Numerical Study on Hydrodynamic Responses of Floating Rope Enclosure in Waves and Currents
Round 1
Reviewer 1 Report
Missing Data
The value of this paper is mostly due to the applicability of results for designers of fish farms structures and mooring. Hence, the mathematical model and the experiments need to be completely specified. The models (mathematical and experimental) represent a full scale prototype that must be specified as well. I find the following data missing:
1.1. Prototype structure materials and sizes (Nets, Mooring Ropes, Floats, Anchors, Weights along bottom of net panels).
1.2. Submerged weights of all the components, the balancing, and tension applied to the net panels.
1.3. Pre tension in the mooring lines.
1.4. Design Environmental conditions (currents, waves) at the design site.
1.5. I suggest adding an engineering drawing of the prototype.
1.6. Please show more specifically the details of connections of mooring lines.
Similarity of the experimental model and Scale effects
Although not indicated, I guess that the model similarity is based on Froude number, which is proper for inertia loads and high Reynolds numbers (full turbulence flow) drag loads. However, the structure contains small floats, thin mooring ropers and nets of very thin yarn, for which considerable scale effects are expected. Please discuss this issue and justify that the scale effects are acceptable for design. Do you consider the scale effects in the interpretation of model results to prototype, and how?
Assumptions and Formulation Simulation model
The formulation of the numerical model is not completely presented. Known published theory, like the dispersion relation, Morison equation, and simple geometry calculations are presented; while the difficulties of modeling; like large motion of structure of small stiffens, convergence difficulties, are not presented. Please present the complete formulation of the representation of a net panel by spring and mass elements and the solution considering large deformations.
The formulation also needs to include all the drag and inertia coefficients of all the elements.
Current and wave directions
The single wave direction parallel to the current direction is, to my opinion, not sufficient for design. Practically at most sites, the waves are not parallel to the current. Several currents and waves direction should be investigated to properly represent the design site conditions.
Pre tension
The pre tension of the mooring lines (at calm sea with no waves and currents) are important to the results and must be specified.
Bottom lines loads and motion
The authors indicate the importance of holding the bottom lines of the net panels; however do not present how it is done and what is the required anchoring submerged weight. Details of the connections to prevent damage at motion are also needed.
More detailed results
I suggest adding typical figures of the time series for the mooring lines tensions and all the displacements simultaneously. The line tension is determined by the position of its connection to the structure, and such relations may be analyzed and discussed for checking the accuracy of results and understanding the mooring design. Such a data processing can improve the study.
Figure 11 presents forces at different times around the bottom contour. It may be more valuable for designers to present the maximum (over time) forces around the bottom contour, for several combinations of extreme wave and current directions.
As the currents and waves loads are reacted by the mooring lines and by the seabed net contour, is important to present (from the numerical model) the hydrodynamic loads applied to the nets (load per area) at several representative locations and to show the current only and wave + current loads.
Relative importance of current and waves
I do not agree with the conclusions that wave height are less important relative to current and that wave periods have minor effect. The relative importance depends mainly on the mooring stiffness. Long lines will reduce the wave loads, however occupy more space. High wave periods will increase the wave induced flow near the seabed.
Author Response
Response to Reviewer 1 Comments
Point 1: Missing Data
1.1. Prototype structure materials and sizes (Nets, Mooring Ropes, Floats, Anchors, Weights along bottom of net panels).
Response: Prototype structure materials and sizes have been supplemented in Table 1.
1.2. Submerged weights of all the components, the balancing, and tension applied to the net panels.
Response: Submerged weights of all the components have been supplemented in Table 1. The net is in a relative relax state. When the structure is in a balancing state, about half of the floaters are submerged in the water.
1.3. Pre tension in the mooring lines.
Response: The pre-tension of each mooring line is 0.03 N.
1.4. Design Environmental conditions (currents, waves) at the design site.
Response: Design Environmental conditions (currents, waves) at the design site have been supplemented in Table 2.
1.5. I suggest adding an engineering drawing of the prototype.
Response: The size of the prototype is shown in Figure 1.
1.6. Please show more specifically the details of connections of mooring lines.
Response: In the experiment, the mooring line is attached to the structure by fastening to the net. During the experiment, no pictures are taken for the connections of mooring line due to poor consideration.
Point 2: Similarity of the experimental model and Scale effects
Although not indicated, I guess that the model similarity is based on Froude number, which is proper for inertia loads and high Reynolds numbers (full turbulence flow) drag loads. However, the structure contains small floats, thin mooring ropers and nets of very thin yarn, for which considerable scale effects are expected. Please discuss this issue and justify that the scale effects are acceptable for design. Do you consider the scale effects in the interpretation of model results to prototype, and how?
Response: In general, the floating rope enclosure model should meet the geometric similarity, kinematic similarity and dynamic similarity. However, it is difficult to completely meet the similarity law. Since the size of the float is too small according to the scale, the entire floating system adopts equivalent buoyancy, the floater size not scaled according to the prototype, but can provide equal buoyancy. If the model net is designed strictly according to the geometric similarity principles, two difficult problems arise. First, the yarn used for the model net will be very thin, which is difficult to manufacture. Second, because the model yarn is so thin, the Reynolds number (Re) for the model net will change significantly relative to the prototype net, leading to a large difference in hydrodynamic behavior between the model and prototype nets. Thus, the extended gravity similarity criteria are applied. Two geometric scales for the net are used in the extended gravity similarity criteria: λ (1/50) is the global scale and λ’ (1/5) is the scale for the yarn diameter and net mesh size. The full-scale values can be calculated based on the extended gravity similarity criteria. More details about the similarity law and the calculation of full-scale values can be found in Gui (2006) and Li (2010).
Point 3: Assumptions and Formulation Simulation model
The formulation of the numerical model is not completely presented. Known published theory, like the dispersion relation, Morison equation, and simple geometry calculations are presented; while the difficulties of modeling; like large motion of structure of small stiffness, convergence difficulties, are not presented. Please present the complete formulation of the representation of a net panel by spring and mass elements and the solution considering large deformations. The formulation also needs to include all the drag and inertia coefficients of all the elements.
Response: The formulation of the numerical model, drag and inertia coefficients and the specific modeling method for each components have been supplemented in detail in Section 2.
Point 4: Current and wave directions
The single wave direction parallel to the current direction is, to my opinion, not sufficient for design. Practically at most sites, the waves are not parallel to the current. Several currents and waves direction should be investigated to properly represent the design site conditions.
Response: Different incident angles between waves and current have been supplemented in section 4.1.2. Keep the incident wave forward along the X-axis constant, but through changing the incident direction of current to investigate its influence on the maximum mooring line tension.
Point 5: The pre tension of the mooring lines (at calm sea with no waves and currents) are important to the results and must be specified.
The pre-tension of each mooring line at calm sea with no waves and currents is 0.03 N.
Point 6: Bottom lines loads and motion
The authors indicate the importance of holding the bottom lines of the net panels; however do not present how it is done and what is the required anchoring submerged weight. Details of the connections to prevent damage at motion are also needed.
Response: Thanks for your advice, I found the shortcomings in the work. But in the numerical simulation, the bottom of net is assumed to be fixed, so the motion of the bottom is not considered. This content will be improved in the future work.
Point 7: I suggest adding typical figures of the time series for the mooring lines tensions and all the displacements simultaneously. The line tension is determined by the position of its connection to the structure, and such relations may be analyzed and discussed for checking the accuracy of results and understanding the mooring design. Such a data processing can improve the study.
Response: The mooring line tension is not only determined by the position of its connection to the structure. According to the results of Wilson [27], the mooring line tension is related to the elongation of mooring line. The formula is presented below:
Where represents the mooring line tension, represents the elongation of the mooring line; represents the original mooring line length.
The elongation of mooring line in this study is codetermined by the position of its connection to the structure and the position of the mooring line. So the time series for the elongation of mooring line is given to check the accuracy of results as shown below.
Time history of mooring line elongation
Point 8: Figure 11 presents forces at different times around the bottom contour. It may be more valuable for designers to present the maximum (over time) forces around the bottom contour, for several combinations of extreme wave and current directions.
Response: The maximum (over time) forces around the bottom contour have been described in detail in Section 4.1.3.
Point 9: As the currents and waves loads are reacted by the mooring lines and by the seabed net contour, is important to present (from the numerical model) the hydrodynamic loads applied to the nets (load per area) at several representative locations and to show the current only and wave + current loads.
Response: The hydrodynamic loads applied to the nets (load per area) at several representative locations have been described in Section 4.1.3.
Point 10: Relative importance of current and waves
I do not agree with the conclusions that wave height are less important relative to current and that wave periods have minor effect. The relative importance depends mainly on the mooring stiffness. Long lines will reduce the wave loads, however occupy more space. High wave periods will increase the wave induced flow near the seabed.
Response: Thank for these precious comments and suggestions. The content of this part does have vulnerability, so this part has been deleted.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In the "Introduction", I suggest that "natural bait" is replaced by "life food".
The Authors wrote "low possibility of fish diseases". It should be explained why there is a low possibility. Is it because the densities are low? Wild animals and pathogenic agents can contact with the animals that are being produced.
Author Response
Response to Reviewer 2 Comments
Point 1: In the "Introduction", I suggest that "natural bait" is replaced by "life food".
Response: It has been revised in the Introduction Part.
Point 2: The Authors wrote "low possibility of fish diseases". It should be explained why there is a low possibility. Is it because the densities are low? Wild animals and pathogenic agents can contact with the animals that are being produced.
Response: Compared with fish cage aquaculture, enclosure aquaculture can reduce the possibility of fish diseases mainly due to the increase of breeding water and the decrease of breeding density. The modifications are given in the Introduction part.
Reviewer 3 Report
The authors claim that "The hydrodynamic force on the floating ball can be calculated by Morison formula". Morison formula was derived for slender bodies (actually for vertical piles). This statement needs clarification. It is said that "For the calculation of the hydrodynamic force on the mooring line, the mooring line is divided into a series of lumped mass point based on the lumped mass method". It should be clarified how the hydrodynamic force on the mooring line is calculated. I assume Morison formula is used to calculate forces on each line segment, but the sentence is confusing. Cd and Cm values used in the evaluation of hydrodynamic forces on each element should be reported. Figure 2 refers to "mass-spring" model so I understand that spring elements are used to model the rope and mooring segments. However, this is not mentioned in the text. Please give details on this (including properties of the spring elements used). If spring elements are used, are those linear? In that case, can they withstand compression? In that case, they can lead to unrealistic behaviour. This should be (at least) discussed in the result analysis section, showing maps of tension values in the net elements to check if the resulting compression effects are or not negligible. This is important to assess the validity of the proposed model. Regarding the mooring lines, are they pre-stressed? If so, please include this information in the particulars of the physical model. Otherwise, please discuss whether compression effects are relevant. No information is given on the discretized scheme used to integrate the numerical. If no damping/stabilizing effects are included (and this not mentioned in the manuscript) I would expect that approach to give a noise signal. Surprisingly, figure 9 (b) shows a smooth time history, is this signal filtered? It is necessary to give details on the integration scheme of the numerical model, including sensibility to parameters like time step. Actually, it would ideal to offer any data required to facilitate the reproducibility of the model.
Author Response
Response to Reviewer 3 Comments
Point 1: The authors claim that "The hydrodynamic force on the floating ball can be calculated by Morison formula". Morison formula was derived for slender bodies (actually for vertical piles). This statement needs clarification.
Response: Thanks for suggestions. The calculation for floaters is referred to the study by Xu et al.
Xu, T.J.; Zhao, Y.P.; Dong, G.H.; Li, Y.C.; Gui, F.K. Analysis of hydrodynamic behaviors of multiple net cages in combined wave-current flow. J. Fluids Struct. 2013, 39, 222-236.
Xu, T.J.; Dong, G.H.; Zhao, Y.P.; Li, Y.C.; Gui, F.K.; Numerical investigation of the hydrodynamic behaviors of multiple net cages in waves. Aquacult. Eng. 2012, 48, 6–18.
Point 2: It is said that "For the calculation of the hydrodynamic force on the mooring line, the mooring line is divided into a series of lumped mass point based on the lumped mass method". It should be clarified how the hydrodynamic force on the mooring line is calculated. I assume Morison formula is used to calculate forces on each line segment, but the sentence is confusing.
Response: Numerical details have been supplemented in Section 2. The formulation of the numerical model, drag and inertia coefficients and the specific modeling method for each components have been supplemented in detail in Section 2. In numerical calculations, the mooring line is also simplified to a series of lumped mass points connected by massless springs. Morison formula is used to calculate forces on each line segment.
Point 3: Cd and Cm values used in the evaluation of hydrodynamic forces on each element should be reported.
Response: The formulation of the numerical model, drag and inertia coefficients and the specific modeling method for each components have been supplemented in detail in Section 2.
Point 4: Figure 2 refers to "mass-spring" model so I understand that spring elements are used to model the rope and mooring segments. However, this is not mentioned in the text. Please give details on this (including properties of the spring elements used). If spring elements are used, are those linear? In that case, can they withstand compression? In that case, they can lead to unrealistic behavior. This should be (at least) discussed in the result analysis section, showing maps of tension values in the net elements to check if the resulting compression effects are or not negligible. This is important to assess the validity of the proposed model. Regarding the mooring lines, are they pre-stressed? If so, please include this information in the particulars of the physical model. Otherwise, please discuss whether compression effects are relevant.
Response: The specific modeling method for each components have been supplemented in detail in Section 2. The fishing net is modeled as a series of lumped mass points that are interconnected with springs without mass. The mooring line is also simplified to a series of lumped mass points connected by massless springs. We adopt the linear spring element and the spring elements cannot withstand compression, if the length of the spring is less than its original length, the tension will be set as zero. The mooring lines are pre-stressed with a tension of 0.03 N for experiments and the numerical calculation. The formulation of the numerical model, drag and inertia coefficients and the specific modeling method for each components have been supplemented in detail in Section 2.
Point 5: No information is given on the discretized scheme used to integrate the numerical. If no damping/stabilizing effects are included (and this not mentioned in the manuscript) I would expect that approach to give a noise signal. Surprisingly, figure 9 (b) shows a smooth time history, is this signal filtered? It is necessary to give details on the integration scheme of the numerical model, including sensibility to parameters like time step. Actually, it would ideal to offer any data required to facilitate the reproducibility of the model.
Response: The 4th-order Runge-Kutta (RK4) time-integration scheme is adopted for the time stepping process. Several different time steps have been tested and dt = 0.001 s is found to be sufficient for each of the cases. During the beginning of the numerical simulation, an abrupt initial condition should be avoided, thus a ramp function is imposed to modulate the incident wave field so that the incident wave can smoothly develop from the calm water surface to the specified wave field. It makes the simulation more stable and reach the steady state earlier. In this paper, a cosine ramp function Rm is adopted
where Tm is the ramp time, here chosen as 2T with T the incident wave period.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
More detailed results
I suggest adding typical figures of the time series for the mooring lines tensions and all the displacements simultaneously. The line tension is determined by the position of its connection to the structure, and such relations may be analyzed and discussed for checking the accuracy of results and understanding the mooring design. Such a data processing can improve the study.
Response: The mooring line tension is not only determined by the position of its connection to the structure. …
Reviewer Comment: Since the anchoring point is fixed, the elongation, and so the tension of a mooring line is determined by the position (at a certain time) of its connection to the structure.
Anyhow, I accept the response.
Author Response
Thank you very much for your comments, which are very helpful to the improvement of the article.
Reviewer 3 Report
Last sentence in page 2. Correct "Several different time steps have ..." by "Different time steps have ...".
Last sentence in page 2. "dt = 0.001 s is found to be sufficient for each of the cases". Can you clarify that sentence? Have you carried out a convergence study?
Last sentence in page 5. "The large number of mass points makes the calculation difficult, so mesh grouping method [26] is adopted to reduce the computational difficulty". This sentence should be further discussed. Can you give the number of degrees of freedom of the original and 'grouped' model? Can you give the 'facteur de globalisation (grouping factor)' used? Have you carried out a convergence study on the 'facteur de globalisation'?
Author Response
Point 1: Last sentence in page 2. Correct "Several different time steps have ..." by "Different time steps have ...".
Response: Last sentence in page 2 has been corrected.
Point 2：Last sentence in page 2. "dt = 0.001 s is found to be sufficient for each of the cases". Can you clarify that sentence? Have you carried out a convergence study?
Response: The convergence test is carried out with respect to different time steps using dt = 0.002 s, 0.001 s and 0.0005 s, as shown below. It is seen that the numerical results are almost identical with each other and thus dt = 0.001 s is chosen for each of the following cases.
Point 3: Last sentence in page 5. "The large number of mass points makes the calculation difficult, so mesh grouping method [26] is adopted to reduce the computational difficulty". This sentence should be further discussed. Can you give the number of degrees of freedom of the original and 'grouped' model? Can you give the 'facteur de globalisation (grouping factor)' used? Have you carried out a convergence study on the 'facteur de globalisation'?
Response: In this paper, the mesh grouping method is adopted and equivalent meshes are used in the numerical calculation rather than the actual meshes. Equivalent meshes have the same projected area of the netting, specific mass and the weight as the actual meshes. The original net used in the experiment is 300 ×15 diamond meshes with mesh size of 20 mm and a diameter of 1 mm. There are 22800 mass points and 136800 equations to be solved for the original net. In the numerical simulation, the equivalent meshes are adopted with a mesh size of 100 mm and a diameter 5 mm, which reduce the number of mass points and equations to 960 and 5760. For the original net in this problem, it is very time-consuming to calculate it, since the size of the system of equations to be solved is too large. As a result, it is hard to analyze the difference between the results based on the grouped model and original model. However, many researchers has verified the mesh grouping method for plane net, such as Tsukrov et al. (2003), Li et al. (2005) and Zhao (2007). According to the calculations of Tsukrov et al. (2003), when using 2×2, 3×3 and 16×16 meshes to model the same panel, the numerical results are similar with each other in the predicted hydrodynamic forces.
Tsukrov, I., Eroshkin, O., Fredriksson, D., Robinson, S.M., Celikkol, B., 2003. Finite element modeling of net panels using a consistent net element. Ocean Engineering 30, 251–270.
Li, Y.C, Zhao, Y.P., Gui, F.K., Teng, B., 2006. Numerical simulation of the hydrodynamic behaviour of submerged plane nets in current. Ocean Engineering 33, 2352-2368.
Zhao, Y.P., 2007. Numerical investigation on hydrodynamic behavior of deep-water Gravity Cage [D]. Dalian University of Technology.
Author Response File: Author Response.pdf
