Impeller Optimization in Crossflow Hydraulic Turbines

Round 1

Reviewer 1 Report

This paper present an interesting research, the part of numerical simulation  need to be improve, and the structure of the paper need to be change.

Review the reference of the paper. Also, in some part of the text, the author duplicate the name of the tables.

Introduction: the introduction needs to be improved with description of similar case of study.

Fluid dynamics investigation

Line 169: why you select this size of the mesh? Do you do a sensitive analysis of the mesh quality?

What is the effect of turbulence in the turbine? Maybe it is the reason for the variation of differente number of blades of different aurthors specify in the table 2.

Why you use a 2D hydraulic model in both of 3D numerical simulation, it is a crossflow turbine that have a three-dimensional behaviour, it can generate some effect in the results? What is the flow rate introduce? Do you campare with different flow rate, or only with one comparison between 2D and 3D?

The proposed methodology for impeller design: The method of the paper need to be before.

Conclusions: The conclusion need to be rewrite, quantify the results of the paper.

Figure 13: Describe with lines and name.

Figure 1, Figure3: Include the size or measure of the model.

In the Figure 3: specify the bondary conditions of the numerical model.

Describe n/nmax of the figure 3, because it is not describe in the paper.

Figure 7: Change the scale of the level, because the range is too big.

Author Response

Dear Reviewer,

we would like to thank you for your careful and thorough reading of this paper and for the comments and the constructive suggestions.

Our response follows (the reviewer’s comments are in italics font).

 

Point 1: Review the reference of the paper. Also, in some part of the text, the author duplicate the name of the tables.

Reply

All references have been revised and corrected. We checked all occurrences of the tables in the text and we removed the duplicated ones.

Point 2: Introduction: the introduction needs to be improved with description of similar case of study.

Reply

In many of the papers cited in the introduction several examples of efficiency optimization with respect to single parameters in Banki-type turbines can be found, but in literature we did not find any study case investigating the nexus between the search of hydraulic efficiency and the requirements for structural safety.

Point 3: Line 169: why you select this size of the mesh? Do you do a sensitive analysis of the mesh quality?

Reply

In the new paper we added Figure 3, where we show the shaft torques computed for different mesh densities, plotted versus the corresponding number of elements of the rotor domain. We observe that with more than 14 million of elements in the rotor domain the shaft torque increment becomes negligible. For this reason we selected this grid as the optimal one, as mentioned in the revised paper.

Point 4: What is the effect of turbulence in the turbine? Maybe it is the reason for the variation of difference number of blades of different authors specify in the table 2.

Reply

According to our experience, the optimal number of blades depends on the selection of the other turbine parameters, more than on the selection of the specific turbulence model. For example, the increment of the internal/external diameter ratio is likely to increment the optimal number of blades, but a large number of blades leads to a strong energy dissipation inside the channels due to the wall friction effect. A very important issue, that has been never discussed in the literature, is the reduction of the net cross flow area due to the blade thickness, which also depends on the maximum admissible stress. The motivation of table 2 (numbered 3 in the revised paper) is only to select a range of possible number of blades to be investigated with the proposed methodology.  

Point 5: Why you use a 2D hydraulic model in both of 3D numerical simulation, it is a crossflow turbine that have a three-dimensional behavior, it can generate some effect in the results? What is the flow rate introduce? Do you compare with different flow rate, or only with one comparison between 2D and 3D?

Reply

At the beginning of section 3 of the revised paper we state that, regardless of the required computational effort, a direct global optimization could “easily” be found using 3D fully coupled structural and hydrodynamic simulations. The problem is that this direct approach would require an enormous computational time, at least with standard computational resources. This is the motivation of the “thrifty” approach proposed in section 6, where only the final designed turbine is tested through a fully 3D CFD simulation, coupled with a 3D structural analysis of the entire impeller.

Point 6: The proposed methodology for impeller design: The method of the paper need to be before.

Reply

We prefer to present the numerical tools and the physical analysis at the basis of the design procedure before the presentation of the procedure itself, in order to prevent possible queries of the reader (e.g. the use of 2D CFD models or the cubic profile of the blades). On the other hand, we agree with the reviewer that the section on the numerical model should be put before the discussion on the cubic profile. We also redefined section 7 on the admissible stress computation as a subsection 5.1 of the structural analysis.

To avoid any possible initial misunderstanding on the paper structure and aim, we also added at the end of the introduction a short list of the section definitions.

Point 7: Conclusions: The conclusion need to be rewrite, quantify the results of the paper-

Reply

We think that the major conclusion of the paper is that it is possible to carry on a coupled hydrodynamic and structural optimization of the impeller within reasonable time and using standard computational resources, also assuming a cubic profile of the blades instead of a circular one. To quantify this improvement, with reference to the case study, we added the following comment:

 “In the study case, a total number of 30 2D CFD simulations and 7 3D blade structural analysis has been carried out, with a total computational time of 600 hours on a computer working with several CPU Intel® Xeon(R) E5-2650 v3 processors. The same problem, solved as the search of a 3D coupled structural and hydrodynamic optimization of the whole impeller, subject to the admissible stress constraint, would require a computational time of 16 days per simulation. Even with only 2 optimization parameters (number of blades and maximum thickness), the required computational time would have been larger than the actual one of several orders of magnitude.”

We also think that the comment on the use of 3D printing for the construction of the blades or their molds is important to support the use of a cubic profile instead of a simpler circular one and that it should remain.

Point 8: Figure 13: Describe with lines and name.

Reply

We agree with the reviewer and we have revised Figure 13 (numbered 15 in the revised paper).

Point 9: Figure 1, Figure3: Include the size or measure of the model.

Reply

In the revised paper we corrected the description of Figure 1, which is a simple sketch of a cross-flow turbine and not a section of a specific device. We agree with the reviewer and we have added a reference size in Figure 3 (numbered 6 in the revised paper).

Point 10: In the Figure 3: specify the boundary conditions of the numerical model.

Reply

Boundary conditions of the numerical model in Figure 3 and Figure 5 (numbered 6 and 8 in revised paper) are both pressure for inlet and outlet. We add this information in the new paper.

Point 11: Describe n/nmax of the figure 3, because it is not describe in the paper.

Reply

h/h_max  is the ratio between the efficiency get by the impeller designed with a given maximum blade thickness t_max (and corresponding j angle in the circular profile) and the maximum efficiency obtained according to an angle j = b₁ both in the circular and cubic profiles (see Figure 5 in revised paper). We add this description in the new paper, where we also specify that the optimal number of blades is different according to the selected maximum thickness t_max.

Point 12: Figure 7: Change the scale of the level, because the range is too big.

Reply

We did it in the revised paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

This research explains how 2D CFD simulations could be coupled with 3D FEM calculations. Although the research is of interest, the results presented in this manuscript are not convincing as there are important parts that are missing for the reader to be able to understand and assess if/how the procedure works. This work might be publishable if additional information/ explanations/justifications are provided.

Major points:

• The CFD methodology, either 2D or 3D is not explained/described in detail. The only bits of information are the turbulence model used, the time-step, the convergence criterion, and the number of elements for the rotor and stator. This is clearly not enough, especially as the research is mainly about CFD. Even if previous studies were published elsewhere, enough details should be provided to the reader without the need to reach another paper.
• Where is the mesh independence study? What is the surface treatment used, what is the y+ value at the wall? Which numerical schemes were used, and why?
• The authors claimed that the 3D results are in agreement with the 2D ones. Looking at the velocity distribution only is probably not enough. Besides, the differences are not quantified here. A 2D plot of the velocity at a specific position would provide more insight. What about other parameters such as the turbulence quantities for instance?
• The authors wrote at different places: “not documented here for brevity”, Line 107, Line 120, Line 352. Even if this cannot be fully detailed for brevity indeed, the reader should understand what was done, and why. Corresponding references are also required.
• Lines 117-119: “We… Surface” How can we observe this from Fig.3?
• Line 143: Why is t_min empirically set equal to 0.1tmax? Based on what?
• Line 148: Why is rf empirically set equal to 0.1t_max?
• Lines 182-184: “this difference… impeller geometries”. Why?
• Lines 186-187: “The results… procedure”. How does it show good matching for the accuracy required?
• Line 273: Please explain why the ratio R_f/t_max=0.833 is also a reasonable design choice?
• Line 292: A numerical checking or numerical comparison is not a validation. A validation is always against experimental data.
• Lines 326-327: Why this safety factor of 3?
• Line 370: “approximately validated” What does this mean? Either it is validated, or it is not, but it cannot be approximately validated!
• How can the authors be sure that their results are accurate or even plausible? There is no discussion on the influence of physical or numerical parameters in this work.

Minor points:

• Line 28: “the potential energy of owned by the water”. Not clear, please re-write…
• Line 91 & Line 102, Line 124: Replace “Observe” by “Note”
• Line 114: Replace by “Table 1 lists all the parameters…”
• Line 196: replace by “Figure 8 shows…”
• Line 200: The trend of τ shows …”
• Line 209: “in Section…”
• Typo for “increase” in Figure 10
• Line 275: Please replace by “… equal to 10% of t_max...”
• Line 286: DOFs needs to be defined

Author Response

Dear Reviewer,

we would like to thank you for your careful and thorough reading of this paper and for the comments and the constructive suggestions.

Our response follows (the reviewer’s comments are in italics font).

Point 1. The CFD methodology, either 2D or 3D is not explained/described in detail. The only bits of information are the turbulence model used, the time-step, the convergence criterion, and the number of elements for the rotor and stator. This is clearly not enough, especially as the research is mainly about CFD. Even if previous studies were published elsewhere, enough details should be provided to the reader without the need to reach another paper.

Reply

The main goal of the paper is not the development of an improved CFD model, but the proposition of a new strategy for the design of a Cross-Flow type turbine, according to the procedure described in section 6. The advantage of the proposed procedure is the iterative use of only 2D CFD models and of 3D structural models, these last ones with a computational domain restricted to a single blade. The solution of a fully 3D CFD and structural model of the entire impeller is carried out only once to validate the maximum stress of the final impeller.

To better support the proposed strategy, in the new paper we added anyway most of the information required by the reviewer.

 

 

Point 2. Where is the mesh independence study? What is the surface treatment used, what is the y+ value at the wall?

Reply

In the new Figure 3 of the revised paper we show the shaft torques computed for different mesh densities, plotted versus the corresponding number of elements. From the same figure we note that above 14 million of elements the torque increment is negligible and for this reason this grid is selected as the final one. See also reply to point 1.

Point 3. Which numerical schemes were used, and why?

Reply

At the beginning of section 3 of the revised paper we say that all numerical simulations have been carried out by means of ANSYS^® CFX commercial code, after discretization of the computational domains in tetrahedral and prismatic elements.

Point 4. The authors claimed that the 3D results are in agreement with the 2D ones. Looking at the velocity distribution only is probably not enough. Besides, the differences are not quantified here. A 2D plot of the velocity at a specific position would provide more insight. What about other parameters such as the turbulence quantities for instance?

Reply

We agree with the reviewer that the comparison of the norms of the velocities computed by 2D and 3D models is  qualitative and is used only to justify the choice of a 2D model. It is also well known that the efficiencies computed in the 3D models are lower than the efficiencies computed in the 2D models, mainly due to the vorticity components normal to the axis direction, missing in the 2D models. The underlying idea is that energy dissipations occurring in the axis direction do not affect the number of blades and the maximum thickness that optimize the impeller efficiency. 

In Table 2 of the revised paper (see also next point 8), we compare the efficiencies of three different impellers computed using CFD 2D and 3D models. We observe that the 3D efficiencies are all lower than the corresponding 2D, but the optimal geometry is the same, regardless the choice between the 2D or the 3D numerical models.  

 

Point 5. The authors wrote at different places: “not documented here for brevity”, Line 107, Line 120, Line 352. Even if this cannot be fully detailed for brevity indeed, the reader should understand what was done, and why. Corresponding references are also required.

Reply

To better support the optimality condition claimed for the angle f=b₁, in the case of external circular profile, as suggested by the reviewer, we added in Figure 6 of the revised paper also the relative efficiencies of the turbine PRS2, and we took off the comment cited by the reviewer. See also reply to point 1).

Point 6. Lines 117-119: “We… Surface” How can we observe this from Fig.3?

Reply

In the revised paper we added the reference to Figure 2 (numbered 5 in the revised paper), where it is clear that the angle j = b₁ corresponds to the tangent condition.

Point 7. Line 143: Why is t_min empirically set equal to 0.1_tmax? Based on what?

Reply

Sharp edges are well known to provide a stress concentration along the same edges, that can be avoided by rounding off the edges with a circular profile. A value t_min = 0.1 t_max corresponds to a maximum stress located inside the blade, without a significant reduction of the hydraulic efficiency with respect to the value attained at t_min = 0. This comment has been added in the revised paper.

Point 8. Line 148: Why is rf empirically set equal to 0.1tmax?

Reply

See reply to previous point 7).

Point 9. Lines 182-184: “this difference… impeller geometries”. Why?

Reply

See reply to point 4). In the revised paper we rephrased the sentence in the following way: “most important, this difference does not affect the optimality of the 2D parameters, because the reduction of efficiency observed in 3D models is not dependent on the their setting. To this end, observe in Table 2 the efficiencies computed by solving three different configurations of the PRS1 turbine using 2D and 3D models. The 3D efficiencies are all lower than the 2D ones, but the optimal configuration is the same for both models.”   

Point 10. Lines 186-187: “The results… procedure”. How does it show good matching for the accuracy required?

Reply

See reply to points 4 and 9.

Point 11. Reviewer

Line 273: Please explain why the ratio Rf/tmax=0.833 is also a reasonable design choice?

Reply

In the revised paper we add Figure 13, that shows stress level plateau for rf/tmax bigger than 0.8333

Point 12. Reviewer

Line 292: A numerical checking or numerical comparison is not a validation. A validation is always against experimental data.

Reply

We changed the term “Validation…” with “A numerical validation…”

Point 13. Lines 326-327: Why this safety factor of 3?

Reply

We added the following two literature references:

Marko Katinić, Dražan Kozak, Ivan Gelo, Darko Damjanović. Corrosion fatigue failure of steam turbine moving blades: A case Study. Engineering Failure Analysis 106 (2019) 104136

Hermod Brekke. Hydraulic Turbines Design, Erection and Operation. Norwegian university of Science and Technology (NTNU) publications, Norway. Book, 324 Pages, 2015.

Point 14: Line 370: “approximately validated” What does this mean? Either it is validated, or it is not, but it cannot be approximately validated!

Reply

See reply to point 4 and 8.

Point 15: How can the authors be sure that their results are accurate or even plausible? There is no discussion on the influence of physical or numerical parameters in this work.

Reply

The experimental validation of the Cross-flow type turbines, and of the relative 2D and 3D simulation models, has been carried out also by the same authors in several previous papers, most of them cited in the submitted paper ([9], [12], [14], [15] in the revised version). The goal of this paper is different: we want to define a practical procedure leading to the design of an efficient turbine with a maximum stress lower than the admissible one.

Point 16: Line 28: “the potential energy of owned by the water”. Not clear, please re-write…

Reply

The word “of” has been taken off.

Point 17: Line 91 & Line 102, Line 124: Replace “Observe” by “Note”

Reply

We agree with the reviewer and we have revised lines

Point 18: Line 114: Replace by “Table 1 lists all the parameters…”

Reply

We agree with the reviewer and we replace term.

Point 19: Line 196: replace by “Figure 8 shows…”

Reply

We accepted the correction and we revised line

Point 20: Line 200: The trend of τ shows …”

Reply

We accepted the correction and we revised line

Point 21: Line 209: “in Section…”

Reply

We revised in the new paper.

Point 22:Typo for “increase” in Figure 10

Reply

We corrected typo in the new paper

Point 23: Line 275: Please replace by “… equal to 10% of tmax...”

Reply

We accepted suggestion and revised in the new paper

Point 24: Line 286: DOFs needs to be defined.”

Reply

We changed the acronym DOFs with “Degrees of Freedom”

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Many thanks for addressing most of the points raised in the first review and for providing justifications where needed. There are however a few points that still need some attention.

• Point 3.

Which numerical schemes were used, and why?

Reply At the beginning of section 3 of the revised paper we say that all numerical simulations have been carried out by means of ANSYS® CFX commercial code, after discretization of the computational domains in tetrahedral and prismatic elements.

The authors did not provide the answer to my question. Which numerical schemes were selected in the CFD model to run the simulations and why? Which order, 1^st, 2^nd, etc? Even if the paper is not about optimizing CFD, CFD is being mentioned and used, so it is important for readers to have this information.

• Point 11.

Line 273: Please explain why the ratio Rf/tmax=0.833 is also a reasonable design choice?

Reply In the revised paper we add Figure 13, that shows stress level plateau for rf/tmax bigger than 0.8333

Thanks for adding Figure 13. However, the “plateau for rf/tmax > 0.833” is arguable. The stress level decreases… always, even if the decrease becomes smoother as rf/tmax increases. I don’t think using the word “plateau” here is the right word. You might want to use a milder term, something like “the stress level seems to converge for values higher than 0.833”.

Minor:

L139 of the revised paper. Please replace: “To this end, observe in Table 2 the efficiencies…” with “To this end, Table 2 provides the efficiencies…”

Author Response

Manuscript ID WATER-1031502

Author's Reply to the Review Report

 

Dear Reviewer,

we would like to thank you for your careful and thorough reading of this paper and for the comments and the constructive suggestions.

Our response follows (the reviewer’s comments are in italics font).

Point 1. The authors did not provide the answer to my question. Which numerical schemes were selected in the CFD model to run the simulations and why? Which order, 1st, 2nd, etc? Even if the paper is not about optimizing CFD, CFD is being mentioned and used, so it is important for readers to have this information.

 Reply

We add in section 3: “Simulations were carried out using the Ansys CFX commercial code, solving the Reynolds-averaged Navier Stokes (RANS) equations [12, 18]. CFX gives the option to select one among different advection models. We chose the high resolution scheme, that uses second order differencing for the advection terms in flow regions with low variable gradients [18]. The high resolution scheme uses the first order advection terms in areas where the gradients change sharply, to prevent overshoots and undershoots and maintain robustness.”.

 

Point 2. Thanks for adding Figure 13. However, the “plateau for rf/tmax > 0.833” is arguable. The stress level decreases… always, even if the decrease becomes smoother as rf/tmax increases. I don’t think using the word “plateau” here is the right word. You might want to use a milder term, something like “the stress level seems to converge for values higher than 0.833”.

Reply

We accepted suggestion and we replace with: “It was found that the stress level seems to converge for values of Rf/tmax ratio higher than 0.833.” in the new paper.

 

Point 3. L139 of the revised paper. Please replace: “To this end, observe in Table 2 the efficiencies…” with “To this end, Table 2 provides the efficiencies…”

Reply

We accepted the correction and we revised line.

Author Response File: Author Response.pdf