Research Article Analysis of the Influence of Inlet Guide Vanes ...

Research ArticleAnalysis of the Influence of Inlet Guide Vanes on thePerformance of Shaft Tubular Pumps

Haifeng Jiao 1 Chong Sun 2 and Songshan Chen 3

1College of Hydraulic Science and Engineering Yangzhou University Yangzhou 225000 Jiangsu China2Shandong Water Diversion Project Operation and Maintenance Center Jinan 250000 Shandong China3College of Electrical Energy and Power Engineering Yangzhou University Yangzhou 225000 Jiangsu China

Correspondence should be addressed to Chong Sun yzcss08163com

Received 7 June 2021 Accepted 28 October 2021 Published 16 December 2021

Academic Editor MI Herreros

Copyright copy 2021 Haifeng Jiao et al is 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

To study the influence of inlet guide vanes (IGVs) on the pressure pulsation of a shaft tubular pump this paper first conducts anexperiment to study IGVs en numerical calculations of the shaft tubular pump with and without IGVs are performed toanalyze the hydraulic performance and pressure fluctuation characteristics Finally the reliability and accuracy of the data areverified by a model test Numerical simulation results show that with additional IGVs the pressure pulsation amplitude at theimpeller inlet first decreases and then increases under small-flow and design conditions but gradually increases under large-flowconditions When the IGVs are added to the impeller inlet of the shaft tubular pump the hydraulic loss in front of the impellerinlet increases resulting in a significant drop in the head and efficiency of the pump device when the flow rate is less than 112 Qdwhen the flow rate is greater than 112Qd the head and efficiency of the pump device do not change significantly IGVs canimprove the condition of impeller water inflow and reduce pressure fluctuation on the blade surface

1 Introduction

A shaft tubular pump is a kind of axial flow pump In Chinashaft tubular pumps are widely used in large-flow and low-head pump stations e shaft tubular pump has the ad-vantages of straight flow passage smooth internal flow andsmall hydraulic loss [1ndash5] However in the actual con-struction process of the shaft tubular pumping station thesize of the pump is large and the flow channel usually adoptsa reinforced concrete structure e tensile performance ispoor so it is necessary to add IGVs at the impeller inlet tosupport the flow channel e addition of IGVs can not onlyimprove the overall structural strength of the inlet channelbut also improve the flow pattern of the pump ereforethe study of IGVs has great reference significance for en-gineering practice In addition to its application in waterpumps IGVs are also widely used in compressors gasturbines and other applications [6ndash12]

In the present paper the airfoil design and placementangle of the IGVs are based on the research results of some

experts on centrifugal pumps [13ndash15] Wang [16] et alstudied the effect of IGVs on unsteady flow in centrifugalpumps e results showed that after installing the IGVs ofminus36deg to 36deg the pressure fluctuation in the impeller andvolute changed a little After installing IGVs of minus60deg and+60deg the pressure pulsation amplitude increased signifi-cantly due to the blocking effect of the IGVs Liu [17] et alstudied the difference in pressure pulsation in centrifugalpumps without IGVs and with 2D and 3D IGVs e studyfound that under the design conditions the main frequencyamplitude of the pump was reduced by installing IGVs at theimpeller inlet 3D IGVs had a better reduction effect on themain frequency of pressure pulsation than 2D IGVs Shiet al [18] studied the effect of the angle difference of impellerblades on the performance of an axial flow pumpe resultsshowed that the blade angle deviation caused irregularpressure changes in the impeller and the low-frequencypressure pulsation increased significantly Yang et al [19]designed several IGVs of axial flow pumps with differentinstallation angles rough numerical calculation it was

HindawiShock and VibrationVolume 2021 Article ID 5177313 17 pageshttpsdoiorg10115520215177313

found that IGVs with a 0deg angle had little effect on thehydraulic characteristics of the pumps in high-efficiencyareas and low-flow conditions e larger hydraulic lossfrom the IGVs was the main reason for the low efficiency ofthe pumps under large-flow conditions

ere have been a relatively large number of studies onrear guide vanes [20ndash26] Yang et al [27] studied the angle ofthe IGVs of an axial flow pump When the angle of the bladewas adjusted from positive to negative the performancecurve shifted in the direction of large flow Zhao et al [28]studied the IGVs of an axial flow pump in turbine mode Itwas found that the efficiency range of the pump was ex-panded by the IGVs Kim et al [29] found that IGVs greatlyinterfered with the steady and unsteady characteristics of apump In particular the efficiency was most affected by theIGVs Guo et al [30] found that the installation angle ofIGVs had a greater impact on the cavitation of a pump Yanget al [31] studied the influence of the impeller inlet baffle onits performance It was found that the distance between theinlet baffle and the impeller had the greatest impact on waterpump performance e inlet baffle could constrain thebackflow of the impeller inlet and improve the efficiency ofthe pump Xing et al [32] set a baffle plate at the impellerinlet and analyzed it numerically e study found that thebaffle plate mainly affected the tangential velocity of theimpeller inlet and could improve the impeller workingability Dai et al [33] researched the positions of IGVs ecloser the IGVs were to the impeller the better the workingcondition of the impeller was e efficiency of the pump setwas also improved Deng et al [34] found that IGVs had asubstantial impact on the external characteristics and vi-bration characteristics of pumps

e present paper adopts a research method thatcombines numerical simulation and model tests [35ndash38]First the influence of the number of IGVs on the perfor-mance and pressure pulsation of the shaft tubular pump isstudied through model tests en the 5 IGVs schemewhich offers better performance than other schemes and theshaft tubular pump without IGVs are selected for numericalsimulation and comparison Finally several model tests areused to prove the accuracy of the calculation data Wemainly analyze the influence of the number of IGVs and theaddition of IGVs on the performance and pressure pulsationcharacteristics of the pump unite purpose of this article isto derive the change law of the pressure pulsation of the shafttubular pump [39ndash41] and provide guidance for thestructural design and operation of pump stations

2 Model Test

21 Test Scheme Design A shaft tubular pump withoutIGVs and a shaft tubular pump with 4 IGVs 5 IGVs and 6IGVs were designed Tests on the external characteristicsand pressure fluctuations were performed on a hydraulicmachinery test bench that was accurately calibrated esystem error eS and measurement error eR of the testbench are plusmn0231 and plusmn0171e test speed is the sameas the calculation which is 1163 rmin Figure 1 is aschematic diagram of the test bench e impeller

diameter of the shaft tubular pump is 300mm Figure 2(a)shows a physical picture of the impeller e number ofblades is 3 and they are made of brass e guide vanesand IGVs are welded with 5mm thick steel materials eguide vanes and IGVs are shown in Figures 2(b) and 2(c)ndash2(e)ree monitoring points P1 lowast at the IGVs inlet P2 lowastat the impeller inlet and P3 lowast at the guide vane outletwere measured in the pressure fluctuation test Figure 2(f )is the physical map of the test device and the layout of themeasuring points

22 Test Results and Analysis Figure 3 shows the test resultsof the external characteristics of pumps with 4 IGVs 5 IGVsand 6 IGVs e change trends of the head and efficiencycurves of the three schemes are basically the same enumber of IGVs has an obvious effect on the efficiency of thepump but has little effect on the head When the number ofIGVs gradually increases the efficiency of the pump firstincreases and then decreases e efficiency of the pumpwith 5 IGVs is the highest under the design condition whichis approximately 126 higher than that of the shaft tubularpump with 4 IGVs

To analyze the pressure pulsation the nondimensionalparameters of the pressure pulsation coefficient Cp andpressure pulsation intensity Clowastp are introduced to express theresults e formulas are as follows

CP P minus P

05ρu2

CPlowast

1113936ni1 C

2P

n

1113971

(1)

where P is the average pressure at the monitoring point PaP is the instantaneous pressure at the monitoring point Pa ρis the liquid density kgm3 n is the impeller revolution andu is the impeller outlet circumferential velocity rads

Figure 4 shows the test results for the pressure fluctu-ation of shaft tubular pumps with 4 IGVs 5 IGVs and 6IGVs Since the IGVs have an obvious influence on thepressure fluctuation at the impeller inlet the following in-vestigation mainly analyzes point P1lowast at the impeller inlete figure shows that with increasing flow rate the pressurefluctuation amplitude at the impeller inlet of the threeschemes gradually decreases When the number of IGVsgradually increases the amplitude of pressure fluctuation atthe impeller inlet first decreases and then increases undersmall-flow conditions and design conditions but graduallyincreases under large flow conditions Under the designconditions the pressure fluctuation amplitudes of the 4IGVs and 6 IGVs shaft tubular pumps are approximately 26times and 18 times that of the 5 IGVs shaft tubular pumprespectively According to the results of the tests on thepressure fluctuation and external characteristics the per-formance of the shaft tubular pump with 5 IGVs is the besterefore the following selection of the 5 IGVs scheme andno IGVs scheme shaft tubular pump are numerically cal-culated and compared

2 Shock and Vibration

3 Numerical Calculation

31CalculationModel Numerical simulations of the 5 IGVsschemes and the scheme without IGVs are performed espeed of the pump is 1163 rmin Under the design conditionQd when the temperature is 25degC the Reynolds number ofthe inlet section of the impeller of the shaft tubular pump is1510268 e hub diameter D1 of the shaft tubular pump is110mm and the impeller diameter D is 300mm e pumphas 3 impellerse tip clearance d is 015mme hub ratiodr is 04 e design flow Qd is 288 Ls e single-sidedspread angle of the guide vane shroud is 5 degrees e IGVsadopt 2D a straight blade form e installation angle of theIGVs is set to 0 degrees e number of IGVs is 5 and theirthickness is 5mm e distance between the IGVs and theimpeller is set at 085D Figure 5 shows the three-dimen-sional model of the shaft tubular pump impeller

e calculation model of the scheme without IGVs iscomposed only of impellers guide vanes inlet channels andoutlet channels In addition to the above four parts thecalculationmodel of the IGVs scheme adds the IGVs sectione grids of the impeller guide vanes and IGVs are modeledby TurboGrid and divided into structured grids e gridnumber of guide vanes is approximately 840000 e gridnumber of IGVs is approximately 960000 e inlet andoutlet flow channels are first modeled by Creo and thendivided into structured grids using ICEM e numbers ofgrid elements are approximately 141 million and 710000e mesh of each part of the model is shown in Figure 6After the mesh of each part is completed the calculationmodel is assembled in CFXe three-dimensional diagramsof the calculation model are shown in Figure 7

Because the convergence of the calculation is greatlyaffected by the grid quality grid-independence analysis of

21 3

4 5 6 7

8 9 10 11 12

Figure 1 Two-dimensional diagram of the hydraulic machinery test bench (1 auxiliary pump motor 2 auxiliary pump 3 solenoid globevalve 4 shut-off valve 5 auxiliary pump 6 electromagnetic flowmeter 7 electric control gate valve 8 vacuum water tank 9 main motor10 shaft tubular pump device 11 pressure water tank and 12 water storage tank)

(a) (b) (c) (d) (e)

Inlet Outlet

P1 P2 P3

(f )

Figure 2 (a) Impeller (b) guide vanes (c) 4 IGVs (d) 5 IGVs (e) 6 IGVs and (f ) diagram of test device

Shock and Vibration 3

5

4

3

2

1

004 05 06 07 08 09

QQd

10 11 12

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()

Q-H curve (4 IGVs)Q-H curve (5 IGVs)Q-H curve (6 IGVs)

Q-η curve (4 IGVs)Q-η curve (5 IGVs)Q-η curve (6 IGVs)

Figure 3 Test results for shaft tubular pumps with 4 5 and 6 IGVs

0 3 6 9 12 15 18 21 244

5

6

00076

00152

00228

00304

00380

Frequency MultiplierNumber of Inlet Guide Vanes

Cp

Cp=000283

Cp=000545

Cp=000686

(a)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


CpCp=000561

Cp=000215

Cp=000392

(b)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


Cp

Cp=000135

Cp=000187

Cp=000197

(c)

Figure 4 Test results for the pressure pulsation test of shaft tubular pumps with 4 5 and 6 IGVs (a) 075Qd and (b) Qd and 125Qd


the shaft tubular pump with and without IGVs is performedFigure 8 shows the relationship between the grid elementnumber and the efficiency of the pump device

When the number of grid elements for the pump devicewithout and with IGVs is 32 million and 4 million re-spectively the efficiency is basically no longer affected bychanges in the grid To reduce the workload of the numericalcalculations a total number of grid elements of the pumpdevice without and with IGVs are selected to be 343 millionand 44 million respectively

32 Governing Equation e basic governing equation inthis article is the N-S equation e turbulence model usesRNG k-ε turbulence model e k-ε turbulence model is acommon calculation model suitable for most projects eRNG k-ε turbulence model is an improved equation basedon the standard k-ε turbulence model which can deal withswirling and large aberration flows so it is more widely used

(1) e k equation and ε equation of the RNG k-εturbulence model are

z(ρk)

z(t)+

z ρkui( 1113857

z xi( 1113857

z

zxj

αkμeff

zk

zxj

1113890 1113891 + μt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus ρε

z(ρε)z(t)

+z ρεui( 1113857

z xi( 1113857

z

zxj

αεμeff

zε

zxj

1113890 1113891 +C1ε middot ε

kμt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus C2ερε2

kminus R

(2)

Figure 5 ree-dimensional model of the impeller

(a) (b) (c) (d) (e)

Figure 6 Grid of each part (a) Inlet channel (b) Outlet flow channel (c) IGVs (d) Impeller (e) Guide vanes

Sha inlet channelOutlet channel

ImpellerGuide vane

(a)

Sha inlet channel Outlet channelImpeller

Guide vaneInlet guide vane

(b)

Figure 7 ree-dimensional diagram of the calculation model of the pump device (a) Scheme of the shaft tubular pump without IGVs(b) Scheme of the shaft tubular pump with IGVs


where ρ is the fluid density xi and xj are the co-ordinate components μt is the turbulent viscosity ui

and uj are the time-averaged velocity componentsαk and αε are the corresponding coefficients of k andε respectively and μeff is the effective turbulent flowviscosity coefficient

μeff μ + μt

μt ρCμk2

ε

R Cμρφ

3 1 minus φφ0( 1113857ε2

1 + βφ31113872 1113873k

Cμ 00845

C1ε 142

C2ε 168

φ 2Eij1113872 1113873k

3

Eij 12

zui

zxi

+zuj

zxj

1113888 1113889

φ0 4377

β 0012

(3)

(2) e three-dimensional incompressible turbulentcontinuity equation and momentum equation are

zρzt

+ nabla middot (ρU) 0

zρU

zt+ nabla middot ρU middot Uprime( 1113857 minus nabla middot μeffnabla middot Uprime1113872 1113873 nablaPprime + nabla middot μeffnablaU1113872 1113873

T+ B

(4)

where Pprime P + 23ρK is the static pressure μprime is thevelocity component and B is the sum of additionalforces

33BoundaryConditionandPressureFluctuationMonitoringPoints e governing equation is the N-S equation in theunsteady numerical simulation of the pump device eRNG k-ε turbulence model is a basic turbulence model[42 43] e inlet boundary condition is set as the totalpressure inlet and its pressure value is one atmosphere eoutlet boundary condition is set as the mass flow outlet eimpeller is set as rotating domain e other parts are set asstatic domain e nonslip condition satisfying viscous fluidis adoptede dynamic and static interface adopts the stageinterface model with average speed e other parts of theinterface adopt the none interface type [44 45] e timestep is calculated and set to 47619times10minus4 s e total timestep is the time required to rotate 8 revolutions which is setto 045714286 s To verify the independence of the time steptwo time steps of 15873times10minus4 s (equivalent to 1 degreeimpeller rotation time) and 3174610times10minus4 s (equivalent to 2degree impeller rotation time) are calculated for the tubularpump without IGVs We extract the pressure pulsation atpoint P5 at the impeller inlet under the design condition Qdfor comparison as shown in Figure 9 e difference inpressure pulsation calculated by the three time steps is

740

250 350300 450400Number of Elements (Ten ousand)

500

745

750

755

760

765

770

775

Effic

ienc

y η

()

3436043

4397423

IGVs SchemeNo IGVs Scheme

Figure 8 Grid-independence analysis


relatively small erefore to reduce the calculation time itis reasonable to select 3 degrees as a time step for calculation

We arrange monitoring points in the shaft tubular pumpto analyze the pressure fluctuation characteristicse P1-P4monitoring points are arranged radially on the IGVs inletsection e P5-P8 monitoring points are arranged radiallyon the impeller inlet section e P9-P12 monitoring pointsare arranged radially on the impeller outlet sectione P13-P16 monitoring points are arranged radially on the guidevane outlet section e three-dimensional layout of mon-itoring points is shown in Figure 10

4 Comparison of the Results of the Calculationand the Experiment

41ExternalCharacteristicResults emodel test results forthe shaft tubular pumpwith and without IGVs are comparedwith the calculation results Figure 11 shows the comparisonresult e figure shows that when the operating conditiondeviates from the design condition the efficiency measuredby the model test is higher than that of the calculationWhenthe flow is higher than the design flow conditions the headcurve fits better e head deviation is larger when it is lessthan the design flow but the maximum relative error doesnot exceed 5 is shows that the numerical simulationresults of the shaft tubular pump are accurate and credibleis also demonstrates that the performance of the shafttubular pump will be significantly affected by the IGVs

42 Pressure PulsationResults emodel test also tested thepressure pulsation at point P1lowast under three characteristicworking conditions (075Qd Qd and 125 Qd) of the shafttubular pump with 5 IGVs and no IGVs Figures 12 and 13show the comparison between the pressure pulsation testand the numerical calculation results emain frequency ofthe pressure fluctuation of the two schemes is the impellerpassing frequency and the amplitude deviation is small e

calculation results of the pressure fluctuation are shown tobe accurate and reliable

5 Numerical Results

51 Analysis of the Hydraulic Performance To analyze theperformance difference of the shaft tubular pump withoutIGVs and with 5 IGVs schemes numerical simulationcalculations are performed on the two pump devices Fig-ure 14 shows the comparison results of the performancecurves After adding the IGVs in front of the impeller thepump head and efficiency are reduced under design con-ditions and small-flow conditions e smaller the flow isthe greater the drop in the head and efficiency of the shafttubular pump device are However there is basically nochange in the head and efficiency under large-flow condi-tions Under the design condition the efficiency of the pumpwith IGVs is nearly 163 lower than that of the schemewithout the IGVs and the head is nearly 006m lower eIGVs have a greater impact on the performance of the shafttubular pump

To further analyze the influence of the IGVs Figure 15 isthe comparison of the flow uniformity Vu and the speedweighted average angle θ of the impeller inlet of the twopump schemes With increasing flow the uniformity of theflow velocity and the velocity-weighted average angle of theimpeller inlet section of the two schemes gradually increaseAfter adding the IGVs in front of the impeller the flowuniformity of the impeller inlet section increases by ap-proximately 111 and the speed-weighted average angle isreduced by approximately 07deg is shows that the IGVs canimprove the hydraulic conditions of the impeller of the shafttubular pump

Vu 1 minus1

Va

1113936ni1 Vai minus Va( 1113857

2

m

1113971

⎛⎜⎝ ⎞⎟⎠ times 100 (5)

0020000 002 004

t (s)006 008

0025

0030

0035

0040

0045

0050

CP

(1 degree)(2 degree)(3 degree)

Figure 9 Independence of the time step


P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet

Inlet guide vane Guide vaneImpeller

Figure 10 ree-dimensional schematic diagram of the layout of monitoring points

6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()

Numerical simulation Q-H curveModel test Q-H curveNumerical simulation Q-η curveModel test Q-η curve

(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)

Figure 11 Comparison between the results of the calculation and the test (a) Shaft tubular pump without IGVs and (b) shaft tubular pumpwith IGVs

00000 3 6 9 12

Frequency Multiplier15 18 21 24

0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284

Test of the Model Pump DeviceNumerical Simulation of theModel Pump Device

(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)

Figure 12 Test of the pressure fluctuation and numerical simulation comparison of impeller inlet of shaft tubular pumps with no IGVsunder (a) 075Qd (b) Qd and (c) 125Qd


where Vai is the axial velocity of the ith grid node of theimpeller inlet section ms Va is the average axial velocity ofthe impeller inlet section ms and m is the number of gridsof the impeller inlet section

θ 1113936

ni1 90deg minus arctan VtiVai( 1113857( 1113857Vai

1113936ni1 Vai

(6)

where Vti is the lateral velocity of the ith grid node on theimpeller inlet section ms

Figure 16 shows the change in the static pressure of eachcalculation area in the shaft tubular pump with and withoutIGVs under three characteristic working conditions (075Qd Qd and 125 Qd) H is the average static pressuredifference between each section and the impeller inlet Z isthe distance from the section to the central section of the

impeller [46] After adding the IGVs in front of the impellerunder various working conditions H of the inlet flowpassage and the IGVs section significantly decrease As theflow rate increases H decreases more but the values ofH of the impeller guide vanes and outlet channel basicallydo not change It can be found from the results that thehydraulic loss of the inlet channel will increase by adding theIGVs and the performance of the shaft tubular pump willdecrease

e axial velocity diagrams of the impeller inlet sectionof the shaft tubular pump under three characteristic con-ditions (075Qd Qd and 125 Qd) are considered for com-parison as shown in Figures 17 and 18e figures show thatdue to the influence of the impeller three high-velocity areasand three low-velocity areas appear on the inlet of theimpeller of the two schemes under three working conditions

Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)

Figure 13 Test of the pressure fluctuation and numerical simulation comparison of the impeller inlet of shaft tubular pumps for the 5 IGVsscheme under (a) 075Qd (b) Qd and (c) 125Qd

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()

Numerical simulation Q-H curve (5 IGVs Scheme)Numerical simulation Q-H curve (No IGVs Scheme)Numerical simulation Q-η curve (No IGVs Scheme)Numerical simulation Q-η curve (5 IGVs Scheme)

Figure 14 External characteristic curve of the numerical simulation of the two schemes


90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)

θ (No IGVs Scheme)θ (5 IGVs Scheme)Vu (No IGVs Scheme)Vu (5 IGVs Scheme)

Figure 15 Comparison of the uniformity of the flow velocity and velocity-weighted average angle at the impeller inlet

ndash100ndash20 ndash15 ndash10 ndash05 00 05

ZD10 15 20 25 30 35

ndash075ndash050ndash025

000025050075100125150175200225250275300325350

ΔH (m

)

Inlet channel Outlet channelInlet Guide Vanes

Guide VanesImpeller

5 Inlet Guide Vanes SchemeNo Inlet Guide Vanes Scheme

(a)

ndash125ndash100

ndash20 ndash15 ndash10 ndash05 00 05ZD

10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175

ndash075ndash100ndash125ndash150


10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)

Figure 16 Hydraulic curves of each calculation area of the shaft tubular pump under (a) 075Qd (b) Qd and (c) 125Qd


which are consistent with the number of blades After addingthe IGVs the axial velocity decreases under three workingconditions is is because of the thickness of the IGVs andthe frictional resistance of the contact surface between theblade and the water flow It has an obstructive effect on thewater flow resulting in a decrease in the axial velocity of thewater flow at the inlet of the impeller ere is frictionalresistance between the IGVs and the water flow whichcauses a decrease in the axial velocity of the impeller

52 Pressure Pulsation Analysis To analyze the differencebetween the pressure pulsation in the shaft tubular pump ofthe two schemes the main frequency amplitude of pressurepulsation in the shaft tubular pump under three charac-teristic conditions (075Qd Qd and 125Qd) is taken forcomparison as shown in Figure 19 e inlet of the impelleris the area with the largest amplitude of pressure fluctuationand the second is the impeller outlet Because the inletchannel and the guide vanes are far from the impeller thepressure fluctuation amplitude is small e pressure pul-sation amplitude of the shaft tubular pumps of the twoschemes under small-flow conditions is the smallest underthe three conditions e pressure fluctuation amplitudeunder the design condition is the smallest which is

approximately 25 of that under the small-flow conditionerefore more attention should be given to pressurepulsation under the condition of small flow when the shafttubular pump is running After the IGVs are added to theimpeller inlet the pressure pulsation of the entire pumpdevice is reduced under each flow condition especially thepressure pulsation of the impeller inlet which greatly de-creases is shows that the IGVs can not only improve theuniformity of the impeller inlet flow rate but also suppressthe pressure pulsation at the inlet of the impeller After theIGVs are added the pressure fluctuation amplitude in theinlet channel and the guide vanes is also very small is isbecause the inlet channel and the guide vanes are far fromthe impeller and are less affected by the impeller

e pressure pulsation intensity Clowastp distribution of theimpeller inlet section of the pump under three conditions(075Qd Qd and 125Qd) is taken for comparison as shownin Figures 20 and 21 e figures show that there are 3 high-pressure areas and 3 low-pressure areas at the inlet section ofthe impeller of the two schemes which correspond to thenumber and position of impellers is is because the ro-tation of the impeller is the source of pressure fluctuationinside the pump unit After adding the IGVs the pressurepulsation intensity at the entrance of the impeller will begreatly reduced under all working conditions

0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)

Figure 17 Axial velocity distribution of the pump impeller inlet in the no IGVs scheme (a) 075Qd (b) Qd and (c) 125Qd

0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)

Figure 18 Axial velocity distribution of the pump impeller inlet in the 5 IGVs scheme under (a) 075Qd (b) Qd and (c) 125Qd


To analyze the pressure fluctuation intensity distribu-tion on the blade surface the middle span circumferentialsection (span 05) of the hub and shroud of the impellerwas removed for analysis e midspan surface is shown inFigure 22 Figure 23 shows the pressure pulsation intensitydistribution at the midspan e pressure fluctuation

intensity on the pressure side of the two schemes is higherthan that on the suction sidee existence of IGVs reducesthe pressure fluctuation intensity on the blade surfaceWith the decrease in the flow the effect becomes in-creasingly obvious After adding the IGVs the pressurepulsation amplitude of the pressure side and suction side of

0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631

No Inlet Guide Vanes Scheme5 Inlet Guide Vanes Scheme

(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)

Figure 19 Main frequency of pressure pulsation in the shaft tubular pump under (a) 075Qd (b) Qd and (c) 125Qd

00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)

Figure 20 Pressure fluctuation intensity distribution of the pump impeller inlet in the no IGVs scheme under (a) 075Qd (b) Qd and(c) 125Qd

00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)

Figure 21 Pressure fluctuation intensity distribution of the pump impeller inlet in the 5 IGVs scheme under (a) 075Qd (b) Qd and (c)125Qd


the blade is greatly reduced e maximum pressurefluctuation intensity of the vane pressure side (ignoring theblade head and tail area) and suction side of the vertical welltubular pump without IGVs is approximately 13 times and11 times that of the IGVs scheme

To analyze the effect of the IGVs on the pressure pul-sation of the impeller inlet of the pump device time domaindiagrams at four monitoring points along the radial dis-tribution of the impeller inlet section are taken out forresearch as shown in Figures 24 and 25 e time domain

diagrams of the two pumps are similar in the change trendunder the same flow conditions In a rotation period thetime domain graph has three peaks and troughs Along thedirection from the hub to the shroud the pressure pulsationamplitude at the inlet of the impeller of the two pumpsgradually increases When the flow rate gradually increasesthe pressure pulsation amplitude of the impeller inlet of thetwo pumps first decreases and then increases e reason isthat the pressure difference between the inlet and outlet ofthe impeller is large under the small-flow condition and the

0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10

No IGVs Scheme5 IGVs Scheme

(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)

Figure 23e pressure distribution of the suction surface and pressure surface of the blade in the midspan under (a) 075Qd (b)Qd and (c)125Qd

Outlet

Span=05

Pressure side

Inlet

Figure 22 Schematic diagram of the midspan of the impeller

0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)

Figure 24 Time domain distribution of the shaft tubular pump without IGVs under (a) 075Qd (b) Qd and (c) 125Qd


tip clearance backflow is serious erefore the impact ofbackflow and incoming flow results in a turbulent flowpattern at the inlet It can also be found that the pressurepulsation amplitude of the impeller inlet of the pump devicewithout IGVs is smaller than that of the IGV scheme underall working conditions In the IGV scheme the pressurepulsation amplitude of the impeller inlet P5 of the pump at075 Qd Qd and 125 Qd is approximately 13 35 and 310of the scheme without IGVs

6 Conclusion

First the influence of the number of IGVs on the perfor-mance and pressure fluctuation of the shaft tubular pumpwas experimentally studied en numerical simulations ofthe shaft tubular pump with and without IGVs were per-formed by CFD e influence of the IGVs on the hydraulicperformance and pressure fluctuation characteristics of theshaft tubular pump was studied Finally tests on the externalcharacteristics and pressure fluctuation were performed toprove the accuracy of the calculation data Based on theanalysis of the pressure fluctuation at the impeller inlet thefollowing conclusions were obtained

(1) e number of IGVs has a great impact on theperformance of the shaft tubular pump With theincrease in the number of IGVs the pressure pul-sation amplitude at the inlet of the impeller decreasesfirst and then increases under small-flow conditionsand design conditions but gradually increases underlarge-flow conditions

(2) After the IGVs are added to the impeller inlet thehydraulic losses of the inlet channel and the IGVssection increase At the same time the head andefficiency of the pump device are reduced e IGVscan improve the uniformity of the impeller inlet flowand improve the impeller water inlet condition butthey have a negative impact on the impeller inletaxial speed

(3) e impeller inlet is the area with the largest pressurepulsation amplitude inside the shaft tubular pumpdevice followed by the impeller outlet Since theIGVs and the guide vanes are far from the impeller

the pressure pulsation amplitude is very small Afteradding the IGVs the overall pressure pulsation valueof the shaft tubular pump is reduced In particularthe pressure pulsation at the inlet of the impeller issignificantly weakened

(4) e advantage of the IGVs is that they reduce thepressure pulsation of the pump device and improvethe structure and operation stability of the pumpdevice e disadvantage is that the head and effi-ciency are slightly reduced For the drainagepumping station due to the short running time ofthe pumping station its economic operation issecondary to safety and stability In summary theadvantages of installing IGVs at the inlet of the shafttubular pump are more favorable than thedisadvantages

(5) e results for the numerical simulations and modeltests of the shaft tubular pumps are in good agree-ment is shows that it is accurate and feasible tostudy the hydraulic performance and pressurefluctuation characteristics of shaft tubular pumps bynumerical simulation methods

Abbreviations

n Impeller revolution rmindr Hub ratiod Tip clearanceeS System erroreR Measurement errorCp Pressure pulsation coefficientClowastp Pressure pulsation intensityD Impeller diameter mmP Instantaneous pressure PaQ Flow Lsρ Liquid density kgm3

η Efficiency P Average pressure Pau Circumferential velocity radsQd Design flow LsH Head mD1 Hub diameter mm

0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)

Figure 25 Time domain distribution of the shaft tubular pump with 5 IGVs under (a) 075Qd (b) Qd and (c) 125Qd


ui uj Time-averaged velocity componentαk αε e coefficients of k and εUprime Velocity componentμt Turbulent viscosityxi xj Coordinate componentB Sum of additional forcesμeff Effective turbulent flow viscosity coefficientPprime Static pressure PaVu Flow uniformity Vai Axial velocity of the ith grid node msθ Velocity-weighted average angle degVa Average axial velocity msH Average static pressure PaVti Lateral velocity of the ith grid node msZ Distance from the section to the central section of the

impeller mmm Number of grids of the impeller inlet section

Data Availability

e data can be obtained upon request by contacting thecorresponding author

Conflicts of Interest

e authors declare that this article does not have anypotential conflicts of interest

Authorsrsquo Contributions

Sorting and analysis of test and calculation data were carriedout by Haifeng Jiao Analysis and writing of the paper wereperformed by Songshan Chen Chong Sun reviewed andedited the article

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (51076136) National Science andTechnology Support Plan (2006BAB04A03) Natural ScienceFoundation of Jiangsu Province (BK2008217) Key Programsof Water Conservancy Science and Technology in JiangsuProvince (Grant no 2009053) and the Priority AcademicProgram Development of Jiangsu Higher Education Insti-tutions (Grant no PAPD)

References

[1] F Meng J Pei Y J Li and S Yuan ldquoEffect of guide vaneposition on hydraulic performance of two-direction tubularpump devicerdquo Journal of Agricultural Machinery vol 48no 2 pp 135ndash140 2017

[2] R S Xie F P Tang C Liu and F Yang ldquoComparison ofhydraulic performance between vertical shaft and shaft

extension tubular pumping systemrdquo Journal of AgriculturalMachinery vol 32 no 13 pp 24ndash30 2016

[3] Y Fan C Liu and L W Zhang ldquoPressure pulsations of theblade region in S-shaped shaft-extension tubular pumpingsystemrdquo Mathematical Problems in Engineering vol 2014Article ID 820135 10 pages 2014

[4] L J Shi X Q Liu F P Tang and Y Yao ldquoDesign opti-mization and experimental analysis of bidirectional shafttubular pump devicerdquo Journal of Agricultural Machineryvol 47 no 12 pp 85ndash91 2016

[5] J Liu Y Zheng D Q Zhou and Y Mao ldquoAnalysis of basicflow pattern in shaft front-positioned and shaft rear-posi-tioned tubular pump systemsrdquo Journal of Agricultural Ma-chinery vol 41 no S1 pp 32ndash38 2010

[6] F H Han Z Wang Y J Mao T Jiajian and W Li ldquoEx-perimental and numerical studies on the influence of inletguide vanes of centrifugal compressor on the flow fieldcharacteristics of inlet chamberrdquo Advances in MechanicalEngineering vol 12 no 11 2020

[7] Y Du S X Zheng K Chen et al ldquoExergy loss characteristicsof a recuperated gas turbine and Kalina combined cyclesystem using different inlet guide vanes regulation ap-proachesrdquo Energy Conversion and Management vol 230Article ID 113805 2021

[8] Y Q Ye and J G Yang ldquoAnalysis on the abrupt vibrationcaused by angular deviation of inlet guide vane of gas tur-binerdquo Journal of Engineering for thermal Energy and Powervol 35 no 7 pp 43ndash48 2020

[9] B Dewar M Creamer M Dotcheva J Radulovic andJ M Buick ldquoA 1D mean line model for centrifugal com-pressors with variable inlet guide vanesrdquo Engineering Reportsvol 1 no 1 2019

[10] J Fukutomi and R Nakamura ldquoPerformance and internalflow of cross-flow fan with inlet guide vanerdquoAe Japan Societyof Mechanical Engineers vol 48 no 4 2005

[11] M Coppinger and E Swain ldquoPerformance prediction of anindustrial centrifugal compressor inlet guide vane systemrdquoProceedings of the Institution of Mechanical EngineersmdashPartA Journal of Power and Energy vol 214 no 2 2000

[12] K Kabalyk M Jasek G Liskiewicz and L Horodko ldquoEx-perimental analysis of the influence of outlet network volumeand inlet guide vane positioning on surge behavior in a single-stage low-speed centrifugal compressorrdquo Proceedings of theInstitution of Mechanical EngineersmdashPart A Journal of Powerand Energy vol 232 no 4 p 4 2018

[13] V Barzdaitis P Mazeika M Vasylius V Kartasovas andT Arturas ldquoInvestigation of pressure pulsations in centrifugalpump systemrdquo Journal of Vibroengineering vol 18 no 3pp 1849ndash1860 2016

[14] R Spence and J Amaral-Teixeira ldquoInvestigation into pressurepulsations in a centrifugal pump using numerical methodssupported by industrial testsrdquo Computers amp Fluids vol 37no 6 2007

[15] R Barrio J Parrondo and E Blanco ldquoNumerical analysis ofthe unsteady flow in the near-tongue region in a volute-typecentrifugal pump for different operating pointsrdquo Computersamp Fluids vol 39 no 5 2010


[16] Y C Wang L Tan B S Zhu C ShuLiang and W BinbinldquoNumerical investigation of influence of inlet guide vanes onunsteady flow in a centrifugal pumprdquo Proceedings of theInstitution of Mechanical EngineersmdashPart C Journal of Me-chanical Engineering Science vol 229 no 18 2015

[17] M Liu L Tan and S L Cao ldquoInfluence of geometry of inletguide vanes on pressure fluctuations of a centrifugal pumprdquoJournal of Fluids Engineering vol 140 no 9 2018

[18] L Shi J Zhu Y Yuan et al ldquoNumerical simulation andexperiment of the effects of blade angle deviation on thehydraulic characteristics and pressure pulsation of an axial-flow pumprdquo Shock and Vibration vol 2021 pp 1ndash14 ArticleID 6673002 2021

[19] F Yang C Liu F P Tang W-Z Hu and Y Jin ldquoNumericalsimulation on hydraulic performance of axial-flow pumpingsystem with adjustable inlet guide vanesrdquo Transactions of theChinese Society for Agricultural Machinery vol 45 no 5pp 51ndash58 2014

[20] L Xu D Ji W Shi B XuW Lu and L Lu ldquoInfluence of inletangle of guide vane on hydraulic performance of an axial flowpump based on CFDrdquo Shock and Vibration vol 2020pp 1ndash16 Article ID 8880789 2020

[21] F Wang Z D Qian and Z W Guo ldquoPressure oscillationsprediction of axial flow pump with adjustable guide vanesrdquoTransactions of the Chinese Society for Agricultural Machineryvol 48 no 3 pp 119ndash123 2017

[22] B Maxime K Kan H X Chen et al ldquoFlow instabilitytransferability characteristics within a reversible pump tur-bine (RPT) under large guide vane opening (GVO)rdquo Re-newable Energy vol 179 pp 285ndash307 2021

[23] J Jesline R Mehrdad and C Michel J ldquoStudy of flowcharacteristics inside francis turbine draft tube with adjustableguide vanesrdquo IOP Conference Series Earth and EnvironmentalScience vol 774 no 1 2021

[24] M Binama W Su W H Cai et al ldquoInvestigation on re-versible pump turbine flow structures and associated pressurefield characteristics under different guide vane openingsrdquoScience China Technological Sciences vol 62 no 11 2019

[25] S Chitrakar O G Dahlhaug and H P Neopane ldquoNumericalinvestigation of the effect of leakage flow through erosion-induced clearance gaps of guide vanes on the performance ofFrancis turbinesrdquo Engineering Applications of ComputationalFluid Mechanics vol 12 no 1 2018

[26] S Chitrakar B S apa O G Dahlhaug and H P NeopaneldquoNumerical investigation of the flow phenomena around alow specific speed Francis turbinersquos guide vane cascaderdquo IOPConference Series Earth and Environmental Science vol 49no 6 2016

[27] F Yang W-z Hu C Li C Liu and Y Jin ldquoComputationalstudy on the performance improvement of axial-flow pumpby inlet guide vanes at part loadsrdquo Journal of MechanicalScience and Technology vol 34 no 12 pp 4905ndash4915 2020

[28] Z L Zhao Z W Guo Z D Qian and Q Cheng ldquoPerfor-mance improvement of an axial-flow pump with inlet guidevanes in the turbine moderdquo Proceedings of the Institution ofMechanical EngineersmdashPart A Journal of Power and Energyvol 234 no 3 2020

[29] Y S Kim H-S Shim and K Kwang-Yong ldquoEffects of inletguide vane and blade pitch angles on the performance of asubmersible axial-flow pumprdquo Proceedings of the Institution ofMechanical EngineersmdashPart A Journal of Power and Energyvol 235 no 4 2021

[30] ZW Guo J Y Pan Z D Qian and J Bin ldquoExperimental andnumerical analysis of the unsteady influence of the inlet guide

vanes on cavitation performance of an axial pumprdquo Pro-ceedings of the Institution of Mechanical EngineersmdashPart CJournal of Mechanical Engineering Science vol 233 no 11pp 3816ndash3826 2019

[31] H Yang D D Sun and F P Tang ldquoResearch on the per-formance improvement of axial-flow pump under unstablecondition using CFDrdquo Transactions of the Chinese Society forAgricultural Machinery vol 43 no 11 pp 138ndash141+1512012

[32] Y Y Xing R S Xie and C Xiang ldquoSimulation study onimproving saddle zone of axial flow pump device with frontbafflerdquo Coal Mine Machinery vol 40 no 01 pp 52ndash54 2019

[33] J Dai Y J Li and S Q Yuan ldquoEffect of inlet guide vaneposition on hydraulic performance of bulb tubular pumprdquoJournal of Drainage and Irrigation Machinery Engineeringvol 35 no 9 pp 761ndash766 2017

[34] J Deng J L Lu Y R Xu F JianJun and L XingQi ldquoEffect ofclocking position of front guide vane on pulsation charac-teristic of pressure in centrifugal pumprdquo Journal of NorthwestForestry University vol 44 no 1 pp 217ndash222 2016

[35] X Song and C Liu ldquoExperimental investigation of floor-attached vortex effects on the pressure pulsation at the bottomof the axial flow pump sumprdquo Renewable Energy vol 145pp 2327ndash2336 2020

[36] X H Duan F P Tang W Y Duan W Zhou and L ShildquoExperimental investigation on the correlation of pressurepulsation and vibration of axial flow pumprdquo Advances inMechanical Engineering vol 11 no 11 2019

[37] L Xu L G LuW Chen and GWang ldquoFlow pattern analysison inlet and outlet conduit of shaft tubular pump system ofPizhou pumping station in South-to-North Water DiversionProjectrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 28 no 6 pp 50ndash56 2012

[38] R S Xie Z Wu and Y He ldquoOptimization research onpassage of bidirectional shaft tubular pumprdquo Transactions ofthe Chinese Society for Agricultural Machinery vol 46 no 10pp 68ndash74 2015

[39] A R Al-Obaidi ldquoInvestigation of the influence of variousnumbers of impeller blades on internal flow field analysis andthe pressure pulsation of an axial pump based on transientflow behaviorrdquo Heat Transfer vol 49 no 4 2020

[40] L Shi W Zhang H Jiao et al ldquoNumerical simulation andexperimental study on the comparison of the hydrauliccharacteristics of an axial-flow pump and a full tubularpumprdquo Renewable Energy vol 153 pp 1455ndash1464 2020

[41] X J Song and C Liu ldquoExperimental investigation of pressurepulsation induced by the floor-attached vortex in an axial flowpumprdquo Advances in Mechanical Engineering vol 11 no 32019

[42] L Shi Y Yuan H Jiao et al ldquoNumerical investigation andexperiment on pressure pulsation characteristics in a fulltubular pumprdquo Renewable Energy vol 163 pp 987ndash10002021

[43] C L Xie F P Tang R T Zhang W Zhou W Zhang andF Yang ldquoNumerical calculation of axial-flow pumprsquos pressurefluctuation and model test analysisrdquo Advances in MechanicalEngineering vol 10 no 4 2018

[44] W P Zhang F P Tang L J Shi Q Hu and Y Zhou ldquoEffectsof an inlet vortex on the performance of an axial-flow pumprdquoEnergies vol 13 no 11 2020

[45] C Z Xia L Cheng H Y Jiang and J Xin ldquoHydraulicperformance analysis and optimization on flow passagecomponents of diving tubular pumping systemrdquo Transactions


of the Chinese Society for Agricultural Machinery vol 34no 7 pp 45ndash51+301 2018

[46] T Mu R Zhang H Xu Y Zheng Z Fei and J Li ldquoStudy onimprovement of hydraulic performance and internal flowpattern of the axial flow pump by groove flow controltechnologyrdquo Renewable Energy vol 160 pp 756ndash769 2020


found that IGVs with a 0deg angle had little effect on thehydraulic characteristics of the pumps in high-efficiencyareas and low-flow conditions e larger hydraulic lossfrom the IGVs was the main reason for the low efficiency ofthe pumps under large-flow conditions

ere have been a relatively large number of studies onrear guide vanes [20ndash26] Yang et al [27] studied the angle ofthe IGVs of an axial flow pump When the angle of the bladewas adjusted from positive to negative the performancecurve shifted in the direction of large flow Zhao et al [28]studied the IGVs of an axial flow pump in turbine mode Itwas found that the efficiency range of the pump was ex-panded by the IGVs Kim et al [29] found that IGVs greatlyinterfered with the steady and unsteady characteristics of apump In particular the efficiency was most affected by theIGVs Guo et al [30] found that the installation angle ofIGVs had a greater impact on the cavitation of a pump Yanget al [31] studied the influence of the impeller inlet baffle onits performance It was found that the distance between theinlet baffle and the impeller had the greatest impact on waterpump performance e inlet baffle could constrain thebackflow of the impeller inlet and improve the efficiency ofthe pump Xing et al [32] set a baffle plate at the impellerinlet and analyzed it numerically e study found that thebaffle plate mainly affected the tangential velocity of theimpeller inlet and could improve the impeller workingability Dai et al [33] researched the positions of IGVs ecloser the IGVs were to the impeller the better the workingcondition of the impeller was e efficiency of the pump setwas also improved Deng et al [34] found that IGVs had asubstantial impact on the external characteristics and vi-bration characteristics of pumps

e present paper adopts a research method thatcombines numerical simulation and model tests [35ndash38]First the influence of the number of IGVs on the perfor-mance and pressure pulsation of the shaft tubular pump isstudied through model tests en the 5 IGVs schemewhich offers better performance than other schemes and theshaft tubular pump without IGVs are selected for numericalsimulation and comparison Finally several model tests areused to prove the accuracy of the calculation data Wemainly analyze the influence of the number of IGVs and theaddition of IGVs on the performance and pressure pulsationcharacteristics of the pump unite purpose of this article isto derive the change law of the pressure pulsation of the shafttubular pump [39ndash41] and provide guidance for thestructural design and operation of pump stations

2 Model Test

21 Test Scheme Design A shaft tubular pump withoutIGVs and a shaft tubular pump with 4 IGVs 5 IGVs and 6IGVs were designed Tests on the external characteristicsand pressure fluctuations were performed on a hydraulicmachinery test bench that was accurately calibrated esystem error eS and measurement error eR of the testbench are plusmn0231 and plusmn0171e test speed is the sameas the calculation which is 1163 rmin Figure 1 is aschematic diagram of the test bench e impeller

diameter of the shaft tubular pump is 300mm Figure 2(a)shows a physical picture of the impeller e number ofblades is 3 and they are made of brass e guide vanesand IGVs are welded with 5mm thick steel materials eguide vanes and IGVs are shown in Figures 2(b) and 2(c)ndash2(e)ree monitoring points P1 lowast at the IGVs inlet P2 lowastat the impeller inlet and P3 lowast at the guide vane outletwere measured in the pressure fluctuation test Figure 2(f )is the physical map of the test device and the layout of themeasuring points

22 Test Results and Analysis Figure 3 shows the test resultsof the external characteristics of pumps with 4 IGVs 5 IGVsand 6 IGVs e change trends of the head and efficiencycurves of the three schemes are basically the same enumber of IGVs has an obvious effect on the efficiency of thepump but has little effect on the head When the number ofIGVs gradually increases the efficiency of the pump firstincreases and then decreases e efficiency of the pumpwith 5 IGVs is the highest under the design condition whichis approximately 126 higher than that of the shaft tubularpump with 4 IGVs

To analyze the pressure pulsation the nondimensionalparameters of the pressure pulsation coefficient Cp andpressure pulsation intensity Clowastp are introduced to express theresults e formulas are as follows

CP P minus P

05ρu2

CPlowast

1113936ni1 C

2P

n

1113971

(1)

where P is the average pressure at the monitoring point PaP is the instantaneous pressure at the monitoring point Pa ρis the liquid density kgm3 n is the impeller revolution andu is the impeller outlet circumferential velocity rads

Figure 4 shows the test results for the pressure fluctu-ation of shaft tubular pumps with 4 IGVs 5 IGVs and 6IGVs Since the IGVs have an obvious influence on thepressure fluctuation at the impeller inlet the following in-vestigation mainly analyzes point P1lowast at the impeller inlete figure shows that with increasing flow rate the pressurefluctuation amplitude at the impeller inlet of the threeschemes gradually decreases When the number of IGVsgradually increases the amplitude of pressure fluctuation atthe impeller inlet first decreases and then increases undersmall-flow conditions and design conditions but graduallyincreases under large flow conditions Under the designconditions the pressure fluctuation amplitudes of the 4IGVs and 6 IGVs shaft tubular pumps are approximately 26times and 18 times that of the 5 IGVs shaft tubular pumprespectively According to the results of the tests on thepressure fluctuation and external characteristics the per-formance of the shaft tubular pump with 5 IGVs is the besterefore the following selection of the 5 IGVs scheme andno IGVs scheme shaft tubular pump are numerically cal-culated and compared






21 3

4 5 6 7

8 9 10 11 12


(a) (b) (c) (d) (e)

Inlet Outlet

P1 P2 P3

(f )



5

4

3

2

1

004 05 06 07 08 09

QQd

10 11 12

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




0 3 6 9 12 15 18 21 244

5

6

00076

00152

00228

00304

00380


Cp

Cp=000283

Cp=000545

Cp=000686

(a)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


CpCp=000561

Cp=000215

Cp=000392

(b)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


Cp

Cp=000135

Cp=000187

Cp=000197

(c)







z(ρk)

z(t)+

z ρkui( 1113857

z xi( 1113857

z

zxj

αkμeff

zk

zxj

1113890 1113891 + μt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus ρε

z(ρε)z(t)

+z ρεui( 1113857

z xi( 1113857

z

zxj

αεμeff

zε

zxj

1113890 1113891 +C1ε middot ε

kμt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus C2ερε2

kminus R

(2)


(a) (b) (c) (d) (e)



ImpellerGuide vane

(a)



(b)





μeff μ + μt

μt ρCμk2

ε

R Cμρφ

3 1 minus φφ0( 1113857ε2

1 + βφ31113872 1113873k

Cμ 00845

C1ε 142

C2ε 168

φ 2Eij1113872 1113873k

3

Eij 12

zui

zxi

+zuj

zxj

1113888 1113889

φ0 4377

β 0012

(3)


zρzt


zρU


T+ B

(4)



740


500

745

750

755

760

765

770

775

Effic

ienc

y η

()

3436043

4397423










5 Numerical Results



Vu 1 minus1

Va

1113936ni1 Vai minus Va( 1113857

2

m

1113971

⎛⎜⎝ ⎞⎟⎠ times 100 (5)

0020000 002 004

t (s)006 008

0025

0030

0035

0040

0045

0050

CP




P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet



6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)


00000 3 6 9 12


0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284


(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)




θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References

























































21 3

4 5 6 7

8 9 10 11 12


(a) (b) (c) (d) (e)

Inlet Outlet

P1 P2 P3

(f )



5

4

3

2

1

004 05 06 07 08 09

QQd

10 11 12

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




0 3 6 9 12 15 18 21 244

5

6

00076

00152

00228

00304

00380


Cp

Cp=000283

Cp=000545

Cp=000686

(a)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


CpCp=000561

Cp=000215

Cp=000392

(b)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


Cp

Cp=000135

Cp=000187

Cp=000197

(c)







z(ρk)

z(t)+

z ρkui( 1113857

z xi( 1113857

z

zxj

αkμeff

zk

zxj

1113890 1113891 + μt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus ρε

z(ρε)z(t)

+z ρεui( 1113857

z xi( 1113857

z

zxj

αεμeff

zε

zxj

1113890 1113891 +C1ε middot ε

kμt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus C2ερε2

kminus R

(2)


(a) (b) (c) (d) (e)



ImpellerGuide vane

(a)



(b)





μeff μ + μt

μt ρCμk2

ε

R Cμρφ

3 1 minus φφ0( 1113857ε2

1 + βφ31113872 1113873k

Cμ 00845

C1ε 142

C2ε 168

φ 2Eij1113872 1113873k

3

Eij 12

zui

zxi

+zuj

zxj

1113888 1113889

φ0 4377

β 0012

(3)


zρzt


zρU


T+ B

(4)



740


500

745

750

755

760

765

770

775

Effic

ienc

y η

()

3436043

4397423










5 Numerical Results



Vu 1 minus1

Va

1113936ni1 Vai minus Va( 1113857

2

m

1113971

⎛⎜⎝ ⎞⎟⎠ times 100 (5)

0020000 002 004

t (s)006 008

0025

0030

0035

0040

0045

0050

CP




P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet



6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)


00000 3 6 9 12


0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284


(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)




θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References





















































5

4

3

2

1

004 05 06 07 08 09

QQd

10 11 12

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




0 3 6 9 12 15 18 21 244

5

6

00076

00152

00228

00304

00380


Cp

Cp=000283

Cp=000545

Cp=000686

(a)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


CpCp=000561

Cp=000215

Cp=000392

(b)

0 3 6 9 12 15 18 21 244

5

6

00016

00032

00048

00064

00080


Cp

Cp=000135

Cp=000187

Cp=000197

(c)







z(ρk)

z(t)+

z ρkui( 1113857

z xi( 1113857

z

zxj

αkμeff

zk

zxj

1113890 1113891 + μt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus ρε

z(ρε)z(t)

+z ρεui( 1113857

z xi( 1113857

z

zxj

αεμeff

zε

zxj

1113890 1113891 +C1ε middot ε

kμt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus C2ερε2

kminus R

(2)


(a) (b) (c) (d) (e)



ImpellerGuide vane

(a)



(b)





μeff μ + μt

μt ρCμk2

ε

R Cμρφ

3 1 minus φφ0( 1113857ε2

1 + βφ31113872 1113873k

Cμ 00845

C1ε 142

C2ε 168

φ 2Eij1113872 1113873k

3

Eij 12

zui

zxi

+zuj

zxj

1113888 1113889

φ0 4377

β 0012

(3)


zρzt


zρU


T+ B

(4)



740


500

745

750

755

760

765

770

775

Effic

ienc

y η

()

3436043

4397423










5 Numerical Results



Vu 1 minus1

Va

1113936ni1 Vai minus Va( 1113857

2

m

1113971

⎛⎜⎝ ⎞⎟⎠ times 100 (5)

0020000 002 004

t (s)006 008

0025

0030

0035

0040

0045

0050

CP




P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet



6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)


00000 3 6 9 12


0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284


(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)




θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References

























































z(ρk)

z(t)+

z ρkui( 1113857

z xi( 1113857

z

zxj

αkμeff

zk

zxj

1113890 1113891 + μt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus ρε

z(ρε)z(t)

+z ρεui( 1113857

z xi( 1113857

z

zxj

αεμeff

zε

zxj

1113890 1113891 +C1ε middot ε

kμt

zui

zxj

+zuj

zxi

1113888 1113889zui

zxj

minus C2ερε2

kminus R

(2)


(a) (b) (c) (d) (e)



ImpellerGuide vane

(a)



(b)





μeff μ + μt

μt ρCμk2

ε

R Cμρφ

3 1 minus φφ0( 1113857ε2

1 + βφ31113872 1113873k

Cμ 00845

C1ε 142

C2ε 168

φ 2Eij1113872 1113873k

3

Eij 12

zui

zxi

+zuj

zxj

1113888 1113889

φ0 4377

β 0012

(3)


zρzt


zρU


T+ B

(4)



740


500

745

750

755

760

765

770

775

Effic

ienc

y η

()

3436043

4397423










5 Numerical Results



Vu 1 minus1

Va

1113936ni1 Vai minus Va( 1113857

2

m

1113971

⎛⎜⎝ ⎞⎟⎠ times 100 (5)

0020000 002 004

t (s)006 008

0025

0030

0035

0040

0045

0050

CP




P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet



6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)


00000 3 6 9 12


0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284


(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)




θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References























































μeff μ + μt

μt ρCμk2

ε

R Cμρφ

3 1 minus φφ0( 1113857ε2

1 + βφ31113872 1113873k

Cμ 00845

C1ε 142

C2ε 168

φ 2Eij1113872 1113873k

3

Eij 12

zui

zxi

+zuj

zxj

1113888 1113889

φ0 4377

β 0012

(3)


zρzt


zρU


T+ B

(4)



740


500

745

750

755

760

765

770

775

Effic

ienc

y η

()

3436043

4397423










5 Numerical Results



Vu 1 minus1

Va

1113936ni1 Vai minus Va( 1113857

2

m

1113971

⎛⎜⎝ ⎞⎟⎠ times 100 (5)

0020000 002 004

t (s)006 008

0025

0030

0035

0040

0045

0050

CP




P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet



6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)


00000 3 6 9 12


0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284


(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)




θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References



























































5 Numerical Results



Vu 1 minus1

Va

1113936ni1 Vai minus Va( 1113857

2

m

1113971

⎛⎜⎝ ⎞⎟⎠ times 100 (5)

0020000 002 004

t (s)006 008

0025

0030

0035

0040

0045

0050

CP




P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet



6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)


00000 3 6 9 12


0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284


(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)




θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References





















































P1P2P3P4

P5P6P7P8

P9P10P11P12

P13P14P15P16

Inlet Outlet



6

5

4

3

2

1

003 04 05 06 07 08 09

QQd

10 11 12 13 14

20

10

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(a)

5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 13 14

20

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()


(b)


00000 3 6 9 12


0004

0008

0012

0016

0020

Cp

Cp=001799

Cp=001284


(a)

Cp=000604Cp=000756

00000 3 6 9 12


0002

0004

0006

0008

0010

Cp


(b)

Cp=000739

Cp=001015

00000 3 6 9 12


0002

0004

0006

0008

0012

0010

Cp


(c)




θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References






















































θ 1113936


1113936ni1 Vai

(6)





Cp=000545Cp=000631

00000 3 6 9 12


0002

0004

0006

0008

Cp


(a)

Cp=000233Cp=000187

00000 3 6 9 12


0001

0002

0003

0004

Cp


(b)

Cp=000215Cp=000318

00000 3 6 9 12


0001

0002

0003

0004

Cp


(c)


5

4

3

2

1

005 06 07 08 09

QQd

10 11 12 1320

30

40

50

60

70

80

Hea

d H

(m)

Effic

ienc

y η

()




90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References





















































90

92

94

96

88

86

84

82

8006 07 08 09

QQd

10 11 12 13873

876

879

882

885

888

Velo

city

Uni

form

ity V

u (

)

Velo

city

wei

ghte

d av

erag

e ang

le θ

(˚)




ZD10 15 20 25 30 35


000025050075100125150175200225250275300325350

ΔH (m

)


Guide VanesImpeller


(a)

ndash125ndash100


10 15 20 25 30 35


000025050075100125150175200225250

ΔH (m

)


Guide VanesImpeller


(b)

ndash175



10 15 20 25 30 35

ndash050ndash025

000025050075100125

ΔH (m

)


Guide VanesImpeller


(c)







0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References

























































0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)


0045091136182227272318363409454

Velocity Axial (ms)

(a)

0057114170227284341398454511568

Velocity Axial (ms)

(b)

0068135203270338405472540608675

Velocity Axial (ms)

(c)





0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References























































0020

0016

0012

0008

0004

0P1 P5

Monitor

CP

P9 P13

CP=001799

CP=000631


(a)

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=000756

CP=000318


(b)

0010

0012

0008

0006

0004

0002

0P1 P5

Monitor

CP

P9 P13

CP=001015

CP=000233


(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)


00200027003400410048005500620069007600830090

CP

(a)

00200023002600290032003500380041004400470050

CP

(b)

00200024002800320036004000440048005200560060

CP

(c)






0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References
























































0025

0020

0015

0010

0005

00 02

Streamwise

CP

04 06 08 10


(a)

0016

0012

0008

0004

00 02

Streamwise

CP

04 06 08 10

PressureSide

SuctionSide


(b)

0015

0012

0009

0006

0003

00 02

Streamwise

CP

04 06 08 10


(c)


Outlet

Span=05

Pressure side

Inlet


0000000125002500037500500006250075000875

ndash001250000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(a)

002500

003125

003750

004375

005000

0018750000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(b)

00625

00750

00875

01000

01125

01250

005000000 0025

Time t (s)

CP

0050 0075 0100 0125

P5P6

P7P8

(c)




6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References






















































6 Conclusion








Abbreviations



0000500100015002000250030

ndash00050 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(a)

0015

0018

0021

0024

0027

00120 0025

Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(b)

0018

0021

0024

0027

0030

0033

0 0025Time t (s)

Cp

0050 0075 0100 0125

P5P6

P7P8

(c)





Data Availability






Acknowledgments


References























































Data Availability






Acknowledgments


References





















































Research Article Analysis of the Influence of Inlet Guide Vanes ...

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Transcript of Research Article Analysis of the Influence of Inlet Guide Vanes ...