Numerical Simulation Study on Flow Characteristics of Multistage Centrifugal Pumps under Different Inlet Gas Void Fractions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study highlights the negative correlation between gas volume fraction and flow rate, indicating the importance of controlling gas content in order to optimize the performance of multistage pumps. However, I have few comments as mentioned below,

1)The study assumes a constant diameter for the gas phase, which may not accurately represent the actual gas bubble sizes and their effects on the flow characteristics.

2)The study provides insights into the gas distribution and energy characteristics but does not directly address the effects of these factors on pump performance, such as efficiency and stability.

3)It is needed to explore the inter-stage differences in gas distribution and turbulence kinetic energy within the impeller passages.

Comments on the Quality of English Language

English can be improved by editing with the help of native language speaker

Author Response

Dear reviewers,

We sincerely thank the editor and all reviewers for their valuable feedback that we have used to improve the quality of our manuscript. The reviewer comments are laid out below in italicized font and specific concerns have been numbered. Our response is given in normal font and changes/additions to the manuscript are given in the red text.

1. The study assumes a constant diameter for the gas phase, which may not accurately represent the actual gas bubble sizes and their effects on the flow characteristics.

Thanks for the advice. Because the Euler-Euler heterogeneous two-fluid model is used here, the diameter of the gas phase needs to be given in the simulation setting. The model can prove the accuracy of numerical simulation. Here I add references to support this view.

2. The study provides insights into the gas distribution and energy characteristics but does not directly address the effects of these factors on pump performance, such as efficiency and stability.

Thanks for the advice. I added the relevant content in the conclusion.

3. It is needed to explore the inter-stage differences in gas distribution and turbulence kinetic energy within the impeller passages.

Thanks for the advice. I have increased the discussion of inter-level differences in Section 4.3.

Reviewer 2 Report

Comments and Suggestions for Authors

This study focuses on the operation of the multistage pump in transporting gas media, with a detailed investigation of the gas distribution characteristics and energy characteristics. However, the content of this paper needs some improvement, and there is a need for significant improvement in the format and details of the paper. This article can be accepted after major revision. The comments are as follows:

1. In section 3, during the comparison between experiments and simulations, the efficiency difference reached its maximum at the rated operating point, while the efficiency difference was small at low and high flow rates. The author should explain in more detail the reasons for this phenomenon.

2. Authors should improve the standardization of their writing. For example, variables need to be italicized, any symbols that appear should be explained, and all formulas should be numbered. I suggest adding the nomenclature in the article.

3. In section 4.1, the author has drawn a large number of speculative conclusions, and may need to add more data and analysis to enhance the rigor of the paper

4. For the definition of positions in the article, such as IMP1, IMP2, and IMP3 (Fig. 8,9), the author should adopt a more intuitive or detailed description to avoid misunderstandings.

5. In section 4.3, there does not seem to be a strong correlation between the distribution of turbulent kinetic energy and gas distribution. There is a similar distribution of turbulent kinetic energy at the third stage impeller to the first two stages, but there is almost no gas phase at the third stage impeller.

6. In the conclusion section, the author should summarize the purpose, achievements, potential contributions, and future work of the research work.

7. Overall, there is a need for some improvement in the content of this paper, and it is strongly recommended to improve the format and details of the paper to reflect the author's rigor in scientific work.

Author Response

Dear reviewers,

We sincerely thank the editor and all reviewers for their valuable feedback that we have used to improve the quality of our manuscript. The reviewer comments are laid out below in italicized font and specific concerns have been numbered. Our response is given in normal font and changes/additions to the manuscript are given in the red text.

1. In section 3, during the comparison between experiments and simulations, the efficiency difference reached its maximum at the rated operating point, while the efficiency difference was small at low and high flow rates. The author should explain in more detail the reasons for this phenomenon.

Thank you for your advice. In response to this suggestion, we are re-testing it. The reason for this phenomenon is that the abscissa flow coefficient cannot be completely consistent with the simulation setting during the test. In the previous drawing, we mistakenly coincided the coefficients of the test and simulation. It has now been corrected.

2. Authors should improve the standardization of their writing. For example, variables need to be italicized, any symbols that appear should be explained, and all formulas should be numbered. I suggest adding the nomenclature in the article

Thanks for the suggestion, an excellent paper does need better specification. I have perfected the writing norms.

3. In section 4.1, the author has drawn a large number of speculative conclusions, and may need to add more data and analysis to enhance the rigor of the paper。

Thanks for the advice. I have added and improved the relevant data and analysis to enhance the rigor of the paper.

4. For the definition of positions in the article, such as IMP1, IMP2, and IMP3 (Fig. 8,9), the author should adopt a more intuitive or detailed description to avoid misunderstandings.

Thanks for the suggestion, I have changed the full name to avoid misunderstanding.

5. In section 4.3, there does not seem to be a strong correlation between the distribution of turbulent kinetic energy and gas distribution. There is a similar distribution of turbulent kinetic energy at the third stage impeller to the first two stages, but there is almost no gas phase at the third stage impeller

Thanks for the suggestion, I have increased the description of the difference in turbulent kinetic energy between the third-stage impeller and the first two-stage impeller and the correlation between turbulent kinetic energy and gas distribution in different stages of impeller. Here is what I want to express. Under this condition, the turbulent kinetic energy distribution in the first two stages is mainly affected by the gas phase distribution, and the third stage is mainly due to the excessive flow rate of the fluid.

6. In the conclusion section, the author should summarize the purpose, achievements, potential contributions, and future work of the research work.

Thanks for the advice. I have added this part at the end of the conclusion.

7. Overall, there is a need for some improvement in the content of this paper, and it is strongly recommended to improve the format and details of the paper to reflect the author's rigor in scientific work.

Thanks for the suggestion, I have improved the format and details of the paper.

Reviewer 3 Report

Comments and Suggestions for Authors

This study focused on the complex flow dynamics of gas-liquid mixed media in multistage centrifugal pumps. The research was conducted based on numerical simulations using the Euler-Euler heterogeneous two-fluid model, with the corresponding experiments for model validation. This study offers insights into the impacts of gas content, aggregation, flow patterns, and turbulence on the multistage pump performance. The results highlighted gas accumulation on the suction side of each impeller stage, decreasing progressively with subsequent stages. Increasing interstage gas volume fraction intensified gas accumulation within the pump. Gas volume fraction is inversely correlated with flow rate, especially in the impeller. Turbulence kinetic energy distribution in the impeller was influenced by gas distribution, showing fluctuations at specific flow rates. The study suggests that gas presence expands the high-efficiency area of the multistage pump, offering insights for pump design and operational adjustments for gas-liquid mixed pumps.

 

The article is well-organized and well-written. However, the authors should address the following questions before it could be considered for publication:

 

1. Did you consider the rotation of the impeller using dynamic mesh? If not, please discuss how it impacts your simulation accuracy in your manuscript. Additionally, what is the mass force associated with the impeller rotation F in Line 128? More details (model, governing equations, discussion, etc.) need to be included for it.

 

2. In Figure 3, what does the unit of “w” mean in the x-axis? It should be in “million” or similar. The legend should not be included if you only have one curve. 

 

3. For Eqn. (2), how did you model the gas-liquid phase-to-phase interaction? The governing equations for the interfacial force M. 

 

4. Why did you assume a constant sphere diameter (0.3 mm) for your gas phase? The bubble diameter varies when running the pump at different speeds. Normally, the faster the speed, the smaller the diameter. Please illustrate the accuracy of this assumption. 

 

5.  Why did you use a constant pressure of 10 kPa as an inlet boundary condition? The pump inlet pressure typically changes with different flow rates. The mass flow rate range in your simulations varies from 7.39 kg/s to 54.44 kg/s.

 

6. The experimental validation was conducted when the pump was under 750 RPM with a flow rate of 36 CMH and a two-stage setup. However, your results and discussions are all based on a pump configuration of 2875 RPM, 140 CMH, and a three-level setup. Your model accuracy has not yet been evaluated under this condition.

 

Comments on the Quality of English Language

 Minor editing of English language required

Author Response

Dear reviewers,

We sincerely thank the editor and all reviewers for their valuable feedback that we have used to improve the quality of our manuscript. The reviewer comments are laid out below in italicized font and specific concerns have been numbered. Our response is given in normal font and changes/additions to the manuscript are given in the red text.

1. Did you consider the rotation of the impeller using dynamic mesh? If not, please discuss how it impacts your simulation accuracy in your manuscript. Additionally, what is the mass force associated with the impeller rotation F in Line 128? More details (model, governing equations, discussion, etc.) need to be included for it.

Thank you for your advice. We are sorry that we have not considered the dynamic mesh for the time being. We use Cfx to simulate the Euler-Euler heterogeneous two-fluid model. The accuracy of the model also increases the reference proof. In addition, the relevant details of the mass force of F have been given.

2. In Figure 3, what does the unit of “w” mean in the x-axis? It should be in “million” or similar. The legend should not be included if you only have one curve. 

Thank you for your tips. Yes, the unit here is wrong. I have changed ' w ' to ' 10⁴ ' and have corrected the legend.

3. For Eqn. (2), how did you model the gas-liquid phase-to-phase interaction? The governing equations for the interfacial force M.

Thank you for your advice. I have added relevant details and references to interpret the equation.

4. Why did you assume a constant sphere diameter (0.3 mm) for your gas phase? The bubble diameter varies when running the pump at different speeds. Normally, the faster the speed, the smaller the diameter. Please illustrate the accuracy of this assumption. 

Thanks for the advice. Because the Euler-Euler heterogeneous two-fluid model is used here, the diameter of the gas phase needs to be given in the simulation setting. The model can prove the accuracy of numerical simulation. Here I add references to support this view.

5. Why did you use a constant pressure of 10 kPa as an inlet boundary condition? The pump inlet pressure typically changes with different flow rates. The mass flow rate range in your simulations varies from 7.39 kg/s to 54.44 kg/s.

Thanks for the suggestion, I agree with the view that the inlet pressure of the pump changes with the flow rate. The inlet boundary condition set on my side refers to the inlet of the inlet section of the pump, that is, the leftmost end of Figure 2 ( A ), and a constant pressure of 10 kPa is set. This is because during the test, the liquid level difference between the inlet section and the water tank is one meter, so the pressure of the inlet boundary condition of the whole system is given a constant 10 kPa in the numerical simulation.

6. The experimental validation was conducted when the pump was under 750 RPM with a flow rate of 36 CMH and a two-stage setup. However, your results and discussions are all based on a pump configuration of 2875 RPM, 140 CMH, and a three-level setup. Your model accuracy has not yet been evaluated under this condition.

Thank you for your advice. The principle here is the similarity theorem, and I have added relevant literature to testify.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This revised version can be accepted for publication in the present form

Comments on the Quality of English Language

Edit english with Native english speaker