research article research on three-dimensional unsteady ...ow of centrifugal pump is a...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 589161 7 pageshttpdxdoiorg1011552013589161

Research ArticleResearch on Three-Dimensional Unsteady TurbulentFlow in Multistage Centrifugal Pump and PerformancePrediction Based on CFD

Zhi-jian Wang1 Jian-she Zheng1 Lu-lu Li2 and Shuai Luo1

1 School of Mechatronics Engineering Shenyang Aerospace University Shenyang Liaoning 110136 China2Haicheng Suprasuny Pump Co Ltd Haicheng Liaoning 114216 China

Correspondence should be addressed to Zhi-jian Wang wangzhijian1974sinacom

Received 24 March 2013 Accepted 15 May 2013

Academic Editor Zhijun Zhang

Copyright copy 2013 Zhi-jian Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The three-dimensional flow physical model of any stage of the 20BZ4 multistage centrifugal pump is built which includes inletregion impeller flow region guide-vane flow region and exit region The three-dimensional unsteady turbulent flow numericalmodel is created based on Navier-Stoke solver and standard 119896-120576 turbulent equations The method of multireference frame (MRF)and SIMPLE algorithm are used to simulate the flow in multistage centrifugal pump based on FLUENT softwareThe distributionsof relative velocity absolute velocity static pressure and total pressure in guide vanes and impellers under design condition areanalyzedThe simulation results show that the flow in impeller is mostly uniform without eddy backflow and separation flow andjet-wake phenomenon appears only along individual blades There is secondary flow at blade end and exit of guide vane Due tothe different blade numbers of guide vane and impeller the total pressure distribution is asymmetric This paper also simulates theflow under different working conditions to predict the hydraulic performances of centrifugal pump and external characteristicsincluding flow-lift flow-shaft power and flow-efficiency are attained The simulation results are compared with the experimentalresults and because of the mechanical losses and volume loss ignored there is a little difference between them

1 Introduction

Pumps are widely used inmany fields and the average electricpower consumption is about 209 of the total consumptionevery year in China [1] Because of the low level of manufac-ture and design of pumps the efficiency of domestic pumpsis about 10 lower than that of the developed countriesAmong the pumps the centrifugal ones are most widelyapplied but there are many problems such as low efficiencyoperated under off-design conditions and low cavitationsperformance Therefore it will have very important practicalsignificance to study the internal flow of centrifugal pumpsin order to optimize the structure of main parts improvethe hydraulic performance increase the efficiency and avoidbeing operated under off-design conditions and thus reachthe goal of increasing efficiency and saving energy

Due to the complex shape of flow channel high-speed-rotating viscous fluid and the interaction between moving

and stationary parts the flow in centrifugal pumps is a three-dimensional viscid and unsteady complex flow It becomesmore and more popular to investigate the internal flow ofthe centrifugal pump based on computational fluid dynamic(CFD) owing to the short design time low price beingobserved directly andmaking up the deficiency of traditionaldesignmethodsWith the rapid development of the computertechnology CFD has been one of the main methods to studythe flow in the centrifugal pump Subsequently it will bepossible to design high-efficiency and energy-saving pumpsand create huge social and economic benefits Si and Dike [2]simulated the whole flow field of sectional multistage pumpand the simulation was performed in a multiple referenceframe and standard 119896-120576 turbulence model Li et al [3] com-bined sliding-mesh and moving-mesh methods to simulateinternal flow during starting procedure of the single-stagepump Liu andWang [4] carried out computer-aided analysis

2 Mathematical Problems in Engineering

Guide plate

Guide plate

Impeller

Impeller flow region

Guidevane Guide-vane

flow region

Figure 1 Sketch of centrifugal pump

Figure 2 Flow region of impeller and guide vane

on internal flow of stamping and welding centrifugal pumpimpeller based on CFD using ANSYS CFX and exploredthe flow mechanism in impeller Barrio et al [5] simulatedinternal flowof centrifugal pump throughCFD such that theycould predict radical force and torsion suffered by impellerJafarzadeh et al [6] simulated fluid flow of low-specific-speedratio centrifugal pump Asuaje et al [7] performed a 3D-CFDsimulation of impeller and volute of a centrifugal pump usingCFX code with a specific speed of 32 and found velocity andpressure fields for different flow rates and radial thrust on thepump shaft Cui et al [8] investigated the effect of number ofsplitting blades for long mid and short blades using a one-equation turbulent model Their results show that the bulkflow in the impeller has an important influence on the pumpperformance Anagnostopoulos [9] simulated 3D turbulentflow in a radial pump impeller for a constant rotational speedof 1500 rpm based on the solution of the RANS equationsFew of the previous works involved study of 3D modelingwithin a full domain considering interaction between rotorand stator of a high-speed multistage centrifugal pump usingvarious turbulence models

This paper uses commercial CFD software FLUENTstandard 119896-120576 turbulent model and multiply reference frameto perform numerical modeling of the full three-dimensional

fluid field for any stage of 20BZ4multistage centrifugal pumpwhich includes the flow region of import channel impellersguide vanes and exit channel The pressure and velocity dis-tributions in the pump under design condition are obtainedand the numerical performance curves are comparedwith theexperimental ones It will provide theoretical basis for furtheroptimizing the structures and improving the performances ofcentrifugal pump

2 Numerical Simulation and Method

21 Physical Model Figure 1 shows the sketch map and flowroute in any stage unit of 20BZ4 multi-stage centrifugalpump which includes guide plates impellers and guidevanes The impeller is made up of front end plate back endplate and blades The blades are equipped between front andback end plates and the number of blades is 5 The structureof guide vanes is radial and the number of blades is 7 It ismade up of positive guide vane and negative guide vane Pos-itive vane can collect fluid and transform kinetic energy intopressure energy while negative vane can change flow direc-tion and transmit the fluid into next unit with the requiredspeed and circulation Guide plate can reduce reflux effec-tively and make uniform and stable flow velocity of the fluidinto the impeller Fluid flows downward through guide platethen through the flow runner of impeller into guide vane andfinally goes into the next pump unit from guide plate

The impeller inlet and guide-vane outlet are extendedrespectively in order to ensure stable convergence of internalflow field The physical model includes inlet region impellerflow region guide-vane flow region and exit region Figure 2shows the flow region model of impeller and guide-vaneStructured grids are used in inlet region and exit regionbecause of the cylindrical shape and the numbers of grids are71607 and 69564 respectively Unstructured grids are used tomesh impeller and guide-vane flow regions and the numbersof grids are 187561 and 133108 respectively Figures 3 and 4show the grids of impeller flow region and guide-vane flowregion respectively

22 Governing Equations and TurbulenceModel The internalflow of centrifugal pump is a three-dimensional viscousand unsteady turbulent flow and flow law follows Navier-Stokes equation Because the heat exchange is very lit-tle in centrifugal pump energy conservation equation isnot considered and only mass conservation equation andmomentum conservation equation need to be solved

Mass conservation equation is as follows

120597120588

120597119905+

120597

120597119909119894

(120588119906119894) = 0 (1)

Momentum conservation equation is as follows

120597

120597119905(120588119906119894) +

120597

120597119909119895

(120588119906119894119906119895) = minus

120597119901

120597119909119894

+120597

120597119909119895

[120583120597119906119894

120597119909119895

minus 12058811990610158401198941199061015840119895] + 119878119894

(2)

where120588 is fluid densityu is velocity p is pressure t is time120583 is

Mathematical Problems in Engineering 3

Figure 3 Grids of impeller flow region

Figure 4 Grids of guide-vane flow region

dynamic viscosity 119878 is source item and 12058811990610158401198941199061015840119895is the Reynolds

stress 119909119894and 119909

119895are the coordinates of 119909 119910 and z and 119909

119894= 119909119895

Standard 119896-120576 turbulence model is used Turbulencekinetic energy 119896 equation is as follows

120597 (120588119896)

120597119905+

120597 (120588119896119906119894)

120597119909119894

=120597

120597119909119895

[(120583 +120583119905

120590119896

)120597119896

120597119909119895

] + 119866119896

minus 120588120576

(3)

Dissipation rate 120576 equation is as follows

120597 (120588120576)

120597119905+

120597 (120588120576119906119894)

120597119909119894

=120597

120597119909119895

[(120583 +120583119905

120590119904

)120597120576

120597119909119895

]

+1198621120576

120576

119896119866119896

minus 1198622120576

1205881205762

119896

(4)

where119866119896is production termof turbulence energy 119896 produced

by average velocity gradient 1198881120576 1198882120576 and 119888

3120576are empirical

constants 120590119896and 120590

119904are Prandtl numbers of turbulence

kinetic energy 119896 and dissipation rate 120576 and turbulenceviscosity is defined as

120583119905

= 120588119862120583

1198962

120576 (5)

where 119862120583is the empirical constant

23 Boundary Conditions and Numerical Model

231 Inlet Boundary Conditions Velocity inlet surfacewhere velocity and other scalars are defined is chosen as theinlet boundary Inlet velocity can be calculated by

119906in =119876

120588120587 (11990321

minus 11990322) (6)

where 119876 is flow and 1199031and 1199032are inlet cross section radii

Inlet turbulence energy 119896 is calculated as

119896in = 00051199062

in (7)

Inlet dissipation rate 120576 is calculated as

120576in =11986212058311989632

in

119897in (8)

where 119897in is inletmixing lengthD is inlet equivalent diameterand 119897in = 05 119863

232 Outlet Boundary Conditions The exit is set as outflowboundary which is mainly used where the exit flow is underfull-developed state The outlet velocity 119906out turbulencekinetic energy 119896out and dissipation rate 120576out are described inthe following equations

120597119906119894(out)

120597119899= 0 (119894 = 1 2 3 )

120597119896out120597119899

= 0

120597120576out120597119899

= 0

(9)

where 119899 is the unit vector orthogonal to exit boundary

233 Wall Boundary Conditions No-slipping wall boundaryconditions are assumed on the wall The impeller boundaryfront and back end plates are set as rotating wall and otherwalls are stationary Because the Reynolds number near thewalls is small and standard 119896-120576 model is not appropriate toturbulent boundary layer region logarithmic wall function isused

24 Numerical Method Multiple reference frame (MRF) isused in FLUENT and unsteady problem can be transferredinto steady problem Steady calculation is done in statorregion while centrifugal force and Coriolis force are calcu-lated in rotor region in inertial frame and inner grids keepstationary during calculation Flow parameters are switchedbetween the interfaces of impellers and guide vanes in orderto keep continuity of interfaces

SIMPLE algorithm is used to couple pressure with veloc-ity and segregated solver and standard discrete scheme arechosen First order upwind scheme is used to solve momen-tum conservation equation turbulence energy equation anddissipation rate equation Underrelaxation factor controls theconvergence speed and is properly updated based on actualconvergence condition


Table 1 Design condition and fluid physical properties

Flow(m3h)

Rotationalspeed(rmin)

Atmosphericpressure(Pa)

Mediumdensity(kgm3)

Dynamicviscosity(Pasdots)

20 2850 101325 9982 1003 times 10minus3

ZY

X

142119890+01

127119890+01

113119890+01

992119890+00

851119890+00

709119890+00

568119890+00

427119890+00

286119890+00

144119890+00

317119890minus02

Figure 5 Relative velocity vector of impellers

25 Design Condition of Pump and Fluid Properties Thedesign condition of pump and fluid physical properties areshown in Table 1

3 Numerical Results

31 Velocity Distribution Figure 5 shows the relative velocityvector of 119909 = 0 section in the middle of front end plate andback end plate of impellers under design condition It can beseen from the figure that the flow is uniform in most fluidregion of impellers without eddy backflow and separationflow Jet-wake phenomenon happens only along individualblades The flow velocity increases gradually from the inletof impeller to exit being slowest at the inlet and fastest atthe exit Because of diffusion function of guide blades kineticenergy of high-speed fluid is transferred into pressure energyand velocity becomes lower when fluid goes into the guideblade Meanwhile a part of the energy is lost when the high-speed fluid flowing out of impellers collides into the pumpcaseThe figure also shows that the relative velocity of suctionsurface is lower than that of pressure surface on the sameradius surface The pressure difference which is produced onthe two sides of impellers due to the asymmetry creates themoment of resistance which is overcome by the prime moverto work on the spindle

Figure 6 shows the absolute velocity of guide vanes underdesign condition From the figure we can see that the velocityis fastest at the inlet of guide vane and slowest at the exit Theguide vanes transfer the kinetic energy of fluid into pressureenergy As a result the velocity decreases gradually along the

Z

Y

X

142119890+01132119890+01123119890+01113119890+01104119890+01945119890+00851119890+00757119890+00662119890+00568119890+00474119890+00380119890+00286119890+00192119890+00973119890minus01317119890minus02

Figure 6 Absolute velocity vector of guide vanes

192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05 Z

Y

X

Figure 7 Static pressure distribution on impellers

direction of the flow in the guide vane and secondary flowappears at blade end and exit

32 Static Pressure Distribution Figure 7 shows the staticpressure distribution on the centrifugal pump impellers of119909 = 0 section It shows that the static pressure increases grad-ually and is ladder-like uniform distribution The minimumpressure area appears at the suction surface of impeller inletThe fluid can get the kinetic energy driven by impellers whenit enters into the impeller flow channel vertically but becausethe velocity direction changes quickly and some energy getslost when the fluid collides into the impeller front endcavitations could happen in these low-pressure areas Figure 8shows the static pressure distribution on suction surface andpressure surface of impellers respectivelyThepressurewhichshows ladder-like distribution gradually increases along the


Suction surface

Pressure surface

192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

ZY

X

Figure 8 Static pressure distribution on suction surface andpressure surface of impellers

192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

Z

Y

X

Figure 9 Static pressure distribution on guide vanes

flow direction on both pressure and suction surfaces Thepressure on pressure surface is higher than that of suctionsurface and the pressure difference causes the moment ofresistance on rotating axis At the inlet of suction surface thepressure is lowest and cavitations may happen here

Figure 9 shows the static pressure distribution on guidevanes of centrifugal pump under the design condition Itshows that the pressure increases gradually along the flowdirection and reaches the maximum value at the exit ofguide vanes The function of guide vanes is to collect thehigh-speed fluid and then transfers kinetic energy of thefluid into pressure energy Because of the crash betweenhigh-speed fluid from impellers and pump case local lowpressure appears in the interface of impellers and guidevanes

675119890+04

435119890+04

195119890+04

minus459119890+03

minus286119890+04

minus527119890+04

minus767119890+04

minus101119890+05

minus125119890+05

minus149119890+05

minus173119890+05

Z

YX

Figure 10 Total pressure distribution of centrifugal pump

but it disappears when the fluid enters into the guidevanes Figure 10 shows the total pressure distribution of thecentrifugal pump on 119909 = 0 section It shows that the totalpressure increases gradually which is ladder-like uniformdistribution when fluid flows from the impeller inlet exitand then enters into the guide blade It displays differentpressure distribution at the impeller export and the entranceof guide vanes because the blade number of the guide vaneis 7 and that of the impellers is 6 Due to the differentblade number the relative location of different flow channelsdisplays asymmetric distribution when the impellers rotate

4 Performance Prediction Based onNumerical Simulation

In order to predict the hydraulic performances of centrifugalpump the external characteristics including flow shaftpowerlift and efficiency are calculated

The flow of inlet surface 119876 in the centrifugal pump isdefined as follows

119876 = int119860

(120588V sdot 119899) 119889119860 (10)

where119860 is the area of the inlet or exit of the centrifugal pumpV is the velocity vector of the calculation element 120588 is fluiddensity and 119899 is direction vector on the inlet surface or theexit surface

The total pressure on the inlet and exit surfaces isrespectively defined by the pattern of the mass average valueas follows

119875119894=

int119860

(120588119901119905 |V sdot 119899|) 119889A

int119860

(120588 |V sdot 119899|) 119889119860 (11)

where 119901119905is the total pressure of the calculation element


The lift of centrifugal pump is shown as follows

119867 =119901out minus 119901in

120588119892+V2out minus V2in

2119892+ Δ119885 (12)

where 119875in and 119875out are respectively the total pressure of theinlet and exit Δ119885 is the vertical distance between the inletand exit Vin and Vout are respectively the speed of the inletand exit 119892 is gravity acceleration

The shaft power is calculated as follows

119875 = 119872119908

119908 =2120587119899

60

(13)

where 119872 is the total moment of pressure surface suctionsurface and front and back end plates around 119911 axis n is therotated speed and 119908 is the angular velocity

The centrifugal pump efficiency is shown as follows

120578 =120588119892119876119867

119872119908 (14)

In addition to the design condition the paper simulatesdifferent flow conditions of 05Q 07Q 08Q 09Q 11Q 12Q13Q and 15Q to attain the lift shaft power and efficiency asshown in Table 2

5 Experiment Verification

In order to verify the reliability of the results of numericalsimulation experiments are designed to test the flow liftshaft power and efficiency of the 20BZ4 centrifugal pumpFigures 11 12 and 13 show respectively the experimentalcharacteristic curves of flow and lift flow and shaft powerand flow and efficiencyThefigures show that there are certaindifferences between the experimental results and numericalresults When the pump physical model is built the gapregion between front and back plates and case is ignoredso the rotation of pump is accompanied by a volume lossFurthermoremechanical loss such as bearing friction loss anddisc loss are also ignored

Figure 11 shows the relation curve between the flow andlift The simulation curve has no hump and it demonstratesthat the centrifugal pump has good performancesThe trendsof experimental curve and simulation curve are consistentBut in addition to the design condition the experimentaldata and calculated data in the high flow and low flowhave larger difference MRF is a kind of assumed steadycalculation flow model relative to the design condition sothe unsteady factors of flow field are fewer near the designcondition and the calculated data and experimental dataare consistent However under off-design conditions thereare many unsteady factors such as the crash between thefluid and pump shell and blade boundary layer separationwhich results in difference between calculated data andexperimental data

Figure 12 shows the relation curve between the flow andshaft power Because the calculated moment is lower than

14

12

10

8

6

4

2

0

Experimental liftSimulation lift

Flow (m3h)

Lift

(m)

5 10 15 20 25 30

Figure 11 Performance curves of flow-lift

the experimental moment so the shaft power of numericalsimulation is lower than that of experiment However underhigh flow conditions the shaft power of numerical simulationis higher than that of experiment which is because the relativeideal numerical model is used and the distribution of theunsteady factors in the flow is not taken into account

Figure 13 shows the relation curve between the flow andefficiency It demonstrates that the curve first goes up andthen down and it becomes relatively flat near the region ofdesign condition The flow region of high efficiency is widewhich demonstrates that the performance is stable around thedesign conditionWhen the pump physicalmodel is built thegap region between front and back plates and case is ignoredso the rotation of pump is accompanied by a volume lossFurthermore mechanical loss such as bearing friction lossand disc loss are also ignored The actual losses cause theefficiency of numerical simulation to be higher than that ofexperiment which can be seen from the figure

6 Conclusions

(1) Complicated three-dimensional flow model is builtincluding inlet region impeller flow region guide-vane flowregion and exit region to simulate flow in 20BZ4 multi-stage centrifugal pump The method of multireference frame(MRF) is used to model rotating blades and stationary bladesby FLUENT

(2) The simulation results show that the flow in impellersis mostly uniform no eddy backflow and separation flowThe Jet-wake along some blades influences the efficiencyThere is secondary flow at blade end and exit of guide vanesThe pressure on pressure surface is higher than that of suctionsurface and the pressure difference causes the moment ofresistance on rotating axis At the inlet of suction surface thepressure is lowest and cavitations may happen there

(3) Besides design condition six off-design conditionsare set to predict the external characteristics of hydraulicperformances The comparison between experimental dataand simulation data shows that the experimental curve agreeswell with the simulation curve under design condition but


Table 2 Performance data under off-design conditions of simulation

Flow (m3h) 05119876 07119876 08119876 09119876 119876 11119876 12119876 13119876 15119876

Lift (m) 1057 989 957 934 873 805 748 638 529

Shaft power (w) 5463 6179 6347 6665 6864 7117 7633 7607 856

Efficiency () 527 612 659 687 693 677 64 594 505

900800700600500400300200100

0

Flow (m3h)

Experimental dataSimulation data

5 10 15 20 25 30

Shaft

pow

er (w

)

Figure 12 Performance curves of flow-shaft power

8070605040302010

0

Flow (m3h)


5 10 15 20 25 30

Effici

ency

()

Figure 13 Performance curves of flow-efficiency

under off-design conditions the unsteady factors of flow fieldinfluence the precision The actual losses cause the efficiencyof numerical simulation to be higher than that of experiment

References

[1] J Shi ldquoThe energy conservation improvement and prospect ofthe centrifugal pumprdquo General Machinery vol 9 pp 24ndash282012

[2] H Si and S Dike ldquoNumerical simulation of the three-dimensional flow field in a multistage centrifugal pump and itsperformance predictionrdquo Mechanical Science and Technologyvol 29 no 6 pp 706ndash708 2010

[3] Z Li DWu LWang and B Huang ldquoNumerical simulation oninternal flow of centrifugal pump during transient operationrdquo

Journal of EngineeringThermophysics vol 30 no 5 pp 781ndash7832009

[4] Y Liu and GWang ldquoComputer-aided analysis on inner flow instamping and welding multistage centrifugal pumprsquos impellersrdquoChinese Journal of Mechanical Engineering vol 43 no 8 pp207ndash211 2007

[5] R Barrio J Fernndez E Blanco and J Parrondo ldquoEstimationof radial load in centrifugal pumps using computational fluiddynamicsrdquo European Journal of Mechanics B vol 30 no 3 pp316ndash324 2011

[6] B Jafarzadeh AHajariMMAlishahi andMHAkbari ldquoTheflow simulation of a low-specific-speed high-speed centrifugalpumprdquo Applied Mathematical Modelling vol 35 no 1 pp 242ndash249 2011

[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005

[8] B Cui Z Zhu J Zhang and Y Chen ldquoThe flow simulation andex perimental study of low-specific-speed high-speed complexcentrifugal impellersrdquo Chinese Journal of Chemical Engineeringvol 14 no 4 pp 435ndash441 2006

[9] J S Anagnostopoulos ldquoNumerical calculation of the flow in acentrifugal pump impeller using Cartesian gridrdquo in Proceedingsof the 2nd WSEAS International Conference on Applied andTheoretical Mechanics pp 20ndash22 Venice Italy 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Guide plate

Guide plate

Impeller

Impeller flow region

Guidevane Guide-vane

flow region

Figure 1 Sketch of centrifugal pump

Figure 2 Flow region of impeller and guide vane

on internal flow of stamping and welding centrifugal pumpimpeller based on CFD using ANSYS CFX and exploredthe flow mechanism in impeller Barrio et al [5] simulatedinternal flowof centrifugal pump throughCFD such that theycould predict radical force and torsion suffered by impellerJafarzadeh et al [6] simulated fluid flow of low-specific-speedratio centrifugal pump Asuaje et al [7] performed a 3D-CFDsimulation of impeller and volute of a centrifugal pump usingCFX code with a specific speed of 32 and found velocity andpressure fields for different flow rates and radial thrust on thepump shaft Cui et al [8] investigated the effect of number ofsplitting blades for long mid and short blades using a one-equation turbulent model Their results show that the bulkflow in the impeller has an important influence on the pumpperformance Anagnostopoulos [9] simulated 3D turbulentflow in a radial pump impeller for a constant rotational speedof 1500 rpm based on the solution of the RANS equationsFew of the previous works involved study of 3D modelingwithin a full domain considering interaction between rotorand stator of a high-speed multistage centrifugal pump usingvarious turbulence models

This paper uses commercial CFD software FLUENTstandard 119896-120576 turbulent model and multiply reference frameto perform numerical modeling of the full three-dimensional

fluid field for any stage of 20BZ4multistage centrifugal pumpwhich includes the flow region of import channel impellersguide vanes and exit channel The pressure and velocity dis-tributions in the pump under design condition are obtainedand the numerical performance curves are comparedwith theexperimental ones It will provide theoretical basis for furtheroptimizing the structures and improving the performances ofcentrifugal pump

2 Numerical Simulation and Method

21 Physical Model Figure 1 shows the sketch map and flowroute in any stage unit of 20BZ4 multi-stage centrifugalpump which includes guide plates impellers and guidevanes The impeller is made up of front end plate back endplate and blades The blades are equipped between front andback end plates and the number of blades is 5 The structureof guide vanes is radial and the number of blades is 7 It ismade up of positive guide vane and negative guide vane Pos-itive vane can collect fluid and transform kinetic energy intopressure energy while negative vane can change flow direc-tion and transmit the fluid into next unit with the requiredspeed and circulation Guide plate can reduce reflux effec-tively and make uniform and stable flow velocity of the fluidinto the impeller Fluid flows downward through guide platethen through the flow runner of impeller into guide vane andfinally goes into the next pump unit from guide plate

The impeller inlet and guide-vane outlet are extendedrespectively in order to ensure stable convergence of internalflow field The physical model includes inlet region impellerflow region guide-vane flow region and exit region Figure 2shows the flow region model of impeller and guide-vaneStructured grids are used in inlet region and exit regionbecause of the cylindrical shape and the numbers of grids are71607 and 69564 respectively Unstructured grids are used tomesh impeller and guide-vane flow regions and the numbersof grids are 187561 and 133108 respectively Figures 3 and 4show the grids of impeller flow region and guide-vane flowregion respectively

22 Governing Equations and TurbulenceModel The internalflow of centrifugal pump is a three-dimensional viscousand unsteady turbulent flow and flow law follows Navier-Stokes equation Because the heat exchange is very lit-tle in centrifugal pump energy conservation equation isnot considered and only mass conservation equation andmomentum conservation equation need to be solved

Mass conservation equation is as follows

120597120588

120597119905+

120597

120597119909119894

(120588119906119894) = 0 (1)

Momentum conservation equation is as follows

120597

120597119905(120588119906119894) +

120597

120597119909119895

(120588119906119894119906119895) = minus

120597119901

120597119909119894

+120597

120597119909119895

[120583120597119906119894

120597119909119895

minus 12058811990610158401198941199061015840119895] + 119878119894

(2)

where120588 is fluid densityu is velocity p is pressure t is time120583 is





stress 119909119894and 119909


119894= 119909119895


120597 (120588119896)

120597119905+

120597 (120588119896119906119894)

120597119909119894

=120597

120597119909119895

[(120583 +120583119905

120590119896

)120597119896

120597119909119895

] + 119866119896

minus 120588120576

(3)


120597 (120588120576)

120597119905+

120597 (120588120576119906119894)

120597119909119894

=120597

120597119909119895

[(120583 +120583119905

120590119904

)120597120576

120597119909119895

]

+1198621120576

120576

119896119866119896

minus 1198622120576

1205881205762

119896

(4)




constants 120590119896and 120590



120583119905

= 120588119862120583

1198962

120576 (5)




119906in =119876

120588120587 (11990321

minus 11990322) (6)



119896in = 00051199062

in (7)


120576in =11986212058311989632

in

119897in (8)



120597119906119894(out)

120597119899= 0 (119894 = 1 2 3 )

120597119896out120597119899

= 0

120597120576out120597119899

= 0

(9)







Flow(m3h)



Mediumdensity(kgm3)


20 2850 101325 9982 1003 times 10minus3

ZY

X

142119890+01

127119890+01

113119890+01

992119890+00

851119890+00

709119890+00

568119890+00

427119890+00

286119890+00

144119890+00

317119890minus02



3 Numerical Results



Z

Y

X

142119890+01132119890+01123119890+01113119890+01104119890+01945119890+00851119890+00757119890+00662119890+00568119890+00474119890+00380119890+00286119890+00192119890+00973119890minus01317119890minus02


192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05 Z

Y

X





Suction surface

Pressure surface

192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

ZY

X


192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

Z

Y

X




675119890+04

435119890+04

195119890+04

minus459119890+03

minus286119890+04

minus527119890+04

minus767119890+04

minus101119890+05

minus125119890+05

minus149119890+05

minus173119890+05

Z

YX






119876 = int119860

(120588V sdot 119899) 119889119860 (10)



119875119894=

int119860

(120588119901119905 |V sdot 119899|) 119889A

int119860

(120588 |V sdot 119899|) 119889119860 (11)




119867 =119901out minus 119901in


2119892+ Δ119885 (12)



119875 = 119872119908

119908 =2120587119899

60

(13)



120578 =120588119892119876119867

119872119908 (14)






14

12

10

8

6

4

2

0


Flow (m3h)

Lift

(m)

5 10 15 20 25 30




6 Conclusions






Flow (m3h) 05119876 07119876 08119876 09119876 119876 11119876 12119876 13119876 15119876

Lift (m) 1057 989 957 934 873 805 748 638 529

Shaft power (w) 5463 6179 6347 6665 6864 7117 7633 7607 856

Efficiency () 527 612 659 687 693 677 64 594 505

900800700600500400300200100

0

Flow (m3h)


5 10 15 20 25 30

Shaft

pow

er (w

)


8070605040302010

0

Flow (m3h)


5 10 15 20 25 30

Effici

ency

()



References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra













stress 119909119894and 119909


119894= 119909119895


120597 (120588119896)

120597119905+

120597 (120588119896119906119894)

120597119909119894

=120597

120597119909119895

[(120583 +120583119905

120590119896

)120597119896

120597119909119895

] + 119866119896

minus 120588120576

(3)


120597 (120588120576)

120597119905+

120597 (120588120576119906119894)

120597119909119894

=120597

120597119909119895

[(120583 +120583119905

120590119904

)120597120576

120597119909119895

]

+1198621120576

120576

119896119866119896

minus 1198622120576

1205881205762

119896

(4)




constants 120590119896and 120590



120583119905

= 120588119862120583

1198962

120576 (5)




119906in =119876

120588120587 (11990321

minus 11990322) (6)



119896in = 00051199062

in (7)


120576in =11986212058311989632

in

119897in (8)



120597119906119894(out)

120597119899= 0 (119894 = 1 2 3 )

120597119896out120597119899

= 0

120597120576out120597119899

= 0

(9)







Flow(m3h)



Mediumdensity(kgm3)


20 2850 101325 9982 1003 times 10minus3

ZY

X

142119890+01

127119890+01

113119890+01

992119890+00

851119890+00

709119890+00

568119890+00

427119890+00

286119890+00

144119890+00

317119890minus02



3 Numerical Results



Z

Y

X

142119890+01132119890+01123119890+01113119890+01104119890+01945119890+00851119890+00757119890+00662119890+00568119890+00474119890+00380119890+00286119890+00192119890+00973119890minus01317119890minus02


192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05 Z

Y

X





Suction surface

Pressure surface

192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

ZY

X


192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

Z

Y

X




675119890+04

435119890+04

195119890+04

minus459119890+03

minus286119890+04

minus527119890+04

minus767119890+04

minus101119890+05

minus125119890+05

minus149119890+05

minus173119890+05

Z

YX






119876 = int119860

(120588V sdot 119899) 119889119860 (10)



119875119894=

int119860

(120588119901119905 |V sdot 119899|) 119889A

int119860

(120588 |V sdot 119899|) 119889119860 (11)




119867 =119901out minus 119901in


2119892+ Δ119885 (12)



119875 = 119872119908

119908 =2120587119899

60

(13)



120578 =120588119892119876119867

119872119908 (14)






14

12

10

8

6

4

2

0


Flow (m3h)

Lift

(m)

5 10 15 20 25 30




6 Conclusions






Flow (m3h) 05119876 07119876 08119876 09119876 119876 11119876 12119876 13119876 15119876

Lift (m) 1057 989 957 934 873 805 748 638 529

Shaft power (w) 5463 6179 6347 6665 6864 7117 7633 7607 856

Efficiency () 527 612 659 687 693 677 64 594 505

900800700600500400300200100

0

Flow (m3h)


5 10 15 20 25 30

Shaft

pow

er (w

)


8070605040302010

0

Flow (m3h)


5 10 15 20 25 30

Effici

ency

()



References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Flow(m3h)



Mediumdensity(kgm3)


20 2850 101325 9982 1003 times 10minus3

ZY

X

142119890+01

127119890+01

113119890+01

992119890+00

851119890+00

709119890+00

568119890+00

427119890+00

286119890+00

144119890+00

317119890minus02



3 Numerical Results



Z

Y

X

142119890+01132119890+01123119890+01113119890+01104119890+01945119890+00851119890+00757119890+00662119890+00568119890+00474119890+00380119890+00286119890+00192119890+00973119890minus01317119890minus02


192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05 Z

Y

X





Suction surface

Pressure surface

192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

ZY

X


192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

Z

Y

X




675119890+04

435119890+04

195119890+04

minus459119890+03

minus286119890+04

minus527119890+04

minus767119890+04

minus101119890+05

minus125119890+05

minus149119890+05

minus173119890+05

Z

YX






119876 = int119860

(120588V sdot 119899) 119889119860 (10)



119875119894=

int119860

(120588119901119905 |V sdot 119899|) 119889A

int119860

(120588 |V sdot 119899|) 119889119860 (11)




119867 =119901out minus 119901in


2119892+ Δ119885 (12)



119875 = 119872119908

119908 =2120587119899

60

(13)



120578 =120588119892119876119867

119872119908 (14)






14

12

10

8

6

4

2

0


Flow (m3h)

Lift

(m)

5 10 15 20 25 30




6 Conclusions






Flow (m3h) 05119876 07119876 08119876 09119876 119876 11119876 12119876 13119876 15119876

Lift (m) 1057 989 957 934 873 805 748 638 529

Shaft power (w) 5463 6179 6347 6665 6864 7117 7633 7607 856

Efficiency () 527 612 659 687 693 677 64 594 505

900800700600500400300200100

0

Flow (m3h)


5 10 15 20 25 30

Shaft

pow

er (w

)


8070605040302010

0

Flow (m3h)


5 10 15 20 25 30

Effici

ency

()



References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Suction surface

Pressure surface

192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

ZY

X


192119890+04

minus130119890+03

minus218119890+04

minus424119890+04

minus629119890+04

minus834119890+04

minus104119890+05

minus125119890+05

minus145119890+05

minus166119890+05

minus186119890+05

Z

Y

X




675119890+04

435119890+04

195119890+04

minus459119890+03

minus286119890+04

minus527119890+04

minus767119890+04

minus101119890+05

minus125119890+05

minus149119890+05

minus173119890+05

Z

YX






119876 = int119860

(120588V sdot 119899) 119889119860 (10)



119875119894=

int119860

(120588119901119905 |V sdot 119899|) 119889A

int119860

(120588 |V sdot 119899|) 119889119860 (11)




119867 =119901out minus 119901in


2119892+ Δ119885 (12)



119875 = 119872119908

119908 =2120587119899

60

(13)



120578 =120588119892119876119867

119872119908 (14)






14

12

10

8

6

4

2

0


Flow (m3h)

Lift

(m)

5 10 15 20 25 30




6 Conclusions






Flow (m3h) 05119876 07119876 08119876 09119876 119876 11119876 12119876 13119876 15119876

Lift (m) 1057 989 957 934 873 805 748 638 529

Shaft power (w) 5463 6179 6347 6665 6864 7117 7633 7607 856

Efficiency () 527 612 659 687 693 677 64 594 505

900800700600500400300200100

0

Flow (m3h)


5 10 15 20 25 30

Shaft

pow

er (w

)


8070605040302010

0

Flow (m3h)


5 10 15 20 25 30

Effici

ency

()



References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119867 =119901out minus 119901in


2119892+ Δ119885 (12)



119875 = 119872119908

119908 =2120587119899

60

(13)



120578 =120588119892119876119867

119872119908 (14)






14

12

10

8

6

4

2

0


Flow (m3h)

Lift

(m)

5 10 15 20 25 30




6 Conclusions






Flow (m3h) 05119876 07119876 08119876 09119876 119876 11119876 12119876 13119876 15119876

Lift (m) 1057 989 957 934 873 805 748 638 529

Shaft power (w) 5463 6179 6347 6665 6864 7117 7633 7607 856

Efficiency () 527 612 659 687 693 677 64 594 505

900800700600500400300200100

0

Flow (m3h)


5 10 15 20 25 30

Shaft

pow

er (w

)


8070605040302010

0

Flow (m3h)


5 10 15 20 25 30

Effici

ency

()



References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Flow (m3h) 05119876 07119876 08119876 09119876 119876 11119876 12119876 13119876 15119876

Lift (m) 1057 989 957 934 873 805 748 638 529

Shaft power (w) 5463 6179 6347 6665 6864 7117 7633 7607 856

Efficiency () 527 612 659 687 693 677 64 594 505

900800700600500400300200100

0

Flow (m3h)


5 10 15 20 25 30

Shaft

pow

er (w

)


8070605040302010

0

Flow (m3h)


5 10 15 20 25 30

Effici

ency

()



References


















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article research on three-dimensional unsteady ...ow of centrifugal pump is a...

Documents