CHINESE JOURNAL OF MECHANICAL ENGINEERING

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Vol. 25, No. 6, 2012

DOI: 10.3901/CJME.2012.06.1184, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn

Numerical Simulation and Experimental Research on the Influence of Solid-phase Characteristics on Centrifugal Pump Performance LI Yi1, ZHU Zuchao1, *, HE Weiqiang2, and HE Zhaohui3 1 Laboratory of Fluid Transmission and Application, Zhejiang Sci-Tech University, Hangzhou 310018, China 2 Hangzhou Dalu Industry Co., Ltd, Hangzhou 311234, China 3 Zhejiang Institute of Mechanical & Electrical Engineering Co., Ltd, Hangzhou 310002, China Received December 8, 2011; revised April 16, 2012; accepted June 25, 2012

Abstract: The law governing the movement of particles in the centrifugal pump channel is complicated; thus, it is difficult to examine the solid-liquid two-phase turbulent flow in the pump. Consequently, the solid-liquid two-phase pump is designed based only on the unary theory. However, the obvious variety of centrifugal-pump internal flow appears because of the existence of solid phase, thus changing pump performance. Therefore, it is necessary to establish the flow characteristics of the solid-liquid two-phase pump. In the current paper, two-phase numerical simulation and centrifugal pump performance tests are carried out using different solid-particle diameters and two-phase mixture concentration conditions. Inner flow features are revealed by comparing the simulated and experimental results. The comparing results indicate that the influence of the solid-phase characteristics on centrifugal-pump performance is small when the flow rate is low, specifically when it is less than 2 m3h. The maximum efficiency declines, and the best efficiency point tends toward the low flow-rate direction along with increasing solid-particle diameter and volume fraction, leading to reduced pump steady efficient range. The variation tendency of the pump head is basically consistent with that of the efficiency. The efficiency and head values of the two-phase mixture transportation are even larger than those of pure-water transportation under smaller particle diameter and volume fraction conditions at the low-flow-rate region. The change of the particle volume fraction has a greater effect on the pump performance than the change in the particle diameter. The experimental values are totally smaller than the simulated values. This research provides the theoretical foundation for the optimal design of centrifugal pump. Key words: solid-liquid two phase, centrifugal pump, performance test, numerical simulation

1

Introduction

∗

As the industry develops rapidly, centrifugal pumps have been widely used for transporting solid–liquid two-phase mixtures. In connection with energy conservation and environment preservation, the poor efficiency of two-phase mixture transportation has gradually attracted the attention of researchers in this field. Compared with single-phase flow, the complexity of solid–liquid two-phase flow significantly increases because the law governing the movement of particles in the pump channel is complicated. Therefore, it is difficult to examine the solid–liquid two-phase turbulent flow in a pump. Previous works on this topic did not arrive at similar conclusions. WU, et al[1], and STEPHAN, et al[2], applied the SIMPLEC arithmetic to simulate a slurry pump, resulting in decreasing pump head and hydraulic efficiency * Corresponding author. E-mail: [email protected] This project is supported by National Natural Science Foundation of China(Grant No. 51076144), and Zhejiang Provincial Key Science Foundation of China(Grant No. 2009C13006) © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2012

along with increasing solid-particle diameter. Meanwhile, ZHU, et al[3–4], analyzed the effect of a solid-liquid mixture on the performance of double-channel pump through performance test at different solid-phase concentration and flow rate conditions. LI, et al[5–6], studied particleconcentration distribution, velocity distribution, and abrasion characteristics in a desulfurization pump. The volume fraction of solid particles along the blade pressure sides is higher than that in the suction sides, increasing when the particle diameter increases. The volume fraction also increases with the increase of particle diameter. Particles collide at the volute wall in a small angle. The angle increases as the particle diameter increases. Solid particles move to the volute outlet along the walls, extruding through the walls due to the effect of centrifugal force. The impact wear occurs near the tongue region. ZHU, et al[7–8], analyzed solid–liquid two-phase flow along the vane surface, while considering the action of centrifugal force. The influence mainly includes hydraulic efficiency, dynamic properties, and theoretical delivery lift. The thickness of the boundary layer decreases with the decrease of the vane bending coefficient and the increase in mass

CHINESE JOURNAL OF MECHANICAL ENGINEERING concentration. The separation point of the boundary layer on the vane pressure surface varies with the change of the vane shape. KADAMBI, et al[9], utilized the particle image velocimetry technique to study particle velocities at the tongue region of a centrifugal pump when the pump speeds are 725 rmin and 1 000 rmin, respectively. The fluctuation kinetic energy increased approximately as the pump speed increased. The directional impingement mechanism is more significant at the pressure side of the blade, tongue, and the casing. This mechanism becomes more important as speed increases. Meanwhile, GANDHI, et al[10], studied the performance characteristics of a slurry pump at different rotational speeds, concluding that the relationships with respect to the head and capacity are applicable only at low solid concentrations, whereas the relationship with respect to input power gives significant errors. Using analytical models to estimate the energy–head losses in the pump based on pump geometry and the solid properties, Ref. [11] predicts the performance of centrifugal slurry pumps through a loss-analysis procedure. The predicted values of the head over the operating range of flow rates are in reasonable agreement with the measurements made at various rotational speeds and solid concentrations. Meanwhile, DONG, et al[12], analyzed the location and process of wear on pumps, simulating the wear process of the flow components based on the geometry and non-linear theory of materials. Simulation results demonstrate the existence of pits on the surface of the flow components due to the impact of coal particles. The distortion degree of the pits and the largest Von Mises stress both increase with the increase of particle diameter, impact velocity, and angle of invasion. Refs. [13–14] use the sub-grid-scale stress model to solve the governing equations of dense solid-liquid two-phase flow in a centrifugal impeller. In the numerical calculation, the SIMPLEC algorithm and a staggered grid system were applied for the discretization of the governing equations. Using the body-fitted coordinate system to simulate the flow over the complex geometry field, their studies resulted in predicted velocity and pressure values that are in good agreement with the experimental results. Ref. [15] used the finite-element model to predict the solid-liquid flowinduced erosion wear in a pump casing, calculating wear rate using empirically determined wear coefficients; this work also examined wear rate along the casing surface as well as the location of high erosion rate. Based on the results, the wear-rate distribution is high near the cut water region. Moreover, the wear distribution is non-uniform, and the wear rate varies significantly from the sides to the centerline of the casing along the other radial sections. In the current study, the performance of a centrifugal pump was analyzed through performance tests and numerical simulations under different particle diameter(Dp) and particle volume fractions(PVF) conditions.

2

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Performance Test Methods and Calculation Models

2.1 Basic parameters of the centrifugal pump At the design point, the centrifugal-pump parameters were flow Q8.5 m3h, head H20 m, and rotational speed n2 900 rmin. The main geometrical parameters of the impeller are listed in Table 1. Table 1. Parameter Value

Main geometrical parameters of the impeller Blade inlet diameter D1mm 44

Blade outlet diameter D2mm 125

Blade number Z 5

2.2 Performance test methods The test loop is shown in Fig. 1. It mainly comprises five packages: solid–liquid two-phase mixing equipment, solid-phase recycle equipment, flow-rate measuring equipment, pressure measuring equipment, and axis power measuring equipment.

Fig. 1.

Solid–liquid two-phase test equipment

1. Motor; 2. Torque instrument; 3. Testing pump; 4, 5. Pressure sensor; 6. Electromagnetic flow meter; 7. Valve; 8. Mixing motor; 9. Agitator; 10. Mixing chamber; 11, 12. Gate valve; 13. Pipeline pump

The solid particles should be uniformly added. Additionally, the lowest velocity in the experimental system must be larger than the solid-phase deposition velocity to avoid sedimentation. 2.3 Calculation models The mixed model is used to simulate the solid–liquid two-phase flow in the centrifugal pump. The continuity and the momentum equations are as follows:

  ( ρ m vm )  0,   (ρ m vm vm )  p     µm (vm  vmT )     2  ρ m g  F     ck ρ k vdr,k vdr,k  ,  k 1 



(1)

(2)

where ρm is the mixture density, ρk is the k-phase density, vm is the mass-weighted average velocity, µm is the mixture viscosity, F is the body force, ck is the k-phase volume fraction, and vdr,k is the drift velocity.

LI Yi, et al: Numerical Simulation and Experimental Research on the Influence of Solid-phase Characteristics on Centrifugal Pump Performance

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The equation of the PVF is given by

  (ck ρ k vm )    (ck ρ k vdr,k ).

3

(3)

Results and Analyses

The centrifugal-pump performance changed due to the coupling effect between the solid and the liquid phases. The degree of the effect differs as the particle diameter and the PVF change. In order to examine the main performance of the centrifugal pump delivering the solid-liquid two-phase mixture, performance test and numerical simulation were carried out using different particle diameters and different PVFs. The results are compared with those of pure-water transportation.

increases to 0.5 mm. In Fig. 3, the head values of the two-phase mixture transportation decrease compared with those of pure-water transportation. The degree of decrease intensifies along with the flow-rate increase, except for the maximum flow rate. The centrifugal pump is simulated with the same flow-rate value as that used in the experiment. The efficiency-flow and head-flow predicted curves for different particle diameters (0.1 mm, 0.25 mm, 0.5 mm, and 1 mm) when the PVF is 1% are shown in Figs. 4 and 5, respectively.

3.1 Results of the different particle diameters The efficiency-flow and head-flow experimental curves for different particle diameters (Dp0.1 mm and Dp0.5 mm) when the PVF is 1% are shown in Figs. 2 and 3, respectively.

Fig. 4.

Fig. 2.

Efficiency-flow predicted curves (different particle diameters)

Efficiency-flow experimental curves (different particle diameters)

Fig. 5. Head-flow predicted curves (different particle diameters)

Fig. 3. Head-flow experimental curves (different particle diameters)

In Fig. 2, the efficiency-flow curves show little change in shape when the flow rate is less than 3 m3h. The efficiency values of the two-phase mixture transportation are even larger than those of pure-water transportation when the flow rate is less than 4.5 m3h. In addition, the maximum efficiency values decrease, and the steady efficient range becomes reduced when the particle diameter

Fig. 4 shows that the efficiency values totally decrease as the particle diameter increases. However, similar to the experimental results, the efficiency values of the two-phase mixture transportation under small particle-diameter (0.1 mm and 0.25 mm) conditions are larger than those of pure-water transportation under low-flow conditions, whose flow rates are less than 2 m3h. The efficiency values reach a maximum near the rated flow point. Fig. 5 shows that the head curves of the solid-phase two-phase mixture transportation are similar in shape to the curves of the pure-water transportation. The degree of decrease intensifies along with the increase in flow rate; in addition, the head values slightly change at the zero flow rate. When the solid-particle diameter is 0.1 mm, the head

CHINESE JOURNAL OF MECHANICAL ENGINEERING values at the low-flow-rate region are even larger than those of pure-water transportation. 3.2 Results of the different particle volume fractions The efficiency-flow and head-flow experimental curves for different PVFs (1%, 2.5%, and 4%), when the particle diameter is 0.1 mm, are shown in Figs. 6 and 7, respectively.

Fig. 6.

Fig. 7.

Efficiency-flow experimental curves(different PVFs)

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The decreased value of H(head) is smaller than the increased value of ρ (mixture density), and the measured value of P (shaft power) has little change under smaller particle diameter and PVF conditions during the test. Therefore, the efficiency ( η  Pu P , where Pu  ρ gQh ) increases accordingly. Fig. 7 shows that, compared with the head values of pure-water transportation, those of the two-phase mixture transportation decrease when the PVF increases. The decreasing tendency is similar to that shown in Fig. 3 with the flow-rate increase. When the PVF increases to 4%, the head curve declines intensively. It follows that the energy conversion between the pump and the solid-phase two-phase mixture changes dramatically. Under this condition, the pump is not suited for solid-phase two-phase mixture transportation. The maximum flow rate decreases gradually with increasing PVF, indicating that the PVF has a greater effect on flow rate than the diameter. The efficiency-flow and head-flow predicted curves for different PVFs (1%, 2.5%, 4%, and 5.5%) when the particle diameter is 0.1 mm are shown in Figs. 8 and 9, respectively. In Figs. 8 and 9, the predicted efficiency curves of the simulation are nearly similar to those of the experimental curves.

Head-flow experimental curves(different PVFs)

Fig. 6 shows that when the two-phase mixture of different PVFs is transported, the efficiency-flow curves also show little change in shape under the low-flow condition. The efficiency values are even larger than those of pure-water transportation when flow rate is below 4 m3h. The maximum efficiency and the corresponding flow rate at the best operation point decrease as the PVF increases. At the same time, the increase results in the unstable operation of the centrifugal pump, which cannot even reach the flow capacity of the design point when the PVF is larger than 4%. The fluctuation of curves under the 2.5% and 4% mixture conditions in Fig. 6 is violent in comparison with that of curve for 0.5 mm particle diameter in Fig. 2, indicating that the impact of particle diameter on efficiency is smaller than that of PVF. The shapes of the curves change a little, and the values slightly increase under the low-flow condition. This can be attributed to the reason described below.

Fig. 8.

Efficiency-flow predicted curves(different PVFs)

Fig. 9.

Head-flow predicted curves(different PVFs)

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LI Yi, et al: Numerical Simulation and Experimental Research on the Influence of Solid-phase Characteristics on Centrifugal Pump Performance

Fig. 8 shows that the efficiency values totally decrease as the PVF increases. When the flow rate is less than 6 m3h, the pump efficiency values have little change compared with those of pure-water transportation, except under the 5.5% PVF condition. The efficiency values under the 2.5% mixture condition are even larger than those of the under 1% mixture and pure-water conditions. The curves are different from those shown in Fig. 4 in that the best efficiency points move toward the low-flowrate direction with increasing PVF. Fig. 9 shows that the pump head values reduce totally as the PVF increases. The variation tendency is consistent with that of the curves shown in Fig. 5. When the flow rate is less than 4 m3h, the head values decrease slightly compared with those of pure-water transportation, except under the 5.5% volume-fraction condition. From the numerical-simulation results described above, the influence of solid-phase existence is small when the PVF is less than 4%. The performance of the centrifugal pump becomes worse when solid–liquid two-phase mixture is transported. However, the steady efficient region is wide and flat when the diameter is 0.1 mm and the volume fraction is 1%. In addition, the efficiency values are even larger than those of pure-water transportation under the low-flow condition. The pump runs unsteadily along with the increase of the particle diameter and volume fraction. 3.3 Comparison and analyses A comparison between the simulation and experiment results under different volume fraction and particle diameter conditions is made. The results of using different PVFs when the particle diameter is 0.1 mm are shown in Fig. 10. The results of using different particle diameters when the volume fraction is 1% are shown in Fig. 11.

assured during the solid–liquid mixture transportation experiment.

Fig. 11. Comparison between the predicted and experimental curves (different particle diameters)

Fig. 11 shows that the changing tendency of the efficiency characteristic curves is generally the same as that shown in Fig. 10. However, the pump head drops as the particle diameter increases to 1 mm, indicating that the calculation error of the predicted head values increases as the particle diameter increases.

4

Conclusions

(1) The efficiency and head values of a centrifugal pump decrease with increasing particle diameter and PVF. (2) The steady efficient region basically reduces with increasing particle diameter and PVF. (3) The influence of the solid phase on the pump performance is small at the low-flow-rate region. (4) The predicted curves are similar in shape to the experimental curves. The predicted values are basically larger than the experimental values. (5) The calculation error of the predicted head values increases. References [1]

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Fig. 10. Comparison between the predicted and experimental curves (different PVFs)

Fig. 10 shows that the predicted characteristic curves are nearly parallel to those of the experiment. The efficiency and head values decrease with increasing PVF in the inlet. The experimental values are also smaller than the simulated values. This is mainly due to the fact that the uniform distribution of the solid-phase in the pump inlet cannot be

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Biographical notes

LI Yi, born in 1973, is currently an associate professor at Laboratory of Fluid Transmission and Application, Zhejiang Sci-Tech University, China. She received her master degree on fluid machinery and engineering from Jiangsu University, China, in 2001. Her research interest includes fluid machinery, especially centrifugal pump. Tel: 86-571-86843348; E-mail: [email protected] ZHU Zuchao, born in 1966, is currently a professor at Laboratory of Fluid Transmission and Application, Zhejiang Sci-Tech University, China. He received his PhD degree from Zhejiang University, China, in 1997. His research interest includes fluid machinery. Tel: 86-571-86843348; E-mail: [email protected] HE Weiqiang, born in 1984, is currently an engineer at Hangzhou Dalu Industry Co., Ltd, China. He received his master degree from Zhejiang Sci-Tech University, China, in 2009. His research interest includes pump design. E-mail: [email protected] HE Zhaohui, born in 1974, is currently a senior engineer at Zhejiang Institute of Mechanical & Electrical Engineering Co., Ltd, China. He received his bachelor degree from Jiangsu University, China, in 1996. His research interest includes fluid machinery. Tel: 86-571-88022551; E-mail: [email protected]