Computers & Fluids 60 (2012) 61–70

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Computers & Fluids

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Numerical study of the effects of some geometric characteristicsof a centrifugal pump impeller that pumps a viscous fluid

M.H. Shojaeefard a, M. Tahani a,⇑, M.B. Ehghaghi b, M.A. Fallahian a, M. Beglari a

a School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iranb Department of Mechanical Engineering, Tabriz University, Tabriz, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 17 July 2011Received in revised form 30 November 2011Accepted 27 February 2012Available online 7 March 2012

Keywords:CFDTurbulence modelingHydraulic oilCentrifugal pumpGeometry

0045-7930/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.compfluid.2012.02.028

⇑ Corresponding author. Tel.: +98 2177240360.E-mail address: Tahani@iust.ac.ir (M. Tahani).

The performance of centrifugal pumps drops sharply during the pumping of viscous fluids. Changingsome geometric characteristics of the impeller in these types of pumps improve their performance. In thisinvestigation, the 3-D flow in centrifugal pump along with the volute has been numerically simulated.This numerical solution has been carried out for different cases of primary geometry, and for the changesmade to the outlet angle and passage width of the impeller, and also for simultaneous modifications ofthese parameters. The finite volume method has been used for the discretization of the governing equa-tions, and the High Resolution algorithm has been employed to solve the equations. Also, the ‘‘k �x SST’’has been adopted as the turbulence model in the simulation. In the steady state, this simulation is definedby means of the multi-reference frame technique, in which the impeller is situated in the rotating refer-ence frame, and the volute is in the fixed reference frame, and they are related to each other through the‘‘Frozen Rotor’’. The obtained numerical results are compared with the experimental ones, and the out-come shows acceptable agreement between the two. The flow analysis indicates that with the modifica-tion of the original geometry of the pump, at the 30� outlet angle and the passage width of 21 mm, thepump head and efficiency increases compared to the other cases; this improvement is due the reductionof losses arising from the generation of eddies in the passage and outlet of the impeller.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the large complexity of flow and geometry in the radialflow pumps, there are still many unknown issues associated withthe complete flow pattern in these pumps, which need to beinvestigated. Moreover, the conduction of experimental studieson samples with different volute and impeller geometries istime-consuming and costly, and because of the complicated geom-etry, it is not possible to carry out a thorough investigation of theflow field for a vast number of operating conditions. Therefore,the numerical flow analysis has recently become an appropriatemethod of investigation of the flow patterns and losses.

Based on the main pioneering researches on the centrifugalpump handling viscous fluid (since 1926), the performance as afunction of oil viscosity was investigated, and the obtained resultswere used for the design and selection of these pumps [1–4]. To-day, because of drastic changes in the design and structure of new-er models of hydraulic pumps, the previously obtained results onolder models cannot be used with high confidence.

Li [5–10] investigated the effects of fluids viscosity on theperformance of centrifugal oil pumps experimentally and

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numerically; he presented the flow pattern inside the impeller.According to these researches, the high viscosity results in rapid in-creases in the disc friction losses over outside of the impellershroud and hub as well as the hydraulic losses in flow channelsof the pump. The viscosity of fluid not only affects the slip coeffi-cient, but also causes the reduction of flow in the impeller and vo-lute. Furthermore, he presented that there is a wide wake near theblade suction side of the centrifugal pump impeller. Also, there isnot a jet near the blade pressure side, and the flow pattern is essen-tially different from the well-known jet/wake model. He obtainedthe optimum number of blades for the impeller when fluids withdifferent viscosities are pumped.

In the year 2004 Asuaje et al. [11] conducted 3D flow solutionby CFD tools. In this research, a design procedure was established.This method was based on the geometrical design and the perfor-mance analysis. Their design tool took into account models andcorrelations resulting from experimental data dealing with manyranges of industrial centrifugal pumps which constitute a signifi-cant database.

In 2007, Kergourlay et al. [12] investigated the effects of sepa-rated blades on the flow field of water in centrifugal pumps.According to this research, adding the splitters has negative andpositive effects on the pump behavior. It increases the head risecompared to the original impeller that is mainly due to the

Nomenclature

b2 passage width of Impeller (mm)BEP best efficiency pointCFD computational fluid dynamicsDH hydraulic diameter (m)g gravity accelerationH head (m)k turbulent kinetic energy (m2/s2)MRF multiple reference framesOL over load performanceP pressure (Pa)Pd discharge pressure (Pa)Ps suction pressure (Pa)PL part load performanceQ flow rate (m3/h)r position vector (m)RNG re-normalization groupS source termSDUSs Skew Upwind Differencing SchemesSST shear stress transport modelt time (s)u relative velocity of fluid (m/s)V capacity (l)

Z altitude (m)

Greek symbolsb2 outlet angle of blade(degree)q density of the fluid (kg/m3)l viscosity (Pa s)lt eddy viscosity (Pa s)t kinematic viscosity (mm2/s)X rotational speed (rpm)s stress tensorg efficiency (%)

Subscripts and superscriptsAvg averaged dischargeelect electricali, j componentsin inletout outlets suctiont total— time-averaged value

62 M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70

increase of the impeller slip factor which helps conduction of theflow.

Shojaeefard et al. [13,14] performed experimental and numeri-cal investigations to obtain the effect of the impeller’s outlet angleduring the pumping of oil. As a result of these researches, when theblade outlet angle increases, the width of wake at the outlet ofimpeller decreases, this phenomenon causes the improvement ofcentrifugal pump performance when handling viscous fluids.

In 2008, Grepsas et al. [15] conducted the numerical study andoptimized design of blades in centrifugal pumps by means of theevolutionary strategy (dynamic algorithm). In this research, com-mercial software for the analysis of flow was used to conduct para-metric studies of the effect of some geometric parameters of acentrifugal pump impeller, and the results revealed that their mod-ifications could have a significant impact on its performance.

In 2009, Anagnostopoulos [16] presented a quick numerical ap-proach for the analysis of flow and the design of impeller blades. Inthis research, a numerical method for the two-dimensional andturbulent flows in the impeller of centrifugal pumps was devel-oped. Spence and Amaral-Teixeira [17] studied the geometricalvariations on the pressure pulsations and performance characteris-tics of a centrifugal pump by CFD method. The results of this paperpresented by concentrating on the selected locations around thepump and provided the detailed information regarding the pres-sure pulsation close to the impeller outlet, in the volute and inthe leakage flow region. There are many other valuable referencescovering the ongoing research and review of the computationalfluid dynamics to study the flow in the impeller of a centrifugalpump [18–21].

In this article, the procedure of 3-D investigation of flow in cen-trifugal pumps includes the sections of geometry definition, meshgeneration, analysis of equations, and processing of results. The fi-nite volume method is used for the discretization of the governingequations of flow. The turbulence model used in the simulation isthe ‘‘ k �x SST’’ model. At the steady state case, this simulationhas been analyzed by using the multi-reference frame technique,in which the impeller is situated in the rotating reference frameand the volute is in the fixed reference frame. The obtained numer-

ical results are compared with the experimental ones, and accept-able correlation is found between the two sets of results.

Numerically solving the complete 3-D geometry of the centrif-ugal pump, offering an impeller for improving the efficiency, sim-ulating and comparing various possible geometries, and plotting ofStatic pressure contours and velocity vectors inside the pump aresome of the significant features of this article.

2. Geometry of the centrifugal pump and the generation ofmesh

In this report, for the numerical investigation of the flow field ofcentrifugal pump, the geometry of the pump model: 65–200 (madeby the Pump Iran Co.) is used. This centrifugal pump has single ax-ial suction and vane less volute casing; equipped with an impellerof 209 mm in outside diameter and six backwards curved blades.The blade outlet and wrapping angles of the impeller are 27.5�and 140� respectively. The shroud of the impeller made of metalis machined. The roughness of the impeller and volute is 100 lm.The pump tested is driven by a three-phase AC electric motor,whose rated power is 5.5 kW and speed is 1450 rpm. First, the ini-tial geometry of this centrifugal pump (which has been designedfor the pumping of water) is simulated by using the available tech-nical specifications. In the next steps, in order to analyze the effectof changing the fluid viscosity, the outlet angle and the flow pas-sage width are modified. In this analysis, the definition of geometrycovers the three pump sections of volute, impeller, and outlet pipe,which are connected together for the analysis of the whole pump(Fig. 1).

Then, in the mesh generation part of this code, mesh configura-tion is produced based on the type of physics that is considered forthe problem. For better conformity of the geometry with the com-putational domain, at the near-wall regions, the structured mesh isused for the boundary layer, and at regions away from the wall, theunstructured mesh configuration is employed to correctly coverthe complex geometry. For producing the unstructured mesh con-figuration, six-sided, pyramid, and wedge-shaped elements areused in appropriate situations, which are shown in Fig. 1.

Fig. 1. General view of the centrifugal pump model and the mesh configuration used for flow analysis.

Fig. 2. A view of the modeled impeller.

M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70 63

2.1. Change of geometry of the initial pump

In Figs. 2 and 3, the geometry of the impeller and the outlet an-gle of blades have been shown, respectively. It can be observed thatthe changes made to the blade are applied on the outlet angle b2.As is clear from these figures, the passage width of the impellercan be modified on the meridian plane; and the changes appliedto the original geometry with the outlet angle of 27.5� and passagewidth of 17 mm are outlined in Table 1. To increase the passagewidth, the distance between the front and back plates in themeridian plane are increased. It should be mentioned that the ap-plied change in the outlet angle of the blade is not accompanied byany change in its inlet angle.

2.2. Governing equations and the selection of a turbulence model

In the averaging of steady-state incompressible flows, the con-servation equations can be solved based on the average Reynolds

values or the time-averaging approach; however, the most com-mon method of modeling turbulent flows is the time-averagingmethod. Using this approach for the case of incompressible flows,the general forms of the governing equations could be expressed asrelations (1)–(4). In these equations, the effect of terms resultingfrom flow rotation, including the Coriolis and centrifugal forcescan be modeled by adding the source term to the equations ofmomentum.

Since the pumped fluid is incompressible and the flow is in asteady state, the continuity equation has the following form:

@ui

@xj¼ 0 ð1Þ

Also, the equation of conservation of momentum together withthe definition of the source term, and the shear stress is expressedas relation (2):

@

@xjðquiujÞ ¼

�@P@xiþ @

@xjðsij � qu0iu

0jÞ þ Sui

ð2Þ

where the source term (including the centrifugal and Coriolis forceterms) is written as Eq. (3) and the average shear stress is obtainedfrom relation (4):

Sui¼ �q½2X

!� u!þ X!� ðX!� r!Þ� ð3Þ

sij ¼ �l @ui

@xjþ @uj

@xi

� �ð4Þ

In order to take advantage of mesh compaction near the rigidwalls, the wall rule function is applied to the turbulence modelequations. This function is selected in such a way that all the meshpoints fall outside the viscous sub-layer.

2.3. Flow in the rotating reference frame

The analysis of flow in centrifugal pumps (because of the flow’srotational motion) leads to the examination of two types flows:

Fig. 3. Meridian plane with two passage widths of 17 and 21 mm.

Table 1Specifications of the modified geometry.

Passage widthof Impeller(b2) (mm)

Outlet angle of blade (b2) (�)

17 27.5 30 32.521 27.5 30 32.5

64 M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70

steady, and unsteady. If the volute has fixed blades (diffuser), be-cause of the alternating motion of blades and the confrontation be-tween the impeller and diffuser blades, the flow is of the unsteadytype, relative to the fixed external reference frame. However, whenthe diffuser doesn’t have fixed blades, the flow can be studied in asteady state by defining a rotating reference frame.

This simulation is defined by means of the multi-referenceframe technique, in which the impeller is situated in the rotatingreference frame, and the volute is in the fixed reference frame,and they are related to each other through the ‘‘Frozen Rotor’’.The frozen rotor method employs a quasi-steady algorithm, wherethe rotor and stator are modeled at a fixed (frozen) position rela-tive to each other. Rotational terms are included in the movingframes, but transient effects are neglected. This provides an effi-cient method for the calculation of interactions between impellersand casings (volutes), and is also a viable option for compact ma-chines with small distances between rotor and stator. In this waythe solution provides a snapshot of the flow regime [22].

When the Navier–Stokes equations of motion are solved in arotating reference frame, the fluid acceleration appears as an addi-tional term in the momentum equations, which was shown in rela-tion (3).

2.4. Turbulence model

With the help of the mixing function value, the SST model auto-matically uses the k �x model in the near-wall regions and thek � e model in the regions away from the wall. This model firstmodifies the energy production term in the kinetic energy transferequation [23,24].

Considering the studies conducted on the two models of k � eand RNG k � e, it is concluded that the near-wall flow can be eval-

uated with high precision using the k �x model and the SST func-tion, and the obtained results enjoy better accuracy than those ofthe k � e model; therefore, the SST turbulence model is used forthe numerical investigation of flow inside the centrifugal pump.

2.5. Discretization of equations and the solution method

In the developed computer code, the finite volume method hasbeen used for the discretization of equations, but the analysis ofthe geometry has been based on the finite element approach. So,the geometrical flexibility of the finite element method can beused; however, the equations are dealt with in the form of finitevolume [22]. As is presented in the following equations, the finitevolume method is implemented by integrating the equations overa selected control volume, with the help of the Gaussian theory. Inthis approach, the computational space is divided into small ele-ments and the surfaces of the control volume are defined on themid plane of each of those elements. The numerical scheme em-ployed in this case, involves generating finite control volumes fromthe mesh, which is shown in Fig. 4.

In this figure, each node is surrounded by a set of surfaces whichcomprise the control volume. The control volume is constructedaround each mesh node using the median-dual discretizationscheme. The boundary of the control volume is defined by linesjoining the centers of the element edges with the element cen-troids surrounding the node, as shown in right hand side of thisfigure.

The governing equations in integral form are applied to each fi-nite control volume such that the relevant quantity (mass ormomentum) is conserved in a discrete sense for each. Consideringan isolated mesh element for simplicity, such as the one shown inleft hand side of this figure, the surface fluxes of the continuousequations must be discretely represented at the three integrationpoints to complete the conversion of the continuous equations intotheir discrete forms. The integration points (ipn) are located at thecenter of each boundary segment surrounding the control volumeas shown in Fig. 4. The surface flow rates are presented separatelyat the integration points, and finally, the discredited forms of theequations are obtained as follows:

@

@t

Zvqdv þ

Zsqui dnj ¼ 0 ð5Þ

Fig. 4. Typical mesh element with nodes (n1, n2 and n3) and integration points (ip1, ip2 and ip3).

M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70 65

@

@t

Zvqui dv þ

Zsqujui dnj

¼ �Z

sP dni þ

Zsl @ui

@xjþ @uj

@xi

� �dnj þ

Zv

Suidv ð6Þ

@

@t

Zvqudv þ

Zsqujudnj

¼ �Z

sC

@u@xj

� �dnj þ

Zsl @ui

@xjþ @uj

@xi

� �dnj þ

Zv

Su dv ð7Þ

In this computer code, all the velocity vector components forsurfaces are determined in the Cartesian coordinates, and all theflow rates are obtained at the integration points. The integrationpoints for each volume are shared by the adjacent volumes, andthe output flow rate of each control volume is equal to the inputflow rate of the adjacent volume. One of the strong points of thisnumerical method is that in this way, the conservation laws arecompletely satisfied for the equations, as follows:

qVq� q�

Dt

� �þX

ip

ðqujDnjÞip ¼ 0 ð8Þ

qVui � u�i

Dt

� �þX

ip

_mipðujÞip

¼X

ip

ðPDniÞip þX

ip

l @ui

@xjþ @uj

@xi

� �Dnj

� �ip

þ SuiV ð9Þ

qVu�u�

Dt

� �þX

ip

_mipuip ¼X

ip

C@u@xj

Dnj

� �ip

þ SuV ð10Þ

The mass flow rate is obtained from the following equation:

_mip ¼ ðqujDnjÞ�ip ð11Þ

The diffusion terms are estimated with the help of the weightfunctions of the finite element method, and in the momentumequations, the surface integral of the pressure gradient terms isdetermined at the integration points. The advection terms are ana-lyzed by the Skew Upwind Differencing Schemes (SUDSs) method,which in this approach, the advection terms are in the streamwisedirection.

In the segregated solution strategy, the momentum equation issolved by using an initial solution for pressure, and then a relationis obtained for pressure modification. Because the ‘‘guess correct’’scheme is a linear system, a large number of iterations togetherwith relaxation coefficients are needed for the variables.

In this computer program, the ‘‘coupled solver’’ has been used,so that the hydrodynamic equations (u, v, w, and p) are solved ina system. This type of solution is used in the totally implicit dis-cretization of equations in the given time step. In solving the stableproblems, the time step acts like an ‘‘accelerator parameter’’, anddirects the approximate solution on the basis of the stable solution,which, for the reduction of the number of required iterations forthe convergence of the stable problem or the reduction of the vol-ume of computations for each time step in the analysis, is indepen-dent of time.

2.6. Boundary conditions and physical properties of working fluids

The static pressure of the reservoir is determined at the en-trance boundary of the pump (entrance to the impeller). Sincethe inflow to the pump from the suction reservoir occurs at a highvolume, and this flow has already been smoothed by baffle plates,the average turbulence intensity is considered as 5%, which, in lightof the existing system and the flow at the entrance to the pump, isa totally empirical value. The mass flow rate or the exit velocity isdefined at the exit plane of the pipe attached to the volute. In addi-tion, the impeller and the rotating section are modeled in the rotat-ing frame, and the volute and the pipe attached to it are modeled inthe fixed reference frame. Since the whole pump is modeled in thisanalysis, at the solid boundaries (including the pump casing,impeller, and the volute), the no-slip condition with relative rough-ness of 100 lm is applied. This roughness value is obtainedthrough the Reynolds stresses and the shear stress terms in theequations. The average tangential velocity between the fixed androtating sections is determined by simultaneously solving thesetwo regions.

The fluids used in the numerical simulation and experimentalinvestigation, are water and oil with the density of 998 and875 kg/m3 and kinematic viscosity of 1 and 43 mm2/s respectivelyat 25 �C.

2.7. Evaluation of the dependency of results from mesh configuration

For the reduction of computation time and the improvement ofaccuracy, the optimum number of mesh elements in the simulationhas been investigated. Also, the total pressure rise inside the pumpand mean differences of circumferential velocities values for thebest efficiency point performance (BEP, with maximum efficiency)has been used as the evaluation parameter for the effect of meshsize on the solution. Finally, the least number of dependentmesh elements for which the output pressure is obtained with neg-ligible change, has been calculated. Table 2 shows the study of the

Table 2Evaluation of the dependency of mesh and summary of CPU time for original impeller.

Elementnumber

Total pressure riseinside the pump atBEP (kPa)

Mean differences ofcircumferentialvelocities values (m/s)

CPU time (forCore2Due CPU of2.5 GHz) (h)

628146 197.983 0.226 14.81045668 186.274 0.304 25.11842482 180.169 0.371 47.42173604 178.888 0.398 58.33277226 178.261 0.402 90.4

66 M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70

dependency of results from mesh configuration and summary ofCPU time for the centrifugal pump for pumping viscous fluids atthe blade outlet angle (b2) of 27.5� and passage width (b2) of17 mm.

Fig. 5. Centrifugal p

Fig. 6. Centrifugal pump performance diagrams at differen

As the numbers in the above table demonstrate, at 3277226 ele-ments, the output pressure does not change much. The number ofmesh elements includes the sum of elements in the impeller, vo-lute, and the outlet pipe.

2.8. Summary of experimental setup

A centrifugal pump test setup, shown in Fig. 5, was used to com-pare the impeller geometries effects on the performance of centrif-ugal pump.

The pipe of the rig was made of stainless steel with inner diam-eter of 80 mm. The tank net volume was 2400 l. The operation con-dition was controlled by a gate valve on the discharge pipe. A digitalpressure transmitter gage was used at the pump inlet and outletpipes to measure the inlet and outlet pressures accurately. Baffleplates were used for damping the disturbance of discharged fluid.

ump test setup.

t working conditions for original Impeller geometry.

Fig. 7. H–Q curve of the centrifugal pump at different geometries.

Fig. 8. Comparison of the numerical and experimental results.

M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70 67

The following parameters were measured under steady condi-tions to draw the main performance diagrams.

The pump head at all stages was computed using Bernoulliequation:

Ps

cþ V2

1

2gþ Z1 þ H ¼ Pd

cþ V2

2

2gþ Z2 þ Hl ð12Þ

For the same inlet and outlet pipe diameter and velocity(V1 = V2):

H ¼ Pd � Ps

c

� �þ Z2 � Z1 þ Hl ð13Þ

where Hl was the head of losses in the outlet pipe.

The centrifugal pump efficiency at all stages was defined as theratio between the pump output power and the input electricalpower consumption.

g ¼ Pout;pump

Pin;pump¼ cQH

Pin;pump; Pin;pump ¼ Pout;elect ¼ gelect � Pin;elct ð14Þ

The efficiency of this electromotor was almost constant (83%).Input electrical power was measured using a three-phasewattmeter.

3. Results and discussions

3.1. Effects of viscosity on performance

The mentioned parameters were measured under steady condi-tions to draw the main performance diagrams (P–Q, g–Q and H–Q),

Fig. 9. Variations of efficiency vs. flow rate for different fluids and impeller geometries.

Fig. 10. Static pressure contours for impellers at BEP at 50% span.

68 M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70

at different working conditions, i.e. part load (PL), best efficiencypoint (BEP), and overload (OL). These diagrams are shown inFig. 6 for different fluids with original impeller without improving

in geometry. This figure shown that, Frictional losses reduce thepressure inside the impeller, diffuser, and volute resulting inreduction of the head and efficiency. On the other hand, the friction

M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70 69

on the discs including the wheel in the case of oil increases theabsorption power compared with the case of water.

Based on these results, at the best efficiency points (that locatedat QBEP(water) = 47.3 and QBEP(oil) = 48.2 m3/h) the efficiency andhead values decrease about 20.5% and 1.4 m respectively, and thepower consumption increases about 1.03 kW during the pumpingof oil. The mentioned factors result in a remarkable reduction inthe performance.

3.2. The numerical head-flow rate (H–Q) curve

For obtaining the H–Q curves of centrifugal pumps in the casesof steady state, turbulent flows and incompressible fluids, theamounts of total pressure at the entrance and exit of the simulatedgeometry (such as experimental test points) are determined, andby using relation (15), the pump head is calculated:

H ¼ Pt2 � Pt1

qgð15Þ

The head-flow rate (H–Q) curve resulting from the numericalsolution for the pumping of viscous fluids has been illustrated inFig. 7.

The numerical results indicate that the centrifugal pump withb2 = 30� and b2 = 21 mm has the highest pressure head in oil pump-ing; therefore, the noted pump has been built, and its results havebeen compared with those of the simulation.

Because of laboratory limitations, the experimental results havebeen exclusively obtained for three different kinds of impellerswith: b2 = 27.5� and b2 = 17 mm; b2 = 32.5� and b2 = 17 mm; and

Fig. 11. Velocity vectors for im

b2 = 30� and b2 = 21 mm. Even with this few numbers of experi-ments, the numerical simulation can be verified for other impellerblade angles and fluid types, and the obtained results can be ac-cepted without further experimentation.

Fig. 8 shows the comparison between the numerical and exper-imental H–Q results during the pumping of water and oil by thecentrifugal pump. Comparing the experimental and numericalvalues of head show that the average difference percentage inthe different cases (27.5�–17 mm-water), (30.0�–21 mm-oil),(32.5�–17 mm-oil) and (27.5�–17 mm-oil) was 4.06%, 3.35%,4.08% and 4% respectively. According to this figure, the numericaland experimental results show satisfactory correlation.

3.3. The efficiency-flow rate (g–Q) curve

Fig. 9 shows the variations of efficiency with the flow rate forwater and oil. It was depicted that increasing the outlet angle inPL performance condition increases the efficiency more thanincreasing the passage width. The Results shown in this figure re-veal that by improving the impeller geometry (outlet blade angleof 30� and impeller passage width of 21 mm), the incrementmagnitude of efficiency around the BEP and OL operating condi-tions was 7.93% for mentioned viscous fluid.

3.4. Static pressure contours and velocity vectors on the blade-to-bladeplane

When the centrifugal pump is pumping a highly viscous fluid,due to the increase of hydraulic losses and skin friction, the pump

pellers at BEP at 50% span.

70 M.H. Shojaeefard et al. / Computers & Fluids 60 (2012) 61–70

head diminishes, compared to the case in which water is pumped;and this fact should also be demonstrated by the static pressurecontours.

The static pressure distribution over the suction and pressureside on the middle-span plane of the impellers for the best effi-ciency point condition for the viscous fluid flow are illustrated inFig. 10. As this figure the pressure increases gradually alongstreamwise direction within impeller blade-to-blade passage andhas higher pressure on pressure side than suction side for eachimpeller. It is demonstrated that the average of pressure in the out-let area of impeller (b2 = 30� and b2 = 21 mm) is higher than otherimpellers. This results cause to increasing the head as well asshown in Fig. 7.

Fig. 11 illustrates the velocity vectors on the middle-span planeof the impellers for the viscous fluid flow in the numerical simula-tions performed at the best efficiency point condition. It is noticedthat a big zone with low velocity exists there in the original impel-ler. The center region of the blade-to-blade passage near the suc-tion side has a low velocity region and is considered as stall flow.This phenomenon could be considered as ‘‘jet-wake’’ structuredevelopment phase. The improvement of performance can be seenin the flow separation in the passage of the impeller. As can beseen, at the impeller blade outlet angle of 30� and passage widthof 21 mm, there is uniform flow with less number of vortices.

4. Conclusion

In this study, the effects of blade outlet angle and passage widthon the performance of a centrifugal pump have been investigatednumerically and experimentally. Considering the comparison be-tween the performances of centrifugal pumps with differentimpellers, during the pumping of water and oil, the following con-clusions can be made:

� The friction on the discs including the wheel in the case of oildecreases the head and efficiency and increases the power con-sumption compared with the case of water. On the other hand,the performance of centrifugal pumps drops sharply during thepumping of viscous fluids (Fig. 6). Changing the original geom-etry of the impeller improves the centrifugal pumpperformance.� Numerical results show that the impeller blade with the angle

of 30� and passage width of 21 mm produces a higher head rel-ative to the other five blade settings (Fig. 7).� The results obtained from the numerical and experimental

investigations on a 65–200 centrifugal pump performance havesatisfactory agreement, and demonstrate that increasing theimpeller passage width from 17 to 21 mm increases the headand hydraulic efficiency due to reduction of the friction losses.Also, the centrifugal pump performance with the impeller pas-sage width equal to 21 mm, at outlet blade angle of 30�improves in comparison with 27.5� and 32.5�. This is due toreduction of the dissipation arising by vortex formation inimpeller passage when the pump handles viscose liquid (Figs.8 and 9).� However, by increasing the blade outlet angle to 30� and the

passage width to 21 mm, the pump efficiency decreases at partload (in comparison with b2 = 32.5� and b2 = 17 mm), butincreases to the highest level at the best efficiency point andthe overload performances, compared with other bladeconfigurations.

� The static pressure contours for impellers at BEP show that thepressure increases gradually along streamwise direction withinimpeller blade-to-blade passage and has higher pressure onpressure surface than suction surface for each configuration. Itis demonstrated that the average of pressure in the outlet areaof impeller (b2 = 30� and b2 = 21 mm) is higher than the others.� Velocity vectors for impellers at BEP show that in the improved

impeller, the width of wake at the outlet of impeller and thehydraulic losses decrease, these phenomena cause the improve-ment of centrifugal pump performance when handling viscousfluids.

References

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