Xiaomei Guo ,Zuchao Zhu *,Baoling CuiYi Li

1 School of Mechanical and Automotive Engineering,Zhejiang University of Water Resources and Electric Power,Hangzhou 310018,China

2 The Zhejiang Provincial Key Laboratory of Fluid Transmission Technology,Zhejiang Science and Technology University,Hangzhou 310018,China

Keywords:Short inducer blade Anti-cavitation performance Splitter-bladed inducer Centrifugal pump Two-phase flow

ABSTRACT In order to evaluate the effects of the short blade locations on the anti-cavitation performance of the splitter bladed inducer and the pump,5 inducers with differentshortblade locations are designed.Cavitation simulations and experimental tests of the pumps with these inducers are carried out.The algebraic slip mixture model in the CFX software is adopted for cavitation simulation.The results show that there is a vortex at the inlet of the inducer.Asymmetric cavitation on the inducer and on the impeller is observed.The analysis shows that the short blade locations have a minor effect on the internal flow field in the inducer and on the external performance of the pump,but have a significant effect on the anti-cavitation performance.It is suggested that the inducer should be designed appropriately.The present simulations found an optimal inducer with better anti-cavitation performance.

1.Introduction

Nowadays,centrifugal pumps are often required to run at high speed conditions.As a result,they are prone to low efficiency,cavitation,and low stability.In order to get high anti-cavitation performance of pumps,an inducer is always designed and placed upstream of the impeller to resist the cavitation.The structure of the splitterbladesis an optimal design for inducers[1–3].

At present,many research works have been done on the impeller with splitterblades.Yang et al.[4]studied the influence of splitter blades on the anti-cavitation performance of a double suction centrifugal pump,and found that the splitter blades could improve the anti-cavitation performance of the pump.Cui et al.[5]calculated three-dimensional turbulent flow in a centrifugal pump with a long-mid-shortblade complex impeller,and found that the back flow in the impeller has an important influence on the performance of the pump.Yuan et al.[6]also found that the splitter blades can reduce the pressure fluctuations.The simulation of Kergourlay et al.[7]indicated that the splitter blades had a positive role in improving the internal flow and hydraulic performance of a centrifugal pump.There are other researches on the effect of the impeller with splitter blades on the performance of centrifugal pumps[8–10].

The splitter blades must be designed carefully with reasonable length,number and angle.Shigemitsu et al.[9]studied splitter blade parameters of the low specific speed centrifugal pump impeller.They developed a design method to select the number,off-setting angle,inlet diameter,and deflection angle of splitter blades.Yang and Miao[11]investigated the effect of splitter blades'main geometry factors on the performance of pumps as turbines,including circumferential biasing degree,outlet deflection angle,outlet diameter and the number of blade.Yamada et al.[12]researched two types of impeller with different numbers of splitter blades.Solis et al.[13]reduced pressure fluctuations by adding splitter blades to the original impeller and by increasing the radial gap between the splitter impeller and the volute tongue.Golcu[14]found that the splitter blade length and blade number were important,and optimized them for a deep well pump.

Splitter blades are applied not only in pump impellers butalso in other turbo-machines.The structure is proved to be beneficial for performance improvement[15–18].Recently,the splitter-bladed inducer is used more and more wildly.Like the splitter-bladed impeller,the geometrical parameters including length,tip clearance,number and screw pitch will affect the anti-cavitation performance of the pump.Several works of simulation and experiment on centrifugal pumps with an inducer are carried out to investigate the effect of an inducer's parameters on the pump performance[1,19–23].However,only a limited number of studies can be found concerning the effects of short blade locations on the anticavitation performance of the splitter-bladed inducer and the pump.

Most studies are mainly focused on the single-phase flow research and hydraulic analysis of the splitter-bladed inducer.In present work,two-phase flow is simulated.The vapor volume fraction distributions on the inducer and on the impeller are both analyzed.Results of simulations and experimental tests are compared correspondingly.Effects of the short blade locations on the anti-cavitation performance of the splitter-bladed inducer and the pump are disclosed.

2.Numerical Simulation of Cavitation

2.1.Pump prototype

The centrifugal pump and the splitter-bladed inducers with different short-bladed locations are investigated in this work(shown in Fig.1).The original design parameters are: flow rate Qd=4 m3·h-1,head Hd=100 m,rotational speed nd=6000 r·min-1,and specific rotation speed ns=23.08.The other main geometric dimensions are shown in Table 1.

Fig.1.Pump and five splitter-bladed inducers with different short blade locations.

Table 1 Main geometric dimensions of the pump with splitter-bladed inducer

In Fig.1,the parameter D is the diameter of the inducer,and L is the distance from the tip of the short blade to the tip of the long blade.To observe the effects of the short blade locations on the anti-cavitation performance of the inducer and the pump, five inducers are designed.They will be denoted IND1–IND5,respectively hereafter.The short blade location is configured in Table 2.

Table 2 Locations of the short blades

2.2.Computational domain and grid

Fig.2 shows the three-dimensional computational domain and grid.The clearance of the blade's tip and the pump is not considered in the present simulation.The inlet pipe and the volute outlet are extended properly to reduce the effect of boundary conditions on the internal flow.The commercial code GAMBIT is used to generate the meshes.Tetrahedral meshes are chosen in the inducer and the impeller domains,while hexahedral meshes are chosen in the inlet pipe and volute domains.The grid sizes of the pump with the various inducers are listed in Table 3.In order to simulate more accurately,mesh independence is analyzed on the case of IND1.The result is given in Table 4.From Table 4,at the case where the mesh interval size is less than 0.5 mm,the head is relatively stable.Thus the mesh interval size is chosen as 0.5 mm.‘EquiAngle Skew’and‘EquiSize Skew’of all grids are less than 0.85,therefore,the grid quality is satisfactory.

2.3.Mixture model

In order to explore the cavitation mechanism in the splitter-bladed inducer and the impeller,cavitation flow is numerically calculated.During simulation,a physical model is based on the assumption that the mixture of water and vapor in a cavitating flow is a homogeneous fluid.The Reynolds average N–S approach is used for turbulent flow in this work.A mixture model is adopted,and the number of the phases is set as two.The two phases are considered as water and vapor[24,25].As the inlet pressure and out let pressure are higher than the saturation pressure,the vapor volume fraction is assumed to be zero at the inlet and at the outlet of the pump.The liquid phase is water under the standard condition.Equations of continuity and of momentum conservation are

with

Volume fraction equation for the vapor phase is

The above equations are formulated in terms of the mass-averaged mixture velocity u and drift velocity of the vapor phase udr,v,which are defined as follows,respectively:

Fig.2.Calculated region and grids along the inducer and the impeller.

Table 3 Grid sizes of the pump with the five inducers

Table 4 Mesh independence test on the case of IND1

Here n is the phase number,and in the present simulation,n=2.airepresents the volume fraction of the i phase.f is given below:

Normal speed is specified at the inlet,vinlet=0.8842 m·s-1.Static pressure is specified at the outlet,Poutlet=1.00818×106Pa.No slip boundary condition is specified at the wall.The moving coordinate system is specified on the inducer and the impeller with a rotational speed of 6000 r·min-1.The static coordinate system is specified on the inlet pipe and the volute.Transient rotor–stator option is selected to specify the inlet pipe–inducer and inducer–volute interfaces.Simulations on the centrifugal pumps with an inducer are calculated using the ANSYS-CFX software.

2.4.Calculated results and analysis

Fig.3 shows the streamline distributions on the middle axial section of the inducers.From Fig.3,it can be seen that there is a vortex at the inlet of the inducer,which is in conformity with the results in the literature[3,26].The vortex is mainly located on the inlet of the long blade near the pipe wall,and quite similar for five inducers.Only for IND3,the vortex is a little smaller than others.The average vorticity magnitude on the axial section is listed in Table 5,showing that their values are very close,but IND3 has the minimum.Thus,the short blade location has minor effects on the internal flow field of the inducer.By the way,some researcher[27]recommended placing an orifice upstream of the inducer to eliminate the vortex.

The degree of cavitation is roughly expressed by the vapor volume fraction.So,the vapor volume fraction distributions on the impeller and on the inducer are configured in Figs.4 and 5.

From Fig.4,one can thus identify:The cavitation is mainly located on regions 1 and 2 for IND1,IND2 and IND3 inducers.For IND4 and IND5 inducers,there is no cavitation.The average vapor volume fraction on the impeller with different inducers is listed in Table 6.So,when the blade location L/D increases,the anti-cavitation performance of the inducer is improved.The phenomena can be explained:when L/D is big,the short blades occupied less passage,which makes the bubbles generated by low pressure prone to fade away.Asymmetric distribution of the vapor volume fraction on the inducer is also observed.This conforms with the results in the literature[28,29].From Fig.5,one can thus identify:the vapor volume fraction is mainly concentrated on passages 1 and 2,which are closer to the pump outlet.In the case of IND3,the cavity is smaller than others.So the short blade location has a definite influence on the anti-cavitation performance of the pump,but the regularity is not so obvious.From Figs.4 and 5,it can be deduced that the effects of short blade location L/D on the anti-cavitation performance of the inducer and on that of the impeller are different.

Through the above simulations,parameters such as pressure,velocity and torque can be obtained.Head(H)and efficiency(η)of the pump can be calculated by Eqs.(8)and(9)[30]:

where Poutis the total pressure of volute outlet,Pinis the total pressure of the inlet,and Δh is the altitude difference between the impeller center and volute outlet.These values all can be obtained through calculations,including

Fig.3.Streamline maps in the axial section of the inducers.

Table 5 Average vorticity magnitude on the axial section

where Q is the discharge flow rate,M is the torque of the impeller and inducer,ω is the angular speed,D2is the impeller outlet diameter,nsis the specific speed and K*is a coefficient.

From the above equations,corresponding H and η can be calculated,and the results are shown in Fig.6(a).

3.Experimental Tests

The experimental test rig in Fig.7 consists of a water tank,centrifugal pump unit,pipeline,and measurement system.The high centrifugal pump with a splitter-bladed inducer is assembled on the closed system.The volume of the circulated water tank is 31 m3.A type 2H-30A vacuum pump is connected to the system.At a rotational speed of 490 r·min-1,its vacuity is up to 6 × 10-2Pa.The transport medium is pure water at ambient conditions.The driving motor of the tested pump is a frequency conversion motor(type GSB-22-06 E13 B3,Shanghai Senlima Power Transmission Technology Co.)with a rated output power of 15 kW.A type NJ1G rotational torque meter is chosen to measure the rotation speed and shaft power.The allowable rotation speed is from 0 to 10000 r·min-1.The frequency conversion motor,sensor and pump must be assembled in good concentricity as seen in Fig.8.The external characteristic curves in Fig.6(b)are obtained by experiments.

From Fig.6,it can be seen that head and efficiency of the pumps with five inducers obtained by simulations and those obtained by experimental tests are in good agreement.The largest difference of the head is about 6.8 m.The relative difference of the head is within 6.75%,and the relative difference of the efficiency is about 5.6%.Simulations and experimental results both show that the head and efficiency of the pumps with five inducers are very close.This means that the effects of short blade location L/D on the pump external performance are minor.

Fig.4.Vapor volume fraction distributions on the inducers.

Fig.5.Vapor volume fraction distributions on the impellers.

Table 6 Average of the vapor volume fraction on the impeller with different inducers

Fig.6.External performance of the pump obtained by simulation.

In order to observe the anti-cavitation performance of the pumps with five inducers,the inlet pressure of the pump is reduced continually.Fig.9 shows the head versus inlet pressure curves.

Fig.7.Experimental set-up.

Fig.8.Assembly diagram of the pump,torque meter and frequency conversion motor.

From Fig.9,it can be seen that the higher the flow rate is,the lower the head is.At Q=2 m3·h-1,the first significant head starts to drop is the pump with IND1 inducer,then is that with IND2,IND5,IND4,the last one is that with IND3.At Q=4 m3·h-1,the drop order is same as that at Q=2 m3·h-1.At Q=6.5 m3·h-1,the head appears to not so stable,the last significant head begins to drop is the pump with IND3.At Q=8 m3·h-1,the result will not be analyzed,for the head of the pump is very unstable in this case.In order to explain the anticavitation performance well,NPSHr(net positive suction head must)is calculated,and they are listed in Table 7.

From Table 7,it can be seen that,the short blade location has a significant effect on the anti-cavitation performance of the pump.L/D determines the area of the passage.As the diameter of the hub at the inducer inlet is very small,the passage area is narrow at the inlet,especially when L/D is small.This is why we don't choose four equal length blades.So L/D shouldn't be too small.As the hub of the inducer is diffused,the passage area becomes bigger and bigger from the inlet to the outlet.So if L/D is too large,the passage will also be too large near the outlet,which will affect the head and efficiency.So choosing an appropriate L/D is very important.In the present simulation,althoughunder different flow rates,the anti-cavitation performance of the pump with the inducer is in a different extent,it still can be observed that the best inducer in this work is IND3.

Table 7 NPSHr under different flow rates

4.Conclusions

This work describes the effects of the short blade location on the anti-cavitation performance of the splitter-bladed inducer and the pump.Simulations and experiments of the pump with these five inducers with different short blade locations are carried out,respectively.The results show that the data of simulations are in a good agreement with experiments.

The vortices located at the inlet of the inducer and near the pipe wall are observed.The research shows that the short blade location has minor effects on the flow field in the inducer.Asymmetry of the vapor volume fraction distributions on the inducers is also observed.The larger the L/D is,the less the vapor volume fraction on the inducer is,while it is not observed on the impeller.Combining with experimental results,it is seen that the short blade location has a significant effect on the anticavitation performance of the pump.The inducer should be designed with appropriate L/D,and its performance can be predicted by simulations.In this work,the IND3 inducer is found as the one with better anti-cavitation performance.

Nomenclature

H head,m

Hddesigned head,m

M torque,N·m

n rotational speed,r·min-1

nddesigned rotation speed,r·min-1

nsspecific speed

P pressure,Pa

Pinletinlet pressure,Pa

Poutoutlet pressure,Pa

ΔP pressure difference between outlet pressure and inlet pressure,Pa

Q flow rate,m3·h-1

Fig.9.Head versus inlet pressure curves.

Qddesigned flow rate,m3·h-1

Sihelical pitch,mm

Smaxmaximum thickness of the blade

S0thickness of the blade at inlet

u mixture mass average velocity,m·s-1

v0average velocity at the inlet of the blade

W1thickness of the impeller blades at the tip,mm

W2thickness of the impeller blades at the root,mm

W3thickness of the inducer blades,mm

w average relative velocity

Δz vertical distance between impeller center and pump outlet,m

α volume fraction

β0blade angle at inlet,(°)

η efficiency,%

ρ density,kg·m-3

Subscripts

d design point

v vapor

w liquid

0 inlet