Maintenance Strategies Comparison for Francis Turbine Runner Subjected to Cavitation

Round 1

Reviewer 1 Report

The paper presents a simple and effective logic of optimizing the cost effectiveness of maintenance operations of a Francis turbine. Though of interest to the community in general, certain aspects of the work remain unclear and need to be further emphasized to warrant publication of the work.

• In the first line of the abstract, it might be better to directly refer to the component being investigated as opposed to just calling it a continuously degrading component.
• It would be beneficial to the reader to include a more elaborate discussion of the gamma process that is used in the current work.
• Out of curiosity is NRE – New Renewable Energy a common usage?
• What do the different dots in figure 1 denote? Please make it explicit in the discussion surrounding the figure. Figure 1 also gives the impression that the cost and time required for repair after crossing the moderate and severe thresholds are the same. It is better to differentiate it right off the bat.
• What was the basis of modelling the mass loss Vs time in figure 3?
• I am assuming such an evaluation process needs to be done case specifically. What kind of simulation times are we looking at? Also could the authors comment on what is the typical protocol used to determine the inspection/ maintenance interval.
• What does ‘B’ stand for? Number of cylcles? It would be very useful to include a nomenclature in the paper.

Editorial corrections.

• Line 39: “Consisting in” needs to be “consisting of” or “resulting in”
• Line 141: alpha2 needs to be changed to α2

Author Response

Please see the attachment.

Author Response File: Author Response.doc

Reviewer 2 Report

The manuscript offers a simple methodology to study the continuously degrading component due to cavitation for Francis Turbine runner.

The kind of research is interesting but the reviewer would like to rise some problems:

• The abstract is poorly written.
• The introduction would require major rewriting for sense and the authors should add more references.
• The manuscript structure is not a conventional research article, the article should be written with a conventional structure, 1.- Introduciton 2.- Material and Methods 3.-Results and Discussion 4.-Conclusions
• The authors propose a simplicity model. In a complete model, taking into account more levels of operating losses, with finer results, with the proposed methodology, what errors are obtained?
• This research would be interesting if researchs compared the simple methodology with a complete model, calculating the errors and proposing application criteria.

Therefore, this paper should be rewritten or complemented to meet the standard of the scientific of these manuscripts. I am of the opinion that the article cannot be accepted in the present form

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper focuses on the maintenance strategies for Francis turbine runner due to the cavitation erosion. A visionary top-down approach is applied in the manuscript based on a stochastic model to capture the mass loss due to the cavitation erosion process. This approach is useful to assess the influence of maintenance parameters on the long-time cost criterion. However, the main limitations of this approach are related to the confidence in the data obtained for the Francis turbine runner and the margin of confidence in which the predictions are performed.

It is well known that hydraulic turbines are dedicatedly designed and manufactured for each hydropower plant. Moreover, the operating conditions (head, discharge, suction head) are different for the hydropower units installed in the same hydropower plant. Therefore, a lot of numerical and experimental investigations have been carried out in the last seven decades to quantify the effects of cavitation on the runners of Francis turbines operating under various conditions. Different types of cavitation (attached cavitation, unsteady cloud cavitation, inter blades cavitation vortices and so on) are developed and act on the Francis turbine runners during various operating conditions. As a result, typical eroded areas were identified on the runners of the Francis turbines [Avellan2004HMH Figs. 25-29]. The problem becomes even more complex when considering the mechanisms of degradation by cavitation erosion and changes in the properties of the material due to repair cycle that are only partially known.

The degradation model based on gamma process is summarized in section 2.2. A linear theoretical correlation between the mass loss and the time is depicted based on gamma process in Figure 1. Two degradation thresholds (rho1 and rho2) are considered for moderate and severe erosion levels. The maintenance model with its ingredients is presented in section 3. The case study selected to support the theoretical background is delivered in section 4. 

The degradation threshold value of rho2 = 42 kg is selected in the case study as the material loss level exhibiting a perforation. The perforation limit (maximum cavitation pitting depth [mm]) is related with the thickness of the blade. This absolute value of the rho2 threshold value in kg is directly related to the Francis turbine runner configuration (e.g. geometry and mass) considered as the test case and to the properties of the material selected for its manufacture. The IEC 60609 cavitation pitting standards provides for hydraulic turbines three different parameters (e.g. mass, depth and area). Please explain how is selected this threshold value of rho2 = 42 kg. Three scenarios are proposed selecting three different values of rho1 degradation threshold as follows: 15 kg - more conservative scenario, 24 kg - moderately conservative scenario and 33 kg less conservative scenario. Please explain these scenarios in relation to the relevant data of the test case. Please provide relevant data for the test case to be used by reader. For instance, the relative values and/or entire description of the test case can be used by reader referring to this work. 

Several data are included in Table 2 connecting the GP parameters (u,c,b) with erosion level (low, moderate and high) for investigated Francis runner. How was the correlation between the GP parameters (u, c, b) obtained with the erosion level for the Francis runner?

Please clearly provide the assumptions and limitations of the methodology developed and applied to the Francis runner. The margin of confidence in which the predictions are performed should be clearly stated. Is the margin of confidence within the limit of +/-25%? or +/-50%?

The results included in section 5 are difficult for the reader to follow. In my opinion, a synthetic analysis performed on the results together with comments to guide the reader would better highlight the work.

The approach presented in the manuscript suggests a mass loss prediction versus time for Francis turbine runner without specifications related to the operating conditions and the particularities of the hydroelectric power plant. That is why I called this approach visionary. The consistency and the clarity of the manuscript should be improved before to be accepted for publication in the journal. I am suggesting that the manuscript to be MAJOR REVISED. Several recommendations are provided in my review report to revise the manuscript.

References

Avellan F., Introduction to cavitation in hydraulic machinery. In Proceedings of the 6th International Conference on Hydraulic Machinery and Hydrodynamics, October 21 – 22, Timisoara, Romania, 2004.

International Electrotechnical Commission, Cavitation Pitting Evaluation in Hydraulic Turbines, Storage Pumps and Pump-Turbines, IEC 60609 standard, Geneva, Switzerland, 1999.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have improved the manuscript.

The abstract and introduction has been improved, but there are some considerations that must be clarified.

In my opinion, the structure article should be as follows:

1. Introduction
2. Materials and Methods
   • Degradation
   • Maintenance model
   • Case Study
3. Results and Discussion
4. Conclusion

The authors don’t have complete model avalaible and the methodology is simple, it is not the simplification of a more complex one.

If there are no more complete or complex or similar methodologies, the methodology proposed by the authors will be a novelty, and they should also indicate this.

Author Response

Thank you for your review. Please find attached response to your comments and suggestions. 

Author Response File: Author Response.pdf

Reviewer 3 Report

Recommendation 1 (R1): It is well known that hydraulic turbines are dedicatedly designed and manufactured for each hydropower plant. Moreover, the operating conditions (head, discharge, suction head) are different for the hydropower units installed in the same hydropower plant. Therefore, a lot of numerical and experimental investigations have been carried out in the last seven decades to quantify the effects of cavitation on the runners of Francis turbines operating under various conditions. Different types of cavitation (attached cavitation, unsteady cloud cavitation, inter blades cavitation vortices and so on) are developed and act on the Francis turbine runners during various operating conditions. As a result, typical eroded areas were identified on the runners of the Francis turbines [Avellan2004HMH Figs. 25-29]. The problem becomes even more complex when considering the mechanisms of degradation by cavitation erosion and changes in the properties of the material due to repair cycle that are only partially known.

The degradation threshold value of rho2 = 42 kg is selected in the case study as the material loss level exhibiting a perforation. The perforation limit (maximum cavitation pitting depth [mm]) is related with the thickness of the blade. This absolute value of the rho2 threshold value in kg is directly related to the Francis turbine runner configuration (e.g. geometry and mass) considered as the test case and to the properties of the material selected for its manufacture. The IEC 60609 cavitation pitting standards provides for hydraulic turbines three different parameters (e.g. mass, depth and area). Please explain how is selected this threshold value of rho2 = 42 kg. Three scenarios are proposed selecting three different values of rho1 degradation threshold as follows: 15 kg - more conservative scenario, 24 kg - moderately conservative scenario and 33 kg less conservative scenario. Please explain these scenarios in relation to the relevant data of the test case. Please provide relevant data for the test case to be used by reader. For instance, the relative values and/or entire description of the test case can be used by reader referring to this work. 

Answer 1 (A1): We added at the end of section 4 paragraph 1 the “… degradation thresholds r1 and r2 are determined based on internal maintenance procedures and for a specific runner. Cavitation erosion is usually evaluated (during an inspection) by measuring the area and the depth of affected regions [4]. In this case study, we considered that if material loss reaches 42 kg, it is more likely erosion depth equals blade thickness, resulting in perforation.”

Comment 1 (C1): The following comment is added in the manuscript (lines 163-168) “During operation, evaluating cavitation intensity and resulting erosion is a difficult task because this phenomenon is influenced by several operating conditions (suction head, head, discharge, ...) [3]. For this purpose, different detection methods have been developed and used in industry [16] in conjunction with CFD models. For the sake of simplicity, the present case study consider a turbine subject to constant and steady operation conditions.”

The authors refer to the PhD thesis defended by Dr. Paul Bourdon at LHM/EPFL, Lausanne, Switzerland in 2000 (reference no. 16). The developments from the Dr. Paul Bourdon on this subject have been incorporated in the cavitation erosion monitoring system in operation at Hydro-Québec. However, the data collected during last two decades on the hydropower units are useful to support the method presented in the manuscript. Unfortunately, this data is missing.  

The answer does not provide clarification for the reader. No information about the geometry (e.g. minimum blade thickness of the runner corresponding to the cavitation erosion area) and mass of the runner is added. The reader has no reference value for the test case considered in this investigation. The following specification made by the authors "degradation thresholds r1 and r2 are determined on the basis of internal maintenance procedures and for a specific runner" corresponds to a typical answer provided not to reveal anything about the case under investigation and the connection with the scenarios proposed in the manuscript. Usually, these constraints are imposed by companies not to disclose the date. However, we are talking about the scientific manuscript that has to include relevant data to support the method proposed by the authors. The manuscript has limitations related to the support with relevant data of the proposed scenarios. Unfortunately the study included in the manuscript cannot be used by the reader if relevant data are not provided.

Please include all relevant data for reference no. 3.  

R2: Several data are included in Table 2 connecting the GP parameters (u,c,b) with erosion level (low, moderate and high) for investigated Francis runner. How was the correlation between the GP parameters (u, c, b) obtained with the erosion level for the Francis runner?

A2: We added in section 4, that the moderate erosion parameters were obtained from a study conducted on real Francis turbine in [17] and that the low and high erosion were derived to illustrate the impact of operating conditions or turbine design in terms of cavitation severity.

C2: The authors refer to a study conducted on a real Francis turbine provided in a PhD thesis defended in 2020 (se reference no. 17). What is to be understood from this answer? The reader has to follow the doctoral thesis to identify considerations related to the levels selected in the manuscript for cavitational erosion. Sorry, this approach is not feasible.

I consider that a brief presentation of the considerations related to the selection of the parameters (u,c,b) and their correlation with the investigated Francis runner case helps the reader in understanding and applying the methodology developed by the authors. Indeed, reference 17 is useful if the reader would like to have a deep understanding of the considerations made in the manuscript.

R3: Please clearly provide the assumptions and limitations of the methodology developed and applied to the Francis runner. The margin of confidence in which the predictions are performed should be clearly stated. Is the margin of confidence within the limit of +/-25%? or +/-50%?

A3: For this purpose, we presented the variability of the Monte Carlo simulations in Figure 4. We believe that it is a better indicator to assess the trend. In our case, we don’t pretend to any level of prediction accuracy in the absence of information about the ground truth.

C3: The authors clearly indicate that the variability of Monte Carlo simulations should be the indicator to evaluate the prediction of results. The variability is plotted in Figure 4. The values ​​of variability cover a range from hundreds to thousands. What do these values ​​mean in the margin of confidence of the results obtained? The main question is following: What degree of confidence in the results should the user who applies the method proposed by the authors expect? The margin of confidence of the result is connected with the assumptions taken into account. Unfortunately, the answer provided by the authors is ambiguous and offers no perspective on the margin of confidence in the results obtained with the method proposed in the manuscript.  

R4: The results included in section 5 are difficult for the reader to follow. In my opinion, a synthetic analysis performed on the results together with comments to guide the reader would better highlight the work.

A4: We agree with the reviewer and section 5 has been revised.

C4: Indeed, section 5 is revised by the authors. I reread a few times the section 5 in the revised form of the manuscript. It is suggested that the first inspection to be repaired is mandatory at six years to keep lower cost ratio R. This recommendation can be a valuable one for maintenance process. However, is this recommendation valid for other Francis turbine runners? The reader should be able to apply the method developed in the manuscript to other cases to determine the inspection time. Unfortunately, this is not possible, as the data provided in the manuscript do not support this approach.  

R5: The approach presented in the manuscript suggests a mass loss prediction versus time for Francis turbine runner without specifications related to the operating conditions and the particularities of the hydroelectric power plant. That is why I called this approach visionary. The consistency and the clarity of the manuscript should be improved before to be accepted for publication in the journal.

A5: As mentioned in previous answer, we specified in section 4 that the moderate erosion parameters were obtained from a study conducted on real Francis turbine in [17] and that the low and high erosion were derived from these to illustrate the impact of operating conditions or turbine design changes

C5: It is not enough to mention that the data is obtained on a study conducted on a real Francis turbine. The relevant data has to be provided in the manuscript to support the statement(s). In the current form, not enough relevant data are provided to support the authors' statements.

It is mentioned in my first report that the approach proposed by the authors for selecting the maintenance period for the cavitation of the Francis turbine runner is visionary. In my opinion the visionary approach is the mass loss prediction versus time for Francis turbine runner without specifications related to the operating conditions and the particularities of the hydroelectric power plant. Several recommendations have been provided to improve the consistency and the clarity of the manuscript to be accepted for publication in the journal. The revised form of the manuscript has limitations related to the support with relevant data of the proposed scenarios. Unfortunately the study included in the manuscript cannot be used by the reader if relevant data are not provided. The reader should be able to apply the method developed in the manuscript to other cases to determine the inspection time. Unfortunately, this is not possible, as the data provided in the manuscript do not support this approach. In my opinion, the revised form of the manuscript does not meet the requirements for publication in a journal.

Author Response

Thank you for your review. Please find attached response to your comments and suggestions. 

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

It is mentioned in my first report that the approach proposed by the authors for selecting the maintenance period for the cavitation of the Francis turbine runner is visionary. In my opinion the visionary approach is the mass loss prediction versus time for Francis turbine runner without specifications related to the operating conditions and the particularities of the hydroelectric power plant. Future developments and in situ investigations will develop the capabilities of the method and the limits of confidence in the predicted results. I propose that the paper be accepted in its current form.   

Author Response

Thank you for your comments. This new paper version was reviewed by a profesionnal linguist.

Author Response File: Author Response.pdf