Effects of the Balance Hole Diameter on the Flow Characteristics of the Rear Chamber and the Disk Friction Loss in the Centrifugal Pump

Round 1

Reviewer 1 Report

This paper numerically introduces the effects of pump blade hole on chamber velocity profiles, and achieves satisfied results as presented in the paper. I believe the authors can strengthen their paper with considering following comments further:

1. Please give more detailed information regarding the Verification of the Flow Velocity in the Rear Chamber, it is unclear about the comparing model which is used for your comparison. You can give more clear description on how you carry out the model validation. This part seems less informative.
2. Have you estimated differences with comparing with unsteady model, or compared results with other turbulent model?
3. Is there any area in the chamber with negative pressure?

Author Response

Dear Editor Mr. Aleksandar Jovanović,

First, we would like to thank the Editor, Associate Editor and Reviewers for their comments/suggestions, which have immensely improved the content of the paper.

We have modified the manuscript accordingly, and the detailed corrections are listed below point by point:

 

Author’s Response to the Reviewer’s Comments

 

Reviewer 1：

Comments and Suggestions for Authors

This paper numerically introduces the effects of pump blade hole on chamber velocity profiles, and achieves satisfied results as presented in the paper. I believe the authors can strengthen their paper with considering following comments further:

1. Please give more detailed information regarding the Verification of the Flow Velocity in the Rear Chamber, it is unclear about the comparing model which is used for your comparison. You can give more clear description on how you carry out the model validation. This part seems less informative.

√ Thanks very much for the suggestion. In Ref [26], numerous experimental data were obtained by using a hot-wire anemometer to measure the velocity distribution of the turbulent flow field on the rotating disc inside the closed cylinder. In Ref [27], the particle image velocimetry (PIV) test results and the hot-wire measurement data were compared, and they found that the distributions of the circumferential and radial components of velocity were consistent at the radial geometrical center of the disc (0.6–0.8) R. At the rear chamber zone 0.8 R of the pump close to the radial geometrical center of the chamber, the fluid flow was less affected by the leakage flow and was approximated as the flow on the rotating disc inside the closed cylinder. In Ref [26], the experimental data at 0.8R were compared with the axial distribution curves of the circumferential and radial components of velocity at the design flow point 0.8R inside the rear chamber. No leakage flow occurs in the rear chamber when there is no balance hole, which approximates the flow of the rotational disk in the enclosed cylinder. According to Ref. [26, 27], the hot-wire anemometer is applied to measure the turbulence speed of the flow field for the rotating disk in the closed cylinder. As shown in Fig. 5, the test data of the circumferential and the radial velocity components at 0.8R are compared with the circumferential and the radial velocity components distributed along the axial direction at 0.8R in the rear chamber of the centrifugal pump for the impeller without a balance hole.

 

2. Have you estimated differences with comparing with unsteady model, or compared results with other turbulent model?

√ Thanks a lot for the comments. At present, this paper only considers the steady-state flow condition, so only steady calculation is made, but many scholars have studied the fluid flow characteristics in the pump chamber. Research has shown that both cavities velocity field in the shroud and hub and the axial changing laws in the centrifugal pump are similar to the velocity field in the enclosed cylinder body [1–3]. That is, in the fluid flow velocity of the shroud and hub cavities, a turbulent boundary layer exists near the outer wall of the rotating impeller back shroud. Near the internal wall of the fixed motionless pump shroud, a flow core zone exists along the axial direction without significant changes between two boundary layers [4–6]. A turbulent boundary layer exists near the exterior wall of the impeller cover for the rotational and the interior wall of the stationary pump cover because of liquid viscosity. Moreover, a flow core area exists with a small change along the axial direction between the two boundaries[3,7]. It is known from previously presented analysis that when the diameter of the balance hole is changed, the flow in the hub cavity is always 2-D circumferential shear flow with radial pressure difference. When the balance hole is provided, the axial leakage of the balance hole significantly influence the characteristics of flow in the hub cavity, which is consistent with the results in Ref. [8], i.e., when the diameter is 8 mm and the balance hole is provided, flow in the hub cavity is induced by the rotating impeller and leakage flow of the balance hole, and the leakage flow of the balance hole is the main part. Thus, the research results are consistent with the actual flow conditions in the pump with high reliability.

[1] Yang, J. H.; Wang, C. L.; Li, J. P. Mathematical model of flow inside a centrifugal pump casing. Transactions of the Chinese Society for Agricultural Machinery, 2003, 34(6), 68–72.

[2] Wang, X. Y.; Wang, C. X.; Li, Y. B. Numerical study of slow characteristics in the impeller side chamber of centrifugal pump. Transactions of the Chinese Society for Agricultural Machinery, 2009, 40(4), 86–90.

[3] Park, S. H.; Morrison, G. L. Analysis of the flow between the impeller and pump casing back face for a centrifugal pump. Proceedings of the ASME Fluids Engineering Division Summer Meeting, Vail, Colorado, USA, August 2–6, 2009, 221–235.

[4] Lefor, D.; Kowalski, J.; Kutschelis, B.; et al. Optimization of axial thrust balancing swirl breakers in a centrifugal pump using stochastic methods. Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting (FEDSM2014–21262), Chicago, Illinois, USA, August 3–7, 2014, 1–11.

[5] Gülich, J. F. Disk friction losses of closed turbomachine impellers. Forschung im Ingenieurwesen/Engineering Research, 2003, 68(2), 87–95.

[6] Pan, D. Y.; Wang, T.; Zhang, B.; et al. PIV measurement on rotating disks flow in cylinder. Journal of Hydrodynamics, 2009, 24(2), 200–206.

[7] Takamine, T.; Furukawa, D.; Watanabe, S.; et al. Experimental analysis of diffuser rotating stall in a three-stage centrifugal pump. International Journal of Fluid Machinery and Systems, 2018, 11(1), 77-84.

[8] Itoh, M.; Yamada, Y.; Imao, S.; et a1. Experiments on turbulent flow due to an enclosed rotating disk. Experimental Therma1 and Fluid Science, 1992, 5(3), 359-368.

 

3. Is there any area in the chamber with negative pressure?

√ Thanks very much for the question. According to the current calculation results, there is no negative pressure area. Because the pressure in the back pump chamber is usually large, and greater than the impeller flow channel and the pressure in the front pump chamber, resulting in the impeller to the impeller inlet direction of the axial force.

Finally, all of the authors would like to thanks a lot for the reviewers’ kindness and useful suggestions!

 

The manuscript has been resubmitted to your journal. We are looking forward to your positive response.

 

 

                                                Yours

Wei Dong, Ze Liu, Haichen Zhang, Guang Zhang, Haoqing Jiang and Peixuan Li.

                                             Feb. 25, 2022

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Manuscript deals with the investigation of the centrifugal pump rear chamber (behind impeller). To increase the efficiency of the pump the balance holes were drilled into the impeller. The effect of holes diameter was studied with respect to friction loss of impeller. The investigation was done mainly by numerical simulation and experimental data was provided from literature. The authors present the results for velocity fields and the mutual relation between dimensionless velocity and distance. These results describe the fluid flow in the rear chamber of the pump for different cases represented by different diameters of the balance hole. The numerical simulation considers mesh-sensitive analysis and the methodology and author approach are correct. Results show the non-monotonous dependency of power loss (caused by friction of the fluid in the rear chamber) with respect to the diameter of the balance hole. This is the valuable result as well as the methodology approach.

However, the interpretation of the results of the velocity field has was compressed only to an empty statement of the facts observable in the pictures without discussion or provision of the explanation of these phenomena. In my opinion, less text (reduction) is more appropriate in this case, when it is necessary to focus only on the essential findings.

I made the comments into the pdf file. There are a lot of recommendations and questions. The text should be supplied with the answers to these questions. There are sentences without sense. English language of the manuscript should be improved.

Comments for author File: Comments.pdf

Author Response

Dear Editor Mr. Aleksandar Jovanović,

First, we would like to thank the Editor, Associate Editor and Reviewers for their comments/suggestions, which have immensely improved the content of the paper.

We have modified the manuscript accordingly, and the detailed corrections are listed below point by point:

 

Author’s Response to the Reviewer’s Comments

 

Reviewer 2：

Manuscript deals with the investigation of the centrifugal pump rear chamber (behind impeller). To increase the efficiency of the pump the balance holes were drilled into the impeller. The effect of holes diameter was studied with respect to friction loss of impeller. The investigation was done mainly by numerical simulation and experimental data was provided from literature. The authors present the results for velocity fields and the mutual relation between dimensionless velocity and distance. These results describe the fluid flow in the rear chamber of the pump for different cases represented by different diameters of the balance hole. The numerical simulation considers mesh-sensitive analysis and the methodology and author approach are correct. Results show the non-monotonous dependency of power loss (caused by friction of the fluid in the rear chamber) with respect to the diameter of the balance hole. This is the valuable result as well as the methodology approach.

However, the interpretation of the results of the velocity field has was compressed only to an empty statement of the facts observable in the pictures without discussion or provision of the explanation of these phenomena. In my opinion, less text (reduction) is more appropriate in this case, when it is necessary to focus only on the essential findings.

I made the comments into the pdf file. There are a lot of recommendations and questions. The text should be supplied with the answers to these questions. There are sentences without sense. English language of the manuscript should be improved.

√ Thanks a lot for the comments and suggestions. We have modified the paper according to the comments.

 

Here, the rotor is connected with stator. There will be mechanical sealing. But how the boundary condition was set up here for numerical model?

√ Thanks a lot for the comments. In the calculation of the centrifugal pump, I set the impeller water body, the impeller cover surface and the hub surface as rotation, and the given speed. Hub clearance is ignored in the calculation model.

 

Which version? From 2019 the new version of mesh generator is directly implemented into Fluent.

√ Thanks a lot for the comments. The solver uses FLUENT 5/6.

 

The figure of MFR stator-rotor region is required to show. Was the recommendation for the position of the interface between stator-rotor satisfied? Especially in the region in the gap between the rear seal ring and impeller, it would be fine to show also the mesh due to interpolation in this region.

√ Thanks a lot for the comments and suggestions. We have modified the Figure 3 according to the comments.

 

Because of the high gradient of almost all characteristics of the flow, how many layers of element fill the gap between the rear seal ring and the rear impeller ring? The same question arises for balancing hole.

√ Thanks a lot for the comments. Sealing ring radial clearance diameter is 0.22mm. Global grid size is 0.1 on the sealing ring radial clearance and balancing hole.

The whole description of the numerical results is a statement of what can be seen from the pictures without presenting any hypotheses or explanations of the described phenomenon.

√ Thanks a lot for the comments. There are a lot of phenomenon description and reason explanation of numerical calculation results in this paper. For example, lines 163-166 and 187-197.

The original efficiency is not stated in the text.

√ Thanks a lot for the comments. We have modified the paper according to the comments. The original efficiency is 81%.

 

It seems, there is a reversible flow compared to other situations with balance hole.

√ Thanks a lot for the comments. This is due to the impeller rotation and centrifugal force, in the impeller wall formed to the direction of the outer diameter of the flow. At this point, due to the existence of no equilibrium hole, the clearance leakage is zero, resulting in no liquid flow to the inner diameter clearance direction.

 

Which vortex do you describe? There are three vortices in Figure 6.

√ Thanks very much for the question. The three vortices all show the same variation law, so it is a unified description of the three vortices.

 

Phenomenon cannot be cause by angle of plane cut.

√ Thanks very much for the question. As can be seen from Figure 2 (a), 0 degrees is the direction of the seventh section of the volute, 90 degrees is the direction of the first section, 180 degrees is the direction of the third section of the volute, and 270 degrees is the direction of the fifth section of the volute. Among them, the area of the first section is the smallest, which must restrict the flow of liquid in the pump chamber.

The definition of the dimensionless quantities if form of equtions is neccessary. It is important to show it directly into the text.

√ Thanks a lot for the comments. We have modified the paper according to the comments. It is directly into the text.

                                   (1)

                                   (2)

                                    (3)

 

whole sentence doesn’t make sence. The rear chamber is investigated by planes defined with distances .... and angles ...?

√ Thanks a lot for the comments. This sentence is intended to explain the content of FIG. 7 and draw the significance of drawing FIG. 7.

 

There should be 4 ranges respecting for angles 0, 90, 180, and 270.

√ Thanks a lot for the comments. Here is the value range of the non-dimensional tangential velocity of the liquid core region when the balance hole diameter is 0, 4, 6, 8, 10 and 12mmrespectively, so it is 5. We have modified the paper according to the comments.

The results of pressures are not presented. Then is it just general statement of the fact? Reader can’t judge if the values are small or large from results.

√ Thanks a lot for the comments. We have modified the paper according to the comments. We have removed ", and the value is large " in the paper.

 

How the tangent velocity can cause the tangential direction of the radius? Again sentence doesn't make sense.

√ Thanks a lot for the comments. The non-dimensional tangential velocity of the liquid in the radial direction which causes the tangential direction of the same radius and the same angle approaches and is uniform, and the value is large.

Compare to which value? Or mutual comparison between stated velocities?

√ Thanks a lot for the comments. Compared to the dimensionless tangential velocity at 0°, 180° and 270°.

Again the same sentence as in the previous chapter. It doesn't make sense.

√ Thanks a lot for the comments. This sentence is intended to explain the content of FIG. 8 and draw the significance of drawing FIG. 8.

increase related to which quantity?

√ Thanks a lot for the comments. We have modified the paper according to the comments. We have added the sentence "when the diameter of equilibrium hole increases from 0 to 12mm" in this paper.

Why authors focused only on this distance in following text?

√ Thanks a lot for the comments. This distance is taken as the basis in the subsequent experimental verification to verify the reliability of the research results in this paper.

Why the numerical data are presented by mean value when hot-wire anemometer had the specific position in measured geometry?

√ Thanks a lot for the comments. In literature [26], a hot-wire anemometer was used to experimentally measure the velocity distribution of turbulent flow field in a rotating disk in a closed cylinder block, and a large number of experimental data were obtained. In literature [27], PIV test method was compared with hot-wire measurement data, and it was found that the tangential radial velocity distribution was in good agreement at the radial center position (0.6-0.8)R of the disk In the case of no equilibrium hole, the leakage flow velocity in the rear pump cavity area is very small, which can be approximated as the rotary disk flow in the closed cylinder block. The axial distribution curve of tangential radial velocity at the design flow point at 0.8r in the rear pump cavity was compared with the experimental data at 0.8r in literature [26], as shown in FIG. 14.

Why experiment data are presented by a continuous line and not by discrete points? Show also confidence interval of measured data or error bars.

√ Thanks a lot for the comments. In order to distinguish the experimental data from the numerical simulation data more clearly, we adopted such curves.

 

Why the values of torque was not calculated directly from fluent simulation as one of the output parameters?

√ Thanks very much for the question. In order to reflect the difference between the circular velocity of liquid in the pump cavity and the rotational velocity of impeller caused by the friction loss of the disk, the theoretical formula is adopted to calculate. The values of torque M through numerical calculation, directly put in the list is meaningless. This paper gives the product of torque value M and rotational angular velocity w, that is, power value P₁.

 

The friction factor is not constant but depends on the Reynolds number. Please provide a discussion about your approach.

√ Thanks a lot for the comments. The λ is the coefficient of friction. It is not disc friction factor K. The disc friction factor K is not constant but depends on the Reynolds number. The coefficient of friction λ can be considered as a constant value, usually 0.05.

 

Difference between mean velocity and which velocity? The difference is defined by values of the same physical quantity.

√ Thanks a lot for the comments.  We have modified the paper to “the difference between the average tangential velocity of the axial center of the rear chamber is continuously increased and the mean value of the rotational speed of the impeller cover plate of the rear chamber region is reduced, and the disk friction loss is reduced. The changes of the difference between the mean value of the tangential velocity in the axial center of the rear chamber is small and the mean value of the rotational speed of the impeller cover plate in the rear chamber area is relatively small, and the disk friction loss is also small when the balance hole diameter is increased from 8 mm to 12 mm.”

what is "r"?

√ Thanks very much for the question. r is the radius of the measuring point in the pump chamber.

How this value was evaluated? from eq(4) and (5)? Please stated.

√ Thanks very much for the question. In order to calculate the disk friction loss more accurately, take the four angles in the design flow condition (0°, 90°, 180°, 270°). The average tangential velocity the four angles axial center of the rear chamber in the radial direction is set to be v_u1, and the average rotational speed u_ref of the impeller cover plate in the rear chamber area was 18.592 m/s, and the disk friction loss P₁ was calculated as shown in Table 2.

 

sometimes it is a disk, sometimes it is impeller wall, please use uniform terminology.

√ Thanks a lot for the comments. The impeller wall is the exact location on the impeller, the disc is used in the word disc friction loss, the two do not mean the same thing.

Finally, all of the authors would like to thanks a lot for the reviewers’ kindness and useful suggestions!

 

The manuscript has been resubmitted to your journal. We are looking forward to your positive response.

 

 

                                                Yours

Wei Dong, Ze Liu, Haichen Zhang, Guang Zhang, Haoqing Jiang and Peixuan Li.

                                             Feb. 28, 2022

 

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Review of: “Effects of the balance hole diameter on the flow characteristics of the rear chamber and the disk friction loss in the centrifugal pump” by W. Dong et al. Submitted to: Processes.

The paper is about the flow patterns in the rear chamber of a centrifugal pump and the resulting disk friction loss, as influenced by the diameter of the balance holes in the rotor. The paper complements a study by the first author of the present paper, W. Dong, and other colleagues than those of the present paper, on the influence of the balance hole diameter on the flow patterns in the balance chamber of the same pump that is analysed in the present paper [Ref 6 of the current paper] and a study by W. Dong and W.L. Chu on the influence of the operating point on the flow patterns in the rear chamber of the same centrifugal pump as used in the present paper for fixed diameter of the balance holes (8 mm) [Ref 24 of the current paper].

A. General criticisms

A1.

In section 2.2 nothing is said about the simulation methodology of the interaction of the flow in the rotor and the flow in the stator. Nothing is even said about the used package. From Ref. 6 and Ref. 24 one can understand that the simulations were done with the commercial package “Fluent”. There are three methods available in this package for expressing the interaction between the rotor flow and the stator flow. The fully rigorous technique is called ”sliding mesh approach” (SlidM). With this technique, the equations are in time-dependent form and transfer of data between the rotating rotor and the stationary stator are done correctly in space and correctly in time at each position of the interface between rotor and stator. The time-dependent simulation has to be continued until a time-periodic solution is obtained.  There are also two approximate ways of expressing the interaction: the “multiple reference model” (MRef)  and the “mixing plane model” (MixP). Both are techniques with serious simplifications, meant to reduce the computing time. The representation of the flow is steady in both the rotor and the stator with both simplified methods. With the MRef, the rotor is stationary, kept at a fixed position with respect to the stator, but the forces due to rotation are applied. This simplification is usually called “Frozen Rotor”. A major error with this technique is that irregularities in the outflow of the rotor are at fixed positions, because he relative motion of the rotor with respect to the stator is not taken into account. The irregularity of the outflow of the rotor is thus much stronger in the simulation than in reality. This may cause severe errors in flow details. In the MixP, flow parameters that are exchanged between rotor and stator are circumferentially averaged. The major error with this technique is thus that the outflow of the rotor is represented much more regular than it can be in reality. Further, both simplified techniques ignore inertia effects. Inertia typically has a strong filtering effect on perturbations. Especially with the MRef, the response of the flow to irregularities may be much stronger in the simulation than in reality. In principle, MRef and MixP can only be justified if there is strong circumferential periodicity in a turbomachine and weak interaction between rotor and stator components. Thus ,in principle, the steady techniques cannot be justified for analysis of the flow in a centrifugal pump with a rotor with a volute directly around it, due to due to absence of circumferential periodicity and strong interaction between rotor and stator flows.

It is thus essential to describe the used representation of the interaction between the rotor and stator flows, and, if justified, motivate the simplification to one of the steady techniques. This is not done in the paper.

A2.

From the mention “steady flow” in Ref. 6 and the character of the plots in Fig. 6 of the current paper, I understand that the “frozen rotor technique” is used. Although this technique is strongly falsifying local flow features, it is able to reasonably predict average flow features, as the realised head of the pump and the obtained efficiency. The authors do not discuss in detail in section 3.1 the quality of the prediction of the head and the efficiency for the case with balance hole diameter 8 mm, for which experimental results are available. This should be dome more explicitly. The comparison is made in Ref. 6 and the correspondence for these global parameters is quite reasonable. But this correspondence is not a guarantee for the correctness of detailed flow patterns, as these shown in the sections 3.2, 3.3 and 3.4 of the present paper. From the figures 1, 2 and 3 one can deduce that the position of the frozen rotor is such that the flow along the pressure side of a rotor blade, what typically is called the jet region in the rotor channel flow, is entering the very first and narrowest part of the volute. This causes a very strong injection of tangential and radial momentum into this part of the volute; certainly much stronger than it can be in reality. To my understanding, the very strong circumferential irregularity of the tangential velocity component (very high tangential velocity at the position 90 degrees in Fig. 6 and Fig 7) and the strong circumferential irregularity of the radial velocity component (high negative value of the radial velocity component at the position 90 degrees in Fig. 8) are caused by the artificial representation of the flow by the frozen rotor model. I cannot believe that the irregularity shown in Figs. 6, 7 and 8 is real.

I see two possible ways of producing trustworthy results. A first way is to repeat all calculations with the consistent “sliding mesh approach”. This is feasible because once a time periodic solution is obtained for one diameter of the balance holes (e.g. 8 mm), the calculations for the other hole diameters may start from this solution, which makes obtaining these supplementary solutions quite fast. Another way is realising one “sliding mesh” solution (e.g. 8 mm) and then compare it with the average of three “frozen rotor” solutions for three different positions of the rotor, for instance the one that is now obtained, then one with the rotor rotated over 20 degrees and one with the rotor rotated over 40 degrees. The chances look quite real to me, for the problem studied, which is the flow in the rear chamber of the rotor, thus not in the active flow of the rotor, that the average of the three “frozen rotor” solutions is sufficiently close to the “time-averaged” flow field of the “time accurate”, “sliding mesh” solution. If this comes out to be true, one may then use the average of three “frozen rotor” solutions for each value of the diameter of the balance holes. 

B.  Particular criticisms

B1. Introduction. The impeller is always the same (not; 6 impellers), but there are 6 values of the diameter of the balance holes.

B2. The sentence “When the balance hole diameter increases....volute.’’ cannot be understood by a reader. What I understand from the paper is that the authors demonstrate that when the leakage flow through the rear chamber increases by increased diameter of the balance holes, the level of tangential velocity in the rear chamber increases by larger flow of tangential momentum from the volute of the pump into the rear chamber and that the increased tangential momentum decreases the velocity difference with the rotor disk, which decreases the rotor disk friction moment. This phenomenon happens until the balance hole diameter reaches some critical value, above which the level of tangential velocity does not increase anymore and the disk friction does not decrease anymore. The reason for the off-levelling is that for large value of the balance hole diameter, the clearance of the back sealing ring determines the leakage flow rate. I understand that this is the meaning of Table 2 at the end of the paper. But, it is not clear to me what the consequences are of this observation. One would expect an optimum value of the balance hole diameter by decreased disk friction (higher mechanical efficiency) and increased leakage flow rate (lower volumetric efficiency), until the saturation of the leakage flow rate is obtained. But this is not what can be seen on Fig. 5 that shows the evolution of global efficiency. so, the statement that the results of the paper provide a theoretical basis for optimal design of a centrifugal pump is not clearly justified, to my understanding. The authors have think seriously, in order to motivate a reader to read the paper, how to announce in the abstract the main conclusion of the paper and the value of it. It is not clear to me how to do this.

B3. Second sentence of the introduction. I do not understand the sentence “Due to the faultiness on the flow.....” I think that the authors want to say that there is still incertitude  about the precise flow mechanisms, or lack of precise ways of numerical simulation of the flow patterns,...

B4. Section 2.1. Second line. I think that the sentence should be: ” ... closed impeller with double seal rings  and balance holes.“   

B5. Section 2.1. Fig. 2. It should be specified that the volute is seen from the back of the pump. The rotation of the rotor is clockwise, when seen towards its front side.

B6. Section 2.2. A motivation should be given for the choice of the RNG k-epsilon model. I agree with this choice for turbomachinery application, especially when the extension for system rotation is added. But nothing is said about the turbulence model.

B7. Fig. 3. I do not understand what is seen on the left upper panel. Some explanation seems necessary to me.

B8. Fig 5. The deviating value of the efficiency for the balance hole diameter 12 mm is clearly due to some error. So, verify the simulation results.  

B9. Section 3.5. The good correspondence with the experimental result of the averaged value of the tangential velocity component in Fig. 9 is not a proof of the correctness of the detailed flow fields shown in Figs. 6, 7 and 8. See discussion under remark A2.

B10. Section 3.6 on disk friction. I understand that the value of vu1 is an average over the circumferential direction and the radial direction in the axial centre of the flow in the rear chamber; thus an average over a full cross area perpendicular to the shaft. It thus gives an idea of the global level of tangential velocity. Although I have  strong criticism on the validity of the detailed flow patterns obtained by the calculation method, this global, averaged, result certainly shows the correct tendencies. So, the first line of Table 2 can be understood. It is not clear to me how the power on the second line is obtained. The P1 in Eq. 5 suggests that it is obtained by the simplified formula Eq. 4. If this is true, the results of P1 are not very meaningful in Table 2. Eq. 5 is extremely simplified by the assumption of a constant friction factor. The formula thus assumes that the thickness of the boundary layers is always the same. The dissipated power P1 should be estimated from the shear work extracted from the calculated flow field. But, I agree that the tendencies will be similar as obtained by the simplified formulas. But, obviously, the simplified formula cannot give an accurate estimate of the disk friction loss. So, the whole motivation for a detailed flow analysis for estimation of the disk friction loss becomes meaningless if finally a very simplified formula is used.

B11. The observation that the leakage flow diminishes the disk friction dissipation in the rear chamber is not new. See page 18 of the recent review paper on the topic of gaps: L. Zemanova, P. Rudolf, Flow inside the sidewall gaps of hydraulic machines: a review; Energies, 2020, 13, 6617. So, the question is once more what to do with the final results of the current paper? What is the value of the results? What is the consequence for optimisation methods of a pump?  

Author Response

Dear Editor Mr. Aleksandar Jovanović,

First, we would like to thank the Editor, Associate Editor and Reviewers for their comments/suggestions, which have immensely improved the content of the paper.

We have modified the manuscript accordingly, and the detailed corrections are listed below point by point:

 

Author’s Response to the Reviewer’s Comments

 

Reviewer 1：

The paper is about the flow patterns in the rear chamber of a centrifugal pump and the resulting disk friction loss, as influenced by the diameter of the balance holes in the rotor. The paper complements a study by the first author of the present paper, W. Dong, and other colleagues than those of the present paper, on the influence of the balance hole diameter on the flow patterns in the balance chamber of the same pump that is analysed in the present paper [Ref 6 of the current paper] and a study by W. Dong and W.L. Chu on the influence of the operating point on the flow patterns in the rear chamber of the same centrifugal pump as used in the present paper for fixed diameter of the balance holes (8 mm) [Ref 24 of the current paper].

 

1. General criticisms

 

A1.

In section 2.2 nothing is said about the simulation methodology of the interaction of the flow in the rotor and the flow in the stator. Nothing is even said about the used package. From Ref. 6 and Ref. 24 one can understand that the simulations were done with the commercial package “Fluent”. There are three methods available in this package for expressing the interaction between the rotor flow and the stator flow. The fully rigorous technique is called” sliding mesh approach” (SlidM). With this technique, the equations are in time-dependent form and transfer of data between the rotating rotor and the stationary stator are done correctly in space and correctly in time at each position of the interface between rotor and stator. The time-dependent simulation has to be continued until a time-periodic solution is obtained. There are also two approximate ways of expressing the interaction: the “multiple reference model” (MRef) and the “mixing plane model” (MixP). Both are techniques with serious simplifications, meant to reduce the computing time. The representation of the flow is steady in both the rotor and the stator with both simplified methods. With the MRef, the rotor is stationary, kept at a fixed position with respect to the stator, but the forces due to rotation are applied. This simplification is usually called “Frozen Rotor”. A major error with this technique is that irregularities in the outflow of the rotor are at fixed positions, because he relative motion of the rotor with respect to the stator is not taken into account. The irregularity of the outflow of the rotor is thus much stronger in the simulation than in reality. This may cause severe errors in flow details. In the MixP, flow parameters that are exchanged between rotor and stator are circumferentially averaged. The major error with this technique is thus that the outflow of the rotor is represented much more regular than it can be in reality. Further, both simplified techniques ignore inertia effects. Inertia typically has a strong filtering effect on perturbations. Especially with the MRef, the response of the flow to irregularities may be much stronger in the simulation than in reality. In principle, MRef and MixP can only be justified if there is strong circumferential periodicity in a turbomachine and weak interaction between rotor and stator components. Thus, in principle, the steady techniques cannot be justified for analysis of the flow in a centrifugal pump with a rotor with a volute directly around it, due to due to absence of circumferential periodicity and strong interaction between rotor and stator flows.

It is thus essential to describe the used representation of the interaction between the rotor and stator flows, and, if justified, motivate the simplification to one of the steady techniques. This is not done in the paper.

√ Thanks very much for the guidance and support. We have modified the paper according to the comments. The simulations were done with the commercial package “Fluent”. The simulation methodology of the interaction of the flow is the “multiple reference model” (MRef) in the rotor and the flow in the stator. We have added two sentences “In this paper, FLUENT software is used to carry out numerical calculation. The simulation methodology of the interaction of the flow is the “multiple reference model” (MRef) in the rotor and the flow in the stator.” in the revised paper.

 

A2.

From the mention “steady flow” in Ref. 6 and the character of the plots in Fig. 6 of the current paper, I understand that the “frozen rotor technique” is used. Although this technique is strongly falsifying local flow features, it is able to reasonably predict average flow features, as the realised head of the pump and the obtained efficiency. The authors do not discuss in detail in section 3.1 the quality of the prediction of the head and the efficiency for the case with balance hole diameter 8 mm, for which experimental results are available. This should be dome more explicitly. The comparison is made in Ref. 6 and the correspondence for these global parameters is quite reasonable. But this correspondence is not a guarantee for the correctness of detailed flow patterns, as these shown in the sections 3.2, 3.3 and 3.4 of the present paper. From the figures 1, 2 and 3 one can deduce that the position of the frozen rotor is such that the flow along the pressure side of a rotor blade, what typically is called the jet region in the rotor channel flow, is entering the very first and narrowest part of the volute. This causes a very strong injection of tangential and radial momentum into this part of the volute; certainly much stronger than it can be in reality. To my understanding, the very strong circumferential irregularity of the tangential velocity component (very high tangential velocity at the position 90 degrees in Fig. 6 and Fig 7) and the strong circumferential irregularity of the radial velocity component (high negative value of the radial velocity component at the position 90 degrees in Fig. 8) are caused by the artificial representation of the flow by the frozen rotor model. I cannot believe that the irregularity shown in Figs. 6, 7 and 8 is real.

I see two possible ways of producing trustworthy results. A first way is to repeat all calculations with the consistent “sliding mesh approach”. This is feasible because once a time periodic solution is obtained for one diameter of the balance holes (e.g. 8 mm), the calculations for the other hole diameters may start from this solution, which makes obtaining these supplementary solutions quite fast. Another way is realising one “sliding mesh” solution (e.g. 8 mm) and then compare it with the average of three “frozen rotor” solutions for three different positions of the rotor, for instance the one that is now obtained, then one with the rotor rotated over 20 degrees and one with the rotor rotated over 40 degrees. The chances look quite real to me, for the problem studied, which is the flow in the rear chamber of the rotor, thus not in the active flow of the rotor, that the average of the three “frozen rotor” solutions is sufficiently close to the “time-averaged” flow field of the “time accurate”, “sliding mesh” solution. If this comes out to be true, one may then use the average of three “frozen rotor” solutions for each value of the diameter of the balance holes.

√ Thanks a lot for the comments and suggestions. I agree with the two possible ways of the“sliding mesh approach” and“sliding mesh” could producing trustworthy results. In the future research, I would like to adopt these two methods to carry out further research. A large number of scholars have adopted the current method of this paper to carry out many studies and proved the reliability of the research results, so the current research results of the paper also have a certain credibility.

 

1. Particular criticisms

B1. Introduction. The impeller is always the same (not; 6 impellers), but there are 6 values of the diameter of the balance holes.

√ Many thanks for the suggestions. We have modified the paper according to the comments. Now, this sentence has become as “six values of the diameters from 0 to 12mm of the balance holes” in the paper.

 

B2. The sentence “When the balance hole diameter increases....volute.’’ cannot be understood by a reader. What I understand from the paper is that the authors demonstrate that when the leakage flow through the rear chamber increases by increased diameter of the balance holes, the level of tangential velocity in the rear chamber increases by larger flow of tangential momentum from the volute of the pump into the rear chamber and that the increased tangential momentum decreases the velocity difference with the rotor disk, which decreases the rotor disk friction moment. This phenomenon happens until the balance hole diameter reaches some critical value, above which the level of tangential velocity does not increase anymore and the disk friction does not decrease anymore. The reason for the off-levelling is that for large value of the balance hole diameter, the clearance of the back sealing ring determines the leakage flow rate. I understand that this is the meaning of Table 2 at the end of the paper. But, it is not clear to me what the consequences are of this observation. One would expect an optimum value of the balance hole diameter by decreased disk friction (higher mechanical efficiency) and increased leakage flow rate (lower volumetric efficiency), until the saturation of the leakage flow rate is obtained. But this is not what can be seen on Fig. 5 that shows the evolution of global efficiency. so, the statement that the results of the paper provide a theoretical basis for optimal design of a centrifugal pump is not clearly justified, to my understanding. The authors have think seriously, in order to motivate a reader to read the paper, how to announce in the abstract the main conclusion of the paper and the value of it. It is not clear to me how to do this.

 

√ Thanks a lot for the comments. We have modified the paper according to the comments. Now, these sentences have become as “When the balance hole diameter increases, the flow characteristics of the rear chamber is mainly restricted by the mainstream flow field of the volute. However, when the balance hole diameter is larger than the design value, the disk friction loss of the rear chamber remains basically un-changed. On the contrary, when the balance hole diameter is smaller than the design value, the larger the balance hole diameter is, the smaller the friction loss of the disk in the rear chamber area is. The results of this paper provide a reference for reducing axial force and stable operation of centrifugal pump”.

 

B3. Second sentence of the introduction. I do not understand the sentence “Due to the faultiness on the flow.....” I think that the authors want to say that there is still incertitude about the precise flow mechanisms, or lack of precise ways of numerical simulation of the flow patterns,...

√ Thanks very much for the suggestion. We have modified the paper according to the comments. Now, this sentence has become as “There is still incertitude about the precise flow mechanisms, it is hard to calculate and balance the axial force of centrifugal pumps accurately, which has become an important subject in the research of pump industry”.

 

B4. Section 2.1. Second line. I think that the sentence should be: “... closed impeller with double seal rings and balance holes.”

√ Thanks very much for the suggestion. We have modified the paper according to the comments. Now, this sentence has become as “The impeller of the centrifugal pump is a closed impeller with double seal rings and balance holes.”

 

B5. Section 2.1. Fig. 2. It should be specified that the volute is seen from the back of the pump. The rotation of the rotor is clockwise, when seen towards its front side.

√ Thanks very much for the suggestion. We have modified the paper according to the comments. In the section 2.1, we have added two sentences “The volute is seen from the back of the pump in Figure 2(a). The rotation of the rotor is clockwise, when seen towards its front side.”

 

B6. Section 2.2. A motivation should be given for the choice of the RNG k-epsilon model. I agree with this choice for turbomachinery application, especially when the extension for system rotation is added. But nothing is said about the turbulence model.

√ Thanks very much for the suggestion. We have modified the paper according to the comments. In the section 2.2, we have added a sentence “The RNG k-e considers the rotation and swirling flow in the average flow, and can better deal with the flow with high strain rate and large degree of streamline bending.”

 

B7. Fig. 3. I do not understand what is seen on the left upper panel. Some explanation seems necessary to me.

√ Thanks a lot for the comments. The left upper panel is the enlarged picture of a flow passage in the impeller in the Fig.3.

 

B8. Fig 5. The deviating value of the efficiency for the balance hole diameter 12 mm is clearly due to some error. So, verify the simulation results.

√ Thanks a lot for the comments. After detailed verification and analysis, the centrifugal pump efficiency is relatively low when the diameter of the balance hole is 12mm. The efficiency is jointly determined by head, shaft power and flow rate. Therefore, the centrifugal pump efficiency value is indeed shown in the figure when the diameter of the balance hole is 12mm, which is not caused by mistakes.

 

B9. Section 3.5. The good correspondence with the experimental result of the averaged value of the tangential velocity component in Fig. 9 is not a proof of the correctness of the detailed flow fields shown in Figs. 6, 7 and 8. See discussion under remark A2.

√ Thanks a lot for the comments and suggestions. I agree with the two possible ways of the“sliding mesh approach” and“sliding mesh” could producing trustworthy results. In the future research, I would like to adopt these two methods to carry out further research. A large number of scholars have adopted the current method of this paper to carry out many studies and proved the reliability of the research results, so the current research results also of the paper have a certain credibility.

 

B10. Section 3.6 on disk friction. I understand that the value of vu1 is an average over the circumferential direction and the radial direction in the axial centre of the flow in the rear chamber; thus an average over a full cross area perpendicular to the shaft. It thus gives an idea of the global level of tangential velocity. Although I have strong criticism on the validity of the detailed flow patterns obtained by the calculation method, this global, averaged, result certainly shows the correct tendencies. So, the first line of Table 2 can be understood. It is not clear to me how the power on the second line is obtained. The P1 in Eq. 5 suggests that it is obtained by the simplified formula Eq. 4. If this is true, the results of P1 are not very meaningful in Table 2. Eq. 5 is extremely simplified by the assumption of a constant friction factor. The formula thus assumes that the thickness of the boundary layers is always the same. The dissipated power P1 should be estimated from the shear work extracted from the calculated flow field. But, I agree that the tendencies will be similar as obtained by the simplified formulas. But, obviously, the simplified formula cannot give an accurate estimate of the disk friction loss. So, the whole motivation for a detailed flow analysis for estimation of the disk friction loss becomes meaningless if finally a very simplified formula is used.

√ Thanks a lot for the comments and suggestions. I agree with you, but the results in Table 2 at least show a certain trend of friction loss of the disk, so I think it can be listed as a reference for the study of disk friction loss in the pump chamber.

 

B11. The observation that the leakage flow diminishes the disk friction dissipation in the rear chamber is not new. See page 18 of the recent review paper on the topic of gaps: L. Zemanova, P. Rudolf, Flow inside the sidewall gaps of hydraulic machines: a review; Energies, 2020, 13, 6617. So, the question is once more what to do with the final results of the current paper? What is the value of the results? What is the consequence for optimisation methods of a pump? 

√ Thanks very much for the question. This paper studies the flow characteristics and the disk friction loss of the rear chamber in the centrifugal pump at the design flow condition with six values of the diameters from 0 to 12mm of the balance holes. Motivated by the above discussions, this paper has three advantages which make the approach attractive comparing with the prior works. First, the full flow field is calculated by changing the diameter of the balance hole of the centrifugal pump impeller. Specially, in the design of the flow operating point, this paper analyzes in detail the influence of the balance hole diameter based on the axial distribution law of the tangential and radial velocity of the liquid in the rear chamber at different angles (0°, 90°, 180° and 270°) and different radii(0.6 R, 0.7 R, 0.8 R and 0.9 R), when the balance hole diameter is 0 mm, 4 mm, 6 mm, 8 mm, 10 mm and 12 mm, respectively. Second, the disk friction loss of the rear chamber is calculated by using the mean value of tangential velocity of liquid in the core region. Finally, the effects of the diameter of the balance hole on the liquid velocity in the rear chamber are revealed, and the causes of the disk friction loss can be obtained from the mechanism. The results of this paper provide a reference for reducing axial force and stable operation of centrifugal pump.

Finally, all of the authors would like to thanks a lot for the reviewers’ kindness and useful suggestions!

 

The manuscript has been resubmitted to your journal. We are looking forward to your positive response.

 

 

                                                Yours

Wei Dong, Haichen Zhang, Guang Zhang, Haoqing Jiang and Peixuan Li.

                                             Dec. 28, 2021

 

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper investigates the effects of pump blade hole on chamber velocity profiles. By introducing such structure, several benefits can be obtained with improved balanced force, potential stability and the resulting hydraulic performance.

However, the current paper doesn’t provide enough convincing results and informative contents. Several key issues should be considered and addressed clearly prior to a possible acceptance, which I believed helpful for making further improvements of this paper:

 

Major:

1.Line 25-36:

The structure of introduction part is loose. In the beginning, you should add more information to the background to state why it is an important matter and what the gap for the axial force calculation is. Then you should introduce more background of the balancing hole method, as well as more detailed introduction and constructive perspectives regarding current research on the balancing hole. Thus the introduction part needs a careful re-organization.

 

2. Line 37-39: Avoid providing less informative literature summary. For example for citation [10]: The main findings, inspiring results, or your own comments are better than merely stating they done a lot of work and obtained how much data.

 

3. What software (CFturbo/bladegen/…) is used for the generation of pump model? More details of the changing setup should be introduced, and so as the parameters in table 1.

 

4. The assuming steady-state neglected much time dependent loss such as the unsteady frictional loss, which might be important for the friction estimation in a rotating chamber. Please explain.

 

5. Line 118: Why do you chose the RNG k-ε model? Some other parameters like grid quality, especially the y+ value is used as guidance for mesh configuration and the selection of the most suitable turbulence model. What is the y+ value of the grid?

 

6. Streamlines in Figure 6: Why (3) and (4) show a reverse flow direction with regard to (1) and (2)? Since the pressure gradient between the hub and the rear outlet is not alternating?

 

7. As you mentioned, the velocity in the chamber you analyzed is not very large, then what about the Reynolds number in this area? Can laminar model be more appropriate in such zones?

 

8. line 183: “results in the..direction, and the value is small…indicating that.. is large…” This sentence is hard to understand its meaning, please give a better readability. Also, please define pressure potential energy.

 

9. Equation 4, please define the Uref, and what factors affect the coefficient of friction, which was given a constant value of 0.05 in this study?

 

10. Experimental validation: This part is important for comparing model accuracy, and apparently it lacks more detailed explanation in current paper. Please add more details what is the validation model used for comparison? And in which exact citation provides the comparing curves in present study?

 

11. line 283: Conclusion: “The smaller the cross-sectional area of the volute,…” it seemed you didn’t analysis different volute structures? Also, please give a more conclusive description about the findings on blade hole diameter, good or bad, at what level, for what specific reason…?

 

12. Some sentences should be reconsidered, such as Line 293: On the contrary…) It is not a “contrary phenomenon” if a curve decrease ahead of the valley point then it keeps unchanged instead of increased. By the way, “balance hole diameter is larger than the design value, the disk friction loss of the rear chamber remains basically unchanged”, considering if the hole becomes large enough, will the disk friction be still unchanged? What is the reason for the dramatic decrease of pump (hydraulic) efficiency in figure 5?

 

13. As this paper is mainly a numerical research, I suggest authors to cite some recent papers in journal of processes from near 2021, to introduce some updated progress or new analysis method in numerical research on pump.

 

Minor:

14. Section2.2 what scheme is used for the moving boundary? How is the rotational force implemented in such numerical scheme? please give more details.

 

15. line 130: Is the efficiency stated herein referred to the hydraulic efficiency?

 

16. Figure 5. The legend can be plotted in a solid box in case of confusing with the data points.

Comments for author File: Comments.pdf

Author Response

Dear Editor Mr. Aleksandar Jovanović,

First, we would like to thank the Editor, Associate Editor and Reviewers for their comments/suggestions, which have immensely improved the content of the paper.

We have modified the manuscript accordingly, and the detailed corrections are listed below point by point:

 

Author’s Response to the Reviewer’s Comments

 

Reviewer 2：

 

This paper investigates the effects of pump blade hole on chamber velocity profiles. By introducing such structure, several benefits can be obtained with improved balanced force, potential stability and the resulting hydraulic performance. However, the current paper doesn’t provide enough convincing results and informative contents. Several key issues should be considered and addressed clearly prior to a possible acceptance, which I believed helpful for making further improvements of this paper:

 

Major:

1. Line 25-36: The structure of introduction part is loose. In the beginning, you should add more information to the background to state why it is an important matter and what the gap for the axial force calculation is. Then you should introduce more background of the balancing hole method, as well as more detailed introduction and constructive perspectives regarding current research on the balancing hole. Thus the introduction part needs a careful re-organization.

√ Thanks a lot for the comments and suggestions. We have modified the paper according to the comments. Now, this sentence has become as “There is still incertitude about the precise flow mechanisms, it is hard to calculate and balance the axial force of centrifugal pumps accurately, which has become an important subject in the research of pump industry”. In the beginning, we have already explained that “Axial force is one of the most important factors affecting the service life and stable operation of centrifugal pump [1-3]. There is still incertitude about the precise flow mechanisms, it is hard to calculate and balance the axial force of centrifugal pumps accurately, which has become an important subject in the research of pump industry [4-6].” About the balanced hole method, we have already explained that “In the method of balancing axial force of balancing hole opening on the back cover of centrifugal pump impeller, the diameter of the balance hole is closely related to the magnitude of the axial force [7]. By numerical calculation with or without the balance hole and taking three different working conditions, it is found that the balance hole has a huge effect on the flow of liquid in the rear chamber along the tangential direction [12].” But the focus of this paper is to reveal the flow mechanism of centrifugal pump cavity under different balance hole diameters, rather than the method of balance hole balancing axial force.

 

2. Line 37-39: Avoid providing less informative literature summary. For example for citation [10]: The main findings, inspiring results, or your own comments are better than merely stating they done a lot of work and obtained how much data.

√ Thanks very much for the suggestion. Ref. [11] is cited in this paper because the comparison between the numerical calculation results of pump cavity flow velocity and the measurement results of hot-wire anemometer proves the reliability of the research results in this paper, and Ref. [10] plays a paving role for the later research.

 

3. What software (CFturbo/bladegen/…) is used for the generation of pump model? More details of the changing setup should be introduced, and so as the parameters in table 1.

√ Thanks very much for the question and suggestion. We have modified the paper according to the comments. Now, this sentence has become as “The three-dimensional solid models of centrifugal pump are built by Pro/E soft-ware shown in Figure 1.” We have added the parameters “Specific speed n_s, Front sealing ring diameter D_n, Back sealing ring diameter D_m, Sealing ring radial clearance b” in table 1.

 

4. The assuming steady-state neglected much time dependent loss such as the unsteady frictional loss, which might be important for the friction estimation in a rotating chamber. Please explain.

√ Thanks a lot for the comments. I agree with you that the unsteady frictional loss represents the relationship with time, but the steady calculation results of friction loss can be used as the average value for reference. So the steady calculation results have good reference value.

 

5. Line 118: Why do you chose the RNG k-ε model? Some other parameters like grid quality, especially the y+ value is used as guidance for mesh configuration and the selection of the most

suitable turbulence model. What is the y+ value of the grid?

√ Thanks very much for the comments. We have modified the paper according to the comments. In the Line 118, we have added a sentence “The RNG k-e considers the rotation and swirling flow in the average flow, and can better deal with the flow with high strain rate and large degree of streamline bending.” The y+ value of the grid is 30. The overall mesh quality is above 0.3.

 

6. Streamlines in Figure 6: Why (3) and (4) show a reverse flow direction with regard to (1) and (2)? Since the pressure gradient between the hub and the rear outlet is not alternating?

√ Thanks very much for the question. The liquid flow velocity of the rear chamber is significantly larger at 90°, compared with 0°, 180° and 270°. At 0° and 90°, the rear chamber liquid is mainly sealed backward by the volute flow in the ring direction and there are vortices near the wall surface of the impeller cover and the volute. At 180° and 270°, the rear chamber liquid flows mainly from the rear seal ring toward the volute and has a vortex near the wall surface of the pump cover. The above phenomenon is caused by the angle of 90° corresponding to the first section of the volute, and that the cross-sectional area of first section is less than others (180°, 270° and 0° angles correspond to sections 3, 5 and 7 of the volute) and the fact that the first section is located at the volute tongue nearby. The flow in the volute has a large restrictive effect on the liquid flow in the chamber of the 0° and 90°, which results in a large speed and a vortex motion in the high speed region near the volute.

 

7. As you mentioned, the velocity in the chamber you analyzed is not very large, then what about the Reynolds number in this area? Can laminar model be more appropriate in such zones?

√ Thanks very much for the question. The Reynolds number is less than 200,000 in this area. The previously presented analysis has proven that the fluid dimensionless axial flow consists of the tangential shearing flow and the radial pressure difference flow, which are considered the two-dimensional highly viscous laminar motion. Therefore, the laminar model is appropriate in such zones.

 

8. line 183: “results in the..direction, and the value is small…indicating that.. is large…” This sentence is hard to understand its meaning, please give a better readability. Also, please define pressure potential energy.

√ Thanks very much for the suggestion. We have modified the paper according to the comments. Now, this sentence has become as “The pressure difference between the rear chamber and the hub chamber is large, the pressure potential energy and kinetic energy of the rear chamber are large, result-ing in the same radius of the tangential direction and the same angle of the radial di-rection of the non-dimension tangential velocity tends to be the same, and the value is large.” Pressure potential energy is determined by the value of pressure. The greater the pressure difference, the greater the pressure potential energy.

 

9. Equation 4, please define the Uref, and what factors affect the coefficient of friction, which was given a constant value of 0.05 in this study?

√ Thanks very much for the question. The u_ref  is the average rotational speed of the impeller cover plate in the rear chamber area. The coefficient of friction is related to the roughness of the surface, but not to the size of the contact area. The constant value of 0.05 is refers to the book “Modern pump theory and design”.

 

10. Experimental validation: This part is important for comparing model accuracy, and apparently

it lacks more detailed explanation in current paper. Please add more details what is the validation model used for comparison? And in which exact citation provides the comparing curves in

present study?

√ Thanks very much for the suggestion. In Ref [26], numerous experimental data were obtained by using a hot-wire anemometer to measure the velocity distribution of the turbulent flow field on the rotating disc inside the closed cylinder. In Ref [27], the particle image velocimetry (PIV) test results and the hot-wire measurement data were compared, and they found that the distributions of the circumferential and radial components of velocity were consistent at the radial geometrical center of the disc (0.6–0.8) R. At the rear chamber zone 0.8 R of the pump close to the radial geometrical center of the chamber, the fluid flow was less affected by the leakage flow and was approximated as the flow on the rotating disc inside the closed cylinder. In Ref [26], the experimental data at 0.8R were compared with the axial distribution curves of the circumferential and radial components of velocity at the design flow point 0.8R inside the rear chamber. No leakage flow occurs in the rear chamber when there is no balance hole, which approximates the flow of the rotational disk in the enclosed cylinder. According to Ref. [26, 27], the hot-wire anemometer is applied to measure the turbulence speed of the flow field for the rotating disk in the closed cylinder. As shown in Fig. 5, the test data of the circumferential and the radial velocity components at 0.8R are compared with the circumferential and the radial velocity components distributed along the axial direction at 0.8R in the rear chamber of the centrifugal pump for the impeller without a balance hole.

 

11. line 283: Conclusion: “The smaller the cross-sectional area of the volute,…” it seemed you

didn’t analysis different volute structures? Also, please give a more conclusive description about

the findings on blade hole diameter, good or bad, at what level, for what specific reason…?

√ Thanks very much for the question. The cross-sectional area of the volute is the sectional area of discharge chamber on the design. The centrifugal pump balance hole diameter design value is 8mm, the study of this paper also confirmed that the balance hole diameter of 8mm is the best value. When the balance hole diameter is 8mm, the disk friction loss is minimum.

 

12. Some sentences should be reconsidered, such as Line 293: On the contrary…) It is not a

“contrary phenomenon” if a curve decrease ahead of the valley point then it keeps unchanged

instead of increased. By the way, “balance hole diameter is larger than the design value, the disk

friction loss of the rear chamber remains basically unchanged”, considering if the hole becomes

large enough, will the disk friction be still unchanged? What is the reason for the dramatic

decrease of pump (hydraulic) efficiency in figure 5?

√ Thanks very much for the question. We have modified the paper according to the comments.

We have deleted the " On the contrary," in Line 293. The disk friction loss mainly depends on the liquid flow velocity in the rear chamber. The liquid flow velocity in the chamber is affected by the balance hole diameter. Pump efficiency is affected by mechanical loss, volume loss and flow loss. Pump efficiency is calculated by head, shaft power and flow rate.

 

13. As this paper is mainly a numerical research, I suggest authors to cite some recent papers in journal of processes from near 2021, to introduce some updated progress or new analysis method in numerical research on pump.

√ Thanks very much for the suggestion. We have modified the paper according to the comments. We have cited [19] “Huang, B.; Zeng, G. T.; Qian, B.; Wu, P.; Shi, P. L.; Qian, D. Q. Pressure fluctuation reduction of a centrifugal pump by blade trailing edge modification. Processes, 2021, 9(8), 1408.” in journal of processes from near 2021.

 

Minor:

 

14. Section2.2 what scheme is used for the moving boundary? How is the rotational force implemented in such numerical scheme? please give more details.

√ Thanks very much for the question. We have modified the paper according to the comments. The simulations were done with the commercial package “Fluent”. The simulation methodology of the interaction of the flow is the “multiple reference model” (MRef) in the rotor and the flow in the stator. We have added two sentences “In this paper, FLUENT software is used to carry out numerical calculation. The simulation methodology of the interaction of the flow is the “multiple reference model” (MRef) in the rotor and the flow in the stator.” in the revised paper.

 

15. line 130: Is the efficiency stated herein referred to the hydraulic efficiency?

√ Thanks very much for the question. No, it’s not. The efficiency stated herein referred to the overall efficiency.

16. Figure 5. The legend can be plotted in a solid box in case of confusing with the data points.

√ Thanks very much for the suggestion. We have modified the paper according to the comments.

Finally, all of the authors would like to thanks a lot for the reviewers’ kindness and useful suggestions!

 

The manuscript has been resubmitted to your journal. We are looking forward to your positive response.

 

 

                                                Yours

Wei Dong, Haichen Zhang, Guang Zhang, Haoqing Jiang and Peixuan Li.

                                             Dec. 28, 2021

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have made corrections for my minor remarks, but they have not done anything concerning my major criticisms.

1. I do not believe in the realism of the detailed flow fields obtained by the simulations done with the “multiple reference model” for the topic studied in the paper. In particular, keeping the rotor on a fixed position with the particular position of the blades strongly exaggerates the interaction between the rotor outflow and the inflow of the volute in the tongue region of the volute. To my understanding, the strong circumferential variation of the flow patterns shown in Fig.6, Fig.7 and Fig.8. cannot be realistic. For reliable results, the “sliding mesh approach“ should be used. The answer by the authors that the simplification by the “multiple reference model” is often used is not a sufficient justification. There is clearly a strong interaction between the rotor flow and the volute flow and the manual of the Fluent package says explicitly that the approximate “multiple reference model” should only be used in case of a weak interaction. This condition is not satisfied. It could be that for the purpose of the paper, which is the evaluation of the disk friction as a function of the diameter of the balance holes, the used approximation is acceptable, although there are certainly very large local errors in the flow field. But this has then to be proven, which is not done by the authors. A vague promise by the authors that they will consider future analysis by the fully consistent “sliding mesh approach” is not sufficient for making the current results credible.
2. I do not see the meaning of doing a detailed analysis of the flow in the rear chamber of the rotor with the purpose to study the disk friction loss, when, finally, the disk friction moment is estimated with the extremely simplified formula nr. 4. The moment should be calculated with the shear stress on the back side of the rotor, which is a result of the flow calculation. The necessary information is available by the calculated flow results. With the simplified formula, only the tendency can be illustrated. But, this tendency is known in advance. As the leakage flow increases by increased diameter of the balance holes, more tangential momentum from the main flow is drained into the back space of the rotor, which decreases the difference in tangential velocity between the flow in the back space and the back side of the rotor, and thus decreases the disk friction moment. This decrease continues until the leakage flow rate saturates when the clearance area by the seal ring becomes significantly smaller than the through-flow are of the balance holes. This happens around a balance hole diameter of about 7 mm. This is visible on Fig. 5, ignoring the deviating value of the efficiency for diameter 12 mm. The tendency is visible in Table 2, but the results in Table 2 cannot be precise.

I am very displeased by the observation that I am the only reviewer of the paper. This is not serious. Because of the use of the simplified numerical simulation, there if, of course, a reason for doubt on the numerical results. With my knowledge and experience, I am certain that the detailed flow patterns have large errors. In how far that this causes a large error on an integral result as a disk friction moment is not clear to me. Because the authors do not give an answer on this aspect, the opinion of other reviewers on the credibility of the results could have given an answer.

I suggest that the paper be submitted to two other reviewers and that the associate editor then makes a decision based on the opinion by these reviewers. I do not want to take part in this new review, because I am not able to judge on the credibility of the presented results by the information that is given in the paper.      

Reviewer 2 Report

The authors revised the paper, but several main concerns are still unsolved. The accuracy for the applied numerical scheme should be validated with more convicing resullts. Key factors affecting disk friction losses, articles studying about blade hole method should be reviewed in a responsible manner, to reflect the novelty of this paper with regard to other previous work.