Vortex-Pressure Fluctuation Interaction in the Outlet Duct of Centrifugal Pump as Turbines (PATs)
Round 1
Reviewer 1 Report
The vorticity-pressure fluctuation interaction in the outlet duct of a centrifugal pump as turbines have been investigated by the numerical method. Validation of numerical results was verified through the hydraulic performance test. The comparison between results obtained by CFD and experiment method was performed. The spatial and temporal evolution of vortex in the outlet duct under different operation conditions were compared. The conclusions thoroughly supported by the results presented in the manuscript.
Formatting mistakes:
best efficiency point (BEP) - should be explained in page 2, there it is first time mentioned.
Figure 8, 9, 10 - it is unclear scale - highest and lowest values of static pressure are marked in red or blue colors? In figure 11 - the scale - lowest values of velocity are marked in red (value close to 0) and highest values - in blue (value close to 10)?
Author Response
The vorticity-pressure fluctuation interaction in the outlet duct of a centrifugal pump as turbines have been investigated by the numerical method. Validation of numerical results was verified through the hydraulic performance test. The comparison between results obtained by CFD and experiment method was performed. The spatial and temporal evolution of vortex in the outlet duct under different operation conditions were compared. The conclusions thoroughly supported by the results presented in the manuscript.
Re: Thank you for your comment. We have revised the manuscript according to your suggestion.
- best efficiency point (BEP) - should be explained in page 2, there it is first time mentioned.
Re: Thank you for your suggestion. In the revised manuscript, we have explained the BEP in page 2.
- Figure 8, 9, 10 - it is unclear scale - highest and lowest values of static pressure are marked in red or blue colors? In figure 11 - the scale - lowest values of velocity are marked in red (value close to 0) and highest values - in blue (value close to 10)?
Re: Thank you for point this out. The scale in Figure8, 9, 10 represents the value of local static pressure, the lowest values areas are colored in blue and the highest values areas are colored in red. The scale of the legend has been revised to make it clear.
In figure 11, the scale of non-dimensional parameter V* lowest values are marked in blue (value close to 0) and highest values marked in red (value close to 0.7), the non-dimensional parameter V* is defined as follows:
where v and represent the local velocity of the outlet duct section and the circumferential velocity of the impeller leading edge.
To makes the overall pictures of the manuscript uniform, we revised the color of figure 11.
Figure 11. Streamline by velocity in the outlet duct in different sections at the BEP condition.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Typesetting Problems:
In Figure 5, Image name should be on page 8.
In Figure 4, Figure 6 and Figure 7, the scale line should be inward.
The color of the right axis of Figure 6 is inconsistent with the efficiency curve.
In Figure 11, the bottom left text is overlaid by the background color.
Overall layout is relatively loose, it is recommended to modify part of the map size to make compact layout.
Content Problems:
In Figure 2, what is the relative position of the outlet duct to the impeller? Is the arrow flow direction?
Sensitivity analysis of transient calculation time step is absent in this paper. What is the basis for selecting the last five circles as the results for analysis?
The article lacks the general process of the Q-Vortex identification criterion and the process of the vortex in the outlet duct of this text.
In Figure 8, Figure 9, and Figure 10, what are the parameters represented by the ruler for the representative time of each image?
Can it compare the vortex and static pressure, vorticity and pressure pulsation frequency under at part load condition, the over load condition and BEP condition at the same time?
Key conclusions lack literature support.
Author Response
- In Figure 5, Image name should be on page 8.
Re: Thank you for your comment. We have revised the manuscript according to your suggestion.
- In Figure 4, Figure 6 and Figure 7, the scale line should be inward.
Re: Thank you for your comment. We have revised the orientation of the scale line in Figure 4, Figure 6, and Figure 7 according to your suggestion.
- The color of the right axis of Figure 6 is inconsistent with the efficiency curve.
Re: Thank you for your comment. We have revised the color of the right axis of Figure 6 according to your suggestion.
- In Figure 11, the bottom left text is overlaid by the background color.
Re: Thank you for your comment. We have revised the Figure 11 according to your suggestion.
- Overall layout is relatively loose, it is recommended to modify part of the map size to make compact layout.
Re: Thank you for your suggestion. We have reorganized the overall layout of the manuscript to make a compact layout according to your suggestion.
- In Figure 2, what is the relative position of the outlet duct to the impeller? Is the arrow flow direction?
Re: Thank you for your comment. We have revised Figure 2 and pointed to the relative position of the outlet duct to the impeller outlet.
- Sensitivity analysis of transient calculation time step is absent in this paper. What is the basis for selecting the last five circles as the results for analysis?
Re: Thank you for point this out. We don’t conduct the time independence evaluation in the present study as the limitation of time and numerical simulation resources. However, in the present study, the time step under the transient simulation is set to 5.7471×10−5 s corresponding to one degree of impeller rotation which is short enough time step to capture the hydraulic performance, flow characteristic and pressure variation with the times in the PATs. The similar setting was also adopted by previous researchers and obtained excellent numerical results [1-5]. Shu et al compared three different time steps corresponding to 360, 180, and 120 steps of pump impeller per revolution to verify the time step independence. The results illustrated the fluctuations in pressure at the monitoring point almost coincided during different time steps. Hence, they concluded that the time step influence on the numerical simulation results could be ignored [6].
In addition, we also compared the pressure fluctuations frequency domain of the outlet duct and hydraulic performance of PATs obtained by CFD and test. The results illustrated that the dominant frequency of pressure fluctuation in the outlet duct predicted by CFD is in agreement with the experimental results. The prediction errors of efficiency and head of the PATs are 2.47% and 4.91%, respectively. To sum up, we think the time step adopted in the present transient numerical simulation could ensure the numerical prediction accuracy of the hydraulic and dynamic performance of PATs.
As we know that the more numbers of the time domain signal of vorticity and pressure are selected to transform to the frequency domain signal, the more the frequency component of vorticity and pressure fluctuation is closing to the experiment results. In addition, the pressure time domain signal predicted by the numerical simulation becomes relatively stable in the last five impeller circles as illustrated in Fig.1. Hence, in the present study, to clarify the frequency components corresponding to local high amplitude vorticity and pressure pulsations in the outlet duct, the time domain signal of vorticity and pressure in the last five impeller circles was selected to further research. The similar selecting method was also adopted by previous researchers and obtained excellent results [7-9].
Figure 1. Pressure time domain signal predicted by the CFD
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- Zhang W, Chen Z, Zhu B, et al. Pressure fluctuation and flow instability in S-shaped region of a reversible pump-turbine[J]. Renewable Energy, 2020, 154: 826-840.
- The article lacks the general process of the Q-Vortex identification criterion and the process of the vortex in the outlet duct of this text.
Re: Thank you for your comment. We have added the general process of the Q-Vortex identification criterion in the revised manuscript according to your suggestion. The method is based on the eigenequation of the velocity gradient tensor[1-3]:
Hunt et al defined a region over which the second matrix invariant Q＞0 as a vortex tube [4], where Q is expressed as follows:
where A and S represent the anti-symmetric and symmetric part of the velocity gradient tensor, respectively, corresponding to the rotation and deformation in the flow field, respectively.
- Wang L, Wu T, Gong J, et al. Numerical simulation of the wake instabilities of a propeller[J]. Physics of Fluids, 2021, 33(12): 125125.
- Manolesos M, Papadakis G. Investigation of the three-dimensional flow past a flatback wind turbine airfoil at high angles of attack[J]. Physics of Fluids, 2021, 33(8): 085106.
- Lu J, Chen Q, Liu X, et al. Investigation on pressure fluctuations induced by flow instabilities in a centrifugal pump[J]. Ocean Engineering, 2022, 258: 111805.
- Hunt J C R, Wray A A, Moin P. Eddies, streams, and convergence zones in turbulent flows[J]. Studying turbulence using numerical simulation databases, 2. Proceedings of the 1988 summer program, 1988.
- In Figure 8, Figure 9, and Figure 10, what are the parameters represented by the ruler for the representative time of each image?
Re: Thank you for your comment. We have added the explanation of the representative time of each image, that is T0 and T represent the initial time and the total time of one revolution of the impeller, respectively.
- Can it compare the vortex and static pressure, vorticity and pressure pulsation frequency under at part load condition, the over load condition and BEP condition at the same time?
Re: Thank you for your comment. In the present study, the vortex and static pressure distribution in the outlet duct under different flow rate operation conditions were compared at the same time. However, the numerical simulation results are relatively stable in the last five impeller circles, as shown in reply 7. Hence, the time independence is met to investigate the pressure and vorticity pulsation characteristics. In addition, the numbers of the time domain signal of vorticity and pressure are selected to transform to the frequency domain signal is equal.
- Key conclusions lack literature support.
Re: Thank you for your comment. We have revised the manuscript according to your suggestion. Best wishes to you!
Reviewer 3 Report
Scientific article "Vortex-pressure fluctuation interaction in the Outlet duct of centrifugal pump as turbines(PATs)" is devoted to the actual problem of improving the stabilize the operation and further optimization of PATs.
The paper title clearly describes the content of the work. The paper is well written and the quality of the figures is acceptable. The paper is interesting with some valuable conclusions and is recommended for possible publication in Sustainability journal.
Authors have showed that the flow rates of the turbine significantly affect the spatial and temporal evolution of the vortex rope in the outlet duct.
What are the limitations of this study?
In what way were pressure fluctuations and frequency determined in the CFD? I think that this information should pe presented.
What is the application of this work? Briefly talk about the result and the implication of the result in the abstract. Please discuss how the findings in this work relate to existing studies in this area. The authors should present the key contribution of this manuscript clearly and illustrate the importance of this study.
In general, I think the manuscript can be accepted in its present form without any correction, but in my opinion, some of my comments need to be considered in the future or this work.
Author Response
Scientific article "Vortex-pressure fluctuation interaction in the Outlet duct of centrifugal pump as turbines(PATs)" is devoted to the actual problem of improving the stabilize the operation and further optimization of PATs.
The paper title clearly describes the content of the work. The paper is well written and the quality of the figures is acceptable. The paper is interesting with some valuable conclusions and is recommended for possible publication in Sustainability journal.
Authors have showed that the flow rates of the turbine significantly affect the spatial and temporal evolution of the vortex rope in the outlet duct.
Re: Thank you for your comment. We have revised the manuscript according to your suggestion.
- What are the limitations of this study?
Re: Thank you for your comment. We think our work has some limitations as follows: Firstly, the research object is a single-stage cantilever pump as turbine which is commonly used in the chemical industry, however, the PATs applied to recover hydraulic energy has many types such as double-suction hydraulic turbine, Pelton turbine, mixed flow PATs, and multi-stage radial flow PATs. Different types of PATs have different flow characteristic and shows different vorticity and pressure fluctuation performance. Second, without the visualization experiment in the present research to further verify the vortex pattern and its variation rules even though the transient pressure and state hydraulic performance have been verified in the manuscript. Finally, the performance improvement methods were not proposed in the manuscript to stabilize the operation of PATs based on the present research results.
Although the present research has the above limitations, we think the innovation of our research is revealed the frequency components corresponding to local high amplitude vorticity and pressure pulsations in the outlet duct, and established the relationship between vortex evolution with the pressure pulsations. The present results can give a reference to improve the stabilization of the operation of PATs, and we will fill in the deficiency of current research in our future works.
- In what way were pressure fluctuations and frequency determined in the CFD? I think that this information should be presented.
Re: Thank you for your suggestion. We have added a description of how to obtain the frequency component of pressure and vorticity fluctuation in section 3.2 of the revised manuscript. The specific methods are as follows: firstly, the the vorticity and pressure signal of the outlet duct in the impeller's last five revolutions was extracted from the numerical simulation results in CFX-POST. Second, the Fast Fourier Transform (FFT) algorithm was adopted to transform the time-domain signal of the vorticity and pressure into the frequency-domain signal. Last but not least, the sources for the frequency component of pressure and vorticity fluctuation and their relationship were determined by clarifying the frequency components corresponding to local high amplitude vorticity and pressure pulsations.
- What is the application of this work? Briefly talk about the result and the implication of the result in the abstract. Please discuss how the findings in this work relate to existing studies in this area. The authors should present the key contribution of this manuscript clearly and illustrate the importance of this study.
Re: Thank you for your comment. We have revised the abstract of this manuscript according to your suggestion. Although the many references have made major progress in the research of the flow characteristic, pressure fluctuation, and vortex behaviors in the outlet duct of PATs. The vortex generated mechanism and its revolution relation to local pressure fluctuation characteristics in the outlet duct of PATs are still not clear. And few researchers have revealed the frequency components corresponding to local high amplitude vorticity and pressure pulsations in the outlet duct. We think the innovation of our research is revealed the spatial and temporal evolution of vortex in the outlet duct under different operation conditions, and established the relationship between vortex evolution with the local pressure pulsations. The present results can give a reference to improve the stabilization of the operation of PATs.
In general, I think the manuscript can be accepted in its present form without any correction, but in my opinion, some of my comments need to be considered in the future or this work.
Re: Thank you for your comment. We have revised the manuscript according to your suggestion. Best wishes to you!
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
The paper is suggested to be accepted.
