work also employed CFD (OpenFOAM) with a similar VOF method, but it primarily focused on general wave forces and loading on cylinders without detailed consideration of the harmonic effects or their specific impact on hydrogen infrastructure design.

Novelty: The current article introduces a more specialized investigation into harmonics, nonlinearities, and the implications for hydrogen-based infrastructure, which was not the focus in [Mohseni and Guedes Soares (2022b)].

3. Considered Computational Cases:

Current Article: The study considers multiple cross-sectional geometries with varying corner ratios (circular to square) under short and long waves. It specifically models both Type-1 and Type-2 wave scattering and focuses on run-up heights relevant to hydrogen infrastructure.

[Mohseni and Guedes Soares (2022b)]: The previous study primarily focused on circular cross-sections and did not extensively explore the influence of different geometries on wave scattering, run-up height, or the presence of multiple harmonics.

Novelty: The current study significantly expands the computational cases by introducing geometrical variations and analyzing their impact, which adds more complexity and depth compared to the previous work.

4. Obtained Results:

Current Article: The results emphasize the importance of geometry on the wave run-up, scattering, and nonlinear wave field, particularly for hydrogen infrastructure. The study shows how sharp-cornered cylinders generate different harmonic responses compared to rounded geometries, which is crucial for offshore hydrogen platforms.

[Mohseni and Guedes Soares (2022b)]: The previous study yielded insights on wave amplification and inline forces, but it did not focus on the higher-order harmonics or the effect of geometry to the same extent. The results were more applicable to generic offshore structures rather than being focused on renewable energy applications.

Novelty: The new results are more targeted towards renewable energy infrastructure, offering specific design insights for offshore hydrogen systems.

5. General Structure of the Article:

Current Article: The structure includes a focused section on hydrogen infrastructure, outlining the critical importance of wave-cylinder interactions for ensuring safety in hydrogen production and storage systems. There is a strong emphasis on run-up height, harmonic analysis, and their implications for structural design.

[Mohseni and Guedes Soares (2022b)]: The previous work followed a traditional structure with general sections on wave loads and cylinder interaction without delving into hydrogen infrastructure or offering specific recommendations for renewable energy systems.

Novelty: The current article provides a more application-specific focus, particularly on hydrogen-related infrastructure, making it distinct in its practical implications and target audience.

The scientific novelty of the current article lies in its specific focus on offshore hydrogen infrastructure, its detailed investigation into the effect of cross-sectional geometries on nonlinear wave behavior, and its use of CFD simulations to explore higher-order harmonics and their implications for structural safety. Unlike [Mohseni and Guedes Soares (2022b)], which is more general, this study offers practical insights tailored to the renewable energy sector, particularly concerning hydrogen storage and production platforms.

 

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

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I'm fully satisfied.