Influence of Inlet Angle of Guide Vane on Hydraulic

Research ArticleInfluence of Inlet Angle of Guide Vane on HydraulicPerformance of an Axial Flow Pump Based on CFD

Lei Xu 1 Dongtao Ji1 Wei Shi2 Bo Xu 1 Weigang Lu1 and Linguang Lu1

1College of Hydraulic Science and Engineering Yangzhou University Yangzhou 225009 China2Jiangsu Water Supply Co Ltd In Eastern Route of S-to-N Water Diversion Project Nanjing 210029 China

Correspondence should be addressed to Lei Xu leixuyzueducn

Received 24 September 2020 Revised 24 November 2020 Accepted 5 December 2020 Published 19 December 2020

Academic Editor Yong Zhu

Copyright copy 2020 Lei Xu et al is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Axial flow pump has been widely used in hydraulic engineering agriculture engineering water supply and sewerage works andshipbuilding industry In order to improve the hydraulic performance of pump under off-design working conditions the influenceof the inlet segment axial chord and inlet angle adjustment of the guide vane on the pump segment efficiency and flow filed wassimulated by using the renormalization group (RNG) k minus ε turbulent model based on the Reynolds-averaged NavierndashStokesequations e results indicate that the inlet segment axial chord and inlet angle adjustment of guide vane have a strong influenceon the pump segment efficiency Considering the support function and hydraulic loss of the guide vane the inlet segment axialchord is set to 025 times the axial chord of guide vane On the basis of the inlet angle of the guide vane under design conditionswhen the inlet segment angle is turned counterclockwise the pump segment efficiency is improved in the lower flow rate regionmoreover the pump segment efficiency is improved in the larger flow rate region when the inlet segment angle is turned clockwiseAs the conditions deviate from the design working conditions the influence of the guide vane inlet angle on the pump segmentefficiency increases If the inlet segment angle is properly adjusted under off-design working conditions the flow pattern in theguide vane is improved and the hydraulic loss is decreased because the inlet segment angle matches with the flow direction ofimpeller outlet consequently the pump segment efficiency is increased

1 Introduction

Vane pump is widely used in mechanical engineering hy-draulic engineering civil engineering and military industrye application of vane pump is affected by its stable andefficient operation erefore it is necessary to pay attentionto the optimization of the pump [1ndash4] and paying attentionto the research on pressure pulsation cavitations vibrationand noise is also necessary [5ndash8] Axial flow pump is a kindof vane pump with high specific speed which is charac-terized by low head and large discharge rate Due to thecharacteristics axial flow pump is widely applied to low headpumping stations in the fields of water resource allocationwater environment improvement urban flood control ir-rigation and drainage e guide vane is an important partof the axial flow pump that is used to recover the kineticenergy of the flow at the impeller outlet [9 10]e hydraulic

performance of guide vane has great influence on the hy-draulic performance of axial flow pump and pump systemerefore it is of great significance to study the matching ofguide vane and impeller to improve the hydraulic perfor-mance of axial flow pump

At present studies on the effect of the guide vane on thehydraulic performance of an axial flow pump can besummarized as follows Li et al [11] studied the ability of theguide vane to recover rotational kinetic energy and Hu et al[12] and Durmus Kaya [13] studied the influence of theguide vane on the pump efficiency for cases with and withouta guide vane Zhou et al [14] studied the pump efficiency fordifferent guide vanes and Shi et al [15] studied the hydrauliccharacteristics of axial flow pumps with different guide vanesweep angles Liu et al [16] studied the hydraulic charac-teristics of an axial flow pump with different numbers ofguide vane panels and Luo et al [17] and Feng et al [18]

HindawiShock and VibrationVolume 2020 Article ID 8880789 16 pageshttpsdoiorg10115520208880789

studied the influence of the guide vane on the hydraulicperformance of the pump system

e guide vane is used to undertake the flow from theimpeller outlet and recycle tangential energy For the designworking conditions the guide vane inlet angle matches theflow direction of the impeller outlet For off-design workingconditions the inlet angle of the guide vane is inconsistentwith the flow direction of the impeller outlet which leads toan increased hydraulic loss of the guide vane and a reducedaxial flow pump efficiency In recent years some studies haveexplored adjusting the guide vane angle and its effect on thehydraulic performance of an axial flow pump under off-design working conditions the results indicate that acomplete adjustment of the guide vane angle improves theflow pattern in the guide vane and reduces the hydraulic losswith a head improvement of 04964m and a pump efficiencyimprovement of 21648 measured in [19] Yang et al[20 21] studied a complete adjustment of the guide vaneangle and its effect on the hydraulic performance of an axialflow pump system the results indicate that the high effi-ciency area moves to a large discharge rate when the angle isrotated clockwise and to a small discharge rate when theangle is rotated counterclockwise Qian et al [22] found thatwhen the whole angle of the guide vane is adjusted in thesaddle zone the head increases by 015m the efficiencyincreases by 193 and the flow pattern in the axial flowpump is substantially improved e abovementionedstudies are all about the whole guide vane rotates us farno studies on matching the inlet angle of the guide vane withthe flow direction of the impeller outlet for an axial flowpump have been reported

On the one hand the guide vane of an axial flow pumptakes the flow from the impeller outlet on the other hand theguide vane needs to support the guide-bearing seat [23] Toavoid affecting the support function of the guide vane in thiswork the guide vane is divided into inlet segment middlesegment and outlet segment e inlet segment angle isadjustable while the middle and outlet segments are fixed andused to support the guide-bearing seat CFDmethod has beenwidely used in the studies of pump [24ndash31] and other aspect[32ndash38] In this paper based on the TJ04-ZL-06 pumpmodelwhich has 3 impeller blade components and 5 guide vanecomponents [39] influence of inlet angle of guide vane onhydraulic performance was studied using a 3D turbulent flownumerical simulation According to the numerical simulationresults the reason of the influence of inlet angle of guide vaneon the hydraulic performance was analyzed e study workhas important reference value for the hydraulic design andhydraulic performance improvement of an axial flow pump

2 Mathematical Model and Numerical Setting

21 Governing Equations and Turbulent Model A 3D tur-bulent flow numerical simulation for an axial flow pump isestablished by solving the Reynolds-averaged NavierndashStokesequations [40 41] using FLUENT software

e fluid flow in the axial flow pump is consideredincompressible e method of steady flow numericalsimulation is used to study the flow and hydraulic

performance of the pump e governing equations that areapplied to solve the flow field in the pump include a con-tinuity equation momentum equations and k equation andε equation of the k minus ε turbulent model e Reynolds-av-eraged NavierndashStokes equations are shown as follows

zρzt

+ ρzui

zxi

0

ρzui

zt+ ρ

zuiuj

zxj

minuszp

zxi

+z

zxj

μzui

zxj

+zuj

zxi

1113888 1113889 minus ρuiprimeujprime1113890 1113891 + Fi

(1)

where ρ is the density t is the time ui and uj are the meanvelocity components p is the mean pressure xi and xj arethe coordinate directions μ is the dynamic viscosity Fi is thebody force component minusρui

primeujprime is the Reynolds stress and uj

primeand ujprime are the fluctuating velocity components

e RNG k minus ε turbulent model is chosen to solve theflow in the pump because this model is suitable for solvingcomplicated flows such as rotating flows separated flowsand vortex flows [42ndash46] e k equation and ε equation ofthe RNG k minus ε turbulent model are shown as follows

ρzk

zt+ ρ

zkui

zxi

z

zxj

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk minus ρε

ρzεzt

+ ρzεui

zxi

z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 +C1εε

kGk minus C2ερ

ε2

k

(2)

where Gk is the turbulent kinetic energy production termC1ε is an empirical constant C2ε is an empirical constant σk

is the corresponding Prandtl number for turbulent kineticenergy k and σε is the corresponding Prandtl number for theturbulent kinetic energy dissipation rate ε

22 Computational Domain and Boundary Conditionse computational domain of the flow field in an axial flowpump is composed of a straight inlet pipe conical inlet pipeimpeller and impeller chamber guide vane bent outlet pipeand straight outlet pipe (Figure 1)e inlet boundary for theflow field calculation of an axial flow pump is set at the inletsection of the straight inlet pipee discharge rate is knownand the flow velocity distribution is uniform at the inletsection thus the velocity inlet boundary condition isadopted [47] e outlet boundary for the flow field cal-culation of the axial flow pump is set at the outlet section ofthe straight outlet pipe where the flow is fully developedthus the outflow boundary condition is adopted In the flowfield calculation the sidewalls of the pipes impellerchamber guide vane pump shaft fair water caps at theimpeller inlet and the guide vane outlet are solid and aretreated according to the conditions for a solid wall [48]Since the axial flow pump impeller rotates periodically therotating walls such as the impeller blade and hub adopt themoving wall boundary condition and the rotation speed anddirection are the same as those of the impeller

2 Shock and Vibration

23 Numerical Setting and Calculation Accuracy eGAMBIT software is used to generate the mesh for thecomputational domain e shapes of the straight inlet pipeconical inlet pipe bent outlet pipe and straight outlet pipeare simple structured hexahedral meshes are applied eshapes of the impeller and guide vane are complicatedunstructured meshes are applied Moreover since the flowsin the impeller and guide vane are very complicated themeshes are subject to local refinement e y+ value of thenear-wall mesh scale is in the range of 20ndash70 which meetsthe requirement of numerical simulation During the nu-merical simulation a first-order upwind difference scheme isused to solve the convection-diffusion equation the SIM-PLEC algorithm is used to solve the pressure-velocitycoupling equations and the convergence precision is set to1times 10minus7

A mesh independence verification was performed toensure the calculation accuracy and computation efficiencye calculation parameters for the TJ04-ZL-06 pump modelare as follows the diameter and rated speed of the pumpimpeller are 03m and 1450 rmin respectively and thedesign discharge rate Q is 0375m3s for a blade angle of minus2degaccording to model test results obtained for the test bed ofBeifang Investigation Design and Research Co LtdTianjing China [39]

Pump segment efficiency is an important energy per-formance index of pump which is used as the judgmentbasis for mesh independence analysis e calculation for-mula of pump segment efficiency is as follows

ηb d ρgQHb d

Pbz

times 100 (3)

where ηb d is the pump segment efficiency g is the gravi-tational acceleration Q is the discharge rate Hb d is thepump segment head and Pbz is the pump shaft power

Table 1 shows the relationship between the pump seg-ment efficiency and grid number under the abovementionedconditions When the grid number of computational do-main exceeds 1863552 the pump segment efficiencychanges only slightly Based on the verification results thegrid number of the entire calculation domain is set to ap-proximately 1860000 in the calculations the grid numbersof each component are shown in Table 2e grid generationof the computational domain is shown in Figure 2

Based on the abovementioned numerical method andsetting the pump efficiency of pump model TJ04-ZL-06 wascalculated for a discharge rate between 08ηb d and 12ηb dBased on the calculated results the relationship between thedischarge rate and pump segment efficiency is shown inFigure 3 the flow fields in the pump are shown in Figure 4 Itcould be seen that the pump segment efficiency increasesfirstly and then decreases as the discharge rate increasesBecause the inlet angle of guide vane does not match with theflow direction from the impeller outlet under the off-designconditions there will be vortex on the back of guide vaneunder the condition of small discharge rate and there will bevortex on the front of guide vane under the condition oflarge discharge rate e comparison of numerical calcu-lation and model test results is shown in Figure 3 e testdata of TJ04-ZL-06 pump model is from the model pumptest on the same test bed for the south-to-north water di-version [39] Clearly the trends observed for the numericalsimulation are consistent with those for the model test andthe two curves are similar indicating that the numericalresults are reliable

3 Research Scheme

To satisfy hydraulic design requirements and structure de-mands the guide vane is divided into an inlet segmentmiddle segment and outlet segment (Figure 5) e inletsegment is used to adjust the inlet angle of the guide vane inorder to match the flow direction of the impeller outletunder off-design conditions e middle segment is used tofix the bearing support e outlet segment which is used toadjust the circulation of the guide vane outlet is fixed in thispaper

In Figure 5 the axial chord of the guide vane is H andthe inlet segment axial chord of the guide vane is h (Fig-ure 4) For a given H a larger h corresponds to a shorterfixed region (middle and outlet segments) and the supportfunction of the guide vane will be negatively affectedHowever a smaller h corresponds to a weaker adjustmenteffect for the inlet angle of the guide vaneerefore h valuesof 01H 02H 025H and 033H were employed to study theinfluence of h on the hydraulic performance of the axial flowpump

e inlet angle of the guide vane β0 for the model pumpTJ04-ZL-06 is determined based on the design conditions

Straight inlet pipe

Bent outlet pipe Conical inlet pipe

Guide vane

Guide vane

Impeller

Guide vane hub

Impeller hub

Impeller andimpeller chamber

Straight outletpipe

Figure 1 Computational domain for an axial flow pump

Shock and Vibration 3

(Figure 6) In this paper the inlet angle of the guide vane β0is defined as 0deg Based on β0 if the inlet segment of the guidevane is rotated counterclockwise (Figure 6(b)) the inletangle adjustment Δβ is positive if the inlet segment of theguide vane is rotated clockwise (Figure 6(c)) the angleadjustment Δβ is negative According to the velocity triangleat the impeller outlet when the pump operates under a flowthat is larger than the design condition β0 does not matchthe absolute velocity of the flow at the impeller outlet andthe inlet segment needs to rotate clockwise By contrastwhen the pump operates under smaller flow conditions theinlet segment needs to rotate counterclockwise In an actual

system the pump at a low head pumping station usuallyoperates under a large flow thus the pump system efficiencyis low [49 50] To improve the efficiency the study in thispaper places an additional emphasis on the influence of Δβon the pump segment efficiency under large flow conditionstherefore Δβ is taken as minus15deg minus10deg minus5deg 0deg and +5deg

e inlet segment of the guide vane is based on twogeometrical parameters the inlet segment axial chord h andthe inlet angle adjustment Δβ e calculation schemes aredetermined by h and Δβ the h is selected as 01H 02H025H and 033H and the Δβ is selected as +5deg 0deg minus5deg minus10degand minus15dege combination of the two factors forms a total of20 calculation schemes Based on the model pump TJ04-ZL-06 for a blade angle of minus2deg the calculation discharge rates forthe schemes are taken as 030m3s 0325m3s 035m3s0375m3s 040m3s 0425m3s and 045m3s Note thatwhen Δβ 0deg the scheme is the same as the original guidevane

4 Results and Analysis

41 Calculation Results e pump segment energy per-formance for each calculation scheme was calculated using a3D turbulent flow numerical simulatione curves of pumpsegment efficiency ηb d and discharge rate Q for differentinlet segment axial chords h and inlet angle adjustments Δβare shown in Figure 7

42 Influence of Inlet Segment Axial Chord on Pump SegmentEfficiency Based on the calculation results the pump seg-ment efficiency ηb d and inlet segment axial chord h fordifferent values of discharge rate Q are shown in Figure 8 Itcan be seen that h has a strong effect on ηb d When thedischarge rate is smaller than the optimum operating dis-charge rate if Δβgt 0deg ηb d will increase slightly as h in-creases if Δβlt 0deg ηb d will gradually decrease as h increasesA smaller Δβ corresponds to a greater decrease in ηb d For adischarge rate that is larger than the optimum operatingdischarge rate if Δβgt 0deg ηb d will decrease as h increases ifΔβlt 0deg ηb d gradually increases as h increases In this case asmaller Δβ corresponds to a greater increase in ηbd Figure 8shows that regardless of whether ηb d increases or decreaseswith increasing h when hgt 025H the influence of h on ηb d

decreases erefore considering the support function andhydraulic performance of the guide vane the inlet segmentaxial chord h is taken as 025H

Table 2 Detailed mesh information of computational domain

Domain Straight inletpipe

Conical inletpipe

Impeller and impellerchamber

Guidevane

Bent outletpipe

Straight outletpipe

Grid number(times103) 203 252 317 392 495 201

Straight inlet pipe


Guide vane


Straight outletpipe

Figure 2 Grid generation of the computational domain

100

90

80

70

60

50

40

30025 030 035 040 045

Discharge rate Q (m3middotsndash1)

Pum

p effi

cien

cy (

)

Numerical simulationModel test

Figure 3 Comparison of the numerical simulation and model testresults

Table 1 Relationship between outlet conduit hydraulic loss and grid number

Grid number 788332 967806 1262519 1516022 1863552 1966585 2256251Pump segment efficiency () 8573 8567 8524 8451 8416 8412 8412


43 Influence of Inlet Angle Adjustment on Pump SegmentEfficiency Based on the calculation results the pump seg-ment efficiency ηb d and inlet angle adjustment Δβ for dif-ferent discharge rate Q values with h 025H are shown inFigure 9 It could be seen as follows as the inlet angle ad-justment Δβ increases the pump segment efficiencies ηb d

increase when the discharge rates Q are 030m3s 0325m3s

and 035m3s the pump segment efficiencies ηb d are basicallyconstant when the discharge rates Q are 0375m3s and040m3s and the pump segment efficiencies ηb d decreasewhen the discharge rates Q are 0425m3s and 045m3sWhen the discharge rate is smaller than the optimum op-erating discharge rate a larger Δβ corresponds to a greaterηb d when the discharge rate is larger than the optimumoperating discharge rate a smaller Δβ corresponds to agreater ηb d

Under the condition of h 025H the flow fields in thepump at different discharge rates when the inlet angleadjustments Δβ are +5deg and minus10deg are shown in Figures 10and 11 respectively Comparing the flow fields in Figures 410 and 11 it could be seen as follows under the samedischarge rate condition the flow fields in the impeller arethe same for different inlet angle adjustments when thedischarge rates are 035m3s and 040m3s the flow patternin the guide vane is all good for different inlet angle ad-justments so the pump segment efficiency changes little asthe inlet angle adjustment increases (Figure 9) when thedischarge rate is 030m3s there is flow separation on theback of the guide vane and there is a big range of vortexwhen the inlet angle adjustment is minus10deg the smaller theinlet angle adjustment the worse the flow separation andthe bigger the energy loss therefore the pump segmentefficiency decreases as the inlet angle adjustment decreasesat the small discharge rate (Figure 9) when the dischargerate is 045m3s there is flow separation on the front of theguide vane there is a big range of vortex when the inlet

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)

Figure 4 Flow fields in the pump segment under different conditions of discharge rates (a)Q 030m3s (b)Q 035m3s (c)Q 040m3sand (d) Q 045m3s

H

h

Out

let

segm

ent

Mid

dle

segm

ent

Inle

tse

gmen

t

Figure 5 Segmentation of the guide vane


angle adjustment is +5deg the pump segment efficiency de-creases dramatically the bigger the inlet angle adjustmentthe worse the flow separation and the bigger the energyloss so the pump segment efficiency decreases as the inletangle adjustment increases at the large discharge rate(Figure 9)

44 Matching Relation of the Guide Vane Inlet Angle and theImpeller Outlet Flow Direction

441 Design Working Condition e relationship betweenthe guide vane inlet angle and the impeller outlet flow directionfor an axial flow pump under optimum operating conditions is

Guide vane

β0

(a)

∆β0 gt 0

Guide vane

β0

(b)

Guide vane

β0

∆β0 lt 0

(c)

Figure 6 e datum and turn direction for adjusting the guide vane inlet angle (a) Inlet angle of the guide vane (b) Counterclockwiserotation (c) Clockwise rotation

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)

∆β = +5ordm∆β = 0ordm∆β = ndash5ordm

∆β = ndash10ordm∆β = ndash15ordm

(a)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

Figure 7 Q sim ηb d curves for the different calculation schemes (a) h 010H (b) h 020H (c) h 025H (d) h 033H


85

80

75

70

65

6000 01 02 03 04

Inlet segment axial chord h (H)

Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(e)

90

80

85

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(f )

Figure 8 Continued


shown in Figure 12(a) In the figure β0 is the inlet angle of theguide vane under the design working conditions v0 w0 and u

are the absolute velocity relative velocity and transport ve-locity respectively of the impeller outlet flow under the designworking conditions and α0 is the angle between v0 and uObviously when the axial flow pumpoperates under the designworking conditions β0 is equal to α0 ie the inlet angle of theguide vane matches the flow direction of the impeller outlet

442 Smaller Discharge Condition e relationship be-tween the guide vane inlet angle and the impeller outlet flow

direction for an axial flow pump with a smaller dischargerate is shown in Figure 12(b) When the axial flow pumpoperates with a smaller discharge rate the axial velocity atthe impeller outlet is vms and the absolute velocity of theimpeller outlet flow and the angle between the absolutevelocity and transport velocity are vs and αs respectively Atthis point because αs less than α0and β0 differs fromαs theflow strikes the pressure side of the guide vane Flow sep-aration and vortices will simultaneously occur on the vac-uum side of the guide vane resulting in an additionalhydraulic loss for the guide vane To ensure that the inletangle of the guide vane matches the flow direction of theimpeller outlet for a smaller discharge rate the inlet anglemust be changed by a certain angle counterclockwise basedon β0 as shown by the dotted line in Figure 12(b)

443 Larger Discharge Rate Condition e relationshipbetween the guide vane inlet angle and the impeller outletflow direction for an axial flow pump with a larger dischargerate is shown in Figure 12(c) When the axial flow pumpoperates with a larger discharge rate the axial velocity at theimpeller outlet is vmL and the absolute velocity of the im-peller outlet flow and the angle between the absolute velocityand transport velocity are vL and αL respectively At thispoint because αL larger than α0 and β0 differs from αL theflow strikes the vacuum side of the guide vane Flow sep-aration and vortices will simultaneously arise on the pressureside of the guide vane resulting in additional hydraulic lossfor the guide vane To match the guide vane inlet angle withthe impeller outlet flow direction for a large discharge ratethe inlet angle must change by a certain angle clockwisebased on β0 as shown by the dotted line in Figure 12(c)

45 Influence of the Inlet Angle on the Guide Vane Flow FieldFor Q 045m3s a 3D steady turbulent flow numericalsimulation was performed for the axial flow pump with

90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s

ndash15 ndash10 ndash5 0 5

Pum

p se

gmen

t effi

cien

cy η

hd (

)

Inlet angle adjustment ∆β (ordm)

Figure 9 ηb d sim Δβ curves for different discharge rates whenh 025H

85

80

75

70

65

6000 01 02 03 04

Inlet segment axial chord h (H)Pu

mp

segm

ent e

ffici

ency

ηbd

()



(g)

Figure 8 ηb d sim h curves for each calculation scheme (a) Q 030 m3s (b) Q 0325 m3s (c) Q 035 m3s (d) Q 0375 m3s(e) Q 040 m3s (f ) Q 0425 m3s and (g) Q 045 m3s


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)

Figure 10 Flow fields in the pump segment under different conditions of discharge rates (Δβ+5deg h 025H) (a) Q 030 m3s(b) Q 035 m3s (c) Q 040 m3s and (d) Q 045 m3s

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)

Figure 11 Flow fields in the pump segment under different conditions of discharge rates (Δβ minus10deg h 025H) (a) Q 030 m3s(b) Q 035 m3s (c) Q 040 m3s and (d) Q 045 m3s


Δβ 0deg and Δβ minus10deg For ease of analysis three tori arechosen between the hub and the rim of the guide vane asfollows inner torus (near the hub) middle torus (betweenthe hub and rim) and outer torus (near the rim)

e flow fields of the three tori of the guide vane forΔβ 0deg and Δβ minus10deg are shown in Figures 13 and 14 re-spectively e figures show that for the larger discharge ratecondition when Δβ 0deg the inlet angle of the guide vanedoes not match the flow direction of the impeller outletthus the vacuum side of the guide vane is struck by the flowFlow separation and vortices occur simultaneously on thepressure side of the guide vane therefore the hydraulic loss

of the guide vane is increased For Δβ minus10deg the inlet angleof the guide vane matches the flow direction of the impelleroutlet and the flow to the adjacent guide vane is smoothEssentially no collisions or vortices occur the flow patternin the guide vane is substantially improved and the hy-draulic loss of the guide vane is reduced

At the same time the unsteady flow numerical simulationwas performed for the axial flow pump with Δβ 0deg andΔβ minus10deg when the discharge rate Q is 045 m3s e totalcalculation time was set to 8 times the rotation period of theimpeller the total time T is 033103448 s and the time step twas set as 3448275833times10ndash4 which is the time required for

u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)

Figure 12 Matching relationships between the guide vane inlet angle and the impeller outlet flow direction (a) Design discharge ratecondition (b) Smaller discharge rate condition (αs lt α0) (c) Larger discharge rate condition (αL gt α0)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

Figure 13 Flow fields of the three tori of the guide vane (Δβ 0deg) (a) Inner torus (b) Middle torus (c) Outer torus

02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)

Figure 14 Flow fields of the three tori of the guide vane (Δβ minus10deg) (a) Inner torus (b) Middle torus (c) Outer torus


the impeller to rotate 3deg In consideration of the stability of theflow field calculation the internal flow field was analyzed after4 rotation periods e flow fields of middle tori of pumpsegment at different time in one period T are respectivelyshown in Figures 15 and 16 for Δβ 0deg and Δβ minus10deg byunsteady flow numerical simulation When the inlet angleadjustment Δβ is 0deg there is a tendency of vortexes on thefront of the guide vane at 14T and the vortex is appeared onthe front of the guide vane at 34T it is basically consistentwith the results of steady flow numerical simulation Whenthe inlet angle adjustment Δβ is minus10deg there is no vortex on thefront of the guide vane during the full period it is the samewith the results of steady flow numerical simulation

46 Influence of the Guide Vane Inlet Angle onHydraulic Lossand Efficiency

461 Influence of Δβ on the Hydraulic Loss of the Guide VaneΔhdy In the range of considered working conditions whenQ 045m3s the inlet angle adjustment Δβ has a strongeffect on pump segment efficiency ηb d erefore thisworking condition is chosen for analysis e curves ofηb d sim Δβ and Δhdy sim Δβ for different h values under thechosen working condition are shown in Figure 17 Over therange of minus15deg to +5deg for Δβ the hydraulic loss of the guidevane Δhdy increases substantially as Δβ increases while ηb d

decreases dramatically Δhdy increases under the largerdischarge rate condition because as Δβ increases the mis-match between the inlet angle of the guide vane and the flowdirection of the impeller outlet increases the flow impact

and vortex in the guide vane become greater (Figure 13) andthus Δhdy increases

462 Influence of Δhdy on the Guide Vane Efficiency ηdy andηb d For h 025H curves of ηyl sim Q ηb d sim Q andΔhdy sim Q for each calculation scheme are shown in Fig-ure 18e main energy performance parameters for Δβ 0degand Δβ minus10deg for the pump segment with Q 045m3s arelisted in Table 3 e impeller heads Hyl for Δβ 0deg andΔβ minus10deg are approximately equal at 266m and 269mrespectively when Δβ is adjusted from 0deg to minus10deg Δhdy

decreases from 038m to 017m because the flow pattern inthe guide vane is improved

According to the calculated impeller head Hyl and pumpshaft power Pbz the impeller efficiency ηyl can be calculatedas follows

ηyl ρgQHyl

Pbz

times 100 (4)

where g is the gravitational acceleration Q is the dischargerate and Pbz is the pump shaft power e ηyl values cal-culated from formula (4) for Δβ 0deg and Δβ minus10deg are listedin Table 3

Using the calculated Δhdy and ηyl the guide vane effi-ciency ηdy can be determined as follows

ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)

Figure 15 Flow fields of middle tori of the pump segment at different time in one period T (Δβ 0deg) (a) t 14T (b) t 24T (c) t 34Tand (d) tT


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)

Figure 16 Flow fields of middle tori of the pump segment at different time in one period T (Δβ minus10deg) (a) t 14 T (b) t 24 T(c) t 34 T and (d) t T

85

80

75

70

65

60ndash15 ndash10 ndash5 0 5

01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)

Figure 17 ηb d sim Δβ and Δhdy sim Δβ curves for different h values (a) h 010H (b) h 020H (c) h 025H and (d) h 033H


According to formulas (4) and (5) formula (3) could betransformed as follows

ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)

Pump segment efficiency ηb d is the product of impellerefficiency ηyl and guide vane efficiency ηdy

e ηdy and ηb d values for Δβ 0deg and Δβ minus10deg cal-culated from formulas (5) and (6) are listed in Table 3

e abovementioned results indicate that when Δβ isadjusted from 0deg to minus10deg Hyl and ηyl are basically unchangedand the hydraulic performance of impeller is not affected bythe inlet segment adjustment of the guide vane Howeverwhen the inlet segment angle is minus10deg the inlet angle of guidevane is matched with flow direction at the impeller outlet wellthe flow pattern in the guide vane becomes better and thevortex is eliminated so the Δhdy decreases from 038m to017m and then guide vane efficiency ηdy increases from857 to 934 and pump segment efficiency ηb d improvesfrom 735 to 809 correspondingly

5 Conclusions

(1) e inlet segment axial chord h of the guide vaneinfluences the pump segment efficiency ηb d As h

increases ηb d increases under smaller discharge rate

conditions and decreases under larger discharge rateconditions for Δβgt 0deg in contrast ηb d decreasesunder smaller discharge rate conditions and increasesunder larger discharge rate conditions when Δβlt 0degWhen hgt 025H the influence of h on ηb d weakens

(2) e inlet angle adjustment Δβ of the guide vane has astrong effect on the pump segment efficiency ηb dWhen the inlet angle of the guide vane is rotatedcounterclockwise with respect to the design condi-tion ηb d increases under the smaller discharge ratecondition when the inlet angle of the guide vane isrotated clockwise with respect to the design condi-tion ηb d increases under the larger discharge ratecondition e greater the deviation from the designcondition the larger the influence of Δβ on ηb d

(3) e match between the guide vane inlet angle and theimpeller outlet flow direction has a strong influence onthe pump segment efficiency ηb d because the flowpattern is highly sensitive to deviations in the inlet angleof the guide vane this change in the flow pattern willdirectly influence the hydraulic loss of the guide vane

Data Availability

e data used to support the findings of this study are in-cluded within the article

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)

Figure 18 Influence of Δhdy on ηdy and ηb d for different values of Δβ (a) ηyl +5deg (b) ηdy 0deg (c) Δβ minus5deg (d)ηdy Hb dHyl Hyl minus ΔhdyHyl times 100 minus10deg and (e) Δβ minus15deg

Table 3 Comparison of energy performance for the pump with Δβ 0deg and Δβ minus10deg

Inlet angleadjustment Δβ(deg)

Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)

Hydraulic loss ofguide vane Δhdy

(m)

Impellerefficiency ηyl

()

Pump segmenthead Hb d (m)

Guide vaneefficiency ηdy

()

Pump segmentefficiency ηb d

()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809


Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (Grant nos 51309200 51779215 and52079120) a China Postdoctoral Science Foundation Fun-ded Project (Grant no 2013M540469) and the JiangsuPlanned Projects for Postdoctoral Research Funds (Grantno 1301021A)

References

[1] C Wang W Shi X Wang et al ldquoOptimal design of mul-tistage centrifugal pump based on the combined energy lossmodel and computational fluid dynamicsrdquo Applied Energyvol 187 pp 10ndash26 2017

[2] X He W Jiao C Wang and W Cao ldquoInfluence of surfaceroughness on the pump performance based on computationalfluid dynamicsrdquo IEEE Access vol 7 pp 105331ndash105341 2019

[3] CWang X He D Zhang B Hu andW Shi ldquoNumerical andexperimental study of the self-priming process of a multistageself-priming centrifugal pumprdquo International Journal ofEnergy Research vol 43 pp 1ndash19 2019

[4] H Yan X Su H Zhang et al ldquoDesign approach and hy-drodynamic characteristics of a novel bionic airfoilrdquo OceanEngineering vol 216 Article ID 108076 2020

[5] C Wang X He W Shi X Wang and N Qiu ldquoNumericalstudy on pressure fluctuation of a multistage centrifugal pumpbased on whole flow fieldrdquo AIP Advances vol 9 Article ID035118 2019

[6] M T Shervani-Tabar M M Ettefagh S Lotfan andH Safarzadeh ldquoCavitation intensity monitoring in an axialflow pump based on vibration signals using multi-classsupport vector machinerdquo Proceedings of the Institution ofMechanical Engineers Part C Journal of Mechanical Engi-neering Science vol 232 no 17 pp 3013ndash3026 2018

[7] Y Yang L Zhou W Shi Z He Y Han and Y Xiao ldquoIn-terstage difference of pressure pulsation in a three-stageelectrical submersible pumprdquo Journal of Petroleum Scienceand Engineering vol 196 Article ID 107653 2020

[8] C Wang B Hu Y Zhu X Wang C Luo and L ChengldquoNumerical study on the gas-water two-phase flow in the self-priming process of self-priming centrifugal pumprdquo Processesvol 7 no 6 p 330 2019

[9] F P Tang and G Q Wang ldquoInfluence of outlet guide vanesupon performances of waterjet axial-flow pumprdquo Journal ofShip Mechanics vol 10 pp 19ndash26 2006

[10] F P Tang J R Zhou and B P Yan ldquoAnalysis on the recycleenergy of back guide vane of axial-flow pumprdquo PumpTechnology vol 3 pp 19ndash22 1995

[11] Z Li M G Yang and X K Wang ldquoExperimental study ofguide vane influence on performance of axial-flow pumprdquoDrainage and Irrigation Machinery vol 27 pp 15ndash18 2009

[12] J Hu S Huang and P S Wang ldquoResearch on hydrodynamiccharacteristics of axial waterjet pump with guide vanerdquoJournal of Hydroelectric Engineering vol 27 pp 32ndash36 2008

[13] K Durmus ldquoExperimental study on regaining the tangentialvelocity energy of axial flow pumprdquo Energy Conversion andManagement vol 44 pp 1817ndash1829 2003

[14] Y X Zhou and H F Xu ldquoe influence of diffuser on thefunction of the axial-flow pumprdquo Water Conservancy ampElectric Power Machinery vol 29 pp 28-29 2007

[15] L J Shi F P Tang H L Zhou L L Tu and R S Xie ldquoAxial-flow pump hydraulic analysis and experiment under differentswept-angles of guide vanerdquo Transactions of the ChineseSociety of Agricultural Engineering vol 31 pp 90ndash95 2015

[16] C J Liu Y S Wang and L X Wang ldquoResearch on com-mutating effect optimization of waterjet axial-flow pumpstator based on CFD methodrdquo Journal of Ship Mechanicsvol 14 pp 466ndash471 2010

[17] X Luo Y Zheng and J Feng ldquoHydraulic performanceanalysis of axial pump outlet guide vanerdquo Water Resourcesand Power vol 32 pp 188ndash191 2014

[18] J Feng Y Zheng and X Luo ldquoEffects of exit guide vane onperformance of axial flow pump systemrdquoWater Resources andPower vol 30 pp 126ndash128 2012

[19] Z Qian Y Wang W Huai and Y Lee ldquoNumerical simu-lation of water flow in an axial flow pump with adjustableguide vanesrdquo Journal of Mechanical Science and Technologyvol 24 no 4 pp 971ndash976 2010

[20] F Yang C Liu F P Tang R S Xie and F Chen ldquoNumericalanalysis and prediction of hydraulic performance for axial-flow pumping station with adjustable outlet guide vanerdquoTransactions of the CSAE vol 46 pp 40ndash46 2015

[21] F Yang Research on Hydraulic Performance and Multi-Ob-jective Optimization Design of Low-Lift Pump System Doc-toral thesis Yangzhou China 2013

[22] Z D Qian F Wang Z Y Wang and W Zhou ldquoExperi-mental study on hydraulic performance of saddle zone in axialflow pump with adjustable guide vanerdquo Journal of Drainageand Irrigation Machinery Engineering vol 31 pp 461ndash4652013

[23] X F Guan Axial Flow Pump and Diagonal Flow Pump ChinaAerospace Press Beijing China 2009

[24] X He Y Zhang C Wang et al ldquoInfluence of critical wallroughness on the performance of double-channel sewagepumprdquo Energies vol 13 no 2 p 464 2020

[25] H L Wang B Long Y Yang Y Xiao and C WangldquoModelling the influence of inlet angle change on the per-formance of submersible well pumpsrdquo International Journalof Simulation Modelling vol 19 no 1 pp 100ndash111 2020

[26] H Wang B Long C Wang C Han and L Li ldquoEffects of theimpeller blade with a slot structure on the centrifugal pumpperformancerdquo Energies vol 13 no 7 p 1628 2020

[27] L Shi J Zhu F Tang and C Wang ldquoMulti-disciplinaryoptimization design of axial-flow pump impellers based onthe approximation modelrdquo Energies vol 13 no 4 p 7792020

[28] 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

[29] C Wang X Chen N Qiu Y Zhu and W Shi ldquoNumericaland experimental study on the pressure fluctuation vibrationand noise of multistage pump with radial diffuserrdquo Journal ofthe Brazilian Society of Mechanical Sciences and Engineeringvol 40 p 481 2018

[30] L Zhou W Wang J Hang W Shi H Yan and Y ZhuldquoNumerical investigation of a high-speed electrical sub-mersible pump with different end clearancesrdquo Water vol 12p 1116 2020

[31] G Peng X Huang L Zhou G Zhou and H Zhou ldquoSolid-liquid two-phase flow and wear analysis in a large-scale


centrifugal slurry pumprdquo Engineering Failure Analysisvol 114 Article ID 104602 2020

[32] H Wang Z Qian D Zhang T Wang and C WangldquoNumerical study of the normal impinging water jet at dif-ferent impinging height based on Wray-Agarwal turbulencemodelrdquo Energies vol 13 no 7 p 1744 2020

[33] S Tang S Yuan and Y Zhu ldquoConvolutional neural networkin intelligent fault diagnosis toward rotatory machineryrdquoIEEE Access vol 8 no 1 pp 86510ndash86519 2020

[34] S Tang S Yuan and Y Zhu ldquoDeep learning-based intelligentfault diagnosis methods toward rotating machineryrdquo IEEEAccess vol 8 no 1 pp 9335ndash9346 2020

[35] L Zhou K Deshpande X Zhang and R K Agarwal ldquoProcesssimulation of chemical looping combustion using ASPENplus for a mixture of biomass and coal with various oxygencarriersrdquo Energy vol 195 Article ID 116955 2020

[36] L Zhou C Han L Bai W Shi and R Agarwal ldquoNumericaland experimental study of multiphase transient core-annularflow patterns in a spouted bedrdquo ASME Journal of EnergyResource Technology vol 142 no 9 Article ID 092104 2020

[37] S Tang S Yuan and Y Zhu ldquoData preprocessing techniquesin convolutional neural network based on fault diagnosistowards rotating machineryrdquo IEEE Access vol 8pp 149487ndash149496 2020

[38] L Zhou C Han L Bai W Li M A El-Emam and W ShildquoCFD-DEM bidirectional coupling simulation and experi-mental investigation of particle ejections and energy con-version in a spouted bedrdquo Energy vol 211 Article ID 1186722020

[39] N Liu Y S Wang and G Zhang Model Pump Test on theSame Test-Bed for the South-To-North Water Diversion ChinaWater Power Press Beijing China 2006

[40] C-Y Ge J-J Wang X-P Gu and L-F Feng ldquoCFD sim-ulation and PIV measurement of the flow field generated bymodified pitched blade turbine impellersrdquo Chemical Engi-neering Research and Design vol 92 no 6 pp 1027ndash10362014

[41] L Cheng C Liu F P Tang and J R Zhou ldquo3D numericalsimulation and performance predication of vertical axial flowpumping station by RNG turbulent modelrdquo Journal of Me-chanical Engineering vol 45 no 3 pp 252ndash257 2009

[42] Q G Chen Z Xu and Y J Zhang ldquoApplication of RNG kndashεmodels in numerical simulation of engineering turbulentflowsrdquo Chinese Quarterly of Mechanics vol 24 pp 88ndash952003

[43] Y J Zheng K Wang X C Lei and F Tang ldquo3D numericalsimulation in inlet passages of pumping station by RNG kndashεturbulent model with wall-function lawrdquoWater Resources andPower vol 26 pp 123ndash125 2008

[44] Z H Xu Y L Wu N X Chen Y Liu L Liang and Y ZWuldquoSimulation of turbulent flow in pump based on sliding meshand RNG kndashε modelrdquo Journal of Engineering Hermophyiscsvol 26 pp 66ndash68 2005

[45] J Y Qian Z X Gao B Z Liu and Z J Jin ldquoParametric studyon fluid dynamics of pilot-control angle globe valverdquo ASMEJournal of Fluids Engineering vol 140 no 11 Article ID111103 2018

[46] W Jiao L Cheng J Xu and C Wang ldquoNumerical analysis oftwo-phase flow in the cavitation process of a waterjet pro-pulsion pump systemrdquo Processes vol 7 no 10 p 690 2019

[47] Z Z Han Fluent-Example Calculation and Analysis of FluidEngineering Simulation Beijing Institute Technology PressBeijing China 2009

[48] F J Wang Computational Fluid Dynamics Analysis Principleand Application of CFD Software Tsinghua University PressBeijing China 2004

[49] F P Tang C Liu L Chen and J R Zhou ldquoNew selectionmethod of low head pumprdquo Advanced in Science and Tech-nology of Water Resource vol 21 pp 41ndash43 2001

[50] X S Lv Z F Huang and W Shi ldquoAnalysis on error cause ofhigher pump design head selection for large scale pumpingstationrdquo Shanghai Medium and Large Electrical Machinesvol 2 pp 25ndash28 2011


studied the influence of the guide vane on the hydraulicperformance of the pump system

e guide vane is used to undertake the flow from theimpeller outlet and recycle tangential energy For the designworking conditions the guide vane inlet angle matches theflow direction of the impeller outlet For off-design workingconditions the inlet angle of the guide vane is inconsistentwith the flow direction of the impeller outlet which leads toan increased hydraulic loss of the guide vane and a reducedaxial flow pump efficiency In recent years some studies haveexplored adjusting the guide vane angle and its effect on thehydraulic performance of an axial flow pump under off-design working conditions the results indicate that acomplete adjustment of the guide vane angle improves theflow pattern in the guide vane and reduces the hydraulic losswith a head improvement of 04964m and a pump efficiencyimprovement of 21648 measured in [19] Yang et al[20 21] studied a complete adjustment of the guide vaneangle and its effect on the hydraulic performance of an axialflow pump system the results indicate that the high effi-ciency area moves to a large discharge rate when the angle isrotated clockwise and to a small discharge rate when theangle is rotated counterclockwise Qian et al [22] found thatwhen the whole angle of the guide vane is adjusted in thesaddle zone the head increases by 015m the efficiencyincreases by 193 and the flow pattern in the axial flowpump is substantially improved e abovementionedstudies are all about the whole guide vane rotates us farno studies on matching the inlet angle of the guide vane withthe flow direction of the impeller outlet for an axial flowpump have been reported

On the one hand the guide vane of an axial flow pumptakes the flow from the impeller outlet on the other hand theguide vane needs to support the guide-bearing seat [23] Toavoid affecting the support function of the guide vane in thiswork the guide vane is divided into inlet segment middlesegment and outlet segment e inlet segment angle isadjustable while the middle and outlet segments are fixed andused to support the guide-bearing seat CFDmethod has beenwidely used in the studies of pump [24ndash31] and other aspect[32ndash38] In this paper based on the TJ04-ZL-06 pumpmodelwhich has 3 impeller blade components and 5 guide vanecomponents [39] influence of inlet angle of guide vane onhydraulic performance was studied using a 3D turbulent flownumerical simulation According to the numerical simulationresults the reason of the influence of inlet angle of guide vaneon the hydraulic performance was analyzed e study workhas important reference value for the hydraulic design andhydraulic performance improvement of an axial flow pump

2 Mathematical Model and Numerical Setting

21 Governing Equations and Turbulent Model A 3D tur-bulent flow numerical simulation for an axial flow pump isestablished by solving the Reynolds-averaged NavierndashStokesequations [40 41] using FLUENT software

e fluid flow in the axial flow pump is consideredincompressible e method of steady flow numericalsimulation is used to study the flow and hydraulic

performance of the pump e governing equations that areapplied to solve the flow field in the pump include a con-tinuity equation momentum equations and k equation andε equation of the k minus ε turbulent model e Reynolds-av-eraged NavierndashStokes equations are shown as follows

zρzt

+ ρzui

zxi

0

ρzui

zt+ ρ

zuiuj

zxj

minuszp

zxi

+z

zxj

μzui

zxj

+zuj

zxi

1113888 1113889 minus ρuiprimeujprime1113890 1113891 + Fi

(1)

where ρ is the density t is the time ui and uj are the meanvelocity components p is the mean pressure xi and xj arethe coordinate directions μ is the dynamic viscosity Fi is thebody force component minusρui

primeujprime is the Reynolds stress and uj

primeand ujprime are the fluctuating velocity components

e RNG k minus ε turbulent model is chosen to solve theflow in the pump because this model is suitable for solvingcomplicated flows such as rotating flows separated flowsand vortex flows [42ndash46] e k equation and ε equation ofthe RNG k minus ε turbulent model are shown as follows

ρzk

zt+ ρ

zkui

zxi

z

zxj

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk minus ρε

ρzεzt

+ ρzεui

zxi

z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 +C1εε

kGk minus C2ερ

ε2

k

(2)

where Gk is the turbulent kinetic energy production termC1ε is an empirical constant C2ε is an empirical constant σk

is the corresponding Prandtl number for turbulent kineticenergy k and σε is the corresponding Prandtl number for theturbulent kinetic energy dissipation rate ε

22 Computational Domain and Boundary Conditionse computational domain of the flow field in an axial flowpump is composed of a straight inlet pipe conical inlet pipeimpeller and impeller chamber guide vane bent outlet pipeand straight outlet pipe (Figure 1)e inlet boundary for theflow field calculation of an axial flow pump is set at the inletsection of the straight inlet pipee discharge rate is knownand the flow velocity distribution is uniform at the inletsection thus the velocity inlet boundary condition isadopted [47] e outlet boundary for the flow field cal-culation of the axial flow pump is set at the outlet section ofthe straight outlet pipe where the flow is fully developedthus the outflow boundary condition is adopted In the flowfield calculation the sidewalls of the pipes impellerchamber guide vane pump shaft fair water caps at theimpeller inlet and the guide vane outlet are solid and aretreated according to the conditions for a solid wall [48]Since the axial flow pump impeller rotates periodically therotating walls such as the impeller blade and hub adopt themoving wall boundary condition and the rotation speed anddirection are the same as those of the impeller





ηb d ρgQHb d

Pbz

times 100 (3)




3 Research Scheme




Straight inlet pipe


Guide vane

Guide vane

Impeller

Guide vane hub

Impeller hub


Straight outletpipe












Conical inletpipe


Guidevane

Bent outletpipe

Straight outletpipe


Straight inlet pipe


Guide vane


Straight outletpipe


100

90

80

70

60

50

40

30025 030 035 040 045


Pum

p effi

cien

cy (

)










020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


H

h

Out

let

segm

ent

Mid

dle

segm

ent

Inle

tse

gmen

t






Guide vane

β0

(a)

∆β0 gt 0

Guide vane

β0

(b)

Guide vane

β0

∆β0 lt 0

(c)


90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)



85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(e)

90

80

85

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(f )

Figure 8 Continued








90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s


Pum

p se

gmen

t effi

cien

cy η

hd (

)



85

80

75

70

65

6000 01 02 03 04


mp

segm

ent e

ffici

ency

ηbd

()



(g)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References

























































ηb d ρgQHb d

Pbz

times 100 (3)




3 Research Scheme




Straight inlet pipe


Guide vane

Guide vane

Impeller

Guide vane hub

Impeller hub


Straight outletpipe












Conical inletpipe


Guidevane

Bent outletpipe

Straight outletpipe


Straight inlet pipe


Guide vane


Straight outletpipe


100

90

80

70

60

50

40

30025 030 035 040 045


Pum

p effi

cien

cy (

)










020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


H

h

Out

let

segm

ent

Mid

dle

segm

ent

Inle

tse

gmen

t






Guide vane

β0

(a)

∆β0 gt 0

Guide vane

β0

(b)

Guide vane

β0

∆β0 lt 0

(c)


90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)



85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(e)

90

80

85

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(f )

Figure 8 Continued








90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s


Pum

p se

gmen

t effi

cien

cy η

hd (

)



85

80

75

70

65

6000 01 02 03 04


mp

segm

ent e

ffici

ency

ηbd

()



(g)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References































































Conical inletpipe


Guidevane

Bent outletpipe

Straight outletpipe


Straight inlet pipe


Guide vane


Straight outletpipe


100

90

80

70

60

50

40

30025 030 035 040 045


Pum

p effi

cien

cy (

)










020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


H

h

Out

let

segm

ent

Mid

dle

segm

ent

Inle

tse

gmen

t






Guide vane

β0

(a)

∆β0 gt 0

Guide vane

β0

(b)

Guide vane

β0

∆β0 lt 0

(c)


90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)



85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(e)

90

80

85

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(f )

Figure 8 Continued








90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s


Pum

p se

gmen

t effi

cien

cy η

hd (

)



85

80

75

70

65

6000 01 02 03 04


mp

segm

ent e

ffici

ency

ηbd

()



(g)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References


























































020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


H

h

Out

let

segm

ent

Mid

dle

segm

ent

Inle

tse

gmen

t






Guide vane

β0

(a)

∆β0 gt 0

Guide vane

β0

(b)

Guide vane

β0

∆β0 lt 0

(c)


90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)



85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(e)

90

80

85

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(f )

Figure 8 Continued








90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s


Pum

p se

gmen

t effi

cien

cy η

hd (

)



85

80

75

70

65

6000 01 02 03 04


mp

segm

ent e

ffici

ency

ηbd

()



(g)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References

























































Guide vane

β0

(a)

∆β0 gt 0

Guide vane

β0

(b)

Guide vane

β0

∆β0 lt 0

(c)


90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

90

85

80

75

70

65030 035 040 045


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)



85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(e)

90

80

85

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(f )

Figure 8 Continued








90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s


Pum

p se

gmen

t effi

cien

cy η

hd (

)



85

80

75

70

65

6000 01 02 03 04


mp

segm

ent e

ffici

ency

ηbd

()



(g)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References






















































85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(a)

85

80

75

70

65

6000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(b)

90

85

80

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(c)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(d)

95

90

85

80

75

7000 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(e)

90

80

85

75

70

6500 01 02 03 04


Pum

p se

gmen

t effi

cien

cy η

bd (

)



(f )

Figure 8 Continued








90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s


Pum

p se

gmen

t effi

cien

cy η

hd (

)



85

80

75

70

65

6000 01 02 03 04


mp

segm

ent e

ffici

ency

ηbd

()



(g)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References




























































90

85

80

75

70

65

60

Q = 030m3sQ = 040m3sQ = 0325m3sQ = 0425m3s

Q = 035m3sQ = 045m3sQ = 0375m3s


Pum

p se

gmen

t effi

cien

cy η

hd (

)



85

80

75

70

65

6000 01 02 03 04


mp

segm

ent e

ffici

ency

ηbd

()



(g)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References






















































020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)







u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References


























































u

vm0v0 w0

Guide vane

Impeller blade

β0

α0

(a)

vmsvs ws

u

Guide vane

Impeller blade

αs

βs

(b)

vmLvL wL

u

Guide vane

Impeller blade

βL

αL

(c)


020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)


02013424836247659070481893210461160

(ms

)

(a)

02013424836247659070481893210461160

(ms

)

(b)

02013424836247659070481893210461160

(ms

)

(c)











ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References






























































ηyl ρgQHyl

Pbz

times 100 (4)



ηdy Hb d

Hyl

Hyl minus Δhdy

Hyl

times 100 (5)

020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)



020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References






















































020144268392516640764888101211361260

(ms

)

(a)

020144268392516640764888101211361260

(ms

)

(b)

020144268392516640764888101211361260

(ms

)

(c)

020144268392516640764888101211361260

(ms

)

(d)


85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(a)

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(b)

Figure 17 Continued


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References






















































90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(a)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(b)

10

08

06

04

02

00

90

85

80

75

70

65030 035 040 045

Effic

ienc

y η

()


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(c)

90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00

Effici

ency

η (

)


Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

Q~ηy1

Q~ηbd

Q~∆hdy

(d)

Figure 18 Continued

85

80

75

70

65


01

02

03

04

05

06

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(c)

85

80

75

70

65


015

025

035

045

055

065

Pum

p se

gmen

t effi

cien

cy η

bd (

)


ηbd~∆β

∆hdy~∆β

Hyd

raul

ic lo

ss o

f gui

de v

ane ∆

h dy (

m)

(d)




ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References























































ηb d ρgQHb d

Pbz

ρgQHyl

Pbz

timesHb d

Hyl

ηyl times ηdy (6)




5 Conclusions






Data Availability


90

85

80

75

70

65030 035 040 045

10

08

06

04

02

00Ef

ficie

ncy η

()


Hyd

raul

ic lo

ss g

uide

van

e ∆h d

y (m

)

Q~ηy1

Q~ηbd

Q~∆dy

(e)




Impellerhead Hyl

(m)

Shaftpower Pbz

(kW)


(m)


()



()


()

0deg 266 1367 038 858 228 857 735minus10deg 269 1376 017 862 252 937 809




Acknowledgments


References
























































Acknowledgments


References











































































Documents

Influence of Inlet Angle of Guide Vane on Hydraulic