The Hydrodynamic Performance of a Vertical-Axis Hydro Turbine with an Airfoil Designed Based on the Outline of a Sailfish

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a bio-inspired vertical-axis hydrokinetic turbine system that employs the morphology of Istiophorus platypterus for blade profiling. A parametric optimization framework evaluates four critical airfoil descriptors: arcuate angle (θ), installation angle (α), thickness ratio (δ), and chord-length ratio coefficient (L). The coaxial architecture integrates centrifugal and axial rotors on a shared drivetrain that operates under distinct energy conversion principles. The centrifugal module harnesses tidal current kinetic energy, and the axial-flow module extracts wave orbital motion potential energy.

The presentation of the research methodology and results could be improved.

I have an important question: Is this new blade shape feasible to manufacture?

If so, how would it be made?

Author Response

Open Review

( ) I would not like to sign my review report
(x) I would like to sign my review report

Quality of English Language

( ) The English could be improved to more clearly express the research.
(x) The English is fine and does not require any improvement.

Comments and Suggestions for Authors

This paper presents a bio-inspired vertical-axis hydrokinetic turbine system that employs the morphology of Istiophorus platypterus for blade profiling. A parametric optimization framework evaluates four critical airfoil descriptors: arcuate angle (θ), installation angle (α), thickness ratio (δ), and chord-length ratio coefficient (L). The coaxial architecture integrates centrifugal and axial rotors on a shared drivetrain that operates under distinct energy conversion principles. The centrifugal module harnesses tidal current kinetic energy, and the axial-flow module extracts wave orbital motion potential energy.

The presentation of the research methodology and results could be improved.

Thank you for pointing this out. We agree with this comment. Therefore, figure4,5,7,8,9,10,12,13,14,17,18 have been re-optimized, and a summary description of its results has been added.

I have an important question: Is this new blade shape feasible to manufacture?

1. Design and Modeling Stage

Accurately convert the sailfish outline into a mathematical model of the airfoil. This requires using computational fluid dynamics (CFD) software to analyze its hydrodynamic characteristics by incorporating parameters such as flow velocity and angular velocity, ensuring the mathematical model can precisely reflect the performance of the sailfish - outline - based airfoil. Technically, this step is feasible, as current CFD software can achieve this. 

Thank you for pointing this out. We agree with this comment. We analyze the issue through the following aspects.

1. Material and Processing Technology

- Material Selection: Materials with sufficient strength, corrosion resistance, and other properties to meet the operating conditions of the hydroturbine must be chosen. For metal materials like stainless steel, they can be formed through casting, forging combined with machining. For composite materials such as carbon - fiber composites, processes like molding and 3D printing (if the contour accuracy can be matched) can be utilized. However, the complex contour poses challenges to the material forming ability. For example, to accurately replicate the curved surface transitions of the sailfish outline with composite materials, mold and process parameters need to be optimized. 

- Processing Precision: The curved surface of the sailfish outline is complex. To machine the airfoil in line with the design, high precision is required for CNC (computer numerical control) machines. The subtle curved - surface changes of the airfoil rely on high - precision five - axis linkage machining centers and appropriate tool - path planning. Currently, advanced manufacturing technologies can meet the precision requirements, but the cost and processing time may be relatively high. 

III. Adaptability to Practical Applications 

- Overall Integration of Hydroturbine: A hydroturbine has specific installation space and structural requirements. The sailfish - outline airfoil must be adaptable to components such as the hub and the fairing. Factors like the airfoil size and installation angle need to be considered for matching with the entire hydroturbine. Structural mechanics analysis must be conducted to ensure structural stability during operation. This requires multi - disciplinary collaborative design, and technically, it can be verified through simulation and testing. 

- Mass Production: For industrial application, the feasibility of mass production must be considered. Current mold manufacturing and automated processing lines can theoretically adapt to such complex contours. However, the initial mold development cost is high, so cost - effectiveness must be evaluated to determine if cost reduction can be achieved through process optimization during large - scale production. 

In general, from a technical perspective, by combining modern design, material, and processing technologies, using the sailfish outline as the airfoil of a hydroturbine is feasible in manufacturing. However, it will face challenges such as design adaptation, processing costs, and mass production. These challenges need to be specifically addressed during the research and development process, and actual manufacturing applications can be realized through gradual technical verification and optimization.

If so, how would it be made?

Thank you for pointing this out. We agree with this comment. We analyze the issue through the following aspects.

1. Material Selection and Preparation

- Material Screening: Select materials with high strength, good corrosion resistance, and strong cavitation resistance according to the operating environment of the hydroturbine (such as flow velocity, water quality, pressure, etc.). If metal materials are used, stainless steel is a common choice, as it has both strength and corrosion resistance. If lightweight properties and specific mechanical performances are considered, carbon fiber composites can also be tried, but their adaptability to complex contours needs to be evaluated. For scenarios with eco - friendly requirements, attention should also be paid to the impact of materials on the water environment, and environmentally friendly materials with good biocompatibility should be preferred as much as possible. 

- Material Pretreatment (if needed): Pretreat the selected materials. For example, perform quenching and tempering treatment on metal materials (to improve mechanical properties) and prepare prepregs for composite materials (to prepare for subsequent forming), ensuring that the material properties meet the processing and usage requirements. 

1. Processing and Manufacturing Stage

- Mold Making (for complex contours): If processes such as casting and molding are adopted, high - precision molds need to be made according to the designed sailfish airfoil and the shape of hydroturbine components. For metal casting, a CNC (Computer Numerical Control) machining center can be used to machine the mold core and cavity to ensure the surface accuracy. For composite material molding, the mold should consider the material shrinkage rate, demolding convenience, etc. Molds can be made of metal or high - strength resin, and the mold accuracy can be ensured through processes such as electric discharge machining and milling, accurately reproducing the curved surface transitions and fine structures of the sailfish airfoil. 

- Airfoil and Component Processing 

    - Casting Process (taking metal materials as an example): If the casting method is chosen to manufacture components such as blades, processes like sodium silicate sand casting and investment casting can be adopted. For example, in sodium silicate sand casting, molten metal (such as stainless steel liquid) is poured into the mold. After cooling and forming, processes such as sand cleaning, grinding, and flaw detection are carried out to remove defects and ensure the quality of the castings. Investment casting is suitable for more complex and high - precision components, which can better present the details of the sailfish airfoil, but the cost is relatively high. 

    - Machining Process: For parts with extremely high precision requirements that are difficult to meet by casting, or for forged blanks, machining is carried out. Use a five - axis linkage machining center, cooperate with appropriate cutters (such as ball - nose mills), plan the cutter path according to the designed mathematical model, and perform milling processing on the airfoil surface to realize the complex curved surface modeling of the sailfish contour, and control the machining accuracy (such as dimensional tolerance, surface roughness, etc.) to meet the design requirements. 

    - Composite Material Forming (if composite materials are used): If carbon fiber composites are used, they can be formed by a molding process, in which prepregs are laid in the mold and cured and formed under a certain temperature and pressure. 3D printing technologies (such as fused deposition modeling, stereolithography, etc.) can also be tried to directly print blade components with a sailfish airfoil. However, issues such as printing accuracy and material property consistency need to be concerned. After forming, post - treatments (such as support removal, surface grinding, impregnation treatment, etc.) are carried out to improve the component quality. 

    - Component Assembly: Assemble the processed sailfish airfoil blades with components such as the hub, water - guiding system, volute, and draft tube. The connection between the blades and the hub should be seamless (or the gap should be controlled according to the design requirements). Methods such as welding (for metal materials), bonding (when composite materials meet the strength requirements), and mechanical connection (such as bolt connection) can be adopted. At the same time, parameters such as the installation angle are adjusted to ensure the coordinated operation of all components. 

 III. Quality Inspection and Commissioning 

- Quality Inspection: Conduct various inspections on the manufactured hydroturbine components and the whole machine. For geometric dimension inspection, use equipment such as a coordinate measuring machine to check whether the surface accuracy and dimensional tolerance of the sailfish airfoil blades meet the design requirements. For mechanical property inspection, verify the strength and hardness of materials and components through tensile tests, hardness tests, etc. For hydrodynamic performance inspection, simulate the actual operating conditions on a test bench (such as a circulating water tank, a hydroturbine test bench) to test indicators such as lift, drag, torque, and efficiency to see if they meet the design expectations. It is also necessary to detect performances such as cavitation, vibration, and noise to evaluate the impact on the environment and the equipment itself. 

- Commissioning and Optimization: Commission the hydroturbine according to the inspection results. If the hydrodynamic performance is found to be poor, parameters such as the airfoil installation angle and the water - guiding system can be fine - tuned. If there are structural vibration problems, check the component connection stiffness and perform dynamic balance adjustment. Through repeated commissioning and optimization, make the hydroturbine meet the design requirements in terms of performance, stability, reliability, etc., and have the conditions for practical application. 

From laboratory trials to actual engineering applications, issues such as large - scale production, cost control, and long - term operation and maintenance also need to be considered. Pilot applications can be carried out step by step, operation data can be accumulated, and the manufacturing process and equipment performance can be continuously improved to promote the practical development of hydroturbines with sailfish - contour airfoils.

Submission Date

14 May 2025

Date of this review

03 Jun 2025 20:06:03

Reviewer 2 Report

Comments and Suggestions for Authors

This paper reported a research titling "Research on the Hydrodynamic Performance of a Vertical-Axis Hydro Turbine with an Airfoil Designed Based on the Outline of a Sailfish". So far, the authors have conducted an aerodynamic optimization framework for analysing four key geometric variables governing the airfoil's hydrodynamic characteristics. Moreover, they claimed that they developed a coaxial dual-rotor vertical axis turbine configuration, integrating centrifugal and axial-flow energy conversion mechanisms through a shared drivetrain system. Furthermore, they reported that they conducted transient numerical simulations employing dynamic mesh techniques and user-defined functions within the Fluent environment to analyze rotor interaction, and their results revealed that the installation Angle has a significant influence on the turbine performance. In addition, they argued that their proposed synergistic configuration demonstrates complementary operational characteristics under marine energy conversion scenarios. The manuscript is well written, however, some issues need to be resolved before further proceeding, and a careful and thorough check should be performed, which requires improving the presentation quality of this paper. Some simple editing mistakes should also be corrected before proceeding further, for example, 'section 3' appeared twice, and a lot of bullet-form text is used in the presentation. 

Author Response

Open Review (x) I would not like to sign my review report
( ) I would like to sign my review report Quality of English Language ( ) The English could be improved to more clearly express the research.
(x) The English is fine and does not require any improvement.    

This paper reported a research titling "Research on the Hydrodynamic Performance of a Vertical-Axis Hydro Turbine with an Airfoil Designed Based on the Outline of a Sailfish". So far, the authors have conducted an aerodynamic optimization framework for analysing four key geometric variables governing the airfoil's hydrodynamic characteristics. Moreover, they claimed that they developed a coaxial dual-rotor vertical axis turbine configuration, integrating centrifugal and axial-flow energy conversion mechanisms through a shared drivetrain system. Furthermore, they reported that they conducted transient numerical simulations employing dynamic mesh techniques and user-defined functions within the Fluent environment to analyze rotor interaction, and their results revealed that the installation Angle has a significant influence on the turbine performance. In addition, they argued that their proposed synergistic configuration demonstrates complementary operational characteristics under marine energy conversion scenarios. The manuscript is well written, however, some issues need to be resolved before further proceeding, and a careful and thorough check should be performed, which requires improving the presentation quality of this paper. Some simple editing mistakes should also be corrected before proceeding further, for example, 'section 3' appeared twice, and a lot of bullet-form text is used in the presentation.

Thank you for pointing this out. We agree with this comment.

Therefore, We have thoroughly revised the main headings to prevent recurrence of heading issues.

We have converted the bullet-form text on the page 4, 6,8,10,12,13,14,15,20,21,23 and 30 into non-bullet-form text.

Submission Date 14 May 2025 Date of this review 08 Jun 2025 08:05:31

Reviewer 3 Report

Comments and Suggestions for Authors

Please check attached file.

Comments for author File: Comments.pdf

Author Response

Open Review (x) I would not like to sign my review report
( ) I would like to sign my review report Quality of English Language ( ) The English could be improved to more clearly express the research.
(x) The English is fine and does not require any improvement.

The paper reports a parametric study to optimize power harvesting for a duel vertical axis water turbine, adapting dorsal fin of a sailfish as hydrofoil for coaxial vertical-axis turbine. CFD method was used to obtain aerodynamic forces exerting on hydrofoil. Latin hypercube sampling – a multi-objective optimization framework – was used to obtain lift and drag as functions of geometric variables. Then, the effects of installation angle and tip speed ratio on power harvesting of the water turbine are investigated using ANSYS Fluent. I have following concerns and suggestions.

My major concern is about the connection between part 5 and the rest part of the paper. In part 5 (Numerical simulation of the airfoil), the authors build the functions of lift and drag in dependency of 4 geometric variables (δ, α, L, θ), but these functions seem to have no usage or support for part 6 in which the power harvesting – the main part and the ultimate goal in design of a water turbine – was studied.

Thank you for pointing this out. We agree with this comment.

Therefore, based on the DOE design in the previous chapter, we obtained the optimal solution for a single airfoil: θ=22.7°, L‘=148.2%, α=0.83°, and δ=135.6%. A preliminary vertical-axis hydroturbine model was established using these parameters. Considering the differences between 2D and 3D flow fields, we retained θ, L‘, and δ in the turbine model but adjusted α. Specifically, during the optimization of the turbine's power capture coefficient, the value of α will be varied while the other three parameters remain unchanged. And we have added this paragraph after Equation 37.

My second concern is how much a biomimetic hydrofoil adapted from sailfish’s dorsal f in enhances the performance of the water turbine. We expect that it will provide superior performance compared to conventional hydrofoil. Therefore, it will be more of interest if the authors compare Cp of the current sailfish hydrofoil with Cp harvested by the same water turbine but with a conventional hydrofoil. If it is so time consuming, then a comparison with similar model of other research groups is recommended. Besides, I have following suggestions :

Thank you for pointing this out. We agree with this comment.

We used the NACA 63A610 airfoil for turbine modeling, maintaining geometric parameters consistent with the sailfish's geometry in the paper, and conducted a comparative analysis of energy harvesting efficiency between the sailfish profile and traditional airfoil profiles. The relevant data and descriptions have been added to Chapter 8 of the paper. 

1. The title should be as concise as possible. Removing “Research on” still keeps 100% content of the title, so it is better to remove it.

Thank you for pointing this out. We agree with this comment. Therefore, we have removed “Research on” of title.

2. Lines 167~169: the dimensions of the computational domain are in relative to the chord length “C” (as stated in line 165~166). Thus, “L” in these lines should be “C”.

Thank you for pointing this out. We agree with this comment. We have revised all "line lengths" in the article to L and all " Chord-length ratio coefficient " to L'.

3. Please provide more information on CFD model in Section 5 (Numerical simulation of the airfoil):

• How much is the Reynolds number range?

Reynolds number is about 1.2e5.

• Which flow modeling was used?

This study employs the Shear Stress Transport (SST) k-omega turbulence closure model.

• The element types

Tetrahedral grids are adopted.

• The number of elements on the hydrofoil and computational domain.

The blade surface grid size is 0.5 mm, and the total number of grids in the fluid domain is 1.1 million.

• The heights of the first element layers that simulate boundary layer

The heights of the first boundary layer is 0.01mm.

• The test of grid independence

The grid independence has been added in table 2 and figure 7.

3. There should be more accurate explanation of thickness ratio (δ) and chord-length ratio coefficient (L). These quantities are all non-dimensional coefficients, but by illustration in Figure 5, L and δ are of length dimension. L and δ should be ratios between dimensional quantities. Therefore, please add 1 or 2 equations that express definitions of L and δ in that way.

We define the chord length in the text as L, and change the chord-length ratio coefficient to L’. The thickness is defined as δ, and the thickness ratio is defined as δ’. Additionally, we define L’ = ∆L/L and δ’ = ∆δ/δ. This content has been inserted into the third chapter (page 4).

4. Please add more explanation on definitions of “Arcuate Angle” and “Installation Angle”. Clear explanation will help reader follow the paper easier, and thus the paper can reach a wider audience.

The angle between the tangent line at the leading edge point A and the tangent line at the trailing edge point B is “Arcuate Angle”. The angle between the chord line of the airfoil and the axis of rotation is “Installation Angle”. These content has been inserted into the forth chapter (page 4) and figure 4.

5. In equations (29) and (30), x, y, z, w are small caps. Therefore, “X”, “Y”, “Z”, “W” in lines 432~ 435 should be changed to small caps because they prefer to the same quantities.

We have replaced x, y, z and w in the formula with θ, L‘, α and δ’.

6. In Figure 6, what are unit of “Lift” and “Drag”? Are they non-dimensional terms?

The unit is mN. And we have optimized the figures.

7. “Table 1” in page 17 should be “Table 4”. “Table 2” in page 1

We have rechecked all the figures and tables in the text and sorted them correctly.

9 should be “Table 5”. “Table 3” in page 21 should be “Table 5”. 9. In Table 1 page 17, “a” in “Chord Length La” should be subscript, thus “Chord Length La”, or else, reader may understand it as “L” multiply to “a”. Similar problem to “Span Lb”.

We have rechecked all the figures and tables in the text and sorted them correctly. We replaced "Chord Length La" with "Chord Length/L [mm]". We also replaced "Span Lb" with "Blade length/BL [mm]".

10. In Table 1 page 17, “Attack Angle” is actually “Installation Angle”, if I understand correctly. If they are of the same quantity, please consider using the same name. Similar problem for Figure14 in which “attack angle” was used. In my opinion, “Installation Angle” seems to be more accurate. “Attack angle” by definition is the angle between the flow and the hydrofoil, and thus attack angles are all different for current turbine blades.

Thank you for pointing this out. We agree with this comment. We have checked all parts of the text, and wherever "installation angle" should be used, we have replaced "attack angle" with "installation angle".

Reviewer 4 Report

Comments and Suggestions for Authors

This study proposed a new concept by combining a vertical-axis turbine for tidal energy development with a horizontal-axis turbine for wave energy development. Additionally, biomimetic technology was applied to the vertical-axis turbine blades, and an optimization study was conducted. Fluid-dynamic analysis techniques were employed for performance evaluation, and output performance and flow field analyses were performed. However, a re-examination of the presented CFD results is required.

1. In the process of generating experimental points using LHS, how were the ranges for each variable determined?

2. How many sample points were obtained through this LHS method, and what are the values of each variable at each experimental point?

3. In the analysis results, it was reported that the efficiency of the centrifugal turbine was calculated as 69.1%, but theoretically it cannot exceed Betz’s limit. A re-examination of this result is necessary.

Author Response

Open Review (x) I would not like to sign my review report
( ) I would like to sign my review report Quality of English Language ( ) The English could be improved to more clearly express the research.
(x) The English is fine and does not require any improvement.

This study proposed a new concept by combining a vertical-axis turbine for tidal energy development with a horizontal-axis turbine for wave energy development. Additionally, biomimetic technology was applied to the vertical-axis turbine blades, and an optimization study was conducted. Fluid dynamic analysis techniques were employed for performance evaluation, and output performance and flow field analyses were performed. However, a re-examination of the presented CFD results is required.

1. In the process of generating experimental points using LHS, how were the ranges for each variable determined?

Thank you for pointing this out. We agree with this comment. The upper and lower limits of the parameters are shown in the table below, which is on Page 5 of the paper. The parameters can be seen from following table.

2. How many sample points were obtained through this LHS method, and what are the values of each variable at each experimental point?

Thank you for pointing this out. We agree with this comment. There are two hundred samples. The original data of each variable at each experimental point are quite numerous, so we have plotted them into a curve graph, as shown in Figure 5 of the paper. As can be seen from the figure, the sampling points well cover the upper and lower limits of each variable, and the distribution of sampling points is reasonable.

3. In the analysis results, it was reported that the efficiency of the centrifugal turbine was calculated as 69.1%, but theoretically it cannot exceed Betz’s limit. A re-examination of this result is necessary.

Thank you for pointing this out. We agree with this comment.  We recalculated the energy harvesting coefficients of the centrifugal turbine and axial-flow turbine. The new energy harvesting coefficient of the centrifugal turbine shows that Cp is maximized at 58.62% under λ=1.25 and Re=1.33×10⁵, while the axial-flow turbine achieves an optimal Cp of 57.6% at λ=1.5 and Re=5.53×10⁴. The updated curve graphs are consistent with the content in the article(page 23), and we have added a data parameter table before the graphs(table 8 and table 9).

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Most of the problems in the previous version were well resolved. However, I have one more question. In lines 427~428, the author mentioned that “based on the DOE design in the previous chapter, we obtained the optimal solution for a single airfoil: θ=22.7°, L‘=148.2%, α=0.83°, and δ=135.6%. “. First, the lines are in chapter 6, thus previous chapter is chapter 5 (Airfoil model). However, there is not any information related to DOE design in Chapter 5. Second, the goal of the optimal solution for a single airfoil should be clearly stated. Is it for highest lift, lowest drag or something else?

Author Response

Open Review

(x) I would not like to sign my review report
( ) I would like to sign my review report

Quality of English Language

( ) The English could be improved to more clearly express the research.
(x) The English is fine and does not require any improvement.

Comments and Suggestions for Authors

Most of the problems in the previous version were well resolved. However, I have one more question. In lines 427~428, the author mentioned that “based on the DOE design in the previous chapter, we obtained the optimal solution for a single airfoil: θ=22.7°, L‘=148.2%, α=0.83°, and δ=135.6%. “.

First, the lines are in chapter 6, thus previous chapter is chapter 5 (Airfoil model). However, there is not any information related to DOE design in Chapter 5.

Thank you for pointing this out. We agree with this comment. We have revised this sentence from “Based on the DOE design in the previous chapter,“ to ”Through the DOE sampling calculations in this chapter, as shown in Figures 9 and 13“。  

Second, the goal of the optimal solution for a single airfoil should be clearly stated. Is it for highest lift, lowest drag or something else?

Thank you for pointing this out. We agree with this comment. We add a sentence “The objective function is set to maximize lift and minimize drag.” in lines 148 and 149.

Submission Date

14 May 2025

Date of this review

20 Jun 2025 10:40:46

Reviewer 4 Report

Comments and Suggestions for Authors

The revised manuscript has sufficiently addressed the previously mentioned review comments, and the content can serve as a valuable reference for future related studies. Therefore, I recommend the revised manuscript for publication in the JMSE.

Author Response

Open Review

(x) I would not like to sign my review report
( ) I would like to sign my review report

Quality of English Language

( ) The English could be improved to more clearly express the research.
(x) The English is fine and does not require any improvement.

Comments and Suggestions for Authors

The revised manuscript has sufficiently addressed the previously mentioned review comments, and the content can serve as a valuable reference for future related studies. Therefore, I recommend the revised manuscript for publication in the JMSE.

Thank you, Professor, for acknowledging our work.

Submission Date

14 May 2025

Date of this review

18 Jun 2025 03:26:10

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

Consider the novelty in design of the water turbine and great effort of authors in solving problems and revising the manuscript so far, the paper is accepted for publication. However, it should be taken with caution that highest lift and lowest drag are not appropriate optimal goals for the hydrofoil in design of the water turbine. Instead, it should be the hghest moment that rotates the water turbine around its vertical axis., thus highest power harvesting. High lift and low drag do not mean high rotating moment. For example, when the water flow is perpendicular to the moment arm, high drag will lead to high rotating moment. It is recommended that the authors consider this fact in a future work.