Research ArticleNumerical Prediction and Performance Experiment in an EngineCooling Water Pump with Different Blade Outlet Widths
Wei Li Xiaofan Zhao Weiqiang Li Weidong Shi Leilei Ji and Ling Zhou
Research Center of Fluid Machinery Engineering and Technology Jiangsu University Zhenjiang China
Correspondence should be addressed to Wei Li lwjiangdaujseducn
Received 26 October 2016 Revised 15 January 2017 Accepted 1 March 2017 Published 22 March 2017
Academic Editor Nicolas Gourdain
Copyright copy 2017 Wei Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Changing the blade outlet width is an important method to adjust the performance curves of centrifugal pumps In this studythree impellers with different blade outlet widths in an engine cooling water pump (ECWP) were numerically simulated based onANSYS-CFX software Numerical calculation reliability was validated based on the comparison between simulation results andexperimental datum As the blade outlet width increases from the performance curves the investigated ECWP head increasesgradually and the best efficiency point (BEP) offsets to larger flow rate and the high efficiency region (HER) is becoming largerand the critical cavitation pressure of the investigated ECWP at BEP increases which indicates that the cavitation performance atBEP became worse Compared with the internal flow field we find vortex appears mainly in the blade passage near the tongue andvolute outlet and the region of the low static pressure is located in the blade inlet suction surface and impeller inlet and outlet arethe regions of high turbulence kinetic energy Meanwhile at the same flow rate with the increase of blade outlet width the areasof vortex and low static pressure become obvious and bigger
1 Introduction
The engine cooling water pump (ECWP) is an important partin the motor and engine and it has been widely used forcirculating cooling water and carrying the heat away fromthe engine parts Compared with conventional centrifugalpumps ECWP is always working in the environment withthe high temperature changed rotational speed and therestricted dimension space which leads to its poor cavitationperformance and finally shortens the reliability and life of thecooling system So some effects have been devoted so far tostudy the cavitation performance of ECWP Shi et al [1 2]did structure improvement and optimization of automobilepump based on numerical simulation with opened centrifu-gal impeller Li et al [3 4] predicted cavitation performanceof ECWP and proposed the optimal design of impeller thatcan improve the cavitation performance Discussion on thepump cavitation in LJ465Q series engine was made by Liaoand Xie [5] Some improvement is proposed by Liu et al[2] in a vehicle pump such as decreasing the blade angle attrailing edge expanding the cross section of the outlet pipe
and gradually increasing the depth of the volute along theflow direction to improve the performance of pump
Outlet width one of the main geometric parameters ofthe impeller has an important influence on hydraulic andcavitation performance of centrifugal pumps Shi et al [6]carried out the numerical and experimental study on a deep-well centrifugal pump with four different impeller outletwidths The results show that single stage head and singlestage power both increased and BEP offset to larger flowrate with the increase of impeller outlet width The results ofperformance indicate that the oversize impeller outlet widthwill lead to poor pump performance and will increase shaftpower Song et al [7] investigated the cavitation behaviorin impeller with different blade profiles and found that ithas a key effect on the development of sheet cavitationin impeller and also influences the distribution of sheetcavitation in impeller channels Zhang et al [8] analyzed theimpact on the cavitation performance for centrifugal pumpsby changing the blade leading edge shape The results showthat the leading edge extending forward along the shroud can
HindawiMathematical Problems in EngineeringVolume 2017 Article ID 8945712 11 pageshttpsdoiorg10115520178945712
2 Mathematical Problems in Engineering
Impeller
Casing
Seal
Bearing
Pulley
Shaft sleeve
Shaft
Figure 1 Centrifugal structure of ECWP
11 13 16
30휇
60휇
98휇
Figure 2 Impeller cross section with three different blade outlet widths
improve the inlet flow condition and cavitation performanceBut the cavitation performance has been reduced immenselywhen the leading edge extends backward along the shroudLiu et al [9 10] had done some work about the effectsof impeller outlet width on the performance in two sidechambers of a centrifugal pump However the report aboutthe effect of cavitation performance by changing the bladeoutlet width is extremely lacking
In this work the hydraulic and cavitation performanceand the internal flow of ECWP were researched with threedifferent blade outlet widths of impeller By changing outletwidths of impeller and keeping other parameters constantthree impellers are obtained and were numerically simulatedbased on ANSYS-CFX software In addition fluid staticpressure turbulent kinetic energy distribution and vaporvolume fraction contours of impeller were observed toanalyze the influence of blade outlet width on hydraulic andcavitation performance This work provides a reference forthe performance optimization of ECWP
2 Geometric Model
21 Structure Chart Considering the special requirements ofcylinder structure process and engine the design methodof ECWP is different from traditional centrifugal pump Thecharacteristics of ECWP impeller are as follows semiopenstructure wide outlet width ring cross section of suctionchamber rectangular volute cross section and being drivenby pulleyThe typical structure of ECWP is shown in Figure 1
22 Impeller Design The temperature of ECWP in this workis set as 85∘C plusmn 2∘C the main geometric parameters ofimpeller at the design condition are shown in Table 1
In order to study the influence of different impeller bladeoutlet widths three impellermodels were built with three dif-ferent outlet widths (1198872 = 11mm 13mm and 16mm resp)Figure 2 shows the impeller cross section with different outletwidths Figure 3 shows three-dimensional plot of impeller
Mathematical Problems in Engineering 3
Table 1 Impeller parameters of ECWP
Description Parameter ValueDesign flow rate (Lmin) 119876des 340Head (m) 119867 15Rotational speed (rmin) 119899 3700Outlet width of impeller (mm) 1198872 16Inlet angle of blade (∘) 1205721 19Outlet angle of blade (∘) 1205722 30Wrap angle of blade (∘) 120572 65Number of blades 119885 7Inlet diameter of impeller (mm) 1198891 60Outlet diameter of impeller (mm) 1198892 98
Figure 3 Three-dimensional plot of impeller
3 Numerical Simulation
31 Calculation Model The computational domains includethree parts inlet section outlet section and impeller Allthese parts are completed in the Unigraphics NX softwareand are shown in Figure 4 The calculation is performed on aDell workstation with 2 processors (Windows 7 ProfessionalInter(R) Xeon(R) CPU 64 bit 333GHz and 48GB RAM)Considering the uncertainty about the empirical coefficientsof cavitation condensation and vaporization and maximumdensity ratio at the high temperature which can influencethe compressibility characteristics in the cavitation area andthe mass transfer between liquid and vapor [11] cavitationnumerical simulations at high temperature have a frustratingconvergence and lack of reliability So combined with thesimulation applicability and accuracy the multiphase flowwas numerically simulated in ECWP under 25∘C tempera-ture
32 Mesh Analysis The whole generation process of mesh iscarried out in ANSYS-ICEM software structure mesh wasapplied in computational domains mesh and the impellerdomain is refinedThemesh configuration of whole flow fieldis shown in Figure 5 specially the mesh at blade inlet and
Outlet section
Inlet section
Impeller
Figure 4 The domains of ECWP
volute tongue The mesh can be calculated in ANSYS-CFXfluently and the value of 119910+ is limited under 100 and was inaccordance with the turbulence model which was chosen asfollows
33 Turbulence Model In the condition of single phase tur-bulence models describe the effects of turbulent fluctuationsof velocities and scalar quantities no turbulence model canget satisfactory results for all applications So four turbulencemodels namely RNG 119896-Epsilon model 119896-Epsilon model 119896-Omega model and the shear stress transport model (SSTmodel) are selected to simulate the internal performanceof impeller with 16mm outlet width at standard runningconditions (119876des = 340 Lmin) By comparing numericalresults and the experimental one it can be found in Table 2that SST model is the best one that consists of experimentalresults So SST turbulence model is the most suitable modelfor hydraulic performance simulation
Moreover in the condition of multiphase flows thequantity of terms that need to be modeled in momentumequation is many which makes the modeling of turbulencein multiphase simulations extremely complex [12] So SSTturbulence model is chosen directly as the turbulent modelfor cavitation simulation
34 Governing Equations and Discretization Three steadynumerical simulations are conducted employing the timeaveraged Navier-Stokes equation and the SST turbulentmodel in ANSYS-CFX software The Navier-Stokes equationis solved by two-order accuracy upwind scheme and the fullyimplicit coupling algorithm based on finite volume methodin ANSYS-CFX software The advection terms are in high-resolution format and its convergence accuracy is set as 10minus4
35 Mesh Independence Analysis To reduce computationtime and improve accuracy the optimum quantity of meshelements in the simulation has been investigated Also headwas used as the evaluation indexes to judge mesh sizeFinally the least quantity of dependent mesh elements hasbeen obtained when head is obtained with negligible changeFigure 6 shows the dependency of results by comparingexternal characteristic with different element quantity at340 Lsdotminminus1 flow rate (Q)
4 Mathematical Problems in Engineering
Table 2 Numerical results with different turbulence models
Figure 6 Comparison of the head with different mesh elements
The quantity of mesh elements is the sum of elementsin impeller inlet pipe and outlet pipe Considering thecomputational ability of computer workstation used in thiswork the total mesh number of themesh is about 24millionAs demonstrated in Figure 6 when the quantity of meshelement is about 24 million the change of head is less than2 which indicates the convergence of mesh
Table 3 shows mesh quantity of the whole domains indifferent parts of pump
36 Cavitation Model The cavitation model is based onthe assumption that the water and vapor mixture in theflow can be perceived as a homogeneous fluid Cavitation
Table 3 Information of whole mesh statistics
Components Inlet section Impeller Outlet sectionQuantity of mesh elements 299970 1685215 353175Minimum orthogonal angle∘ 158 364 329
model is the mathematical model used to describe thetransformation between vapor phase and liquid phase Inthis study the Zwart-Gerber-Belamri cavitation model [13]based on Rayleigh-Plesset Equation in the transport equationmodel was selected The full phase mass per unit volumetransmission rate and void volume change rate are defined asfollows∙119898119891119892= 1198653119903119899119906119888 (1 minus 119903119892) 120588119892119877119861 (23
1003816100381610038161003816119901V minus 1199011003816100381610038161003816120588119891 )12
sgn (119901V minus 119901) d119881119861d119905 = d
where 119865 is an empirical coefficient 119877119861 represents the bubbleradius 119903119899119906119888 = 5 times 10minus4 119903119892 = 1 times 10minus6 119901V is the vaporizationpressure and119901 is the pressure of the liquid around the bubble119881119861 is bubble volume
37 Boundary Conditions The numerical simulation flowdomains are divided into two types stationary referenceframe and rotating reference frame And inlet section andoutlet section belong to the former while impeller is situatedin the latter The interface between the stationary reference
Mathematical Problems in Engineering 5
Vacuum pressure gaugeFlow meter
Electric control valveWater tank
Heating pipe
Inlet valve Test pump
Motor
Control valve
Pressure gaugePressure gauge
Figure 7 Closed experiment rig of ECWP
frame and the rotating one is set as frozen rotor Thespecified pitch angles are set as 360∘ and general grid interface(GGI) model is chosen to process data transmission betweenthe stationary and the rotating reference frame The inletboundary is set as absolute total pressure based on the zeroreference absolute pressure while the outlet boundary was setasmass flow rateThewall roughness is set as 125 120583m and thestandard wall function is chosen in the domain near the walland the wall no-slip boundary condition is set as adiabaticwall Meanwhile the volume fraction of water in inlet andbubble volume fraction is set as 1 and 0 respectively
In the simulation of the cavitation performance theoccurrence degree of cavitation was controlled by adjustingthe inlet total pressure the average bubble radius is set as2times10minus6mm and the vaporization pressure119901V is set as 3574 PaIn the simulation of the external characteristics themass flowrate is controlled by changing outlet boundary condition andthe other parameters are kept identical
4 Experimental Verification
41 Experimental Rigs andMethods The closed performanceexperiment rig of ECWP (shown in Figure 7) is set upto verify the accuracy of the numerical simulation whichprecedes the requirements of national standard (GB 3216-89 GB 1882-80 and QCT 2882-2001) The accuracy of theexperiment system is plusmn05
The experiment is performed according to ISO 9906which is the international experiment standard for pumpsThe experimental method and some facilities are the sameas the reference [14] The main technical parameters ofthe experiment bed are as follows rotational speed 119899 le8000 rmin water temperature 119879 le 120∘C and flow rate119876 le 400 Lmin Meanwhile the inlet and outlet pres-sure are measured separately by two pressure transmittersthat the error of measurement is less than 015 whilethe temperature is controlled by PID (Proportion IntegralDerivative) system Besides in order to draw the hydraulicperformance curves the outlet flow rate is adjusted to changethe working condition The flow rate is kept at the Q-BEP(340 Lmin) and the rotational speed is set as 3700 rminthen the inlet pressure is reduced slowly to stimulate thecavitation inception in the cavitation experiment
In the pump performance experiment net positive suc-tion head (NPSH) is defined as follows
NPSH = 119901119904120588119892 + V1199042
2119892 minus 119901V120588119892 (2)
where NPSH is the net positive suction head m 119901119904 is thetotal pressure of pump inlet Pa V119904 is the absolute velocity atinlet ms 119901V is the vaporization pressure for liquid Pa 120588 isthe destiny of water 120588 = 1000 kgm3 119892 is the gravitationalacceleration ratio 119892 = 98msminus2
42 Experimental Results and Analysis According to thedesigned three-dimensional model ECWP experimentalmodel (1198872 = 16mm) was processed into products andthen sent to have the hydraulic performance experimentThe hydraulic performance experiment was carried out with3700 rmin rotational speed and 25∘C temperature To gener-ate cavitation performance the inlet total pressure is variedprogressively by changing the valve opening while keepingthe flow rate and rotational speed remaining 340 Lmin and3700 rmin respectively The hydraulic and cavitation char-acteristic curves obtained by experimental and numericalsimulation were both shown in Figure 8
It can be seen from Figure 8 that the change trend innumerical simulation result is consistent with that in experi-mental result of both hydraulic and cavitation performanceBesides efficiency head and NPSH of numerical simulationare all slightly higher than that of experiment To be specificthe pump simulation efficiency is about 28 higher and thehead is about 2 higher than that of experiment at BEPNPSH is also about 033m higher than that of experimentat 3700 rmin rotational speed and 340 Lmin flow rate Tosum up the reliability of numerical simulation is verified bycomparing the results between experiment and numericalsimulation which indicates that the numerical calculation isthe effective method to predict the hydraulic and cavitationperformance of centrifugal pumps
5 Simulation Results and Discussions
51 Hydraulic Performance Hydraulic performance ofECWP with different blade outlet widths is obtained by
6 Mathematical Problems in Engineering
0 50 100 150 200 250 300 350 40002468
10121416182022
Q (Lmin)
0102030405060708090100
ExperimentSimulation
H (m
)
휂(
)
(a)
ExperimentSimulation
3 4 5 6 7 8 9 10 116789
101112131415161718
NPSH (m)
H (m
)
(b)
Figure 8 Comparison with hydraulic (a) and cavitation (b) performance
50 100 150 200 250 300 350 40002468
10121416182022
Flow rate Q (Lmin)
Hea
d H
(m)
0
10
20
30
40
50
60
70
80
90
100
Effici
ency
휂(
)
b2 = 11mm Hb2 = 13mm Hb2 = 16mm H
b2 = 11mm 휂b2 = 13mm 휂b2 = 16mm 휂
Figure 9 Hydraulic performance with different blade outlet widths
numerical simulation The head and efficiency are shown inFigure 9
According to the performance curves it can be foundthat head increases gradually along with the increase of bladeoutlet widthThe head function (6) can be obtained based onthe velocity triangle about blade outlet width with the sameflow rate Also its first derivative function is more than zeroso it is an increasing function Therefore head will increasewhen blade outlet width becomes larger
119867 = 1199062V1199062 minus 1199061V1199061119892 (3)
119867 = (11990622 minus 1199061V1199061119892 ) minus ( 119876119906211989212058711986321198872 tan120573)11198872
= 119860 minus 1198611198872 (119860 119861 gt 0)
(6)
Table 4 is the flow rate and pump efficiency at BEPwith different blade outlet widths When blade outlet widthchanges from 11mm and 13mm to 16mm BEP offsets tolarger flow rate Similar observation was also found in [6]The flow rate at BEP increased 877 and 968 respectivelyAlso there are some differences of efficiency in three cases atBEP Meanwhile with the blade outlet widths increases thehigh efficiency region (HEG) of ECWP is becoming largerAccording to (6) we know that its second derivative functionis less than zero So it is also a convex function In otherwords head becomes much more sensitive to the change ofblade outlet width when blade outlet width becomes largerAnd the range of blade outlet width is bigger near BEP
52 Discussion of Internal Flow The internal flow fields ofimpeller with three blade outlet widths are simulated at thesame flow condition Figure 10 is the surface streamline in thecross section of impeller with different blade outlet widthsFrom the pictures it can be found that the vortices appearedmainly in two areas blade passage near tongue and voluteoutlet Andwith the blade outlet width increases the vortex atvolute outlet becomes much more obvious and bigger which
Mathematical Problems in Engineering 7
Velocity (ms)1632e + 001
1225e + 001
8178e + 000
4109e + 000
4021e minus 002
(a) 1198872 = 11mm
Velocity (ms)1629e + 001
1228e + 001
8269e + 000
4260e + 000
2516e minus 001
(b) 1198872 = 13mm
Velocity (ms)1703e + 001
1281e + 001
8582e + 000
4356e + 000
1300e minus 001
(c) 1198872 = 16mm
Figure 10 Surface streamline in the cross section
has also been reported in [15] As a result of the interactionflow fields between impeller and tongue which can be seenfrom Figures 10(b) and 10(c) some obvious vortices occurredin the blade passage near tongue and will cause more losses
The static pressure distributions with different bladeoutlet widths in the cross section of impeller are comparedin Figure 11 It can be seen from the figure that the highpressure area always appears at the surface of blade outletpressure And also in the blade inlet suction surface the lowstatic pressure region can be observed With the increasingof the outlet width the low pressure areas become biggerwhich is consistent with the research results in [16] And thepressure value is lower at the impeller blade inlet suctionsurfaceWhen the outletwidth changes from 11mmto 16mmthe maximum value of the static pressure increases from2672 kpa to 2709 kpa while the minimum value of thestatic pressure increases from minus985 kpa to minus620 kpa Andthe differential pressure becomes bigger with the increase ofimpeller blade outlet width
Also the pressure distributions of the cross section withdifferent blade outlet widths at BEP are shown in Figure 12It can be found from Figure 12 that the pressure distribution
of the cross section at the blade inlet is quite different Whenthe blade outlet width is 16mm the lowpressure zone ismuchwider than that of the othersThe pressure distribution in theback chamber is similar to each other and the static pressureincreases gradually along the longitudinal direction From theabove analysis it can be found that great change happens atthe blade inlet which would have influence on the cavitationperformance
The turbulence kinetic energy contours in the crosssection of impeller are shown in Figure 13 It can be foundobviously that high turbulence kinetic energy exists in theregions of impeller inlet and outlet Particularly from Figures13(b) and 13(c) high turbulence kinetic energy can be foundfrom the blade passage near volute tongue from Figures10(b) and 10(c) disorganized surface streamline can be foundAnd both indicate that violent vortex and much more lossesexist in the blade passage near the volute tongue [17 18]When the outlet width changes from 11mm to 16mm themaximum value of turbulence kinetic energy increases from1247m2s2 to 1619m2s2 while the minimum value of theturbulence kinetic energy increases from 0002375m2s2 to0002846m2s2
8 Mathematical Problems in Engineering
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(a) 1198872 = 11mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(b) 1198872 = 13mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(c) 1198872 = 16mm
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
Figure 2 Impeller cross section with three different blade outlet widths
improve the inlet flow condition and cavitation performanceBut the cavitation performance has been reduced immenselywhen the leading edge extends backward along the shroudLiu et al [9 10] had done some work about the effectsof impeller outlet width on the performance in two sidechambers of a centrifugal pump However the report aboutthe effect of cavitation performance by changing the bladeoutlet width is extremely lacking
In this work the hydraulic and cavitation performanceand the internal flow of ECWP were researched with threedifferent blade outlet widths of impeller By changing outletwidths of impeller and keeping other parameters constantthree impellers are obtained and were numerically simulatedbased on ANSYS-CFX software In addition fluid staticpressure turbulent kinetic energy distribution and vaporvolume fraction contours of impeller were observed toanalyze the influence of blade outlet width on hydraulic andcavitation performance This work provides a reference forthe performance optimization of ECWP
2 Geometric Model
21 Structure Chart Considering the special requirements ofcylinder structure process and engine the design methodof ECWP is different from traditional centrifugal pump Thecharacteristics of ECWP impeller are as follows semiopenstructure wide outlet width ring cross section of suctionchamber rectangular volute cross section and being drivenby pulleyThe typical structure of ECWP is shown in Figure 1
22 Impeller Design The temperature of ECWP in this workis set as 85∘C plusmn 2∘C the main geometric parameters ofimpeller at the design condition are shown in Table 1
In order to study the influence of different impeller bladeoutlet widths three impellermodels were built with three dif-ferent outlet widths (1198872 = 11mm 13mm and 16mm resp)Figure 2 shows the impeller cross section with different outletwidths Figure 3 shows three-dimensional plot of impeller
Mathematical Problems in Engineering 3
Table 1 Impeller parameters of ECWP
Description Parameter ValueDesign flow rate (Lmin) 119876des 340Head (m) 119867 15Rotational speed (rmin) 119899 3700Outlet width of impeller (mm) 1198872 16Inlet angle of blade (∘) 1205721 19Outlet angle of blade (∘) 1205722 30Wrap angle of blade (∘) 120572 65Number of blades 119885 7Inlet diameter of impeller (mm) 1198891 60Outlet diameter of impeller (mm) 1198892 98
Figure 3 Three-dimensional plot of impeller
3 Numerical Simulation
31 Calculation Model The computational domains includethree parts inlet section outlet section and impeller Allthese parts are completed in the Unigraphics NX softwareand are shown in Figure 4 The calculation is performed on aDell workstation with 2 processors (Windows 7 ProfessionalInter(R) Xeon(R) CPU 64 bit 333GHz and 48GB RAM)Considering the uncertainty about the empirical coefficientsof cavitation condensation and vaporization and maximumdensity ratio at the high temperature which can influencethe compressibility characteristics in the cavitation area andthe mass transfer between liquid and vapor [11] cavitationnumerical simulations at high temperature have a frustratingconvergence and lack of reliability So combined with thesimulation applicability and accuracy the multiphase flowwas numerically simulated in ECWP under 25∘C tempera-ture
32 Mesh Analysis The whole generation process of mesh iscarried out in ANSYS-ICEM software structure mesh wasapplied in computational domains mesh and the impellerdomain is refinedThemesh configuration of whole flow fieldis shown in Figure 5 specially the mesh at blade inlet and
Outlet section
Inlet section
Impeller
Figure 4 The domains of ECWP
volute tongue The mesh can be calculated in ANSYS-CFXfluently and the value of 119910+ is limited under 100 and was inaccordance with the turbulence model which was chosen asfollows
33 Turbulence Model In the condition of single phase tur-bulence models describe the effects of turbulent fluctuationsof velocities and scalar quantities no turbulence model canget satisfactory results for all applications So four turbulencemodels namely RNG 119896-Epsilon model 119896-Epsilon model 119896-Omega model and the shear stress transport model (SSTmodel) are selected to simulate the internal performanceof impeller with 16mm outlet width at standard runningconditions (119876des = 340 Lmin) By comparing numericalresults and the experimental one it can be found in Table 2that SST model is the best one that consists of experimentalresults So SST turbulence model is the most suitable modelfor hydraulic performance simulation
Moreover in the condition of multiphase flows thequantity of terms that need to be modeled in momentumequation is many which makes the modeling of turbulencein multiphase simulations extremely complex [12] So SSTturbulence model is chosen directly as the turbulent modelfor cavitation simulation
34 Governing Equations and Discretization Three steadynumerical simulations are conducted employing the timeaveraged Navier-Stokes equation and the SST turbulentmodel in ANSYS-CFX software The Navier-Stokes equationis solved by two-order accuracy upwind scheme and the fullyimplicit coupling algorithm based on finite volume methodin ANSYS-CFX software The advection terms are in high-resolution format and its convergence accuracy is set as 10minus4
35 Mesh Independence Analysis To reduce computationtime and improve accuracy the optimum quantity of meshelements in the simulation has been investigated Also headwas used as the evaluation indexes to judge mesh sizeFinally the least quantity of dependent mesh elements hasbeen obtained when head is obtained with negligible changeFigure 6 shows the dependency of results by comparingexternal characteristic with different element quantity at340 Lsdotminminus1 flow rate (Q)
4 Mathematical Problems in Engineering
Table 2 Numerical results with different turbulence models
Figure 6 Comparison of the head with different mesh elements
The quantity of mesh elements is the sum of elementsin impeller inlet pipe and outlet pipe Considering thecomputational ability of computer workstation used in thiswork the total mesh number of themesh is about 24millionAs demonstrated in Figure 6 when the quantity of meshelement is about 24 million the change of head is less than2 which indicates the convergence of mesh
Table 3 shows mesh quantity of the whole domains indifferent parts of pump
36 Cavitation Model The cavitation model is based onthe assumption that the water and vapor mixture in theflow can be perceived as a homogeneous fluid Cavitation
Table 3 Information of whole mesh statistics
Components Inlet section Impeller Outlet sectionQuantity of mesh elements 299970 1685215 353175Minimum orthogonal angle∘ 158 364 329
model is the mathematical model used to describe thetransformation between vapor phase and liquid phase Inthis study the Zwart-Gerber-Belamri cavitation model [13]based on Rayleigh-Plesset Equation in the transport equationmodel was selected The full phase mass per unit volumetransmission rate and void volume change rate are defined asfollows∙119898119891119892= 1198653119903119899119906119888 (1 minus 119903119892) 120588119892119877119861 (23
1003816100381610038161003816119901V minus 1199011003816100381610038161003816120588119891 )12
sgn (119901V minus 119901) d119881119861d119905 = d
where 119865 is an empirical coefficient 119877119861 represents the bubbleradius 119903119899119906119888 = 5 times 10minus4 119903119892 = 1 times 10minus6 119901V is the vaporizationpressure and119901 is the pressure of the liquid around the bubble119881119861 is bubble volume
37 Boundary Conditions The numerical simulation flowdomains are divided into two types stationary referenceframe and rotating reference frame And inlet section andoutlet section belong to the former while impeller is situatedin the latter The interface between the stationary reference
Mathematical Problems in Engineering 5
Vacuum pressure gaugeFlow meter
Electric control valveWater tank
Heating pipe
Inlet valve Test pump
Motor
Control valve
Pressure gaugePressure gauge
Figure 7 Closed experiment rig of ECWP
frame and the rotating one is set as frozen rotor Thespecified pitch angles are set as 360∘ and general grid interface(GGI) model is chosen to process data transmission betweenthe stationary and the rotating reference frame The inletboundary is set as absolute total pressure based on the zeroreference absolute pressure while the outlet boundary was setasmass flow rateThewall roughness is set as 125 120583m and thestandard wall function is chosen in the domain near the walland the wall no-slip boundary condition is set as adiabaticwall Meanwhile the volume fraction of water in inlet andbubble volume fraction is set as 1 and 0 respectively
In the simulation of the cavitation performance theoccurrence degree of cavitation was controlled by adjustingthe inlet total pressure the average bubble radius is set as2times10minus6mm and the vaporization pressure119901V is set as 3574 PaIn the simulation of the external characteristics themass flowrate is controlled by changing outlet boundary condition andthe other parameters are kept identical
4 Experimental Verification
41 Experimental Rigs andMethods The closed performanceexperiment rig of ECWP (shown in Figure 7) is set upto verify the accuracy of the numerical simulation whichprecedes the requirements of national standard (GB 3216-89 GB 1882-80 and QCT 2882-2001) The accuracy of theexperiment system is plusmn05
The experiment is performed according to ISO 9906which is the international experiment standard for pumpsThe experimental method and some facilities are the sameas the reference [14] The main technical parameters ofthe experiment bed are as follows rotational speed 119899 le8000 rmin water temperature 119879 le 120∘C and flow rate119876 le 400 Lmin Meanwhile the inlet and outlet pres-sure are measured separately by two pressure transmittersthat the error of measurement is less than 015 whilethe temperature is controlled by PID (Proportion IntegralDerivative) system Besides in order to draw the hydraulicperformance curves the outlet flow rate is adjusted to changethe working condition The flow rate is kept at the Q-BEP(340 Lmin) and the rotational speed is set as 3700 rminthen the inlet pressure is reduced slowly to stimulate thecavitation inception in the cavitation experiment
In the pump performance experiment net positive suc-tion head (NPSH) is defined as follows
NPSH = 119901119904120588119892 + V1199042
2119892 minus 119901V120588119892 (2)
where NPSH is the net positive suction head m 119901119904 is thetotal pressure of pump inlet Pa V119904 is the absolute velocity atinlet ms 119901V is the vaporization pressure for liquid Pa 120588 isthe destiny of water 120588 = 1000 kgm3 119892 is the gravitationalacceleration ratio 119892 = 98msminus2
42 Experimental Results and Analysis According to thedesigned three-dimensional model ECWP experimentalmodel (1198872 = 16mm) was processed into products andthen sent to have the hydraulic performance experimentThe hydraulic performance experiment was carried out with3700 rmin rotational speed and 25∘C temperature To gener-ate cavitation performance the inlet total pressure is variedprogressively by changing the valve opening while keepingthe flow rate and rotational speed remaining 340 Lmin and3700 rmin respectively The hydraulic and cavitation char-acteristic curves obtained by experimental and numericalsimulation were both shown in Figure 8
It can be seen from Figure 8 that the change trend innumerical simulation result is consistent with that in experi-mental result of both hydraulic and cavitation performanceBesides efficiency head and NPSH of numerical simulationare all slightly higher than that of experiment To be specificthe pump simulation efficiency is about 28 higher and thehead is about 2 higher than that of experiment at BEPNPSH is also about 033m higher than that of experimentat 3700 rmin rotational speed and 340 Lmin flow rate Tosum up the reliability of numerical simulation is verified bycomparing the results between experiment and numericalsimulation which indicates that the numerical calculation isthe effective method to predict the hydraulic and cavitationperformance of centrifugal pumps
5 Simulation Results and Discussions
51 Hydraulic Performance Hydraulic performance ofECWP with different blade outlet widths is obtained by
6 Mathematical Problems in Engineering
0 50 100 150 200 250 300 350 40002468
10121416182022
Q (Lmin)
0102030405060708090100
ExperimentSimulation
H (m
)
휂(
)
(a)
ExperimentSimulation
3 4 5 6 7 8 9 10 116789
101112131415161718
NPSH (m)
H (m
)
(b)
Figure 8 Comparison with hydraulic (a) and cavitation (b) performance
50 100 150 200 250 300 350 40002468
10121416182022
Flow rate Q (Lmin)
Hea
d H
(m)
0
10
20
30
40
50
60
70
80
90
100
Effici
ency
휂(
)
b2 = 11mm Hb2 = 13mm Hb2 = 16mm H
b2 = 11mm 휂b2 = 13mm 휂b2 = 16mm 휂
Figure 9 Hydraulic performance with different blade outlet widths
numerical simulation The head and efficiency are shown inFigure 9
According to the performance curves it can be foundthat head increases gradually along with the increase of bladeoutlet widthThe head function (6) can be obtained based onthe velocity triangle about blade outlet width with the sameflow rate Also its first derivative function is more than zeroso it is an increasing function Therefore head will increasewhen blade outlet width becomes larger
119867 = 1199062V1199062 minus 1199061V1199061119892 (3)
119867 = (11990622 minus 1199061V1199061119892 ) minus ( 119876119906211989212058711986321198872 tan120573)11198872
= 119860 minus 1198611198872 (119860 119861 gt 0)
(6)
Table 4 is the flow rate and pump efficiency at BEPwith different blade outlet widths When blade outlet widthchanges from 11mm and 13mm to 16mm BEP offsets tolarger flow rate Similar observation was also found in [6]The flow rate at BEP increased 877 and 968 respectivelyAlso there are some differences of efficiency in three cases atBEP Meanwhile with the blade outlet widths increases thehigh efficiency region (HEG) of ECWP is becoming largerAccording to (6) we know that its second derivative functionis less than zero So it is also a convex function In otherwords head becomes much more sensitive to the change ofblade outlet width when blade outlet width becomes largerAnd the range of blade outlet width is bigger near BEP
52 Discussion of Internal Flow The internal flow fields ofimpeller with three blade outlet widths are simulated at thesame flow condition Figure 10 is the surface streamline in thecross section of impeller with different blade outlet widthsFrom the pictures it can be found that the vortices appearedmainly in two areas blade passage near tongue and voluteoutlet Andwith the blade outlet width increases the vortex atvolute outlet becomes much more obvious and bigger which
Mathematical Problems in Engineering 7
Velocity (ms)1632e + 001
1225e + 001
8178e + 000
4109e + 000
4021e minus 002
(a) 1198872 = 11mm
Velocity (ms)1629e + 001
1228e + 001
8269e + 000
4260e + 000
2516e minus 001
(b) 1198872 = 13mm
Velocity (ms)1703e + 001
1281e + 001
8582e + 000
4356e + 000
1300e minus 001
(c) 1198872 = 16mm
Figure 10 Surface streamline in the cross section
has also been reported in [15] As a result of the interactionflow fields between impeller and tongue which can be seenfrom Figures 10(b) and 10(c) some obvious vortices occurredin the blade passage near tongue and will cause more losses
The static pressure distributions with different bladeoutlet widths in the cross section of impeller are comparedin Figure 11 It can be seen from the figure that the highpressure area always appears at the surface of blade outletpressure And also in the blade inlet suction surface the lowstatic pressure region can be observed With the increasingof the outlet width the low pressure areas become biggerwhich is consistent with the research results in [16] And thepressure value is lower at the impeller blade inlet suctionsurfaceWhen the outletwidth changes from 11mmto 16mmthe maximum value of the static pressure increases from2672 kpa to 2709 kpa while the minimum value of thestatic pressure increases from minus985 kpa to minus620 kpa Andthe differential pressure becomes bigger with the increase ofimpeller blade outlet width
Also the pressure distributions of the cross section withdifferent blade outlet widths at BEP are shown in Figure 12It can be found from Figure 12 that the pressure distribution
of the cross section at the blade inlet is quite different Whenthe blade outlet width is 16mm the lowpressure zone ismuchwider than that of the othersThe pressure distribution in theback chamber is similar to each other and the static pressureincreases gradually along the longitudinal direction From theabove analysis it can be found that great change happens atthe blade inlet which would have influence on the cavitationperformance
The turbulence kinetic energy contours in the crosssection of impeller are shown in Figure 13 It can be foundobviously that high turbulence kinetic energy exists in theregions of impeller inlet and outlet Particularly from Figures13(b) and 13(c) high turbulence kinetic energy can be foundfrom the blade passage near volute tongue from Figures10(b) and 10(c) disorganized surface streamline can be foundAnd both indicate that violent vortex and much more lossesexist in the blade passage near the volute tongue [17 18]When the outlet width changes from 11mm to 16mm themaximum value of turbulence kinetic energy increases from1247m2s2 to 1619m2s2 while the minimum value of theturbulence kinetic energy increases from 0002375m2s2 to0002846m2s2
8 Mathematical Problems in Engineering
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(a) 1198872 = 11mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(b) 1198872 = 13mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(c) 1198872 = 16mm
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
Description Parameter ValueDesign flow rate (Lmin) 119876des 340Head (m) 119867 15Rotational speed (rmin) 119899 3700Outlet width of impeller (mm) 1198872 16Inlet angle of blade (∘) 1205721 19Outlet angle of blade (∘) 1205722 30Wrap angle of blade (∘) 120572 65Number of blades 119885 7Inlet diameter of impeller (mm) 1198891 60Outlet diameter of impeller (mm) 1198892 98
Figure 3 Three-dimensional plot of impeller
3 Numerical Simulation
31 Calculation Model The computational domains includethree parts inlet section outlet section and impeller Allthese parts are completed in the Unigraphics NX softwareand are shown in Figure 4 The calculation is performed on aDell workstation with 2 processors (Windows 7 ProfessionalInter(R) Xeon(R) CPU 64 bit 333GHz and 48GB RAM)Considering the uncertainty about the empirical coefficientsof cavitation condensation and vaporization and maximumdensity ratio at the high temperature which can influencethe compressibility characteristics in the cavitation area andthe mass transfer between liquid and vapor [11] cavitationnumerical simulations at high temperature have a frustratingconvergence and lack of reliability So combined with thesimulation applicability and accuracy the multiphase flowwas numerically simulated in ECWP under 25∘C tempera-ture
32 Mesh Analysis The whole generation process of mesh iscarried out in ANSYS-ICEM software structure mesh wasapplied in computational domains mesh and the impellerdomain is refinedThemesh configuration of whole flow fieldis shown in Figure 5 specially the mesh at blade inlet and
Outlet section
Inlet section
Impeller
Figure 4 The domains of ECWP
volute tongue The mesh can be calculated in ANSYS-CFXfluently and the value of 119910+ is limited under 100 and was inaccordance with the turbulence model which was chosen asfollows
33 Turbulence Model In the condition of single phase tur-bulence models describe the effects of turbulent fluctuationsof velocities and scalar quantities no turbulence model canget satisfactory results for all applications So four turbulencemodels namely RNG 119896-Epsilon model 119896-Epsilon model 119896-Omega model and the shear stress transport model (SSTmodel) are selected to simulate the internal performanceof impeller with 16mm outlet width at standard runningconditions (119876des = 340 Lmin) By comparing numericalresults and the experimental one it can be found in Table 2that SST model is the best one that consists of experimentalresults So SST turbulence model is the most suitable modelfor hydraulic performance simulation
Moreover in the condition of multiphase flows thequantity of terms that need to be modeled in momentumequation is many which makes the modeling of turbulencein multiphase simulations extremely complex [12] So SSTturbulence model is chosen directly as the turbulent modelfor cavitation simulation
34 Governing Equations and Discretization Three steadynumerical simulations are conducted employing the timeaveraged Navier-Stokes equation and the SST turbulentmodel in ANSYS-CFX software The Navier-Stokes equationis solved by two-order accuracy upwind scheme and the fullyimplicit coupling algorithm based on finite volume methodin ANSYS-CFX software The advection terms are in high-resolution format and its convergence accuracy is set as 10minus4
35 Mesh Independence Analysis To reduce computationtime and improve accuracy the optimum quantity of meshelements in the simulation has been investigated Also headwas used as the evaluation indexes to judge mesh sizeFinally the least quantity of dependent mesh elements hasbeen obtained when head is obtained with negligible changeFigure 6 shows the dependency of results by comparingexternal characteristic with different element quantity at340 Lsdotminminus1 flow rate (Q)
4 Mathematical Problems in Engineering
Table 2 Numerical results with different turbulence models
Figure 6 Comparison of the head with different mesh elements
The quantity of mesh elements is the sum of elementsin impeller inlet pipe and outlet pipe Considering thecomputational ability of computer workstation used in thiswork the total mesh number of themesh is about 24millionAs demonstrated in Figure 6 when the quantity of meshelement is about 24 million the change of head is less than2 which indicates the convergence of mesh
Table 3 shows mesh quantity of the whole domains indifferent parts of pump
36 Cavitation Model The cavitation model is based onthe assumption that the water and vapor mixture in theflow can be perceived as a homogeneous fluid Cavitation
Table 3 Information of whole mesh statistics
Components Inlet section Impeller Outlet sectionQuantity of mesh elements 299970 1685215 353175Minimum orthogonal angle∘ 158 364 329
model is the mathematical model used to describe thetransformation between vapor phase and liquid phase Inthis study the Zwart-Gerber-Belamri cavitation model [13]based on Rayleigh-Plesset Equation in the transport equationmodel was selected The full phase mass per unit volumetransmission rate and void volume change rate are defined asfollows∙119898119891119892= 1198653119903119899119906119888 (1 minus 119903119892) 120588119892119877119861 (23
1003816100381610038161003816119901V minus 1199011003816100381610038161003816120588119891 )12
sgn (119901V minus 119901) d119881119861d119905 = d
where 119865 is an empirical coefficient 119877119861 represents the bubbleradius 119903119899119906119888 = 5 times 10minus4 119903119892 = 1 times 10minus6 119901V is the vaporizationpressure and119901 is the pressure of the liquid around the bubble119881119861 is bubble volume
37 Boundary Conditions The numerical simulation flowdomains are divided into two types stationary referenceframe and rotating reference frame And inlet section andoutlet section belong to the former while impeller is situatedin the latter The interface between the stationary reference
Mathematical Problems in Engineering 5
Vacuum pressure gaugeFlow meter
Electric control valveWater tank
Heating pipe
Inlet valve Test pump
Motor
Control valve
Pressure gaugePressure gauge
Figure 7 Closed experiment rig of ECWP
frame and the rotating one is set as frozen rotor Thespecified pitch angles are set as 360∘ and general grid interface(GGI) model is chosen to process data transmission betweenthe stationary and the rotating reference frame The inletboundary is set as absolute total pressure based on the zeroreference absolute pressure while the outlet boundary was setasmass flow rateThewall roughness is set as 125 120583m and thestandard wall function is chosen in the domain near the walland the wall no-slip boundary condition is set as adiabaticwall Meanwhile the volume fraction of water in inlet andbubble volume fraction is set as 1 and 0 respectively
In the simulation of the cavitation performance theoccurrence degree of cavitation was controlled by adjustingthe inlet total pressure the average bubble radius is set as2times10minus6mm and the vaporization pressure119901V is set as 3574 PaIn the simulation of the external characteristics themass flowrate is controlled by changing outlet boundary condition andthe other parameters are kept identical
4 Experimental Verification
41 Experimental Rigs andMethods The closed performanceexperiment rig of ECWP (shown in Figure 7) is set upto verify the accuracy of the numerical simulation whichprecedes the requirements of national standard (GB 3216-89 GB 1882-80 and QCT 2882-2001) The accuracy of theexperiment system is plusmn05
The experiment is performed according to ISO 9906which is the international experiment standard for pumpsThe experimental method and some facilities are the sameas the reference [14] The main technical parameters ofthe experiment bed are as follows rotational speed 119899 le8000 rmin water temperature 119879 le 120∘C and flow rate119876 le 400 Lmin Meanwhile the inlet and outlet pres-sure are measured separately by two pressure transmittersthat the error of measurement is less than 015 whilethe temperature is controlled by PID (Proportion IntegralDerivative) system Besides in order to draw the hydraulicperformance curves the outlet flow rate is adjusted to changethe working condition The flow rate is kept at the Q-BEP(340 Lmin) and the rotational speed is set as 3700 rminthen the inlet pressure is reduced slowly to stimulate thecavitation inception in the cavitation experiment
In the pump performance experiment net positive suc-tion head (NPSH) is defined as follows
NPSH = 119901119904120588119892 + V1199042
2119892 minus 119901V120588119892 (2)
where NPSH is the net positive suction head m 119901119904 is thetotal pressure of pump inlet Pa V119904 is the absolute velocity atinlet ms 119901V is the vaporization pressure for liquid Pa 120588 isthe destiny of water 120588 = 1000 kgm3 119892 is the gravitationalacceleration ratio 119892 = 98msminus2
42 Experimental Results and Analysis According to thedesigned three-dimensional model ECWP experimentalmodel (1198872 = 16mm) was processed into products andthen sent to have the hydraulic performance experimentThe hydraulic performance experiment was carried out with3700 rmin rotational speed and 25∘C temperature To gener-ate cavitation performance the inlet total pressure is variedprogressively by changing the valve opening while keepingthe flow rate and rotational speed remaining 340 Lmin and3700 rmin respectively The hydraulic and cavitation char-acteristic curves obtained by experimental and numericalsimulation were both shown in Figure 8
It can be seen from Figure 8 that the change trend innumerical simulation result is consistent with that in experi-mental result of both hydraulic and cavitation performanceBesides efficiency head and NPSH of numerical simulationare all slightly higher than that of experiment To be specificthe pump simulation efficiency is about 28 higher and thehead is about 2 higher than that of experiment at BEPNPSH is also about 033m higher than that of experimentat 3700 rmin rotational speed and 340 Lmin flow rate Tosum up the reliability of numerical simulation is verified bycomparing the results between experiment and numericalsimulation which indicates that the numerical calculation isthe effective method to predict the hydraulic and cavitationperformance of centrifugal pumps
5 Simulation Results and Discussions
51 Hydraulic Performance Hydraulic performance ofECWP with different blade outlet widths is obtained by
6 Mathematical Problems in Engineering
0 50 100 150 200 250 300 350 40002468
10121416182022
Q (Lmin)
0102030405060708090100
ExperimentSimulation
H (m
)
휂(
)
(a)
ExperimentSimulation
3 4 5 6 7 8 9 10 116789
101112131415161718
NPSH (m)
H (m
)
(b)
Figure 8 Comparison with hydraulic (a) and cavitation (b) performance
50 100 150 200 250 300 350 40002468
10121416182022
Flow rate Q (Lmin)
Hea
d H
(m)
0
10
20
30
40
50
60
70
80
90
100
Effici
ency
휂(
)
b2 = 11mm Hb2 = 13mm Hb2 = 16mm H
b2 = 11mm 휂b2 = 13mm 휂b2 = 16mm 휂
Figure 9 Hydraulic performance with different blade outlet widths
numerical simulation The head and efficiency are shown inFigure 9
According to the performance curves it can be foundthat head increases gradually along with the increase of bladeoutlet widthThe head function (6) can be obtained based onthe velocity triangle about blade outlet width with the sameflow rate Also its first derivative function is more than zeroso it is an increasing function Therefore head will increasewhen blade outlet width becomes larger
119867 = 1199062V1199062 minus 1199061V1199061119892 (3)
119867 = (11990622 minus 1199061V1199061119892 ) minus ( 119876119906211989212058711986321198872 tan120573)11198872
= 119860 minus 1198611198872 (119860 119861 gt 0)
(6)
Table 4 is the flow rate and pump efficiency at BEPwith different blade outlet widths When blade outlet widthchanges from 11mm and 13mm to 16mm BEP offsets tolarger flow rate Similar observation was also found in [6]The flow rate at BEP increased 877 and 968 respectivelyAlso there are some differences of efficiency in three cases atBEP Meanwhile with the blade outlet widths increases thehigh efficiency region (HEG) of ECWP is becoming largerAccording to (6) we know that its second derivative functionis less than zero So it is also a convex function In otherwords head becomes much more sensitive to the change ofblade outlet width when blade outlet width becomes largerAnd the range of blade outlet width is bigger near BEP
52 Discussion of Internal Flow The internal flow fields ofimpeller with three blade outlet widths are simulated at thesame flow condition Figure 10 is the surface streamline in thecross section of impeller with different blade outlet widthsFrom the pictures it can be found that the vortices appearedmainly in two areas blade passage near tongue and voluteoutlet Andwith the blade outlet width increases the vortex atvolute outlet becomes much more obvious and bigger which
Mathematical Problems in Engineering 7
Velocity (ms)1632e + 001
1225e + 001
8178e + 000
4109e + 000
4021e minus 002
(a) 1198872 = 11mm
Velocity (ms)1629e + 001
1228e + 001
8269e + 000
4260e + 000
2516e minus 001
(b) 1198872 = 13mm
Velocity (ms)1703e + 001
1281e + 001
8582e + 000
4356e + 000
1300e minus 001
(c) 1198872 = 16mm
Figure 10 Surface streamline in the cross section
has also been reported in [15] As a result of the interactionflow fields between impeller and tongue which can be seenfrom Figures 10(b) and 10(c) some obvious vortices occurredin the blade passage near tongue and will cause more losses
The static pressure distributions with different bladeoutlet widths in the cross section of impeller are comparedin Figure 11 It can be seen from the figure that the highpressure area always appears at the surface of blade outletpressure And also in the blade inlet suction surface the lowstatic pressure region can be observed With the increasingof the outlet width the low pressure areas become biggerwhich is consistent with the research results in [16] And thepressure value is lower at the impeller blade inlet suctionsurfaceWhen the outletwidth changes from 11mmto 16mmthe maximum value of the static pressure increases from2672 kpa to 2709 kpa while the minimum value of thestatic pressure increases from minus985 kpa to minus620 kpa Andthe differential pressure becomes bigger with the increase ofimpeller blade outlet width
Also the pressure distributions of the cross section withdifferent blade outlet widths at BEP are shown in Figure 12It can be found from Figure 12 that the pressure distribution
of the cross section at the blade inlet is quite different Whenthe blade outlet width is 16mm the lowpressure zone ismuchwider than that of the othersThe pressure distribution in theback chamber is similar to each other and the static pressureincreases gradually along the longitudinal direction From theabove analysis it can be found that great change happens atthe blade inlet which would have influence on the cavitationperformance
The turbulence kinetic energy contours in the crosssection of impeller are shown in Figure 13 It can be foundobviously that high turbulence kinetic energy exists in theregions of impeller inlet and outlet Particularly from Figures13(b) and 13(c) high turbulence kinetic energy can be foundfrom the blade passage near volute tongue from Figures10(b) and 10(c) disorganized surface streamline can be foundAnd both indicate that violent vortex and much more lossesexist in the blade passage near the volute tongue [17 18]When the outlet width changes from 11mm to 16mm themaximum value of turbulence kinetic energy increases from1247m2s2 to 1619m2s2 while the minimum value of theturbulence kinetic energy increases from 0002375m2s2 to0002846m2s2
8 Mathematical Problems in Engineering
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(a) 1198872 = 11mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(b) 1198872 = 13mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(c) 1198872 = 16mm
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
Figure 6 Comparison of the head with different mesh elements
The quantity of mesh elements is the sum of elementsin impeller inlet pipe and outlet pipe Considering thecomputational ability of computer workstation used in thiswork the total mesh number of themesh is about 24millionAs demonstrated in Figure 6 when the quantity of meshelement is about 24 million the change of head is less than2 which indicates the convergence of mesh
Table 3 shows mesh quantity of the whole domains indifferent parts of pump
36 Cavitation Model The cavitation model is based onthe assumption that the water and vapor mixture in theflow can be perceived as a homogeneous fluid Cavitation
Table 3 Information of whole mesh statistics
Components Inlet section Impeller Outlet sectionQuantity of mesh elements 299970 1685215 353175Minimum orthogonal angle∘ 158 364 329
model is the mathematical model used to describe thetransformation between vapor phase and liquid phase Inthis study the Zwart-Gerber-Belamri cavitation model [13]based on Rayleigh-Plesset Equation in the transport equationmodel was selected The full phase mass per unit volumetransmission rate and void volume change rate are defined asfollows∙119898119891119892= 1198653119903119899119906119888 (1 minus 119903119892) 120588119892119877119861 (23
1003816100381610038161003816119901V minus 1199011003816100381610038161003816120588119891 )12
sgn (119901V minus 119901) d119881119861d119905 = d
where 119865 is an empirical coefficient 119877119861 represents the bubbleradius 119903119899119906119888 = 5 times 10minus4 119903119892 = 1 times 10minus6 119901V is the vaporizationpressure and119901 is the pressure of the liquid around the bubble119881119861 is bubble volume
37 Boundary Conditions The numerical simulation flowdomains are divided into two types stationary referenceframe and rotating reference frame And inlet section andoutlet section belong to the former while impeller is situatedin the latter The interface between the stationary reference
Mathematical Problems in Engineering 5
Vacuum pressure gaugeFlow meter
Electric control valveWater tank
Heating pipe
Inlet valve Test pump
Motor
Control valve
Pressure gaugePressure gauge
Figure 7 Closed experiment rig of ECWP
frame and the rotating one is set as frozen rotor Thespecified pitch angles are set as 360∘ and general grid interface(GGI) model is chosen to process data transmission betweenthe stationary and the rotating reference frame The inletboundary is set as absolute total pressure based on the zeroreference absolute pressure while the outlet boundary was setasmass flow rateThewall roughness is set as 125 120583m and thestandard wall function is chosen in the domain near the walland the wall no-slip boundary condition is set as adiabaticwall Meanwhile the volume fraction of water in inlet andbubble volume fraction is set as 1 and 0 respectively
In the simulation of the cavitation performance theoccurrence degree of cavitation was controlled by adjustingthe inlet total pressure the average bubble radius is set as2times10minus6mm and the vaporization pressure119901V is set as 3574 PaIn the simulation of the external characteristics themass flowrate is controlled by changing outlet boundary condition andthe other parameters are kept identical
4 Experimental Verification
41 Experimental Rigs andMethods The closed performanceexperiment rig of ECWP (shown in Figure 7) is set upto verify the accuracy of the numerical simulation whichprecedes the requirements of national standard (GB 3216-89 GB 1882-80 and QCT 2882-2001) The accuracy of theexperiment system is plusmn05
The experiment is performed according to ISO 9906which is the international experiment standard for pumpsThe experimental method and some facilities are the sameas the reference [14] The main technical parameters ofthe experiment bed are as follows rotational speed 119899 le8000 rmin water temperature 119879 le 120∘C and flow rate119876 le 400 Lmin Meanwhile the inlet and outlet pres-sure are measured separately by two pressure transmittersthat the error of measurement is less than 015 whilethe temperature is controlled by PID (Proportion IntegralDerivative) system Besides in order to draw the hydraulicperformance curves the outlet flow rate is adjusted to changethe working condition The flow rate is kept at the Q-BEP(340 Lmin) and the rotational speed is set as 3700 rminthen the inlet pressure is reduced slowly to stimulate thecavitation inception in the cavitation experiment
In the pump performance experiment net positive suc-tion head (NPSH) is defined as follows
NPSH = 119901119904120588119892 + V1199042
2119892 minus 119901V120588119892 (2)
where NPSH is the net positive suction head m 119901119904 is thetotal pressure of pump inlet Pa V119904 is the absolute velocity atinlet ms 119901V is the vaporization pressure for liquid Pa 120588 isthe destiny of water 120588 = 1000 kgm3 119892 is the gravitationalacceleration ratio 119892 = 98msminus2
42 Experimental Results and Analysis According to thedesigned three-dimensional model ECWP experimentalmodel (1198872 = 16mm) was processed into products andthen sent to have the hydraulic performance experimentThe hydraulic performance experiment was carried out with3700 rmin rotational speed and 25∘C temperature To gener-ate cavitation performance the inlet total pressure is variedprogressively by changing the valve opening while keepingthe flow rate and rotational speed remaining 340 Lmin and3700 rmin respectively The hydraulic and cavitation char-acteristic curves obtained by experimental and numericalsimulation were both shown in Figure 8
It can be seen from Figure 8 that the change trend innumerical simulation result is consistent with that in experi-mental result of both hydraulic and cavitation performanceBesides efficiency head and NPSH of numerical simulationare all slightly higher than that of experiment To be specificthe pump simulation efficiency is about 28 higher and thehead is about 2 higher than that of experiment at BEPNPSH is also about 033m higher than that of experimentat 3700 rmin rotational speed and 340 Lmin flow rate Tosum up the reliability of numerical simulation is verified bycomparing the results between experiment and numericalsimulation which indicates that the numerical calculation isthe effective method to predict the hydraulic and cavitationperformance of centrifugal pumps
5 Simulation Results and Discussions
51 Hydraulic Performance Hydraulic performance ofECWP with different blade outlet widths is obtained by
6 Mathematical Problems in Engineering
0 50 100 150 200 250 300 350 40002468
10121416182022
Q (Lmin)
0102030405060708090100
ExperimentSimulation
H (m
)
휂(
)
(a)
ExperimentSimulation
3 4 5 6 7 8 9 10 116789
101112131415161718
NPSH (m)
H (m
)
(b)
Figure 8 Comparison with hydraulic (a) and cavitation (b) performance
50 100 150 200 250 300 350 40002468
10121416182022
Flow rate Q (Lmin)
Hea
d H
(m)
0
10
20
30
40
50
60
70
80
90
100
Effici
ency
휂(
)
b2 = 11mm Hb2 = 13mm Hb2 = 16mm H
b2 = 11mm 휂b2 = 13mm 휂b2 = 16mm 휂
Figure 9 Hydraulic performance with different blade outlet widths
numerical simulation The head and efficiency are shown inFigure 9
According to the performance curves it can be foundthat head increases gradually along with the increase of bladeoutlet widthThe head function (6) can be obtained based onthe velocity triangle about blade outlet width with the sameflow rate Also its first derivative function is more than zeroso it is an increasing function Therefore head will increasewhen blade outlet width becomes larger
119867 = 1199062V1199062 minus 1199061V1199061119892 (3)
119867 = (11990622 minus 1199061V1199061119892 ) minus ( 119876119906211989212058711986321198872 tan120573)11198872
= 119860 minus 1198611198872 (119860 119861 gt 0)
(6)
Table 4 is the flow rate and pump efficiency at BEPwith different blade outlet widths When blade outlet widthchanges from 11mm and 13mm to 16mm BEP offsets tolarger flow rate Similar observation was also found in [6]The flow rate at BEP increased 877 and 968 respectivelyAlso there are some differences of efficiency in three cases atBEP Meanwhile with the blade outlet widths increases thehigh efficiency region (HEG) of ECWP is becoming largerAccording to (6) we know that its second derivative functionis less than zero So it is also a convex function In otherwords head becomes much more sensitive to the change ofblade outlet width when blade outlet width becomes largerAnd the range of blade outlet width is bigger near BEP
52 Discussion of Internal Flow The internal flow fields ofimpeller with three blade outlet widths are simulated at thesame flow condition Figure 10 is the surface streamline in thecross section of impeller with different blade outlet widthsFrom the pictures it can be found that the vortices appearedmainly in two areas blade passage near tongue and voluteoutlet Andwith the blade outlet width increases the vortex atvolute outlet becomes much more obvious and bigger which
Mathematical Problems in Engineering 7
Velocity (ms)1632e + 001
1225e + 001
8178e + 000
4109e + 000
4021e minus 002
(a) 1198872 = 11mm
Velocity (ms)1629e + 001
1228e + 001
8269e + 000
4260e + 000
2516e minus 001
(b) 1198872 = 13mm
Velocity (ms)1703e + 001
1281e + 001
8582e + 000
4356e + 000
1300e minus 001
(c) 1198872 = 16mm
Figure 10 Surface streamline in the cross section
has also been reported in [15] As a result of the interactionflow fields between impeller and tongue which can be seenfrom Figures 10(b) and 10(c) some obvious vortices occurredin the blade passage near tongue and will cause more losses
The static pressure distributions with different bladeoutlet widths in the cross section of impeller are comparedin Figure 11 It can be seen from the figure that the highpressure area always appears at the surface of blade outletpressure And also in the blade inlet suction surface the lowstatic pressure region can be observed With the increasingof the outlet width the low pressure areas become biggerwhich is consistent with the research results in [16] And thepressure value is lower at the impeller blade inlet suctionsurfaceWhen the outletwidth changes from 11mmto 16mmthe maximum value of the static pressure increases from2672 kpa to 2709 kpa while the minimum value of thestatic pressure increases from minus985 kpa to minus620 kpa Andthe differential pressure becomes bigger with the increase ofimpeller blade outlet width
Also the pressure distributions of the cross section withdifferent blade outlet widths at BEP are shown in Figure 12It can be found from Figure 12 that the pressure distribution
of the cross section at the blade inlet is quite different Whenthe blade outlet width is 16mm the lowpressure zone ismuchwider than that of the othersThe pressure distribution in theback chamber is similar to each other and the static pressureincreases gradually along the longitudinal direction From theabove analysis it can be found that great change happens atthe blade inlet which would have influence on the cavitationperformance
The turbulence kinetic energy contours in the crosssection of impeller are shown in Figure 13 It can be foundobviously that high turbulence kinetic energy exists in theregions of impeller inlet and outlet Particularly from Figures13(b) and 13(c) high turbulence kinetic energy can be foundfrom the blade passage near volute tongue from Figures10(b) and 10(c) disorganized surface streamline can be foundAnd both indicate that violent vortex and much more lossesexist in the blade passage near the volute tongue [17 18]When the outlet width changes from 11mm to 16mm themaximum value of turbulence kinetic energy increases from1247m2s2 to 1619m2s2 while the minimum value of theturbulence kinetic energy increases from 0002375m2s2 to0002846m2s2
8 Mathematical Problems in Engineering
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(a) 1198872 = 11mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(b) 1198872 = 13mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(c) 1198872 = 16mm
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
frame and the rotating one is set as frozen rotor Thespecified pitch angles are set as 360∘ and general grid interface(GGI) model is chosen to process data transmission betweenthe stationary and the rotating reference frame The inletboundary is set as absolute total pressure based on the zeroreference absolute pressure while the outlet boundary was setasmass flow rateThewall roughness is set as 125 120583m and thestandard wall function is chosen in the domain near the walland the wall no-slip boundary condition is set as adiabaticwall Meanwhile the volume fraction of water in inlet andbubble volume fraction is set as 1 and 0 respectively
In the simulation of the cavitation performance theoccurrence degree of cavitation was controlled by adjustingthe inlet total pressure the average bubble radius is set as2times10minus6mm and the vaporization pressure119901V is set as 3574 PaIn the simulation of the external characteristics themass flowrate is controlled by changing outlet boundary condition andthe other parameters are kept identical
4 Experimental Verification
41 Experimental Rigs andMethods The closed performanceexperiment rig of ECWP (shown in Figure 7) is set upto verify the accuracy of the numerical simulation whichprecedes the requirements of national standard (GB 3216-89 GB 1882-80 and QCT 2882-2001) The accuracy of theexperiment system is plusmn05
The experiment is performed according to ISO 9906which is the international experiment standard for pumpsThe experimental method and some facilities are the sameas the reference [14] The main technical parameters ofthe experiment bed are as follows rotational speed 119899 le8000 rmin water temperature 119879 le 120∘C and flow rate119876 le 400 Lmin Meanwhile the inlet and outlet pres-sure are measured separately by two pressure transmittersthat the error of measurement is less than 015 whilethe temperature is controlled by PID (Proportion IntegralDerivative) system Besides in order to draw the hydraulicperformance curves the outlet flow rate is adjusted to changethe working condition The flow rate is kept at the Q-BEP(340 Lmin) and the rotational speed is set as 3700 rminthen the inlet pressure is reduced slowly to stimulate thecavitation inception in the cavitation experiment
In the pump performance experiment net positive suc-tion head (NPSH) is defined as follows
NPSH = 119901119904120588119892 + V1199042
2119892 minus 119901V120588119892 (2)
where NPSH is the net positive suction head m 119901119904 is thetotal pressure of pump inlet Pa V119904 is the absolute velocity atinlet ms 119901V is the vaporization pressure for liquid Pa 120588 isthe destiny of water 120588 = 1000 kgm3 119892 is the gravitationalacceleration ratio 119892 = 98msminus2
42 Experimental Results and Analysis According to thedesigned three-dimensional model ECWP experimentalmodel (1198872 = 16mm) was processed into products andthen sent to have the hydraulic performance experimentThe hydraulic performance experiment was carried out with3700 rmin rotational speed and 25∘C temperature To gener-ate cavitation performance the inlet total pressure is variedprogressively by changing the valve opening while keepingthe flow rate and rotational speed remaining 340 Lmin and3700 rmin respectively The hydraulic and cavitation char-acteristic curves obtained by experimental and numericalsimulation were both shown in Figure 8
It can be seen from Figure 8 that the change trend innumerical simulation result is consistent with that in experi-mental result of both hydraulic and cavitation performanceBesides efficiency head and NPSH of numerical simulationare all slightly higher than that of experiment To be specificthe pump simulation efficiency is about 28 higher and thehead is about 2 higher than that of experiment at BEPNPSH is also about 033m higher than that of experimentat 3700 rmin rotational speed and 340 Lmin flow rate Tosum up the reliability of numerical simulation is verified bycomparing the results between experiment and numericalsimulation which indicates that the numerical calculation isthe effective method to predict the hydraulic and cavitationperformance of centrifugal pumps
5 Simulation Results and Discussions
51 Hydraulic Performance Hydraulic performance ofECWP with different blade outlet widths is obtained by
6 Mathematical Problems in Engineering
0 50 100 150 200 250 300 350 40002468
10121416182022
Q (Lmin)
0102030405060708090100
ExperimentSimulation
H (m
)
휂(
)
(a)
ExperimentSimulation
3 4 5 6 7 8 9 10 116789
101112131415161718
NPSH (m)
H (m
)
(b)
Figure 8 Comparison with hydraulic (a) and cavitation (b) performance
50 100 150 200 250 300 350 40002468
10121416182022
Flow rate Q (Lmin)
Hea
d H
(m)
0
10
20
30
40
50
60
70
80
90
100
Effici
ency
휂(
)
b2 = 11mm Hb2 = 13mm Hb2 = 16mm H
b2 = 11mm 휂b2 = 13mm 휂b2 = 16mm 휂
Figure 9 Hydraulic performance with different blade outlet widths
numerical simulation The head and efficiency are shown inFigure 9
According to the performance curves it can be foundthat head increases gradually along with the increase of bladeoutlet widthThe head function (6) can be obtained based onthe velocity triangle about blade outlet width with the sameflow rate Also its first derivative function is more than zeroso it is an increasing function Therefore head will increasewhen blade outlet width becomes larger
119867 = 1199062V1199062 minus 1199061V1199061119892 (3)
119867 = (11990622 minus 1199061V1199061119892 ) minus ( 119876119906211989212058711986321198872 tan120573)11198872
= 119860 minus 1198611198872 (119860 119861 gt 0)
(6)
Table 4 is the flow rate and pump efficiency at BEPwith different blade outlet widths When blade outlet widthchanges from 11mm and 13mm to 16mm BEP offsets tolarger flow rate Similar observation was also found in [6]The flow rate at BEP increased 877 and 968 respectivelyAlso there are some differences of efficiency in three cases atBEP Meanwhile with the blade outlet widths increases thehigh efficiency region (HEG) of ECWP is becoming largerAccording to (6) we know that its second derivative functionis less than zero So it is also a convex function In otherwords head becomes much more sensitive to the change ofblade outlet width when blade outlet width becomes largerAnd the range of blade outlet width is bigger near BEP
52 Discussion of Internal Flow The internal flow fields ofimpeller with three blade outlet widths are simulated at thesame flow condition Figure 10 is the surface streamline in thecross section of impeller with different blade outlet widthsFrom the pictures it can be found that the vortices appearedmainly in two areas blade passage near tongue and voluteoutlet Andwith the blade outlet width increases the vortex atvolute outlet becomes much more obvious and bigger which
Mathematical Problems in Engineering 7
Velocity (ms)1632e + 001
1225e + 001
8178e + 000
4109e + 000
4021e minus 002
(a) 1198872 = 11mm
Velocity (ms)1629e + 001
1228e + 001
8269e + 000
4260e + 000
2516e minus 001
(b) 1198872 = 13mm
Velocity (ms)1703e + 001
1281e + 001
8582e + 000
4356e + 000
1300e minus 001
(c) 1198872 = 16mm
Figure 10 Surface streamline in the cross section
has also been reported in [15] As a result of the interactionflow fields between impeller and tongue which can be seenfrom Figures 10(b) and 10(c) some obvious vortices occurredin the blade passage near tongue and will cause more losses
The static pressure distributions with different bladeoutlet widths in the cross section of impeller are comparedin Figure 11 It can be seen from the figure that the highpressure area always appears at the surface of blade outletpressure And also in the blade inlet suction surface the lowstatic pressure region can be observed With the increasingof the outlet width the low pressure areas become biggerwhich is consistent with the research results in [16] And thepressure value is lower at the impeller blade inlet suctionsurfaceWhen the outletwidth changes from 11mmto 16mmthe maximum value of the static pressure increases from2672 kpa to 2709 kpa while the minimum value of thestatic pressure increases from minus985 kpa to minus620 kpa Andthe differential pressure becomes bigger with the increase ofimpeller blade outlet width
Also the pressure distributions of the cross section withdifferent blade outlet widths at BEP are shown in Figure 12It can be found from Figure 12 that the pressure distribution
of the cross section at the blade inlet is quite different Whenthe blade outlet width is 16mm the lowpressure zone ismuchwider than that of the othersThe pressure distribution in theback chamber is similar to each other and the static pressureincreases gradually along the longitudinal direction From theabove analysis it can be found that great change happens atthe blade inlet which would have influence on the cavitationperformance
The turbulence kinetic energy contours in the crosssection of impeller are shown in Figure 13 It can be foundobviously that high turbulence kinetic energy exists in theregions of impeller inlet and outlet Particularly from Figures13(b) and 13(c) high turbulence kinetic energy can be foundfrom the blade passage near volute tongue from Figures10(b) and 10(c) disorganized surface streamline can be foundAnd both indicate that violent vortex and much more lossesexist in the blade passage near the volute tongue [17 18]When the outlet width changes from 11mm to 16mm themaximum value of turbulence kinetic energy increases from1247m2s2 to 1619m2s2 while the minimum value of theturbulence kinetic energy increases from 0002375m2s2 to0002846m2s2
8 Mathematical Problems in Engineering
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(a) 1198872 = 11mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(b) 1198872 = 13mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(c) 1198872 = 16mm
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
Figure 8 Comparison with hydraulic (a) and cavitation (b) performance
50 100 150 200 250 300 350 40002468
10121416182022
Flow rate Q (Lmin)
Hea
d H
(m)
0
10
20
30
40
50
60
70
80
90
100
Effici
ency
휂(
)
b2 = 11mm Hb2 = 13mm Hb2 = 16mm H
b2 = 11mm 휂b2 = 13mm 휂b2 = 16mm 휂
Figure 9 Hydraulic performance with different blade outlet widths
numerical simulation The head and efficiency are shown inFigure 9
According to the performance curves it can be foundthat head increases gradually along with the increase of bladeoutlet widthThe head function (6) can be obtained based onthe velocity triangle about blade outlet width with the sameflow rate Also its first derivative function is more than zeroso it is an increasing function Therefore head will increasewhen blade outlet width becomes larger
119867 = 1199062V1199062 minus 1199061V1199061119892 (3)
119867 = (11990622 minus 1199061V1199061119892 ) minus ( 119876119906211989212058711986321198872 tan120573)11198872
= 119860 minus 1198611198872 (119860 119861 gt 0)
(6)
Table 4 is the flow rate and pump efficiency at BEPwith different blade outlet widths When blade outlet widthchanges from 11mm and 13mm to 16mm BEP offsets tolarger flow rate Similar observation was also found in [6]The flow rate at BEP increased 877 and 968 respectivelyAlso there are some differences of efficiency in three cases atBEP Meanwhile with the blade outlet widths increases thehigh efficiency region (HEG) of ECWP is becoming largerAccording to (6) we know that its second derivative functionis less than zero So it is also a convex function In otherwords head becomes much more sensitive to the change ofblade outlet width when blade outlet width becomes largerAnd the range of blade outlet width is bigger near BEP
52 Discussion of Internal Flow The internal flow fields ofimpeller with three blade outlet widths are simulated at thesame flow condition Figure 10 is the surface streamline in thecross section of impeller with different blade outlet widthsFrom the pictures it can be found that the vortices appearedmainly in two areas blade passage near tongue and voluteoutlet Andwith the blade outlet width increases the vortex atvolute outlet becomes much more obvious and bigger which
Mathematical Problems in Engineering 7
Velocity (ms)1632e + 001
1225e + 001
8178e + 000
4109e + 000
4021e minus 002
(a) 1198872 = 11mm
Velocity (ms)1629e + 001
1228e + 001
8269e + 000
4260e + 000
2516e minus 001
(b) 1198872 = 13mm
Velocity (ms)1703e + 001
1281e + 001
8582e + 000
4356e + 000
1300e minus 001
(c) 1198872 = 16mm
Figure 10 Surface streamline in the cross section
has also been reported in [15] As a result of the interactionflow fields between impeller and tongue which can be seenfrom Figures 10(b) and 10(c) some obvious vortices occurredin the blade passage near tongue and will cause more losses
The static pressure distributions with different bladeoutlet widths in the cross section of impeller are comparedin Figure 11 It can be seen from the figure that the highpressure area always appears at the surface of blade outletpressure And also in the blade inlet suction surface the lowstatic pressure region can be observed With the increasingof the outlet width the low pressure areas become biggerwhich is consistent with the research results in [16] And thepressure value is lower at the impeller blade inlet suctionsurfaceWhen the outletwidth changes from 11mmto 16mmthe maximum value of the static pressure increases from2672 kpa to 2709 kpa while the minimum value of thestatic pressure increases from minus985 kpa to minus620 kpa Andthe differential pressure becomes bigger with the increase ofimpeller blade outlet width
Also the pressure distributions of the cross section withdifferent blade outlet widths at BEP are shown in Figure 12It can be found from Figure 12 that the pressure distribution
of the cross section at the blade inlet is quite different Whenthe blade outlet width is 16mm the lowpressure zone ismuchwider than that of the othersThe pressure distribution in theback chamber is similar to each other and the static pressureincreases gradually along the longitudinal direction From theabove analysis it can be found that great change happens atthe blade inlet which would have influence on the cavitationperformance
The turbulence kinetic energy contours in the crosssection of impeller are shown in Figure 13 It can be foundobviously that high turbulence kinetic energy exists in theregions of impeller inlet and outlet Particularly from Figures13(b) and 13(c) high turbulence kinetic energy can be foundfrom the blade passage near volute tongue from Figures10(b) and 10(c) disorganized surface streamline can be foundAnd both indicate that violent vortex and much more lossesexist in the blade passage near the volute tongue [17 18]When the outlet width changes from 11mm to 16mm themaximum value of turbulence kinetic energy increases from1247m2s2 to 1619m2s2 while the minimum value of theturbulence kinetic energy increases from 0002375m2s2 to0002846m2s2
8 Mathematical Problems in Engineering
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(a) 1198872 = 11mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(b) 1198872 = 13mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(c) 1198872 = 16mm
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
has also been reported in [15] As a result of the interactionflow fields between impeller and tongue which can be seenfrom Figures 10(b) and 10(c) some obvious vortices occurredin the blade passage near tongue and will cause more losses
The static pressure distributions with different bladeoutlet widths in the cross section of impeller are comparedin Figure 11 It can be seen from the figure that the highpressure area always appears at the surface of blade outletpressure And also in the blade inlet suction surface the lowstatic pressure region can be observed With the increasingof the outlet width the low pressure areas become biggerwhich is consistent with the research results in [16] And thepressure value is lower at the impeller blade inlet suctionsurfaceWhen the outletwidth changes from 11mmto 16mmthe maximum value of the static pressure increases from2672 kpa to 2709 kpa while the minimum value of thestatic pressure increases from minus985 kpa to minus620 kpa Andthe differential pressure becomes bigger with the increase ofimpeller blade outlet width
Also the pressure distributions of the cross section withdifferent blade outlet widths at BEP are shown in Figure 12It can be found from Figure 12 that the pressure distribution
of the cross section at the blade inlet is quite different Whenthe blade outlet width is 16mm the lowpressure zone ismuchwider than that of the othersThe pressure distribution in theback chamber is similar to each other and the static pressureincreases gradually along the longitudinal direction From theabove analysis it can be found that great change happens atthe blade inlet which would have influence on the cavitationperformance
The turbulence kinetic energy contours in the crosssection of impeller are shown in Figure 13 It can be foundobviously that high turbulence kinetic energy exists in theregions of impeller inlet and outlet Particularly from Figures13(b) and 13(c) high turbulence kinetic energy can be foundfrom the blade passage near volute tongue from Figures10(b) and 10(c) disorganized surface streamline can be foundAnd both indicate that violent vortex and much more lossesexist in the blade passage near the volute tongue [17 18]When the outlet width changes from 11mm to 16mm themaximum value of turbulence kinetic energy increases from1247m2s2 to 1619m2s2 while the minimum value of theturbulence kinetic energy increases from 0002375m2s2 to0002846m2s2
8 Mathematical Problems in Engineering
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(a) 1198872 = 11mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(b) 1198872 = 13mm
Pressure (Pa)2662e + 005
2410e + 005
2159e + 005
1907e + 005
1655e + 005
1404e + 005
1152e + 005
9001e + 004
6484e + 004
3967e + 004
1450e + 004
(c) 1198872 = 16mm
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
Figure 11 Static pressure distribution in the cross section
Pressure (Pa)2620e + 005
2358e + 005
2096e + 005
1834e + 005
1572e + 005
1310e + 005
1048e + 004
7860e + 004
5240e + 004
2620e + 004
1450e minus 002b2 = 11mm b2 = 13mm b2 = 16mm
Figure 12 Pressure distribution between the pump casing and impeller hub
Mathematical Problems in Engineering 9
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(a) 1198872 = 11mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(b) 1198872 = 13mm
1000e + 001
9010e + 000
8020e + 000
7030e + 000
6040e + 000
5050e + 000
4060e + 000
3070e + 000
2080e + 000
1090e + 000
1000e minus 001
Turbulence kineticenergy (m2s2)
(c) 1198872 = 16mm
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
Figure 13 Turbulence kinetic energy contours in the cross section
53 Cavitation Performance at BEP The cavitation perfor-mance at BEP with different blade outlet widths is numeri-cally simulated and is shown in Figure 14The results indicatethat the cavitation in ECWP has a significant influence onhead especially in the period of cavitation developmentwhich always causes a large loss of head
From the cavitation performance the critical point ofcavitation is marked by the NPSH at which the head hasfallen by 3 The critical cavitation pressure increases withthe increase of blade outlet width It can be seen fromFigure 14 that when blade outlet width is 11mm 13mm and16mm the critical cavitation pressure is respectively about337 kPa 354 kPa and 378 kPa among them 11mm outletwidth has the smallest critical cavitation pressure That isto say cavitation performance of the 11mm impeller is theoptimal one The analysis results are also consistent withthe conclusion that BEP offsets to larger flow rate becausecavitation of centrifugal pump becomes worse at the highflow rate conditions
3 4 5 6 7 8 9 10 116789
101112131415161718
H (m
)
NPSH (m)
160
414
96
146
1
11mm (CFD)13mm (CFD)16mm (CFD)
Figure 14 Cavitation performance with different blade outletwidths at BEP
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
Figure 15 10 bubble volume concentration distribution of the three impeller models
54 Bubble Volume Distribution at BEP Bubbles the directproduct of cavitation are broken suddenly after moving intothe high pressure areas which will cause cavitation damagesuch as shortening the ECWP reliability and producingvibration and noise Figure 15 shows 10 bubble volume con-centration distribution of three pump models with differentblade outlet widths at the same inlet total pressure
From Figure 15 it can be found that the bubble vol-ume concentration in impeller gradually increases with theincrease of the blade outlet width Furthermore 11mmimpeller has the latest experiment and smallest bubble areawhich proves that the cavitation performance of the impellerwith 11mm impeller is better than others and the analysisresults are also consistent with the cavitation performancecurves
6 Conclusion
In this study the numerical calculation reliability is validatedwhich indicates that the numerical calculation is the effectivemethod to predict the hydraulic and cavitation performanceof centrifugal pumps
It is an important way to adjust the performance curvesof centrifugal pump by changing the blade outlet widthWiththe increase of blade outlet width head of ECWP increasesgradually and BEP offsets to larger flow rate and the highefficiency region (HER) is becoming larger while there is asmall change in the efficiency at BEP
The internal flow in ECWP is extremely complex Vortexappeared mainly in the blade passage near the tongue andvolute outlet the low static pressure is located in the surface ofblade inlet suction while the high turbulence kinetic energyregions are located in inlet and outlet of impeller Meanwhileat the same flow rate as the blade outlet width increases thearea of vortex and low static pressure becomes obvious andbigger
The impeller with different blade outlet widths has itsown BEP at the same rotational speed From 11mm to13mm and 16mm of blade outlet width the bubble volumeconcentration in the impeller gradually increases at the sameinlet absolute pressure and the critical cavitation pressure of
the investigated ECWP is also increased which are consistentwith the conclusion that BEP offsets to larger flow ratebecause cavitation of centrifugal pump becomes worse at thehigh flow rate conditions
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (no 51409127) PAPD Six TalentsPeak Project of Jiangsu Province (no HYZB-002) KeyResearch andDevelopment Projects of Jiangsu Province (nosBE2015119 and BE2015001-4) the Natural Science Founda-tion of Jiangsu Province (no BK20161472) and ScientificResearch Start Foundation Project of Jiangsu University (no13JDG105)
References
[1] W Shi B Pei W Lu C Wang and W Li ldquoOptimization ofautomobile pump based on CFDrdquo Journal of Drainage andIrrigation Machinery Engineering vol 31 no 1 pp 15ndash19 2013
[2] T-T Liu T Wang B Yang and C-G Gu ldquoNumerical simu-lation and structure improvement for a car pump with openedcentrifugal impellerrdquo Journal of EngineeringThermophysics vol30 no 6 pp 961ndash963 2009
[3] W Li W-D Shi B Pei H Zhang and W-G Lu ldquoNumericalsimulation and improvement on cavitation performance ofengine cooling water pumprdquo Transactions of CSICE vol 31 no2 pp 165ndash170 2013
[4] W Li W Shi H Zhang B Pei and W Lu ldquoCavitation perfor-mance prediction of engine coolingwater pump based onCFDrdquoJournal of Drainage and Irrigation Machinery Engineering vol30 no 2 pp 176ndash180 2012
[5] N Liao and D Xie ldquoDiscussion on the pump cavitation inLJ465Q Seriesrdquo Engine Equipment Manufacturing Technologyvol 02 pp 177ndash179 2010
Mathematical Problems in Engineering 11
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
[6] W Shi L Zhou W Lu B Pei and T Lang ldquoNumerical pre-diction and performance experiment in a deep-well centrifugalpump with different impeller outlet widthrdquo Chinese Journal ofMechanical Engineering vol 26 no 1 pp 46ndash52 2013
[7] P Song Y Zhang C Xu X Zhou and J Zhang ldquoNumericalstudies on cavitation behavior in impeller of centrifugal pumpwith different blade profilesrdquo International Journal of FluidMachinery and Systems vol 8 no 2 pp 94ndash101 2015
[8] S Zhang R Zhang S Zhang and J Yang ldquoEffect of impellerinlet geometry on cavitation performance of centrifugal pumpsbased on radial basis functionrdquo International Journal of RotatingMachinery vol 2016 Article ID 6048263 9 pages 2016
[9] H Liu YWang and SQ Yuan ldquoEffects of impeller outlet widthon the vibration and noise from centrifugal pumps induced byflowrdquo Journal of Huazhong University of Science and Technologyvol 40 no 1 pp 123ndash127 2012
[10] H Liu J Ding M Tan J Cui and Y Wang ldquoAnalysis andexperimental of centrifugal pump noise based on outlet widthof impellerrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 29 no 16 pp 66ndash73 2013
[11] B Ji X Luo Y Wu X Peng and Y Duan ldquoNumerical analysisof unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoilrdquo InternationalJournal of Multiphase Flow vol 51 pp 33ndash43 2013
[12] E Goncalves and B Charriere ldquoModelling for isothermalcavitation with a four-equation modelrdquo International Journal ofMultiphase Flow vol 59 pp 54ndash72 2014
[13] J Philip A G G Zwart and T A Belamri ldquoTwo-phase flowmodel for predicting cavitation dynamicsrdquo in Proceedings of theInternational Conference onMultiphase Flow Yokohama Japan2004
[14] T812662 Internal Combustion Engine Cooling Water PumpsPart 2 Assemblies and Test Methods China Machine PressBeijing China 2010
[15] Z Weihua The study of water pump with high efficiency for themotor [PhD thesis] Tsinghua University Beijing China 2011
[16] Z Tingting Y Shouqi L Jianrui Z Jinfeng and P BingldquoImpact of impeller parameters on performance of an automo-bile cooling pumprdquo Chinese Journal of Automotive Engineeringvol 3 no 2 pp 100ndash105 2013
[17] J F Gulich Centrifugal Pumps vol 5 Springer Berlin Ger-many 2014
[18] Y Z Chen Z Y Cao G Q Deng and H M Huang PumpHandbook China Petrochemical Beijing China 3rd edition2003
