International Journal of Fluid Machinery and Systems DOI: http://dx.doi.org/10.5293/IJFMS.2016.9.2.107 Vol. 9, No. 2, April-June 2016 ISSN (Online): 1882-9554 Original Paper

Numerical And Experimental Study Of Single stage And Multistage Centrifugal Mixed Flow Submersible Borewell Pumps

C.Murugesan1 & Dr. R.Rudramoorthy2

1 Aquasub Engineering, Coimbatore, India, cmurugesan@aquagroup.in 2 Principal, PSG College of Technology, Coimbatore, India, principal@psgtech.edu

Abstract

This paper focuses on the single stage and multistage performance characteristics of centrifugal mixed flow submersible borewell pump. This study reveals that the performance of single stage pump is higher than that of multistage pumps. The head, input power and efficiency of single stage pump are higher than the per stage head, per stage input power and efficiency of multistage pumps. This study is divided into three parts. In the first part, five prototype pumps were made in single stage and multistage construction and the performance tests were conducted. In the second part, numerical validation has been done for different turbulence models and grid sizes. k-Omega SST model has been selected for the performance simulation and was validated with the performance of the test pump with static pressure tappings .In the third part, single and three stage pump performance were simulated numerically and compared with experimental results. The detailed analysis of pressure and velocity distributions reveals the difference in performance of single and three stage pump, due to non-uniform flow and difference in averaged flow velocities at the subsequent impeller inlets except the 1st stage impeller inlet.

keywords: Submersible bore well pump, Multistage, Single stage, k-Omega SST, Per stage input power , Efficiency, Averaged flow velocity, Non uniform flow, Recirculation.

1.Introduction At present, in the pump industry it is assumed that the efficiency of single stage and lower stage pumps is lower compared to

that of higher stage pumps. Manufacturers of multistage submersible pumps all over the world give performance catalogue [1] which contains family curves of series of different discharge rates with a foot note to reduce the efficiency points for 2 stage and single stage pumps from the given average efficiency curve. Also various national pump standards [2] specifies the same practice of reducing the efficiency values for lower stages. This study focuses on the single stage and multistage performance characteristics of centrifugal mixed flow submersible borewell pumps.

The multistage centrifugal mixed flow pumps are used in the borewell pumping of water .The pumps are submersible type and coupled directly with the wet winding submersible induction motors. The number of pumps used for this purpose is increasing in the last two decades all over the world and in India. More and more borewells are drilled for tapping the ground water sources. The sizes of borewells range from diameters 100mm, 150mm, 200mm, 250mm and upto350mm.The majority of the borewells is in 100mm and 150mm sizes. The present study is of the pumps used in the 150mm diameter bore wells.

The submersible pump of mixed flow type is shown in Fig.1.The inlet bracket(1)is used to guide the water flow into the first stage mixed flow impeller(2).The rotating blade system in the impeller imparts energy to the water and the high velocity water comes out in a conical spiral pattern. The diffuser (3) blade passages collect the water and diffuse its velocity. Also they direct the water to the next stage impeller. The velocity of the water at the second stage is kept same as that of the first stage, but the pressure energy is higher which is gained at the first impeller. The same process repeats in all the subsequent stages and the energy is added in all the stages by the work done at the impeller passages. The discharge casing (4) is at the end of the stages. It collects the high energy water and directs it to the column pipe (5) which is transferring the water to the ground level. Also column pipe is supporting the entire pumpset i.e. pump coupled with the motor and the axial down thrust caused by the pump impellers during running.

In the last decade, various studies were conducted on the impeller and volute interaction of centrifugal pumps and the results were published. The numerical simulation of the dynamic effects due to impeller-volute interaction in a centrifugal pump was given by Jose Gonzalez, et al. [3] which explains the capability of numerical simulation in capturing the dynamic and unsteady effects inside the centrifugal pump. The head and flow distribution within the volute of a centrifugal pump in comparison with the characteristics of the impeller without casing and unsteady behavior of velocity at impeller exit was given by P.Hergt et al..[4]. Also Akhras.A et al.[5] discussed the flow rate influence on the interaction of a radial pump impeller and the diffuser. Jianjun

Received March 16 2015; accepted for publication December 20 2015: Review conducted by Tadashi Tanuma, Ph.D . (Paper number O15014J) Corresponding author: C.Murugesan, cmurugesan@aquagroup.in.

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Feng, et al.[6] described the numerical investigation on pressure fluctuation for different configurations of vane diffuser pumps and the impact of radial gap between impeller and diffuser. The virtual performance experiment of a centrifugal pump was given by Zhang Shujia, et al. [7].The CFD application and validation for a turbo machinery design system was described by Anderson,M.R. et al. [8].

The numerical analysis of the unsteady flow in the near tongue region in a volute-type centrifugal pump for different operation point was presented by Raul barrio, et al. [9].Perez.J,et al. [10]have done experiments in a two stage radial flow pump and compared it with numerical simulations.B.Jafarzadeh,et al.[11] have studied the flow simulation of turbulent fluid flow in a low specific speed centrifugal pump. Paul Cooper,et al.[12] have analysed the complex internal flows in the centrifugal pumps and explained the use of CFD in finding the flow distortions and magnitude of non uniformities in multistage volute pump cross over. Stefania Della Gatte, et al. [13] have done CFD for the assessment of axial thrust balance in radial flow multistage pumps. Milan Sedlar, et al. [14] have numerically analysed the mixed-flow pump with volute. Masahiro Miyabe ,et al. [15] have studied the flow instability in a mixed-flow pump using CFD and DPIV. This instability is caused by the sudden increase of head loss at vaned diffuser inlet. Li Yi-bin ,et al. [16] have studied the role of guide vane in a mixed flow conditions by numerical simulation. Milan Sedlar,[17] analyzed the cavitation flow in the mixed flow pump which suffers from noise and vibration over the wide flow conditions. Jin-Hyuk Kim,[18] analyzed the optimization procedure for high-efficiency design of a mixed flow pump based on a weighted average surrogate model.

The analysis of flow inside the multistage mixed flow centrifugal pump was not thoroughly done in the past. Few research articles were available in the technical journals. So the authors have decided to take up the study of flow inside the multistage mixed flow pump and analyse the interaction between the impeller and diffuser in detail.

2. Objective of the study There are two objectives in this study. The first objective is to test experimentally and compare the following performance of

single stage and multistage submersible mixed flow pumps. a) Head vs Discharge Rate of Single Stage and Multistage Pumps. b) Pump Input Power vs Discharge Rate of Single Stage and Multistage Pumps. c) Pump Efficiency vs Discharge Rate of Single Stage and Multistage Pumps.

Second objective is the validation by numerical simulation and detailed analysis of the performance characteristics with the help of pressure and velocity distribution given by the CFD analysis.

3. Experimental study and Pump parameters Five pumps were constructed with similar impeller and diffuser stages starting from "single stage" to "five stages" for this

study purpose. The details of the test pumps are given below.

Parameter Value Unit Hn 8 m Qn .008 m³/s N 2880 rpm

Ns = n Qn0.5 Hn

-0.75 54.15 (min-1, m³/s ,m) D1 Shroud/ D1 Hub 64 / 27 mm D2 Shroud / D2 Hub 94 /93 mm

b2 13 mm b1 21.5 mm Zi 7 - t 3 mm

D3 108 mm D5 50 mm Zd 8 - Pn 1.25 HP

Fig.1 Submersible pump Mixed flow type

Table 1 Specification of the Test Pump

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3.1 Test Setup

All the pumps were tested in the experimental test set-up as per the ISO pump testing standard ISO 9906.The test rig scheme is shown in Fig. 2. The single stage pump and three stage pump were having static pressure tapping positions on their diffuser passages to measures the static pressure at these locations. The pressure measurements were taken for different discharge rates of the pumps. The input to the pump is measured in kW and the output is the product of head and mass flow rate.

3.2 Experimental Performance Comparison The head vs. discharge rate performance curves were drawn for all the five pumps and analysed (Fig. 3 and Fig. 4).The single

stage pump shut-off head has achieved a higher value i.e. 1.65 times the nominal head, Hn (Fig. 4a). The power curves for each pump were shown in Fig.3c and Fig.4c. From the efficiency curves (Fig.3b & Fig.4b), the BEP for a single stage pump is at the nominal flow. The two stage BEP discharge rate is 1.1 times the nominal flow. The three stage BEP discharge rate is 1.125 times the nominal flow. The four stage pump BEP discharge rate is 1.17 times the nominal flow and that of a five stage pump is 1.18 times the nominal flow. From single stage pump to multistage pumps, the BEP discharge rate is gradually shifting from nominal discharge to 1.18 times the nominal discharge rate. The single stage maximum pump efficiency is higher when compared with the maximum efficiency of multistage pumps. The efficiency value is 69% at nominal flow for the single stage pump. The two stage pump efficiency is 68%. The efficiencies of three stage, four stage and five stage pumps are 64% at 1.125 times the nominal flow, 64% at 1.18 times the nominal flow and 65% at 1.19 times the nominal flow respectively.

3.3 Per Stage Performance Comparison

The per stage head vs. discharge rate curves are drawn in Fig.4a. The shut-off head of a single stage pump is higher than that of other multistage pumps. From “Zero” discharge to BEP discharge rate, the head performance is better than the multistage pumps. From the BEP discharge rate to “Fully Open Valve” discharge rate the head performance of the single stage pump is equal to that of the multistage pumps. The per stage head vs. discharge rate performance of multistage pumps, i.e. 2 stages to 5 stages is approximately equal from “Shut-Off” to “Fully Open Valve” discharge rate. They are grouping into a small bandwidth. At “shut-off” condition, the single stage pump head is 3m higher than the rest of the multistage pumps. Up to 0.25 Qn, the difference in head is linearly decreasing. From 0.25 Qn to Qn, the difference in head is 1m approximately. From Qn to 1.25 Qn the difference is gradually decreasing and at 1.25 Qn the head performance is equal for all the pumps. From 1.25 Qn to “Fully Open valve” condition the head performance is equal for all the pumps.

4. Numerical Simulation

Numerical analysis of these pumps were made by a CFD code that solves the basic governing equations. The flow domain were modeled for single stage and multistage pumps. The meshing of the flow domain were done with different grid sizes and optimum grid size was arrived. Also different turbulence models were tried and k-omega model was selected for all the simulations. Inlet pressure, outlet pressure and rotation speed are given as initial boundary condition to the flow volume domain. After the convergence of solution the surface integrals for the pressure difference across inlet and outlet is calculated and total head is arrived. The surface integral of mass flow rate at outlet gives the volume flow rate. The impeller surfaces and blade surfaces where the momentum is imparted to the fluid are selected. The surface integral of the momentum in these surfaces were calculated to arrive at the torque imparted by the impeller and the input power to the pump. From the given total head and arrived volume flow rate the output is calculated.

Fig. 2 Experimental Test Setup as per ISO 9906

Pumpset

Outlet

Baffle Collecting tank Delivery pipe Testing panel

Control valve Pressure transducer

Magnetic flow meter Sump

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Fig. 4a Per stage Total head Ratio Vs Discharge rate Ratio

Comparison of "Per Stage" Performance characteristics of Single and Multistage Pumps by Experimental Method

0

2

4

6

8

0 0.5 1 1.5 2 2.5Discharge Rate Ratio (q= Q/Q n)

Tota

l Hea

d R

atio

(h =

H/H

n)

1 stage2 Stage3 stage4 stage5 Stage

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5Discharge Rate Ratio (q= Q/Q n)

Nom

inal

Pum

p In

put

(kW

) .

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5Discharge Rate Ratio (q= Q/Q n)

Per S

tage

Nom

inal

Inpu

t Pow

er (k

W)

Fig. 4c Per Stage Nominal Pump Input Vs Discharge rate Ratio

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5Discharge Rate Ratio (q= Q/Q n)

Per S

tage

Tot

al H

ead

Rat

io (h

= H

/H n

) .

Fig. 4b Per Stage Pump Efficiency Vs Discharge rate Ratio

Comparison of "Per Stage" Performance characteristics of Single and Multistage Pumps by Experimental Method

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5

Ove

rall

Pum

p Ef

ficie

ncy

(%)

Discharge Rate Ratio (q= Q/Q n)

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5

Per S

tage

Pum

p Ef

ficie

ncy

(%)

Discharge Rate Ratio (q= Q/Q n)

Fig. 3a Total head Ratio Vs Discharge rate Ratio

Fig. 3b Overall Pump Efficiency Vs Discharge rate Ratio

Fig. 3c Nominal Pump Input Vs Discharge rate Ratio

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4.1Numerical set up In the numerical simulation selection of turbulence models, grid size and computational resources affects the accuracy of the

predictions. The selection of maximum possible turbulence model, grid size and computational resources would increase the computational time and cost. Optimal turbulence model and consistent grid size were selected to minimize the time and cost for all the simulations.

The numerical domain was generated using a 3d modeling package that includes a suction pipe, impeller, diffuser and a delivery pipe. In this study the numerical model around the wear ring region and on the top surface of the impeller is also modeled for each stage in order to account the leakage flow losses as this would be a major loss when considering a multistage pump. Figure 5 shows the views of a bowl and impeller. Figure 6 shows the surface meshes of the bowl and impeller. Figure 7 shows the numerical domain used for the simulation and details of the rotating and stationary domains with the interfaces generated across the each stage. Interface were generated for each impeller and bowl to define the stationary and rotating domain and an additional interface was generated in between each stage at the outlet of the bowl to measure the velocity, pressure and mass flow at each stage.

The discritization of flow domain i.e meshing was done using Ansys workbench software. Initial discritization was done using tetrahedral cells to adopt the most part of the complex geometry and the very fine wear ring clearance of 0.125mm in pre-processing. Later it was converted to polyhedral cells to achieve faster convergence as well as accurate prediction. The mesh was refined at blades of both the impellers and bowl.

The flow through the numerical domain was simulated using the commercial CFD code Ansys Fluent which solves the Navier strokes 3D incompressible flow equations by the finite volume method. The flow model was solved using pressure based solver with relative velocity formulation. Turbulence model was selected by comparing all possible models. Coupled algorithm was selected for pressure velocity coupling.

The convergence residuals were set to the order of 10-4 for x,y,z velocities and turbulence models. The simulations were performed for five flow rates from 0.2 to 1.6 times of the nominal flow rate. The simulation is checked for its dependency with respect to grid size and turbulence model before proceeding with the bulk of the simulations.

Fig 5 - Sectional view Fig 6 - Polyhedral Mesh

Fig. 7 Flow Domain

Inlet

Bowl-1

Bowl-2

Bowl -3

Outlet

Impeller 1

Impeller 2

Impeller 3

Interface

Interface

Interface

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4.2Numerical dependency study The values of grid size and selection of turbulence models plays a vital role in having close matching with experimental data.

The investigation is required before carrying out the rest of the simulations. The flow volume was split into 4 domains (inlet duct, outlet duct, diffuser and impeller) as shown in the Fig.7. For the single stage and multistage analysis the inlet and outlet domain remains same, only the diffuser and impeller domains were copied to maintain the same geometry and also the gird cells. Before proceeding with the multistage, the grid dependency study was done in the single stage with the grid cells ranging from .25 million to 1 million for the entire mass flow region from 0.125 to 1.6 times the nominal flow to check for the variations caused due to the grid cells in the input and output of the pump. Refer Fig. 8 for the complete performance plot for the 4 set of grid cells.0.75 million grid cells were selected considering accuracy ,computation time and Fig. 8 also shows a very marginal difference in performance for 0.75 million and 1 million grid cells.

The influence of turbulence models on the predictions was investigated with the selected grid cells and it is shown in Fig 9. The investigation was done on the k-Epsilon Standard,k-Epsilon RNG, k-Omega standard and k-Omega SST. It was observed that the k-Omega SST model gives accurate predictions in higher flow rate off design conditions also .The k -Omega SST model was chosen finally for the further multistage analysis.

4.3 Validation of numerical setup by the experimantal measurement of static pressure using test pump with pressure tappings

To validate the numerical analysis, a three stage pump was consructed with pressure tappings at different locations as shown in Fig.10a and the static pressure readings were measured during the performance testing(Fig 10b). The measured values were compared with numerically predicted values (Fig.11) and it is plotted in Fig.12. The CFD predicted static pressure values were marginally higher than the experimental values.

Fig. 10a Locations of pressure tappings

Fig. 10b Locations of pressure tappings

Fig. 12 Experimental and Numerical Comparison

0

0.5

1

1.5

2

2.5

3

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18Tapping Positions

Stat

ic P

ress

ure(

bar)

Experimantal Numerical

Fig. 8 Grid Sensitivity Plot Fig. 9 Turbulence Models Plot

0

20

40

60

80

0

1

2

3

4

5

0 0.5 1 1.5 2

Effic

ienc

y (%

)

Tota

l Hea

d R

atio

(h =

H/H

n )

Discharge Rate Ratio (q = Q / Qn ) 0.25 Million 0.5 Million0.75 Million 1 Million

0

20

40

60

80

0

0.5

1

1.5

2

0 0.5 1 1.5 2

Effi

cien

cy (%

)

Tota

l Hea

d R

atio

(h =

H/H

n)

Discharge Rate Ratio (q = Q /Qn ) k- Omega Standard k - Epsilon Standardk- Omega SST k -Epsilion RNG

Fig. 11 Numerical Pressure Plot

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5. Results and Discussion 5.1 Comparitive study of Experimental and Numerical performance characteristics

The comparitive study of experimental and numerical performance characteristics were done for single and three stage pumps and graphs are shown in Fig.13a& 13b. Numerical results are matching closely with experimental results. Numerical results also confirms the increase in head for single stage pump.

5.2 Comparitive study of Single stage and 3 stage pump performance characteristics

The single stage and 3 stage pump performance characteristics were compared by using per stage head Vs discharge rate and per stage pump input Vs discharge rate curves as shown in Fig. 4a &4c. Figure 4c clearly shows that the pump input power absorbed by the single stage impeller is considerably more than the 3 stage pump from zero discharge rate to full open valve discharge rate. Also the per stage total head Vs discharge rate comparison shows that the total head of single stage is more from zero discharge rate to 1.25 Qn rate and equal to per stage head of 3 stage pump from1.25 Qn to full open valve discharge rate because of the smooth and higher diffusion in the single stage pump outlet section. So there is more pressure recovery and higher total head. 5.3 Analysis of pump performance using Numerical results

To study the per stage pump performance differences, the numerical results for the single stage pump and 3 stage pump were analysed for nominal discharge rate condition and 0.125 Qn condition i.e low discharge rate at near shutoff condition. The pathline patterns of flow at Qn are plotted in Fig.14&15. The total pressure distribution and velocity distribution of single stage pump at nominal discharge rate Qn are shown in Fig.18 & 19. Figure 18 clearly shows that the total head (8.1mWC) is achieved at the outlet pipe. The average suction velocity at inlet is 2.94 m/s which is normal design velocity at nominal flow and it increases upto 9 m/s at the outlet of the impeller. It gradually diffuses in the diffuser passage and reaches a value of 4.35 m/s at the outlet of the diffuser vane. Further it diffuses to a value of 2.64 m/s at the pump outlet and gains a pressure of 78622 Pa (8.1 meter of water column).It is to be noted particularly that flow velocity doesn't reduces to approximately 2.94 m/s at the diffuser outlet which is the optimum requirement at the next stage impeller inlet when the same impeller and diffuser are used in the multistage pump construction. Also the flow velocity distribution at the diffuser outlet is not uniform because the flow tends to move away from the outer wall of the diffuser shroud as shown in Fig.20.This causes low and high velocity zones where flow velocities are not uniform and is 4.35 m/s which is higher than the normal design velocity at the inlet of the impeller.

Fig. 13a Total Head Ratio Vs Discharge Rate Ratio of Experimental & Numerical methods

Fig. 13b Nominal Pump Input power Vs Discharge Rate Ratio of Experimental & Numerical methods

Fig.14 Single Stage Pathline at Qn

3rd Stage Diffuser outlet

Fig. 15 3 Stage Pathline at Qn

1st Stage Diffuser outlet / 2nd Stage Inlet

2nd Stage Diffuser outlet / 3rd Stage Inlet

Outlet Pipe

Fig.16 Single stage pathline at 0.125Qn

Fig.17 3 stage pathline at 0.125Qn

No Recirculation Recirculation

Inlet

1st Stage Outlet

Outlet Pipe

0

1

2

3

4

5

0 0.5 1 1.5 2Discharge Rate Ratio (q= Q/Qn)

Tota

l Hea

d R

atio

( h

= H

/H n

)

3 & 1 Stage Experimental3 & 1 Stage CFD

0

1

2

3

4

0 0.5 1 1.5 2Discharge Rate Ratio (q= Q/Qn)

Nom

inal

Pum

p In

put (

kW)

113

The total pressure distribution and velocity distribution of 3 stage pump at nominal discharge rate Qn are shown in Fig.21 &22. Figure 21 clearly shows that the average pressure gained at each stage diffuser outlet is approximately 80000Pa (8.1 meter of water column) which is the optimum requirement expected out from the pump. Figure 22 reveals that the average velocity at the 1st stage diffuser outlet and the 2nd stage diffuser outlet is 4.26 m/s and at the 3rd stage diffuser outlet is 4.38 m/s. The velocities at the 2nd and 3rd stage impeller inlet are higher than the normal design velocity at the 1st stage impeller inlet and the velocity distributions are also not uniform. Due to this non uniformity, the power imparted by the 2nd stage and 3rd stage impellers to the water is reduced which is matching with the experimental results shown in Fig.4c and also the per stage head developed by the three stage is less compared to that of single stage pump which is shown in Fig.4a.

The total pressure distribution and velocity distribution of single stage pump at off-design condition(low discharge rate),0.125Qn are shown in Fig.23 &24 .In this condition the flow pattern becomes totally chaotic, recirculation and secondary flows of all types are found as shown in Fig.16 (Path line pattern at 0.125Qn).The flow passages are designed and constructed for Qn flow with suitable area at various cross sections of impeller and diffuser. Now when the pump is handling only a fraction of the nominal flow, i.e., 0.125Qn in the same passage area, the fluid flow takes its own course of reducing the mean flow area by its recirculation flows and secondary flows or eddy flows.

Inlet Pipe

Avg.: 0 Pa (0 mWC) Avg.: 81322 Pa (8.3 mWC)

Avg.:78622 Pa (8.1 mWC) Inlet Pipe 1st Stage Diffuser outlet Outlet Pipe

Fig. 18 Single stage Total Pressure distribution at Nominal Discharge rate Qn

Avg.:4.35 m/s Avg.:2.94 m/s Avg.:2.64 m/s Avg.:9.08 m/s

Fig. 19 Single stage Flow Velocity distribution at Nominal Discharge rate Qn

Velocity distribution (m/s) at Qn Velocity distribution (m/s) at 0.125 Qn

Fig. 20 Sectional view of Flow Velocity

Impeller Outlet 1st Stage Diffuser outlet Outlet

Flow is not following the Hub & Shroud wall

Flow is not following the Shroud wall

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Inlet

1st Stage Diffuser Outlet / 2nd Stage Impeller Inlet

Avg.: 0 Pa (0 mWC)

Avg.: 16054 Pa (16.3 mWC)

Avg.: 24116 Pa (24.5 mWC)

Avg.: 23771 Pa (24.2 mWC)

Outlet

2nd Stage Diffuser Outlet / 3rd Stage Impeller Inlet

3rd Stage Diffuser Outlet

Fig. 21 Total Pressure distribution at Nominal Discharge rate Qn for 3 Stage pump

2nd Stage Diffuser Outlet / 3rd Stage Impeller Inlet

Avg.: 2.96m/s

Inlet

Avg.: 4.26m/s

1st Stage Diffuser Outlet / 2nd Stage Impeller Inlet

Avg.: 4.26m/s

Avg.: 4.38m/s 3rd Stage Diffuser Outlet

Avg.: 2.64m/s Outlet

Fig. 22 Flow Velocity distribution at Nominal Discharge rate Qn for 3 Stage pump

Avg.: 80050 Pa (8.1 mWC)

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This can be observed in detail from the vector plots of Fig.25.In the single stage impeller inlet large recirculation at the outer area of suction eye is found. At the single stage diffuser outlet,recirculaiton from one vane passage to another vane passage of the diffuser is found. The average pressure achieved is 127056 Pa (12.9 meter of water column) at the single stage diffuser outlet. The average flow velocity is 6.52m/s higher than the impeller inlet velocity of 3.43 m/s.

The same chaotic flow patterns are observed in the 3 stage pump passages at this low discharge flow rate of 0.125Qn. The recirculation at suction pipe and the 1st,2nd and 3rd stage diffuser outlets are shown in the velocity vector plots in Fig.27.The path-line pattern for the three stage pump in Fig.17 shows the recirculation at all the flow regions.

From the Fig.26 the average pressure achieved at the 1st,2nd and 3rd diffuser outlets are 126156pa (12.8 meter of water column),228259 Pa(23.2 meter of water column) and 299392Pa (30.5 meter of water column).The first stage pressure gain is 12.8 meter of water column whereas the at 2nd stage and 3rd stage outlet the pressure gains are 10.4 meter of water column and 7.3 meter of water column. The average per stage pressure or head developed is only 10.16 meter of water column lesser value than that of the single stage pump, i.e. 12.9 meter of water column.

The velocity distribution at 0.125Qn(low discharge rate)flow of 3 stage pump are shown in Fig 27.The average suction velocity at the 1st stage impeller inlet is 3.18m/s whereas at 2nd and 3rd stage diffuser outlets the velocities are 6.65 m/s and 6.91 m/s. The flow is not uniform and full of recirculation after the first stage which is clearly shown in Fig 27.

Avg.: 8567 Pa (0.8 mWC) Avg.: 127056 Pa (12.9 mWC) Avg.: 124123 Pa (12.6 mWC)

Fig 23 Single stage Total Pressure distribution at 0.125 Qn (low discharge rate) off-duty point

Avg.: 3.43m/s Avg.: 6.52m/s Avg.: 0.88m/s

Fig 24 Single stage Flow velocity distribution at 0.125 Qn (low discharge rate) off-duty point

Recirculation at Impeller Inlet

1st Stage Impeller Inlet 1st Stage Diffuser Outlet

Recirculation from one vane passage to another vane passage of the diffuser

Fig 25 Single stage Flow Velocity vectors at 0.125 Qn (low discharge rate) off-duty point

Inlet Pipe 1st Stage Diffuser outlet Outlet Pipe

Inlet Pipe 1st Stage Diffuser outlet Outlet Pipe

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6. Conclusion

From the analysis of numerical simulation and experimental results, it is found that per stage head of multistage pump is less than the single stage pump due to the difference in averaged inlet velocities in the subsequent impellers and also the non- uniformity in the flow. The flow is not following the impeller and diffuser shroud and hub walls where there is change of direction of flow. Secondary flows are also seen at the diffuser passage even at the nominal flow rate Qn. This flow pattern reduces the second stage and subsequent stage impeller effective inlet areas and increases the flow velocities than the design inlet velocity.

The difference in averaged velocity from the design velocity at the subsequent impeller inlets is observed even at the nominal flow rate Qn. The averaged flow velocity at second stage impeller inlet increases to 4.26 m/s from 2.96 m/s for Qn. The difference in averaged flow velocities from the design velocity is more at the 0.125Qn (low discharge rate) flow rate. The averaged flow velocity at second stage impeller inlet increases to 6.65 m/s from 3.18 m/s for 0.125Qn.

Due to this the pump input power absorbed by the single stage pump is considerably higher than that of the stages of multistage pumps. Also the efficiency of single stage pump is higher, that is 69% compared to 65% for three stage pump and above stages.

Further research work can be carried out to reduce non uniform flow and the difference in averaged inlet flow velocities in the multistage pumps. There is scope for reducing the losses inside the impeller and diffuser passages and increase the overall efficiency of the multistage pumps.

Acknowledgement The authors thank Dr.K.M.Srinivasan, Dr.P.R.Thiyagarajan, Dr.K.Mayilsamy and Dr.T.Prabhu of PSG College of Technology

for their valuable inputs during this study. Authors thank the management of M/s Aquasub Engineering, P.Ramesh and G.Prasath for their support in carrying out the experimental study.

Avg.: 7817 Pa (0.79 mWC) Avg.: 126156 Pa (12.8 mWC)

Avg.: 228259 Pa (23.2 mWC) Avg.:299392 Pa (30.5 mWC) Avg.: 303921 Pa (31.0 mWC)

Fig.26 Three stage Total Pressure distribution at 0.125 Qn (low discharge rate) off-duty point

Avg.: 3.18m/s Avg.: 6.65 m/s Avg.: 6.91m/s Avg.: 0.98 m/s Inlet Pipe

1st Stage Diffuser Outlet / 2nd Stage Impeller Inlet

2nd Stage Diffuser Outlet / 3rd Stage Impeller Inlet

3rd Stage Diffuser Outlet

Fig.27 Three stage velocity vector plot at 0.125 Qn (low discharge rate) off-duty point

Inlet

1st Stage Diffuser Outlet / 2nd Stage Impeller Inlet

2nd Stage Diffuser Outlet / 3rd Stage Impeller Inlet

3rd Stage Diffuser Outlet Outlet

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Nomenclature Hn Head per Stage (Nominal) at BEP (m) D3 Diffuser Inlet Diameter, Mean (mm) Qn Discharge Rate (Nominal) at BEP (m³/s) D5 Diffuser Outlet Diameter, Mean (mm) N Speed of Rotation (rpm) Zd No. of Diffuser Vanes Ns Specific Speed (metric) (min-1, m³/s ,m) Pn Per stage Power Rating (Pump Input) (HP)

D1 Shroud / D1 Hub Impeller Diameter, Inlet (mm) Zi No. of Impeller Vanes D2 Shroud / D2 Hub Impeller Diameter, Outlet (mm) t Vane Thickness (mm)

b2 Impeller Width, Outlet (mm) BEP Best Efficiency Point b1 Impeller Width, Inlet (mm) mWC Meter of Water Column

Reference

[1] Franklin Pump Systems (FPS) , USA Catalogue website: www.franklinwater.com. [2] IS8034:2002 Indian Standard Submersible Pumpsets - Specification (Second Revision), Bureau of Indian Standards, Manak Bhavan New Delhi November 2002. [3] Jose G, Joaquin F, Eduardo B & Carlos S, "Numerical Simulation of the Dynamic Effects Due to Impeller – Volute Interaction in a Centrifugal Pump," J Fluids Eng,Trans ASME,124 (2002) 348-355. [4] Peter H, Stephan M & Bernd S,"The Flow and Head Distribution within the Volute of a Centrifugal Pump in Comparison with the Characteristics of the Impeller Without Casing," J Comput Appl Mech , Miskolc University Press, Hungary, 5 (2004), 275-285. [5] Akhras A, El Hajem E, Morel R & Champagne J Y, "The Flow Rate Influence on the Interaction of a Radial Pump Impeller and the Diffuser," Int J Rotating Mach, Taylor & Francis,10(2004), 309–317. [6] Jianjun F, Friedrich-Karl B & Hans J D, "Numerical Investigation on Pressure Fluctuations for Different Configurations of Vaned Diffuser Pumps," IJRM, Hindawi ,2007. [7] Zhang S, Zhu B,Hu Qo & Li X, "Virtual Performance Experiment of a Centrifugal Pump," Proc 16th Int Conf on Artificial Reality and Teleexistence ( ICAT 06), IEEE,2006. [8] Anderson M R, Gu, Fahua, MacLeod P D ,"Application & Validation of CFD in a Turbo Machinery Design System," Int Mech Engg Congress and R & D Expo,ASME. [9] Barrio R, Fernandez J, Blanco E & Parrondo J,"Estimation of radial load in centrifugal pumps using computational fluid dynamics," Eur J Mech B-Fluid 30(2011)316-324. [10] Perez J, Chiva S, Segala W,Morales R,Negrao C, Julia E & Hernandez L,"Performance Analysis of Flow in a Impeller-Diffuser Centrifugal Pumps using CFD: Simulation and Experimental Data Comparisons," EECMV,ECCOMAS CFD 2010. [11] Jafarzadeh B,Hajari A,Alishahi M M & Akbari M H, "The flow simulation of a low - specific- speed high- speed centrifugal pump," Appl Math Model, Elsevier, 35,( 2011), 242–249. [12] Paul C, Edward G & Timothy L, "Computational Fluid Dynamics Analysis of Complex Integral Flows in Centrifugal Pumps," Proc Int Pump Users Sym, (Turbomachinery Laboratory, Texas A & M University System), 1994. [13] Stefania D G, Simone S, Paolo A & Laura B, "CFD Study For Assessment of Axial Thrust Balance in Centrifugal Multistage Pumps," Proc Int Conf Fluid Flow Tech, CMFF06. [14] Milan S, "Numerical Investigation of Flow in Mixed-Flow Pump with Volute," Task’u, 5 (2001), 595–602. [15] Masahiro Miyabe, "A Behavior of the Diffuser Rotating Stall in a Low Specific Speed Mixed-Flow Pump," International Journal of Fluid Machinery and Systems Vol. 2, No. 1, January-March 2009. [16] Li Yi-bin," The Numerical Simulation of Unsteady Flow in a Mixed flow Pump Guide Vane," International Journal of Fluid Machinery and Systems, Vo l . 6, No. 4, October-December 2013. [17] Milan Sedlar, "CFD Analysis of Cavitation Phenomena in Mixed-Flow Pump," International Journal of Fluid Machinery and Systems, Vol. 5, No. 1, January-March 2012 [18] Jin-Hyuk Kim, "Optimization of Vane Diffuser in a Mixed-Flow Pump for High Efficiency Design," International Journal of Fluid Machinery and Systems, Vol. 4, No. 1, January-March 2011.

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