JSIR 72(6) 373-378

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373CHAKRABORTY et al : PERFORMANCE PREDICTION OF CENTRIFUGAL PUMPSJournal of Scientific & Industrial ResearchVol. 72, June 2013, pp. 373-378

*Author for correspondenceE-mail: [email protected]

Performance prediction of Centrifugal Pumps with variations of blade number

Sujoy Chakraborty1, Kishan Choudhuri2, Prasenjit Dutta3, Bishop Debbarma4

1,2,3,4 Department of Production Engineering N.I.T Agartala, Tripura, India

Received 25 July 2012; revised 07 December 2012; accepted 28 March 2013

Centrifugal pumps are used extensively for hydraulic transportation of liquids over short to medium distance through pipelines where the requirements of head and discharge are moderate. At present, the influence of blade number on inner flow fieldand the characteristics of centrifugal pump have not been understood completely. The use of numerical analysis tools allow us toobtain data in inaccessible positions for the experimentations. In this paper, a two dimensional numerical study of steady, static pressure distribution and incompressible flow characteristics inside the passage with different numbers of blades of centrifugal

pump impeller has been carried out. The investigation focuses mainly on the efficiency of the pump. Centrifugal pumps withimpeller blades 5, 6 and 7 have been modeled and its efficiency at 3000 rpm is evaluated by FLUENT 6.3 software. The numericalanalysis displays that with the increase of blade number, the head and static pressure of the model increases, but the efficiency of centrifugal pump varies with number of blades and shows maximum for 7 number of blade.

Keywords: Centrifugal pump, Blade number, CFD, Numerical analysis, Performance prediction.

Introduction

From such literature, it was found that most previousresearch, especially research based on numericalapproaches, had focused on the design or near-designstate of pumps. Few efforts were made to study the off-design performance of pumps. Centrifugal pumps are

widely used in many applications, so the pump systemmay be required to operate over a wide flow range insome special applications. Thus, knowledge about off-design pump performance is a necessity. On the other hand, it was found that few researchers had comparedflow and pressure fields among different types of pumps.Therefore, there is still a lot of work to be done in thesefields. A centrifugal pump delivers useful energy to thefluid on pump age largely through velocity changes thatoccur as this fluid flows through the impeller and theassociated fixed passage ways of the pump. It is

converting of mechanical energy to hydraulic energy of the handling fluid to get it to a required place or height bythe centrifugal force of the impeller blade. The input power of centrifugal pump is the mechanical energy andsuch as electrical motor of the drive shaft driven by the prime mover or small engine. The output energy is

hydraulic energy of the fluid being raised or carried. In acentrifugal pump, the liquid is forced by atmospheric or other pressure into a set of rotating vanes. A centrifugal pump consists of a set of rotation vanes enclosed withina housing or casing that is used to impart energy to afluid through centrifugal force 1.

Computational Fluid Dynamics (CFD) is the analysisof systems involving fluid flow, heat transfer andassociated phenomena such as chemical reactions bymeans of computer-based simulation. The heat and masstransfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, in thenatural environment, and in living organisms play a vitalrole in a great variety of practical situations. Nearly allmethods of power production involve fluid flow and heattransfer as essential processes. The same processesgovern the heating and air conditioning of buildings. Major

segments of the chemical and metallurgical industriesuse components such as furnaces, heat exchangers,condensers, and reactors, where thermo-fluid processesare at work. Aircraft and rockets owe their functioningto fluid flow, heat transfer, and chemical reaction. CFDconstitute a new third approach in the philosophical studyand development of the whole discipline of fluidmechanics. In the seventeenth century, the foundationsof experimental fluid dynamics were laid in France and

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J SCI IND RES VOL 72 JUNE 2013374

England. The eighteenth and nineteenth centuries sawthe gradual development of theoretical fluid dynamics,again primarily in Europe. As a result, throughout mostof the twentieth century the study and practice of fluiddynamics involved the use of pure theory on the onehand and pure experiment on the other hand. However

the advantage of high speed digital computers combinedwith the development of accurate numerical algorithmsfor solving physical problems on these computers asrevolutionized the way we study practical fluid dynamicstoday. It has introduced a fundamentally important newthird approach in fluid dynamics i.e. the approach of computational fluid dynamics.

CFD analysis is very useful for predicting pump performance at various mass-flow rates. For designers, prediction of operating characteristics curve is mostimportant. All theoretical methods for prediction of

efficiency merely give a value; but one is unable todetermine the root cause for the poor performance. Dueto the development of CFD code, one can get theefficiency value as well as observe actual. The predictionof behavior in a given physical situation consists of thevalues of the relevant variables governing the processesof interest. Let us consider a particular example. In acombustion chamber of a certain description, a complete prediction should give us the values of velocity, pressure,temperature, concentrations of the relevant cherI1icalspecies, etc., throughout the domain of interest; it should

also provide the shear stresses, heat fluxes, and massflow rates at the confining walls of the combustionchamber. The prediction should state how any of thesequantities would change in response to proposed changesin geometry, flow rates, fluid properties, etc.Computational Fluid Dynamics is now an establishedindustrial design tool, helping to reduce design time scalesand improve processes throughout the engineering world.CFD provides a cost-effective and accurate alternativeto scale model testing with variations on the simulation being performed quickly offering obvious advantages.The CFD occupies today a very significant place in thedisciplines of fluid mechanics and turbo machinery dueto the great progress in the development of numericalmethods and computing power. However, the initially useof CFD tools to design a new machine represents a nonrealistic procedure (Ar none, 1999) 2. The design of anew machine (or upgrading an existing machine) wouldrequire a great investment of time without guarantee of success. Along with the introduction of CFD tools, its

incorporation of computer aided design (CAD) codeshas speeded up the design process because of a faster geometry and grid generation (Asuaje, 2002)3. Nevertheless, the problem always reduces down to theselection of reasonable values for a number of geometric parameters. At this point, the “know-how,” skills andtalent of the designer remain the principal ingredientsfor designing and optimizing a machine. This studyassesses a two-dimensional numerical analysis of steady,static pressure distribution and incompressible flowcharacteristics inside the passage between 5, 6 and 7number of blades of centrifugal pump impeller at 3000 rpm.

Methodology

CFD code of commercial software Fluent 6.3 is usedto simulate the inner flow field under steady condition.The standard k-e turbulence model and SIMPLEC

algorithm applied to solve the RANS equations. Thestandard k-e model is a semi-empirical model based onmodel transport equations for the turbulence kinetic (k)and its dissipation rate (e). The model transport equationfor k is derived from the exact equation, while the modeltransport equation for e is obtained using physicalreasoning and bears little resemblance to itsmathematically exact counterpart. In the derivation of the k-e model, it is assumed that the flow is fully turbulent,and the effects of molecular viscosity are negligible. Thesimulation is steady and moving reference frame is

applied to take into account the impeller-volute interactiondue to convergence precision of residuals 10-5. For modeling of centrifugal pumps with impeller blade from5 to 7, GAMBIT, a preprocessor of CFD code of commercial software Fluent 6.3 has been used.

Mathematical Formulation

Mathematical model can be defined as thecombination of dependent and independent variables andrelative parameters in the form of a set of differentialequations which defines and governs the physical

phenomenon. In the following subsections differentialform of the governing equation are provided accordingto the computational model and their correspondingapproximation and idealizations.

Governing Equations

The steady, conservative form of Navier-Stokesequations in two dimensional form for the incompressibleflow of a constant viscosity fluid are as follows:

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375CHAKRABORTY et al : PERFORMANCE PREDICTION OF CENTRIFUGAL PUMPS

Continuity.

U¶

¶+

C¶¶ VU

= 0 …(1)

X- momentum:

)2

2

2

2(

R 1)V()(

U¶

¶+

C¶

¶+

C¶

R¶-=

U¶

¶+

C¶

¶ UUUUU

e

n …(2)

Y- momentum:

)2V2

2V2

(R 1)VV()V(

U¶

¶+

C¶

¶+

C¶

R¶-=

U¶

¶+

C¶

¶

e

nU …(3)

Where,

m

Dρu

eR ,uv V,

uu,

ρuP

nP,Dy

Y,Dx X

2¥

=

¥=

¥=

¥

=== U

X, Y represents Global co-ordinate; U, V representsVelocity along X, Y co-ordinate; Pn represents Pressurein global co-ordinate; u, v represents velocity along x, yco-ordinate; p represents pressure in local co-ordinate;R e = Reynolds number.

Transport Equation for the Standard k-ε model

The simplest and most widely used two-equationturbulence model is the standard k-å model that solvestwo separate transport equations to allow the turbulentkinetic energy and its dissipation rate to be independentlydetermined. The transport equations for k and å in thestandard k- e model are:

M bGkG])[( U--++

¶

¶

¶+

¶¶

= e

m

m

i x

k

k

t

i xt D

DK …(4)

k k i

xt

i xt D

D 2εε2C)Gb

ε3Ck G( 1C])ε

[( -+++

¶¶

¶+

¶¶=

e e

e m m e

…(5)

Where turbulent viscosity,

e m m

2k t c=

In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity

gradients. G b is the generation of turbulence kineticenergy due to buoyancy. Ók and s are the turbulentPrandtl numbers for k and , respectively. ρ representsdensity. YM represents the contribution of the fluctuatingdilatation in compressible turbulence to the overalldissipation rate. C1

, C2

, C3

, Cµ are constants. AllAllthe variables including turbulent kinetic energy k, itsdissipation rate are shared by the fluid and the volumefraction of each fluid in each computational volume istracked throughout the domain.

Pumps GeometryThe pump (impeller + volute) parameters are

presented in Table 1.

Boundary Conditions

Pressure inlet and pressure-outlet are set as boundaryconditions. As to wall boundary condition, no slipcondition is enforced on wall surface andstandard wall function is applied to adjacent region.

Grid Independent Test

The grid independence test has been done for 5, 6

and 7 bladed impeller centrifugal pump at 3000 (rpm)rotational speed. In the grid independence test, maximumtotal pressure has been taken as a criterion for independence. Based on the different grids, analysis has been made and it was observed that after refining thegrid from nodes 316798 for every blade at 3000 rpm,results are not varying significantly. So, nodes 316798have been used for further analysis.

Table 1 — Pumps geometry

Impeller

Description Value

Blade number 5,6,7

Inlet blade angle 25º

Outlet blade angle 33º Shape blade Circular arc

Impeller inlet diameter 80 mm

Impeller outlet diameter 168 mm

Volute casing

Description Value

Inlet diameter 80 mm

Volute tongue radius 52 mm

Є

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Numerical simulation

The CFD analysis of the centrifugal pump with 5, 6and 7 bladed impeller at 3000 rpm has been shown below.

Simulation and analysis of inner flow field

Static pressure (Bar) distribution at 3000 rpm

Static pressure (Bar) distribution at the mid span of the pump is shown in Fig.1 From Fig.1,it can be seen clearly that for different blade number, thestatic pressure gradually increase from impeller inlet to

outlet, the static pressure on pressure side is evidentlylarger than that on suction side at the same impeller radius. With the increase of blade number, the static pressure at volute outlet grows all the time and theuniformity of static pressure distribution at screw section become worse and worse, but at diffusion section become better and better. The impellers with different bladenumber all have an obvious low pressure area at the

suction side of blade inlet. With the increase of the bladenumber, the area flow pressure region growscontinuously, which indicates that the blade number hassignificant effects of pumps characteristics.

Total pressure (Bar) distribution at 3000 rpm

Total pressure (Bar) distribution at the mid span of the pump is shown in Fig.2 In Fig.2 total pressuredistribution of centrifugal pump with different blade number s has been shown. From that

it can be seen clearly that for different blade number, thetotal pressure gradually increases. It is also seen thatthe pressure is less in the impeller inlet side whereas pressure is more in the impeller outlet side.

Velocity vectors

The relative velocities inside the impeller are shownin the fig.3. The flow rate is lower than the nominal oneand we could see the trend the separation on the suction

Blade no. 5 Blade no. 6 Blade no. 7

Blade no. 5 Blade no. 6 Blade no. 7

Fig.1 — Static pressure distribution at the mid span for different impellers

Fig. 2 — Total pressure distribution at the mid span for different impellers

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377CHAKRABORTY et al : PERFORMANCE PREDICTION OF CENTRIFUGAL PUMPS

side of the trailing edge. From the figure it is clearlyvisible the flow direction of the impeller. Fig 3. Theabsolute velocity vectors near the tongue for a flow rategreater than the nominal are represented in the fig.5.Here is clearly visible the separation on the outlet sideand the blockage between the tongue and the impeller.Fig.4

Curve characteristics

Fig. 5 shows the static pressure distribution alongthe space between blades. The x- axis of the plot denotesthe distance along the circumference between the blades.The lower part of the figure is towards the impeller inletand upper part of the figure is towards the impeller outlet

of the pump. As it is seen from the figure the pressure isless in the impeller inlet side whereas pressure is morein the impeller outlet side.

Head and Efficiency calculation

Head H of centrifugal pump is calculatedas follows 4:

ρginP -outP

H = …(6)

Where pout is the total pressure of volute outlet, pin is the total pressure of impeller inlet, r is density of the fluid, d, and g is the gravity acceleration.

Total efficiency h is calculated as follows:

)03.0ePdP

hv

1( +

D+=

h h h … (7)

where Pe is the water power and Pe=ρg å QH, DPd isthe disk friction loss, calculation method is described inRef.5. hh is the hydraulic efficiency and h

v is the volume

efficiency.Results and discussion

Rotational speed and total pressure is an important parameter to ca lculate hea d as well as the tota lefficiency. The head and efficiency of pump model withdifferent blade number under design condition are shownin Table.2. From Table 2, it’s easily visible that with theincrease of blade number the head increases. But the

Table 2 — Predicted values of head and efficiency

Parameter Blade Blade Bladenumber 5 number 6 number 7

Head H/m 30.93 31.05 32.20Efficiency h/% 72.60 72.16 73.71

Fig. 3 — Relative velocities inside the impeller. Fig. 4 - Absolute velocities near the tongue.

Fig. 5 — Static pressure (Bar) distribution at various positions(near the blade region)

-1

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efficiency of centrifugal pump varies with number of blades. Here at 7 numbers of blades, the efficiency is of maximum. So the optimum blade number of the model pump in this paper for efficiency is 7 respectively. It isobserved that with the increase of blade number, thestatic pressure is gradually increasing. With the increase

of blade number the static pressure at volute outlet growsall the time.

Conclusion

The numerical studies on performance of centrifugal pump were investigated by using the FLUENT 6.3software. It has been observed that with the increase of the blade number, the limitation between blade and flowstream gets more, and also the area of low pressureregion at the suction of the blade inlet grows continuouslyand the static pressure is gradually increasing .Theuniformity of static pressure distribution at screw section become worse and worse, while at diffuser section, it becomes better and better. With the increase of bladenumber, the head of centrifugal pump grows all the timeand pressure too, but the change regulations of efficiencyis little bit complex. It varies with number of blades. Herethe optimum blade number of the model pump in this paper for efficiency is 7 respectively.

Acknowledgements

Authors are very much grateful to the reviewers for their valuable advice for significant modification and

better presentation of the paper.

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JSIR 72(6) 373-378