Research Article Numerical Investigation of a First Stage of a...
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Hindawi Publishing Corporation ISRN Mechanical Engineering Volume 2013, Article ID 578072, 15 pages http://dx.doi.org/10.1155/2013/578072 Research Article Numerical Investigation of a First Stage of a Multistage Centrifugal Pump: Impeller, Diffuser with Return Vanes, and Casing Nicolas La Roche-Carrier, Guyh Dituba Ngoma, and Walid Ghie University of Quebec in Abitibi-T´ emiscamingue, School of Engineering’s Department, 445 Boulevard de l’Universit´ e, Rouyn-Noranda, QC, Canada J9X 5E4 Correspondence should be addressed to Walid Ghie; [email protected] Received 4 April 2013; Accepted 4 May 2013 Academic Editors: A. A. Kendoush, A. Z. Sahin, and Z. Yu Copyright © 2013 Nicolas La Roche-Carrier et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is paper deals with the numerical investigation of a liquid flow in a first stage of a multistage centrifugal pump consisting of an impeller, diffuser with return vanes, and casing. e continuity and Navier-Stokes equations with the - turbulence model and standard wall functions were used. To improve the design of the pump’s first stage, the impacts of the impeller blade height and diffuser vane height, number of impeller blades, diffuser vanes and diffuser return vanes, and wall roughness height on the performances of the first stage of a multistage centrifugal pump were analyzed. e results achieved reveal that the selected parameters affect the pump head, brake horsepower, and efficiency in a strong yet different manner. To validate the model developed, the results of the numerical simulations were compared with the experimental results from the pump manufacturer. 1. Introduction Nowadays, multistage centrifugal pumps are widely used in industrial and mining enterprises. One of the most important components of a multistage centrifugal pump is the impeller (Peng [1]). e performance characteristics related to the pump including the head, brake horsepower, and efficiency rely heavily on the impeller. For a more performing multi- stage pump, its design parameters, such as the number of stages, impeller blades, diffuser vanes and diffuser return vanes, angle of the impeller blade, height of the impeller blade and diffuser vane, the width of the impeller blade and diffuser vane, the impeller and diffuser diameter, the rotating speed of the impeller, and the casing geometry must be determined accurately. Moreover, a stage of a multistage centrifugal pump is composed of an impeller, diffuser, and casing. Given the three-dimensional and turbulent liquid flow in a multistage centrifugal pump, it is very important to be aware of the liquid flow’s behavior when flowing through a pump stage accounting for the wall roughness. is can be achieved by taking all stage components into consideration in the planning, design, and optimization phases in design and off- design conditions. Many experimental and numerical studies have been conducted on the liquid flow through a single centrifugal pump (Cheah et al. [2], Ozturk et al. [3], Li [4], Liu et al. [5], Gonz´ alez et al. [6], Asuaje et al. [7], and Kaupert and Staubli [8]) and a multistage centrifugal pump (Huang et al. [9], Miyano et al. [10], Kawashima et al. [11], and Gantar et al. [12]), where Cheah et al. [2] had numerically investigated the complex pump internal flow field in a centrifugal pump in design and off-design conditions using a CFD code. From the numerical simulation, it was found that the impeller passage flow at the design point was quite smooth and followed the blade curve; however, flow separation was observed at the leading edge due because the inflow was not tangential. More- over, Ozturk et al. [3] had numerically investigated using a CFD code the impacts of the flow behavior in a centrifugal pump whose diffuser was subjected to different radial gaps were investigated. When the gap ratio decreased, it was shown that the jet was influenced within the diffuser because of the flow squeezing in small gap areas. Also, pump efficiency was
Transcript of Research Article Numerical Investigation of a First Stage of a...
Hindawi Publishing CorporationISRNMechanical EngineeringVolume 2013 Article ID 578072 15 pageshttpdxdoiorg1011552013578072
Research ArticleNumerical Investigation of a First Stage of a MultistageCentrifugal Pump Impeller Diffuser with Return Vanesand Casing
Nicolas La Roche-Carrier Guyh Dituba Ngoma and Walid Ghie
University of Quebec in Abitibi-Temiscamingue School of Engineeringrsquos Department 445 Boulevard de lrsquoUniversiteRouyn-Noranda QC Canada J9X 5E4
Correspondence should be addressed to Walid Ghie walidghieuqatca
Received 4 April 2013 Accepted 4 May 2013
Academic Editors A A Kendoush A Z Sahin and Z Yu
Copyright copy 2013 Nicolas La Roche-Carrier et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
This paper deals with the numerical investigation of a liquid flow in a first stage of a multistage centrifugal pump consisting ofan impeller diffuser with return vanes and casing The continuity and Navier-Stokes equations with the 119896-120576 turbulence modeland standard wall functions were used To improve the design of the pumprsquos first stage the impacts of the impeller blade heightand diffuser vane height number of impeller blades diffuser vanes and diffuser return vanes and wall roughness height onthe performances of the first stage of a multistage centrifugal pump were analyzed The results achieved reveal that the selectedparameters affect the pumphead brake horsepower and efficiency in a strong yet differentmanner To validate themodel developedthe results of the numerical simulations were compared with the experimental results from the pump manufacturer
1 Introduction
Nowadays multistage centrifugal pumps are widely used inindustrial andmining enterprises One of themost importantcomponents of a multistage centrifugal pump is the impeller(Peng [1]) The performance characteristics related to thepump including the head brake horsepower and efficiencyrely heavily on the impeller For a more performing multi-stage pump its design parameters such as the number ofstages impeller blades diffuser vanes and diffuser returnvanes angle of the impeller blade height of the impeller bladeand diffuser vane the width of the impeller blade and diffuservane the impeller and diffuser diameter the rotating speedof the impeller and the casing geometry must be determinedaccuratelyMoreover a stage of amultistage centrifugal pumpis composed of an impeller diffuser and casing Given thethree-dimensional and turbulent liquid flow in a multistagecentrifugal pump it is very important to be aware of theliquid flowrsquos behavior when flowing through a pump stageaccounting for the wall roughness This can be achievedby taking all stage components into consideration in the
planning design and optimization phases in design and off-design conditions
Many experimental and numerical studies have beenconducted on the liquid flow through a single centrifugalpump (Cheah et al [2] Ozturk et al [3] Li [4] Liu et al [5]Gonzalez et al [6] Asuaje et al [7] and Kaupert and Staubli[8]) and a multistage centrifugal pump (Huang et al [9]Miyano et al [10] Kawashima et al [11] and Gantar et al[12]) where Cheah et al [2] had numerically investigated thecomplex pump internal flow field in a centrifugal pump indesign and off-design conditions using a CFD code From thenumerical simulation it was found that the impeller passageflow at the design point was quite smooth and followed theblade curve however flow separation was observed at theleading edge due because the inflowwas not tangentialMore-over Ozturk et al [3] had numerically investigated usinga CFD code the impacts of the flow behavior in a centrifugalpump whose diffuser was subjected to different radial gapswere investigatedWhen the gap ratio decreased it was shownthat the jet was influenced within the diffuser because of theflow squeezing in small gap areas Also pump efficiency was
2 ISRNMechanical Engineering
(a) 10-stage pump (b) Cross-sectional view of 2-stage pump
Figure 1 Typical multistage centrifugal pump [13]
Inlet
Back stageside
Outlet
(a) Centrifugal pump stage
Diffuser with
Impeller
return vanes
Casting
(b) Stage components
Figure 2 Model of a centrifugal pump stage
only slightly affected by the impeller-diffuser gap distancewhich decreased in the design flow conditions In additionLi [4] and Liu et al [5] had experimentally examined theimpacts of the number of impeller blades on the pumprsquos per-formances Furthermore Gonzalez et al [6] had investigatednumerically using a CFD code the dynamic impacts stem-ming from the impeller-volute interaction within a centrifu-gal pump whereas the impacts of the volute on the velocityand pressure fields were examined by Asuaje et al [7] andKaupert and Staubli [8] Furthermore Huang et al [9] hadnumerically simulated using a CFD code a three-dimensionalturbulent flow through an entire stage of a multistage cen-trifugal pump including flows in a rotating impeller andstationary diffuser They had found that the reverse flowsexisted near the impeller outlet resulting in the flow fieldbeing asymmetric andunstableTherewas considerable inter-ference on the velocity field at the impeller exit because of theinteraction between the impeller blades and diffuser vanesAdditionally Miyano et al [10] had experimentally investi-gated the impacts of the return vane profile on the perfor-mances of the multistage centrifugal pump to optimize thestationary components in the multistage centrifugal pump Itwas found among other things that the return vane whosetrailing edge was set at the outer wall radius of the down-stream annular channel and discharged the swirl-less flowhad a positive impact on pump performances while
Kawashima et al [11] had experimentally investigated theimpacts of the diffuser vane on the performances of themultistage centrifugal pump accounting for the interactionsamong the diffuser vane return vane and next stage impellerThe relevance in matching the diffuser vane and return vaneproperly to improve the pump efficiency of the multistagecentrifugal pump was shown It was also found that the effi-ciency could be improved by making the cross-sectional areaof the channel from the diffuser vane outlet to the return vaneinlet as large as possible Moreover Gantar et al [12] hadexperimentally examined the multistage pump problems inconjunction with the axial thrust The Laser DopplerAnemometry (LDA) was used to determine the fluid rotationin the impeller side chamber and its impact on the impellerhydraulic axial thrust for different leakage flow regimesMoreover the influence of the increased wear ring radialclearance on the axial thrust was analyzed with the solutionfor pump hydraulic axial thrust reduction
Thorough analysis of previous works clearly demon-strated that the research results obtained are specific to thedesign parameters and configuration of the rotating andstationary components in single centrifugal pumps andmultistage centrifugal pumps and thus cannot always begeneralized Therefore in this study to enhance the designand performances of multistage centrifugal pumps as shownin Figure 1 accounting for the particularities of the geometry
ISRNMechanical Engineering 3
Blades
(a) Impeller
Return vanes
Vanes
(b) Diffuser
Suction side (inlet) Discharge side (outlet)
(c) Stage combined impeller and diffuser
Figure 3 Domain fluids of the stage components
Outlet
Inlet
Interface impeller-diffuser
Figure 4 Domains of inlet outlet and interface
and configuration of the impeller and diffuser with returnvanes a numerical investigation was conducted using theANSYS-CFX code (Ansys Inc [14]) This was done togain further insight into the characteristics of the three-dimensional turbulent liquid flow through a stage of a multi-stage centrifugal pump while also considering various flowconditions and pump design parameters including theheights of the impeller blade and diffuser vane (16mm23mm and 29mm) the numbers of impeller blades (5 6 and7) the number of diffuser vanes (7 8 and 12) the numberof diffuser return vanes (3 8 and 11) and the height ofthe wall roughness (0mm 0002mm and 2mm) for theimpeller diffuser and inner casing wall Upon applying thecontinuity andNavier-Stokes equations the liquid flowveloc-ity and liquid pressure distributions in a pump stage weredetermined while accounting for boundary conditions andconsidering a constant rotating speed for the impeller Thepump stage head brake horsepower and efficiency wererepresented as a function of the volume flow rate wherethe objective was to identify the values of selected designparameters that might improve pump stage performanceswith respect to their value ranges
2 Mathematical Formulation
The model of a first stage of the multistage centrifugal pumpconsidered in this study is shown in Figure 2 It consists of animpeller diffuser with return vanes and casting The diffuser
return vane passages are composed of the back diffuser wallback diffuser vanes and casing wall
To run the numerical simulations the used domain fluidsof the impeller and diffuser with return vanes are shown inFigure 3
In the centrifugal pump stagersquos governing equations forliquid flow the following assumptions were made (i) asteady-state three-dimensional and turbulence flow usingthe 119896-120576 model was assumed (ii) it was an incompressibleliquid (iii) it was a Newtonian liquid and (iv) the liquidrsquosthermophysical properties were constant with the tempera-ture
To account for these assumptions the theoretical analysisof the liquid flow in the impeller passages diffuser vanepassages and diffuser return vane passages was based on thecontinuity and Navier-Stokes [14] equations For the three-dimensional liquid flow through these components of acentrifugal pump stage as shown in Figure 3 the continuityequations are expressed by
nabla sdot vel = 0 (1)
where vel = vel(119906(119909 119910 119911) V(119909 119910 119911) 119908(119909 119910 119911)) is the liquidflow velocity vector
Using the coordinate system (1) can be rewritten as
120597119906
120597119909+120597V
120597119910+120597119908
120597119911= 0 (2)
and the Navier-Stokes equations are given by
120588nabla sdot (vel otimes vel)
= minusnabla119901 + 120583effnabla sdot (nablavel + (nablavel)119879
) + 119861
(3)
where 119901 is the pressure 120588 is the density 120583eff is the effectiveviscosity accounting for turbulenceotimes is a tensor product and119861 is the source term For flows in an impeller rotating at aconstant speed 120596 the source term can be written as follows
119861 = minus120588 (2119909vel + 119909 (119909 119903)) (4)
where 119903 is the location vector 2119909vel is the centripetalacceleration and 119909(119909 119903) is the Coriolis acceleration
4 ISRNMechanical Engineering
Start
Geometry data pump stage (impeller diffuser and casing cover)
3D geometry modelling with inventor software fluid domains of impeller and diffuser
Import of 3D geometry model from inventor software to DesignModeler module
Mesh generation of 3D geometry model from DesignModeler using Mesh-Meshing
3D mesh model to CFX-pre combined impeller and diffuser Boundaryconditions inlet outlet wall and interference frozen-rotor Continuity and
3D numerical model to CFX-solver numerically solving of continuity and Navier-Stokes equations accounting for the boundary conditions and interference condition
Numerical simulation results to CFX-post module combined impeller and diffuser
brake horsepower and efficiency)
rArr 3D geometry model combined impeller and diffuser
module combined impeller and diffuser rArr 3D mesh model
Navier-Stokes equations Solver control rArr3D numerical model
Combined impeller and diffuser rArr numerical simulation results
rArr Velocity and pressure fields (contour vector streamlines )rArr Calculating of performance parameters (head hydraulic power
Figure 5 Steps from 3D geometry model to 3D numerical model and to numerical simulation results
119861 is zero for the flow in the stationary components like thediffuser Using the coordinate system (3) can be rewritten as
120588(119906120597119906
120597119909+ V
120597119906
120597119910+ 119908
120597119906
120597119911)
= minus120597119901
120597119909+ 120583eff (
1205972119906
1205971199092+1205972119906
1205971199102+1205972119906
1205971199112) + 119861
119909
120588 (119906120597V
120597119909+ V
120597V
120597119910+ 119908
120597V
120597119911)
= minus120597119901
120597119910+ 120583eff (
1205972V
1205971199092+1205972V
1205971199102+1205972V
1205971199112) + 119861
119910
120588 (119906120597119908
120597119909+ V
120597119908
120597119910+ 119908
120597119908
120597119911)
= minus120597119901
120597119911+ 120583eff (
1205972119908
1205971199092+1205972119908
1205971199102+1205972119908
1205971199112) + 119861
119911
(5)
where
119861119909= 120588 (120596
2
119911119903119909+ 2120596119911V)
119861119910= 120588 (120596
2
119911119903119910minus 2120596119911119906)
119861119911= 0
(6)
Furthermore 120583eff is defined as
120583eff = 120583 + 120583119905 (7)
where 120583 is the dynamic viscosity and 120583119905is the turbulence
viscositySince the 119896-120576 turbulence model is used in this work
because convergence is better than with other turbulencemodels 120583
119905is linked to turbulence kinetic energy 119896 and
dissipation 120576 via the following relationship
120583119905= 1198621205831205881198962120576minus1 (8)
where 119862120583is a constant
ISRNMechanical Engineering 5
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
119867(m
)
119876 (m3h)
16 m23 mm29 mm
Figure 6 Pump stage head versus volume flow rate (parameterblade height and vane height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
16 m23 mm29 mm
Figure 7 Brake horsepower versus volume flow rate (parameterblade height and vane height)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
16 m23 mm29 mm
Figure 8 Efficiency versus volume flow rate (parameter bladeheight and vane height)
The values for 119896 and 120576 stem directly from the differentialtransport equations for turbulence kinetic energy and turbu-lence dissipation rates as follows
nabla sdot (120588vel119896) = nabla sdot [(120583 +120583119905
120590119896
)nabla119896] + 119901119896minus 120588120576
nabla sdot (120588vel120576) = nabla sdot [(120583 +120583119905
120590120576
)nabla120576] +120576
119896(1198621205761119901119896minus 1198621205762120588120576)
(9)
where 1198621205761 1198621205762 and 120590
120576are constants 119901
119896is the turbulence
production due to viscous and buoyancy forces which ismodeled using the following
119901119896= 120583119905nablavel sdot (nablavel + nabla
119879
vel)
minus2
3nabla sdot vel (3120583119905nabla sdot vel + 120588119896) + 119901
119896119887
(10)
119901119896119887= minus
120583119905
120588120590120588
119892 sdot nabla120588 (11)
where 119901119896119887can be neglected for the 119896-120576 turbulence model
Moreover for the flow modeling near the wall the loga-rithmic wall function is used to model the viscous sublayer[14]
To solve (2) and (5) numerically while accounting forthe boundary conditions and turbulence model 119896-120576 thecomputational fluid dynamics ANSYS-CFX code based onthe finite volume method was used to obtain the liquid flowvelocity and pressure distributions Pressure velocity cou-pling is calculated in ANSYS-CFX code using the Rhie Chowalgorithm [14]
In the cases examined involving the pump stage theboundary conditions were formulated as follows the staticpressure provided was given at the stage inlet (impeller inlet)while the flow rate provided was specified at the stage outlet(outlet of the diffuser return vane passage) The frozen rotorcondition was used for the impeller-diffuser interface A no-slip condition was set for the flow at the wall boundariesFigure 4 shows the inlet outlet and interface domains for theselected pump stage while the other domains were identifiedas the wall
Furthermore the ANSYS-CFX code includes the fol-lowing modules DesignModeler Mesh-Meshing CFX-preCFX-solver and CFX-post In Figure 5 the steps that werespecifically used to obtain the numerical simulation resultsfrom the geometry models to the numerical model for thepump stage are depicted
The pump stage head is formulated as follows
119867 =119901119905119900minus 119901119905119894
120588119892 (12)
where 119901119905119894is the total pressure at the pump stage inlet and
119901119905119900the total pressure at the pump stage outlet as shown in
Figure 3 They are expressed as
119901119905119894= 119901119894+120588
21198812
vel119894 119901119905119900= 119901119900+120588
21198812
vel119900 (13)
6 ISRNMechanical Engineering
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Diffuser return vane passages
(a) Height = 16mm and Δ119901 = 407792Pa
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Diffuser return vane passages
(b) Height = 23mm and Δ119901 = 479427Pa
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004Diffuser return vane passages
(c) Height = 29mm and Δ119901 = 519683Pa
Figure 9 Static pressure contour
Furthermore the hydraulic power of the pump stage is givenby
119875ℎ= 120588119876119892119867 (14)
where119876 is the volume flow rate and119867 is the pump stage headIn addition the brake horsepower of the pump stage is
expressed as follows
119875119904= 119862120596 (15)
where 120596 is the angular velocity and 119862 is the impeller torque
From the hydraulic power and the brake horsepower theefficiency of the pump stage can be written as follows
120578 =119875ℎ
119875119904
(16)
The efficiency can also be formulated in terms of the hydraulicefficiency 120578
ℎ the volumetric efficiencies 120578V and mechanical
efficiency 120578119898 as
120578 = 120578ℎ120578V120578119898 (17)
ISRNMechanical Engineering 7
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000Diffuser return vane passages
(a) Height = 16mm
Velo
city
vec
tor 1
(m sminus
1)
Diffuser return vane passages
3063119890+001
2722119890+001
2382119890+001
2042119890+001
1701119890+001
1361119890+001
1021119890+001
6806119890+000
3403119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
3063119890+0012722119890+0012382119890+0012042119890+0011701119890+0011361119890+0011021119890+0016806119890+0003403119890+0000000119890+000
(b) Height = 23mm
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000Diffuser return vane passages
(c) Height = 29mm
Figure 10 Liquid flow velocity vector
3 Results and Discussion
Water was used as the working liquid for all simulationruns in this study and was considered to have the followingreference values temperature of 25∘C for water dynamicviscosity of 120583 = 8899 times 10
minus4 Pas and density of 120588 =
997 kgm3 The main reference data for the impeller anddiffuser appears in Table 1
31 Case Studies Five parameters of the first stage of amultistage centrifugal pump were selected for examinationof their impacts mainly on pump performances blade height
and vane height for the impeller and diffuser respectively(16mm 23mm and 29mm) number of impeller blades (56 and 7) number of diffuser vanes (7 8 and 12) number ofdiffuser return vanes (3 8 and 11) and wall roughness height(0mm 0002mm and 2mm) for the impeller diffuser withreturn vanes and inner casingwallThenumerical simulationresults presented in this work were obtained with the highestaccuracy by conducting mesh-independent solution tests ineach case study using different numbers of mesh elements
311 Impact of the Height of Impeller Blades and DiffuserVanes To analyze the impact of the height of impeller blades
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
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2 ISRNMechanical Engineering
(a) 10-stage pump (b) Cross-sectional view of 2-stage pump
Figure 1 Typical multistage centrifugal pump [13]
Inlet
Back stageside
Outlet
(a) Centrifugal pump stage
Diffuser with
Impeller
return vanes
Casting
(b) Stage components
Figure 2 Model of a centrifugal pump stage
only slightly affected by the impeller-diffuser gap distancewhich decreased in the design flow conditions In additionLi [4] and Liu et al [5] had experimentally examined theimpacts of the number of impeller blades on the pumprsquos per-formances Furthermore Gonzalez et al [6] had investigatednumerically using a CFD code the dynamic impacts stem-ming from the impeller-volute interaction within a centrifu-gal pump whereas the impacts of the volute on the velocityand pressure fields were examined by Asuaje et al [7] andKaupert and Staubli [8] Furthermore Huang et al [9] hadnumerically simulated using a CFD code a three-dimensionalturbulent flow through an entire stage of a multistage cen-trifugal pump including flows in a rotating impeller andstationary diffuser They had found that the reverse flowsexisted near the impeller outlet resulting in the flow fieldbeing asymmetric andunstableTherewas considerable inter-ference on the velocity field at the impeller exit because of theinteraction between the impeller blades and diffuser vanesAdditionally Miyano et al [10] had experimentally investi-gated the impacts of the return vane profile on the perfor-mances of the multistage centrifugal pump to optimize thestationary components in the multistage centrifugal pump Itwas found among other things that the return vane whosetrailing edge was set at the outer wall radius of the down-stream annular channel and discharged the swirl-less flowhad a positive impact on pump performances while
Kawashima et al [11] had experimentally investigated theimpacts of the diffuser vane on the performances of themultistage centrifugal pump accounting for the interactionsamong the diffuser vane return vane and next stage impellerThe relevance in matching the diffuser vane and return vaneproperly to improve the pump efficiency of the multistagecentrifugal pump was shown It was also found that the effi-ciency could be improved by making the cross-sectional areaof the channel from the diffuser vane outlet to the return vaneinlet as large as possible Moreover Gantar et al [12] hadexperimentally examined the multistage pump problems inconjunction with the axial thrust The Laser DopplerAnemometry (LDA) was used to determine the fluid rotationin the impeller side chamber and its impact on the impellerhydraulic axial thrust for different leakage flow regimesMoreover the influence of the increased wear ring radialclearance on the axial thrust was analyzed with the solutionfor pump hydraulic axial thrust reduction
Thorough analysis of previous works clearly demon-strated that the research results obtained are specific to thedesign parameters and configuration of the rotating andstationary components in single centrifugal pumps andmultistage centrifugal pumps and thus cannot always begeneralized Therefore in this study to enhance the designand performances of multistage centrifugal pumps as shownin Figure 1 accounting for the particularities of the geometry
ISRNMechanical Engineering 3
Blades
(a) Impeller
Return vanes
Vanes
(b) Diffuser
Suction side (inlet) Discharge side (outlet)
(c) Stage combined impeller and diffuser
Figure 3 Domain fluids of the stage components
Outlet
Inlet
Interface impeller-diffuser
Figure 4 Domains of inlet outlet and interface
and configuration of the impeller and diffuser with returnvanes a numerical investigation was conducted using theANSYS-CFX code (Ansys Inc [14]) This was done togain further insight into the characteristics of the three-dimensional turbulent liquid flow through a stage of a multi-stage centrifugal pump while also considering various flowconditions and pump design parameters including theheights of the impeller blade and diffuser vane (16mm23mm and 29mm) the numbers of impeller blades (5 6 and7) the number of diffuser vanes (7 8 and 12) the numberof diffuser return vanes (3 8 and 11) and the height ofthe wall roughness (0mm 0002mm and 2mm) for theimpeller diffuser and inner casing wall Upon applying thecontinuity andNavier-Stokes equations the liquid flowveloc-ity and liquid pressure distributions in a pump stage weredetermined while accounting for boundary conditions andconsidering a constant rotating speed for the impeller Thepump stage head brake horsepower and efficiency wererepresented as a function of the volume flow rate wherethe objective was to identify the values of selected designparameters that might improve pump stage performanceswith respect to their value ranges
2 Mathematical Formulation
The model of a first stage of the multistage centrifugal pumpconsidered in this study is shown in Figure 2 It consists of animpeller diffuser with return vanes and casting The diffuser
return vane passages are composed of the back diffuser wallback diffuser vanes and casing wall
To run the numerical simulations the used domain fluidsof the impeller and diffuser with return vanes are shown inFigure 3
In the centrifugal pump stagersquos governing equations forliquid flow the following assumptions were made (i) asteady-state three-dimensional and turbulence flow usingthe 119896-120576 model was assumed (ii) it was an incompressibleliquid (iii) it was a Newtonian liquid and (iv) the liquidrsquosthermophysical properties were constant with the tempera-ture
To account for these assumptions the theoretical analysisof the liquid flow in the impeller passages diffuser vanepassages and diffuser return vane passages was based on thecontinuity and Navier-Stokes [14] equations For the three-dimensional liquid flow through these components of acentrifugal pump stage as shown in Figure 3 the continuityequations are expressed by
nabla sdot vel = 0 (1)
where vel = vel(119906(119909 119910 119911) V(119909 119910 119911) 119908(119909 119910 119911)) is the liquidflow velocity vector
Using the coordinate system (1) can be rewritten as
120597119906
120597119909+120597V
120597119910+120597119908
120597119911= 0 (2)
and the Navier-Stokes equations are given by
120588nabla sdot (vel otimes vel)
= minusnabla119901 + 120583effnabla sdot (nablavel + (nablavel)119879
) + 119861
(3)
where 119901 is the pressure 120588 is the density 120583eff is the effectiveviscosity accounting for turbulenceotimes is a tensor product and119861 is the source term For flows in an impeller rotating at aconstant speed 120596 the source term can be written as follows
119861 = minus120588 (2119909vel + 119909 (119909 119903)) (4)
where 119903 is the location vector 2119909vel is the centripetalacceleration and 119909(119909 119903) is the Coriolis acceleration
4 ISRNMechanical Engineering
Start
Geometry data pump stage (impeller diffuser and casing cover)
3D geometry modelling with inventor software fluid domains of impeller and diffuser
Import of 3D geometry model from inventor software to DesignModeler module
Mesh generation of 3D geometry model from DesignModeler using Mesh-Meshing
3D mesh model to CFX-pre combined impeller and diffuser Boundaryconditions inlet outlet wall and interference frozen-rotor Continuity and
3D numerical model to CFX-solver numerically solving of continuity and Navier-Stokes equations accounting for the boundary conditions and interference condition
Numerical simulation results to CFX-post module combined impeller and diffuser
brake horsepower and efficiency)
rArr 3D geometry model combined impeller and diffuser
module combined impeller and diffuser rArr 3D mesh model
Navier-Stokes equations Solver control rArr3D numerical model
Combined impeller and diffuser rArr numerical simulation results
rArr Velocity and pressure fields (contour vector streamlines )rArr Calculating of performance parameters (head hydraulic power
Figure 5 Steps from 3D geometry model to 3D numerical model and to numerical simulation results
119861 is zero for the flow in the stationary components like thediffuser Using the coordinate system (3) can be rewritten as
120588(119906120597119906
120597119909+ V
120597119906
120597119910+ 119908
120597119906
120597119911)
= minus120597119901
120597119909+ 120583eff (
1205972119906
1205971199092+1205972119906
1205971199102+1205972119906
1205971199112) + 119861
119909
120588 (119906120597V
120597119909+ V
120597V
120597119910+ 119908
120597V
120597119911)
= minus120597119901
120597119910+ 120583eff (
1205972V
1205971199092+1205972V
1205971199102+1205972V
1205971199112) + 119861
119910
120588 (119906120597119908
120597119909+ V
120597119908
120597119910+ 119908
120597119908
120597119911)
= minus120597119901
120597119911+ 120583eff (
1205972119908
1205971199092+1205972119908
1205971199102+1205972119908
1205971199112) + 119861
119911
(5)
where
119861119909= 120588 (120596
2
119911119903119909+ 2120596119911V)
119861119910= 120588 (120596
2
119911119903119910minus 2120596119911119906)
119861119911= 0
(6)
Furthermore 120583eff is defined as
120583eff = 120583 + 120583119905 (7)
where 120583 is the dynamic viscosity and 120583119905is the turbulence
viscositySince the 119896-120576 turbulence model is used in this work
because convergence is better than with other turbulencemodels 120583
119905is linked to turbulence kinetic energy 119896 and
dissipation 120576 via the following relationship
120583119905= 1198621205831205881198962120576minus1 (8)
where 119862120583is a constant
ISRNMechanical Engineering 5
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
119867(m
)
119876 (m3h)
16 m23 mm29 mm
Figure 6 Pump stage head versus volume flow rate (parameterblade height and vane height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
16 m23 mm29 mm
Figure 7 Brake horsepower versus volume flow rate (parameterblade height and vane height)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
16 m23 mm29 mm
Figure 8 Efficiency versus volume flow rate (parameter bladeheight and vane height)
The values for 119896 and 120576 stem directly from the differentialtransport equations for turbulence kinetic energy and turbu-lence dissipation rates as follows
nabla sdot (120588vel119896) = nabla sdot [(120583 +120583119905
120590119896
)nabla119896] + 119901119896minus 120588120576
nabla sdot (120588vel120576) = nabla sdot [(120583 +120583119905
120590120576
)nabla120576] +120576
119896(1198621205761119901119896minus 1198621205762120588120576)
(9)
where 1198621205761 1198621205762 and 120590
120576are constants 119901
119896is the turbulence
production due to viscous and buoyancy forces which ismodeled using the following
119901119896= 120583119905nablavel sdot (nablavel + nabla
119879
vel)
minus2
3nabla sdot vel (3120583119905nabla sdot vel + 120588119896) + 119901
119896119887
(10)
119901119896119887= minus
120583119905
120588120590120588
119892 sdot nabla120588 (11)
where 119901119896119887can be neglected for the 119896-120576 turbulence model
Moreover for the flow modeling near the wall the loga-rithmic wall function is used to model the viscous sublayer[14]
To solve (2) and (5) numerically while accounting forthe boundary conditions and turbulence model 119896-120576 thecomputational fluid dynamics ANSYS-CFX code based onthe finite volume method was used to obtain the liquid flowvelocity and pressure distributions Pressure velocity cou-pling is calculated in ANSYS-CFX code using the Rhie Chowalgorithm [14]
In the cases examined involving the pump stage theboundary conditions were formulated as follows the staticpressure provided was given at the stage inlet (impeller inlet)while the flow rate provided was specified at the stage outlet(outlet of the diffuser return vane passage) The frozen rotorcondition was used for the impeller-diffuser interface A no-slip condition was set for the flow at the wall boundariesFigure 4 shows the inlet outlet and interface domains for theselected pump stage while the other domains were identifiedas the wall
Furthermore the ANSYS-CFX code includes the fol-lowing modules DesignModeler Mesh-Meshing CFX-preCFX-solver and CFX-post In Figure 5 the steps that werespecifically used to obtain the numerical simulation resultsfrom the geometry models to the numerical model for thepump stage are depicted
The pump stage head is formulated as follows
119867 =119901119905119900minus 119901119905119894
120588119892 (12)
where 119901119905119894is the total pressure at the pump stage inlet and
119901119905119900the total pressure at the pump stage outlet as shown in
Figure 3 They are expressed as
119901119905119894= 119901119894+120588
21198812
vel119894 119901119905119900= 119901119900+120588
21198812
vel119900 (13)
6 ISRNMechanical Engineering
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Diffuser return vane passages
(a) Height = 16mm and Δ119901 = 407792Pa
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Diffuser return vane passages
(b) Height = 23mm and Δ119901 = 479427Pa
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004Diffuser return vane passages
(c) Height = 29mm and Δ119901 = 519683Pa
Figure 9 Static pressure contour
Furthermore the hydraulic power of the pump stage is givenby
119875ℎ= 120588119876119892119867 (14)
where119876 is the volume flow rate and119867 is the pump stage headIn addition the brake horsepower of the pump stage is
expressed as follows
119875119904= 119862120596 (15)
where 120596 is the angular velocity and 119862 is the impeller torque
From the hydraulic power and the brake horsepower theefficiency of the pump stage can be written as follows
120578 =119875ℎ
119875119904
(16)
The efficiency can also be formulated in terms of the hydraulicefficiency 120578
ℎ the volumetric efficiencies 120578V and mechanical
efficiency 120578119898 as
120578 = 120578ℎ120578V120578119898 (17)
ISRNMechanical Engineering 7
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000Diffuser return vane passages
(a) Height = 16mm
Velo
city
vec
tor 1
(m sminus
1)
Diffuser return vane passages
3063119890+001
2722119890+001
2382119890+001
2042119890+001
1701119890+001
1361119890+001
1021119890+001
6806119890+000
3403119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
3063119890+0012722119890+0012382119890+0012042119890+0011701119890+0011361119890+0011021119890+0016806119890+0003403119890+0000000119890+000
(b) Height = 23mm
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000Diffuser return vane passages
(c) Height = 29mm
Figure 10 Liquid flow velocity vector
3 Results and Discussion
Water was used as the working liquid for all simulationruns in this study and was considered to have the followingreference values temperature of 25∘C for water dynamicviscosity of 120583 = 8899 times 10
minus4 Pas and density of 120588 =
997 kgm3 The main reference data for the impeller anddiffuser appears in Table 1
31 Case Studies Five parameters of the first stage of amultistage centrifugal pump were selected for examinationof their impacts mainly on pump performances blade height
and vane height for the impeller and diffuser respectively(16mm 23mm and 29mm) number of impeller blades (56 and 7) number of diffuser vanes (7 8 and 12) number ofdiffuser return vanes (3 8 and 11) and wall roughness height(0mm 0002mm and 2mm) for the impeller diffuser withreturn vanes and inner casingwallThenumerical simulationresults presented in this work were obtained with the highestaccuracy by conducting mesh-independent solution tests ineach case study using different numbers of mesh elements
311 Impact of the Height of Impeller Blades and DiffuserVanes To analyze the impact of the height of impeller blades
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
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ISRNMechanical Engineering 3
Blades
(a) Impeller
Return vanes
Vanes
(b) Diffuser
Suction side (inlet) Discharge side (outlet)
(c) Stage combined impeller and diffuser
Figure 3 Domain fluids of the stage components
Outlet
Inlet
Interface impeller-diffuser
Figure 4 Domains of inlet outlet and interface
and configuration of the impeller and diffuser with returnvanes a numerical investigation was conducted using theANSYS-CFX code (Ansys Inc [14]) This was done togain further insight into the characteristics of the three-dimensional turbulent liquid flow through a stage of a multi-stage centrifugal pump while also considering various flowconditions and pump design parameters including theheights of the impeller blade and diffuser vane (16mm23mm and 29mm) the numbers of impeller blades (5 6 and7) the number of diffuser vanes (7 8 and 12) the numberof diffuser return vanes (3 8 and 11) and the height ofthe wall roughness (0mm 0002mm and 2mm) for theimpeller diffuser and inner casing wall Upon applying thecontinuity andNavier-Stokes equations the liquid flowveloc-ity and liquid pressure distributions in a pump stage weredetermined while accounting for boundary conditions andconsidering a constant rotating speed for the impeller Thepump stage head brake horsepower and efficiency wererepresented as a function of the volume flow rate wherethe objective was to identify the values of selected designparameters that might improve pump stage performanceswith respect to their value ranges
2 Mathematical Formulation
The model of a first stage of the multistage centrifugal pumpconsidered in this study is shown in Figure 2 It consists of animpeller diffuser with return vanes and casting The diffuser
return vane passages are composed of the back diffuser wallback diffuser vanes and casing wall
To run the numerical simulations the used domain fluidsof the impeller and diffuser with return vanes are shown inFigure 3
In the centrifugal pump stagersquos governing equations forliquid flow the following assumptions were made (i) asteady-state three-dimensional and turbulence flow usingthe 119896-120576 model was assumed (ii) it was an incompressibleliquid (iii) it was a Newtonian liquid and (iv) the liquidrsquosthermophysical properties were constant with the tempera-ture
To account for these assumptions the theoretical analysisof the liquid flow in the impeller passages diffuser vanepassages and diffuser return vane passages was based on thecontinuity and Navier-Stokes [14] equations For the three-dimensional liquid flow through these components of acentrifugal pump stage as shown in Figure 3 the continuityequations are expressed by
nabla sdot vel = 0 (1)
where vel = vel(119906(119909 119910 119911) V(119909 119910 119911) 119908(119909 119910 119911)) is the liquidflow velocity vector
Using the coordinate system (1) can be rewritten as
120597119906
120597119909+120597V
120597119910+120597119908
120597119911= 0 (2)
and the Navier-Stokes equations are given by
120588nabla sdot (vel otimes vel)
= minusnabla119901 + 120583effnabla sdot (nablavel + (nablavel)119879
) + 119861
(3)
where 119901 is the pressure 120588 is the density 120583eff is the effectiveviscosity accounting for turbulenceotimes is a tensor product and119861 is the source term For flows in an impeller rotating at aconstant speed 120596 the source term can be written as follows
119861 = minus120588 (2119909vel + 119909 (119909 119903)) (4)
where 119903 is the location vector 2119909vel is the centripetalacceleration and 119909(119909 119903) is the Coriolis acceleration
4 ISRNMechanical Engineering
Start
Geometry data pump stage (impeller diffuser and casing cover)
3D geometry modelling with inventor software fluid domains of impeller and diffuser
Import of 3D geometry model from inventor software to DesignModeler module
Mesh generation of 3D geometry model from DesignModeler using Mesh-Meshing
3D mesh model to CFX-pre combined impeller and diffuser Boundaryconditions inlet outlet wall and interference frozen-rotor Continuity and
3D numerical model to CFX-solver numerically solving of continuity and Navier-Stokes equations accounting for the boundary conditions and interference condition
Numerical simulation results to CFX-post module combined impeller and diffuser
brake horsepower and efficiency)
rArr 3D geometry model combined impeller and diffuser
module combined impeller and diffuser rArr 3D mesh model
Navier-Stokes equations Solver control rArr3D numerical model
Combined impeller and diffuser rArr numerical simulation results
rArr Velocity and pressure fields (contour vector streamlines )rArr Calculating of performance parameters (head hydraulic power
Figure 5 Steps from 3D geometry model to 3D numerical model and to numerical simulation results
119861 is zero for the flow in the stationary components like thediffuser Using the coordinate system (3) can be rewritten as
120588(119906120597119906
120597119909+ V
120597119906
120597119910+ 119908
120597119906
120597119911)
= minus120597119901
120597119909+ 120583eff (
1205972119906
1205971199092+1205972119906
1205971199102+1205972119906
1205971199112) + 119861
119909
120588 (119906120597V
120597119909+ V
120597V
120597119910+ 119908
120597V
120597119911)
= minus120597119901
120597119910+ 120583eff (
1205972V
1205971199092+1205972V
1205971199102+1205972V
1205971199112) + 119861
119910
120588 (119906120597119908
120597119909+ V
120597119908
120597119910+ 119908
120597119908
120597119911)
= minus120597119901
120597119911+ 120583eff (
1205972119908
1205971199092+1205972119908
1205971199102+1205972119908
1205971199112) + 119861
119911
(5)
where
119861119909= 120588 (120596
2
119911119903119909+ 2120596119911V)
119861119910= 120588 (120596
2
119911119903119910minus 2120596119911119906)
119861119911= 0
(6)
Furthermore 120583eff is defined as
120583eff = 120583 + 120583119905 (7)
where 120583 is the dynamic viscosity and 120583119905is the turbulence
viscositySince the 119896-120576 turbulence model is used in this work
because convergence is better than with other turbulencemodels 120583
119905is linked to turbulence kinetic energy 119896 and
dissipation 120576 via the following relationship
120583119905= 1198621205831205881198962120576minus1 (8)
where 119862120583is a constant
ISRNMechanical Engineering 5
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
119867(m
)
119876 (m3h)
16 m23 mm29 mm
Figure 6 Pump stage head versus volume flow rate (parameterblade height and vane height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
16 m23 mm29 mm
Figure 7 Brake horsepower versus volume flow rate (parameterblade height and vane height)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
16 m23 mm29 mm
Figure 8 Efficiency versus volume flow rate (parameter bladeheight and vane height)
The values for 119896 and 120576 stem directly from the differentialtransport equations for turbulence kinetic energy and turbu-lence dissipation rates as follows
nabla sdot (120588vel119896) = nabla sdot [(120583 +120583119905
120590119896
)nabla119896] + 119901119896minus 120588120576
nabla sdot (120588vel120576) = nabla sdot [(120583 +120583119905
120590120576
)nabla120576] +120576
119896(1198621205761119901119896minus 1198621205762120588120576)
(9)
where 1198621205761 1198621205762 and 120590
120576are constants 119901
119896is the turbulence
production due to viscous and buoyancy forces which ismodeled using the following
119901119896= 120583119905nablavel sdot (nablavel + nabla
119879
vel)
minus2
3nabla sdot vel (3120583119905nabla sdot vel + 120588119896) + 119901
119896119887
(10)
119901119896119887= minus
120583119905
120588120590120588
119892 sdot nabla120588 (11)
where 119901119896119887can be neglected for the 119896-120576 turbulence model
Moreover for the flow modeling near the wall the loga-rithmic wall function is used to model the viscous sublayer[14]
To solve (2) and (5) numerically while accounting forthe boundary conditions and turbulence model 119896-120576 thecomputational fluid dynamics ANSYS-CFX code based onthe finite volume method was used to obtain the liquid flowvelocity and pressure distributions Pressure velocity cou-pling is calculated in ANSYS-CFX code using the Rhie Chowalgorithm [14]
In the cases examined involving the pump stage theboundary conditions were formulated as follows the staticpressure provided was given at the stage inlet (impeller inlet)while the flow rate provided was specified at the stage outlet(outlet of the diffuser return vane passage) The frozen rotorcondition was used for the impeller-diffuser interface A no-slip condition was set for the flow at the wall boundariesFigure 4 shows the inlet outlet and interface domains for theselected pump stage while the other domains were identifiedas the wall
Furthermore the ANSYS-CFX code includes the fol-lowing modules DesignModeler Mesh-Meshing CFX-preCFX-solver and CFX-post In Figure 5 the steps that werespecifically used to obtain the numerical simulation resultsfrom the geometry models to the numerical model for thepump stage are depicted
The pump stage head is formulated as follows
119867 =119901119905119900minus 119901119905119894
120588119892 (12)
where 119901119905119894is the total pressure at the pump stage inlet and
119901119905119900the total pressure at the pump stage outlet as shown in
Figure 3 They are expressed as
119901119905119894= 119901119894+120588
21198812
vel119894 119901119905119900= 119901119900+120588
21198812
vel119900 (13)
6 ISRNMechanical Engineering
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Diffuser return vane passages
(a) Height = 16mm and Δ119901 = 407792Pa
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Diffuser return vane passages
(b) Height = 23mm and Δ119901 = 479427Pa
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004Diffuser return vane passages
(c) Height = 29mm and Δ119901 = 519683Pa
Figure 9 Static pressure contour
Furthermore the hydraulic power of the pump stage is givenby
119875ℎ= 120588119876119892119867 (14)
where119876 is the volume flow rate and119867 is the pump stage headIn addition the brake horsepower of the pump stage is
expressed as follows
119875119904= 119862120596 (15)
where 120596 is the angular velocity and 119862 is the impeller torque
From the hydraulic power and the brake horsepower theefficiency of the pump stage can be written as follows
120578 =119875ℎ
119875119904
(16)
The efficiency can also be formulated in terms of the hydraulicefficiency 120578
ℎ the volumetric efficiencies 120578V and mechanical
efficiency 120578119898 as
120578 = 120578ℎ120578V120578119898 (17)
ISRNMechanical Engineering 7
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000Diffuser return vane passages
(a) Height = 16mm
Velo
city
vec
tor 1
(m sminus
1)
Diffuser return vane passages
3063119890+001
2722119890+001
2382119890+001
2042119890+001
1701119890+001
1361119890+001
1021119890+001
6806119890+000
3403119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
3063119890+0012722119890+0012382119890+0012042119890+0011701119890+0011361119890+0011021119890+0016806119890+0003403119890+0000000119890+000
(b) Height = 23mm
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000Diffuser return vane passages
(c) Height = 29mm
Figure 10 Liquid flow velocity vector
3 Results and Discussion
Water was used as the working liquid for all simulationruns in this study and was considered to have the followingreference values temperature of 25∘C for water dynamicviscosity of 120583 = 8899 times 10
minus4 Pas and density of 120588 =
997 kgm3 The main reference data for the impeller anddiffuser appears in Table 1
31 Case Studies Five parameters of the first stage of amultistage centrifugal pump were selected for examinationof their impacts mainly on pump performances blade height
and vane height for the impeller and diffuser respectively(16mm 23mm and 29mm) number of impeller blades (56 and 7) number of diffuser vanes (7 8 and 12) number ofdiffuser return vanes (3 8 and 11) and wall roughness height(0mm 0002mm and 2mm) for the impeller diffuser withreturn vanes and inner casingwallThenumerical simulationresults presented in this work were obtained with the highestaccuracy by conducting mesh-independent solution tests ineach case study using different numbers of mesh elements
311 Impact of the Height of Impeller Blades and DiffuserVanes To analyze the impact of the height of impeller blades
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
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4 ISRNMechanical Engineering
Start
Geometry data pump stage (impeller diffuser and casing cover)
3D geometry modelling with inventor software fluid domains of impeller and diffuser
Import of 3D geometry model from inventor software to DesignModeler module
Mesh generation of 3D geometry model from DesignModeler using Mesh-Meshing
3D mesh model to CFX-pre combined impeller and diffuser Boundaryconditions inlet outlet wall and interference frozen-rotor Continuity and
3D numerical model to CFX-solver numerically solving of continuity and Navier-Stokes equations accounting for the boundary conditions and interference condition
Numerical simulation results to CFX-post module combined impeller and diffuser
brake horsepower and efficiency)
rArr 3D geometry model combined impeller and diffuser
module combined impeller and diffuser rArr 3D mesh model
Navier-Stokes equations Solver control rArr3D numerical model
Combined impeller and diffuser rArr numerical simulation results
rArr Velocity and pressure fields (contour vector streamlines )rArr Calculating of performance parameters (head hydraulic power
Figure 5 Steps from 3D geometry model to 3D numerical model and to numerical simulation results
119861 is zero for the flow in the stationary components like thediffuser Using the coordinate system (3) can be rewritten as
120588(119906120597119906
120597119909+ V
120597119906
120597119910+ 119908
120597119906
120597119911)
= minus120597119901
120597119909+ 120583eff (
1205972119906
1205971199092+1205972119906
1205971199102+1205972119906
1205971199112) + 119861
119909
120588 (119906120597V
120597119909+ V
120597V
120597119910+ 119908
120597V
120597119911)
= minus120597119901
120597119910+ 120583eff (
1205972V
1205971199092+1205972V
1205971199102+1205972V
1205971199112) + 119861
119910
120588 (119906120597119908
120597119909+ V
120597119908
120597119910+ 119908
120597119908
120597119911)
= minus120597119901
120597119911+ 120583eff (
1205972119908
1205971199092+1205972119908
1205971199102+1205972119908
1205971199112) + 119861
119911
(5)
where
119861119909= 120588 (120596
2
119911119903119909+ 2120596119911V)
119861119910= 120588 (120596
2
119911119903119910minus 2120596119911119906)
119861119911= 0
(6)
Furthermore 120583eff is defined as
120583eff = 120583 + 120583119905 (7)
where 120583 is the dynamic viscosity and 120583119905is the turbulence
viscositySince the 119896-120576 turbulence model is used in this work
because convergence is better than with other turbulencemodels 120583
119905is linked to turbulence kinetic energy 119896 and
dissipation 120576 via the following relationship
120583119905= 1198621205831205881198962120576minus1 (8)
where 119862120583is a constant
ISRNMechanical Engineering 5
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
119867(m
)
119876 (m3h)
16 m23 mm29 mm
Figure 6 Pump stage head versus volume flow rate (parameterblade height and vane height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
16 m23 mm29 mm
Figure 7 Brake horsepower versus volume flow rate (parameterblade height and vane height)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
16 m23 mm29 mm
Figure 8 Efficiency versus volume flow rate (parameter bladeheight and vane height)
The values for 119896 and 120576 stem directly from the differentialtransport equations for turbulence kinetic energy and turbu-lence dissipation rates as follows
nabla sdot (120588vel119896) = nabla sdot [(120583 +120583119905
120590119896
)nabla119896] + 119901119896minus 120588120576
nabla sdot (120588vel120576) = nabla sdot [(120583 +120583119905
120590120576
)nabla120576] +120576
119896(1198621205761119901119896minus 1198621205762120588120576)
(9)
where 1198621205761 1198621205762 and 120590
120576are constants 119901
119896is the turbulence
production due to viscous and buoyancy forces which ismodeled using the following
119901119896= 120583119905nablavel sdot (nablavel + nabla
119879
vel)
minus2
3nabla sdot vel (3120583119905nabla sdot vel + 120588119896) + 119901
119896119887
(10)
119901119896119887= minus
120583119905
120588120590120588
119892 sdot nabla120588 (11)
where 119901119896119887can be neglected for the 119896-120576 turbulence model
Moreover for the flow modeling near the wall the loga-rithmic wall function is used to model the viscous sublayer[14]
To solve (2) and (5) numerically while accounting forthe boundary conditions and turbulence model 119896-120576 thecomputational fluid dynamics ANSYS-CFX code based onthe finite volume method was used to obtain the liquid flowvelocity and pressure distributions Pressure velocity cou-pling is calculated in ANSYS-CFX code using the Rhie Chowalgorithm [14]
In the cases examined involving the pump stage theboundary conditions were formulated as follows the staticpressure provided was given at the stage inlet (impeller inlet)while the flow rate provided was specified at the stage outlet(outlet of the diffuser return vane passage) The frozen rotorcondition was used for the impeller-diffuser interface A no-slip condition was set for the flow at the wall boundariesFigure 4 shows the inlet outlet and interface domains for theselected pump stage while the other domains were identifiedas the wall
Furthermore the ANSYS-CFX code includes the fol-lowing modules DesignModeler Mesh-Meshing CFX-preCFX-solver and CFX-post In Figure 5 the steps that werespecifically used to obtain the numerical simulation resultsfrom the geometry models to the numerical model for thepump stage are depicted
The pump stage head is formulated as follows
119867 =119901119905119900minus 119901119905119894
120588119892 (12)
where 119901119905119894is the total pressure at the pump stage inlet and
119901119905119900the total pressure at the pump stage outlet as shown in
Figure 3 They are expressed as
119901119905119894= 119901119894+120588
21198812
vel119894 119901119905119900= 119901119900+120588
21198812
vel119900 (13)
6 ISRNMechanical Engineering
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Diffuser return vane passages
(a) Height = 16mm and Δ119901 = 407792Pa
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Diffuser return vane passages
(b) Height = 23mm and Δ119901 = 479427Pa
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004Diffuser return vane passages
(c) Height = 29mm and Δ119901 = 519683Pa
Figure 9 Static pressure contour
Furthermore the hydraulic power of the pump stage is givenby
119875ℎ= 120588119876119892119867 (14)
where119876 is the volume flow rate and119867 is the pump stage headIn addition the brake horsepower of the pump stage is
expressed as follows
119875119904= 119862120596 (15)
where 120596 is the angular velocity and 119862 is the impeller torque
From the hydraulic power and the brake horsepower theefficiency of the pump stage can be written as follows
120578 =119875ℎ
119875119904
(16)
The efficiency can also be formulated in terms of the hydraulicefficiency 120578
ℎ the volumetric efficiencies 120578V and mechanical
efficiency 120578119898 as
120578 = 120578ℎ120578V120578119898 (17)
ISRNMechanical Engineering 7
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000Diffuser return vane passages
(a) Height = 16mm
Velo
city
vec
tor 1
(m sminus
1)
Diffuser return vane passages
3063119890+001
2722119890+001
2382119890+001
2042119890+001
1701119890+001
1361119890+001
1021119890+001
6806119890+000
3403119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
3063119890+0012722119890+0012382119890+0012042119890+0011701119890+0011361119890+0011021119890+0016806119890+0003403119890+0000000119890+000
(b) Height = 23mm
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000Diffuser return vane passages
(c) Height = 29mm
Figure 10 Liquid flow velocity vector
3 Results and Discussion
Water was used as the working liquid for all simulationruns in this study and was considered to have the followingreference values temperature of 25∘C for water dynamicviscosity of 120583 = 8899 times 10
minus4 Pas and density of 120588 =
997 kgm3 The main reference data for the impeller anddiffuser appears in Table 1
31 Case Studies Five parameters of the first stage of amultistage centrifugal pump were selected for examinationof their impacts mainly on pump performances blade height
and vane height for the impeller and diffuser respectively(16mm 23mm and 29mm) number of impeller blades (56 and 7) number of diffuser vanes (7 8 and 12) number ofdiffuser return vanes (3 8 and 11) and wall roughness height(0mm 0002mm and 2mm) for the impeller diffuser withreturn vanes and inner casingwallThenumerical simulationresults presented in this work were obtained with the highestaccuracy by conducting mesh-independent solution tests ineach case study using different numbers of mesh elements
311 Impact of the Height of Impeller Blades and DiffuserVanes To analyze the impact of the height of impeller blades
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
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ISRNMechanical Engineering 5
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
119867(m
)
119876 (m3h)
16 m23 mm29 mm
Figure 6 Pump stage head versus volume flow rate (parameterblade height and vane height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
16 m23 mm29 mm
Figure 7 Brake horsepower versus volume flow rate (parameterblade height and vane height)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
16 m23 mm29 mm
Figure 8 Efficiency versus volume flow rate (parameter bladeheight and vane height)
The values for 119896 and 120576 stem directly from the differentialtransport equations for turbulence kinetic energy and turbu-lence dissipation rates as follows
nabla sdot (120588vel119896) = nabla sdot [(120583 +120583119905
120590119896
)nabla119896] + 119901119896minus 120588120576
nabla sdot (120588vel120576) = nabla sdot [(120583 +120583119905
120590120576
)nabla120576] +120576
119896(1198621205761119901119896minus 1198621205762120588120576)
(9)
where 1198621205761 1198621205762 and 120590
120576are constants 119901
119896is the turbulence
production due to viscous and buoyancy forces which ismodeled using the following
119901119896= 120583119905nablavel sdot (nablavel + nabla
119879
vel)
minus2
3nabla sdot vel (3120583119905nabla sdot vel + 120588119896) + 119901
119896119887
(10)
119901119896119887= minus
120583119905
120588120590120588
119892 sdot nabla120588 (11)
where 119901119896119887can be neglected for the 119896-120576 turbulence model
Moreover for the flow modeling near the wall the loga-rithmic wall function is used to model the viscous sublayer[14]
To solve (2) and (5) numerically while accounting forthe boundary conditions and turbulence model 119896-120576 thecomputational fluid dynamics ANSYS-CFX code based onthe finite volume method was used to obtain the liquid flowvelocity and pressure distributions Pressure velocity cou-pling is calculated in ANSYS-CFX code using the Rhie Chowalgorithm [14]
In the cases examined involving the pump stage theboundary conditions were formulated as follows the staticpressure provided was given at the stage inlet (impeller inlet)while the flow rate provided was specified at the stage outlet(outlet of the diffuser return vane passage) The frozen rotorcondition was used for the impeller-diffuser interface A no-slip condition was set for the flow at the wall boundariesFigure 4 shows the inlet outlet and interface domains for theselected pump stage while the other domains were identifiedas the wall
Furthermore the ANSYS-CFX code includes the fol-lowing modules DesignModeler Mesh-Meshing CFX-preCFX-solver and CFX-post In Figure 5 the steps that werespecifically used to obtain the numerical simulation resultsfrom the geometry models to the numerical model for thepump stage are depicted
The pump stage head is formulated as follows
119867 =119901119905119900minus 119901119905119894
120588119892 (12)
where 119901119905119894is the total pressure at the pump stage inlet and
119901119905119900the total pressure at the pump stage outlet as shown in
Figure 3 They are expressed as
119901119905119894= 119901119894+120588
21198812
vel119894 119901119905119900= 119901119900+120588
21198812
vel119900 (13)
6 ISRNMechanical Engineering
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Diffuser return vane passages
(a) Height = 16mm and Δ119901 = 407792Pa
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Diffuser return vane passages
(b) Height = 23mm and Δ119901 = 479427Pa
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004Diffuser return vane passages
(c) Height = 29mm and Δ119901 = 519683Pa
Figure 9 Static pressure contour
Furthermore the hydraulic power of the pump stage is givenby
119875ℎ= 120588119876119892119867 (14)
where119876 is the volume flow rate and119867 is the pump stage headIn addition the brake horsepower of the pump stage is
expressed as follows
119875119904= 119862120596 (15)
where 120596 is the angular velocity and 119862 is the impeller torque
From the hydraulic power and the brake horsepower theefficiency of the pump stage can be written as follows
120578 =119875ℎ
119875119904
(16)
The efficiency can also be formulated in terms of the hydraulicefficiency 120578
ℎ the volumetric efficiencies 120578V and mechanical
efficiency 120578119898 as
120578 = 120578ℎ120578V120578119898 (17)
ISRNMechanical Engineering 7
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000Diffuser return vane passages
(a) Height = 16mm
Velo
city
vec
tor 1
(m sminus
1)
Diffuser return vane passages
3063119890+001
2722119890+001
2382119890+001
2042119890+001
1701119890+001
1361119890+001
1021119890+001
6806119890+000
3403119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
3063119890+0012722119890+0012382119890+0012042119890+0011701119890+0011361119890+0011021119890+0016806119890+0003403119890+0000000119890+000
(b) Height = 23mm
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000Diffuser return vane passages
(c) Height = 29mm
Figure 10 Liquid flow velocity vector
3 Results and Discussion
Water was used as the working liquid for all simulationruns in this study and was considered to have the followingreference values temperature of 25∘C for water dynamicviscosity of 120583 = 8899 times 10
minus4 Pas and density of 120588 =
997 kgm3 The main reference data for the impeller anddiffuser appears in Table 1
31 Case Studies Five parameters of the first stage of amultistage centrifugal pump were selected for examinationof their impacts mainly on pump performances blade height
and vane height for the impeller and diffuser respectively(16mm 23mm and 29mm) number of impeller blades (56 and 7) number of diffuser vanes (7 8 and 12) number ofdiffuser return vanes (3 8 and 11) and wall roughness height(0mm 0002mm and 2mm) for the impeller diffuser withreturn vanes and inner casingwallThenumerical simulationresults presented in this work were obtained with the highestaccuracy by conducting mesh-independent solution tests ineach case study using different numbers of mesh elements
311 Impact of the Height of Impeller Blades and DiffuserVanes To analyze the impact of the height of impeller blades
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
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6 ISRNMechanical Engineering
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Pres
sure
cont
our 1
(Pa)
7370119890+0056813119890+0056256119890+0055700119890+0055143119890+0054586119890+0054029119890+0053472119890+0052916119890+0052359119890+0051802119890+0051245119890+0056884119890+0041317119890+004
minus4251119890+004minus9819119890+004minus1539119890+005
Diffuser return vane passages
(a) Height = 16mm and Δ119901 = 407792Pa
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Pres
sure
cont
our 1
(Pa)
8138119890+0057566119890+0056994119890+0056421119890+0055849119890+0055277119890+0054705119890+0054133119890+0053561119890+0052989119890+0052417119890+0051845119890+0051273119890+0057008119890+0041287119890+004
minus4433119890+004minus1015119890+005
Diffuser return vane passages
(b) Height = 23mm and Δ119901 = 479427Pa
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004Diffuser return vane passages
(c) Height = 29mm and Δ119901 = 519683Pa
Figure 9 Static pressure contour
Furthermore the hydraulic power of the pump stage is givenby
119875ℎ= 120588119876119892119867 (14)
where119876 is the volume flow rate and119867 is the pump stage headIn addition the brake horsepower of the pump stage is
expressed as follows
119875119904= 119862120596 (15)
where 120596 is the angular velocity and 119862 is the impeller torque
From the hydraulic power and the brake horsepower theefficiency of the pump stage can be written as follows
120578 =119875ℎ
119875119904
(16)
The efficiency can also be formulated in terms of the hydraulicefficiency 120578
ℎ the volumetric efficiencies 120578V and mechanical
efficiency 120578119898 as
120578 = 120578ℎ120578V120578119898 (17)
ISRNMechanical Engineering 7
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000Diffuser return vane passages
(a) Height = 16mm
Velo
city
vec
tor 1
(m sminus
1)
Diffuser return vane passages
3063119890+001
2722119890+001
2382119890+001
2042119890+001
1701119890+001
1361119890+001
1021119890+001
6806119890+000
3403119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
3063119890+0012722119890+0012382119890+0012042119890+0011701119890+0011361119890+0011021119890+0016806119890+0003403119890+0000000119890+000
(b) Height = 23mm
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000Diffuser return vane passages
(c) Height = 29mm
Figure 10 Liquid flow velocity vector
3 Results and Discussion
Water was used as the working liquid for all simulationruns in this study and was considered to have the followingreference values temperature of 25∘C for water dynamicviscosity of 120583 = 8899 times 10
minus4 Pas and density of 120588 =
997 kgm3 The main reference data for the impeller anddiffuser appears in Table 1
31 Case Studies Five parameters of the first stage of amultistage centrifugal pump were selected for examinationof their impacts mainly on pump performances blade height
and vane height for the impeller and diffuser respectively(16mm 23mm and 29mm) number of impeller blades (56 and 7) number of diffuser vanes (7 8 and 12) number ofdiffuser return vanes (3 8 and 11) and wall roughness height(0mm 0002mm and 2mm) for the impeller diffuser withreturn vanes and inner casingwallThenumerical simulationresults presented in this work were obtained with the highestaccuracy by conducting mesh-independent solution tests ineach case study using different numbers of mesh elements
311 Impact of the Height of Impeller Blades and DiffuserVanes To analyze the impact of the height of impeller blades
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
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International Journal of
ISRNMechanical Engineering 7
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2903119890+001
2580119890+001
2258119890+001
1935119890+001
1613119890+001
1290119890+001
9675119890+000
6450119890+000
3225119890+000
0000119890+000Diffuser return vane passages
(a) Height = 16mm
Velo
city
vec
tor 1
(m sminus
1)
Diffuser return vane passages
3063119890+001
2722119890+001
2382119890+001
2042119890+001
1701119890+001
1361119890+001
1021119890+001
6806119890+000
3403119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
3063119890+0012722119890+0012382119890+0012042119890+0011701119890+0011361119890+0011021119890+0016806119890+0003403119890+0000000119890+000
(b) Height = 23mm
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000
Velo
city
vec
tor 1
(m sminus
1)
2979119890+001
2648119890+001
2317119890+001
1986119890+001
1655119890+001
1324119890+001
9930119890+000
6620119890+000
3310119890+000
0000119890+000Diffuser return vane passages
(c) Height = 29mm
Figure 10 Liquid flow velocity vector
3 Results and Discussion
Water was used as the working liquid for all simulationruns in this study and was considered to have the followingreference values temperature of 25∘C for water dynamicviscosity of 120583 = 8899 times 10
minus4 Pas and density of 120588 =
997 kgm3 The main reference data for the impeller anddiffuser appears in Table 1
31 Case Studies Five parameters of the first stage of amultistage centrifugal pump were selected for examinationof their impacts mainly on pump performances blade height
and vane height for the impeller and diffuser respectively(16mm 23mm and 29mm) number of impeller blades (56 and 7) number of diffuser vanes (7 8 and 12) number ofdiffuser return vanes (3 8 and 11) and wall roughness height(0mm 0002mm and 2mm) for the impeller diffuser withreturn vanes and inner casingwallThenumerical simulationresults presented in this work were obtained with the highestaccuracy by conducting mesh-independent solution tests ineach case study using different numbers of mesh elements
311 Impact of the Height of Impeller Blades and DiffuserVanes To analyze the impact of the height of impeller blades
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
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International Journal of
8 ISRNMechanical Engineering
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
5 blades6 blades7 blades
119867(m
)
119876 (m3h)
Figure 11 Pump stage head versus volume flow rate (parameterblade number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
119875119904
(kW
)
119876 (m3h)
5 blades6 blades7 blades
Figure 12 Brake horsepower versus volume flow rate (parameterblade number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
120578(
)
119876 (m3h)
5 blades6 blades7 blades
Figure 13 Efficiency versus volume flow rate (parameter bladenumber)
Table 1 Main reference data for the impeller and diffuser
m80Impeller DiffuserInner diameter (mm) 195 Inner diameter (mm) 407016Outer diameter (mm) 406 Outer diameter (mm) 5715Number of blades 6 Number of vanes 8
Rotating speed (rpm) 1750 Number of returnvanes 11
and diffuser vanes on the pump stage head brake horsepowerand efficiency the values of 16mm 23mm and 29mmwere selected for the impeller blade height and diffuser vaneheight while keeping the other parameters constant Figure 6shows the pump stage head as a function of the volume flowrate with the blade height and vane height as a parameterwhere it can be observed that the pump stage head decreaseswith an increasing volume flow rate due to decreasing liquidpressure In addition the pump stage head increases withincreasing blade height and vane height This is explainedby the fact that when the volume flow rate is kept constantthe increased blade height leads to the decreasing meridionalvelocity which increases the pump stage head since the outlettangential velocity and outlet blade angle remain constant Inother words the liquid pressure drops in the impeller and thediffuser decreases as a function of the increase in the bladeheight and vane height
The curves expressing the pump stage brake horsepoweras a function of the volume flow rate are shown in Figure 7illustrating that the brake horsepower increases with increas-ing volume flow rate This can be explained by the additionaldecrease in liquid pressure relative to the volume flow rateAlso the brake horsepower increases relative to the impellerblade height due to the requested increase in pump shafttorque relative to the increased blade height
The curves representing pump stage efficiency as a func-tion of the volume flow rate is depicted in Figure 8 where itis observed that the efficiency for the blade height and vaneheight of 16mm decreases rapidly to the right of the bestefficiency point (BEP) The efficiency of the blade height andvane height of 23mm is highest at large volume flow rateswhereas the efficiency of the blade height and vane heightof 29mm is lowest at volume flow rates ranging between150m3h and 550m3h
Figures 9 and 10 show the corresponding contours forstatic pressure and liquid flow velocity vectors for 119876 =
464m3h Figure 9 clearly shows that the static pressureincreases with the increasing blade height and vane heightThis is duemainly to the decrease in liquid flow velocity at theimpeller outlet as depicted in Figure 10 where average liquidflow velocities at the impeller outlet decrease from 1843for 16mm to 1567ms for 29mm Also the recirculationphenomenon is observed in the diffuser return vane passagesFurthermore the distribution of pressure difference (Δ119901 =
119901119900minus 119901119894) in the stage components is presented in Table 2
312 Impact of the Number of Impeller Blades To inves-tigate the impact of the number of impeller blades on
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
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International Journal of
ISRNMechanical Engineering 9
7771119890+0057213119890+0056654119890+0056095119890+0055536119890+0054978119890+0054419119890+0053860119890+0053301119890+0052743119890+0052184119890+0051625119890+0051066119890+0055076119890+004
minus5110119890+003minus6098119890+004minus1169119890+005
Pres
sure
cont
our 1
(Pa)
(a) 5 blades and Δ119875 = 474962Pa
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
(b) 6 blades and Δ119875 = 519683 Pa
8450119890+0057934119890+0057418119890+0056902119890+0056386119890+0055870119890+0055354119890+0054838119890+0054322119890+0053806119890+0053290119890+0052774119890+0052258119890+0051742119890+0051226119890+0057101119890+0041942119890+004
Pres
sure
cont
our 1
(Pa)
(c) 7 blades and Δ119875 = 564968 Pa
Figure 14 Static pressure contour
Table 2 Distribution of the pressure difference
Blade or vaneheight
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
16mm 424908 74626 minus91742 40779223mm 485468 92713 minus98754 47942729mm 512751 108942 minus102010 519683
the pump stage head the brake horsepower and efficiencythree impellers with 5 6 and 7 blades were selected for adiffuser with 11 vanes and 8 return vanes while the otherparameters were kept constant Figure 11 shows the head asa function of the volume flow rate illustrating that the headand the static pressure keep increasing as the number ofblades increases Thus the ideal head is produced when thenumber of impeller blades becomes infinite Additionally asshown in Figure 12 the brake horsepower increases relativeto the increased number of impeller blades This is due to theincrease in the request pump shaft torque as the number ofimpeller blades also increases
Furthermore Figure 13 shows the efficiency curvesshowing that impellers with 5 and 6 blades are not as efficientas impellers with 7 blades for large volume flow rates
Furthermore Figure 13 shows the efficiency curvesshowing that the impellers with 5 and 6 blades have the sameefficiency that is lower than the efficiency for the impellerwith 7 blades for large volume flow rates
Moreover Figures 14 and 15 depict the correspondingstatic pressure contour and liquid flow velocity vector for
Table 3 Distribution of pressure difference
Blade numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
5 476784 98196 minus100018 4749626 512751 108942 minus102010 5196837 547270 120316 minus102618 564968
119876 = 464m3h respectively These figures thus clearly showthe increased static pressure difference between the stageoutlet and impeller inlet relative to the increasing number ofbladesThis confirms the reduction in the liquid flow velocityat the impeller outlet relative to the greater number of bladesas represented in Figure 15 where the average liquid flowvelocities at the impeller outlet were 1813ms 1567ms and1432ms for 5 blades 6 blades and 7 blades respectivelyIn addition the distribution of the pressure difference in theimpeller diffuser and diffuser return vane passages is indi-cated in Table 3
313 Impact of the Number of Diffuser Vanes To analyze theimpact that the number of diffuser vanes has on the pumpstage head brake horsepower and efficiency three diffusermodels (with 7 8 and 12 vanes and 8 return vanes) wereselected considering an impeller with 5 blades while otherparameters were kept constant Figure 16 shows the head as afunction of the volume flow rate where it is observed that thehead obtained with diffusers with 7 and 8 vanes is almost the
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 ISRNMechanical Engineering
Velo
city
vec
tor 1
(m sminus
1)
3274119890+0012910119890+0012546119890+0012182119890+0011819119890+0011455119890+0011091119890+0017275119890+0003637119890+0000000119890+000
(a) 5 blades
2979119890+0012648119890+0012317119890+0011986119890+0011655119890+0011324119890+0019930119890+0006620119890+0003310119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 6 blades
3087119890+0012744119890+0012401119890+0012058119890+0011715119890+0011372119890+0011029119890+0016861119890+0003430119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 7 blades
Figure 15 Vectors of liquid flow velocity contour
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119867(m
)
119876 (m3h)
Figure 16 Pump stage head versus volume flow rate (parametervane number)
same for a volume flow rate smaller than 320m3h whereasthe head with the diffuser with 12 vanes is smallest For largevolume flow rates the head with the diffuser with 12 vanesis the highest This is due to a rise in static pressure throughthe reduction in flow velocity in a diffuser (diffusion effect)The flow guidance and friction effect depend on the numberof diffuser vanes and the volume flow rateWhen the numberof diffuser vanes increases the diffuser vane passages becomenarrower This leads to better fluid guidance In other wordsflow loss decreases as the number of diffuser vanes increasesFriction loss increases with an increasing number of diffuser
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
119875119904
(kW
)
Figure 17 Brake horsepower versus volume flow rate (parametervane number)
vanes Furthermore flow guidance friction loss and staticpressure conversion are affected by the volume flow rateThus there is an antagonistic impact between the diffusionimpact and the friction loss in the range of the volume flowrate considered As depicted in Figure 17 brake horsepowervariation due to the number of diffuser blades is also smalleven if the lowest brake horsepower is reachedwith 12 diffuserblades
Furthermore Figure 18 shows that for low and highvolume flow rates the efficiency of 12 diffuser vanes is highest
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
ISRNMechanical Engineering 11
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
7 vanes8 vanes12 vanes
119876 (m3h)
120578(
)
Figure 18 Efficiency versus volume flow rate (parameter vanenumber)
Table 4 Distribution of pressure difference
Vane numberPressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages 998779119901total
7 500556 70817 minus89149 4822248 496559 87279 minus85170 49866812 476198 103252 minus78607 500843
whereas the efficiency for 7 and 8 diffuser vanes is nearly thesame for a volume flow rate smaller than 320m3hThis figurealso indicates that the efficiency is lowest for 7 diffuser vanesfor a volume flow rate higher than 320m3h Additionally thebest efficiency point (BEP) moves towards large volume flowrates and rises as the number of diffuser vanes increases
Moreover Figures 19 and 20 depict the correspondingstatic pressure contour and liquid flow velocity vector for119876 =
403m3h respectively showing that for these figures there isa correlation between increased static pressure difference anddecreased liquid flow velocity at the diffuser outlet with anincreased diffuser vane number The average liquid flowvelocity values at the diffuser outlet of 1394ms 1314msand 11ms were found for 7 8 and 12 vanes respectivelyas shown in Figure 20 Also Table 4 indicates the pressuredifference in the impeller diffuser and diffuser return vanepassages
314 Impact of the Number of Diffuser Return Vanes Toinvestigate the impact that the number of diffuser returnvanes has on the pump stage head brake horsepower andefficiency three diffuser models with 3 8 and 11 return vanesand 11 vanes were selected considering an impeller with 6blades while other parameters were kept constant Figure 21shows the head as a function of the volume flow rate where itis observed that the head obtained with the 3 diffuser returnvanes is the lowest This can be explained by the fact that thevariation in the number of diffuser return vanes affects flowloss due to flow guidance and friction loss in diffuser return
Table 5 Distribution of pressure difference
Return vanenumber
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
3 517349 103444 minus122147 4986468 512751 108942 minus102010 51968311 516752 107500 minus92048 532204
Table 6 Distribution of pressure difference
Wall roughnessheight mm
Pressure difference Δp Pa
Impeller Diffuser Diffuser returnvane passages Δ119901total
0 512751 108942 minus102010 5196832 486786 79951 minus80182 486555
vanes As depicted in Figure 22 the brake horsepower is onlyslightly affected by the number of diffuser return vanes
Furthermore Figure 23 shows that for higher volumeflow rates the efficiency of the diffuser with 11 return vanes ishighest This figure also indicates that the efficiency is lowestfor 5 diffuser vanes
Additionally Table 5 indicates the pressure difference inthe impeller diffuser and diffuser return vane passageswhere it can be observed that the highest pressure loss in thediffuser with 3 return vanes
315 Impact of Wall Roughness Height To investigate theimpact of the wall roughness height of the impeller diffuserand casting on the pump stage head brake horsepower andefficiency three wall roughness heights (0mm 0002mmand 2mm) were chosen while the other parameters werekept constant Figure 24 shows the head as a function of thevolume flow rate where it is observed that the head is notaffected by the value of thewall roughness height at 0mmand0002mmOn the contrary it decreases when the wall rough-ness height increases furtherThis is explained by the fact thatthe friction loss rises with significantly increasing wall rough-ness height In other words the wall roughness increasesthe flow resistance in turbulent flow This confirms thatthe casting process used for the impeller diffuser and castinghas an impact on their surface finish which influences thefriction loss in flow passage and thus the head As depictedin Figure 25 the brake horsepower increases with increasingwall roughness height for large volume flow rates due to therising of friction loss with increasing wall roughness heightfor large volume flow rates Thus the requested pump torqueincreases
Furthermore Figure 26 shows the efficiency as a functionof the volume flow rate where it is observed that the efficiencyis not influenced by the value of the wall roughness height for0mm and 0002m while it decreases with the value of thewall roughness height at 2mm due to the increase in frictionloss Moreover the BEP moves towards a lower volume flowrate at the wall roughness height of 2mm
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 ISRNMechanical Engineering
8114119890+0057614119890+0057113119890+0056613119890+0056113119890+0055612119890+0055112119890+0054612119890+0054111119890+0053611119890+0053111119890+0052610119890+0052110119890+0051610119890+0051109119890+0056091119890+0041088119890+004
Pres
sure
cont
our 1
(Pa)
(a) 7 vanes and Δ119875 = 482224Pa
8047119890+0057542119890+0057036119890+0056531119890+0056025119890+0055520119890+0055015119890+0054509119890+0054004119890+0053499119890+0052993119890+0052488119890+0051983119890+0051477119890+0059720119890+0044666119890+004
minus3873119890+003
Pres
sure
cont
our 1
(Pa)
(b) 8 vanes and Δ119875 = 498668Pa
7613119890+0057154119890+0056695119890+0056235119890+0055776119890+0055317119890+0054858119890+0054398119890+0053939119890+0053480119890+0053020119890+0052561119890+0052102119890+0051643119890+0051183119890+0057240119890+0042647119890+004
Pres
sure
cont
our 1
(Pa)
(c) 12 vanes and Δ119875 = 500843 Pa
Figure 19 Static pressure contour
3061119890+0012721119890+0012381119890+0012041119890+0011700119890+0011360119890+0011020119890+0016802119890+0003401119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(a) 7 vanes
3021119890+0012686119890+0012350119890+0012014119890+0011679119890+0011343119890+0011007119890+0016714119890+0003357119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(b) 8 vanes
3002119890+0012669119890+0012335119890+0012001119890+0011668119890+0011334119890+0011001119890+0016671119890+0003336119890+0000000119890+000
Velo
city
vec
tor 1
(m sminus
1)
(c) 12 vanes
Figure 20 Vectors of liquid flow velocity
Furthermore Figure 27 depicts the corresponding staticpressure contour for 119876 = 464m3h which shows thedistribution of static pressure in the impeller anddiffuserwithreturn vanes Also Table 6 presents the pressure differencesin the impeller diffuser and diffuser return vane passagesobtained for the wall roughness heights of 0mm and 2mm
As previously mentioned this clearly shows the decreasein total pressure difference with increasing wall roughnessheight
32 Model Comparison To validate the model developed forthe first stage of a multistage centrifugal pump composed
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
ISRNMechanical Engineering 13
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119867(m
)
119876 (m3h)
Figure 21 Pump stage head versus volume flow rate (parameterreturn vane number)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
119875119904
(kW
)
Figure 22 Brake horsepower versus volume flow rate (parameterreturn vane number)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600 700
3 return vanes8 return vanes11 return vanes
119876 (m3h)
120578(
)
Figure 23 Efficiency versus volume flow rate (parameter returnvane number)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119867(m
)
119876 (m3h)
Figure 24 Pump stage head versus volume flow rate (parameterwall roughness height)
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
119875119904
(kW
)
Figure 25 Brake horsepower versus volume flow rate (parameterwall roughness height)
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
0 mm0002 mm2 mm
119876 (m3h)
120578(
)
Figure 26 Efficiency versus volume flow rate (parameter wallroughness height)
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
14 ISRNMechanical Engineering
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
8045119890+0057513119890+0056981119890+0056449119890+0055917119890+0055384119890+0054852119890+0054320119890+0053788119890+0053255119890+0052723119890+0052191119890+0051659119890+0051126119890+0055943119890+0046203119890+003
minus4702119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(a) 0mm and Δ119901 = 519683Pa
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
7485119890+0057004119890+0056522119890+0056040119890+0055559119890+0055077119890+0054596119890+0054114119890+0053632119890+0053151119890+0052669119890+0052188119890+0051706119890+0051224119890+0057428119890+0042612119890+004
minus2204119890+004
Pres
sure
cont
our 1
(Pa)
Diffuser return vane passages
(b) 2mm and Δ119901 = 486555Pa
Figure 27 Static pressure contour
0
20
40
60
80
100
120
140
50 150 250 350 450 550 650
Num EffExp Eff
119867(m
)119875119904
(kW
)120578
()
119876 (m3h)
Num 119867Exp 119867Num 119875119904
Exp 119875119904
Figure 28 Comparison between the numerical results and experi-mental results
of an impeller diffuser with return vanes and castingthe numerical simulation results were compared with theexperimental results obtained fromTechnosub [13] Figure 28shows the comparison between the experimental and numer-ical curves for the head brake horsepower and efficiencyThis comparison confirms that all the numerical curvesfollow the trend of the experimental curves
The discrepancies observed can be explained amongother things by the fact that the mechanical power lossand leakage power loss were not taken into account in thenumerical simulations conducted The values used for themechanical efficiency and volumetric efficiency in thenumerical simulations were as assumed to be constant how-ever the additional parameters which affect the gap betweenthe numerical results and experimental results are beingmore thoroughly investigated in the experimental andnumerical sides to increasingly enhance the approach devel-oped for the first stage of a multistage centrifugal pump
4 Conclusion
In this study a steady-state liquid flow in the three-dimensional first stage of a multistage centrifugal pump wasnumerically investigated A model of a centrifugal pumpstage composed of an impeller diffuser and casting wasdeveloped to analyze the impacts of the height of the impellerblades and diffuser vanes the number of impeller bladesdiffuser vanes and diffuser return vanes and the wall rough-ness height on the pump stage head brake horse power andefficiency The results obtained demonstrate among otherthings that the pump stage head and brake horsepowerincrease as the height of the impeller blades and diffuservanes and the number of impeller blades increase Moreoverthe head and efficiency increase for large volume flow rates
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
ISRNMechanical Engineering 15
with increasing numbers of diffuser vanes and diffuser returnvanes The brake horsepower hardly varies at all regardlessof the number of diffuser vanes and diffuser return vanesFurthermore higher wall roughness heights of the impellerand diffuser negatively affect the head brake horsepowerand efficiency In all the numerical curves obtained for thehead brake horsepower and efficiency follow the trend of theexperimental results
Nomenclature
119861 Sourceterm (Nmminus3)119862 Torque (Nm)119892 Acceleration of gravity (m sminus2)119867 Head (m)119875 Power (W)119901 Pressure (Nmminus2)119901119896 Turbulence production due to viscous andbuoyancy forces
119876 Volume flow rate (m3 sminus1)119903 Radial coordinate (m)119881 Velocity (m sminus1)119906 Flow velocity in 119909 direction (m sminus1)V Flow velocity in 119910 direction (m sminus1)119908 Flow velocity in 119911 direction (m sminus1)119909 119909-coordinate (m)119910 119910-coordinate (m)119911 119911-coordinate (m)
Greek Symbols
Δ Difference120576 Turbulence dissipation (m2 sminus3)120578 Efficiency119896 Turbulence kinetic energy (kgmminus2 sminus2)120588 Fluid density (kgmminus3)120583 Dynamic viscosity (Pa s)120583eff Effective viscosity (Pa s)120583119905 Turbulence viscosity (Pa s)
120596 Angular velocity (rad sminus1)
Subscripts
1 Inlet2 Outletℎ Hydraulic119894 Inlet119898 Mechanical119900 Outlet119904 Shaft119905 TotalV Volumetricvel Velocity
Acknowledgments
The authors are grateful to the Foundation of Universityof Quebec in Abitibi-Temiscamingue (FUQAT) and thecompany Technosub Inc
References
[1] W Peng Fundamentals of Turbomachinery John Wiley andSons Hoboken NJ USA 2008
[2] K W Cheah T S Lee S H Winoto and Z M ZhaoldquoNumerical flow simulation in a centrifugal pump at designand off-design conditionsrdquo International Journal of RotatingMachinery vol 2007 Article ID 83641 8 pages 2007
[3] A Ozturk K Aydin B Sahin and A Pinarbasi ldquoEffect ofimpeller-diffuser radial gap ratio in a centrifugal pumprdquo Journalof Scientific and Industrial Research vol 68 no 3 pp 203ndash2132009
[4] W G Li ldquoInfluence of the number of impeller blades on theperformance of centrifugal oil pumpsrdquo World Pumps no 427pp 32ndash35 2002
[5] H Liu Y Wang S Yuan M Tan and K Wang ldquoEffects ofblade number on characteristics of centrifugal pumpsrdquo ChineseJournal of Mechanical Engineering vol 23 no 6 pp 742ndash7472010
[6] J Gonzalez J Fernandez E Blanco and C Santolaria ldquoNumer-ical simulation of the dynamic effects due to impeller-voluteinteraction in a centrifugal pumprdquo Journal of Fluids Engineeringvol 124 no 2 pp 348ndash355 2002
[7] M Asuaje F Bakir S Kouidri F Kenyery and R ReyldquoNumerical modelization of the flow in centrifugal pumpvolute influence in velocity and pressure fieldsrdquo InternationalJournal of Rotating Machinery vol 2005 no 3 pp 244ndash2552005
[8] K A Kaupert and T Staubli ldquoThe unsteady pressure field in ahigh specific speed centrifugal pump impellermdashPart I influenceof the voluterdquo Journal of Fluids Engineering vol 121 no 3 pp621ndash626 1999
[9] S Huang M F Islam and P Liu ldquoNumerical simulation of3D turbulent flow through an entire stage in a multistagecentrifugal pumprdquo International Journal of Computational FluidDynamics vol 20 no 5 pp 309ndash314 2006
[10] M Miyano T Kanemoto D Kawashima A Wada T Haraand K Sakoda ldquoReturn vane installed in multistage centrifugalpumprdquo International Journal of Fluid Machinery and Systemsvol 1 no 1 pp 57ndash63 2008
[11] D Kawashima T Kanemoto K Sakoda A Wada and T HaraldquoMatching diffuser vanewith return vane installed inmultistagecentrifugal pumprdquo International Journal of FluidMachinery andSystems vol 1 no 1 2008
[12] M Gantar D Florjancic and B Sirok ldquoHydraulic axial thrustin multistage pumpsmdashorigins and solutionsrdquo Journal of FluidsEngineering vol 124 no 2 pp 336ndash341 2002
[13] Technosub Inc httpwwwtechnosubnet[14] Ansys inc 2011 ANSYS-CFX (CFX Introduction CFX Refer-
ence Guide CFX Tutorials CFX-Pre Userrsquos Guide CFX-SolverManager Userrsquos Guide CFX-Solver Modeling Guide CFX-Solver Theory Guide) release 14 0 USA
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
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