Influence of Eccentricity on Hydrodynamic Characteristics of Nuclear Reactor Coolant Pump under Different Cavitation Conditions
Round 1
Reviewer 1 Report
Major comments
1. Pages 3-6: The quality of figures is very low, see e.g. Figs. 1, 2, 3, 4, 5, 6a). The figures should have larger dimensions and better resolution. At the current state of the figures it is impossible to understand the figures as well as their descriptions in the text. Why the upper part of the larger circle in Fig. 1 is flatten? What is in the bottom part of Fig. 1? What are the two diameters shown in Fig. 1? Where is the inlet/outlet in Fig. 1? Please give a few explanations to Fig. 1 - give those explanations in Fig. 1. Similar comment is valid also for Fig. 2 - give explanations to the details given in Fig. 2.
2. Page 4, line 125:
a) Why have you assumed so large values of eccentricity? Have you or other engineers observed such large values of shaft eccentricities in nuclear coolant pumps? Can you give any literature sources confirming the assumed values, e.g. the very large value of $e=20$ mm?
b) What is the cause of the assumed shaft eccentricity in the coolant pump? Is this eccentricity due to a flexible deformation of the shaft line or due to a deformation of the bearings or the deformation of the bearings’ supports???
3. Page 5, Fig. 4: There are very few details of the assumed FEM model given.
a) It is not clear if the FEM model shown in Fig. 4 is the 2D or 3D model? If you consider the flow in 3D than please give another plot showing that it is really a 3D model.
b) It is not clear if the rotor in the model shown in Fig. 4 rotates? If it rotates then how do you update the mesh? If it does not rotate, then does the water/vapor around it rotate?
4. Page 13, lines 363-383: Please explain the practical importance of the obtained “Conclusions”. How can the nuclear power plant engineer benefit from the results obtained by you? How can he/she benefit from the fact that “Under severe cavitation conditions, the difference of eccentricity schemes is most significant in the range of 90 to 240 degrees” or that “Under critical and severe cavitation conditions, the maximum axial force amplitude of the nuclear reactor pump appears at 2 times of the blade frequency”?
Minor points
1. Pages 2, 3 and 4: Equations (1) - (7) are not used in the rest of the paper. I recommend removing those equations from the paper.
2. Page 2, line 90: How have you obtained the empirical formulae Eq. (1)? Is it your own contribution or do you cite it from some literature source?
3. Page 3, line 94: Please, explain in a figure the following quantity: “$B_2$ - the blade outlet width included the cover plate, m”.
4. Page 3, line 96: “The flow in maximum efficiency point;” - What are the units of this “flow”? How do you define the maximum efficiency point?
5. Page 3, lines 100-106: “Using the hydraulic... ... ... balance the pressure at the S3.” - It is impossible to understand these descriptions, when the quality of Figs. 1 and 2 is very low. What do you mean by “the downward eccentric delta of the impeller center line $\Delta$”? Where are S1, S2 and S3 regions in Fig. 2?
6. Pages 3 and 4: The quantities given in Eqs. (2) - (7) are unclear when Fig. 2 is of so low quality. Those quantities should be explained in Fig. 2.
7. Page 4, line 117: In Fig. 3 the eccentricity is marked as $d$ but in the explanations below Fig. 3 this eccentricity is denoted as $e$. Please take care of the consistency of denotations.
8. Page 4, lines 131, 132: “... the size of the prototype pump is reduced and tested.” - Can you explain the reduction of the pump’s size? How much has been the pump reduced in size? What do you understand by the statement that the “size of the prototype pump is ... tested”. How have you tested the size of the pump?
9. Page 5, line 136:
a) Why the same values are given twice in Tab. 1? There are the same values in two different rows of the table.
b) What are the units for the “Specific speed” $n_s$ in Tab. 1?
c) The designed head $H$ is given as 3.37 m in Tab. 1, yet in the text in lines 153-154 (or in Fig. 5) this head is given as 106.17 m, 110.41 m and 110.63 m - which values of the head are correct?
10. Page 5, line 137: The quality of Fig. 4 must be improved.
11. Page 5, line 144: Figure 5 does not explain anything and can be deleted - the explanations given in the text in lines 153-154 are enough.
12. Page 6, line 178:
a) Please denote the coolant pump in Fig. 6a).
b) Please enlarge Fig. 6b) and improve its quality.
13. Page 7-12: Figures 6 - 11 should be renumbered as 7 - 12.
14. Page 7, line 196: Is Fig. 7 a part of Fig. 4? If yes, then which part of Fig. 4 is presented in Fig. 6? If not, then how have you obtained Fig. 6?
15. Page 7, line 199: “The vapor phase volume fraction diagram of three different inlet blades...” - There are rather 5 blades shown in Fig. 6 - not 3.
16. Pages 7, 11 : From Figs. 7c) and 10c) it is clear that the simulation time of 0.24324 s is too short - the presented curves do not stabilize but decrease/increase constantly.
17. Page 11, lines 314, 315: “The maximum amplitude of the five groups... are 385 N, 306 N, 377 N, 375 N and 395 N...” - These low values can be observed also in Fig. 12a) but in Fig. 11a) those values are extremely larger - of about -149500 N? How have you obtained Fig. 12? Is Fig. 12 based on the results presented in Fig. 11?
18. Page 12: Please denote the frequency peaks described in the text (“shaft frequency”, “blade frequency”, “three times of blade frequency”, “2 times of blade frequency”, “7 times the blade frequency”.
Language mistakes
Page 1, line 12: Explain the acronym “RNG”
Page 1, line 20: “... the radial force changed... was small.” -> “... the radial force changes... is small.”
Page 1, line 21: “... of radial force was... impeller appeared.” -> “... of radial force is... impeller appears.”
Page 1, lines 22, 23: “... the axial force value of impeller decreases, but the corresponding amplitude of the impeller increases.” - What do you mean by the “corresponding amplitude”?
Page 1, line 29: “... the axial force of the impeller is the smallest, but the amplitude is the largest...” - What “amplitude” do you mean?
Page 1, lines 37, 39: “... hottest topics[29]. ... nuclear power plant[3].” -> “... hottest topics [29]. ... nuclear power plant [3].” - There should be a space between the word and the literature reference - correct in lines 37, 39 and in other places in the text.
Page 3, line 94: “The blade outlet width included the cover plate, m” -> “the blade outlet width including the cover plate width, m”??? - the meaning of this sentence is unclear.
Page 3, line 96: “The flow in maximum efficiency point;” -> “the flow rate in the maximum efficiency point;”
Page 3, line 109: “The areaS1, S2 and S3are used to approximate representation the pressure.” -> “The areas S1, S2 and S3 are used to approximate the representation of the pressure.”
Page 3, line 110: “... among them meat the in equation (2):” -> “... among them to meet equation (2):” ???
Page 4, line 113: “The guide vane diameter;” -> “the guide blade diameter;” ???
Page 4, line 114: “Half of the central Angle...” -> “half of the central angle...”
Page 6, line 183: “... 140 KPa, 110 KPa and 100 KPa...$ -> “... 140 kPa, 110 kPa and 100 kPa...”
Page 8, line 216: “Fig. 7 shown that...” -> “Fig. 8 shows that...”
Page 9, lines 250, 251: “... the radial force in the adjacent four cycles is close, and the periodic variation of the original radial force is not obvious.” - The meaning of this sentence is unclear. What do you mean by the “close... radial force” or “not obvious ... radial force”?
Page 10, line 271: “Compare the three pictures...” -> “Comparing the three pictures...”
Author Response
Reviewer 1
Comments and Suggestions for Authors
Major comments
Pages 3-6: The quality of figures is very low, see e.g. Figs. 1, 2, 3, 4, 5, 6a). The figures should have larger dimensions and better resolution. At the current state of the figures it is impossible to understand the figures as well as their descriptions in the text. Why the upper part of the larger circle in Fig. 1 is flatten? What is in the bottom part of Fig. 1? What are the two diameters shown in Fig. 1? Where is the inlet/outlet in Fig. 1? Please give a few explanations to Fig. 1 - give those explanations in Fig. 1. Similar comment is valid also for Fig. 2 - give explanations to the details given in Fig. 2.
Figure 1 and figure 2 represent the same meaning, and it is finally decided to leave figure 1 out. FIG. 2 (which has been changed to FIG. 1) is a schematic diagram of the annular volute structure, which is a hydraulic design method that shifts the center line of the impeller to the lower part of the volute center line to form eccentric pressure (regions S1 and S2 in the figure). The purpose of this method is to balance the pressure at the exit relative to the position (the S3 area in the figure).
Page 4, line 125: a) Why have you assumed so large values of eccentricity? Have you or other engineers observed such large values of shaft eccentricities in nuclear coolant pumps? Can you give any literature sources confirming the assumed values, e.g. the very large value of $e=20$ mm?
This is for better comparison, thus highlighting the significance of eccentricity in this study. And the eccentricity value e=20mm is not large.
b) What is the cause of the assumed shaft eccentricity in the coolant pump? Is this eccentricity due to a flexible deformation of the shaft line or due to a deformation of the bearings or the deformation of the bearings’ supports???
This is because the volute is not completely symmetrical (due to the existence of the outlet), so the circumferential pressure of the impeller is not balanced, so the eccentric design is adopted to solve this problem.
Page 5, Fig. 4: There are very few details of the assumed FEM model given. a) It is not clear if the FEM model shown in Fig. 4 is the 2D or 3D model? If you consider the flow in 3D than please give another plot showing that it is really a 3D model.
Modifications have been made in the text.
b) It is not clear if the rotor in the model shown in Fig. 4 rotates? If it rotates then how do you update the mesh? If it does not rotate, then does the water/vapor around it rotate?
Modifications have been made in the text. The impeller, as a rotating part, adopts a rotating coordinate system, and the definition domain is set as Rotating domain. The rotation speed of the impeller is set as 1480r/min. There are three main interfaces to be set in this paper, namely the interface of inlet section - impeller, impeller - guide vane and guide vane - volute, which are set as the Frozen Rotor.
Page 13, lines 363-383: Please explain the practical importance of the obtained “Conclusions”. How can the nuclear power plant engineer benefit from the results obtained by you? How can he/she benefit from the fact that “Under severe cavitation conditions, the difference of eccentricity schemes is most significant in the range of 90 to 240 degrees” or that “Under critical and severe cavitation conditions, the maximum axial force amplitude of the nuclear reactor pump appears at 2 times of the blade frequency”?
Modifications have been made in the text. It can provide reference for the design of nuclear main pump.
Minor points
Pages 2, 3 and 4: Equations (1) - (7) are not used in the rest of the paper. I recommend removing those equations from the paper.
It has been deleted in the text.
Page 2, line 90: How have you obtained the empirical formulae Eq. (1)? Is it your own contribution or do you cite it from some literature source?
This equation is a formula for calculating axial and radial forces of the volute in the pump theory manual.
Page 3, line 94: Please, explain in a figure the following quantity: “$B_2$ - the blade outlet width included the cover plate, m”.
Modifications have been made in the text. (Some worthless formulas have been deleted.)
Page 3, line 96: “The flow in maximum efficiency point;” - What are the units of this “flow”? How do you define the maximum efficiency point?
The unit of flow is m3/h, and the maximum efficiency point is the maximum efficiency obtained by numerical simulation on the external characteristic curve. The flow here is considered the flow at the maximum efficiency point.
Page 3, lines 100-106: “Using the hydraulic... ... ... balance the pressure at the S3.” - It is impossible to understand these descriptions, when the quality of Figs. 1 and 2 is very low. What do you mean by “the downward eccentric delta of the impeller center line $\Delta$”? Where are S1, S2 and S3 regions in Fig. 2?
This is because the volute is not completely symmetrical (due to the existence of water outlet), the circumferential fluid pressure of the impeller is not balanced, mainly S1, S2 and S3 regions will generate eccentric force of the impeller. Therefore, the eccentric design is adopted to solve this problem.
Pages 3 and 4: The quantities given in Eqs. (2) - (7) are unclear when Fig. 2 is of so low quality. Those quantities should be explained in Fig. 2.
Modifications have been made in the text.
Page 4, line 117: In Fig. 3 the eccentricity is marked as $d$ but in the explanations below Fig. 3 this eccentricity is denoted as $e$. Please take care of the consistency of denotations.
Modifications have been made in the text.
Page 4, lines 131, 132: “... the size of the prototype pump is reduced and tested.” - Can you explain the reduction of the pump’s size? How much has been the pump reduced in size? What do you understand by the statement that the “size of the prototype pump is ... tested”. How have you tested the size of the pump?
The flow rate of the impeller of the prototype pump reached 17886m3/h, which could not be met by the test bed. Therefore, according to the similar transformation, the prototype pump was shrunk to carry out the test. According to the principle of similarity transformation, the flow law of the reduced pump is also similar.
Page 5, line 136: a) Why the same values are given twice in Tab. 1? There are the same values in two different rows of the table.
Modifications have been made in the text. And table 1 is changed to the parameters of the prototype pump, and table 2 is the parameters of the converted model pump.
b) What are the units for the “Specific speed” $n_s$ in Tab. 1?
The specific speed formula is . It is an industry standard that defines a pump parameter.
c) The designed head $H$ is given as 3.37 m in Tab. 1, yet in the text in lines 153-154 (or in Fig. 5) this head is given as 106.17 m, 110.41 m and 110.63 m - which values of the head are correct?
3.37m is the design head of the prototype pump, and 111.3m is the head of the converted pump. In this paper, the head is specified as 106.17m, 110.41m and 110.63m, which are obtained by the original model pump simulation, not by experiment.
Page 5, line 137: The quality of Fig. 4 must be improved.
Modifications have been made in the text.
Page 5, line 144: Figure 5 does not explain anything and can be deleted - the explanations given in the text in lines 153-154 are enough.
Modifications have been made in the text.
Page 6, line 178: a) Please denote the coolant pump in Fig. 6a). b) Please enlarge Fig. 6b) and improve its quality.
Modifications have been made in the text.
Page 7-12: Figures 6 - 11 should be renumbered as 7 - 12.
Modifications have been made in the text.
Page 7, line 196: Is Fig. 7 a part of Fig. 4? If yes, then which part of Fig. 4 is presented in Fig. 6? If not, then how have you obtained Fig. 6?
FIG. 7 is the expansion diagram of five blades in FIG. 4, which is part of FIG. 4.
Page 7, line 199: “The vapor phase volume fraction diagram of three different inlet blades...” - There are rather 5 blades shown in Fig. 6 - not 3.
It should be“The vapor phase volume fraction diagram of three different inlet pressure condition”. Modifications have been made in the text.
Pages 7, 11 : From Figs. 7c) and 10c) it is clear that the simulation time of 0.24324 s is too short - the presented curves do not stabilize but decrease/increase constantly.
In the simulation, the rotation time of the impeller is 60/1480=0.0405, while in the unsteady calculation of CFX, 0.24324s is the rotation of the impeller for 6 turns. In this paper, the simulation result of the 6th turn is selected for analysis, and the calculation result meets the requirements.
Page 11, lines 314, 315: “The maximum amplitude of the five groups... are 385 N, 306 N, 377 N, 375 N and 395 N...” - These low values can be observed also in Fig. 12a) but in Fig. 11a) those values are extremely larger - of about -149500 N? How have you obtained Fig. 12? Is Fig. 12 based on the results presented in Fig. 11?
The maximum amplitudes of the five groups refer to the radial force, and the approximately -149500N shown in figure 11 refers to the axial force. The +Z axis is pointed from the front cover plate of the impeller to the rear cover plate. The axial force is negative in the figure, indicating that the axial force direction points to the impeller inlet. Both axial and radial forces are obtained by numerical simulation.
Page 12: Please denote the frequency peaks described in the text (“shaft frequency”, “blade frequency”,“three times of blade frequency”, “2 times of blade frequency”, “7 times the blade frequency”.
The impeller speed of the pump designed in this paper is 1480r/min, and the number of blades is 5. The axial frequency can be calculated as 24.67Hz and the blade frequency as 123.33Hz. “Three times of blade frequency”, “2 times of blade frequency”, “7 times the blade frequency” respectively refer to multiplying the blade frequency by several times.
Language mistakes
Page 1, line 12: Explain the acronym “RNG”
Modifications have been made in the text. This is a common turbulence model.
Page 1, line 20: “... the radial force changed... was small.” -> “... the radial force changes... is small.”
Modifications have been made in the text.
Page 1, line 21: “... of radial force was... impeller appeared.” -> “... of radial force is... impeller appears.”
Modifications have been made in the text.
Page 1, lines 22, 23: “... the axial force value of impeller decreases, but the corresponding amplitude of the impeller increases.” - What do you mean by the “corresponding amplitude”?
The amplitude is the range in which the axial force fluctuates up and down based on the mean value (equivalent size).
Page 1, line 29: “... the axial force of the impeller is the smallest, but the amplitude is the largest...” - What “amplitude” do you mean?
The amplitude is the range in which the axial force fluctuates up and down based on the mean value (equivalent size). And the amplitude refers to the vibration amplitude of the impeller's shaft.
Page 1, lines 37, 39: “... hottest topics[29]. ... nuclear power plant[3].” -> “... hottest topics [29]. ... nuclear power plant [3].” - There should be a space between the word and the literature reference - correct in lines 37, 39 and in other places in the text.
Modifications have been made in the text.
Page 3, line 94: “The blade outlet width included the cover plate, m” -> “the blade outlet width including the cover plate width, m”??? - the meaning of this sentence is unclear.
This section has been removed from this article.
Page 3, line 96: “The flow in maximum efficiency point;” -> “the flow rate in the maximum efficiency point;”
This section has been removed from this article.
Page 3, line 109: “The areaS1, S2 and S3are used to approximate representation the pressure.” -> “The areas S1, S2 and S3 are used to approximate the representation of the pressure.”
Modifications have been made in the text.
Page 3, line 110: “... among them meat the in equation (2):” -> “... among them to meet equation (2):” ???
Modifications have been made in the text.
Page 4, line 113: “The guide vane diameter;” -> “the guide blade diameter;” ???
Modifications have been made in the text.
Page 4, line 114: “Half of the central Angle...” -> “half of the central angle...”
Modifications have been made in the text.
Page 6, line 183: “... 140 KPa, 110 KPa and 100 KPa...$ -> “... 140 kPa, 110 kPa and 100 kPa...”
Modifications have been made in the text.
Page 8, line 216: “Fig. 7 shown that...” -> “Fig. 8 shows that...”
Modifications have been made in the text.
Page 9, lines 250, 251: “... the radial force in the adjacent four cycles is close, and the periodic variation of the original radial force is not obvious.” - The meaning of this sentence is unclear. What do you mean by the “close... radial force” or “not obvious ... radial force”?
Modifications have been made in the text. This sentence indicates that when cavitation develops to severe cavitation, the variability of radial force on the impeller between 90° and 240° is less than that in other directions, and the peak value of the radial force in the adjacent four cycles is close, and the periodic change of radial force in the original scheme of e=0mm is not obvious.
Page 10, line 271: “Compare the three pictures...” -> “Comparing the three pictures...”
Modifications have been made in the text.
Reviewer 2 Report
The statement that"Small break loss of coolant accident(SBLOCA), a very common accident condition" is incorrent. It is a commonly analyzed accident condition, but not a common accident condition. Figures 1 and 2 could be improved to make clearer what are the important differences. It was not clear why the selected total pressures were chosen. They represent different levels of cavitation, and this should be poited out when they are introduced. The overall numerical analysis and description of results were exceptional. This is a very worthwhile investigation. I would prefer to see the results generalized so as to identify limiting conditions. Or perhaps the impact of the results on possible pump failure. I realize this is not a structural analysis paper, but some comments on the impact of the results on pump failure as part of the accident scenario would be appropriate given the effort put into calculating radial and axial forces.
Author Response
Reviewer 2
Comments and Suggestions for Authors
The statement that"Small break loss of coolant accident(SBLOCA), a very common accident condition" is incorrent. It is a commonly analyzed accident condition, but not a common accident condition. Figures 1 and 2 could be improved to make clearer what are the important differences. It was not clear why the selected total pressures were chosen. They represent different levels of cavitation, and this should be poited out when they are introduced. The overall numerical analysis and description of results were exceptional. This is a very worthwhile investigation. I would prefer to see the results generalized so as to identify limiting conditions. Or perhaps the impact of the results on possible pump failure. I realize this is not a structural analysis paper, but some comments on the impact of the results on pump failure as part of the accident scenario would be appropriate given the effort put into calculating radial and axial forces.
Modifications have been made in the text.
Round 2
Reviewer 1 Report
I am mostly satisfied with the Authors responses and/or corrections to the text. However a few points need further clarification/improvement. My comments to the Authors reponses are given below and marked in yellow.
Major comments
Pages 3-6: The quality of figures is very low, see e.g. Figs. 1, 2, 3, 4, 5, 6a). The figures should have larger dimensions and better resolution. At the current state of the figures it is impossible to understand the figures as well as their descriptions in the text. Why the upper part of the larger circle in Fig. 1 is flatten? What is in the bottom part of Fig. 1? What are the two diameters shown in Fig. 1? Where is the inlet/outlet in Fig. 1? Please give a few explanations to Fig. 1 - give those explanations in Fig. 1. Similar comment is valid also for Fig. 2 - give explanations to the details given in Fig. 2.
Figure 1 and figure 2 represent the same meaning, and it is finally decided to leave figure 1 out. FIG. 2 (which has been changed to FIG. 1) is a schematic diagram of the annular volute structure, which is a hydraulic design method that shifts the center line of the impeller to the lower part of the volute center line to form eccentric pressure (regions S1 and S2 in the figure). The purpose of this method is to balance the pressure at the exit relative to the position (the S3 area in the figure).
OK.
Page 4, line 125: a) Why have you assumed so large values of eccentricity? Have you or other engineers observed such large values of shaft eccentricities in nuclear coolant pumps? Can you give any literature sources confirming the assumed values, e.g. the very large value of $e=20$ mm?
This is for better comparison, thus highlighting the significance of eccentricity in this study. And the eccentricity value e=20mm is not large.
I am not satisfied with your response. Can you give any literature sources confirming such large values of shaft eccentricity of $e=20$ mm in nuclear cooling pumps?
b) What is the cause of the assumed shaft eccentricity in the coolant pump? Is this eccentricity due to a flexible deformation of the shaft line or due to a deformation of the bearings or the deformation of the bearings’ supports???
This is because the volute is not completely symmetrical (due to the existence of the outlet), so the circumferential pressure of the impeller is not balanced, so the eccentric design is adopted to solve this problem.
I am not satisfied with this response.
a) As I understand you define the eccentricity as the difference between the centerline of the impeller and the centerline of the volute - is that right? From Fig. 2. it is not clear how you define the eccentricity.
b) As I understand this difference (the eccentricity) occurs as a result of different pressures in sections S1, S2 and S3 - thus as a result of different radial forces in sections S1, S2 and S3 applied to the shaft. So my question is: does the shaft flexibly deform due to this difference in forces? Or do the bearings deform? Or do the bearings supports deform? Which is the physical explanation for the appearance of the shaft eccentricity?
c) If you assume that the shaft eccentricity is $e=20$ mm, then it follows that the rub occurs between the blade tips of the impeller and the volute - is it right? I mean the contact between the blade tips and the volute occurs during the rotation of the impeller?
Page 5, Fig. 4: There are very few details of the assumed FEM model given. a) It is not clear if the FEM model shown in Fig. 4 is the 2D or 3D model? If you consider the flow in 3D than please give another plot showing that it is really a 3D model.
Modifications have been made in the text.
OK.
b) It is not clear if the rotor in the model shown in Fig. 4 rotates? If it rotates then how do you update the mesh? If it does not rotate, then does the water/vapor around it rotate?
Modifications have been made in the text. The impeller, as a rotating part, adopts a rotating coordinate system, and the definition domain is set as Rotating domain. The rotation speed of the impeller is set as 1480r/min. There are three main interfaces to be set in this paper, namely the interface of inlet section - impeller, impeller - guide vane and guide vane - volute, which are set as the Frozen Rotor.
OK.
Page 13, lines 363-383: Please explain the practical importance of the obtained “Conclusions”. How can the nuclear power plant engineer benefit from the results obtained by you? How can he/she benefit from the fact that “Under severe cavitation conditions, the difference of eccentricity schemes is most significant in the range of 90 to 240 degrees” or that “Under critical and severe cavitation conditions, the maximum axial force amplitude of the nuclear reactor pump appears at 2 times of the blade frequency”?
Modifications have been made in the text. It can provide reference for the design of nuclear main pump.
I am not satisfied with this response. There are no modifications in the text explaining the practical importance of your conclusions.
From your response it follows that the conclusions are important when the design of a new nuclear pump is considered. So please include the following sentence from your response in the “Introduction” (in line 76) and in the “Conclusion” (in line 378):
“The obtained results can provide reference for the design of new nuclear main pumps.”
Anyhow, do you really want to design a new nuclear main pump? Do you want to become the manufacturer of such new pumps?
I suppose not, so the practical importance of the obtained results and of the conclusions is marginal.
I hope you agree with me?
Minor points
Pages 2, 3 and 4: Equations (1) - (7) are not used in the rest of the paper. I recommend removing those equations from the paper.
It has been deleted in the text.
OK.
Page 2, line 90: How have you obtained the empirical formulae Eq. (1)? Is it your own contribution or do you cite it from some literature source?
This equation is a formula for calculating axial and radial forces of the volute in the pump theory manual.
OK.
Page 3, line 94: Please, explain in a figure the following quantity: “$B_2$ - the blade outlet width included the cover plate, m”.
Modifications have been made in the text. (Some worthless formulas have been deleted.)
OK.
Page 3, line 96: “The flow in maximum efficiency point;” - What are the units of this “flow”? How do you define the maximum efficiency point?
The unit of flow is m3/h, and the maximum efficiency point is the maximum efficiency obtained by numerical simulation on the external characteristic curve. The flow here is considered the flow at the maximum efficiency point.
OK.
Page 3, lines 100-106: “Using the hydraulic... ... ... balance the pressure at the S3.” - It is impossible to understand these descriptions, when the quality of Figs. 1 and 2 is very low. What do you mean by “the downward eccentric delta of the impeller center line $\Delta$”? Where are S1, S2 and S3 regions in Fig. 2?
This is because the volute is not completely symmetrical (due to the existence of water outlet), the circumferential fluid pressure of the impeller is not balanced, mainly S1, S2 and S3 regions will generate eccentric force of the impeller. Therefore, the eccentric design is adopted to solve this problem.
OK.
Pages 3 and 4: The quantities given in Eqs. (2) - (7) are unclear when Fig. 2 is of so low quality. Those quantities should be explained in Fig. 2.
Modifications have been made in the text.
OK.
Page 4, line 117: In Fig. 3 the eccentricity is marked as $d$ but in the explanations below Fig. 3 this eccentricity is denoted as $e$. Please take care of the consistency of denotations.
Modifications have been made in the text.
OK.
Page 4, lines 131, 132: “... the size of the prototype pump is reduced and tested.” - Can you explain the reduction of the pump’s size? How much has been the pump reduced in size? What do you understand by the statement that the “size of the prototype pump is ... tested”. How have you tested the size of the pump?
The flow rate of the impeller of the prototype pump reached 17886m3/h, which could not be met by the test bed. Therefore, according to the similar transformation, the prototype pump was shrunk to carry out the test. According to the principle of similarity transformation, the flow law of the reduced pump is also similar.
OK.
Page 5, line 136: a) Why the same values are given twice in Tab. 1? There are the same values in two different rows of the table.
Modifications have been made in the text. And table 1 is changed to the parameters of the prototype pump, and table 2 is the parameters of the converted model pump.
OK.
b) What are the units for the “Specific speed” $n_s$ in Tab. 1?
The specific speed formula is . It is an industry standard that defines a pump parameter.
OK.
c) The designed head $H$ is given as 3.37 m in Tab. 1, yet in the text in lines 153-154 (or in Fig. 5) this head is given as 106.17 m, 110.41 m and 110.63 m - which values of the head are correct?
3.37m is the design head of the prototype pump, and 111.3m is the head of the converted pump. In this paper, the head is specified as 106.17m, 110.41m and 110.63m, which are obtained by the original model pump simulation, not by experiment.
From the modified Tabs. 1 and 2 it follows that the design head of the prototype pump is 111.3 m and the designed head of the converted pump is 3.83 m. Is this right?
Page 5, line 137: The quality of Fig. 4 must be improved.
Modifications have been made in the text.
I asked only to improve the quality of (previous) Fig. 4 - not to remove this figure. Please include (previous) Fig. 4 in your paper - together with a new Fig. 2 it explains much of your numerical model.
Page 5, line 144: Figure 5 does not explain anything and can be deleted - the explanations given in the text in lines 153-154 are enough.
Modifications have been made in the text.
OK.
Page 6, line 178: a) Please denote the coolant pump in Fig. 6a). b) Please enlarge Fig. 6b) and improve its quality.
Modifications have been made in the text.
OK.
page 7-12: Figures 6 - 11 should be renumbered as 7 - 12.
Modifications have been made in the text.
OK.
Page 7, line 196: Is Fig. 7 a part of Fig. 4? If yes, then which part of Fig. 4 is presented in Fig. 6? If not, then how have you obtained Fig. 6?
FIG. 7 is the expansion diagram of five blades in FIG. 4, which is part of FIG. 4.
Please, do not remove (previous) Fig. 4.
It seems that Fig. 4 is the top view and Fig. 7 is the side view of the numerical model - is it right?
Page 7, line 199: “The vapor phase volume fraction diagram of three different inlet blades...” - There are rather 5 blades shown in Fig. 6 - not 3.
It should be“The vapor phase volume fraction diagram of three different inlet pressure condition”. Modifications have been made in the text.
OK.
Pages 7, 11 : From Figs. 7c) and 10c) it is clear that the simulation time of 0.24324 s is too short - the presented curves do not stabilize but decrease/increase constantly.
In the simulation, the rotation time of the impeller is 60/1480=0.0405, while in the unsteady calculation of CFX, 0.24324s is the rotation of the impeller for 6 turns. In this paper, the simulation result of the 6th turn is selected for analysis, and the calculation result meets the requirements.
I do not understand why you chose exactly the 6th turn for analysis (not the 5th nor the 7th turn) - please explain this.
I hope you agree that taking into consideration Figs. 6c) and 10c) the simulation time is too short?
Page 11, lines 314, 315: “The maximum amplitude of the five groups... are 385 N, 306 N, 377 N, 375 N and 395 N...” - These low values can be observed also in Fig. 12a) but in Fig. 11a) those values are extremely larger - of about -149500 N? How have you obtained Fig. 12? Is Fig. 12 based on the results presented in Fig. 11?
The maximum amplitudes of the five groups refer to the radial force, and the approximately -149500N shown in figure 11 refers to the axial force. The +Z axis is pointed from the front cover plate of the impeller to the rear cover plate. The axial force is negative in the figure, indicating that the axial force direction points to the impeller inlet. Both axial and radial forces are obtained by numerical simulation.
The captions of Figs. 10 and 11 clearly indicate that both those figures present the amplitudes of the axial force - not of the radial force. So why are there differences in the amplitudes of the axial force in Fig. 10a) (about -149500 N) and in Fig. 11a) (about 385 N, 306 N, 377 N, 375 N and 395 N)?
Page 12: Please denote the frequency peaks described in the text (“shaft frequency”, “blade frequency”,“three times of blade frequency”, “2 times of blade frequency”, “7 times the blade frequency”.
The impeller speed of the pump designed in this paper is 1480r/min, and the number of blades is 5. The axial frequency can be calculated as 24.67Hz and the blade frequency as 123.33Hz. “Three times of blade frequency”, “2 times of blade frequency”, “7 times the blade frequency” respectively refer to multiplying the blade frequency by several times.
Please denote the frequency peaks in Fig. 11 - make denotations in Fig. 11, e.g. denote the frequencies in the text as follows:
$f_s$ - shaft frequency, $f_b$ - blade frequency
and then put the following denotations in Fig. 11:
$f_s$, $f_b$, $2f_b$, $3f_b$, $7f_b$.
It is difficult to indicate $2f_b$ or $7f_b$ peaks in Fig. 11. Introducing these denotations will improve following your descriptions in the text.
Language mistakes
I accept the corrections and/or explanations to language mistakes.
Author Response
Page 4, line 125: a) Why have you assumed so large values of eccentricity? Have you or other engineers observed such large values of shaft eccentricities in nuclear coolant pumps? Can you give any literature sources confirming the assumed values, e.g. the very large value of $e=20$ mm?
This is for better comparison, thus highlighting the significance of eccentricity in this study. And the eccentricity value e=20mm is not large.
I am not satisfied with your response. Can you give any literature sources confirming such large values of shaft eccentricity of $e=20$ mm in nuclear cooling pumps?
The volute of this pump is an annular volute, and the pump is relatively large, relatively large gap, e=20mm is very normal.
b) What is the cause of the assumed shaft eccentricity in the coolant pump? Is this eccentricity due to a flexible deformation of the shaft line or due to a deformation of the bearings or the deformation of the bearings’ supports???
This is because the volute is not completely symmetrical (due to the existence of the outlet), so the circumferential pressure of the impeller is not balanced, so the eccentric design is adopted to solve this problem.
I am not satisfied with this response.
a) As I understand you define the eccentricity as the difference between the centerline of the impeller and the centerline of the volute - is that right? From Fig. 2. it is not clear how you define the eccentricity.
b) As I understand this difference (the eccentricity) occurs as a result of different pressures in sections S1, S2 and S3 - thus as a result of different radial forces in sections S1, S2 and S3 applied to the shaft. So my question is: does the shaft flexibly deform due to this difference in forces? Or do the bearings deform? Or do the bearings supports deform? Which is the physical explanation for the appearance of the shaft eccentricity?
c) If you assume that the shaft eccentricity is $e=20$ mm, then it follows that the rub occurs between the blade tips of the impeller and the volute - is it right? I mean the contact between the blade tips and the volute occurs during the rotation of the impeller?
a) That is not right The eccentric distance e is defined as the distance between the centerline of the impeller and the centerline of the volute. As shown in e in figure 2.
b) The shaft is flexible because of different forces, not bearing deformation, nor bearing support deformation.
c) This pump is larger, which impeller and guide vane is one, and the volute is a ring volute. So the clearance between blade tip and volute of impeller is very big, will not produce friction.
Page 13, lines 363-383: Please explain the practical importance of the obtained “Conclusions”. How can the nuclear power plant engineer benefit from the results obtained by you? How can he/she benefit from the fact that “Under severe cavitation conditions, the difference of eccentricity schemes is most significant in the range of 90 to 240 degrees” or that “Under critical and severe cavitation conditions, the maximum axial force amplitude of the nuclear reactor pump appears at 2 times of the blade frequency”?
Modifications have been made in the text. It can provide reference for the design of nuclear main pump.
I am not satisfied with this response. There are no modifications in the text explaining the practical importance of your conclusions.
From your response it follows that the conclusions are important when the design of a new nuclear pump is considered. So please include the following sentence from your response in the “Introduction” (in line 76) and in the “Conclusion” (in line 378):
“The obtained results can provide reference for the design of new nuclear main pumps.”
Anyhow, do you really want to design a new nuclear main pump? Do you want to become the manufacturer of such new pumps?
I suppose not, so the practical importance of the obtained results and of the conclusions is marginal.
I hope you agree with me?
I agree with you. The obtained results can provide reference for the design of new nuclear main pumps. And modifications have been made in the text.
5) this head is given as 106.17 m, 110.41 m and 110.63 m - which values of the head are correct?
3.37m is the design head of the prototype pump, and 111.3m is the head of the converted pump. In this paper, the head is specified as 106.17m, 110.41m and 110.63m, which are obtained by the original model pump simulation, not by experiment.
From the modified Tabs. 1 and 2 it follows that the design head of the prototype pump is 111.3 m and the designed head of the converted pump is 3.83 m. Is this right?
Yes this is right. The design head of the prototype pump is 111.3 m and the designed head of the converted pump is 3.83 m.
Page 5, line 137: The quality of Fig. 4 must be improved.
Modifications have been made in the text.
I asked only to improve the quality of (previous) Fig. 4 - not to remove this figure. Please include (previous) Fig. 4 in your paper - together with a new Fig. 2 it explains much of your numerical model.
Modifications have been made in the text.
Page 7, line 196: Is Fig. 7 a part of Fig. 4? If yes, then which part of Fig. 4 is presented in Fig. 6? If not, then how have you obtained Fig. 6?
FIG. 7 is the expansion diagram of five blades in FIG. 4, which is part of FIG. 4.
Please, do not remove (previous) Fig. 4.
It seems that Fig. 4 is the top view and Fig. 7 is the side view of the numerical model - is it right?
FIG. 7 is an expansion diagram of the five blades in FIG. 4. In other words, only the blades are shown, not the side view of the numerical model.
Pages 7, 11 : From Figs. 7c) and 10c) it is clear that the simulation time of 0.24324 s is too short - the presented curves do not stabilize but decrease/increase constantly.
In the simulation, the rotation time of the impeller is 60/1480=0.0405, while in the unsteady calculation of CFX, 0.24324s is the rotation of the impeller for 6 turns. In this paper, the simulation result of the 6th turn is selected for analysis, and the calculation result meets the requirements.
I do not understand why you chose exactly the 6th turn for analysis (not the 5th nor the 7th turn) - please explain this. I hope you agree that taking into consideration Figs. 6c) and 10c) the simulation time is too short?
The time selected in the simulation is a stable period. During the operation, the pump runs relatively steadily from the 6th turn, so I choose the 6th turn for analysis.
Page 11, lines 314, 315: “The maximum amplitude of the five groups... are 385 N, 306 N, 377 N, 375 N and 395 N...” - These low values can be observed also in Fig. 12a) but in Fig. 11a) those values are extremely larger - of about -149500 N? How have you obtained Fig. 12? Is Fig. 12 based on the results presented in Fig. 11?
The maximum amplitudes of the five groups refer to the radial force, and the approximately -149500N shown in figure 11 refers to the axial force. The +Z axis is pointed from the front cover plate of the impeller to the rear cover plate. The axial force is negative in the figure, indicating that the axial force direction points to the impeller inlet. Both axial and radial forces are obtained by numerical simulation.
The captions of Figs. 10 and 11 clearly indicate that both those figures present the amplitudes of the axial force - not of the radial force. So why are there differences in the amplitudes of the axial force in Fig. 10a) (about -149500 N) and in Fig. 11a) (about 385 N, 306 N, 377 N, 375 N and 395 N)?
The amplitude in the time domain diagram is the sum of the amplitudes of all the frequencies at that moment. And the amplitude in the frequency domain is the maximum amplitude at that frequency. So there are differences in the amplitudes of the axial force in Fig. 10a) (about -149500 N) and in Fig. 11a) (about 385 N, 306 N, 377 N, 375 N and 395 N)?
Page 12: Please denote the frequency peaks described in the text (“shaft frequency”, “blade frequency”,“three times of blade frequency”, “2 times of blade frequency”, “7 times the blade frequency”.
The impeller speed of the pump designed in this paper is 1480r/min, and the number of blades is 5. The axial frequency can be calculated as 24.67Hz and the blade frequency as 123.33Hz. “Three times of blade frequency”, “2 times of blade frequency”, “7 times the blade frequency” respectively refer to multiplying the blade frequency by several times.
Please denote the frequency peaks in Fig. 11 - make denotations in Fig. 11, e.g. denote the frequencies in the text as follows:
$f_s$ - shaft frequency, $f_b$ - blade frequency and then put the following denotations in Fig. 11:
$f_s$, $f_b$, $2f_b$, $3f_b$, $7f_b$.
It is difficult to indicate $2f_b$ or $7f_b$ peaks in Fig. 11. Introducing these denotations will improve following your descriptions in the text.
The expert's advice is very good, and modifications have been made in the text. Table 3 The frequency and amplitude analysis table of the axial force of the impeller in the pump. Cavitation states e=0 mm e=5 mm e=10 mm e=15 mm e=20 mm Critical cavitation The maximum amplitudes(N) 355 306 377 375 355 Blade frequency(f) 3 f 3 f 2 f 2 f 3 f Severe cavitation The maximum amplitudes(N) 345 226 398 381 370 Blade frequency(f) 2 f 2 f 2 f 2 f 1 f Fracture cavitation The maximum amplitudes(N) 1424 1675 1408 1435 1464 Blade frequency(f) 1 f 1 f 1 f 1 f 1 f Note: f- the blade frequency
