Hydrodynamic Analysis of a Novel Modular Floating Structure System Integrated with Floating Artificial Reefs and Wave Energy Converters

Round 1

Reviewer 1 Report

 

The work presents a testing of a novel modular floating structure. Numerical analysis were carried out to assess the hydrodynamic response of the model. The main shortcoming is that research questions are unclear and innovation/advantages of the proposed model are not explained. In the current state the work lacks scientific soundness and technically not interesting. Results section is however solid, although some improvement can be done in the visualization of the outputs. The work can be improved with some minor and major addings. Here are my comments:

- Although literature review is satisfactory, the introduction lacks a clear research question nor hypothesis. The presentation of the work (lines 78-85) is poor and does not explain clearly what is the advantadge of the proposed new module in comparison with present models, what are the shortcomings of the current modules, why it is worth to consider such a design and what are the expected results.

- Concerning Chapter 2.1 reasoning about sha**, sizing, mechanical junctions choice were not explained properly. A paragraph about the range of application and the specific motivation behind the design of the module should be presented and thoroughly explained.

- Eq 1 - Not clear what 6 and 7 stays for in the summation. Same applies for Eq. 4 and Eq. 5. Please consider to use symbols to eventually associate with a numerical value, e.g. sum goes from i=1 to N where N is the number of (I suppose modules? NOT CLEAR).

Line 181 – The results lack context about what kind of seastate the authors are experimenting and why. What is a "typical sea case"? Why you chose H = 2 m and how did you associate the period T = 6? Are these regular or irregular waves? If those are regular, why not considering irregular waves? Are those linear or nonlinear waves? Are they associated with extreme events (I suppose not)? Are there any seabed effects?

- Although currents are not investigated, a discussion about the absence of the effects of currents must be AT LEAST discussed. I suggest to check the effects of combined waves and currents on a surface (e.g. seabed) are described in Faraci et al. (2021)  A definitely more thorough explanation about the chosen conditions are necessary.

Minor comments:

- Eq. 4 - the c in Kc should be undercase

- Fig. 4 - please increase font size of graphs

- Figure 4 and 5 - please the caption in the same page of the figure!! Also in this case please resize fontsize

- Eq. 7 omega_ref not explaind in text

 

References
Faraci, C., Musumeci, R. E., Marino, M., Ruggeri, A., Carlo, L., Jensen, B., ... & Elsaßer, B. (2021). Wave-and current-dominated combined orthogonal flows over fixed rough beds. Continental Shelf Research, 220, 104403.

 

 

Author Response

Dear editors and reviewers:

We sincerely thank the editor and all reviewers for their valuable feedback, which we have used to improve the quality of our manuscript. The reviewers’ comments are laid out below in italicized font and specific concerns have been numbered. Our response is given in normal font and changes/additions to the manuscript are given in blue text. Revised portions are marked in red in the revised manuscript.

Response to the comments of reviewer #1:

1. Comment: Although literature review is satisfactory, the introduction lacks a clear research question nor hypothesis. The presentation of the work (lines 78-85) is poor and does not explain clearly what is the advantage of the proposed new module in comparison with present models, what are the shortcomings of the current modules, why it is worth to consider such a design and what are the expected results.

Response: Thank you for your comment! We have added detailed introduction to explain a clear research question, and the expected results of the novel proposed modular floating structure are added in lines 81-90. The applicable sea environment of the proposed MFS system is also supplemented. The revised contents are as follows:

“Therefore, the present work proposes a novel MFS system moored by tension legs, which is composed of hexagonal floating modules, floating artificial reefs and WECs. The proposed novel MFS system is initially designed for a representative sea zone with well shield effect of natural surrounding islands in South China Sea. Compared with the current general MFS [11, 13], the integration of floating artificial reefs can provide habitats for marine species, thereby improving the marine ecological environment around the MFS system. The outmost floating artificial reefs module coupled with WECs can attenuate wave loads, as well as producing considerable wave energy. In addition, the hexagonal floating structure has the advantage of multi-directional expansion, which is beneficial for future scale expansion.”

11. Jiang, C.; El Moctar, O.; Schellin, T. E., Hydrodynamic Sensitivity of Moored and Articulated Multibody Offshore Structures in Waves. J. Mar. Sci. Eng. 2021, 9 (9), 1028.
12. Jiang, D.; Tan, K. H.;  Dai, J.;  Ang, K. K.; Nguyen, H. P., Behavior of concrete modular multi-purpose floating structures. Ocean Eng. 2021, 229, 108971.

2. Comment: Concerning Chapter 2.1 reasoning about sha**, sizing, mechanical junctions choice were not explained properly. A paragraph about the range of application and the specific motivation behind the design of the module should be presented and thoroughly explained.

Response: Thank you for your comment! In view of good multi-directional expansibility of the hexagonal module, the hexagonal module is selected as the key module of the MFS system, the hydrodynamic performance of which is similar to that of the rectangular module. The module size of the proposed MFS system is selected based on both the dimension of most existing dock (usually with the width less than 45m) and our previous study [12, 21]. The selected connector types for the proposed MFS system are also based on both our previous related study [12, 21] and the typical dynamic characteristics of the proposed MFS system. We have further explained the specific motivation behind the design of the module in the first paragraph of the section 2.1. The revised contents are as follows:

“Hexagonal floating structure has good multi-directional expansibility. Two floating artificial reefs coupled with WECs are combined to both sides of the MFS, which are aim to attenuate wave loads, as well as produce considerable wave energy using relative motions between the outermost reef module and adjact inner hexagonal module. Floating artificial reefs also provide a habitat for marine species, which is aim to improve the Marine ecological environment around the MFS system to a certain extent. In addition, fenders are installed at the bottom edge of adjacent connected modules to monitor possible collisions. The simplified sketch is given in Figure 1. Main parameters of the MFS system are given in Table 1, which refer to the references [12, 21].”

12. Michailides, C.; Loukogeorgaki, E.; Angelides, D. C., Response analysis and optimum configuration of a modular floating structure with flexible connectors. Appl. Ocean Res. 2013, 43, 112-130.

21. Ren, N.; Zhang, C.;  Magee, A. R.;  Hellan, Ø.;  Dai, J.; Ang, K. K., Hydrodynamic analysis of a modular multi-purpose floating structure system with different outermost connector types. Ocean Eng. 2019, 176, 158-168.

3. Comment: Eq 1 - Not clear what 6 and 7 stays for in the summation. Same applies for Eq. 4 and Eq. 5. Please consider to use symbols to eventually associate with a numerical value, e.g. sum goes from i=1 to N where N is the number of (I suppose modules? NOT CLEAR).

Response: Thank you for your comment! We have explained the meaning of i and j in the second paragraph of the section 2.2. The revised contents are as follows:

“where ϕ_I is the incident potential of the wave without disturbance by the floating body. ϕ_D is the diffraction potential generated after the wave passes through the floating body. i (i=1~7) denotes the number of the i-th module. j (j=1~6) denotes the j-th modal of the six degrees of freedom (6-DOF).”

4.Comment: Line 181 – The results lack context about what kind of seastate the authors are experimenting and why. What is a "typical sea case"? Why you chose H = 2 m and how did you associate the period T = 6? Are these regular or irregular waves? If those are regular, why not considering irregular waves? Are those linear or nonlinear waves? Are they associated with extreme events (I suppose not)? Are there any seabed effects?

Response: Thank you for your comment! The proposed novel MFS system is initially designed for a representative sea zone with well shield effect of natural surrounding islands in South China Sea. (Fig. 1). Referring to the research of Wang et al., 2014, the annual and monthly average wave heights of the selected sea area are both less than 2 m, and the wave period of 6 s is of the most probability. Therefore, a regular wave (H = 2 m and T = 6 s) are selected as a typical sea case for the investigation. The effect of different wave periods on the proposed MFS system has also been discussed in this paper. Although the real sea is always with the nature of irregular waves, the analysis under regular waves is very helpful to obtain the general dynamic characteristics (or regularity) of the complex MFS system. Furthermore, main hydrodynamic responses of the proposed MFS system have also been analyzed under a typical extreme sea case (irregular waves) to verify its safety. Both regular waves and nonlinear irregular waves have been considered in this work. The seabed effect has not been considered in this work due to the lack of detailed seabed information, so we suppose the seabed is flat. However, we would like to do further study on the seabed effect with more detailed seabed information. A reference [36] has been added to explain typical sea cases.

36. Wang, Z.; Zhou, L.;  Dong, S.;  Wu, L.;  Li, Z.;  Mou, L.; Wang, A., Wind wave characteristics and engineering environment of the South China Sea. J. Ocean U. China 2014, 13 (6), 893-900.

 

5. Comment: Although currents are not investigated, a discussion about the absence of the effects of currents must be AT LEAST discussed. I suggest to check the effects of combined waves and currents on a surface (e.g. seabed) are described in Faraci et al. (2021) A definitely more thorough explanation about the chosen conditions are necessary.

Response: Your suggestion is valuable! We agree with you that the effects of combined waves and currents are not negligible, but the current of the selected sea zone is very small due to the shelter effect of surrounding islands. In addition, the proposed MFS system is composed of seven modules, which is a complicated system. The shielding effect of the current between adjacent modules may be difficult to be well considered by AQWA code, which should be based on CFD codes or scale model tests. Considering the limited time for revising the manuscript, the corresponding works have been listed in the future work section (further investigating the effects of combined waves and currents based on both numerical methods and scale model tests). The corresponding reference has been added, and the revised contents are as follows. Special thanks for your valuable comments.

“Many works still need to be further studied for the MFS system, including the optimization design of each module, the validation of the scale model test, and the attracting effect of the floating artificial reef. In addition, effects of the seabed and the current [37] on dynamic responses of the proposed MFS system should be further investigated based on more detailed sea information. These challenging works should be investigated in future.”

37. Faraci, C.; Musumeci, R. E.;  Marino, M.;  Ruggeri, A.;  Carlo, L.;  Jensen, B.;  Foti, E.;  Barbaro, G.; Elsaßer, B., Wave- and current-dominated combined orthogonal flows over fixed rough beds. Cont. Shelf Res. 2021, 220, 104403.

Response to minor comments

1. Comment: Eq. 4 - the c in Kc should be undercase

Response: Thank you for your comment! We have modified in Eq. 4.                           

2. Comment: Fig. 4 - please increase font size of graphs

Response: Thank you for your comment! We have increased font size in Fig. 4.

  3. Comment: Figure 4 and 5 - please the caption in the same page of the figure!! Also in this case please resize fontsize

Response: Thank you for your comment! We have revised and increased font size in Figure 4 and 5. In addition, the font size in all figures has been increased accordingly.

4. Comment: Eq. 7 omega_ref not explaind in text

Response: Thank you for your comment! We have added the explanation of the . The added explanation is as follows:

“where  denotes the corresponding relative pitch velocity between the floating artificial reef module and its adjacent hexagonal floating structure module. M_Bpto and K_p denote the bending moment and the linear pitch dam**, respectively.”

 

Thanks for your valuable time and kind consideration!

Sincerely yours,

Best regards,

Yanwei Li

Author Response File: Author Response.docx

Reviewer 2 Report

The paper presents a numerical study on a modular floating structure, connected to the seabed via tension legs, integrated with artificial reefs and rotational-based WECs. The modules can provide usable space for numerous activities, while the artificial reef can provide habitat for marine species and the WECs energy to the whole system. This combined approach also enables wave load attenuation and a mitigation of significant motions. A thorough analysis on module number, interconnections, layout and PTO dam** was carried out over a wide range of regular wave periods and directions. This was extended to an extreme wave scenario where the modular platform demonstrated its resilience. Despite all of this work, there are several topics that need improvement and clarifications. A key remark is that the paper should be improved in terms of result discussion and interpretation, as the results are quite interesting but seem, at times, ill-developed and explained to the reader.

The Abstract is concise and informative on the paper’s subjective, but I would recommend that some concrete data is included. The keywords are suitable, but can be slightly improved. The English is overall good, with minor and punctual errors. The paper seems to be of a suitable dimensions and ratio between figures/tables and text.  

I believe that the paper would be of great interest for readers of the journal. Even so, it is my opinion that it should be improved in numerous aspects, in line with my comments. As such, I recommend that the paper be subjected to major revisions prior to acceptation. I hope that my comments will be helpful to the authors if they intent on a future re-submission.

2.1.            Major comments:

1-      The first paragraph of the Introduction should be slightly improved and further developed, so as to better understand the contribute of MFS towards “increasing population and the land scarcity of coastal cities”;

2-      The final paragraph of the Introduction section should list and summarize the remaining sections of the paper;

3-      Is the TLP solution suitable for this type of depths? Or are you assuming a less standard mini-TLP approach?;

4-      Line 181: what reference do you use to assume such regular wave conditions as typical?;

5-      Is the heave response for modules M2 and M6, from Figure 5, conditioned by the presence of the mobile artificial reefs/WEC connections and the incoming waves? If so, this ought to be an interesting discussion to introduce in the paragraph from Line 213 onwards. You can also overlap these results with Figure 6, as it seems that the sway motions are overcompensating the surge motions for a greater incident wave angle, leading to greater connector forces at 60º;

6-      Line 240: could you please develop on why WEC2’s performance improves with the incident wave angle (greater exposure and less shielding?);

7-      Is the pitch peak from Figure 8 attributed to system resonance? From the connector forces, it may be interesting, also, to check if there is coupling between the different DoFs, as several force peaks overlap within the same wave period range;

8-      Line 291: could it also be due to WEC resonance? Notice that the peak of the previous connector Figures, for pitch, is at twice the wave period as that of the power output from the WECs. I believe this requires further interpretation. Also, how are you able to get such high average power output values with such small pitch angles and despite the rotational constraints?;

9-      In Section 3.5, what reference did you use to define Hs=4.0 m and Tp=10s as an extreme sea-state? Also, mind that preceding paragraphs mention regular wave cases as representative of ocean waves, which is very rarely the case due to the irregular nature of waves at sea;

10-  In Table 3, how does a rather low My produce such a significant power output for the H-h-h-h-h-H case?.

2.2.            Minor comments:

1-      Please avoid abbreviations in the Abstract;

2-      If possible, indicate a few metrics associated with your study in the Abstract (e.g., peak power output), based on your results;

3-      For the keywords, I would suggest upgrading the first one into “wave-structure hydrodynamic interactions” and including “numerical modelling” or “ANSYS Aqwa” for greater visibility. You might also want to mention that your study is of a numerical nature in the Abstract;

4-      Line 94: I believe that you mean module corresponds to M and connector to C, but reading it one interprets it the other way around;

5-      Please indicate in Figure 1 where WEC1 and WEC2 are, alongside the artificial reefs (I assume it is on the M1 and M7 modules, but a designation would be welcome);

6-      In Equation 1, please check if the first summation is correct (shouldn’t it be from 1 to 6, for the 6 DoFs?);

7-      Line 141: please correct “added dam**” to “radiation dam**”;

8-      In Equation 3, Ci also accounts for the radiation dam**, aside from the non-linear hydrodynamic dam** component;

9-      Line 190: please correct 5KW to 5 kW and update Figure 4 accordingly;

10-  The Conclusions should highlight some additional results from the study, including metrics and relevant values.

Author Response

Dear editors and reviewers:

We sincerely thank the editor and all reviewers for their valuable feedback, which we have used to improve the quality of our manuscript. The reviewers’ comments are laid out below in italicized font and specific concerns have been numbered. Our response is given in normal font and changes/additions to the manuscript are given in blue text. Revised portions are marked in red in the revised manuscript.

 

Response to the comments of reviewer #2:

Response to major comments

1. Comment: The first paragraph of the Introduction should be slightly improved and further developed, so as to better understand the contribute of MFS towards “increasing population and the land scarcity of coastal cities”;

Response: Your suggestion is valuable! A detailed introduction to illustrate the contribution of MFS has been added. The revised contents are as follows:

“Modular floating structure (MFS) provides a feasible way to create useable land on the sea for solving challenges brought from the increasing population and the land scarcity of coastal cities, because about 70% of the earth is covered by the sea [1-4]. Compared with the traditional very large floating structure (VLFS), the production, transportation, installation and maintenance of the MFS are more convenient [5-7]. More importantly, it can greatly reduce the hydroelastic response of the structure [8].”

2. Comment: The final paragraph of the Introduction section should list and summarize the remaining sections of the paper;

Response: Thank you for your comment! We have added the final paragraph of the introduction section to list and summarize the remaining sections of the paper. The added contents are as follows:

“This paper is structured as follows. Both the conceptual design and numerical model of the proposed MFS system are described in Section 2; Numerical results of the MFS system under typical sea cases are shown and discussed in section 3. Finally, main conclusions are summarized in section 4.”

3. Comment: Is the TLP solution suitable for this type of depths? Or are you assuming a less standard mini-TLP approach?;

Response: Thank you for your comment! Based on our previous study [1, 2], the TLP is suitable for modular floating structures with the depth (80m). Compared with the mooring line system, the tension leg system has significant advantages for the MFS. It can effectively limit the pitch and the heave responses of each module, as well as beneficial for future expansion with more modules due to the characteristic of vertical installation.

1. Ren, N.; Ma, Z.;  Shan, B.;  Ning, D.; Ou, J., Experimental and numerical study of dynamic responses of a new combined TLP type floating wind turbine and a wave energy converter under operational conditions. Renewable Energy 2020, 151, 966-974.

2. Ren, N.; Wu, H.;  Ma, Z.; Ou, J., Hydrodynamic analysis of a novel modular floating structure system with central tension-leg platforms. Ships and Offshore Structures 2019, 15 (9), 1011-1022.

3. Comment: Line 181: what reference do you use to assume such regular wave conditions as typical?;

Response: Thank you for your comment! The proposed novel MFS system is initially designed for a representative sea zone with well shield effect of natural surrounding islands in South China Sea. (Fig. 1). Referring to the research of Wang et al., 2014, the annual and monthly average wave heights of the selected sea area are both less than 2 m, and the wave period of 6 s is of the most probability. Therefore, a regular wave (H = 2 m and T = 6 s) are selected as a typical sea case for the investigation. The effect of different wave periods on the proposed MFS system has also been discussed in this paper. A reference [36] has been added to explain the typical sea case.

36. Wang, Z.; Zhou, L.;  Dong, S.;  Wu, L.;  Li, Z.;  Mou, L.; Wang, A., Wind wave characteristics and engineering environment of the South China Sea. J. Ocean U. China 2014, 13 (6), 893-900.

5. Comment: Is the heave response for modules M2 and M6, from Figure 5, conditioned by the presence of the mobile artificial reefs/WEC connections and the incoming waves? If so, this ought to be an interesting discussion to introduce in the paragraph from Line 213 onwards. You can also overlap these results with Figure 6, as it seems that the sway motions are overcompensating the surge motions for a greater incident wave angle, leading to greater connector forces at 60º;

Response: Yes, the heave responses of the M2 and the M6 are affected by both the connection of floating artificial reef module and the incident wave direction. The connection of floating artificial reef modules leads to greater heave responses for adjacent module M2 and M6, and the heave response increases with the incident wave angle to some degree. Compared with the surge, the sway is more significant with a greater wave angle, which is due to less shielding effect. We have added this interesting discussion in lines 236-237 and lines 241-243. Thank you for your valuable suggestion!

“Compared with the surge, the sway is more significant with greater wave angles, which are due to less modules’ shielding effect.”

“The connection of floating artificial reef module tends to lead to greater both heave and pitch responses for adjacent module M2 and M6, especially for greater wave angles.”

6. Comment: Line 240: could you please develop on why WEC2’s performance improves with the incident wave angle (greater exposure and less shielding?);

Response: Yes, the WEC2’s performance improves with the incident wave angle, which is due to the greater exposure. Less shielding effect of the M7 leads to more significant pitch responses. We have added this interesting discussion in lines 267-268.Thank you for your valuable suggestion!

“The WEC2’s performance improves with the increase of the incident wave angle, which due to more significant pitch responses of the M7 with less shielding effect.”

7. Comment: Is the pitch peak from Figure 8 attributed to system resonance? From the connector forces, it may be interesting, also, to check if there is coupling between the different DoFs, as several force peaks overlap within the same wave period range;

Response: Thank you for your valuable comment! Just as the reviewer said, the pitch peak phenomenon of each module is attributed to the module resonance. The Fx, the Fy, the My peaks all occur within the same wave period range, which is due to the coupling effect between different DoFs. We have added this interesting discussion in lines 287-289 and lines 302-304.

“The pitch peak phenomenon of each module is attributed to the module certain natural period. In addition, the pitch of the head-wave M2 is much larger than other hexagonal modules, due to the less shielding effect.”

“The peaks of main connector load for different connectors occur in the wave period range from 6 s and 12 s, which are due to the coupling effect between different degrees of freedom..”

8. Comment: Line 291: could it also be due to WEC resonance? Notice that the peak of the previous connector Figures, for pitch, is at twice the wave period as that of the power output from the WECs. I believe this requires further interpretation. Also, how are you able to get such high average power output values with such small pitch angles and despite the rotational constraints?;

Response: Thank you for your comment! The average output power peak occurs at about 6s, which is due to the WEC resonance. We have checked the pitch bending moment peak of the C1, which is identical to the output power peak. They all occur at 6 s. The pitch is relatively small caused by the limitation of the PTO dam** (3e8 Nms/rad), which is aim to prevent collisions between the floating artificial reef module and its adjacent hexagonal floating structure module. Meanwhile, considering the PTO dam** coefficient reaches 3e8 Nms/rad, so even a small pitch angle can lead to a considerable wave power production. Therefore, the corresponding results have been checked again, which are reasonable for getting such output power.

8. Comment: In Section 3.5, what reference did you use to define Hs=4.0 m and Tp=10s as an extreme sea-state? Also, mind that preceding paragraphs mention regular wave cases as representative of ocean waves, which is very rarely the case due to the irregular nature of waves at sea;

Response: Thank you for your comment! The proposed novel MFS system is initially designed for a representative sea zone with well shield effect of natural surrounding islands in South China Sea. (Fig. 1). Based on our collected information of the selected sea zone and our previous study, Hs=4.0 m and Tp=10 s may be a typical extreme sea condition [36]. Although the real sea case is irregular wave, the researches under regular waves are necessary and helpful to discover the dynamic characteristics of the complex MFS system. Meanwhile, the calculation under regular waves is more efficient. We also analyzed the hydrodynamic response of the proposed MFS system under extreme sea case (irregular wave), and the safety has been well verified.

36. Wang, Z.; Zhou, L.;  Dong, S.;  Wu, L.;  Li, Z.;  Mou, L.; Wang, A., Wind wave characteristics and engineering environment of the South China Sea. J. Ocean U. China 2014, 13 (6), 893-900.

10. Comment: In Table 3, how does a rather low My produce such a significant power output for the H-h-h-h-h-H case?

Response: Thank you for your comment! We have rechecked the data in Table 3, and the results are correct. The maximum My (C4, about 240MNm) for the H-h-f-f-h-H case is relatively lager, which is due to the fixed connector type. Therefore, one survival strategy H-h-h-h-h-H case has been proposed, which can efficiently reduce the bending moment My. The maximum My (C1) is about 13 MNm, which can drive WEC1 to produce energy about 600kW.

Response to minor comments

1. Comment: Please avoid abbreviations in the Abstract;

Response: Thank you for your comment! We have reduced most abbreviations in the Abstract. However, considering the high frequency of both the MFS and the WEC, we have not revised these in order to better express and read. The revised contents are as follows:

“Abstract: A novel modular floating structure (MFS) system moored by tension legs has been proposed, which is composed of hexagonal floating modules, floating artificial reefs and wave energy converters (WECs). The integration of floating artificial reefs and WECs into the MFS can improve marine environment and produce considerable energy. Effects of different wave characteristics and module quantity on hydrodynamic responses of the MFS system have been emphatically studied based on time-domain numerical analysis. Both the modules’ hydrodynamic interaction effect and the connectors’ mechanical coupling effect have been considered. Results indicate that floating artificial reefs combined with WECs can effectively reduce wave loads and convert wave energy into electricity for the MFS system. More modules involving in the MFS system can significantly reduce motion responses and produce more wave energy output, which indicates that the MFS system is suitable for large-scale expansion. The effect of different power take-off dam** coefficients on WECs’ performance has been further investigated, and the optimal dam** coefficient has been recommended. Finally, main extreme responses of the MFS system have been further investigated, and its safety has been well checked. One survival strategy has been proposed in term of extreme sea case, which can efficiently reduce extreme connector forces Fz and My by about 50% and 95%, respectively.”

2. Comment: If possible, indicate a few metrics associated with your study in the Abstract (e.g., peak power output), based on your results;

Response: Thank you for your comment! We have added key metrics in the Abstract. The revised contents are as follows:

“Finally, main extreme responses of the MFS system have been further investigated, and its safety has been well checked. One survival strategy has been proposed, which can efficiently reduce extreme connector forces by more than 50%.”

3. Comment: For the keywords, I would suggest upgrading the first one into “wave-structure hydrodynamic interactions” and including “numerical modelling” or “ANSYS Aqwa” for greater visibility. You might also want to mention that your study is of a numerical nature in the Abstract;

Response: Thank you for your valuable suggestion! We have modified accordingly. The revised contents are as follows:

“Keywords: Wave-structure hydrodynamic interactions; Modular floating structure; Wave energy converters; Floating artificial reefs; Hexagonal tension leg platform”

4. Comment: Line 94: I believe that you mean module corresponds to M and connector to C, but reading it one interprets it the other way around;

Response: Thank you for your reminding! We have corrected accordingly. The revised contents are as follows:

“Each module and each connector are marked as Mi (i=1~7) and Ci (i=1~6), respectively, as shown in Figure 1.”

5. Comment: Please indicate in Figure 1 where WEC1 and WEC2 are, alongside the artificial reefs (I assume it is on the M1 and M7 modules, but a designation would be welcome);

Response: Thank you for your valuable comment! We have marked the WEC1 and the WEC2 in Figure 1.

6. Comment: In Equation 1, please check if the first summation is correct (shouldn’t it be from 1 to 6, for the 6 DoFs?);

Response: Thank you for your comment! We have checked the Equation 1. i (i=1~7) denotes the number of the i-th module. j (j=1~6) denotes the j-th modal of the six degrees of freedom (6-DOF). The revised contents are as follows:

“where ϕ_I is the incident potential of the wave without disturbance by the floating body. ϕ_D is the diffraction potential generated after the wave passes through the floating body. i (i=1~7) denotes the number of the i-th module. j (j=1~6) denotes the j-th modal of the six degrees of freedom (6-DOF).”

7. Comment: Line 141: please correct “added dam**” to “radiation dam**”;

Response: Thank you for your valuable comment! We have modified accordingly. The revised contents are as follows:

“where F_i,Wave is the wave exciting force induced by scattering potential (ϕ_I and ϕ_D), and the radiation force is induced by the interaction radiation potential of multi-body. A_ij and B_ij denote added mass and radiation dam**, respectively.”

8. Comment: In Equation 3, Ci also accounts for the radiation dam**, aside from the non-linear hydrodynamic dam** component;

Response: Thank you for your comment! The corresponding description has been revised.

8. Comment: Line 190: please correct 5KW to 5 kW and update Figure 4 accordingly;

Response: Thank you for your comment! We have modified accordingly.

 

Figure 4c. Average output power.

10. Comment: The Conclusions should highlight some additional results from the study, including metrics and relevant values.

Response: Thank you for your comment! We have added key metrics and relevant values in the conclusions. The revised contents are as follows:

“(3)  A survival strategy of the MFS system with inner hinge connectors has been proposed for reducing extreme connector loads, especially for the bending moment and the shear force. The extreme connector forces Fz and My can be efficiently reduced by about 50% and 95%, respectively.”

 

Thanks for your valuable time and kind consideration!

Sincerely yours,

Best regards,

Yanwei Li

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

All questions have been answered adequately, for which i commend the authors. I only ask a final check of English for potential typo errors. Afterwards, i recommend acceptance of the paper. Congratulations!

Author Response

Dear editors and reviewers:

We sincerely thank very much for the reviewer’s comments concerning our manuscript. The English of our manuscript has been further checked and improved. Revised portions are marked in red for the revised version.

Response to the comments of reviewer #2:

1. Comment: All questions have been answered adequately, for which I commend the authors. I only ask a final check of English for potential typo errors. Afterwards, I recommend acceptance of the paper. Congratulations!

Response: Thanks very much for this comment!

The English of our manuscript has been further checked and improved. Revised portions are marked in red for the revised version.

 

Thanks for your valuable time and kind consideration!

Sincerely yours,

Best regards,

Yanwei Li

Author Response File: Author Response.docx

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.