Three-Dimensional Modified Cross-Section Hydrofoil Design and Performance Study

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript describes CFD simulations for maneuvering hydrofoils at a number of different planforms of the wing. The flow is extremely complex, with large recirculation zones: the most difficult flow to simulate. Today, there does not yet exist turbulence models that are safe to use for this kind of flow. Here, with the word 'safe' I mean that they are capable to give reliable results that may be interpreted with a physical eye. That means that it is of utmost importance to quantify the numerical and modeling errors before any conclusions can be made.

The theory presented in the manuscript, like the discussion of planforms, is at the level of a first class on aerodynamics. So nothing spectacular there. In the manuscript, the simulations have been done with existing Fluent software, using the Spalart-Allmaras turbulence model. This model was developed for transonic aerodynamic flow featuring shockwave- boundary layer interaction. Thus it is widely used in the airplane industry to design wings in cruise condition under small angles of attack (so basically non-separated flow). The present application is completely different, with strongly varying angle of attack and extensive boundary-layer separation.  Hence the authors first have to validate the SA model for their application; they cannot rely on positive experiences in the literature.

This type of flow is not only difficult to model, but also is very sensitive to numerical errors, in particular numerical diffusion - codes like Fluent often have too much of this nonphysical diffusion. Hence, before physical conclusions are being made the authors should convince the readers that the numerical errors are small. They do carry out a grid refinement study in which the number of elements ranges from 300k to 470k. So in average the cell size has been reduced by only 25%. This is not a grid refinement study. The cell size should at least be halved, preferably two times. As a compromise I would propose a grid halving the cell size (hence 1200k cells) and a grid where the cell size is divided by 3 (2700k cells). I realize that this will lead to longer CPU times, but I consider this to be essential. The differences that I see in the current manuscript after the small change in grid size are worrying me.

In conclusion, the manuscript is not ready to be presented to a wider audience.

 

 

Comments on the Quality of English Language

Several sentences are 'cripple'. Please ask a native english-speaking colleague to have a look at the text.

Author Response

1. Comment: The manuscript describes CFD simulations for maneuvering hydrofoils at a number of different planforms of the wing. The flow is extremely complex, with large recirculation zones: the most difficult flow to simulate. Today, there does not yet exist turbulence models that are safe to use for this kind of flow. Here, with the word 'safe' I mean that they are capable to give reliable results that may be interpreted with a physical eye. That means that it is of utmost importance to quantify the numerical and modeling errors before any conclusions can be made.

Response: Thank you for your careful guidance. The simulation error of the simulation analysis is indeed important and we have set the error with sufficient accuracy when doing the experiments. We have added in subsection 3.1 of the manuscript that the convergence error of the simulation is 10^-5.

2. Comment: The theory presented in the manuscript, like the discussion of planforms, is at the level of a first class on aerodynamics. So nothing spectacular there. In the manuscript, the simulations have been done with existing Fluent software, using the Spalart-Allmaras turbulence model. This model was developed for transonic aerodynamic flow featuring shockwave- boundary layer interaction. Thus it is widely used in the airplane industry to design wings in cruise condition under small angles of attack (so basically non-separated flow). The present application is completely different, with strongly varying angle of attack and extensive boundary-layer separation. Hence the authors first have to validate the SA model for their application; they cannot rely on positive experiences in the literature.

Response: Thanks to your thoughtful and careful work. We have added turbulence model validation, where we found that the k-w and SST models were more difficult to converge and yielded less favorable data results compared to the S-A model.

“In order to verify the effects of different turbulence models on the hydrodynamic performance of 3D hydrofoils and to select a more suitable turbulence model, the S-A, k-, and SST models were initially selected for the simulation experiments under the same working conditions mentioned above. The coefficient values of the third, fourth, fifth and sixth cycles after the hydrofoil motion is stabilized are selected for comparison, and the results are shown in Table 3-2. The experimental results show that the peak lift coefficient, average drag coefficient and average power coefficient of the k-w and SST models fluctuate greatly, while the coefficients of the S-A model are more stable. In addition, in the simulation parameter setting, the k- model and SST model need to increase the convergence error to to make the simulation converge, so the S-A turbulence model is selected for the subsequent experiments in this paper.

 

Table 3-2 Result of simulation coefficients for different turbulence models.

turbulence model
	3rdT	4thT	5thT	6thT	3rdT	4thT	5thT	6thT	3rdT	4thT	5thT	6thT
S-A	1.52	1.52	1.51	1.53	2.60	2.61	2.61	2.62	0.81	0.80	0.81	0.81
k-	1.56	1.51	1.47	1.42	2.70	2.71	2.60	2.51	0.78	0.81	0.83	0.84
SST	1.61	1.55	1.50	1.51	2.51	2.54	2.63	2.67	0.82	0.81	0.81	0.85

”

3. Comment: This type of flow is not only difficult to model, but also is very sensitive to numerical errors, in particular numerical diffusion - codes like Fluent often have too much of this nonphysical diffusion. Hence, before physical conclusions are being made the authors should convince the readers that the numerical errors are small. They do carry out a grid refinement study in which the number of elements ranges from 300k to 470k. So in average the cell size has been reduced by only 25%. This is not a grid refinement study. The cell size should at least be halved, preferably two times. As a compromise I would propose a grid halving the cell size (hence 1200k cells) and a grid where the cell size is divided by 3 (2700k cells). I realize that this will lead to longer CPU times, but I consider this to be essential. The differences that I see in the current manuscript after the small change in grid size are worrying me.

Response: We are very grateful for your careful work. We have already added two more sets of experiments in subsection 3-2, increasing the number of grids to 12000000, and the results of the experiments did not change much, so it makes more sense to choose the solution with a grid number of 4000000.

“

Table 3-3 Comparison of different grid quantity factors.

Number of cells
300 0000	1.541	2.615	0.511	0.812
350 0000	1.555	2.616	0.518	0.794
400 0000	1.561	2.621	0.523	0.811
470 0000	1.552	2.612	0.519	0.809
800 0000	1.553	2.619	0.521	0.810
120 0000	1.550	2.620	0.520	0.811

 

The differences in the calculated coefficients for the six grid number models are 1.3% for the average drag , 0.03% for the peak lift coefficient , 2.3% for the peak moment coefficient , and 2.27% for the average power coefficient . When the number of grids is lower than 4 000 000, there is a large difference in the calculated values of the coefficients, and when the number of grids is gradually increased to 1 200 000, the values fluctuate within 0.6%, while the computer running time increases by a factor of three. Taken together, the subsequent experiments in this paper adopt the setup scheme with a grid number of 4 000 000.The number of grids is about 4 000 000, the time step of one cycle is taken as T/1000, and 6 cycles are calculated, and the results are shown in Table 3-4.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The introduction section cites numerous works but lacks thematic organization. Grouping works by categories (2D, 3D hydrofoils, passive, active control) can improve readability and highlight research gaps. 

The authors need to explain why chose NACA0015 as the research object instead of other hydrofoils. Additionally, the authors used the computational data from reference 26 for validation; why not use the existing experimental data for NACA0015 for validation?

The grid independence study and time-step validation lacks statistical rigor. Error percentages are provided, but no convergence criteria or detailed justification for selecting 4 million mesh and T/1000 time steps. 

The work focuses on λ and frequency but does not explore other potentially influential factors (such as Reynolds number, motion amplitudes).

"As λ decreases the enhancement effect on the average power gradually decreases." (line 362) lacks a physical explanation. A deeper discussion linking pressure distribution, tip vortex dynamics, and energy extraction efficiency is better. 

The resolution of several figures (Figure 6, 11) is poor.

The conclusions summarize key findings but lack a concise synthesis of how these findings advance the tidal energy.

Author Response

1.Comment: The introduction section cites numerous works but lacks thematic organization. Grouping works by categories (2D, 3D hydrofoils, passive, active control) can improve readability and highlight research gaps.

Response: Thanks you for your careful work. We changed the cited numerical order of reference [26] to [29] due to revision needs. Since hydrofoil research objects are more diverse, if the literature is categorized into two-dimensional, three-dimensional, active hydrofoils, passive hydrofoils may weaken the relevance of each other's research. In this paper, the references are tentatively divided into practical experiments and simulation experiments.

2.Comment: The authors need to explain why chose NACA0015 as the research object instead of other hydrofoils. Additionally, the authors used the computational data from reference [29] for validation; why not use the existing experimental data for NACA0015 for validation?

Response: Thank you very much for your careful review. We selected NACA0015 as the base airfoil for our study mainly because of its well - documented aerodynamic and hydrodynamic characteristics. It is a widely - used and well - studied airfoil, which provides a reliable starting point for our variable - section hydrofoil design. Its symmetric shape simplifies the initial design process and allows us to focus on the effects of cross - section modification more clearly. We have added this in subsection 2.2. Official experimental data on NACA 0015 under specific operating conditions are not available, while reference [29] is an authoritative paper published in the relevant field and is of high reference significance, and the paper has been widely used as an experimental reference.

We have made the following modifications in the revised manuscript:

“NACA 0015 is a very mature airfoil widely used in aerospace and marine applications, and using this airfoil as a base can avoid some unnecessary mistakes.”

3.Comment: The grid independence study and time-step validation lacks statistical rigor. Error percentages are provided, but no convergence criteria or detailed justification for selecting 4 million mesh and T/1000 time steps.

Response: We appreciate your careful work very much. We have added that the convergence error is  in subsection 3.1. We have already added in subsection 3.1 that the initial experimental setup in this paper is referenced from Ref. [29], e.g., time step, working conditions, mesh density.

We have made the following modifications in the revised manuscript:

“the convergence error is. Referring to Ref. [29], we set the number of the background grids for meshing to 960 thousand”

4.Comment: The work focuses on  and frequency but does not explore other potentially influential factors (such as Reynolds number, motion amplitudes).

Response: We appreciate your careful work very much. The work in this paper focuses on the geometrical design of the hydrofoil, and the parameter  is used to characterize the cross-sectional variation of the hydrofoil. Subsequent work will discuss the performance of this hydrofoil around other factors.

5.Comment: "As  decreases the enhancement effect on the average power gradually decreases." (line 362) lacks a physical explanation. A deeper discussion linking pressure distribution, tip vortex dynamics, and energy extraction efficiency is better.

Response:Thank you very much for your careful review. We have added in the fifth paragraph of subsection 4.1.

We have made the following modifications in the revised manuscript:

“As the cross - sectional coefficient  decreases, the pressure center on the hydrofoil surface moves, with the high - pressure part concentrating more in the middle when  is small. This change affects lift and drag forces; over - concentration may increase drag and reduce net power. Regarding tip vortex dynamics,  reduction shifts vortex shedding backward and increases tip vortex size and intensity, leading to more energy loss. In terms of energy extraction efficiency, while the reduction in pitching moment initially boosts the average power coefficient, the negative impacts of pressure distribution and tip vortex changes, like increased drag and vortex - related losses, gradually prevail. Consequently, the overall enhancement of the average power coefficient weakens as  continues to decrease.”

6.Comment: The resolution of several figures (Figure 6, 11) is poor.

Response: We are very grateful for your careful work. We have re-edited the images so that thesis images are all at 300 dpi.

7.Comment: The conclusions summarize key findings but lack a concise synthesis of how these findings advance the tidal energy.

Response: Thanks to your careful work, we add to the review in Section 5: “This work will help to enrich the design of hydrofoil structures and increase the power of hydrofoil devices used to capture tidal energy.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have seriously reacted to my earlier comments, by adding a discussion on turbulence models, and by extending their grid-refinement study. But I am getting confused about the number of grid points: in the earlier version it ranged between 300 000 and 470 000; in the response this was enlarged to 1 200 000. But in the manuscript I read 3 000 000 upto  12 000 000 (a factor of 10 difference).  Please check this number. Apart from this point. the manuscript can now be accepted.

Author Response

Dear Editor and Reviewers:

  Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Three-dimensional modified cross-section hydrofoil design and performance study” (ID:actuators-3519603 ). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have checked the manuscript and revised the manuscript in accordance to the reviewers’ comments. Revised portions are marked in red color in the manuscript. Should you have any questions, please do not hesitate to contact us.

The point to point responds to the reviewer’s comments are listed as the following:

 

Reviewer #1

1. Comment: The authors have seriously reacted to my earlier comments, by adding a discussion on turbulence models, and by extending their grid-refinement study. But I am getting confused about the number of grid points: in the earlier version it ranged between 300 000 and 470 000; in the response this was enlarged to 1 200 000. But in the manuscript I read 3 000 000 upto 12 000 000 (a factor of 10 difference). Please check this number. Apart from this point. the manuscript can now be accepted.

Response: Thank you for your careful guidance. We've examined the experiments and the manuscript. This paper refers to the case in reference 29 to verify the reliability of the model in this paper. Since the mesh density has an important effect on the hydrofoil wall flow, the number of meshes in this paper ranges from 3 000 000 to 12 000 000, which consumes a large amount of computational resources but is important for the computational results.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

All the questions have been properly replied to. 

Author Response

Dear Editor and Reviewers:

  Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Three-dimensional modified cross-section hydrofoil design and performance study” (ID:actuators-3519603 ). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have checked the manuscript and revised the manuscript in accordance with the reviewers’ comments. Should you have any questions, please do not hesitate to contact us.