Effects of the Splitter Blade on the Performance of a Pump...

Research ArticleEffects of the Splitter Blade on the Performance ofa Pump-Turbine in Pump Mode

Guidong Li YangWang Puyu Cao Jinfeng Zhang and JieyunMao

National Research Center of Pumps Jiangsu University Zhenjiang 212013 Jiangsu China

Correspondence should be addressed to Guidong Li liguidong1201163com

Received 12 June 2018 Revised 4 August 2018 Accepted 27 September 2018 Published 11 October 2018

Academic Editor Zhengbiao Peng

Copyright copy 2018 Guidong Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The pumped hydro energy storage is the most effective way to store large-scale electricity and has been widely used in the worldAs the key equipment in the pumped hydro energy storage it is significant and urgent to improve the performance and operationstability of the pump-turbine In this study the effect of runners with and without splitter blade on the performances and innerflow characteristics of a pump-turbine in pump mode was analyzed by the method of numerical calculation The results suggestthat larger tangential velocity at runner outlet and higher pressure at the trailing edge of pressure side in splitter blade runnerscheme contribute to higher headThe area of backflow at runner outlet the highest values of entropy generation rate and vorticitydistribution in splitter blade runner scheme are well smaller than those in prototype runner without splitter blade which isconducive to improving model performance

1 Introduction

Clean energies such as wind energy solar energy nuclearenergy and hydropower are starting to play a significant rolein the process of social development due to the progressiveexhaustion of fossil fuels (coal and petroleum etc) and thesevere environment pollution However a new issue hasappeared how to feed these energies to the current electricitysystem according to the changeable electricity consumptionThe pumped hydro energy storage is a good solution to thisissue As a result it is widely used to keep a balance betweenthe electricity production and consumption and improve theelectricity use efficiency and the stability of power gridThereare two reversible storage and generation working modesin the pumped storage power plant as shown in Figure 1It is a special kind of hydropower with very high efficiencythat can convert the electricity to the potential energy ofwater at low power grid loads (pump mode) and generateelectricity with the stored water at high power grid loads(turbine mode) [1 2] As the most promising and effectiveway to store electricity the pumped storage power plant hasbeen widely used in Japan America Europe China and soon [3ndash5]

The key equipment of pumped storage power plant is thepump-turbine which can be used as a pump or turbine atdifferent operation conditions and switch between two work-ing modes rapidly Therefore some high requirements on thedesign stage of the pump-turbine are proposed to improvethe performance and cavitation ability keeping stable duringstart-up and modes switches [6] Some researchers haveworked on the unstable characteristics rotor-stator interac-tion flow patterns cavitation and so on of the reversiblepump-turbine contributing to the rapid development andapplication of pump-turbines Yan et al [7] investigated theeffect of water compressibility on the rotor-stator interactionby using simulation and experiment The results showedthat the compressible calculation had more accurate pres-sure fluctuations prediction in vaneless region but higherpressure values in penstock and spiral case Olimstad etal [8] studied the effect of different runner leading edge(curvature radius and inlet blade angle) on the characteristicsof pump-turbine in turbine mode The results showed thatlarger radius and smaller inlet blade angle provided lesssteep characteristics however the latter also exacerbated theunstable curves in both turbine and pump modes Yin et

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 2403179 10 pageshttpsdoiorg10115520182403179

2 Mathematical Problems in Engineering

al [9] found that broadening the meridional passage in therunner of pump-turbine could suppress the form of unstablecurve Yang et al [10] adopted the inverse design methodcombining with computational fluid dynamics to design theblade profile according to the blade loading distributions anda design-of-experiment method to decide the test pointswhich was validated by experiment to be effective Jese etal [11] studied the hump-shaped curve and rotating stall ina high head reversible pump-turbine at different guide vaneopenings The results indicated that the hump had a greatrelationship with the rotating stall and at larger opening thehump was lighter Zhang et al [12] compared the dynamicand steady characteristics in a pump-turbine by couplingwiththe corresponding water delivery system during runawayThe results presented the fact that the dynamic method gavemore similar key transient parameters and unstable behaviorswhich influenced looping trajectories

The splitter blade runner a special structure runner withlong and short blades placed alternately in the circumferencedirection was proposed in centrifugal pumps [13 14] andcompressors [15 16] It has advantages of improving hydraulicperformance and reducing the blade load the appearanceof secondary flow pressure fluctuation vibration and soon The first pump-turbine with a splitter blade runnerwas successfully applied in the real power plant in 2003manufactured by Toshiba Corporation [17] however therewere a few studies on the pump-turbine Tezuka [18] pro-posed a design method of splitter blade with the blade inletequal and outlet unequal pitch arrangement By using thismethod two different specific-speed runners in Azumi andKarmagawa pumped storage power plants were designedinstalled and verified to have high reliability and betterhydraulic performance Meng et al [19] studied the influenceof splitter blade length on the pump-turbine efficiency andpressure fluctuation The results suggested that the pressurefluctuation was lower with relatively high efficiency when thelength ratio of splitter blade to long blade equaled 085

With the development of computational fluid dynamicsnumerical calculation technique as a significant approachof prediction and analysis has been reported in the fluidmachinery [20 21] Therefore after summarizing previousstudies this paper conducts a more detailed mechanismstudy of the inner flow characteristics of the pump-turbinein pump mode and takes into account the effect of splitterblade runner scheme on the performance The numericalsimulations are performed by ANSYS-CFX code In additionthe simulation calculations are contrasted with experimentalresults at different flow rates The velocity contours pressuredistribution entropy generation rate and vorticity distribu-tion are analyzed to illustrate the differences of two schemesFinally this paper will provide some references on splitterblade design in pump-turbines to improve the performance

2 Numerical Simulation Method

21 Geometry Model A reduced scale of a reversible pump-turbine with nominal flow rate of 119876d=410 kgs nominalhead of 119867d=50 m and a rotating speed of 1300 rmin

Table 1 Mesh information

DomainElementsnumber

(thousand)

Quality(determinant 2x2x2)

Runner (prototype) 21667 056Runner (splitter blade scheme) 21617 068Draft tube 16748 072Guide vanes 10036 089Stay vanes 14783 056Spiral casing 11245 056

is studied in this paper The three-dimensional geometricmodel of the pump-turbine is showed in Figure 2 composedof five components spiral casing stay vanes guide vanesrunner and draft tube corresponding to the real machineIt has 20 stay vanes and 20 guide vanes Figure 3 shows theschemes of two runners without and with splitter blade Theprototype runner has nine main blades whereas the splitterblade runner has six main blades and six splitter bladesrespectively The splitter blade is distributed at the middle ofpassage and the leading edge is located at 045-time radius ofrunner

22 Mesh Generation The pump-turbine computationaldomain was composed of five parts as the geometry modelThe mesh was generated by means of ANSYS-ICEM codeas shown in Figure 4 As the mesh quality has a significantrelationship with the calculation result the hexahedral struc-tured grid was adopted to obtain the results with less elementnumber short computing time and small truncation errorThe number and location of nodes on each pair of interfaceswere refined for overcoming the interface influence on theflow fields and improving calculation accuracy Furthermorethemeshwas refined near solidwall surface such as blade andvane surfaces where it is easy to capture the pressure gradi-ents and flow separation phenomenon Since the calculationresult is sensitive to the grid number several different setsof grids with increasing numbers were generated to performthe mesh independence analysis at two flow rates for theprototype pump-turbine as shown in Figure 5 The headsat two different flow rates exhibit larger deviations from thetest results when the total mesh elements are less than 61213thousand After this mesh number the head gets closer to thetest and behaves almost flat with mesh elements increase Asa result the grid number for the whole computation domainwas chosen to approximate 74479 thousand The detailedmesh information of each component for two schemes islisted in Table 1

23 Numerical Simulation Setup The numerical simula-tion was carried out with commercial ANSYS-CFX codeby solving the Reynolds-averaged Navier-Stokes (RANS)equations based on the finite volume method Shear stresstransport (SST) model [21 22] was complemented to

Mathematical Problems in Engineering 3

Upper basin

Lower basin

Pump-turbineStorage-pumping mode

Motor-generator

Power grid

Power grid

Upper basin

Motor-generator

Generation-turbine modePump-turbine

penstock

Penstock

Lower basin

Figure 1 Electricity storage and generation in pumped storage power plant

Draft tube

RunnerGuide vanes

Stay vanes

Spiral casing

Figure 2 The three-dimensional geometric model of the pump-turbine

simulate turbulence flow in the pump-turbine and auto-matic wall function was chosen for the near wall treat-ment The discretization methods for time and space wereselected as second-order backward Euler and high resolu-tion respectively The rotating reference frame was appliedto the runner while the stationary reference frame wasinstalled at other parts In addition total pressure wasimposed as boundary condition at the draft tube inlet Themass flow with stochastic fluctuation of the velocity wasinstalled at the spiral casing outlet in sympathy with testcondition The calculation was considered to be conver-gence with the root mean square (RMS) residual less than10minus5

3 Experimental Validation

In this study the performance experiments of pump-turbinemodel were carried out at one guide vane opening (25mmGVO) in pump mode and compared with the simulationresults as shown in Figure 6The test performance curve wasexpected to be stable with a negative slope when the flow ratewas larger than 340 kgs However a hump region marked bya positive slope was also found during part-load conditionsThenumerical simulation head of the prototype shows a goodagreement with the test curve (the maximum error is 64)which proves the numerical calculation is reliable and is thefoundation of the following detailed studies Therefore thesame numerical method was adopted for the splitter bladerunner scheme and the head is also presented in Figure 6

Because the efficiency obtained fromANSYS-CFX is onlyhydraulic efficiency without considering the electric motorandmechanical efficiency and volumetric efficiency it cannotbe compared with test system efficiency directly Thereforethe difference in simulation hydraulic efficiency between thesplitter blade runner scheme and the prototype is showedin Figure 7 It can be observed that the efficiency of splitterblade runner scheme is higher than that of the prototypeat full flow rates with the maximum difference of 24Combining Figure 6 with Figure 7 it can be concluded thatsplitter blade runner scheme improves the head and efficiencyof the pump-turbine in pump mode and reduces the humpregion to a certain degree As a result four operation pointsA B C andD corresponding to flow rates 266 kgs 3113 kgs3914 kgs and 4758 kgs were chosen to investigate the innerflow characteristics for a single guide vane opening in thefollowing parts


Prototype Splitter blade scheme

Figure 3 The prototype runner (left) and the splitter blade runner (right)

Draft tube

Runner

Guide vanes

Stay vanes

Spiral casing

Figure 4 The mesh details of pump-turbine computation domain

4 Results and Discussions

41 e Radial and Tangential Velocity Distributions at theRunner Outlet The contours of the tangential component ofabsolute velocity at runner outlet normalized by runner tipcircumference velocity 1198802 for the runners with and withoutsplitter blade at four different flow rates are presented inFigure 8 According to Eulerrsquos equation the theoretical headin pump mode equals 119867119905ℎ = (11988111990521198802 minus 11988111990511198801)119892 where 1198801and 1198802 are the circumference velocity and 119881t1 and 119881t2 arethe tangential velocity at runner inlet and outlet respectively

In this expression 1198802 is constant in two runner schemesand 119881t11198801 is very small compared with 119881t21198802 Therefore thetheoretical head is determined almost by the runner outlettangential velocity 119881t2 Generally 119881t2 decreases with increaseof the flow rate for both runner schemes in Figure 8 Thedistributions of local high velocity regions near shroud sideand low velocity regions near hub side correspond to thepassage positions at flow rates 3914 kgs and 4758 kgswhereas they exhibit more complex structure at 266 kgs and3113 kgs The tangential velocities in runner with splitterblade are evidently larger than that in runner without splitter

Mathematical Problems in Engineering 5H

[m] 48776

61213 7447930428

16253

1000 2000 3000 4000 5000 6000 7000 800046

47

48

49

50

51

52

53

Mesh elements [thousand]

Simulation of Q = 266 kgsTest of Q = 266 kgsSimulation of Q = 3914 kgsTest of Q = 3914 kgs

Figure 5 Mesh independence analysis at two flow rates

150 200 250 300 350 400 450 500 550 60030

35

40

45

50

55

60

65

H [m

]

Q [kgs]

Prototype (test)Prototype (simulation)Splitter blade scheme (simulation)

Figure 6 The head curves comparison between tests and simula-tions

blade particularly at flow rates 266 kgs and 3113 kgsTherefore the splitter blade runner contributes to higherhead in agreement with the performance curve in Figure 6

Figure 9 presents the contours of the radial componentof relative velocity at runner outlet at different flow rateswhich is normalized by runner tip circumference velocity1198802 As can be seen the distribution of radial velocity has anapparent relationship with the runner passages The high andlow radial velocity regions are distributed alternatively alongthe circumference direction of the runner outlet This couldbe partly because the classical jet-wake pattern occurs atrunner outlet region that is the high radial velocity appearsnear the pressure side of blade while the low radial velocity

150 200 250 300 350 400 450

C

D

500 55006

09

12

15

18

21

24

27

Q [kgs]

Δ

[] A B

Figure 7The simulation hydraulic efficiency difference between thesplitter blade runner scheme and the prototype

emerges adjacent to the suction side of blade according torelevant references [23 24] For prototype runner at flow rate4758 kgs three high radial velocity regions located evenlyat runner outlet can be observed from the passage mid-plane to the hub When the flow rate reduces to 3914 kgsthe high radial velocity regions almost disappear whereasthe area of low radial velocity increases even with negativevaluesThat is some small backflows appear in these passagesnear shroud side Then these backflow regions with negativeradial velocity progressively move to hub side at 266 kgsand 3113 kgs and extend with the decrease of flow rate Thebackflow regions are blade wake in which the momentuminterchanges strongly and the hydraulic loss exists As aresult the hydraulic loss in prototype runner increases withthe decrease of flow rate As for the runner with splitterblade the evolution of radial velocity with flow rate issimilar to that of prototype runner but with evidently smallerbackflow regions particularly at the flow rates 266 kgsand 3113 kgs at which the backflow regions with negativeradial velocity nearly disappear The reason could be thatthe backflow is suppressed due to the improved jet-wakepattern by the splitter blade It can be concluded that thesplitter blade runner scheme optimizes the structure of jet-wake pattern decreases the hydraulic loss and improves therunner performance especially at low flow rates

42 e Pressure and Streamline Distributions The pressureand streamline distributions on the pressure side of runnerblade are presented in Figure 10 at four different flow ratesThe area of low-pressure zone at the leading edge in theprototype is evidently larger than that in splitter blade runnerscheme at flow rate 266 kgs This indicates that the bladedoes not fully deliver energy on the fluid in this region Thereason could be that the blade number at the runner inlet ofsplitter blade runner scheme is less than that of the prototypewhich decreases the inlet blockage and flow velocity resultingin an increase of shock angle and static pressure Meanwhileaccording to streamline distribution of the main blade the


Q = 266 kgs Q = 3914 kgsQ = 3113 kgs Q = 4758 kgs

Splitter blade schemePrototype

６Ｎ５2６Ｎ５2６Ｎ５2６Ｎ５2090

079

067

056

045

034

022

011

000

090

079

067

056

045

034

022

011

000

080

074

068

061

055

049

043

036

030

080

075

070

065

060

055

050

045

040

Figure 8 The contours of the tangential component of absolute velocity at runner outlet



６r５2 ６r５2 ６r５2

６r５2

６r５2030

025

020

015

010

005

000

minus005

minus010

030

025

020

015

010

005

000

minus005

minus010

030

026

022

018

014

011

007

minus001

025

022

019

016

013

009

006

003

000

003

Figure 9 The contours of the radial component of relative velocity at runner outlet

nonuniform streamline with a high curvature in prototyperunner deviates from hub to shroud near the blade frontpart which might be one of the reasons for the low-pressureregion Furthermore the main blade of splitter blade runnerscheme at the trailing edge has a larger high-pressure zonethan the prototype which contributes to a higher head

In Figure 10 it can also be observed that the splitterblade runner scheme has better streamline distributionsthan the prototype on the pressure side of the main bladeThe streamline distributions in both schemes are relativelysmooth at larger flow rates 4758 kgs and become distortionat the other three flow rates Therefore combining theunstable region of performance curve in Figure 6 detailedanalyses are carried out at lower flow rate to reveal the effect ofadding splitter blade on the internal flow characteristics andthe performance in the following study

43 e Entropy Generation Rate Distribution The energyloss in a pump-turbine is caused by the effects of Reynoldsstress and viscous stress This process is irreversible andthe lost energy converts to internal energy resulting inthe entropy generation As recommended by Denton [25]entropy is an extremely useful method to measure the losswhich directly represents the devastation of useful workMeanwhile some relevant studies on the entropy generationrate [25 26] were proposed to analyze unsteady turbulenceflow situation in the operation process of fluid machineryMoore [27] applied the entropy generation rate to the eddyviscosity turbulence flow model In this model the internalheating source was neglected and the entropy generation rateper volume was first defined in (1) The turbulent viscousdissipation term on the right hand in this equation wasexpressed by using eddy viscosity as in (2)



Leading edge

Trailing edge

Main blade

Splitter blade

Q = 266 kgs Q = 3113 kgs

Q = 3914 kgs Q = 4758 kgs

Pressure [Pa]

Pressure [Pa] Pressure [Pa]

Pressure [Pa]55e+005

48e+005

41e+005

34e+005

27e+005

20e+005

13e+005

60e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

48e+005

42e+005

36e+005

30e+005

24e+005

17e+005

11e+005

51e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

Figure 10 The contours of pressure and streamline distributions on the pressure side of runner blade

119879120590 = 119896119879 [[( 120597119879120597119909119894)

2 + (1205971198791015840120597119909119894 )2]]+ 120591119894119895 120597119906119894120597119909119895 + 1205911015840119894119895

1205971199061015840119894120597119909119895 (1)

1205911015840119894119895 1205971199061015840119894120597119909119895 =120583119905120583 120591119894119895120597119906119894120597119909119895 (2)

According to [28] the rotatory machinery model can beconsidered as adiabatic excluding the thermal diffusion effectThe final entropy generation rate per volume 120590 is expressed asfollows

120590 = 1119879 (120591119894119895120597119906119894120597119909119895 +120583119905120583 120591119894119895120597119906119894120597119909119895) (3)

120591119894119895 = 120583( 120597119906119894120597119909119895 +120597119906119895120597119909119894 minus23120597119906119896120597119909119896 120575119894119895) (4)

where 120591119894119895 is the viscous stress sensor 120583119905 and 120583 are eddyviscosity and turbulent dynamic viscosity respectively and

119879 is temperature of working flow which is considered to beconstant of 298 K

Figure 11 presents the distributions of entropy generationrate (EGR) per volume at mid span in runner guide vanesand stay vanes of the prototype and splitter blade runnerscheme at flow rate 266 kgs Large entropy generation ratein the runner can be found at the leading edge of bladesuction side due to small incident angle in the passageand at the trailing edge of main blades due to blade wakeeffectThe largest entropy generation rate concentrates on theinterface between runner and guide vanes the leading edgeof guide vanes and the suction side of stay vanes causingenergy loss and a drop of efficiency The area of high entropygeneration rate in the splitter runner blade scheme is wellsmaller than that in prototypeThismeans that adding splitterblade can effectively reduce the energy loss in the runnerguide vanes and stay vanes conducing to the improvementof the efficiency

44 e Vorticity Distribution at Guide Vanes and Stay VanesThe vorticity can be used to indicate the local ration rate and



EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]

Figure 11 The contours of entropy generation rate distribution at mid span for both schemes

Region ARegion B

Region ARegion B

Region A Region ARegion B Region B



v [ms]220

193

165

138

110

83

55

28

00

Vorticity [s^-1]1000

875

750

625

500

375

250

125

0

Figure 12 The vorticity and velocity distributions of guide vanes and stay vanes at mid span


turbulence of the fluid It can be defined by the followingexpression

120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)

Figure 12 shows the vorticity and velocity distributionsof guide vanes and stay vanes at mid span in prototypeand splitter blade runner scheme at flow rate 266 kgs Asobserved the area of high vorticity in the prototype is welllarger than that in splitter blade runner scheme especially inregion A and region B which is mainly due to the deviationeffect of the incoming flow The large vorticity indicates thatfluid produces a large rotational angular velocity and intenseperturbation in the flow field which is not conducive toenergy conversion and transportation It may even be oneof the significant reasons for the formation of the humpregion in the prototype Meanwhile according to the localvelocity distributions in regions A and B in Figure 12 somesmall vortices and flow separation that can be found inthe prototype improved in splitter blade scheme This isbecause the splitter blade added at the rear part of the runnerchannel decreases the velocity slip enhances the control tothe fluid optimizes the jet-wake flow patterns and makesthe flow coming out from runner more uniform Then theuniform incoming flow reduces the impingement on theguide vane inlet and makes the flow flatter in the guide vanechannels which can effectively improve flow instability andflow separation phenomenon As a result the splitter bladerunner scheme has smoother flow patterns and less energyloss in the guide vanes and stay vanes contributing to betterperformance

5 Conclusions

Theeffects of adopting runner without and with splitter bladeon the performance of the pump-turbine in pump modewere investigated by means of the numerical simulationsThe numerical calculations showed a good agreement withthe test results in performance prediction Various quanti-ties including the velocity pressure streamline distributionentropy generation rate and vorticity distribution wereadopted to verify and analyze internal flow characteristicsinside the pump-turbine for different runner schemes Someconclusions are drawn as follows

(1) The runner with splitter blade can effectively improvethe performance for a pump-turbine in pump mode Com-pared to prototype runner the maximum increased values ofthe head and the efficiency are 2m and 24 at full operatingconditions in splitter blade runner scheme respectively

(2)When the flow rate is less than 3914 kgs in prototyperunner the radial component of relative velocity at the runneroutlet reduces to zero and even negative values and thestreamlines on the pressure side of the blade cause an obviousdistortion which result in serious backflow andhydraulic lossrelative to splitter blade runner scheme

(3) The tangential component of absolute velocity atrunner outlet and the distribution of high-pressure region onthe pressure side of the blade in splitter blade runner scheme

is evidently larger than that in runner without splitter bladeparticularly at flow rates 266 kgs and 3113 kgs contributingto higher head

(4) At lower flow rate 266 kgs the areas of high entropygeneration rate and high vorticity in guide vanes and stayvanes for the splitter blade runner scheme are well smallerthan those for the prototype scheme which decreases theenergy loss and enhances the energy conversion and trans-portation

Nomenclature

119892 [ms2] Gravitational acceleration119867 [m] Head119867d [m] Nominal head119867th [m] Theoretical head119896 [Wm K] Thermal conductivity119899 [rmin] Rotational speed119876 [m3h] Mass flow rate119876d [m3h] Nominal flow rate119879 [K] Temperature1198801 [ms] Circumferential velocity at runner inlet1198802 [ms] Circumferential velocity at runner outlet119906i [ms] Liquid velocity in the xyz directionV [ms] Relative velocity119881r [ms] Radial component of relative velocity119881t1 [ms] Tangential velocity at runner inlet119881t2 [ms] Tangential velocity at runner outlet119909j xyz directionΔ120578 The difference of hydraulic efficiency120583 [kgsdotmminus1sdotsminus1] Dynamic viscosity120583t [kgsdotmminus1sdotsminus1] Eddy viscosity120590 [Wsdotmminus3sdotKminus1] Entropy generation rate per unit volume120591119894119895 Viscous stress sensor120596 [sminus1] Vorticity

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declared no potential conflicts of interest withrespect to the research authorship andor publication of thisarticle

Acknowledgments

The authors disclosed receipt of the following financialsupport for the research authorship andor publication ofthis article This work was supported by the National NaturalScience Foundation of China (Grant No 51409123) ChinaPostdoctoral Science Foundation (2015M581734) a projectfunded by the Priority Academic Program Development ofJiangsu Higher Education Institutions (PAPD) and Innova-tion Project for Postgraduates of Jiangsu Province (Grant NoKYLX15 1064)


References

[1] G Ardizzon G Cavazzini and G Pavesi ldquoA new generationof small hydro and pumped-hydro power plants Advances andfuture challengesrdquo Renewable amp Sustainable Energy Reviewsvol 31 pp 746ndash761 2014

[2] Z Zuo S Liu Y Sun and Y Wu ldquoPressure fluctuations inthe vaneless space of High-head pump-turbines - A reviewrdquoRenewable amp Sustainable Energy Reviews vol 41 pp 965ndash9742015

[3] J P Deane B P O Gallachoir and E J McKeogh ldquoTechno-economic review of existing and new pumped hydro energystorage plantrdquo Renewable amp Sustainable Energy Reviews vol 14no 4 pp 1293ndash1302 2010

[4] P Punys R Baublys E Kasiulis A Vaisvila B Pelikan andJ Steller ldquoAssessment of renewable electricity generation bypumped storage power plants in EUMember StatesrdquoRenewableamp Sustainable Energy Reviews vol 26 pp 190ndash200 2013

[5] Z Ming F Junjie X Song W Zhijie Z Xiaoli and W YuejinldquoDevelopment of Chinarsquos pumped storage plant and relatedpolicy analysisrdquo Energy Policy vol 61 pp 104ndash113 2013

[6] T Hino and A Lejeune ldquoPumped storage hydropower develop-mentsrdquo Comprehensive Renewable Energy vol 6 pp 405ndash4342012

[7] J Yan J Koutnik U Seidel and B Hubner ldquoCompressibleSimulation of Rotor-Stator Interaction in Pump-TurbinesrdquoeInternational Journal of Fluid Machinery and Systems vol 3 no4 pp 315ndash323 2010

[8] G Olimstad T Nielsen and B Boslashrresen ldquoDependency onrunner geometry for reversible-pump turbine characteristics inturbine mode of operationrdquo Journal of Fluids Engineering vol134 no 12 2012

[9] J Yin DWang XWei and LWang ldquoHydraulic Improvementto Eliminate S-Shaped Curve in Pump Turbinerdquo Journal ofFluids Engineering vol 135 no 7 p 071105 2013

[10] W Yang and R Xiao ldquoMultiobjective optimization design of apump-turbine impeller based on an inverse design using a com-bination optimization strategyrdquo Journal of Fluids Engineeringvol 136 no 1 2014

[11] U Jese R Fortes-Patella and M Dular ldquoNumerical studyof pump-turbine instabilities under pumping mode off-designconditionsrdquo in Proceedings of the ASMEJSMEKSME 2015 JointFluids Engineering Conference AJKFluids 2015 Republic ofKorea July 2015

[12] X Zhang Y Cheng L Xia J Yang and Z Qian ldquoLoopingDynamic Characteristics of a Pump-Turbine in the S-shapedRegionDuringRunawayrdquo Journal of Fluids Engineering vol 138no 9 p 091102 2016

[13] G Kergourlay M Younsi F Bakir and R Rey ldquoInfluenceof splitter blades on the flow field of a centrifugal pumptest-analysis comparisonrdquo International Journal of RotatingMachinery vol 2007 Article ID 85024 2007

[14] G Cavazzini G Pavesi A Santolin G Ardizzon and RLorenzi ldquoUsing splitter blades to improve suction performanceof centrifugal impeller pumpsrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol229 no 3 pp 309ndash323 2015

[15] S A Moussavi A Hajilouy Benisi and M Durali ldquoEffect ofsplitter leading edge location on performance of an automotiveturbocharger compressorrdquo Energy vol 123 pp 511ndash520 2017

[16] XHe andX Zheng ldquoMechanisms of sweep on the performanceof transonic centrifugal compressor impellersrdquoApplied Sciences(Switzerland) vol 7 no 10 2017

[17] R Du X Q Wang and E Yasuyuki ldquoApplication of splitterblades runner pump turbine in Qing Yuan Pump StorageStationrdquoHydropower amp Pumped Storage vol 2 pp 39ndash44 2016

[18] K Tezuka ldquoDevelopment and application of new type runnerwith splitter blades to pumped storage power plantsrdquo in 8thAsian International Fluid Machinery Conference 2005

[19] L Meng S P Zhang L J Zhou and Z W Wang ldquoStudy onthe Pressure Pulsation inside Runner with Splitter Blades inUltra-High Head Turbinerdquo IOP Conference Series Earth andEnvironmental Science vol 22 no 3 p 032012 2014

[20] Wei Li Xiaofan Zhao Weiqiang Li Weidong Shi Leilei Ji andLing Zhou ldquoNumerical Prediction and Performance Experi-ment in an Engine Cooling Water Pump with Different BladeOutlet Widthsrdquo Mathematical Problems in Engineering vol2017 Article ID 8945712 11 pages 2017

[21] L Deyou W Hongjie X Gaoming G Ruzhi W Xianzhuand L Zhansheng ldquoUnsteady simulation and analysis for humpcharacteristics of a pump turbine modelrdquo Journal of RenewableEnergy vol 77 pp 32ndash42 2015

[22] C Widmer T Staubli and N Ledergerber ldquoUnstable charac-teristics and rotating stall in turbine brake operation of pump-turbinesrdquo Journal of Fluids Engineering vol 133 no 4 pp 41101ndash41101-9 2011

[23] D Eckardt ldquoDetailed flow investigations within a high-speedcentrifugal compressor impellerrdquo Journal of Fluids Engineeringvol 98 no 3 pp 390ndash399 1976

[24] J Keller E Blanco R Barrio and J Parrondo ldquoPIV measure-ments of the unsteady flow structures in a volute centrifugalpump at a high flow raterdquo Experiments in Fluids vol 55 no 102014

[25] J D Denton ldquoThe 1993 IGTI scholar lecture loss mechanismsin turbomachinesrdquo Journal of Turbomachinery vol 115 no 4pp 621ndash656 1993

[26] D Li H Wang Y Qin L Han X Wei and D Qin ldquoEntropyproduction analysis of hysteresis characteristic of a pump-turbine modelrdquo Energy Conversion and Management vol 149pp 175ndash191 2017

[27] J Moore and J G Moore ldquoEntropy Production Rates FromViscous Flow Calculations Part I mdash A Turbulent BoundaryLayer Flowrdquo in Proceedings of the ASME 1983 InternationalGas Turbine Conference and Exhibit p V001T01A032 PhoenixArizona USA

[28] P Newton C Copeland R Martinez-Botas and M Seiler ldquoAnaudit of aerodynamic loss in a double entry turbine under fulland partial admissionrdquo International Journal of Heat and FluidFlow vol 33 no 1 pp 70ndash80 2012

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al [9] found that broadening the meridional passage in therunner of pump-turbine could suppress the form of unstablecurve Yang et al [10] adopted the inverse design methodcombining with computational fluid dynamics to design theblade profile according to the blade loading distributions anda design-of-experiment method to decide the test pointswhich was validated by experiment to be effective Jese etal [11] studied the hump-shaped curve and rotating stall ina high head reversible pump-turbine at different guide vaneopenings The results indicated that the hump had a greatrelationship with the rotating stall and at larger opening thehump was lighter Zhang et al [12] compared the dynamicand steady characteristics in a pump-turbine by couplingwiththe corresponding water delivery system during runawayThe results presented the fact that the dynamic method gavemore similar key transient parameters and unstable behaviorswhich influenced looping trajectories

The splitter blade runner a special structure runner withlong and short blades placed alternately in the circumferencedirection was proposed in centrifugal pumps [13 14] andcompressors [15 16] It has advantages of improving hydraulicperformance and reducing the blade load the appearanceof secondary flow pressure fluctuation vibration and soon The first pump-turbine with a splitter blade runnerwas successfully applied in the real power plant in 2003manufactured by Toshiba Corporation [17] however therewere a few studies on the pump-turbine Tezuka [18] pro-posed a design method of splitter blade with the blade inletequal and outlet unequal pitch arrangement By using thismethod two different specific-speed runners in Azumi andKarmagawa pumped storage power plants were designedinstalled and verified to have high reliability and betterhydraulic performance Meng et al [19] studied the influenceof splitter blade length on the pump-turbine efficiency andpressure fluctuation The results suggested that the pressurefluctuation was lower with relatively high efficiency when thelength ratio of splitter blade to long blade equaled 085

With the development of computational fluid dynamicsnumerical calculation technique as a significant approachof prediction and analysis has been reported in the fluidmachinery [20 21] Therefore after summarizing previousstudies this paper conducts a more detailed mechanismstudy of the inner flow characteristics of the pump-turbinein pump mode and takes into account the effect of splitterblade runner scheme on the performance The numericalsimulations are performed by ANSYS-CFX code In additionthe simulation calculations are contrasted with experimentalresults at different flow rates The velocity contours pressuredistribution entropy generation rate and vorticity distribu-tion are analyzed to illustrate the differences of two schemesFinally this paper will provide some references on splitterblade design in pump-turbines to improve the performance

2 Numerical Simulation Method

21 Geometry Model A reduced scale of a reversible pump-turbine with nominal flow rate of 119876d=410 kgs nominalhead of 119867d=50 m and a rotating speed of 1300 rmin

Table 1 Mesh information

DomainElementsnumber

(thousand)

Quality(determinant 2x2x2)

Runner (prototype) 21667 056Runner (splitter blade scheme) 21617 068Draft tube 16748 072Guide vanes 10036 089Stay vanes 14783 056Spiral casing 11245 056

is studied in this paper The three-dimensional geometricmodel of the pump-turbine is showed in Figure 2 composedof five components spiral casing stay vanes guide vanesrunner and draft tube corresponding to the real machineIt has 20 stay vanes and 20 guide vanes Figure 3 shows theschemes of two runners without and with splitter blade Theprototype runner has nine main blades whereas the splitterblade runner has six main blades and six splitter bladesrespectively The splitter blade is distributed at the middle ofpassage and the leading edge is located at 045-time radius ofrunner

22 Mesh Generation The pump-turbine computationaldomain was composed of five parts as the geometry modelThe mesh was generated by means of ANSYS-ICEM codeas shown in Figure 4 As the mesh quality has a significantrelationship with the calculation result the hexahedral struc-tured grid was adopted to obtain the results with less elementnumber short computing time and small truncation errorThe number and location of nodes on each pair of interfaceswere refined for overcoming the interface influence on theflow fields and improving calculation accuracy Furthermorethemeshwas refined near solidwall surface such as blade andvane surfaces where it is easy to capture the pressure gradi-ents and flow separation phenomenon Since the calculationresult is sensitive to the grid number several different setsof grids with increasing numbers were generated to performthe mesh independence analysis at two flow rates for theprototype pump-turbine as shown in Figure 5 The headsat two different flow rates exhibit larger deviations from thetest results when the total mesh elements are less than 61213thousand After this mesh number the head gets closer to thetest and behaves almost flat with mesh elements increase Asa result the grid number for the whole computation domainwas chosen to approximate 74479 thousand The detailedmesh information of each component for two schemes islisted in Table 1

23 Numerical Simulation Setup The numerical simula-tion was carried out with commercial ANSYS-CFX codeby solving the Reynolds-averaged Navier-Stokes (RANS)equations based on the finite volume method Shear stresstransport (SST) model [21 22] was complemented to


Upper basin

Lower basin


Motor-generator

Power grid

Power grid

Upper basin

Motor-generator


penstock

Penstock

Lower basin


Draft tube

RunnerGuide vanes

Stay vanes

Spiral casing









Draft tube

Runner

Guide vanes

Stay vanes

Spiral casing






[m] 48776

61213 7447930428

16253

1000 2000 3000 4000 5000 6000 7000 800046

47

48

49

50

51

52

53




150 200 250 300 350 400 450 500 550 60030

35

40

45

50

55

60

65

H [m

]

Q [kgs]





150 200 250 300 350 400 450

C

D

500 55006

09

12

15

18

21

24

27

Q [kgs]

Δ

[] A B







６Ｎ５2６Ｎ５2６Ｎ５2６Ｎ５2090

079

067

056

045

034

022

011

000

090

079

067

056

045

034

022

011

000

080

074

068

061

055

049

043

036

030

080

075

070

065

060

055

050

045

040




６r５2 ６r５2 ６r５2

６r５2

６r５2030

025

020

015

010

005

000

minus005

minus010

030

025

020

015

010

005

000

minus005

minus010

030

026

022

018

014

011

007

minus001

025

022

019

016

013

009

006

003

000

003







Leading edge

Trailing edge

Main blade

Splitter blade

Q = 266 kgs Q = 3113 kgs

Q = 3914 kgs Q = 4758 kgs

Pressure [Pa]



48e+005

41e+005

34e+005

27e+005

20e+005

13e+005

60e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

48e+005

42e+005

36e+005

30e+005

24e+005

17e+005

11e+005

51e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004


119879120590 = 119896119879 [[( 120597119879120597119909119894)

2 + (1205971198791015840120597119909119894 )2]]+ 120591119894119895 120597119906119894120597119909119895 + 1205911015840119894119895

1205971199061015840119894120597119909119895 (1)

1205911015840119894119895 1205971199061015840119894120597119909119895 =120583119905120583 120591119894119895120597119906119894120597119909119895 (2)


120590 = 1119879 (120591119894119895120597119906119894120597119909119895 +120583119905120583 120591119894119895120597119906119894120597119909119895) (3)

120591119894119895 = 120583( 120597119906119894120597119909119895 +120597119906119895120597119909119894 minus23120597119906119896120597119909119896 120575119894119895) (4)







EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]


Region ARegion B

Region ARegion B




v [ms]220

193

165

138

110

83

55

28

00


875

750

625

500

375

250

125

0




120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018









Upper basin

Lower basin


Motor-generator

Power grid

Power grid

Upper basin

Motor-generator


penstock

Penstock

Lower basin


Draft tube

RunnerGuide vanes

Stay vanes

Spiral casing









Draft tube

Runner

Guide vanes

Stay vanes

Spiral casing






[m] 48776

61213 7447930428

16253

1000 2000 3000 4000 5000 6000 7000 800046

47

48

49

50

51

52

53




150 200 250 300 350 400 450 500 550 60030

35

40

45

50

55

60

65

H [m

]

Q [kgs]





150 200 250 300 350 400 450

C

D

500 55006

09

12

15

18

21

24

27

Q [kgs]

Δ

[] A B







６Ｎ５2６Ｎ５2６Ｎ５2６Ｎ５2090

079

067

056

045

034

022

011

000

090

079

067

056

045

034

022

011

000

080

074

068

061

055

049

043

036

030

080

075

070

065

060

055

050

045

040




６r５2 ６r５2 ６r５2

６r５2

６r５2030

025

020

015

010

005

000

minus005

minus010

030

025

020

015

010

005

000

minus005

minus010

030

026

022

018

014

011

007

minus001

025

022

019

016

013

009

006

003

000

003







Leading edge

Trailing edge

Main blade

Splitter blade

Q = 266 kgs Q = 3113 kgs

Q = 3914 kgs Q = 4758 kgs

Pressure [Pa]



48e+005

41e+005

34e+005

27e+005

20e+005

13e+005

60e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

48e+005

42e+005

36e+005

30e+005

24e+005

17e+005

11e+005

51e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004


119879120590 = 119896119879 [[( 120597119879120597119909119894)

2 + (1205971198791015840120597119909119894 )2]]+ 120591119894119895 120597119906119894120597119909119895 + 1205911015840119894119895

1205971199061015840119894120597119909119895 (1)

1205911015840119894119895 1205971199061015840119894120597119909119895 =120583119905120583 120591119894119895120597119906119894120597119909119895 (2)


120590 = 1119879 (120591119894119895120597119906119894120597119909119895 +120583119905120583 120591119894119895120597119906119894120597119909119895) (3)

120591119894119895 = 120583( 120597119906119894120597119909119895 +120597119906119895120597119909119894 minus23120597119906119896120597119909119896 120575119894119895) (4)







EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]


Region ARegion B

Region ARegion B




v [ms]220

193

165

138

110

83

55

28

00


875

750

625

500

375

250

125

0




120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018











Draft tube

Runner

Guide vanes

Stay vanes

Spiral casing






[m] 48776

61213 7447930428

16253

1000 2000 3000 4000 5000 6000 7000 800046

47

48

49

50

51

52

53




150 200 250 300 350 400 450 500 550 60030

35

40

45

50

55

60

65

H [m

]

Q [kgs]





150 200 250 300 350 400 450

C

D

500 55006

09

12

15

18

21

24

27

Q [kgs]

Δ

[] A B







６Ｎ５2６Ｎ５2６Ｎ５2６Ｎ５2090

079

067

056

045

034

022

011

000

090

079

067

056

045

034

022

011

000

080

074

068

061

055

049

043

036

030

080

075

070

065

060

055

050

045

040




６r５2 ６r５2 ６r５2

６r５2

６r５2030

025

020

015

010

005

000

minus005

minus010

030

025

020

015

010

005

000

minus005

minus010

030

026

022

018

014

011

007

minus001

025

022

019

016

013

009

006

003

000

003







Leading edge

Trailing edge

Main blade

Splitter blade

Q = 266 kgs Q = 3113 kgs

Q = 3914 kgs Q = 4758 kgs

Pressure [Pa]



48e+005

41e+005

34e+005

27e+005

20e+005

13e+005

60e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

48e+005

42e+005

36e+005

30e+005

24e+005

17e+005

11e+005

51e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004


119879120590 = 119896119879 [[( 120597119879120597119909119894)

2 + (1205971198791015840120597119909119894 )2]]+ 120591119894119895 120597119906119894120597119909119895 + 1205911015840119894119895

1205971199061015840119894120597119909119895 (1)

1205911015840119894119895 1205971199061015840119894120597119909119895 =120583119905120583 120591119894119895120597119906119894120597119909119895 (2)


120590 = 1119879 (120591119894119895120597119906119894120597119909119895 +120583119905120583 120591119894119895120597119906119894120597119909119895) (3)

120591119894119895 = 120583( 120597119906119894120597119909119895 +120597119906119895120597119909119894 minus23120597119906119896120597119909119896 120575119894119895) (4)







EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]


Region ARegion B

Region ARegion B




v [ms]220

193

165

138

110

83

55

28

00


875

750

625

500

375

250

125

0




120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018









[m] 48776

61213 7447930428

16253

1000 2000 3000 4000 5000 6000 7000 800046

47

48

49

50

51

52

53




150 200 250 300 350 400 450 500 550 60030

35

40

45

50

55

60

65

H [m

]

Q [kgs]





150 200 250 300 350 400 450

C

D

500 55006

09

12

15

18

21

24

27

Q [kgs]

Δ

[] A B







６Ｎ５2６Ｎ５2６Ｎ５2６Ｎ５2090

079

067

056

045

034

022

011

000

090

079

067

056

045

034

022

011

000

080

074

068

061

055

049

043

036

030

080

075

070

065

060

055

050

045

040




６r５2 ６r５2 ６r５2

６r５2

６r５2030

025

020

015

010

005

000

minus005

minus010

030

025

020

015

010

005

000

minus005

minus010

030

026

022

018

014

011

007

minus001

025

022

019

016

013

009

006

003

000

003







Leading edge

Trailing edge

Main blade

Splitter blade

Q = 266 kgs Q = 3113 kgs

Q = 3914 kgs Q = 4758 kgs

Pressure [Pa]



48e+005

41e+005

34e+005

27e+005

20e+005

13e+005

60e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

48e+005

42e+005

36e+005

30e+005

24e+005

17e+005

11e+005

51e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004


119879120590 = 119896119879 [[( 120597119879120597119909119894)

2 + (1205971198791015840120597119909119894 )2]]+ 120591119894119895 120597119906119894120597119909119895 + 1205911015840119894119895

1205971199061015840119894120597119909119895 (1)

1205911015840119894119895 1205971199061015840119894120597119909119895 =120583119905120583 120591119894119895120597119906119894120597119909119895 (2)


120590 = 1119879 (120591119894119895120597119906119894120597119909119895 +120583119905120583 120591119894119895120597119906119894120597119909119895) (3)

120591119894119895 = 120583( 120597119906119894120597119909119895 +120597119906119895120597119909119894 minus23120597119906119896120597119909119896 120575119894119895) (4)







EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]


Region ARegion B

Region ARegion B




v [ms]220

193

165

138

110

83

55

28

00


875

750

625

500

375

250

125

0




120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018











６Ｎ５2６Ｎ５2６Ｎ５2６Ｎ５2090

079

067

056

045

034

022

011

000

090

079

067

056

045

034

022

011

000

080

074

068

061

055

049

043

036

030

080

075

070

065

060

055

050

045

040




６r５2 ６r５2 ６r５2

６r５2

６r５2030

025

020

015

010

005

000

minus005

minus010

030

025

020

015

010

005

000

minus005

minus010

030

026

022

018

014

011

007

minus001

025

022

019

016

013

009

006

003

000

003







Leading edge

Trailing edge

Main blade

Splitter blade

Q = 266 kgs Q = 3113 kgs

Q = 3914 kgs Q = 4758 kgs

Pressure [Pa]



48e+005

41e+005

34e+005

27e+005

20e+005

13e+005

60e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

48e+005

42e+005

36e+005

30e+005

24e+005

17e+005

11e+005

51e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004


119879120590 = 119896119879 [[( 120597119879120597119909119894)

2 + (1205971198791015840120597119909119894 )2]]+ 120591119894119895 120597119906119894120597119909119895 + 1205911015840119894119895

1205971199061015840119894120597119909119895 (1)

1205911015840119894119895 1205971199061015840119894120597119909119895 =120583119905120583 120591119894119895120597119906119894120597119909119895 (2)


120590 = 1119879 (120591119894119895120597119906119894120597119909119895 +120583119905120583 120591119894119895120597119906119894120597119909119895) (3)

120591119894119895 = 120583( 120597119906119894120597119909119895 +120597119906119895120597119909119894 minus23120597119906119896120597119909119896 120575119894119895) (4)







EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]


Region ARegion B

Region ARegion B




v [ms]220

193

165

138

110

83

55

28

00


875

750

625

500

375

250

125

0




120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018










Leading edge

Trailing edge

Main blade

Splitter blade

Q = 266 kgs Q = 3113 kgs

Q = 3914 kgs Q = 4758 kgs

Pressure [Pa]



48e+005

41e+005

34e+005

27e+005

20e+005

13e+005

60e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004

48e+005

42e+005

36e+005

30e+005

24e+005

17e+005

11e+005

51e+004

minus10e+004

50e+005

44e+005

37e+005

31e+005

24e+005

18e+005

11e+005

49e+004

minus15e+004


119879120590 = 119896119879 [[( 120597119879120597119909119894)

2 + (1205971198791015840120597119909119894 )2]]+ 120591119894119895 120597119906119894120597119909119895 + 1205911015840119894119895

1205971199061015840119894120597119909119895 (1)

1205911015840119894119895 1205971199061015840119894120597119909119895 =120583119905120583 120591119894119895120597119906119894120597119909119895 (2)


120590 = 1119879 (120591119894119895120597119906119894120597119909119895 +120583119905120583 120591119894119895120597119906119894120597119909119895) (3)

120591119894119895 = 120583( 120597119906119894120597119909119895 +120597119906119895120597119909119894 minus23120597119906119896120597119909119896 120575119894119895) (4)







EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]


Region ARegion B

Region ARegion B




v [ms]220

193

165

138

110

83

55

28

00


875

750

625

500

375

250

125

0




120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018










EGR15000

13125

11250

9375

7500

5625

3750

1875

0

[W m^-3 K^-1]


Region ARegion B

Region ARegion B




v [ms]220

193

165

138

110

83

55

28

00


875

750

625

500

375

250

125

0




120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018










120596 = 120597V119910120597119909 minus120597V119909120597119910 (5)


5 Conclusions







Nomenclature


Data Availability




Acknowledgments



References




































Journal of












Journal of







Volume 2018






Volume 2018









References




































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Effects of the Splitter Blade on the Performance of a Pump...

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