Numerical Investigation of Hybrid Darrieus/Savonius Vertical Axis Wind Turbine Subjected to Turbulent Airflows

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I would like to thank the editor for sending me this manuscript and the authors for their effort in preparing it. I enjoyed reading the paper, and I believe that, after substantial revision, it has the potential to become an interesting research article. That being said, my main conclusion is that the manuscript requires major revisions before it can be considered further. Of course, I have to say also why I believe that this should happened. Thus, in the following, I will write my comments. First, some general ones, and then the specific ones. The specifics are more technical and, at this point, I didn’t mention many since the general picture of the paper, at least in my opinion, at this moment, is not clear.

General remarks

The first main issue of this manuscript is related to the scope of the paper. Why were the authors performing this study? Although the introduction provides context and mentions previous works, it is unclear why the numerical simulations were performed. Thus, a separate chapter, where the problem is described, should be introduced after the introduction. In other words, what is the story behind this paper?

In Chapter 3.1, the manuscript uses the term advective interpolation function (AIF). While this term may be formally correct, in the context of Ansys Fluent it would be clearer to refer to these as discretization schemes, since AIF is usually used in a different context. There, the AIF is usually used in a different context. That is the formal part of the problem related to this section. The more important issue is related to the conclusions drawn. The second-order discretization schemes appear to give worse results than the first-order scheme. Typically, first-order schemes are used only in the early stages of the simulation to aid convergence, while the final solution is obtained with higher-order schemes. While the results you obtained are fitting well with the data obtained in previous papers related to VAWT, this may actually be a case where you obtain good results but for the wrong reasons. For start, I suggest that you perform a mesh dependence study. It doesn't have to be in a transient regime.

Specific comments

1. Line 36. Reference (s) is/are needed
2. Lines 44-55. Nothing about HAWT. Some advantages. Why even think about VAWT? After all, all the fields are filled with HAWT nowadays.
3. Reference/definition needed. What are AIC and BIC?
4. After Line 129 a whole section is missing. See General remarks.
5. Line 138. I am not sure that “proportional” is the correct word. Find another way to describe the rotational region.
6. Figure 1. u=v=0 m/s????
7. Also, V_infty at line 161 is a scalar, is a vector? Is the axial component of the velocity? In the context of Figure 1, the notations are quite confusing.
8. Table 2. Why are different TSR values tested for Savonius and others for Darrieus/Hybrid?
9. I would use C_P instead of C_p. It is the power coefficient, not the pressure coefficient. Also, please be consistent. In some places, I saw P, I others, p.
10. Line 201. You should give a reference that supports this statement. I am not saying that it is not true, but it should be backed up.
11. (16). In NS equations, you are using dynamic viscosity. Here, for the definition of y+, you are using kinematic viscosity. Be consistent. Also, what is \tau_w?
12. 274-275 it’s confusing. The present study is about VAWTs or about the influence of advective interpolation functions?
13. Figure 6 and Figure 7. I think that a polar representation would give better insights. Also, why does the evolution of C_P and C_M differ with the function of the blade ?! Normally, they should be the same. Of course, out of phase, but the same.
14. Figure 6d) and Figure 7d) are the same. This should be put in a different figure.
15. Table 6. Drag instead of Moment. Also, the motivation for computing the drag coefficient is unclear. Please explain.

Author Response

Reviewer 1:

I would like to thank the editor for sending me this manuscript and the authors for their effort in preparing it. I enjoyed reading the paper, and I believe that, after substantial revision, it has the potential to become an interesting research article. That being said, my main conclusion is that the manuscript requires major revisions before it can be considered further. Of course, I have to say also why I believe that this should happened. Thus, in the following, I will write my comments. First, some general ones, and then the specific ones. The specifics are more technical and, at this point, I didn’t mention many since the general picture of the paper, at least in my opinion, at this moment, is not clear.

General remarks

The first main issue of this manuscript is related to the scope of the paper. Why were the authors performing this study? Although the introduction provides context and mentions previous works, it is unclear why the numerical simulations were performed. Thus, a separate chapter, where the problem is described, should be introduced after the introduction. In other words, what is the story behind this paper?

            We deeply appreciate the Reviewer’s thorough evaluation and detailed remarks. The suggestions provided were extremely helpful in addressing key aspects of the manuscript and in ensuring a clearer and more consistent presentation of the research.

            The main objective of the present work is to investigate the influence of a hybrid Darrieus/Savonius turbine on power performance, as well as to identify changes in its behavior compared to an isolated Darrieus configuration under the same airflow conditions. To better understand the contribution of the Savonius rotor in the hybrid setup, simulations were also performed for an isolated Savonius turbine under the same conditions. Furthermore, to gain insight into the local behavior of hybrid and Darrieus turbines, the moment and drag coefficients of each blade were monitored as a function of the rotation angle, which has not been previously investigated in the literature. Another important aspect, which represents a secondary objective, concerns the limited exploration of different computational parameters and their influence on turbine performance in literature. Therefore, distinct numerical parameters were tested here to provide recommendations regarding simulation procedures for this type of problem. The best parameters were then applied in the simulations of the hybrid Darrieus/Savonius turbine, which were compared to the isolated Darrieus and Savonius configurations. To improve the description of the work scope, the above-mentioned information was included in the revised version of the manuscript.

The main advantage of using numerical simulations is the ability to explore different conditions at a significantly lower cost than experimental setups. Consequently, several recent studies, as highlighted in the introduction, have employed this approach. However, despite these contributions, only a few numerical studies on Darrieus, Savonius, and hybrid turbines have presented the numerical procedures in detail. This lack of information motivated the present investigation, which examines different interpolation functions and provides an in-depth description of the numerical procedures applied in the simulations. In response to the reviewer’s request, the original Chapter 2 (Mathematical and Numerical Modeling) was divided into two chapters: one describing the problem and the other presenting the mathematical and numerical modeling. The problem description was thoroughly revised to improve the reader’s understanding of the study.

 

In Chapter 3.1, the manuscript uses the term advective interpolation function (AIF). While this term may be formally correct, in the context of Ansys Fluent it would be clearer to refer to these as discretization schemes, since AIF is usually used in a different context. There, the AIF is usually used in a different context. That is the formal part of the problem related to this section. The more important issue is related to the conclusions drawn. The second-order discretization schemes appear to give worse results than the first-order scheme. Typically, first-order schemes are used only in the early stages of the simulation to aid convergence, while the final solution is obtained with higher-order schemes. While the results you obtained are fitting well with the data obtained in previous papers related to VAWT, this may actually be a case where you obtain good results but for the wrong reasons. For start, I suggest that you perform a mesh dependence study. It doesn't have to be in a transient regime.

            We thank the reviewer for this very insightful and important comment.​

            We have changed the term “advective interpolation function (AIF)” to “discretization schemes” every time that the original term appears.

We agree entirely with the reviewer's premise that higher-order schemes are generally preferable for final solutions due to their lower numerical diffusion and better accuracy. Our initial expectation was to achieve better results with a second-order discretization scheme, even though the study was limited to applying a single discretization scheme throughout each entire simulation, i.e., without switching schemes during the process.

In our investigation, the simulations employing second-order upwind schemes consistently exhibited stability problems. These numerical instabilities prevented the solution from reaching convergence with low residual (1.0 × 10^-8 for mass and 1.0 × 10^-6 for the other equations). ​Given these convergence and stability issues, the first-order upwind scheme was selected for the runs. Our primary goal was to capture the overall aerodynamic performance, which we were able to achieve consistently with the first-order approach.

            A new mesh convergence analysis was performed following the Grid Convergence Index method and Richardson Extrapolation, as recommended in the literature. Three different meshes were considered, in accordance with the standard practice of the method, and the procedure was applied as described in reference [35]. The convergence analysis was carried out in hybrid turbine configuration because this is the most complex geometry, and TSR = 0.50. This ensures that the numerical results are sufficiently independent of the mesh resolution.

            A new Figure 5 was added to illustrate the convergence of the solution, and the remaining figures were renumbered. Also, a new Table 5 was introduced with the mesh parameters employed in this analysis. Furthermore, an explanation of the mesh convergence procedure and results was added, as follows:

            A mesh sensitivity analysis was conducted to ensure that the numerical results are independent of the mesh resolution. The Hybrid turbine configuration was selected for this analysis, as it represents the most complex mesh and encompasses the other configurations (Savonius solo and Darrieus solo). The mesh convergence analysis was performed for TSR = 0.50. The Grid Convergence Index (GCI) method, combined with Richardson extrapolation, was applied following the procedure described by Meana-Fernández [35].

Three meshes with varying refinement in the cross-streamwise direction were considered. Table 5 summarizes the grid characteristics near the airfoil walls and the total number of volumes for each mesh. Once the mesh independence has been confirmed, the finest mesh is used for the subsequent simulations.

Table 5. Parameters of the mesh independence study for the three computational meshes.

Mesh	Mesh 1	Mesh 2	Mesh 3
Cells in streamwise direction	300	300	300
Cells in cross-streamwise direction	130	65	32
Grid increasing ratio (cross-streamwise direction)	1.1	1.1	1.1
Number of volumes	334296	286889	253559
results for  s	0.04634	0.04609	0.04160
TSR	0.50	0.50	0.50

Figure 5 shows the variation of the mean power coefficient (C_P) as a function of the grid characteristic size (h). The points are fitted using a polynomial interpolation (dashed blue line). The curve exhibits an asymptotic behavior at C_P = 0.0463, indicated by the Richardson extrapolation point (red circle) in the figure. This confirms that the finest mesh (Mesh 1) provides results sufficiently independent of the mesh resolution.

Figure 5. Richardson extrapolation of the average power coefficient for the three meshes.

The following reference was included in the manuscript:

[35] Meana-Fernández, A.; Fernández Oro, J.M.; Argüelles Díaz, K.M.; Galdo-Vega, M.; Velarde-Suárez, S. Application of Richardson Extrapolation Method to the CFD Simulation of Vertical-Axis Wind Turbines and Analysis of the Flow Field. Engineering Applications of Computational Fluid Mechanics 2019, 13, 359–376, doi:10.1080/19942060.2019.1596160.

 

Specific comments

1. Line 36. Reference (s) is/are needed

            Two references were added to support the following statement (lines 34 - 36):

In the last decades, extreme climate events have intensified as a result of environmental changes, leading to substantial material damage, human and economic losses, and increased health risks [1,2].

[1] AR6 Synthesis Report: Summary for Policymakers Headline Statements Available online: https://www.ipcc.ch/report/ar6/syr/resources/spm-headline-statements (accessed on 23 September 2025).

[2]  Otto, F.E.L. Attribution of Extreme Events to Climate Change. Annual Review of Environment and Resources 2023, 48, 813–828, doi:10.1146/annurev-environ-112621-083538.

 

1. Lines 44-55. Nothing about HAWT. Some advantages. Why even think about VAWT? After all, all the fields are filled with HAWT nowadays.

            We thank the reviewer for this valuable comment.

Our study focuses exclusively on VAWTs. Although HAWTs dominate the wind energy sector, VAWTs remain relevant in scenarios where HAWTs are not the most suitable option, due to their large dimensions, higher noise levels, need for alignment with wind direction, and reduced efficiency under lower or more irregular wind conditions. The urban environment is a representative example of such scenarios. Therefore, the purpose of our research is precisely to investigate potential alternatives to enhance the efficiency of VAWTs, aiming to enable their broader use in specific contexts such as urban applications in the future. Another interesting aspect is related to the arrangement of turbines for VAWTs and HAWTs in offshore conditions, the association of VAWTs with oil platforms, and the advantages for situations where floating turbines are required in offshore conditions. Therefore, the study of VAWTs can bring new insights to diversify the exploitation of wind renewable energy.

Based on the above-mentioned aspects, only slight modifications were made in the text to clarify that the advantages listed for VAWTs are presented in contrast to the use of HAWTs:

Although HAWTs dominate large-scale wind farms due to their high efficiency, VAWTs present several advantages, including design simplicity, the absence of a yaw mechanism, ease of maintenance, and the ability to operate under irregular wind conditions, which makes them particularly suitable for urban applications [7]. Moreover, floating VAWTs also presented advantages in comparison with HAWTs as higher stability, lower aerodynamic wakes, easily of operation and maintainance, which can be important for implementation of offshore wind farms [X1].

[8] A. Ghigo, E. Faraggiana, G. Giorgi, G. Mattiazzo, G. Bracco. Floating Vertical Axis Wind Turbines for offshore applications among potentialities and challenges: A review. Renewable and Sustainable Energy Reviews 2024, 193, 114302. https://doi.org/10.1016/j.rser.2024.114302

 

1. Reference/definition needed. What are AIC and BIC?

            In order to improve the clarity of the manuscript, we have now included a brief explanation of the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) in the manuscript. Both are statistical criteria to predict new data based on maximum likelihood estimation.

            This explanation was included in the revised version of the manuscript.

 

1. After Line 129 a whole section is missing. See General remarks.

We revised the text to share the Mathematical and Numerical Modeling section in two sections, including a Problem description section. Please, see the modifications informed in General remarks.

 

1. Line 138. I am not sure that “proportional” is the correct word. Find another way to describe the rotational region.

            The rotational region was defined as a function of the turbine diameter in each case. Specifically, it was set to approximately 1.5 times the corresponding turbine diameter (Savonius, Darries, and Hybrid), ensuring consistency and proportionally in the computational domain. In order to clarify this question, we have changed the sentence in lines 139-140. The sentences are shown as follows:

The computational domain adopted in this study is shown in Figure 1. It is divided into two regions: a rotational zone (gray) and a stationary zone (outside the rotational zone). The diameter of the rotational region is defined to ensure that the simulation results are not influenced by domain boundaries. This value was set to approximately 1.5 times the turbine diameter, and all rotors are modeled to rotate counterclockwise under a constant angular velocity  imposed within the rotating domain to simulate a stable flow condition around the turbine.

 

1. Figure 1. u=v=0 m/s????

            In Figure 1, u = v = 0 m/s represents the no-slip boundary condition on the wall of the blades, i.e., the velocity components are null in relation to rotational region where the turbine is placed. Figure 1 has been modified to make the information more objective and clear.

 

1. Also, V_infty at line 161 is a scalar, is a vector? Is the axial component of the velocity? In the context of Figure 1, the notations are quite confusing.

            The V_infty is a scalar. This is the horizontal component of the velocity. To improve clarity, this explanation was added to the manuscript at lines 161-162.

where  represents the fluctuation averaged field (Reynolds stress), and V_∞ represents the free-stream horizontal component of the wind flow velocity [26].

            Figure 1 was also revised to improve clarity.

 

1. Table 2. Why are different TSR values tested for Savonius and others for Darrieus/Hybrid?

            The difference is related to the radius of reference used in the calculus of TSR magnitudes. For the isolated Savonius turbine, the radius of the Savonius turbine is used, while for Darrieus and hybrid configurations, the radius of the Darrieus turbine is used as a reference.

 

1. I would use C_P instead of C_p. It is the power coefficient, not the pressure coefficient. Also, please be consistent. In some places, I saw P, I others, p.

To improve the consistency of the manuscript, the text and figures were modified according to the reviewer’s comment. The changes are highlighted in red in the revised version.

 

1. Line 201. You should give a reference that supports this statement. I am not saying that it is not true, but it should be backed up.

The following references were added to support this statement:

[30] ANSYS, Inc. Ansys Fluent: User Guide; ANSYS, 2022;

[31] Menter, F.R.; Kuntz, M.; Langtry, R. Ten Years of Industrial Experience with the SST Turbulence Model. Heat and Mass Transfer, 2003.

 

1. (16). In NS equations, you are using dynamic viscosity. Here, for the definition of y+, you are using kinematic viscosity. Be consistent. Also, what is \tau_w?

            In the y+ equation, the kinematic viscosity was used because the term  represents the friction velocity . The term  represents the wall shear stress. This information was added in line 246 for clarity:

where   represents the wall shear stress (Pa).

            Equation (16) was also modified to make the manuscript more notationally consistent.

 

1. 274-275 it’s confusing. The present study is about VAWTs or about the influence of advective interpolation functions?

            The present study focuses on the VAWTs behavior in Savonius, Darrieus, and Hybrid configuration. The statement “In this study” has been replaced with “In this section” for clarity. This step is only to verify if the discretization schemes have an influence on the numerical results.

 

1. Figure 6 and Figure 7. I think that a polar representation would give better insights. Also, why does the evolution of C_P and C_M differ with the function of the blade ?! Normally, they should be the same. Of course, out of phase, but the same.

We changed the Figures according to the reviewer's request.

 

1. Figure 6d) and Figure 7d) are the same. This should be put in a different figure.

            All Figures have been revised. Figures 6d) and 7d) were unified in a new Figure 7.

 

1. Table 6. Drag instead of Moment. Also, the motivation for computing the drag coefficient is unclear. Please explain.

            The results for the moment in the turbine blades were presented in Table 5. In Table 6, we included the drag coefficient as an additional parameter, seeking to improve the comprehension of the comparison between the hybrid and isolated Darrieus and Savonius turbines.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors This paper presents a systematic and rigorous numerical study on the performance of a hybrid Darrieus/Savonius vertical axis wind turbine under turbulent conditions. The author not only verified the reliability of the isolated turbine model through detailed CFD simulations, but also delved into the performance of the hybrid configuration at different tip speed ratios, which has strong engineering application value. The research design is reasonable and the method description is clear, especially providing new insights into the improvement of Darrieus turbine self starting ability by hybrid turbines under low tip speed ratio conditions. In addition, the selection of turbulence models and the description of grid processing demonstrate the author's profound understanding of computational fluid dynamics problems. The overall work is solid and the data is sufficient, which has positive reference significance for the optimization design of wind turbines.   1. Although some relevant studies are cited in the article, there has been relatively little progress in recent years in the optimization of hybrid turbine structures, the application of new airfoils, and field synergy effects. Suggest adding more recent literature from 2020 onwards to enhance the comprehensiveness and timeliness of the argument background.   2. The text in some illustrations is too small, the line differentiation is insufficient (such as Figures 5 and 6), and there is a lack of necessary legend explanations. Suggest re optimizing the image resolution and unifying the annotation style to enhance readability and scientificity.   3. The author may appropriately increase the discussion on the practical engineering application potential and current model limitations of the research results to enhance the depth and practicality of the paper.

Author Response

Reviewer 2:

This paper presents a systematic and rigorous numerical study on the performance of a hybrid Darrieus/Savonius vertical axis wind turbine under turbulent conditions. The author not only verified the reliability of the isolated turbine model through detailed CFD simulations, but also delved into the performance of the hybrid configuration at different tip speed ratios, which has strong engineering application value. The research design is reasonable and the method description is clear, especially providing new insights into the improvement of Darrieus turbine self starting ability by hybrid turbines under low tip speed ratio conditions. In addition, the selection of turbulence models and the description of grid processing demonstrate the author's profound understanding of computational fluid dynamics problems. The overall work is solid and the data is sufficient, which has positive reference significance for the optimization design of wind turbines.  

We sincerely thank the Reviewer for the valuable comments and insightful recommendations. These observations have been carefully considered and incorporated into the revised manuscript, leading to significant improvements in clarity, organization, and scientific quality.

 

1. Although some relevant studies are cited in the article, there has been relatively little progress in recent years in the optimization of hybrid turbine structures, the application of new airfoils, and field synergy effects. Suggest adding more recent literature from 2020 onwards to enhance the comprehensiveness and timeliness of the argument background.  

It was identified that the main progress in optimization is restricted to isolated Darrieus and Savonius turbines. We had several difficulties in finding recent works related to the optimization of hybrid turbines. We observed in the literature two recent studies related to the optimization of a pair and one arrangement with three turbines. These references were included in the revised version of the manuscript:

[15] M.H. Abdel-razak, M. Emam, S. Ookawara, H. Hassan, Study the performance of a novel design of twin hybrid Darrieus-Savonius vertical-axis wind turbines integrated with building water storage tanks: 3D optimization study, Renewable Energy 2026, 256, 124024. Doi: https://doi.org/10.1016/j.renene.2025.124024

[16] M.H. Abdel-razak, M. Emam, S. Ookawara, H. Hassan, Optimization of the power performance for three hybrid Darrieus-Savonius rotors based on the Taguchi method, Journal of Physics: Conference Series 2024, 2857, 012011. Doi: 10.1088/1742-6596/2857/1/012011

 

2. The text in some illustrations is too small, the line differentiation is insufficient (such as Figures 5 and 6), and there is a lack of necessary legend explanations. Suggest re optimizing the image resolution and unifying the annotation style to enhance readability and scientificity.  

            All the Figures have been revised to improve their quality and readability. We have changed the legend of Figures to improve explanations.

 

3. The author may appropriately increase the discussion on the practical engineering application potential and current model limitations of the research results to enhance the depth and practicality of the paper.

            We thank the reviewer for the recommendation.

The text of the results section was revised to include insights about current model limitations and practical engineering applications of the research performed in the present work.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper deals with the hybrid Darrieus/Savonius VAWT topic by investigating numerically the performances of a such wind turbine under turbulent airflows. The simulation results of 37 scenarios show interesting and useful conclusions. The paper presents a significant contribution on the topic, the manuscript is well organized, and the results are extensively commented on.  Noteworthy the excellent English style. However, the manuscript should be revised as there are several issues to be addressed for the sake of clarity and simplicity.

 

Minor issues

1. Abstract: please define explicitly the novelty addressed by your research.
2. Proposal to consider the much significant syntagma “AuthorName et al. [x]...” instead of anonymous “[x] did…” or “Ref. [x]”. E.g. “[8] performed…”, “Ref. [4]”, etc.
3. Typically, the paper structure (its remaining Sections) is briefly presented at the end of Introduction.
4. Solve the typing mistakes, e.g. “Leeward wind” – probably “leeward”, “Arrieta-Gomez et al” – obviously, use “et al.”, “800mm” – use a space char between a value and its unit, etc. Check carefully the entire manuscript for other similar mistakes.
5. “Total of 37 simulations are performed” Justify this number of simulations (why not more or less). Is it the optimum number of simulations? Similarly, the selection of TSR value range.
6. “Moment coefficient Cd ̅̅̅̅” (Table 6) – probably “drag coefficient”. Define it!

 

 

Major issues

7. The literature review: state clearly the limits of the recent results in literature, the specific gap and the new / innovative aspects of your approach. The statement “the exploration of different computational parameters on the turbine’s performance have been explored few” must be better justified, state explicitly the addressed parameters, and thus justifying the gap and your novel approach.
8. A flowchart of the proposed approach is welcomed before introducing all mathematical approaches.
9. “the Darrieus and Savonius turbines are assumed to have the same height.” This assumption should be commented by considering the influence of real cases of hybrid VAWTs where the two turbines have constructively different heights, when Savonius rotor is placed at the middle of a Darrieus rotor. A second comment is needed on the wind speed received by the Savonius turbine.
10. “For the validation cases, the turbine dimensions were set as follows: the Darrieus turbine had a diameter of 800mm, and Savonius turbine, 1800mm.” By considering the proposed simulation study on the hybrid VAWT where “the Darrieus and Savonius diameters were DD = 800mm and DS = 320mm”, please comment the portability of Savonius turbine simulation values (DD = 800mm) vs. validation values (DD = 1800mm). Generally, the assumptions must be completely and extensively introduced.

Author Response

Reviewer 3:

The paper deals with the hybrid Darrieus/Savonius VAWT topic by investigating numerically the performances of a such wind turbine under turbulent airflows. The simulation results of 37 scenarios show interesting and useful conclusions. The paper presents a significant contribution on the topic, the manuscript is well organized, and the results are extensively commented on.  Noteworthy the excellent English style. However, the manuscript should be revised as there are several issues to be addressed for the sake of clarity and simplicity.

            We thank the Reviewer for the substantial recommendations, which have greatly contributed to improving the clarity, rigor, and overall quality of the manuscript. We carefully addressed each comment and incorporated the suggested changes, which we believe have strengthened the paper and made it more consistent.

Minor issues

1. Abstract: please define explicitly the novelty addressed by your research.

            We revised the abstract to reinforce the novelty of the work.

 

1. Proposal to consider the much significant syntagma “AuthorName et al. [x]...” instead of anonymous “[x] did…” or “Ref. [x]”. E.g. “[8] performed…”, “Ref. [4]”, etc.

            To make the manuscript more consistent, the recommendation was attended and all references have been revised.

 

1. Typically, the paper structure (its remaining Sections) is briefly presented at the end of Introduction.

            We thank the reviewer for this helpful suggestion. Following this recommendation, an outline of the paper structure has been introduced at the end of the introduction section as follows (lines 131 - 138):

            The remainder of this paper is organized as follows. Section 2 presents the problem description, including the computational domain, boundary conditions and the performance indicators of the turbines. Section 3 details the mathematical and numerical model, describing the governing equations, the simulation parameters, the mesh parameters employed, and the ANSYS Fluent setup. Section 4 presents the results and discussion, including the influence of the discretization schemes, numerical model validation, mesh independence study, and turbine behavior and performance indicators for the different cases. Finally, Section 5 summarizes the main conclusions of the research.

 

1. Solve the typing mistakes, e.g. “Leeward wind” – probably “leeward”, “Arrieta-Gomez et al” – obviously, use “et al.”, “800mm” – use a space char between a value and its unit, etc. Check carefully the entire manuscript for other similar mistakes.

            The manuscript was revised to correct these mistakes and to avoid further errors.

 

1. “Total of 37 simulations are performed” Justify this number of simulations (why not more or less). Is it the optimum number of simulations? Similarly, the selection of TSR value range.

            The number of simulations was defined based on the minimum number of cases necessary to allow a comprehensive investigation of the numerical parameters to be used in the computational method, to obtain the verification/validation for isolated configurations (Darrieus and Savonius), and to obtain new recommendations on the effect of TSR on the power coefficient for three different configurations: hybrid, Darrieus, and Savonius. The total computational effort for all performed simulations were nearly 1200 h (50 days). Previous tests for grid independence mesh, definition of the number of cells along and transversal to the blades, and tests with distinct turbulence closure models were not counted in the number of total simulations.

 

1. “Moment coefficient Cd ̅̅̅̅” (Table 6) – probably “drag coefficient”. Define it!

            We thank the reviewer for the observation. This error has been fixed.

 

Major issues

1. The literature review: state clearly the limits of the recent results in literature, the specific gap and the new / innovative aspects of your approach. The statement “the exploration of different computational parameters on the turbine’s performance have been explored few” must be better justified, state explicitly the addressed parameters, and thus justifying the gap and your novel approach.

            We revised the abstract to reinforce the main contribution of the present work. Moreover, we also revised the last paragraph of introduction seeking to explain in more detail the novelty of the present paper and the parameters investigated in the present work.

 

1. A flowchart of the proposed approach is welcomed before introducing all mathematical approaches.

            We revised the methodology, sharing the Mathematical and Numerical modeling section in two different sections: problem description, and the mathematical and numerical modeling. We also rigorously revised these two sections to clarify for the reader the studied problem, the cases to be simulated, and the procedures employed in the simulations.

 

1. “the Darrieus and Savonius turbines are assumed to have the same height.” This assumption should be commented by considering the influence of real cases of hybrid VAWTs where the two turbines have constructively different heights, when Savonius rotor is placed at the middle of a Darrieus rotor. A second comment is needed on the wind speed received by the Savonius turbine.

We thank the Reviewer for this important comment.

It is indeed true that some hybrid models adopt different heights between the turbines. However, others are designed with equal heights for both rotors. In this study, we assumed the latter configuration for the following reasons: (a) the investigation conducted here did not address geometric variations of the turbines, including for example the ratio between heights of two rotors; (b) in two-dimensional cases, it becomes impractical to employ different heights between turbines in the hybrid configuration, but it is possible to observed some trends in the interaction between the turbines (for simplified condition where ratio between the heights of turbines are unity); (c) we assume that, for a given height ratio between the turbines, a similar trend in the power coefficient would be obtained, i.e., the C_P as function of TSR​ curve would likely present a similar behavior, although with different magnitudes. We agree with the reviewer that the wind speed received by the Savonius turbine can be affected by the height ratios of the rotors, but it is out of the scope of the present study.

To clear the limitations adopted here, the manuscript was revised to highlight the simplifications of the study in problem description and results sections of the manuscript.

 

1. “For the validation cases, the turbine dimensions were set as follows: the Darrieus turbine had a diameter of 800mm, and Savonius turbine, 1800mm.” By considering the proposed simulation study on the hybrid VAWT where “the Darrieus and Savonius diameters were DD = 800mm and DS = 320mm”, please comment the portability of Savonius turbine simulation values (DD = 800mm) vs. validation values (DD = 1800mm). Generally, the assumptions must be completely and extensively introduced.

We thank the reviewer for this important comment.

We performed different simulations for the validation/verification investigation of the Savonius turbine, and simulations for the comparison among hybrid, isolated Darrieus, and isolated Savonius turbines.

            At the beginning of our investigation, the Savonius turbine had a diameter of D_S = 1800 mm since our research group had previously performed the validation/verification in the works of dos Santos et al. [24] and Santos et al. [20] using this dimension. However, when we constructed the hybrid configuration, this original dimension of the Savonius turbine could not be adopted due to the diameter is higher than that planned for the Darrieus turbine. Then, we reduced the size of the Savonius turbine, keeping constant the Reynolds number, and the overlap parameters e/c and s/c. We remade the curve of C_P as a function of TSR for the new size D_S = 320 mm and for Re_DS = 867,000 with the purpose to validate the code using the reduced size. Then, the verification/validation cases with D_S = 1800 mm had no function in the present study, being this discussion removed. For the comparison with hybrid turbine, the simulation of the Savonius turbine changed the Reynolds number to 1.73 × 10⁵ due to imposition of velocity used in Darrieus rotor.

To avoid mistakes about the verification/validation process of Savonius turbine and the study of comparison with hybrid configuration, the problem description section was rigorously revised and the information about Savonius turbine was corrected in the manuscript. 

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

No additional recommendations.