Optimization Design of Centrifugal Pump Auxiliary Blades Based on Orthogonal Experiment and Grey Correlation Analysis
Round 1
Reviewer 1 Report
The article focuses on optimizing the design of auxiliary vanes in multistage centrifugal pumps to enhance their hydraulic performance. The study utilizes orthogonal experiments and grey relational analysis to optimize the blade design. The manuscript can be accepted after following suggestions for improvement:
Suggestions for Improvement:
· Explain Orthogonal Experiments in Detail: Provide a comprehensive explanation of orthogonal experiments, including the methodology, principles, and advantages. Clarify how the L9 (3^4) orthogonal array was utilized and the reasoning behind selecting the specific factors and levels. This will improve the readers' understanding of the experimental design.
· Elaborate on Grey Relational Analysis: Provide a detailed description of the grey relational analysis method used to verify the accuracy of the experimental results. Explain the steps involved in the analysis and how it complements the range analysis of orthogonal experiments. This will enhance the readers' understanding of the data analysis process.
· Include Comparative Analysis: Conduct a comparative analysis to evaluate the performance of the optimized design against other existing methods or designs in the field of multistage centrifugal pumps. Compare the improvements in pump efficiency and head achieved by the optimized design with alternative approaches, if available. This will provide a more comprehensive evaluation of the proposed optimization method.
· Discuss Limitations and Practical Considerations: Address the limitations or potential constraints associated with the proposed optimization approach. Discuss any assumptions made during the study and practical considerations that may affect the applicability of the optimized design in real-world scenarios. This will provide a balanced perspective on the limitations and challenges of implementing the proposed approach.
By addressing these suggestions, the article will provide a more comprehensive analysis of the optimization of auxiliary vanes in multistage centrifugal pumps, enhancing the understanding of the research methodology and its implications in the field.
Author Response
Response to Reviewer 1 Comments
Point 1: Explain Orthogonal Experiments in Detail: Provide a comprehensive explanation of orthogonal experiments, including the methodology, principles, and advantages. Clarify how the L9 (3^4) orthogonal array was utilized and the reasoning behind selecting the specific factors and levels. This will improve the readers' understanding of the experimental design.
Response 1:
According to the reviewer’s comments, Orthogonal design is a method for designing and analyzing experiments with multiple factors. It explores the effects of factors on experimental results by systematically selecting and arranging factors at different levels.
The principle of orthogonal design is based on mathematical statistics principles and methods. Its core idea is to use orthogonal arrays to combine different levels of factors, so that the main effects and interaction effects of each factor can be accurately estimated in the experiment. The design of orthogonal arrays takes into account the interactions between factors, allowing the experimental results to accurately reflect the independent and combined effects of each factor on the results.
Orthogonal design has many advantages, including efficient utilization of resources, providing reliable results, reducing errors and variances, and being able to detect and differentiate the effects of different factors on experimental results.
- Efficient utilization of resources: Orthogonal design can obtain comprehensive and reliable data with relatively small number of experiments, saving time and resources.
- Providing reliable results: Orthogonal design, based on rigorous mathematical statistical principles, can provide reliable experimental results and data analysis.
- Reducing errors and variances: By selecting orthogonal arrays, orthogonal design can reduce the impact of experimental errors and variances, improving the accuracy and credibility of experimental results.
- Detecting and differentiating factor effects: Orthogonal design can clearly differentiate the independent effects of each factor on experimental results and the interaction effects between factors, helping researchers to understand the relationships between factors.
In orthogonal design, the selection of specific factors and levels is crucial. First, the research objectives and the factors of interest need to be determined. Then, appropriate levels are chosen based on experimental requirements and feasibility. Generally, the higher the number of levels, the higher the reliability and accuracy of experimental results, but the complexity of the experiment also increases.
In this study, the factors chosen were the number of auxiliary blades (Z), inner diameter size (R), and width (W), as these geometric dimensions were found to have an impact on the head and pump efficiency through CFD analysis. Three factors were selected, and each factor had three levels. By using the L9 (3^4) orthogonal array, nine different combinations of experimental conditions could be conducted, with each level of each factor being considered in the experiment. This way, you can observe the main effects of each factor as well as the interaction effects between factors.
In summary, orthogonal design is an efficient and reliable method for designing and analyzing experiments with multiple factors. By selecting specific factors and levels, and applying orthogonal arrays, you can comprehensively study the effects of different factors on experimental results.
New content add to article shown as below picture.
Point 2: Elaborate on Grey Relational Analysis: Provide a detailed description of the grey relational analysis method used to verify the accuracy of the experimental results. Explain the steps involved in the analysis and how it complements the range analysis of orthogonal experiments. This will enhance the readers' understanding of the data analysis process.
Response 2:
According to the reviewer’s comments, reference information shown as below.
- Gray correlation analysis method is used to validate the accuracy of experimental results. It can assess the degree of correlation between different experimental results and identify the factors that have the greatest impact on the results. The detailed description of the gray correlation analysis method and its complementarity with orthogonal experimental range analysis are as follows, with the analysis steps outlined:
(1) Data preprocessing: Normalize the experimental results to eliminate the influence of different dimensions. Common normalization methods include linear normalization and exponential normalization.
(2) Determine the correlation function: Choose an appropriate correlation function to measure the degree of correlation between the experimental results. Common correlation functions include absolute correlation function and relative correlation function.
(3) Calculate correlation coefficients: Based on the selected correlation function, calculate the correlation coefficients between each experimental result and other results. The correlation coefficient values range from 0 to 1, indicating the strength of the correlation.
(4) Determine the optimal factor: Compare the correlation coefficients of different factors with the experimental results to determine the factor that has the greatest impact on the results. Factors with higher correlation coefficients have a greater influence on the results.
- Complementarity between gray correlation analysis method and orthogonal experimental range analysis:
Orthogonal experimental range analysis mainly focuses on the interaction between factors and optimization design, providing a comprehensive analysis of the factors' effects. Gray correlation analysis method, on the other hand, emphasizes the correlation between experimental results, validating the accuracy and reliability of the experimental results. They complement each other and provide a more comprehensive experimental analysis.
Orthogonal experimental range analysis can reveal the influence of factors on results by designing different combinations of factor levels, covering a comprehensive experimental space. Gray correlation analysis method, on the other hand, can discover patterns of variation in experimental results and evaluate their degree of correlation to determine key factors.
- When the factors in the orthogonal experiment have different dimensions, gray correlation analysis can perform dimensional transformation to provide a detailed explanation of the impact on the experimental results. The steps for dimensional transformation are as follows:
(1) Determine the dimensions of the experimental results: Based on the measurement units of the experimental results, determine the dimensions of each experimental result, such as length, mass, time, etc.
(2) Perform transformation based on dimensions: Choose appropriate transformation methods, such as standardization, normalization, mean difference method, etc., to perform dimensional transformation based on the different dimensions.
(3) Calculate gray correlation coefficients: For the transformed results with the same dimensions, use gray correlation analysis method to calculate the correlation coefficients and evaluate the impact of different factors on the results.
New content add to article shown as below picture.
Point 3: Include Comparative Analysis: Conduct a comparative analysis to evaluate the performance of the optimized design against other existing methods or designs in the field of multistage centrifugal pumps. Compare the improvements in pump efficiency and head achieved by the optimized design with alternative approaches, if available. This will provide a more comprehensive evaluation of the proposed optimization method.
Response 3:
According to the reviewer’s comments, reference information shown as below.
There are many articles studying the reduction of leakage in the volute of centrifugal pumps, with two main approaches focused on reducing the flow velocity and changing the volute cross-sectional area. The research direction that receives more attention is the reduction of the volute cross-sectional area to minimize leakage.
Multistage centrifugal pumps are common fluid transportation devices composed of multiple centrifugal pump stages in series. The volute clearance size refers to the gap between the inlet end and the impeller. Reducing the volute clearance size may have the following effects on the pump's head and efficiency:
- Increased head: Reducing the volute clearance size can reduce internal recirculation and leakage, thereby improving the pump's head capacity. When the clearance is reduced, the fluid entering the pump experiences stronger impeller driving, reducing internal leakage flow and increasing the efficiency of centrifugal force transmission, resulting in an increase in head.
- Increased efficiency: Reducing the volute clearance size can reduce leakage flow and eddy current losses, thereby improving the pump's efficiency. Smaller clearances reduce backflow and leakage between the impeller and the stationary components, reducing energy losses. In addition, reducing the clearance can also reduce the generation of eddy currents, further improving pump efficiency.
In an article by Liu Dong on the influence of volute clearance on the stability of high-temperature pump rotors, it was found that when the volute clearance increased from 0.4mm to 1mm, the pump's head and efficiency decreased by 5.95% and 6.26% respectively. Zhao Cunsheng stated in a numerical simulation article on the flow characteristics of volute clearance in centrifugal pumps that when the volute clearance was selected as 0, 0.5, 0.7, and 1.06mm, the pump's head decreased by approximately 20% and efficiency decreased by approximately 19%.
The advantages of reducing the volute clearance for improving pump performance are evident. However, this also increases the difficulty and production cost of manufacturing. Some pumps, due to their inherent limitations, cannot further reduce the volute clearance. The auxiliary blade structure is based on the principle of reducing the fluid velocity at the volute region, optimizing the volume loss at the volute without reducing the clearance. It requires low production and manufacturing capabilities with almost no cost change, making it highly manufacturable. Importantly, the principle of the auxiliary blade structure is different from that of reducing the volute clearance, so they can be used simultaneously in a pump without conflicts, providing better optimization of the pump's volume loss.
Point 4: Discuss Limitations and Practical Considerations: Address the limitations or potential constraints associated with the proposed optimization approach. Discuss any assumptions made during the study and practical considerations that may affect the applicability of the optimized design in real-world scenarios. This will provide a balanced perspective on the limitations and challenges of implementing the proposed approach.
By addressing these suggestions, the article will provide a more comprehensive analysis of the optimization of auxiliary vanes in multistage centrifugal pumps, enhancing the understanding of the research methodology and its implications in the field.
Response 4:
According to the reviewer’s comments, reference information shown as below.
When discussing the limitations or potential constraints related to the proposed optimization methods, the following factors need to be considered:
- Technical limitations: Currently, there is limited foundational theory in auxiliary blade research, requiring extensive experimentation and the formulation of empirical formulas. The optimization methods may be influenced by technical limitations. For example, in the design of multi-stage centrifugal pumps, there may be technical limitations related to material strength, manufacturing processes, or impeller structure, which can restrict the range and variation of optimization parameters.
- Cost limitations: Cost is an important factor to consider during the optimization design process. For larger diameter impellers, changing certain parameters or adopting specific design choices may lead to increased costs, which can be limiting in practical applications. It is necessary to balance the relationship between design performance and cost to determine feasible optimization solutions.
- Actual operating conditions: Optimization design needs to be evaluated based on actual operating conditions, including fluid properties, working environments, and varying operating loads. These factors should be assumed and considered during the design process to ensure the applicability and reliability of the optimization design in real-world scenarios.
- Feasibility and manufacturability: Optimization design should take into account feasibility and manufacturability. Some designs for larger diameter impellers may be theoretically optimal but challenging to implement or produce in practice. Therefore, in optimization design, factors such as manufacturing processes, production equipment, and available materials need to be considered to ensure the feasibility of the design solution.
- Operational stability and reliability: Optimization design needs to consider the operational stability and reliability of the pump system. Design changes can affect the stability and reliability of the pump. Therefore, thorough analysis and evaluation are required to ensure that the optimization design maintains good operational performance under various operating conditions.
In conclusion, the optimization design process requires a comprehensive consideration of technical limitations, costs, actual operating conditions, feasibility and manufacturability, as well as operational stability and reliability. Reasonable assumptions and a comprehensive practical approach will help ensure the applicability of the optimization design in real-world scenarios and address potential limitations and challenges.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1- The title is not soft to understand, and it should be improved.
2- Mention the main outcome in the abstract.
3- All the mathematical equations need references.
4- Define all the parameters mentioned in the equation in the text.
5- The cation of figure 1 should be more detailed.
6- There are many statements the discussion section with no justifications. Please, answer ‘’why’’ for each statement.
7- Quantify some of the main outcome in the conclusion.
8- The main issue of this work is that the references are not up-to-date. The authors need to use the major references with the most recent work in this field.
1- The title is not soft to understand, and it should be improved.
2- Mention the main outcome in the abstract.
3- All the mathematical equations need references.
4- Define all the parameters mentioned in the equation in the text.
5- The cation of figure 1 should be more detailed.
6- There are many statements the discussion section with no justifications. Please, answer ‘’why’’ for each statement.
7- Quantify some of the main outcome in the conclusion.
8- The main issue of this work is that the references are not up-to-date. The authors need to use the major references with the most recent work in this field.
Author Response
Response to Reviewer 2 Comments
Point 1: The title is not soft to understand, and it should be improved.
Response 1: According to the reviewer’s comments, the new title shown as below.
Optimization Design of Centrifugal Pump Auxiliary Blades Based on Orthogonal Experiment and Grey Correlation Analysis
Point2: Mention the main outcome in the abstract.
Response 2: According to the reviewer’s comments, new more detailed information shown in the below picture by red letter marked.
Point 3: All the mathematical equations need references.
Response 3: According to the reviewer’s comments, all equation with reference, shown in below picture.
Point 4: Define all the parameters mentioned in the equation in the text.
Response 4: According to the reviewer’s comments, Define shown in the below picture.
Point 5: The cation of figure 1 should be more detailed.
Response 5: According to the reviewer’s comments, new more detailed picture shown in the attached.
Point 6: There are many statements the discussion section with no justifications. Please, answer ‘’why’’ for each statement.
Response 6: According to the reviewer’s comments, new content shown in the below picture.
Point 7: Quantify some of the main outcome in the conclusion.
Response 7: According to the reviewer’s comments,
Point 8: The main issue of this work is that the references are not up-to-date. The authors need to use the major references with the most recent work in this field.
Response 8: According to the reviewer’s comments, add below new recent references.
Author Response File: Author Response.pdf
Reviewer 3 Report
-In the Introduction, the research gaps are mentioned but the significance of this study is not mentioned explicitly. How this study will help in the design and optimization?
-Please provide the citation for the pump specifications from the manufacturer or if this is built in-house please provide the design drawing in the supplementary materials.
-the figure of the mesh is not shown. Please provide an appropriate figure of mesh.
- Please perform an appropriate mesh independence study, and use the method in the following article.
Ikhlaq, Muhammad, Yasir M. Al-Abdeli, and Mehdi Khiadani. "Nozzle exit conditions and the heat transfer in non-swirling and weakly swirling turbulent impinging jets." Heat and Mass Transfer 56 (2020): 269-290.
- Figure 11 there are four black boxes but they serve no purpose.
-Which solution technique for moving part is used either moving mesh or sliding mesh? steady state or transient?
The overall manuscript seems ok, provided the ababove-mentionedhanges are being made.
Please check the grammar using some grammar tools and make sure that you have used the oxford comma for listing things.
Author Response
Response to Reviewer 3 Comments
Point 1: In the Introduction, the research gaps are mentioned but the significance of this study is not mentioned explicitly. How this study will help in the design and optimization?
Response 1:
According to the reviewer’s comments, my reply shown as below.
Adding auxiliary blades to the impeller of a multistage centrifugal pump can increase the pump's head and reduce the leakage rate of the casing seal. The sealing of the casing area is achieved through a non-contact method, which improves the sealing life and is of great importance for the design of casing seals in water pumps. By using orthogonal experiments and gray correlation analysis, the impact of auxiliary blade dimensions on the pump head can be studied, providing the following design and optimization assistance:
- Determining the optimal auxiliary blade dimensions: By studying the correlation between auxiliary blade dimensions and pump head, the optimal parameters for auxiliary blade dimensions can be determined. This helps optimize the pump design to achieve higher head performance.
- Improving pump performance: The addition of auxiliary blades can enhance the pump head. By studying the impact of auxiliary blade dimensions on the pump head, the optimal design scheme for auxiliary blades can be found, thereby improving pump performance and efficiency.
- Optimizing pump design: Studying the influence of auxiliary blade dimensions on pump head and identifying the primary and secondary factors affecting it contributes to the optimization of pump design. By selecting suitable auxiliary blade dimensions, the flow characteristics of the pump can be improved, reducing energy losses and enhancing fluid flow.
- Enhancing pump reliability and stability: Studying the impact of auxiliary blade dimensions on pump head allows for the optimization of pump operating conditions. An optimized pump design can reduce vibration and casing friction, thereby improving pump reliability and stability.
In summary, studying the addition of auxiliary blades to the impeller of a multistage centrifugal pump and analyzing the impact of auxiliary blade dimensions on pump head using orthogonal experiments and gray correlation analysis can provide important guidance and assistance for pump design and optimization, ultimately improving pump performance and efficiency.
Point 2: Please provide the citation for the pump specifications from the manufacturer or if this is built in-house please provide the design drawing in the supplementary materials.
Response 2:
According to the reviewer’s comments, the pump drawing shown as below and attach it into article. It is belong to company new development vane, to avoid conflict, I am so sorry that I couldn’t offer detailed dimension.
Point 3: The figure of the mesh is not shown. Please provide an appropriate figure of mesh.
Response 3:
According to the reviewer’s comments, the mesh picture shown in the below.
Point 4: Please perform an appropriate mesh independence study, and use the method in the following article.
Ikhlaq, Muhammad, Yasir M. Al-Abdeli, and Mehdi Khiadani. "Nozzle exit conditions and the heat transfer in non-swirling and weakly swirling turbulent impinging jets." Heat and Mass Transfer 56 (2020): 269-290.
Response 4:
According to the reviewer’s comments, thanks for reviewer good suggestion, GCI is calculated as below. The method is from Ikhlaq, Muhammad, Yasir M. Al-Abdeli, and Mehdi Khiadani. "Nozzle exit conditions and the heat transfer in non-swirling and weakly swirling turbulent impinging jets." Heat and Mass Transfer 56 (2020): 269-290.
And I add it as reference in the article.
|
Grid |
Ni |
ri |
Head (m) |
GCIi+1,i |
|
Fine |
29536784 |
2 |
36.62 |
0.11% |
|
Medium |
15263763 |
2 |
36.54 |
0.75% |
|
Coarse |
8021591 |
1* |
37.13 |
- |
1*: Base size or initial size of the grid
-
Point 5: Figure 11 there are four black boxes but they serve no purpose.
Response 5:
According to the reviewer’s comments, the black boxes are deleted.
Point 6: Which solution technique for moving part is used either moving mesh or sliding mesh? steady state or transient?
Response 6:
According to the reviewer’s comments, the reply shown as below.
- I use sliding mesh。
- Steady state analysis was used in the article analysis, such as the orthogonal experiment section. After obtaining the optimal solution, transient analysis was used in the comparative analysis. Some sample shown in the below picture.
Steady state analysis:
Transient analysis:
Author Response File: Author Response.pdf
Reviewer 4 Report
The paper is aimed at evaluating the benefits of implementing auxiliary blades on the impellers of multistage pumps in terms of head and efficiency using orthogonal experiments and grey relational analysis. The width W, inner diametres R, and number Z of the blades were identified as factors, each on three levels, in order to identify the nine different combinations. The topic is significantly interesting and in compliance with the scope of Water Journal.
In the first chapter, there is a comparison between the results obtained by CFD and those obtained experimentally, however, it would be appropriate to describe in detail the setup used for the experimental tests. In addition, the performance curve related to the CFD analyses could also be added in Figure 5.
It would also be good to clarify how the deviation was calculated (line 138).
The results are fascinating, and they meet the objective of this paper, allowing us to observe allow us to observe an improvement in terms of head, efficiency and reduction of head fluctuations. The comparisons between the various solutions are interesting and very clear. despite this, it is suggested that the difference between optimized and optimal solution should be better clarified.
I repute that the topic is interesting and the paper achieved attractive results thus I suggest to consider the manuscript through Minor Revision.
You can find suggestions and typing errors as follows:
- The figures are not aligned with the center of the text;
- In lines 128 and 130 index “i” must be a subscript;
- In Figure 5, the scale of the efficiency axis does not start from 0;
- In the legend of figure 15 replace "origiunal" with "original"
- On the x-axis of Figure 15, enter the unit of measurement
Author Response
Response to Reviewer 4 Comments
Point 1:In the first chapter, there is a comparison between the results obtained by CFD and those obtained experimentally, however, it would be appropriate to describe in detail the setup used for the experimental tests. In addition, the performance curve related to the CFD analyses could also be added in Figure 5.
Response 1: According to the reviewer’s comments, reply shown as below.
1.Add test instruction.
2, Thanks for reviewer’s good suggestion to add other date line in the Fig.5, Because the main focus of this curve is to observe the trend of head variation, the inclusion of additional efficiency curves results in a higher density of data points on the graph, making it difficult to distinguish the head values. Moreover, the simulated efficiency curve lacks torque data, leading to significant deviations and potential misinterpretations. The primary objective of this table is to identify the trend of head variation at the optimal operating point determined by the experiments. Since there may be inaccuracies in the simulated efficiency values, the optimal operating point can deviate. If multiple efficiency curves have different optimal operating points, it can confuse readers. Therefore, to ensure accuracy, we did not include other CFD curves. We hope the reviewer understands it. Thank you once again.
Point 2:It would also be good to clarify how the deviation was calculated (line 138).
Response 2: According to the reviewer’s comments, add calculation method instruction, which shown in the below picture marked by red color.
Point 3:The results are fascinating, and they meet the objective of this paper, allowing us to observe allow us to observe an improvement in terms of head, efficiency and reduction of head fluctuations. The comparisons between the various solutions are interesting and very clear. despite this, it is suggested that the difference between optimized and optimal solution should be better clarified.
Response 3: According to the reviewer’s comments, thanks for your good suggestion. Additional comment is in the article shown as below.
Point 4:
I repute that the topic is interesting and the paper achieved attractive results thus I suggest to consider the manuscript through Minor Revision.
You can find suggestions and typing errors as follows:
- The figures are not aligned with the center of the text;
- In lines 128 and 130 index “i” must be a subscript;
- In Figure 5, the scale of the efficiency axis does not start from 0;
- In the legend of figure 15 replace "origiunal" with "original"
- On the x-axis of Figure 15, enter the unit of measurement
Response 3: According to the reviewer’s comments, reply shown as below.
- The figures are not aligned with the center of the text;
- In lines 128 and 130 index “i” must be a subscript;
- In Figure 5, the scale of the efficiency axis does not start from 0;
- In the legend of figure 15 replace "origiunal" with "original"
- On the x-axis of Figure 15, enter the unit of measurement
Author Response File: Author Response.pdf
