A Simplified Optimization Model for Hydrokinetic Blades with Diffuser and Swept Rotor
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsPlease read the attachment. Thank you.
Comments for author File: 
Comments.pdf
Author Response
Detailed Response to Reviewer 1
We are pleased to resubmit the revised version of sustainability-2670021 “Sweep Effect and Cavitation Analysis on the Optimization of Diffuser-Augmented Hydrokinetic Blades”. We appreciated the constructive comments and criticisms of the Reviewer. We have addressed each of his concerns as outlined below.
Reviewers’ Comments
General comments:
The manuscript explores the optimization of hydrokinetic turbine blades equipped with a diffuser to mitigate cavitation. The authors focus on the impact of blade sweep angles on cavitation and use a novel optimization procedure considering both the sweep effect and the presence of a diffuser. The study claims to offer valuable insights into designing hydrokinetic turbine blades to enhance performance while minimizing cavitation risks. Overall, the manuscript presents a clear and well-structured investigation of the subject matter. However, several points should be addressed to strengthen the manuscript. In short, the paper presents relevant and timely research. It contributes to the existing literature on the impact of the pandemic on food systems and the role of SFSCs in enhancing resilience.
Specific comments:
- Keywords: Please provide between 5 and 10 keywords that are not repeated in the words or phrases on the title.
Answer: Thank you for your suggestion. The keywords were changed as per the suggestion.
- Introduction: please add a paragraph to introduce the outline of the manuscript.
Answer: Thank you for your comment. We have added a paragraph about the outline of the manuscript in Introduction.
- All equations should be mentioned or explained in the main text.
Answer: Thank you for your suggestion. We corrected this in the manuscript, mentioned the equations in the text and replaced "Eq." for “equation”, marked in red.
- Figures in the main text should be unique usages. In this manuscript, sometimes the authors use “Fig. x” and “Figure x.” Please revise them and use only one style.
Answer: Thank you for your suggestion. We corrected this in the manuscript, replaced "Fig." for “Figure”, marked by red.
- Please provide a mesh-independent test.
Answer: We appreciate your comment. The work uses BEMT as a methodology, therefore, we disregard an independent mesh test. This methodology is essentially an integral method, with semi-empirical information from aerodynamics forces in airfoil sections issued from two-dimensional airfoil flow model or experimental data. A text on this explanation was added at the beginning of page 3.
- The literature review could be expanded to include a more comprehensive overview of existing research on hydrokinetic turbine blade design, cavitation
mitigation techniques, and the role of diffusers. This addition would help readers better understand the research gaps the manuscript aims to address. Literature review: Please add more literature reviews of supply chains related to the current topic. The following works could be helpful.
+ CFD Analysis and Optimum Design for a Centrifugal Pump Using an Effectively Artificial Intelligent Algorithm
+ Centrifugal Pump Design: An Optimization.
Answer: The authors would like to thank the reviewer for the comments. We updated the literature review with relevant content added in the Introduction. Additional texts (marked in red) have been included. The following references have been added:
- Nunes, M. M; Mendes, R. C.F; Oliveira, T. F.; Brasil Junior, A. C.P. An experimental study on the diffuser-enhanced propeller hydrokinetic turbines. Renewable Energy 2019, 133, 840–848.
- Stadler, C. ; Wack, J. ; Riedelbauch, S. Investigation of the Operating Principle of Diffuser Augmented Hydrokinetic Turbines. IOP Conference Series: Earth and Environmental Science 2021, 774, 012138.
- Rezek, T.J. ; Camacho, R.G.R. ; Filho, N. M. ; Limacher, E.J.Design of a Hydrokinetic Turbine Diffuser Based on Optimization and Computational Fluid Dynamics. Applied Ocean Research 2021, 107, 102484.
- Wang, C.-N.; Yang, F.-C.; Nguyen, V.T.T.; Vo, N.T.M. CFD Analysis and Optimum Design for a Centrifugal Pump Using an Effectively Artificial Intelligent Algorithm. Micromachines 2022, 13, 1208.
- Nguyen, V. T. T. ; Vo, T. M. N. Centrifugal Pump Design: An Optimization. In International Conference on Research in Engineering, Technology and Science (ICRETS), July 01-04, 2022, Baku/Azerbaijan.
- Li, G.; Ding, X.; Wu, Y.; Wang, S.; Li, D.; Yu, W.; Wang, X.; Zhu, Y.; Guo, Y. Liquid-vapor two-phase flow in centrifugal pump: Cavitation, mass transfer, and impeller structure optimization. Vacuum 2022, 201, 111102.
- Amoozgar, M.R.; Shaw, A.D.; Friswell, M.I. The effect of curved tips on the dynamics of composite rotor blades. Aerospace Science and Technology 2020, 106, 106197.
- Sessarego, M.; Feng, J. ; Ramos-Garcia, N.; Horcas, S. G. Design optimization of a curved wind turbine blade using neural networks and an aero-elastic vortex method under turbulent inflow. Renewable Energy 2020, 146, 1524-1535.
- Thangavelu, S. K. ; Chow, S. F. ; Sia, C. C. V. ; Chong, K. H. Aeroelastic performance analysis of horizontal axis wind turbine (HAWT) swept blades. Materials Today: Proceedings 2021, 47, 4965–4972.
- Verelst, D. R.; Larsen, T. J. Load Consequences when Sweeping Blades - A Case Study of a 5 MW Pitch Controlled Wind Turbine. In Danmarks Tekniske Universitet, Riso National laboratoriet for Baredygtig Energi.Denmark. Forskningscenter Risoe. Risoe-R No. 1724(EN)
- Abutunis, A.; Hussein, R.; Chandrashekhara, K. A neural network approach to enhance blade element momentum theory performance for horizontal axis hydrokinetic turbine application. Renewable Energy 2019, 136, 1281–1293.
- Tahir, A.; Elgabaili, M. ; Rajab, Z. ; Buaossa, N. ; Khalil , A.; Mohamed, F. Optimization of small wind turbine blades using improved blade element momentum theory. Wind Engineering 2019, 43, 299–310. 357.
- Vaz, J.; Wood, D. Blade element analysis and design of horizontal-axis turbines. In Small Wind and Hydrokinetic Turbines; Clausen, P., Whale, J., Wood, D., Eds.; 1. ed. Institution of Engineering and Technology. 2021; pp. 157– 191.
- Hou, H. Shi, W.; Xu, Y.; Song, Y. Actuator disk theory and blade element momentum theory for the force-driven turbine. Ocean Engineering2023, 285, 115488.
- Conclusion: The conclusion summarizes the key findings and contributions of the manuscript well. However, it would be beneficial to offer insights into potential future research directions or practical applications stemming from this work.
Answer: Thank you for the comment. We added a paragraph suggesting future work in the Conclusion.
- Please format the manuscript as the journal template.
Answer: Thank you. The article was corrected in the Template of the Journal.
- References: please improve the related work with some essential references
missing.
Answer: Thank you for your comment. The work references were reviewed as suggested.
Constructive questions:
- How does the proposed optimization procedure specifically account for the combined effects of blade sweep angles and diffusers on hydrokinetic turbine performance, and can you provide more insights into the mathematical formulation or algorithms used in this procedure?
Answer: Thank you for your constructive question. So, according to Gemaque et al. [25], the sweep effect may strongly increase non shrouded turbine performance operating at tip-speed ratio higher than 4. But they did their study only for hydrokinetic turbine without diffuser. We are unaware of any study for analyzing turbine performance with both effects, sweep and diffuser. To include these effects into BEMT model for performance analysis it is complex due to the variation of tip-speed ratio. In our case, we expect the same behavior as found by Gemaque et al. [25]. The objective of this work is to propose an optimization method to reduce or even eliminate cavitation from hydrokinetic blades using sweep effect, as diffuser increases such a phenomenon.
- In light of the findings that certain sweep angles can mitigate or even prevent cavitation, could the manuscript discuss the practical implications of these optimized blade designs for the hydrokinetic turbine industry, such as potential improvements in energy extraction, turbine longevity, and operational efficiency?
Answer: The procedure has the potential to improve turbine longevity because cavitation leads to performance loss and damage to the blade surfaces. This occurs because cavitation is a two-phase (water and water-vapor) interaction that involves vaporization of water and condensation of water-vapor. Cavitation primarily occurs in separated, accelerated and recirculating flow regions near curved surfaces, such as in the turbine rotor. So, avoiding cavitation certainly may improve operational efficiency. Also, as stated before, the authors expect that the turbine performance will increase using the combined effects of diffuser and sweep. However, more studies need to be done.
The reviewer hopes that his point of view could help the authors improve their work and highly appreciates your contributions.
Answer: The authors really appreciated all the constructive comments, suggestions, and criticisms of the Reviewer.
Thank you for reading.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for Authors1. The abstract is too long. Please limit the number of words.
2. The method of this paper adopts computational fluid dynamics, however, the article does not mention simulation methods, setting of boundary conditions and the computational domain. Please complete it.
3. This article does not indicate the correctness of the computational simulation scheme. There are no experimental data to verify that your calculation method is correct or other aspects to explain the feasibility of the calculation scheme. Please add this content.
4. The conclusion should be clear and concise.This article is about optimization of diffuser-augmented hydrokinetic blades, so what is the optimal structure of the blade.
5. The numbers in figure 6 are overlapped and missing a parenthesis. Figure 7 lack of units in the ordinate.
6. This article is about the blade optimization. So the pressure distribution on the blade is very important. What is the effect of cavitation on the efficiency of the blade? Please improve this part.
Author Response
Detailed Response to Reviewer 2
We are pleased to resubmit the revised version of sustainability-2670021 “Sweep Effect and Cavitation Analysis on the Optimization of Diffuser-Augmented Hydrokinetic Blades”. We appreciated the constructive comments and criticisms of the Reviewer. We have addressed each of his concerns as outlined below.
Comments and Suggestions for Authors:
Review
1.The abstract is too long. Please limit the number of words.
Answer: Thank you for your comment. The abstract was reduced to 197 words, adhering to the maximum limit of 200 words.
2.The method of this paper adopts computational fluid dynamics, however, the article does not mention simulation methods, setting of boundary conditions and the computational domain. Please complete it.
Answer: Thank you for your comment. The method used in this article is based on BEMT (Blade Element Momentum Theory), which does not consider three-dimensional aspects of the flow around the rotor. A more refined description of the flow based on the CFD method was not addressed, however, it is suggested for future work. BEMT methodology is essentially an integral method, with semi-empirical information from aerodynamics forces in airfoil sections issued from two-dimensional airfoil flow model or experimental data. A text on this explanation was added at the beginning of page 3.
3.This article does not indicate the correctness of the computational simulation scheme. There are no experimental data to verify that your calculation method is correct or other aspects to explain the feasibility of the calculation scheme. Please add this content.
Answer: Thank you for your suggestion. So, as stated before, BEMT is essentially an integral method, with semi-empirical information from aerodynamics forces in airfoil sections issued from two-dimensional airfoil flow model or experimental data. The optimization method was compared with Silva et al. [28], as the authors are unaware of any experimental study on swept rotors with diffuser available in the literature.
- The conclusion should be clear and concise. This article is about optimization of diffuser-augmented hydrokinetic blades, so what is the optimal structure of the blade.
Answer: Thank you for your comment. The proposed optimization is applied for any operating condition of the turbine. So, to get the optimal structure of the blade, first it is necessary to know the operating condition of the rotor, which depends on the site where the turbine will be placed. We improved the Conclusion with this information.
- The numbers in figure 6 are overlapped and missing a parenthesis. Figure 7 lack of units in the ordinate.
Answer: Thank you, figures 6 and 7 were corrected in the text.
- This article is about the blade optimization. So, the pressure distribution on the blade is very important. What is the effect of cavitation on the efficiency of the blade? Please improve this part.
Answer: Thank you for your comment. We have added the explanation in the introduction.
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsReview
1. In this study, the authors present a new optimization model applied to hydrokinetic turbines with diffuser and swept blades. The research is very interesting and it has great potential for hydrodynamic turbine design engineers.
Comment 1: At what sweep angles did the authors study cavitation process?
Comment 2: It is not entirely clear from the work which factor is most significant in reducing cavitation ‒ the sweep or diffuser of the blade?
2. The "Introduction" section is presented clearly and in detail.
3. The "Sweep Effect on the Blade Element Momentum Theory with Diffuser" section contains detailed information on theories of axial moment and blade element momentum, including optimization model for swept blades under diffuser effect.
4. The main "Results and Discussion" section of the paper are quite informative and does not raise doubts about their reliability.
Comment 3: The study is purely theoretical without any comparison with experiment. Have such hydrokinetic turbines been or will they be studied experimentally?
5. The "Conclusions" section quite fully reflects the goals of the study set by the authors. Based on the results obtained, the authors established that the diffuser increases the possibility of cavitation, because it increases the axial velocity on the blade, but the sweep effect can avoid it.
6. The number of self-citations meets the requirements of the Sustainability journal and is less than 15 percent. Most of the cited publications contain relevant and up-to-date information.
In general, the paper contains interesting results on the study of sweep effect and cavitation analysis on the optimization of diffuser-augmented hydrokinetic blades and it has scientific value for Sustainability journal readers. I recommend accepting the paper after correcting minor editing English in the text.
Comments on the Quality of English LanguageI recommend accepting the paper after correcting minor editing English in the text.
Author Response
Detailed Response to Reviewer 2 We are pleased to resubmit the revised version of sustainability-2670021 “Sweep Effect and Cavitation Analysis on the Optimization of Diffuser-Augmented Hydrokinetic Blades”. We appreciated the constructive comments and criticisms of the Reviewer. We have addressed each of his concerns as outlined below.
Comments and Suggestions for Authors:
Review
1.The abstract is too long. Please limit the number of words.
Answer: Thank you for your comment. The abstract was reduced to 197 words, adhering to the maximum limit of 200 words.
2.The method of this paper adopts computational fluid dynamics, however, the article does not mention simulation methods, setting of boundary conditions and the computational domain. Please complete it.
Answer: Thank you for your comment. The method used in this article is based on BEMT (Blade Element Momentum Theory), which does not consider three-dimensional aspects of the flow around the rotor. A more refined description of the flow based on the CFD method was not addressed, however, it is suggested for future work. BEMT methodology is essentially an integral method, with semi-empirical information from aerodynamics forces in airfoil sections issued from two-dimensional airfoil flow model or experimental data. A text on this explanation was added at the beginning of page 3.
3.This article does not indicate the correctness of the computational simulation scheme. There are no experimental data to verify that your calculation method is correct or other aspects to explain the feasibility of the calculation scheme. Please add this content.
Answer: Thank you for your suggestion. So, as stated before, BEMT is essentially an integral method, with semi-empirical information from aerodynamics forces in airfoil sections issued from two-dimensional airfoil flow model or experimental data. The optimization method was compared with Silva et al. [28], as the authors are unaware of any experimental study on swept rotors with diffuser available in the literature.
- The conclusion should be clear and concise. This article is about optimization of diffuser-augmented hydrokinetic blades, so what is the optimal structure of the blade.
Answer: Thank you for your comment. The proposed optimization is applied for any operating condition of the turbine. So, to get the optimal structure of the blade, first it is necessary to know the operating condition of the rotor, which depends on the site where the turbine will be placed. We improved the Conclusion with this information.
- The numbers in figure 6 are overlapped and missing a parenthesis. Figure 7 lack of units in the ordinate.
Answer: Thank you, figures 6 and 7 were corrected in the text.
- This article is about the blade optimization. So, the pressure distribution on the blade is very important. What is the effect of cavitation on the efficiency of the blade? Please improve this part.
Answer: Thank you for your comment. We have added the explanation in the introduction.
Author Response File: Author Response.docx
Reviewer 4 Report
Comments and Suggestions for AuthorsDear Authors,
The paper attempts to address the effect of sweep for hydrokinetic turbines along with a diffuser to increase the efficiency further than the Betz limit. The problem statement is clear and the method implemented does show promise however it needs a bit more scientific rigor to have more value.
1) The title should include 'low fidelity' since that is the space where the design and optimization is conducted
2) Define the radial transformation function used. Explain the tool used for BEMT analysis, what numerical method is used to converge the solution. Has any validation been done with your adaptation of the tool? It is important to validate.
3) Which airfoil is used? How are you getting the lift and drag values for it?
4) Please explain your optimizer in a subsection. What is the method used, how many iterations and why this particular method was chosen.
5) Could you plot the axial and induction factors for the swept blades and compare them with the unswept ones?
6) How do you deal with the angle of attack correction due to the sweep? In other words, your effective angle of attack for swept blades is different than the unswept blade.
7) Have you looked at the stress for these highly swept blades? They need to be addressed.
Comments on the Quality of English LanguageI would suggest just reading once more to catch any missed errors.
Author Response
Detailed Response to Reviewer 4 We are pleased to resubmit the revised version of sustainability-2670021 “Sweep Effect and Cavitation Analysis on the Optimization of Diffuser-Augmented Hydrokinetic Blades”. We appreciated the constructive comments and criticisms of the Reviewer. We have addressed each of his concerns as outlined below.
Comments and Suggestions for Authors
Dear Authors,
The paper attempts to address the effect of sweep for hydrokinetic turbines along with a diffuser to increase the efficiency further than the Betz limit. The problem statement is clear and the method implemented does show promise however it needs a bit more scientific rigor to have more value.
1) The title should include 'low fidelity' since that is the space where the design and optimization is conducted.
Answer: Thank you for your suggestion, but we do not understand the meaning in to include “low fidelity” in the paper title??? As stated in [19] chapter 7, models based on BEMT are accurate. It is further investigated in [26]. BEMTmethodology is essentially an integral method, with semi-empirical information from aerodynamics forces in airfoil sections issued from two-dimensional airfoil flow model or experimental data. A text on this explanation was added at the beginning of page 3. Please we ask the Reviewer to clarify his suggestion, and thanks in advance.
2) Define the radial transformation function used. Explain the tool used for BEMT analysis, what numerical method is used to converge the solution. Has any validation been done with your adaptation of the tool? It is important to validate.
Answer: Thank you for your comment. The proposed optimization is solved straightforward through the analytical equations (14), (16) and (18). Only equation (14) needs the Newton-Raphson method. This is because the procedure is based on BEMT methodology, which uses energy, momentum, and mass conservation applied to the control volume illustrated in Figure 1.
3) Which airfoil is used? How are you getting the lift and drag values for it?
Answer: Thank you for your comment. The airfoil used is NACA 65(3) - 618 as described by [28]. This is informed in subsection 3.1. According to [28], lift and drag were obtained using the free software XFoil, for Reynolds number between 1x106 to 3x106 for a rotor with 10 m diameter, as in Table 1.
4) Please explain your optimizer in a subsection. What is the method used, how many iterations and why this particular method was chosen.
Answer: Thank you for your comment. A text explain the proposed optimization was added right before the Algorithm 1.
5) Could you plot the axial and induction factors for the swept blades and compare them with the unswept ones?
Answer: Thank you for your comment. Figure 9 was added, which shows that the optimum axial induction factor is constant for straight and swept blades in the proposed model (a = 0.128). This result is expected, as equation (14) depends only on the diffuser parameters. On the other hand, the tangential induction factor, a', varies for each blade section, but not in relation to the sweep angle. This occurs because a' is inversely proportional to the local speed ratio, equation (17). The main effect of the optimization is on the geometric parameters, chord and twist angle, equations (16) and (18), respectively, which strongly vary with the radial transformation shown in equation (1). A text on this explanation was added right before Figure 8.
6) How do you deal with the angle of attack correction due to the sweep? In other words, your effective angle of attack for swept blades is different than the unswept blade.
Answer: Thank you for your comment. So, optimization models based on BEMT, as Glauert’s approach, uses fixed angle of attack, in which the blade is optimized to ensure that the effective angle of attack has an optimum value at each section. The optimum angle of attack is assumed to be the one at maximum Cl/Cd. A text to clarify this was added right before the Algorithm 1.
7) Have you looked at the stress for these highly swept blades? They need to be addressed.
Answer: Thank you for your comment. So, the authors did not have a look to the stress of swept blades, as the present paper deal with hydrodynamic optimization. But we agree with the reviewer that it is an important issue to be addressed for a future work. A text on this regard was added at the end of the Conclusion section.
Comments on the Quality of English Language: I would suggest just reading once more to catch any missed errors.
Answer: Thank you for your comment. The paper has been thoroughly reviewed to improve quality of English Language. We have also improved the poor expressions.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe revisions have been well completed based on the previous review comments. The conclusion is suggested to be concise.
Author Response
Detailed Response to Reviewer 2
We are pleased to resubmit the revised version of sustainability-2670021 “Sweep Effect and Cavitation Analysis on the Optimization of Diffuser-Augmented Hydrokinetic Blades”. We appreciated the constructive comments and criticisms of the Reviewer. We have addressed each of his concerns as outlined below.
Comments and Suggestions for Authors:
Review
The revisions have been well completed based on the previous review comments. The conclusion is suggested to be concise.
Answer: Thank you for your suggestion. The Conclusion now is more concise as described below:
“The present work presents a new optimization model for hydrokinetic turbines, considering diffuser and swept blades. The analysis highlights the influence of sweep and diffuser on the chord and blade twist distribution, avoiding cavitation in swept rotors. The proposed optimization, based on BEMT with a radial transformation function, demonstrated the importance of considering the sweep effect on the circulation and loss of the blade tip, whereas the Prandtl factor proved to be insensitive to the sweep effect, as it is on classical models that do not foresee this effect. Regarding cavitation, under the criterion of the minimum pressure coefficient in the string optimization process, it was observed that this phenomenon did not occur in each radial section. Therefore, the sweep effect (for β > 27◦) is the most significant factor in reducing cavitation in hydrokinetic turbines with a diffuser. This work theoretically investigated the sweep and diffuser effects on hydrokinetic turbine blades. In future research, blades optimized with this model will be manufactured to obtain experimental results. Furthermore, as a suggestion for future work, the occurrence of cavitation in the rotor blades can be analyzed through numerical simulation using CFD, which can be compared with the results obtained in this work. Additionally, stress on high sweep angle blades is an important issue to be addressed in the future.”
Author Response File: Author Response.docx
Reviewer 4 Report
Comments and Suggestions for AuthorsDear Authors,
This revision looks good.
The comment about low-fidelity is that if no 3D CFD is performed then it is thought as a low-fidelity model. Hence it is important for the title to be appropriate with the level of complexity in numerical modeling implemented.
The manuscript is accepted once the title is corrected as mentioned.
Author Response
Detailed Response to Reviewer 4
We are pleased to resubmit the revised version of sustainability-2670021 “Sweep Effect and Cavitation Analysis on the Optimization of Diffuser-Augmented Hydrokinetic Blades”. We appreciated the constructive comments and criticisms of the Reviewer. We have addressed each of his concerns as outlined below.
Comments and Suggestions for Authors
Dear Authors,
This revision looks good.
Answer: The authors are thankful to the reviewer comments and suggestions to improve the paper.
The comment about low-fidelity is that if no 3D CFD is performed then it is thought as a low-fidelity model. Hence it is important for the title to be appropriate with the level of complexity in numerical modeling implemented.
The manuscript is accepted once the title is corrected as mentioned.
Answer: Thank you for your explanation. The title has been modified, including the term “A Simple Optimization Model” as follows:
"A Simplified Optimization Model for Hydrokinetic Blades with Diffuser and Swept Rotor"
Author Response File: Author Response.docx
