J. Cent. South Univ. (2015) 22: 1695−1706 DOI: 10.1007/s11771-015-2688-2

Effect of impeller reflux balance holes on pressure and axial force of centrifugal pump

CAO Wei-dong(曹卫东), DAI Xun(代珣), HU Qi-xiang(胡啟祥)

Technical and Research Center of Fluid Machinery Engineering, Jiangsu University, Zhenjiang 212013, China

© Central South University Press and Springer-Verlag Berlin Heidelberg 2015

Abstract: The size of impeller reflux holes for centrifugal pump has influence on the pressure distribution of front and rear shrouds and rear pump chamber, as well as energy characteristics of whole pump and axial force. Low specific-speed centrifugal pump with Q=12.5 m3/h, H=60 m, n=2950 r/min was selected to be designed with eight axial reflux balance holes with 4.5 mm in diameter. The simulated Q−H curve and net positive suction head (NPSH) were in good agreement with experimental results, which illustrated that centrifugal pump with axial reflux balance holes was superior in the cavitation characteristic; however, it showed to little superiority in head and efficiency. The pressure in rear pump chamber at 0.6 times rate flow is 29.36% of pressure difference between outlet and inlet, which reduces to 29.10% at rate flow and 28.33% at 1.4 times rate flow. As the whole, the pressure distribution on front and rear shrouds from simulation results is not a standard parabola, and axial force decreases as flow rate increases. Radical reflux balance holes chosen to be 5.2 mm and 5.9 mm in diameter were further designed with other hydraulic parts unchanged. With structural grids adopted for total flow field, contrast numerical simulation on internal flow characteristics was conducted based on momentum equations and standard turbulence model (κ−ε). It is found that axial force of pump with radical reflux balance holes of 5.2 mm and 5.9 mm in diameter is significantly less than that with radical reflux balance holes of 4.5 mm in diameter. Better axial force balance is obtained as the ratio of area of reflux balance holes and area of sealing ring exceeds 6. Key words: centrifugal pump; low specific-speed; radical reflux balance holes; numerical simulation; pressure gradient; axial force

1 Introduction

During the operation of centrifugal pump, there is large force acting on rotor parts such as impeller, and the axial component of the force is known as axial force [1]. As for impeller of centrifugal pump, projection areas on the plane perpendicular to axis of front and rear shrouds are generally different, and the fluid pressure difference between front and rear shrouds is one of the main reasons of the axial force imbalance of whole rotor parts [2−3]. Axial force has great effect on operation stability of centrifugal pump. The unbalanced axial force may lead to axial movement of rotor. Owing to the collision of rotor with fixed parts, parts damage or operation stopping emerges, which even may result in motor’s burning down.

To reduce the negative effects of axial force on centrifugal pump during operation, experts and scholars have done various researches on balancing axial force of centrifugal pump. When there was no instrument for direct measurement of axial force, to investigate the

cause of axial force acting on impeller in peripheral pump, the axial force acting on impeller was obtained indirectly through measuring the pressure in working chamber and it is confirmed that there is no axial force in couplings [4]; to prolong the service life of oil-immersed pump for oil pumping in deep ocean, a method was put forward to balance axial force with oblique cutting impeller and the feasibility is verified through durability performance experiment [5]. To balance the axial force of shielding pump, double wear- ring structure was applied to rear shrouds of impeller to enlarge the diameters of front and rear wear-rings. Inner and outer rings of double wear-ring act as the throttling gear, leading to pressure equalizing; while balance holes act as the controlling valve. Radial position of rotor had an effect on the cover area of balance holes, which further affected leaking and pressure-relief [6]. And for fear of emergency shutdown caused by excessive wear of balancing device resulting from design deficiency, based on the hydrodynamic theory, the universal formula is also deduced for axial force consistent with the actual situation [7]. These earlier researches are almost on the

Foundation item: Project(51179075) supported by the National Natural Science Foundation of China; Project(BK20131256) supported by the Natural

Science Funds of Jiangsu Province, China; Project supported by the Priority Academic Program Development of Jiangsu High Education Institutions, China

Received date: 2014−03−14; Accepted date: 2014−10−11 Corresponding author: CAO Wei-dong, Associate Professor; Tel: +86−13952816468; E-mail: cwd@ujs.edu.cn

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basis of tradition balancing device, in which traditional research method was adopted to study the mechanism of axial force. In recent years, the study on traditional balancing device tends to become popular with the development of correlation technique and CFD. By simulating operation condition of floating impeller with specialized equipment, through which the test curve of front and rear pressure of rear wear-ring was obtained and characteristic curve of leakage in balancing chamber was calculated, the problem of relationship between leakage and pressure change in balancing chamber for floating impeller was solved [8]. The internal flow structure inside balancing device as well as the mechanism of axial force balancing was investigated CFD method, from which the significant difference of flow structures in clearance of sliding bearing under the different conditions of inlet and outlet pressure difference was carried out. Owing to the change of mechanism of bearing support, balance force and relative leakage increased nonlinearly with the growth of axial and radial clearance. With the increase of the ratio of length to diameter, variation of balance force presented an approximately linear character and the variation of relative leakage just the opposite [9]. Furthermore, the relationship between the diameter and balancing axial force was investigated through enlarging the diameter of rear wear-ring, which was verified with contrast between experiment and numerical simulation [10]. Some investigators also put forward the production mechanism of axial force and deduced several conclusions which cannot be totally verified by experiments [11−12]. As for these researches, however, there are not many innovative approaches, letting alone the research based on new balancing device. The mathematical equations of clearance leakage and pressure difference [13] in application document are used to calculate the axial force acting on end-stage impeller and deduce the relational expression between geometric dimension and axial force [14]. In addition, depending on new invention device [15], the method raising from the head maximum approach of expending diameter of front shroud [16] creatively presented great results for balancing axial force, thus in turn improving the cavitation performance, as well as efficiency of whole pump. Moreover, with the aid of innovative device, the effects of different clearances on axial force and pressure [17] in pump chamber were investigated. Summarizing the early and resent researches on the aspect of axial force of centrifugal pump, it is mainly concentrated on various balancing devices, such as balance holes, balance tube, back-blade, balance drum and balance disc. Nevertheless, the major variation lied in the difference between traditional theoretical analysis and numerical simulation. It is the tendency of future research on axial force of

pumping devices exploring balance principle in great depth with CFD based on new balancing device of axial force.

As for above study, there are many devices balancing axial force; while the research on balance holes is in the minority: contrast experiment was carried out through removing balance holes of impeller and rear wear-ring to investigate the influence of balance holes on head, efficiency and NPSH [18]. Reserving rear wear- ring for centrifugal pump under the condition of high temperature and high pressure, the comparison between numerical simulation and experiment was conducted for two schemes with and without balance holes to analyze the effect of balance holes on pump performance and axial force, and the result of reducing axial force was investigated [19]. The fluid pressure and axial force in single-stage, single-suction centrifugal pump were studied by adopting different diameters for rear sealing ring of impeller [20]. But these researches were all based on traditional balancing device. As shown in Fig. 1, rear wear-ring in radius Rm drilled at the bottom is set upon the rear shroud of impeller. Rm is equal to or slightly larger than the radius of front wear-ring. Owing to the resistance loss of fluid flowing through seal ring clearance, high pressure fluid flows into impeller passage through balance holes to mix with mainstream. The force acting on the rear shroud drops, thus the axial force is balanced [21]. For the traditional axial reflux balance holes, however, the process of high pressure fluid in chamber behind reflux holes flowing into impeller passage tends to exaggerate volume loss and reduce efficiency, declining the force acting on shroud. Meanwhile, the high pressure fluid flowing through balance holes into impeller impacts to mainstream, breaking normal flow condition and naturally decreasing the anti-cavitation erosion performance.

Fig. 1 Centrifugal pump with balance holes and double

wear-ring (R2 is radius of impeller; Rm is radius of rear

wear-ring; d is diameter of balance holes; Rh is radius of

impeller hub; RB is distance between balance hole centerline

and impeller axis)

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Therefore, the design of new radical reflux balance holes, in contrast to traditional axial balance holes, is capable of enhancing the anti-cavitation erosion performance and efficiency [15]. In this work, CFD software is adopted to study the innovative radical reflux balance holes. Under the identical precondition of location of balance holes, diameter of holes is changed to investigate the effects on pressure in front and rear pump chambers and axial force, as well as the regularity of this variation, which can provide theoretical foundation and object reference for later study. 2 Design parameters

Table 1 illustrates the design parameters of centrifugal pump with radical reflux balance holes, and Fig. 2 reflects its structure. Then, the impeller model of centrifugal pump with radical reflux balance holes is shown in Fig. 3.

Table 1 Design parameters of centrifugal pump with radical

reflux balance hole

Design flow

rate/(m3·h−1) Head/m Speed/(r·min−1) Specific speed

12.5 60 2950 29

Fig. 2 Centrifugal pump with radical reflux balance holes:

1−Inlet; 2−Front wear-ring; 3−Impeller with radical reflux

balance holes; 4−Shield ring nut; 5−Rear wear-ring; 6−Pressure

monitoring point; 7−Outlet

In Fig. 4, the detail structure of impeller with radical

reflux balance holes and the partial enlarged structure of balance holes are shown [22]. The main geometry parameters of impeller are listed in Table 2.

Fig. 3 Impeller with radical reflux balance holes

Compared with the traditional reflux balance holes

in Fig. 1, through which reflux flows into mainstream passage from high pressure area, the application of radical reflux balance holes makes the reflux fluid block by shield ring for shaft segment nut. Thus, the reflux fluid flows into mainstream passage radically; in this way the flow regime in mainstream passage escapes from the destruction, resulting from the reflux high pressure fluid. This radical reflux balance holes structure enhances the head and efficiency of the pump, and further improves the anti-cavitation erosion performance [17]. The object diagram is demonstrated in Fig. 5.

In general, the diameter of rear wear-ring of impeller with reflux balance holes is equal to or slightly larger than that of front wear-ring. When the total flow area is 5−8 times the area of clearance flow area of rear seal ring, residual force acting on shroud accounts for 10%−20% of the force acting on shroud without balance holes. For these reasons, front and rear wear-rings are designed with the same diameter, and 8 balance holes are drilled at the location of 34 mm diameter on rear shroud, as shown in Fig. 6. 3 Theoretical analysis

Based on the formula of leakage of balance holes and balance degree [1]:

22 2

p 2 B 2 2m B

m1= ( )

8 2Bq

H u ug g F F

(1)

2 2 m Bp 2 B 2 2

m B

1= 2 /

8q H u u g

g F F

(2)

where Hp is potential head, 2

p t 2= [1 /(2 )];H H gH u u2 and uB are the circumferential velocities at the outlet of impeller and at the centerline of balance holes,

Table 2 Main geometry parameters of impeller Blade

number Inlet blade angle/(°)

Outlet blade angle/(°)

Blade wrap angle/(°)

Blade outlet width/mm

Impeller outer diameter/mm

Reflux balance hole diameter/mm

Reflux balance hole number

4 25 29 170 5 218 34 8

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Fig. 4 Impeller (a) and partial enlarged detail (b) for balance holes

Fig. 5 Contrast between traditional (a) and radical reflux

balance (b) holes

respectively; ζm is resistance coefficient of seal clearance, ζm=1.5+λL/(2b), λ=0.04 to 0.06; ζB is resistance coefficient of balance holes, generally ζB=2; Fm is flow area of seal clearance, Fm=Dmπb; FB is total area of balance holes, FB=d2πz/4.

Fig. 6 Radical reflux balance holes

From Eq. (2), it can be seen that the formula of the ratio of the total flow area of balance holes to the flow area of rear seal ring clearance is:

2B m m/ /(4 )n F F d z D b (3)

Empirically, when n ranges from 5 to 8, the

variation of value means different influence on volume loss deriving from balancing force and shrinking reflux holes. As reflected from Eq. (3), capacity of balancing axial force is in relation with the diameter of rear seal ring, seal clearance as well as the number and diameter of balance holes. Thus, the reliability of numerical simulation results is verified through comparing the experiment and numerical simulation for centrifugal pump with holes of 4.5 mm in diameter, and then the numerical simulations of centrifugal pump with holes of 5.2 mm and 5.9 mm are carried out and compared. Only the diameter varies for these three schemes; while the center remains unchanged. The total flow areas of balance holes for three schemes respectively are 127.23, 169.90 and 218.72 mm2. As the flow area of rear wear-ring clearance keeps the same, 20.73 mm2, the flow area ratios of three schemes are 6, 8 and 10, respectively. 4 Numerical simulation 4.1 Calculating model

The process of mechanical energy translating into fluid energy is associated with different losses, and it mainly covers the disc friction loss resulting from the friction between fluid with front and rear shrouds and casing surface. The volume loss resulting from part of the fluid reverses through wear-ring and reflux holes from pump chamber, and mechanical loss from bearings, etc. To calculate the flow field loss of whole pump, total fluid field is adopted to accurately calculate the disc friction loss and volume loss in front and rear chambers. Three-dimensional model for fluid body of total fluid field of centrifugal pump is built with Core Pragmatic 2.0 from Parametric Technology Corporation (PTC). The

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fluid body model of centrifugal pump with radical reflux balance holes is shown in Fig. 7.

Fig. 7 Fluid body: 1−Inlet; 2−Front pump chamber; 3−Impeller;

4−Volute; 5−Rear pump chamber; 6−Retainer ring for radical

reflux balance holes; 7−Chamber behind reflux holes

During external characteristic numerical experiment,

sufficient length is taken at the inlet part, thus the inlet velocity is constant, which means that velocity has a linear relation with radical position. Therefore, according to reference document, the inlet velocity of impeller tends to stabilize as the length of inlet part becomes more than two times the inlet diameter. In this work, the length is chosen to be 360 mm.

For the model of total fluid field, unilateral dimension of wear-ring clearance is just 0.2 mm. Provided unstructured grid is adopted, and the grid requires refinement under the precondition of ensuring calculation precision; however, sharp increasing in grid quantity wastes the computational resource. For this reason, numerical simulation is carried out with structured grid. Compared with tetrahedral grid, hexahedral grid is capable of controlling the distribution in mainstream direction as well as the orthogonally in boundary layer direction. It also has the advantage for precision of numerical simulation and computation speed. Nevertheless, the unilateral clearance for wear ring of 0.2 mm is too small compared with the size of front and rear pump chamber. Figure 8 illustrates the cross section of front pump chamber and Fig. 9 shows the partitioning method for fluid body of front chamber and section diagram of local grid. As can be seen, the part in red box is the transition part of clearance fluid body and front pump chamber, where the dimensional ratio exceeds 10. The orthogonality of grid also needs to be taken into consideration.

Fig. 8 Section diagram for front pump chamber water model

Fig. 9 Partitioning method for fluid body of front chamber (a)

and section diagram of local grid (b)

Numerical simulation is performed by using a

commercial software package, CFX. General gird interfaces (GGI) patched grid technology is employed for the interface of dynamic and static water during the CFX pre-processing. The numerical model is based on the time-averaged Navier-Stokes equations as the basic governing equations with the standard κ−ε as the turbulence model. Standard k−ε model is widely used in engineering fluid field simulation. Although this model has wide application range and is economic, it leaves the rotation in mean flow and rotation flow out of consideration. Simulation accuracy depends on the reasonable choice of grid quality, boundary conditions, turbulence model and convergence precision, renormalization group (RNG) turbulence model is appropriate for the simulation of separation flow and vortex flow. For most centrifugal pumps, standard k−ε turbulence model is proved to be the precision- guaranteed common method. The second-order upwind is adopted and the SIMPLE algorithm is used for the pressure−velocity coupling [23].

Pressure set to 1.013×105 Pa (standard atmosphere) is applied at inlet boundary of computational domain, and mass flow rate is applied at the outlet boundary. No-slip boundary conditions are imposed on all solid walls, the impeller solid walls are defined as rotating boundary and velocity at boundary is given as the circumferential velocity. Standard wall function is used to account for the turbulence flow. The computational domain including the entire rotor is set to be rotating for truly reflecting the flow pattern of total flow field in centrifugal pump. The speed is set to −2950 r/min based on the right-hand rule. Wall surfaces contacting with front and posterior pump chamber as well as volute wall are stationary, thus these wall surfaces are set to reverse rotate relative to the rotating water body, i.e., 2950 r/min.

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4.2 Grid sensitivity analyses The whole mesh generation was carried out by the

ANSYS ICEM CFD 14 software, and the multi-block structured grid was utilized to discrete the computational domain. With the increasing of grid number, the error caused by the grid number will be reduced gradually until it disappears. However, considering the configuration and calculating time, the number of grids cannot be too large. In this work, eleven different grid numbers were selected for the numerical simulation. In addition, owing to the different diameters of three schemes, the computation domains of balance holes are divided separately. And the diameter means little to overall grid number. Total flow field model of the first scheme is selected for the verification of grid independence. The numerical simulation of this work is focused on the change of external characteristic as well as pressure in pump chamber.

As can be seen from the results of external characteristic in Fig. 10, grid number has little effect on the external characteristic when total grid number rises to more than 2.5 million. The final whole structured grid is shown in Fig. 11.

Fig. 10 Grid independence verification

Fig. 11 Whole structured grid

5 Experimental devices

Although the structure of the centrifugal pump is simple，the flow in it is so complex. To study and analyze the flow in centrifugal pump thoroughly, it is essential to carry out experimental research. The model pump in this work was produced by Nanjing Lanshen Pump Producer Company, and the performance characteristic experiment of the model pump was employed on opening experiment stand in an irrigation machinery production quality testing center (Zhenjiang) of mechanical industry in China. Experiment device and the opening stand of centrifugal pump are shown in Fig. 12.

Fig. 12 Experiment device (a, b) and opening stand (c): 1−Inlet

valve; 2−Experimental pump; 3−Pressure transducer; 4−Outlet

valve; 5−Turbine flow meter; 6−Power distribution cabinet;

7−Data collector; 8−Computer; 9−Electric motor;

10−Experiment pool

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6 Numerical results 6.1 Performance characteristic

Performance characteristic curves (Q−H, Q−P and Q−η) of the pump are shown in Fig. 13. Numerical results show predicted head of the model pump is 65.69 m at the design flow rate, and compared with the design head of 60 m, the relative error is 9.5%. If the predicted head is compared with the experiment value of 61.96 m, the relative error is 6.2%. The predicted power

Fig. 13 Performance characteristic: (a) Q−H; (b) Q−P; (c) Q−η;

(Hn−Numerical head; He−Experimental head; Pn−Numerical

power; Pe−Experimental power; ηn−Numerical efficiency;

ηe−Experimental efficiency)

is 5.53 kW, and compared with the experiment value of 5.4 kW, the relative error is 2.4%. The predicted value of efficiency is 40.45%, and compared with the experiment value of 39.06%, the relative error is 3.6%. Overall, there are lower head, higher efficiency and larger power corresponding to increasing flow for the model pump. The numerical results are higher than experimental results, the maximum deviation of simulation results from experimental results is lower than 10%. Due to manufacturing deviation of pump and motor, experiment deviation and model simplification in simulation, low precision is common in simulation for low specific speed pump. There is some error between simulation value and experiment results. Nevertheless, the error is totally within the normal range.

In this experiment, pressure monitoring points are located in the position behind the reflux flow balance holes about 42 mm in axial direction (Fig. 2). Consequently, in CFX-Post, we obtain the static pressure in point (42, 35, 0); compared with the experimental value correspondingly, the static pressure was verified at the monitor point in back pump chamber in different flow rate. The comparison of the static pressure at monitoring point between simulation and experiment is shown in Fig. 14.

Fig. 14 Static pressure between simulation and experiment

(ppn−Numerical static pressure; ppe−Experimental static

pressure)

From the results mentioned above, at the monitoring

point, the maximum relative error of static pressure between simulation and experiment is 15.8% under the condition of low flow rate; the minimum relative error is 3%; the average relative error is below 10%. Due to the unsteady flow at the operation of low flow rate, the higher the flow rate is, the smaller the relative error is. The relative error less than 10% is acceptable which confirms that numerical results have a fine agreement with experiment results. However, the purpose of the simulation of three schemes is to further study the different influence under different diameters of balance holes.

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6.2 Pressure at rear pump chamber and axial force Experience formula of impeller axial force is:

2 21 m hπ( )F gH R R (4)

where F is total axial force; H1 is head of single stage; Rm is radius of impeller seal ring; Rh is radius of valid impeller rub; κ is correction factor.

From Eq. (4), the head gets lower with the increasing flow rate, and the axial force declines monotonically. For the impeller with reflux flow holes of 4.5 mm in diameter, the curve of the ratio of pressure at simulation monitor point as well as the axial force variation curve is shown in Fig.15. As can be seen from the figure, at 0.6Qopt, (rate flow) the ratio of pressure in pump chamber behind the reflux flow balance hole to the design head is 29.36%; the ratio is 29.10% at 1.0Qopt; the ratio decreases to 28.33% at 1.4Qopt. The pressure ratio in monitor point is decreasing; the axial force presents upgrade firstly, then descending later with the increasing flow rate. Specifically at design flow rate, the axial force drops to a minimum. With the increasing of the flow rate, the static pressure inside pump tends to decline continually. Nevertheless, from the numerical results, the axial force has a slight increasing trend at larger flow rate. It may result from the location of reference pressure point which is settled at the inlet of whole computational domain rather than the inlet of impeller passage. It is known that the background pressure at passage inlet is bound to produce additional axial force. Thus, the background static pressure is certain to rise as flow rate increases.

Fig. 15 Ratio of pressure at simulation monitoring point and

axial force

6.3 Pressure at monitoring point with different

balance hole diameters By comparing the three schemes shown in Fig. 16,

the diameters of radial reflux balance holes of the impeller are different and the pressure at monitoring point changes with the variation of flow for the same

centrifugal pump. As the diameter increases, the ratio of the total flow area of holes and the flow area of rear wear-ring clearances increases. Supposing the pressures in front of and behind the rear wear-ring clearance remain constant, namely, the rear chamber pressure of balance holes remains the same. With the increase of diameter, when fluid with high pressure enters the impeller passage, the passage pressure reduces, the outlet pressure declines and the pressure of both sides of the rear wear-ring clearances also decrease. This process is mutual. Therefore, the rear wear-ring pressure decreases with the increase of diameter. This comparison proves that the increasing of diameter leads to pressure reduction of pump chamber behind reflux holes.

Fig. 16 Pressure with different balance hole diameters

6.4 Axial force with different balance hole diameters

Comparing the effects of different diameter on axial force for the whole pump, as shown in Fig. 17, it can be seen that the axial force increases with the growth of diameter. Owing to the increasing of diameter, the passage area ratio increases. With higher passage area ratio, the effect of balancing the axial force reduces and the pressure difference between front and rear shrouds increases. It is found that the balancing effect of balance holes of 4.5 mm in diameter is obvious by contrast. With

Fig. 17 Axial force with different balance hole diameters

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the increase of the diameter, the passage area ratio increases from 6 to 10, and the effect becomes worse; the balancing effect is the best when the passage area ratio is about 6 in this pump. 6.5 Head and efficiency with different balance hole

diameters Comparing the effects of different diameters on

head, power and efficiency of the whole pump, it can be seen that the head, power and efficiency decrease with the increase of diameter. Owing to the increase of diameter, the “upstream” fluid flowing into the impeller passage from the rear pump chamber increases, and this part of the fluid indirectly reduces the flow in a centrifugal pump impeller passage and lowers the head and efficiency. The external characteristic comparison of three schemes is consistent with the flow regularity. Combining with the data in Fig. 17 and Table 3, reflux balance holes with 4.5 mm in diameter have better effect on balancing the axial force and a relatively minimal impact on head, power and efficiency. Table 3 External characteristic of three schemes

Hole diameter/mm Flow H/m P/kW η/%

4.5

0.4Qopt 69.38 4.62 20.43

0.6Qopt 68.32 4.98 27.99

0.8Qopt 66.66 5.24 34.61

1.0Qopt 65.69 5.53 40.45

1.2Qopt 64.86 5.81 45.55

1.4Qopt 62.40 6.13 48.46

5.2

0.4Qopt 69.31 4.63 20.39

0.6Qopt 68.28 5.00 27.88

0.8Qopt 66.43 5.25 34.42

1.0Qopt 65.59 5.54 40.27

1.2Qopt 64.44 5.84 45.03

1.4Qopt 62.30 6.15 48.27

5.9

0.4Qopt 69.30 4.65 20.30

0.6Qopt 68.24 5.01 27.83

0.8Qopt 66.33 5.27 34.24

1.0Qopt 65.37 5.55 40.05

1.2Qopt 63.74 5.85 44.50

1.4Qopt 61.32 6.15 47.52

6.6 Flow fields with different balance hole diameters

Total pressures of the three schemes are compared as shown in Fig. 18. Because the high pressure fluid flowing into the impeller passage through the reflux holes mixes with fluid in the flow passage with the same diameter, the pressure gradient near the blade inlet abruptly changes where holes are mainly near the reflux.

Meanwhile, although the diameter increases, the location of balance holes remain at the same, thus the location of pressure gradient mutation near the inlet part un changes. Then, “upstream” fluid flows into the impeller passage in the same position and mixes with mainstream. As illustrated in the figure, pressure gradient of different balance holes almost keep un-changed at the same flow rate, not leading to qualitative changes on pressure gradient of the whole impeller passage.

The distribution of the relative velocity at impeller inlet part increases with high flow rate in the three schemes as shown in Fig. 19. As the flow rate is small, velocity mutation is visible, which indicates that the localized pre-rotation appears in inlet at small flow rate. With the increasing of the flow rate, the distribution of inlet velocity is close to be stable and almost has no obvious mutation after reaching the rated flow. The above phenomenon reflects the inlet flow instability of low specific speed centrifugal pump in this work under small flow rate condition, and even extending the inlet water body cannot change the fact. The velocity from the reflux holes to the position nearby reflux holes shield ring decreases obviously because the fluid from the high pressure area to the impeller passage is blocked by the reflux holes shield ring. While no obvious velocity mutation occurs in impeller passage, showing that the radial reflux balance hole changes the direction of fluid into the passage through the shaft segment shield ring, so that the fluid from the high pressure area to the impeller passage has good transition. Comparing different balance holes at the same flow rate, it can be drawn that, no matter how much the flow is, the change of the diameter does not alter the steady flow role of reflux hole, which also verifies the innovative role of radial reflux balance hole, namely, the fluid flowing through radial reflux holes into the impeller passage has better effect compared with the traditional reflux hole structure.

Arbitrary radius position of the pressure can be expressed as follows [1]:

22 2

3 2 28 xp p R R (5)

where p2 is the static pressure at the outlet of impeller; p3 is the pressure at monitoring points; ω is the angular velocity of the impeller; R2 the impeller radius; Rx is the monitoring point radius; ρ is the density of fluid.

From the above formula, it can be conducted that when p2, ω, R2 and ρ are constants, in the range of Rx to R2, the distribution of pressure is a parabola.

Figure 20 shows the comparison of pressure distribution in rear pump chamber with different holes at the same flow rate. The theoretical value is monotonically increasing parabolically. Although there are errors between the s imulated value and the

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Fig. 18 Total pressure of pump chamber with different balance holes: (a1, a2, a3) 4.5 mm; (b1, b2, b3) 5.2 mm; (c1, c2, c3) 5.9 mm; (a1,

b1, c1) 0.4Qopt; (a2, b2, c2) 1.0Qopt; (a3, b3, c3) 1.4Qopt

Fig. 19 Relative velocity distribution of pump chamber: (a1−a6) 4.5 mm; (b1−b6) 5.2 mm; (c1−c6) 5.9 mm; (a1, b1, c1) 0.4Qopt; (a2, b2,

c2) 0.6Qopt; (a3, b3, c3) 0.8Qopt; (a4, b4, c4) 1.0Qopt; (a5, b5, c5) 1.2Qopt; (a6, b6, c6) 1.4Qopt

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Fig. 20 Pressure distribution change trend of balance holes with different balance hole diameters: (a) 0.4Qopt; (b) 0.6Qopt; (c) 0.8Qopt;

(d) 1.0Qopt; (e) 1.2Qopt; (f) 1.4Qopt

theoretical value, the simulated value is also monotonically. The main reason is that disk friction loss emerges from hub and there is vortex in rear pump chamber in the numerical simulation results. According to Eq. (5), the theoretical value can only reflect the changing trends under ideal condition. Maybe the simulation is more realistic. It can also be seen that the difference is smaller in the pump chamber when the balance hole diameter is 4.5 mm. In general, when the diameter of 4.5 mm is selected, and the flow area ratio is about 6, better balancing effects are obtained, and it has

little influence on head and efficiency in the centrifugal pump. 7 Conclusions

1) With the radical reflux balance holes, the direction and velocity of liquid flowing into impeller passages are changed by the shaft-end retainer ring. Compared with the traditional axial balance holes, the reflux balance holes have better effect on regime stability through the passages as well as cavitation performance.

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As for the low specific speed centrifugal pump, the flow regime at impeller inlet is dramatically unstable at small flow rate. It is prone to pre-rotation and backflow phenomenon.

2) Comparing the three schemes (4.5 mm, 5.2 mm and 5.9 mm in diameter for reflux holes), the flow regime near reflux holes is distinctly under the influence of reflux holes. However, the variation of diameter of reflux holes has little effect on the flow regime in impeller passages. When diameter of reflux holes is 4.5 mm, namely, the ratio of total area of reflux balance holes to the area of the sealing ring is about 6, better effect of axial force balance is obtained and the influence on head and efficiency is smaller. References [1] GUAN Xing-fan. Modern pumps theory and design [M]. Beijing:

Chinese Astronautics Press, 2011. (in Chinese)

[2] LU Wei-gang, ZHANG Jin-feng, YUAN Shou-qi. A new method to

axial thrust self-balance for centrifugal pump impeller [J]. Chinese

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