SHAPE OPTIMIZATION OF SUBMERSIBLE PUMP IMPELLER DESIGN · 2017. 11. 28. · design was casted and...

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 8, Issue 11, November 2017, pp. 204–219, Article ID: IJMET_08_11_024

Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=11

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

SHAPE OPTIMIZATION OF SUBMERSIBLE

PUMP IMPELLER DESIGN

Joe Ajay A

Scholar, Department of Mechanical Engineering,

Karunya University, Coimbatore, India

S. Elizabeth Amudhini Stephen

Associate Professor of Mathematics,

Karunya University, Coimbatore, India

ABSTRACT

Submersible pumps are universally used in recent days. These pumps which are

immersed in the working fluid, work on Forced vortex principle. Impeller shape

optimization for a specific purpose has its effect on the H-Q curve of the pump, as

stated by 2nd

law of thermodynamics. Hence this research work was focused on the

improvement of duty head of the pump without changing the outlet & inlet diameter of

the impeller. This optimization was done by means of minimising the head losses that

occur in the impeller. Optimization was carried out using optimization algorithms like

GA,SA,PS etc and the optimized values are used for design of new impeller. The

optimized result was tested using CFD with common turbulence models. The resulting

design was casted and experimentation was carried out.

Key words: Design optimization, Shape optimization, Turbo machinery, Centrifugal

pump

Cite this Article: Joe Ajay A, S. Elizabeth Amudhini Stephen, Shape Optimization of

Submersible Pump Impeller Design, International Journal of Mechanical Engineering

and Technology 8(11), 2017, pp. 204–219.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=11

1. INTRODUCTION

Three important characteristics of a pump are Pressure, friction and flow. In any pump

system, there are always losses which are added to the overall performance of the system [2].

The losses that contribute to the overall performance of the pump are: Electrical, Hydraulic

and Mechanical losses. Design optimization has become part and parcel of design process.

Such design optimization can be carried out by minimizing the losses. In the present work

head losses are minimized to get maximum head. New optimization techniques that take

much less time for computation such as Genetic Algorithm, Particle swarm optimization etc.,

are used for design optimization [4]. The head of the pump with losses was formulated and

found to be nonlinear hence these algorithms were used and evaluated in terms of time and

accuracy. The result from the algorithms was studied with CFD and a comparative

Shape Optimization of Submersible Pump Impeller Design


experimental study of the pump was done to evaluate the existing and optimized designs.

Theoretical model to predict the centrifugal pump performance when its impeller is equipped

with splitters[2]. This paper compares the differences of the pump with splitter blades with the

conventional pump. Hydraulic loss was evaluated to theoretically evaluate the performance of

centrifugal pumps and compare with the experimental results given in [8] has found the losses

associated with the performance of the pump and formulated in terms of expressions, [12] has

used, artificial bee colony algorithm for optimization and shown an improvement of 3.59% in

efficiency, [3] has increased the head of the pump by 6% by varying the outlet angle, [10] has

used design of experiments method and optimized the head of the pump using CFD analysis.

2. METHODOLOGY

The research work carried out is postulated in steps as shown in fig-1. A pump of 5HP rating

was taken for study and its duty head was experimentally found to be 25m. The head

formulation along with head losses were carried out at first. CFD study with 3 different

turbulence models of the existing design was done next. The expression involving the head

was taken to be the objective function and optimization techniques were used for

optimization. The final part involves the CFD analysis of the optimized design of the impeller

and experimentation for the same as in fig -1.

Figure 1 Procedure

3. RESEARCH METHODOLOGY

3.1. Head Formulation

From Euler's equation for turbo machinery the head of the centrifugal pump without whirl is

given as [6]:

Hth =

(1)

The losses that contribute to the head of the pump are:

Circulation head Loss: As described in [2], is caused by increase in relative velocity at

inlet and decrease in relative velocity at the outlet of the impeller,

Hc = ( )

(2)

Joe Ajay.A, S. Elizabeth Amudhini Stephen


Inlet incidence loss: has been calculated as described in [2]

Hi = ( )

(3)

Impeller friction loss: A s described in [8] due to surface of the impeller and vanes the

there would be emery dissipation and this would be given as

Hf = ( )( )

(4)

Where The hydraulic radius Hr = (

)

(

)

Hence the net total head with losses will be:the following with respect to equations 1 to 4

Hnet = Hth Hc Hi Hf (5)

3.2. Experimentation

In order to evaluate the performance of the pump, experimentation was carried out. The

pump was immersed fully in the tank. 415V is set at the Digital Power panel (as it was

industry standard voltage for testing the pump) and the pump was started. The discharge valve

is completely closed at first and the discharge head is noted using the pressure gauge, this

condition is called shut off condition. The discharge valve is gradually opened until its

completely open and the corresponding discharge is noted using the flow meter. This type of

experimentation was called as performance experimentation, the duty point was found to be

0.00605m3/s and head of 25m. The experimental layout is as of fig-2.

Figure 2 Experimental layout

3.3. CFD Analysis

The simulation of the experiment for the duty point was carried out, As stated in [11] three

predominant turbulence models were used to simulate the flow the result were checked with

the mathematical model prepared in section 3.1. The existing impeller dimension that

contribute to the head were measured:



Inlet diameter(D1) : 76mm

Outlet diameter(D2) :160.4mm

Inlet blade angle(β1) : 300

Outlet blade angle (β 2): 300

Inlet impeller width (b1): 18mm

Outlet impeller width(b2) : 10.2mm

No. of vanes(Z) : 6

Rotational velocity of 2810rpm with boundary conditions of the duty point was specified

in the pre processing stage. The three turbulence models taken as per [11] are:

K-ε

K- ε EARMS

Shear stress Transport model (SST)

4. OPTIMIZATION METHODS

For the proposed problem, design optimization would be to performed to improve the duty

point head (25m). As described in Section 3.1, since the expression for head involves

nonlinear terms it would be of choice to use non-traditional optimization techniques.

According to the work done in [4], it was identified to use 3 popular solvers namely:

Genetic algorithm (GA)

Particle swarm optimization (PSO)

Pattern search (PS)

4.1. Genetic Algorithm

Genetic Algorithm (GA) is a search algorithm based on the conjecture of natural selection and

genetics. The algorithm is a multi-path that searches many peaks in parallel, and hence

reducing the possibility of local minimum trapping. GA works with a coding of parameters

instead of the parameters themselves. The coding of parameter will help the genetic operator

to evolve the current state into the next state with minimum computations. GA evaluates the

fitness of each string to guide its search instead of the optimization function. There is no

requirement for derivatives or other auxiliary knowledge. GA explores the search space where

the probability of finding improved performance is high.

4.2. Particle Swarm Optimization

Particle swarm optimization (PSO) is a population-based stochastic approach for solving

continuous and discrete optimization problems. In particle swarm optimization, simple software

agents, called particles, move in the search space of an optimization problem. The position of

a particle represents a candidate solution to the optimization problem at hand. Each particle

searches for better positions in the search space by changing its velocity according to rules

originally inspired by behavioral models of bird flocking.

4.3. Pattern Search

Pattern search [5] finds a local minimum of an objective function by the following method,

called polling. In this description, words describing pattern search quantities are in bold. The

search starts at an initial point, which is taken as the current point in the first step:



1. Generate a pattern of points, typically plus and minus the coordinate directions, times

a mesh size, and center this pattern on the current point.

2. Evaluate the objective function at every point in the pattern.

3. If the minimum objective in the pattern is lower than the value at the current point, then

the poll is successful, and the following happens:

3a. the minimum point found becomes the current point.

3b. the mesh size is doubled.

3c. the algorithm proceeds to Step 1.

4. If the poll is not successful, then the following happens:

4a. the mesh size is halved.

4b. if the mesh size is below a threshold, the iterations stop.

4c. Otherwise, the current point is retained, and the algorithm proceeds at Step 1.

5. RESULTS & DISCUSSION

5.1. Existing Design Performance Evaluation

As described in section 3.2 experiments was conducted on existing design and the head losses

were estimated theoretically, with the dimensions of the impeller measured.

Table 1 Theoretical head developed by the impeller

Experimental

Discharge

(m3/s)

Theoretical

Head (m)

-

1-

Circulation

head loss (m)

-2-

Inlet Incident

loss (m)

-3-

Frictional

head loss (m)

-4-

Net Head (m)

=1-2-3-4

0 41.9106

14.8634

0 0 27.0472

0.00605 38.29 0.2121 0.0179 23.1967

0.01034 35.7227 0.6196 0.0522 20.1876

0.01372 33.7 1.0908 0.0919 17.6539

0.0158 32.4553 1.4466 0.1218 16.0234

0.0166 31.9765 1.5969 0.1345 15.3818

The result of the experimental test is postulated below and it can be noted that the duty

point had delivery of 0.00605m3/s and the duty delivery head of 25m.

Table 2 Existing impeller performance test

Discharge

(m3/s)

Experimental

Head (m)

Water Power

(W)

Experimental

Power (W)

Efficiency

(%)

0 28 0 4414 0

0.00605 25 1484 5731 26

0.01034 20 2029 6495 31

0.01372 15 2019 6838 30

0.0158 12 1860 7042 26

0.0166 8 1303 7098 18

It can be seen that the circulation head contributes to the maximum; this is due to the fact

that the speed is taken is constant [10]. Inlet incident loss contributes less, this is because of

the fact that, the whirl velocity involved in the loss (1.3), is dependent on the discharge and

the same is applicable for the frictional loss (1.4).



Figure 3 Performance Chart of the existing design

From the fig-3, it is evident that the pump has an efficiency of 26% at duty point. The best

efficiency point (BEP) has the discharge of 0.01034m3/s and head of 20m, but as the industry

sells the pump at 0.00605m3/s and 25m head, this point was taken as duty point.

5.2. Simulation of Existing Design

Studies suggest few of the common turbulence models to be used for CFD analysis of pump

[11] .. Hence common available turbulence models were chosen and used to simulate the duty

point of the existing design of the impeller

Table 3 Turbulence model comparison

Turbulence model Head (m)

K-ε 38.22

K- ε EARMS 38.15

SST 38.6

From table-5.3 we find that the K-ε model is much closer to the net theoretical head

(38.29m), hence it would be convenient to use the same for simulation purpose of the

optimized model.

Figure 4 Simulation of existing design

From fig-4, it is evident that the head has converged to the value of 38.22m at the outlet.

5.3. Optimization Computation

The design optimization described is coded with MATLAB in the described algorithms were

used for optimization. Twenty trails were performed as described in [4] and the average for

each parameter was taken as the design parameters from the each solver. The net head was

evaluated theoretically for each parameter from the solvers.

0

20

40

0 0.00605 0.01034 0.01372 0.0158 0.0166

Dischatge (m3/s)

Performance Chart

Experimental Head (m) Efficiency



Table 4 GA result table

Trial .No b1 (m) b2 (m) B1 (deg) B2 (deg) Z

1 0.01971 0.011205 32.22278 27.00377 6.99811

2 0.0198 0.011219 31.72584 27.03114 6.998719

3 0.01979 0.011193 32.23771 27 6.994889

4 0.019032 0.011217 32.97973 27.0132 6.999988

5 0.019741 0.011195 29.51032 27.0003 6.99833

6 0.019677 0.011184 30.28991 27.00998 6.997203

7 0.019786 0.011215 32.99356 27 6.998972

8 0.018781 0.011204 32.42831 27.00353 6.989807

9 0.01979 0.011193 32.98755 27.00222 6.992399

10 0.019737 0.011216 32.9468 27.00058 6.998951

11 0.016839 0.011172 32.87619 27.01357 6.999877

12 0.019782 0.011174 32.99054 27.0041 6.990989

13 0.01978 0.011118 32.45682 27.01457 6.99466

14 0.019654 0.011168 32.73113 27 6.999756

15 0.019784 0.011205 32.02996 27.04251 6.996918

16 0.019771 0.011202 32.96209 27.02306 6.998907

17 0.019768 0.011148 32.51205 27.00315 6.997679

18 0.019154 0.011216 32.99998 27.12727 6.998472

19 0.019762 0.011144 32.77239 27 6.99693

20 0.019592 0.011178 31.64257 27.00767 6.998228

0 10 20

0.017

0.018

0.019

0.0200.01110

0.01115

0.01120

0.0112529

30

31

32

33

3427.00

27.05

27.10

27.15

6.990

6.995

7.000

0 10 20

b1 (m

)

Trails

b2(m

)

B1(de

g)

B2(de

g)

Z

Figure 5 Performance of Genetic algorithm

From the fig-5 we see that there are not much variations in inlet width and outlet angle

parameter but No. of vanes, outlet width and inlet angle show considerable variations during

trail runs.

Table 5 PS result table

Trial. No b1(m) b2(m) B1(deg) B2(deg) Z

1 0.018 0.0102 30 30 6

2 0.018 0.0102 30 30 6

3 0.018 0.0102 30 30 6

4 0.018 0.0102 30 30 6

5 0.018 0.0102 30 30 6

6 0.018 0.0102 30 30 6

7 0.018 0.0102 30 30 6

8 0.018 0.0102 30 30 6

9 0.018 0.0102 30 30 6

10 0.018 0.0102 30 30 6

11 0.018 0.0102 30 30 6



12 0.018 0.0102 30 30 6

13 0.018 0.0102 30 30 6

14 0.018 0.0102 30 30 6

15 0.018 0.0102 30 30 6

16 0.018 0.0102 30 30 6

17 0.018 0.0102 30 30 6

18 0.018 0.0102 30 30 6

19 0.018 0.0102 30 30 6

20 0.018 0.0102 30 30 6

0 10 20

-0.8-0.6-0.4-0.20.00.20.40.60.81.0

-0.8-0.6-0.4-0.20.00.20.40.60.81.0

27.0

28.5

30.0

31.5

33.0

27.0

28.5

30.0

31.5

33.0

5

6

7

0 10 20

b1(m

)

Trails

b2(m

)

B1(de

g)

B2(de

g)

Z

Figure 6 Performance of Pattern Search algorithm

From Fig 6, it is evident that there has not been any change in the existing design that the

Pattern Search solver identifies and there has not been any change in the head of the pump.

Table 6 PSO result table

Trial. No b1(m) b2(m) B1(deg) B2(deg) Z

1 0.0198 0.01122 32.99999 27 7

2 0.0198 0.01122 33 27 6.999999

3 0.0198 0.01122 33 27 7

4 0.0198 0.01122 32.97518 27 7

5 0.0198 0.01122 32.99998 27 7

6 0.0198 0.01122 32.99998 27 7

7 0.0198 0.01122 32.98641 27 7

8 0.0198 0.01122 33 27 7

9 0.0198 0.01122 32.99998 27 7

10 0.0198 0.01122 32.99999 27 7

11 0.0198 0.01122 33 27 7

12 0.0198 0.01122 32.99837 27.00047 7

13 0.0198 0.01122 32.99995 27 7

14 0.0198 0.01122 33 27 7

15 0.016914 0.011219 33 27 7

16 0.016914 0.01122 32.99999 27.00002 6.999999

17 0.0198 0.01122 32.99998 27 7

18 0.0198 0.01122 32.99999 27 7

19 0.0198 0.01122 33 27 7

20 0.0198 0.01122 32.99992 27.00016 7



0 10 20

0.017

0.018

0.019

0.0200.0112194

0.0112196

0.0112198

0.011220032.97

32.98

32.99

33.00

27.0000

27.0002

27.0004

27.0006

6.9999990

6.9999995

7.0000000

0 10 20

b1(m

)

Trails

B1(d

eg)

B2(d

eg)

Figure 7 Performance of Particle swarm Optimization algorithm

From Fig-7, it is identified that there is not been much variations in any of the parameter

and the solver solves more evenly than that of GA and PS, The head for these parameters the

head of the pump increases significantly.

Table 7 Optimized parameters

Method

Inlet

width-b1

(m)

Outlet

width-b2

(m)

Inlet

angle-β1

(deg)

Outlet

angle-β2

(deg)

No.of

blades-Z Head (m)

Existing Design 0.018 0.0102 30 30 6 23.2

GA 0.0195 0.011 32 27 7 29.36

PS 0.018 0.0102 30 30 6 23.2

PSO 0.0195 0.011 33 27 7 29.37

From table 5.7 it is identified that the maximum head of 29.37m is contributed by PSO.

Hence these design parameters are taken for simulation purposes.

5.4. Theoretical characteristics of optimized design:

The design changes contributed by PSO were used to calculate the theoretical head developed

along with the loss estimation.

Table 8 Theoretical head of optimized design

Discharge

(m3/s)

Theoretical

Head (m)

Circulation

head (m)

Inlet Incident

Loss (m)

Frictional

head (m)

Net Head

(m)

0 45.2063

11.5677

0 0 33.64

0.00605 41.103 0.1428 0.0181 29.37

0.01034 38.1934 0.4173 0.0529 26.16

0.01372 35.901 0.7346 0.0931 23.51

0.0158 34.4903 0.9743 0.1234 21.83

0.0166 33.9477 1.0754 0.1363 21.17

Z



Figure 8 Circulation head loss comparison

From fig-8, indicates that the circulation head for the pump has decreased by 22.17%. The

circulation head loss remains constant due to the fact that the speed remains constant [1]. The

decrease is due to the increase in the slip developed in the flow at outlet and independent of

the discharge.

Figure 9 Inlet incident loss comparison

From the fig-9, indicates a decrease of 32.67% in the inlet incident loss at duty point. This

is contributed by the increase in inlet width of the impeller, by the fact that the outlet whirl

velocity is dependent on the discharge and so it is observed as in Eq-3.

Figure 10 Frictional head loss comparison

From the fig-10, it is identified an increase by 1.11% in frictional loss which is

contributed by decrement in the outlet angle. This value of increase is not significant for all

the discharge.

0

2

4

6

8

10

12

14

16

0 0.00605 0.01034 0.01372 0.0158 0.0166

Hea

d (

m)

Discharge (m3/s)

Circulation Head Loss

Existing Circulatoin head (m) Optimized Circulatoin head (m)

0

0.5

1

1.5

2

0 0.00605 0.01034 0.01372 0.0158 0.0166

Hea

d (

m)

Discharge (m3/s)

Inlet Incident Loss

Existing Inlet Incident Loss (m) Optimized Inlet Incident Loss (m)

0

0.05

0.1

0.15

0 0.00605 0.01034 0.01372 0.0158 0.0166

Hea

d (

m)

Discharge (m3/s)

Frictional Head Loss

Existing Frictional head (m) Optimized Frictional head (m)



5.5. Simulation of the Optimized Design

Finally the optimized design was simulated to find its effectiveness compared to the existing

design. This design was tested as in the section 5.3; k-epsilon turbulence model was used to

simulate the model and it was found that there is 2.36% improvement in the head.

Figure 11 Simulated result of optimized impeller

This improvement is mainly contributed by increased number of vanes in other words the

increased slip of the flow at the impeller outlet, head has increased.

5.6. Experimentation of the Optimized Design

After simulation the design was fabricated with grey cast iron and it was tested according to

the industry specified voltage of 415V. The Discharge valve was fully closed to measure the

shutoff condition and fully opened for 'full open condition'. The discharge was noted by

varying the head in terms of 5m, the results are tabulated in table-5.9.

Table 9 Optimized impeller performance by experimentation

Discharge (m3/s) Experimental head(m)

Input Power

(W)

Water Power

(W) Efficiency (%)

0 30 4077 0 0

0.00681 25 5357 1670.2 31.2

0.00997 20 6051 1956.1 32.3

0.01318 15 6338 1939.4 30.6

0.01487 12 6646 1750.5 26.3

0.01621 5 6683 795.1 11.9

Figure 12 Efficiency comparison

From the Fig-12, it is clear that the efficiency of the pump at duty point has significantly

increased by 20.42%. This increase was compensated at the full open condition of the pump

0

20

40

0 0.00605 0.01034 0.01372 0.0158 0.0166

Eff

icie

ncy (

%)

Discharge (m3/s)

Efficiency

Optimized Efficency (%) Existing Efficiency (%)



by decrease of 33.4% according to 2nd

law of thermodynamics, but as the pump is not

operated at full open condition, this could be neglected.

Figure 13 Head Vs discharge curve comparison

From Fig-13, it is clear that there has been significant increase in head and at duty point

the increase is 12.56%. But this increase is compensated at the full open condition by a

discharge of 0.01621m3/s, by 2

nd law of thermodynamics.

Figure 14 Performance graph of optimized impeller

Fig-14 was constructed according to [1]. It shows optimized head with increased

discharge by 12.56%. As the discharge increases the efficiency calculated by Eq-7 remains

almost a straight line in the range of 26% to 31%. The head exhibits almost linear

characteristics.

The work is wrapped up by comparing the improvement in the performance and the

changes in the parameters. It could be shown in table-5.10 that the changes in the parameters

are within the 10% variation [12]. All the means of evaluating the performance has shown

the improvement and is listed in table-5.11.

Table 10 Design parameters of the impeller

Parameters Existing dimension Optimized dimension

Inlet width (m) 0.018 0.0195

Outlet width (m) 0.0102 0.011

Inlet angle (deg) 30 33

Outlet angle (deg) 30 27

No.of blades 6 7

0

5

10

15

20

25

30

35

00.6

61.3

21.9

82.6

43.3

3.9

64.6

25.2

85.9

46.6

7.2

67.9

28.5

89.2

49.9

10

.56

11

.22

11

.88

12

.54

13

.213

.86

14

.52

15

.18

15

.84

16

.5

Hea

d (

m)

Discharge (L/s)

H Vs Q Curve

Experimental Head (m) Optimized Head (m)

0

5

10

15

20

25

30

35

0 0.00681 0.00997 0.01318 0.01487 0.01621

Discharge (m3/s)

Optimized Performance

Optimized Efficency (%) Optimized Experimental head(m)



Table 11 Optimized Head

Method Percentage improvement (%)

Theoretical 17.48

Simulation 2.36

6. CONCLUSIONS

A commercially available pump with duty point delivery head of 25m and discharge of

0.00605m3/s was desired to improve the delivery head of the pump. In order to optimize the

head, the head losses within the impeller were identified and the design parameters of

impeller that contribute to these losses were measured and used to calculate the head of the

pump. The existing performance of the pump was evaluated by experimentation and the H-Q

characteristics were determined. Once the design was optimized, to check the optimization

CFD simulation was performed on the existing design for choosing the turbulence model. As

suggested by [11] different turbulence models were used to simulated the duty point condition

and K-ε model proved close to the net theoretical head, hence it was chosen to evaluate the

optimized design. The mathematical model developed for the head (with losses) was used as

objective function and design parameters were given variation of 10% from the existing

dimensions. Popular algorithms for design optimization as specified in [4] were used,

include: Genetic algorithm (GA), Particle swarm optimization (PSO), Pattern search

algorithm (PS). The optimization code was made to run for 20 trails as in [4] and the average

were taken as the optimized parameters. It was observed that PSO algorithm contributed

maximum head by 17.48% improvement. The changes in losses were: Circulation loss

decreased by: 22.17%; Inlet incident loss decreased by 32.67% ; Frictional loss increased by

1.11%. The increase in frictional loss is due to the fact that there is decrease in the outlet

angle. As a pre-final step in the design process simulation of the duty point was done for the

pump with K- ε model and it was found that there was an improvement by 2.36% in the head.

The optimized impeller design was then casted and experimentation as described in [1] were

conducted and it was found that there was an improvement of 12.56% in delivery head of the

pump at duty point and efficiency of the pump at duty point increased by 20.42%.

Figure 15 Existing impeller



Figure 16 Optimized impeller

Figure 17 Existing and optimized impeller cut section

7. NOMENCLATURE

Hth - Theoretical head (m)

Hc - Circulation head loss (m)

Hi - Inlet incident loss (m)

Hf - Frictional head loss (m)

Hnet - Net theoretical head loss (m)

Q-Discharge (m3/s)

b2- Width at exit (m)

b1- Width at entrance (m)

β2- Blade angle at exit (0)

β1- Blade angle at entrance (0)

D2- Impeller outer diameter (m)

D1- Impeller inlet diameter (m)

Slip µ=

Inlet tangential velocity U1 =

Outlet tangential velocity U2 =



Inlet whirl velocity C1 =

Outlet whirl velocity C2 =

Inlet whirl velocity at blade exit Cu1 = µ*

+

Outlet whirl velocity at blade exit Cu2 = µ*

+

REFERENCES

[1] Austin.J.L, Church.H, "Centrifugal pumps and Blowers," in Centrifugal pumps and

Blowers. Alahabad, India: Metropolitan Book Co, Pvt, Ltd, 1973, ch. 10, p. 214.

[2] Berge Djebedjian, "Theoretical model to predict the performance of centrifugal pump

equipped with splitter blades," Mansoura Engineering Journal, pp. M50-M70, 2009.

[3] Bacharoudis.E.C, Filios.A.E, Mentzos.M.D, Margaris.D.P, "Parametric Study of a

Centrifugal Pump Impeller by Varying the Outlet Blade Angle," The Open Mechanical

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