A Coupled Hydrodynamic–Structural Model for Flexible Interconnected Multiple Floating Bodies
Round 1
Reviewer 1 Report
Dear Authors,
Coupling of hydrodynamics and structural model is crucial for off-shore platforms and the manuscript attempts to develop a frequency-time domain model for such analysis. The problem statement is clear and the theory and equations used to develop the model is well explained. The results are valuable to the readers.
Some questions to be answered to improve the scientific rigor are below:
1) Please add more references showing prior work in frequency-time domain methods
2) Was the method validated with an experiment? All numerical models should be validated. AQWA solver is a commercial code so validation is important.
3) What numerical discretization schemes were used to develop this model-spatial and temporal?
4) Have you tried this method for other configurations than the one mentioned in 3.1?
5) How does the model scale? As in what happens if the gap width to 2m, 1m?
Author Response
Responses to Reviewer 1’s Comments
Point 1: Please add more references showing prior work in frequency-time domain methods
Response 1: Thanks for suggestion. More relevant works on the frequency-time domain methods had been used as references at paragraph 4 of Introduction.
‘The frequency-time domain method was firstly proposed by Cummins [35], and this method have been widely adopted in standard time-domain simulation packages, like AQWA [36-38].
Point 2: Was the method validated with an experiment? All numerical models should be validated. AQWA solver is a commercial code so validation is important.
Response 2: Many thanks for the comment. In this study, the developed CPHSTDM is not validated with experiment. Since CPHSTDM is a combination of the multi-body time-domain hydrodynamic model and structural model for the flexible connector, the validations of the developed CPHSTM are mainly based on the authors’ previous work. The validation of substructuring and static condensation method for the flexible connector was done by Chen et al. [5]. In addition, the validation of constant parameter time domain model for multiple bodies with strong hydrodynamic interaction was done by Zou et al. [6]. In this study, the validation of the developed CPHSTDM is performed by comparing the response amplitude operator (RAO) obtained in the frequency domain and the results of CPHSTDM, as shown in Fig. 12, since the time-domain and frequency-domain models are equivalent for the flexibly interconnected multiple floating bodies under linear wave excitation loads.
Point 3: What numerical discretization schemes were used to develop this model-spatial and temporal?
Response 3: Thanks for the comment. In this study, the 4th order Runge-Kutta method was applied to perform numerical integration in the time domain and the time step convergence was ensured. For the development of model, the hydrodynamic coefficients in frequency domain were obtained via the well-proven three dimensional panel code AQWA and the mesh convergence was ensured.
Point 4: Have you tried this method for other configurations than the one mentioned in 3.1?.
Response 4: Thanks for the comment. In this study, we focused on the three-module hydrodynamic-structural model. In the author’s previous researches [5], the condensation method was used to analyze the catamaran tow for a Spar float-over deck installation. In addition, the same method was applied by Eatock Taylor [50] to analyse the performance of the M4 wave energy convertor. Furthermore, we will apply the developed CPHSTDM to other configurations in future study, for example, the floating photovoltaic system as analysed by Li and Choung [61].
Point 5: How does the model scale? As in what happens if the gap width to 2m, 1m?
Response 5: Thanks for the comment. The single module used in the study has a length of 100 m, a width of 50 m and a draught of 2 m, which has been analysed by Chen et al. [1]. The gap between adjacent modules is 5 m, which is much smaller than the length of module. The effects of different gap widths were investigated in Chen et al. [1], which significantly influence the hydrodyamic interaction characteristics. Due to the limit of paper page length and content, this study only selects the gap width of 5 m for analysis, which shows lightly damped characteristics in the impulse response functions. The established CPHSTDM acturally works well for various gap widths, provided that an appropriate damping lid ratio is chosen in the frequency domain hydrodynamic analyses.
Reviewer 2 Report
The present manuscript presents a numerical model of three connected floating structures by using joints and connectors based on the ANSYS AQWA commercial software. The dynamic response of the floating system (three connected structures) is investigated in the frequency-time domain numerical model. The work presented here is interesting to the present rend of research and will have applications in offshore structures for ocean space utilization. However, I’ve some suggestions and clarifications that need to be incorporated in the manuscript for wider readability and interest to the researchers.
1. The title is too long and needs to be short by considering the following suggestion "multi-module floating system" may be replaced by "articulated"
2. Introduction: Some very relevant and recent interesting references (associated with the same approach and same numerical software) are missing that need to be considered in the present work.
For example:
https://doi.org/10.1016/j.oceaneng.2022.110785
https://www.taylorfrancis.com/chapters/edit/10.1201/9781003320289-35
3. Could you please explain the detail on the consideration methods among the joints and connectors and their importance?
4. The computational cost of the numerical simulation should be discussed in the manuscript.
5. How about the rotational stiffness effect on the structure? What is the critical value of the rotational stiffness in your model?
Author Response
Responses to Reviewer 2’s Comments
Point 1: The title is too long and needs to be short by considering the following suggestion "multi-module floating system" may be replaced by "articulated".
Response 1: Many thanks for the suggestion. In the study, the modules in the multi-module floating system were actually connected via flexible slender bars rather than simply articulated. Therefore, we have changed the title as ‘A coupled hydrodynamic-structural model for flexibly interconnected multiple floating bodies’. We will expand the application of the developed model to multi-module floating system with various connection types in future study, such as articulated connection, rigid connection with flexible beam, ball connection.
Point 2: Introduction: Some very relevant and recent interesting references (associated with the same approach and same numerical software) are missing that need to be considered in the present work.
For example:
https://doi.org/10.1016/j.oceaneng.2022.110785
https://www.taylorfrancis.com/chapters/edit/10.1201/9781003320289-35
Response 2: Thanks for the suggestions. The relevant references mentioned above are reviewed in the revised manuscript. The exact location is the fourth paragraph in Section 1.
‘Bispo et al. [33,34] investigated the wave interactions of multi-floating systems with articulated and hinged connections using potential-flow based model and analytical models.’
Point 3: Could you please explain the detail on the consideration methods among the joints and connectors and their importance?
Response 3: Thanks for the comment. If I understand correctly, the reviewer means the condenstaion method. The condensation method is to condense the mass and stiffness of a substructure onto the super nodes of the substructure, which are known as the master degrees of freedom (DOFs). Except for the super nodes, the other nodes are the slave DOFs. For the static condensation methods, the dynamic effects of the substructure are ignored. In this study, the substructure system is the connecting beams with joint. The master DOFs are the connecting points between the beam and the floater and the slave DOF is the hinged joint. In this way, for solving the dynamics of the multi-module system, the effects of mass and stiffness of the substructure are all taken into account. In this study, both frequency-domain and time-domain hydrodynamic-structural model for flexibly interconnected multiple floating bodies are established. For the time-domain model, the convolution integral in Cummins equation is replaced by state-space modes, resulting in the constant parameter hydrodynamic-structural time domain model (CPHSTDM) with high efficiency. The importance of the joint and beam stiffness is analysed in this study. Detailed imformation can be found in the researches cited in this article, which are listed as follows:
- Chen, M.; Zou, M.; Zhu, L. Frequency-domain response analysis of adjacent multiple floaters with flexible con-nections. Journal of Ship Mechanics 2018, 22, 1164-1180.
- Sun, L.; Choo, Y.S.; Eatock Taylor, R.; Llorente, C. Responses of floating bodies with flexible connections. In: Proceed-ings of the The 2nd Marine Operations Specialty Symposium, 2012, 229-243.
- Eatock Taylor, R.; Taylor, P.; Stansby, P. A coupled hydrodynamic–structural model of the M4 wave energy converter. Journal of Fluids and Structures 2016, 63, 77-96.
- Sun, L.; Eatock Taylor, R.; Choo, Y.S. Responses of interconnected floating bodies. The IES Journal Part A: Civil & Structural Engineering 2011, 4, 143-156.
Point 4: The computational cost of the numerical simulation should be discussed in the manuscript.
Response 4: Thanks for the suggestion. The computational cost of numerical simulation is given in the revised manuscript. The exact location is on the 5th paragraph of Subsection 3.3.
‘The numerical simulation costs about 100 s for a simulation duration of 500 s (AMD Ryzen 7 2700 Eight-Core Processor 3.20 GHz).
The numerical efficiency of the developed time domain model using state-space model had been discussed in our previous studies, see, Zou et al. (2023). In that study, it was found that time domain model showed better efficiency by adopting state-space model.
‘The numerical simulation costs about 50 s for a simulation duration of 500 s (Intel (R) Xeon(R) CPU E5-2643 v4 @ 3.40GHz 3.39 GHz).
Point 5: How about the rotational stiffness effect on the structure? What is the critical value of the rotational stiffness in your model?
Response 5: The rotaional stiffness of the connectors are considered, which is set to be equal to the bending stiffness of the beam, which is applied to constrain the relative motions between the adjacent modules. The rotational hydrostatic stiffness of the structure provides restoring force when the module itself have motion in pitch direction. When the constraint force (moment) is close to the restoring force (moment), resonance will happen in the system, causing unstable results in time-domain, which is because the structural damping effects of the substructure are ignored in this study. In this study, the rotational hydrodynamic stiffness of the module is 4.1732E10 Nm/rad and the rotational stiffness of the connectors varies from 1E6 to 1E9 Nm2.
Round 2
Reviewer 1 Report
The paper is acceptable for publishing.
Reviewer 2 Report
The authors have taken care of my previous comments and suggestions to revise the paper. However, there is an error of the abbreviations in the authors name of the reference list 33 and 34. The corrections are provided below:
"Bispo, I.; Mohapatra, S.;" should be corrected as "Bispo, I.B.S; Mohapatra, S. C.;""
