 Open Access
 Total Downloads : 83
 Authors : J. C. Statharas , E. S. Valamontes , P. Filiousis , N. W. Vlachakis
 Paper ID : IJERTV8IS060319
 Volume & Issue : Volume 08, Issue 06 (June 2019)
 Published (First Online): 14062019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Strategies for Predicting Centrifugal Pump Performance Characteristics by Validating Blade Shape Configurations. Introducing the Trojan Horse Method
J. C. Statharasa*, E. S. Valamontesb, P. Filiousisa, N. W. Vlachakisa
aNational and Kapodistrian University of Athens, Sciences General Department, Psachna, Evias, 34400, Greece.
bE.S. Valamontes, Professor, Department of Electrical & Electronics Engineering, University of West Attica, Greece.
a Professor, Corresponding Author a Ingenieur, External Research Fellow a Professor, Research Fellow
AbstractA simple and easy to apply numerical method – called Trojan Horse methodfor pump head and efficiency estimation is presented. This is a contribution on centrifugal pump characteristics prediction using empirical relations based on performance maps of known pumps developed by some researchers. The present method evaluates a specific flow rates parameter, as well as some empirical equations for impeller geometrical data. The introduced modelling equations based on the blade shape configurations provide the pump characteristic lines. The method is validated by applying it to various commercial centrifugal pumps with known performance maps produced by their developers. From the cases examined, it can be stated that the present model can be applied to predict performances of centrifugal pumps of any diameter, particularly at all efficiency regions that the pump is supposed to operate according to its geometrical data. As a result the proposed method provides a satisfactory approximation of industrial centrifugal pumps performance curves, constituting a potential tool for pump researchers and manufacturers.
Rotating Shaft
Impeller
Hub Plate
Outflow
Blade
Inflow
KeywordsCentrifugal pump, performance map, empirical method, impeller, characteristic line, numerical prediction.
1 INTRODUCTION

Centrifugal pump description
Centrifugal pumps are the most common type of pumps used to move fluids through a piping system. They are devices that find extensive applications particularly in mining, chemical and mechanical industry.The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward or axially into a diffuser or volute chamber, from where it exits into the downstream piping system. The main parts of a centrifugal (or radial) pump are shown in Fig.1.1.
Casing
Eye
Fig.1.1. Main components of a centrifugal pump (Taken from [47])

Impeller's geometry
The basic component of a centrifugal pump is a rotor (or impeller) in which a number of blades is attached (see Fig.1.2). Fig.1.3 shows the impeller geometry explaining its main geometrical characteristics.
Fig. 1.2: Schematic view for a fivebladed impeller model
Fig. 1.3: Impeller's main geometrical characteristics (Taken from [48]) D1=impeller inlet diameter, D2=impeller exit diameter, b1=blade angle at impeller leading edge, b2=blade angle at impeller trailing edge, w=wrap
angle.

Previous Design efforts
Centrifugal pumps are designed in order to be fitted to installations and work over a wide range of operating conditions. In such cases the prediction of performance is of primary importance for safe and effective operation of pumps and constitutes an important challenge for the pump designer. The challenge becomes particularly difficult when it is necessary to predict the performance of different types of centrifugal pumps varying from low to high volume flow rates.
Improving pump efficiency needs a good understanding of its components behavior at design point and offdesign conditions. As measurement technologies for more accurate flow field studies are limited and they are expensive, due to complicated nature of geometry and the flow itself, numerical models have been developed and extended for performance prediction and primary design steps. However,
numerical results would be more reliable if more experimental data were available for validation.
Last years the trend in pump industry [16] is to emphasize to the blade shape configuration. The reason behind this trend is the need for an effective way to achieve fast predictions methods for pump maps construction avoiding multiple steps in the test rig, [711] .
The principal objective of centrifugal pump design effort, according to [1218] is the effective matching between pump operation and impeller geometry. It is important to choose such a centrifugal pump morphology that the pumps operating line falls within the pumps highefficiency region [1927] . Therefore, a variety of approximate methods or numerical precedures have been developed aiming to predict centrifugal pump performance characteristics [28,33] .
Predictions of centrifugal pump performance maps were also obtained by using advanced 3D Computational Fluid Dynamics (CFD) techniques, most commonly solving the Reynolds Averaged Navier Stokes (RANS) equations, coupled with a turbulence model. However there are a number of disadvantages when using CFD methods except their high computational cost and the lack of experimental data for validation.
Sometimes for example, prediction of centrifugal pump performance constitutes an important challenge when a pump has to be manufactured in order to be fitted in a given installation and to work over a wide range of operating conditions, [30], [31], [32]. The challenge becomes particularly difficult when is needed to predict the performance of different types of centrifugal pumps varying from low to high volume flow rates Pfeiderer [7]. In all these cases characteristic curves are not always available to evaluate the adequacy of the pumps performance for a particular situation and CFD methods canot help adequately. As a result there is a need for fast practical but accurate methods as the one presented in this work.

The current approach
The present study presents a fast method to estimate pump performance characteristics requiring only a few pump geometrical data. Centrifugal pump performance curves were produced using polynomial functions while the experimental data points were known by the pumps test rig measurements. By using efficiency curves from six different known pumps,we tried to find a closed form for the coefficients of the head performance that approximates the performance maps. Alternative curve fitting methods using exponential as well as polynomial functions for the blade angle =f() or the volute radius =g() were proposed too.
The first step of method presented here, (named The Trojan horse method) is to propose algorithms for the internal geometry of the impeller blades. As a second step calculates the distribution of the degree of efficiency as a function of both the nq and the morphology of the blade curvature. From the proposed efficiency polynomial results by integrationwith appropriate approachesthe polynomial of manometer characteristic distribution. That is, that starting from internal blading we finally end up by obtaining the final pump characteristics. Due to the fact that starting with a few internal pump features we finally get to know the characteristics of the
pump as a whole we have called our method: The Trojan horse method.
The overall efficiency is estimated, not only the head. The numerical predictions are compared to experimental data for centrifugal pumps delivering low, medium and high volume flows. The data was either obtained in the test rig or found in the literature.
The results show that the proosed method can be used as a tool to the pump designer in order to obtain a quick assessment of performance curves.
Taking into account the challenging complexity of centrifugal pump performance map prediction, the present article aims to simplify and generalize to the extent that it is possible a method focused on sizing centrifugal pumps, predicting their performance map from very low to very high volume flow rate, requiring only a minimum number of geometrical data that is readily available.
Most of the authors cited in the literature survey above have analyzed several pumps geometries in their studies. In the present article these pumps are examined as applications to evaluate the increased applicability of the method, called Trojan horse method.

CALCULATIONS METHODOLOGY

General Assumptions
According to the present design procedure, we assume that there is a casing that encloses the outer circumference of the radial impeller.The design approach assumes that a vortex phenomenon is mainly responsible for the fluid transport[34 38]. The present method employs a group of empirical euations in terms of a polynomial algorithm in order to estimate the pump performances.The input data required are the following:

Impeller inlet diameter, D1,

Impeller exit diameter, D2

Number of impeller blades, z

Blade angle at impeller trailing edge, 2
The basic assumptions of the present method are the following:
(i) Empirical equations for max are developed for different impeller's rotational speeds,
(ii) The prediction method takes into account the flow in the pump impeller as well as the effect of volute.


Methodology
The main steps of the pump performance map prediction procedure are the following :
Step 1: Estimation of the operable volume flow rate employing novel empirical relations and using impeller geometrical data.
Step 2: Approximation of the performance curves for various impeller speeds by means of novel empirical functions.
The originality of the present method lies on:

the calculation of the shutoff maximum head attained by the pump,

the derivation of a set of equations that estimate the volume flow rates at each constant speed characteristic line of the centrifugal pump and

the suggestion of novel empirical relations for the shape of the characteristic curves of the performance map such as a(,wrap angle) and b ( nq ).
2.2.1 Distribution Strategy
All the above described equations contain an algorithm for the pump impeller geometrical data, its blade number and its rotational speed.
When designing centrifugal impeller, the pump impeller and the geometric parameters of the design point must achieve the pump design conditions and maximum efficiency, max. However max varies with w. We used Eq.3.6 to examine the effect of wrap angle on max. The results are shown in Table

and Fig.2.1. We see that.max increases until w=1000, then decreases. Thus, each centrifugal pump with exact parameters at the design point has perfect max at a specific wrap angle.
Table 2.1 Calculations of efficiency as a function of wrap angle
w
max=1.6[2(106)w3+0.00045w20.03w+1.1] [28]
50
0.76
55
0.7656
60
0.7808
65
0.8032
70
0.8304
75
0.86
80
0.8896
85
0.9168
90
0.9392
95
0.9544
100
0.96
105
0.9536
110
0.9328
115
0.8952
120
0.8384
125
0.76
1,2
1
0,8
0,6
0,4
0,2
0
40 50 60 70 80 90 100 110 120 130
w
1,2
1
0,8
0,6
0,4
0,2
0
40 50 60 70 80 90 100 110 120 130
w
n max
n max
Fig.2.1.Efficiency as function of wrap angle
,2
0,15
0,1
0,05
0
0,05
0,1
0,15
0,
,2
0,15
0,1
0,05
0
0,05
0,1
0,15
0,
Convenient forms of the blade angle are shown below in Tables 2.2 and 2.3 where: (r1) = 1 , (r2) = 2 or r(1) = r1 , r(2) = r2 . The constants and c in Tables 2.2 and 2.3 are calculated by curve fitting experimental results.

In the case that we know r and try to find then any distribution pattern for r from Table 2.2 can be chosen. In the case however that we only choose the algorithmic status for a parameter or r, then the combinations may be variegally complex or they can only come from the linear patterns. This
means that when a model function is selected, the other one 0 2
must be linear.
Table 2.2: The blade angle distribution models
= (r)
Conditions : 1=(r1), 2=(r2)
= r+c/r
1= r 1+ c/ r 1 , 2= r 2+ c/ r 2
= r ecr
= r ecr1 = r ecr2
1 1 , 2 2
= ecr
= ecr1 = ecr2
1 , 2
= r2 + c
= r 2+ c = r 2+ c
1 1 , 2 2

In the case that we know and try to find r then any distribution pattern for from Table 2.2 can be chosen..
In addition to Sigloch [40], Menny [41] or Bowade [42] fluid dynamic models, practical applications allows the presentation of functions that can analogously approximate the curvature that clearly results from the impeller geometry.
Table 2.3: The blade mean line configuration models
r = r ()
Conditions: r1=r(1), r2=r(2)
r = r e( a + c) 2
r = r e(a 1+ c ) r = r e(a 2+ c ) 1 2 , 2 2
r = r 1+ c
r 1= r 1+ c1 , r 2= r 2+ c2
r = (/ ) ec
r = ( / )ec r = ( / )ec
1 1 , 2 2
r = e(a 2+ c)
r = e( a 2+ c ) r = e( a 2+ c)
1 2
1 , 2

Criteria for optimum pump design
For a certain number of revolutions, both the angle selection as well as the manometer head and the flow rate should give a tracking match to the blade curvature (Fig.2.2) for the different methods (Sigloch [40] , Menny [41] , Bowade
[42] ) for = max = w [39].Fig.2.2 : Representation of a present study model
The details of the calculations and a summary of the various impeller geometrical constants are tabulated in Table 2.4.
r=*e(c/)
Xr=rcos(w/180)
<>Yr=rsin(w/180) w (linear)
0W
0.0391612
0.03916121
0
0
0.0431289
0.04140874
0.012058868
14.68679
0.0473821
0.04015604
0.025150709
29.37359
0.0519305
0.03509634
0.038275598
44.06038
0.0567829
0.02621048
0.050371751
58.74718
0.061948
0.01376966
0.060398232
73.43397
0.0674334
0.0016848
0.067412309
88.12077
0.0732463
0.019381
0.070635657
102.8076
0.0793932
0.0383706
0.069505244
117.4944
0.0858798
0.0575919
0.063706558
132.1812
r=*e(c/)
Xr=rcos(w/180)
Yr=rsin(w/180)
w (linear)
0W
0.0391612
0.03916121
0
0
0.0431289
0.04140874
0.012058868
14.68679
0.0473821
0.04015604
0.025150709
29.37359
0.0519305
0.03509634
0.038275598
44.06038
0.0567829
0.02621048
0.050371751
58.74718
0.061948
0.01376966
0.060398232
73.43397
0.0674334
0.0016848
0.067412309
88.12077
0.0732463
0.019381
0.070635657
102.8076
0.0793932
0.0383706
0.069505244
117.4944
0.0858798
0.0575919
0.063706558
132.1812
Table 2.4 Blade drawing positions
360 n 3.793 2 n + 434.9 2
w= [ 0.5793exp( q ) + 2.158exp( q ) ]
z 89.87
1087
,(2.1)
The basic function of a blade (Fig.2.2, Table.2.4) is to guide the flow. This means, that to impose a certain direction to the flow, the blade angle at a certain radius (r) should be imposed to the flow, guiding the flow to follow the same direction (Fig.2.2, Table.2.4 ).

Volume flow estimation
The pump total head depends on the tangential velocity at impeller outlet (see Fig.2.3) expressed as:
u2=D2n
Fig.2.3: Velocity triangle at impeller
There is a variety of available correlations for the slip factor introduced in and verified against experimental data. The correlation adopted here, is the one suggested:

Head estimation
The present method proposes an original formula to calculate the head attainable, where a correction coefficient depending on the exit diameter D2 is adopted.
Equation approximates the maximum efficiency of centrifugal pump as a function of the blade tip configuration , based on the flow analysis performed.
The maximum head obtained by a centrifugal pump corresponds to throttling conditions, where the volume flow is zero.

Efficiency performance curves estimation
It is intended to approximate the shape of characteristic lines by means of a function which starts from a head high value when the ratio is close to zero (corresponding to shut – off) and decays asymptotically as the ratio approaches the value 1 (corresponding to maximum value of the efficiency). The challenge of equations is to approximate the different shapes of centrifugal pump characteristic lines varying from low to high rotational speeds.

Volute design
The volute contour of the investigated pumps [9] when operating at a design volume flow rate, was found by applying some models that appear in Table. 2.5. In this Table, refers to the volute wall curvature and 0 is the diffusor's angle. A program of experiments to see the formation of the flow, particularly through the region of the fixed pump blades was carried out in.
Table 2.5: The volute shape models
R=R() the volute shape
The shape design
The Archimedes' Shaped Spiral
for 2 < < 4
Model
X=Rcos(1.57/90)
for 0 < < 2
y=Rsin(1.57/90)
R=ar2+c
The LogarithmicShaped
for 2 < < 4
Spiral Model
X=R*cos(1.57*/90)
for 0 < < 2
y=R*sin(1.57*/90)
R = 1.1r2ea+c
Diffusor shape
Coordinates positions of the blade tip
x y
1 0
2
for 2 < < 4, 1 < < 1.95
1 = r2e[(ln2)/360ln2]
2=r2(1.01+0.08nq/100+0.07HBEP/
1000)
Diffusor wall
diffusor angle 0<<5 = 1+2tan(1.57/90)
The form and the constructional details of the volute geometry model are illustrated in Fig.2.4.
Fig.2.4: Typical arrangement of the casing with diffusor



RESULTS
In order to evaluate the accuracy of the model described above, various commercial pumps were considered as test cases, since their performance maps are available by their manufacturers. These maps were digitized using an appropriate software in order to be compared with the present methods results. For these pumps there were found numerical predictions in the literature, according to the authors knowledge. Table 3.1 summarizes the most important data of the pumps chosen for the performance map prediction.
Pump name 
b2 (mm) 
D2 (mm) 
2 
z 
QBEP (m3/h) 
HBEP (m) 
n (RPM) 
[1] 
10 
200 
490 
9 
62.5 
62 
3000 
[4] 
9 
200 
240 
5 
45.68 
46,41 
2900 
[2] 
11 
160 
230 
7 
25 
7 
1450 
[5] 
15 
130 
200 
6 
3.6 
6 
1500 
[3] 
30 
300 
220 
6 
200 
20 
1450 
[6] 
26 
240 
250 
6 
98 
68 
2900 
62
Pump name 
b2 (mm) 
D2 (mm) 
2 
z 
QBEP (m3/h) 
HBEP (m) 
n (RPM) 
[1] 
10 
200 
490 
9 
62.5 
3000 

[4] 
9 
200 
240 
5 
45.68 
46,41 
2900 
[2] 
11 
160 
230 
7 
25 
7 
1450 
[5] 
15 
130 
200 
6 
3.6 
6 
1500 
[3] 
30 
300 
220 
6 
200 
20 
1450 
[6] 
26 
240 
250 
6 
98 
68 
2900 
Table 3.1: pumps characteristics at BEP
The calculational procedure for predicting the pump characteristic Curves, has as follows:
Qo=QBEP/q (3.2)
Qmax =1.6Qo (3.3)
J=Qi/QBEP (3.4)
The coefficient j modulates the empirical equations to the real performance curves of the pump geometry (Fig.2.3 ). The coefficient j, represents the time interval of pumping time required for the volume flow to reach volume flow at BEP .
1=[32+145log(nq)41(log(nq))2]0.01 (3.5)
2=[2(106)w3+0.00045w20.03w+1.1]1.6 (3.6)
1,9 0,1 0,5
1,9 0,1 0,5
max=(1 2 ) (3.7)
=0.86max[(z/7)0,1)(1.33j0,70.3j3)] (3.8)
H =Hu[10.1j1,70.035j4] (3.9)
0,66
0,66
2 1
2 1
Hu=HBEP/h, Hth=(u 2u 2)/9.81, Hshut off =HBEP/m (3.10) where
q=1/[1+0.28/nq ] is the volumetric efficiency (3.11) m=1/[1+1/nq] is the mechanical efficiency (3.12)

GrapsasAnagnostopoulosPapantonis [1]
70
50
40
50
40
HeadH(m)
HeadH(m)
60
grapsas et al
grapsas et al
30
20
10
0
0 20 40 60 80 100
Flow rate Q(m3/h)
Figure 3.2 Using present model to predict pump [1] ead characteristics

Zhang Yongxue, Zhou Xin, Ji Zhongli and Jiang Cuiwei [4]
h=10.071/QB 0,25 is the hydraulic efficiency (3.13)
EP
is the blade number effect factor [3438,4346] as
=0.013z2+0.1725z+0.51 (3.14)
is the overall efficiency and nq is the specific speed
We used Eq.3.8 and Eq.3.9 to obtain head and efficiency for different numbers of blades (z=59). The simulation (Fig.3.1) showed strong effect of the number of blades on . The blade effect factor (Fig.3.1) increases obviously with a specific number of blades, then decreases. Thus, each centrifugal pump with exact parameters at the design point has perfect head and efficiency performances at a specific blade number.
70
60
HeadH(m)
HeadH(m)
50
Zhang Yongxue et al
Zhang Yongxue et al
40
30
20
10
0
20 25 30 35 40 45 50 55 60 65 70
Flow rate Q(m3/h)
Blade numper effect factor
Blade numper effect factor
1,2
1
0,8
0,6
0,4
0,2
0
0 1 2 3 4 5 6 7 8 9 10
1,2
1
0,8
0,6
0,4
0,2
0
0 1 2 3 4 5 6 7 8 9 10
Figure 3.3 Using present model to predict pump [4] ead characteristics

Lei Tan, Shuliang Cao, Yuming Wang and Baoshan Zhu [2]
Blade numper Z
Blade numper Z
Fig.3.1. The relation between blade number effect factor and the
number of blades z.
Figs.3.23.7 present the calculational results of the above equations (3.23.14) compared to the real pump data of Table
3.1. In these figures the two procedures (experimental vs predicted) are shown as poly. As we can see, (Figs.3.23.7) the approach with the new prediction method is very good, since the curves created are close to the actual operating points of the pumps given by the six authors [16].
10
9
8
lei tan et al
lei tan et al
7
HeadH(m)
HeadH(m)
6
5
4
3
2
1
0
5 10 15 20 25 30 35
Flow rate Q(m3/h)
Figure 3.4a Using present model to predict pump [2] ead
characteristics
0,9
0,8
0
0
0
0
Efficiency
Efficiency
0,7
,6
,5
0,4
0,3
0,2
0,1
0
5 10 15 20 25 30 35
Flow rate Q(m3/h)
3.5 Xin Zhou, Yongxue Zhang, Zhongli Ji, and Long Chen [3]
25
15
10
15
10
lei tan et al
lei tan et al
HeadH(m)
HeadH(m)
20
xin zhou et al
xin zhou et al
5
Figure 3.4b Using present model to predict pump [2] efficiency

A. Farid Ayad Hassan, H. M. Abdalla, A. Abou El Azm Aly [5]
6
5
HeadH(m)
HeadH(m)
4
A. Farid Ayad et al
A. Farid Ayad et al
3
2
1
8 10 12 14
8 10 12 14
0
0
0,9
0,8
0,7
0
0
0
0
0
0
Efficiency
Efficiency
,6
,5
,4
0,3
0,2
0,1
0
50 100 50 300
150 200 2
150 200 2
Flow rate Q(m3/h)
Figure 3.6a Using present model to predict pump [3] ead
characteristics
xin zhou
xin zhou
2 4 6
Flow rate Q(m3/h)
16 18 20
50 100 50 300
150 200 2
150 200 2
Flow rate Q(m3/h)
Figure 3.5a Using present model to predict pump [5] ead
characteristics
Figure 3.6b Using present model to predict pump [3] efficiency
3.6 Tahani & Pourheidari [6]
0,9
0,8
0,7
0
0
0
0
0
0
Efficiency
Efficiency
,6
,5
,4
0,3
0,2
0,1
0
8 10 12 14
8 10 12 14
A. Farid Ayad et al
A. Farid Ayad et al
2 4 6 16 18 20
Flow rate Q(m3/h)
90
80
70
60
40
30
40
30
HeadH(m)
HeadH(m)
50
20
10
0
80 90 100110120
80 90 100110120
40 50 60 70 130140
Flow rate Q(m3/h)
tahani et al
Figure 3.5b Using present model to predict pump [5] efficiency
Figure 3.7a Using present model to predict pump [6] ead
characteristics.
0,8
0,7
0,6
0
0
0
0
0
0
Efficiency
Efficiency
,5
,4
,3
0,2
0,1
0
40 60
80 100
80 100
Flow rate Q(m3/h)
120 140
tahani et al
performance curves of six pumps. The pump characteristics performances have been tested on different types of centrifugal pumps and the obtained results prove the accuracy and high capability of the implemented method.
Conclusively, the proposed method could be beneficial to the pump industry in the early design stages. Future work will cope with the extension of the method to predict the head and the efficiency of more than 100 centrifugal pumps.
td>
Impeller angular velocity
Nomenclature
D
Impeller diameter
n
Rotational speed
H
Pump Head
z
Blade number
Q
Volumetric flow rate
b
Blade width
R
Radius
Greeks
Blade angle
Efficiency
Inclination angle
Fluid density
Subscripts
1
Impeller inlet
2
Impeller outlet
Nomenclature
D
Impeller diameter
n
Rotational speed
H
Pump Head
z
Blade number
Q
Volumetric flow rate
b
Blade width
R
Radius
Greeks
Blade angle
Efficiency
Inclination angle
Fluid density
Impeller angular velocity
Subscripts
1
Impeller inlet
2
Impeller outlet
Figure 3.7b Using present model to predict [6] pump efficiency

CONCLUSIONS
In this study, an original methodology for the challenging topic of centrifugal pump performance prediction for industrial applications was presented. The motivation for this work was to introduce a fast engineering assessment tool which is able to predict both the operating limits of centrifugal pumps in terms of volume flow rates as well as the shape of its performance curves. The model is based on a pioneering methodology using empirical relations of the mean flow upstream and downstream of the centrifugal impeller. The minimum and the maximum volume flows are approximated by means of genuine fist issued empirical equations. The Head and the efficiency that any pump can reach is estimated by means of the impeller outlet diameter and the local max.
Two original functions are introduced in order to generate the shape of the performance curves of the pump, namely polynomial functions. Evaluation of the method is done by considering commercial pumps with known performance maps from their researchers, of various speeds. The results obtained can be summarized in the following Table 4.1:

Good agreement at intermediate RPM

Better agreement with measurements when the polynomial functions are used

Good agreement at intermediate RPM

Better agreement with measurements when the polynomial functions are used
Table 4.1: Evaluation of results
The simple and fast method presented here was validated succesfully against some models of centrifugal pumps for which experimental data were found in the literature or from the test rig. Comparisons between numerical and experimental data obtained in the test rig show that the proposed model can satisfactorily predict performance characteristics of centrifugal pumps, for the cases examined.
As it could be observed, the approximation between performance curves estimated via experiments test or via empirical mathematical formulas is quite good. In this way the performance of a typical centrifugal pump could be mathematically provided without the need of the expensive experimental procedure.
The development of the present study calculational procedure is due to the fact that centrifugal pumps have an important contribution in industrial world. Accordingly to the international standards of centrifugal pumps, the present study presents an analysis system for obtaining the
REFERENCES

Vasilios A. Grapsas, John S. Anagnostopoulos and Dimitrios E. Papantonis, PARAMETRIC STUDY AND DESIGN OPTIMIZATION OF A RADIAL FLOW PUMP IMPELLER , 2nd International Conference From Scientific Computing to Computational Engineering 2nd ICSCCE Athens, 58 July,2006Â©ICSCCE

Lei Tan, Shuliang Cao, Yuming Wang and Baoshan Zhu Direct and inverse iterative design method for centrifugal pump impellers , Proc IMechE Part A: J Power and Energy 112 , IMechE 2012

Xin Zhou, Yongxue Zhang, Zhongli Ji, and Long Chen , The Impeller Improvement of the Centrifugal Pump Based on BVF Diagnostic Method , Hindawi Publishing Corporation Advances in Mechanical Engineering 2014.

Zhang Yongxue, Zhou Xin, Ji Zhongli and Jiang Cuiwei , Numerical Design and Performance Prediction of Low Specific Speed Centrifugal Pump Impeller , International Journal of Fluid Machinery and Systems DOI: 10.5293/IJFMS.2011.4.1.133 Vol. 4, No. 1, JanuaryMarch 2011

A. Farid Ayad Hassan , H. M. Abdalla , A. Abou ElAzm Aly CENTRIFUGAL PUMP PERFORMANCE ENHANCEMENT BY BLADE SHAPE MODIFICATION , Proceedings of ASME Turbo Expo 2017 : Turbomachinery Technical Conference and Exposition GT2017 June 2630, 2017, Charlotte, NC, USA

M. Tahani, V, Pourheidari , Numerical Study of Incompressible Viscous and Turbulent Flow through the Centrifugal Pump ,Fluid Mechanics Letters 1 (2017) 2735

Pfeiderer, C., 1938, Vorausbestimmung der Kennlinien schnelllÃ¤ufiger Kreiselpumpen. VDI, DÃ¼sseldorf.

Engeda, A., 1987, Untersuchungen an Kreiselpumpen mit offenen und geschlossenen LaufrÃ¤dern im Pumpen und Turbinenbetrieb. Ph.D. thesis TU Hannover.

Athanassiadis, doctor thesis 1961 ETHZuerich ,Potential flow through spiral casings,

GÃ¼lich, J.F., 1988, Bemerkungen zur KennlinienstabilitÃ¤t von Kreiselpumpe. Pumpentagung Karlruhe, B3.

Japikse, D., Marscher, W.D., Furst, R.B., 1997. Centrifugal Pump Design and Performance, Concepts ETI Inc., Vermond.

Karassik, I.J., Krutzsch, W.C., Fraser, W.H. and Messina J.P., 1976, Pump Handbook, McGrawHill Book Co, New York.

Amminger, W.L., Bernbaum, H.M. 1974. Centrifugal pump performance prediction using computer aid, Computers and Fluids, 2, pp.163172.

Yedidiah S., 2003, An overview of methods for calculating the head of a rotordynamic impeller and their practical significance, Proceedings of the Institution of Mechanical Engineers, Part A: Journal Process Mechanical Engineering, 217(3), pp.221232.

Auslaender J.,Hauptabmessungen von Kreiselpumpen, Zeitschrift Konstruktion, 10 Jahrgang, 1958, pp 407410.

Bohl W., Stroemungsmaschinen I and II, VogelVerlag, 1998.

Vlachakis N. 1974. Vergleich zweier GeschwindigkeitansÃ¤tze fÃ¼r die radiale Spaltrichtung in Bezug auf das Drehmoment der rotierenden Scheibe. Bericht Uni Karlsruhe

Berichte von Stroemungsmaschinenstroemungslehre reihe ,
Universitaet Karlsruhe

Wesche, W.: Experimentelle Untersuchungen am Leitrad einer radialen Kreiselpumpe. Dissertation, TU Braunschweig (1989)

Schubert,F.:Untersuchungen der Drucku. Geschwindigkeitsverteilung in RadseitenrÃ¤umen radialer Kreiselpumpen. Dissertation, TU Braunschweig (1988)

Pfleiderer, C.: Die Kreiselpumpen fÃ¼r FlÃ¼ssigkeiten und Gase, 5. Aufl.
Springer, Berlin 1961

Stepanoff, A.J.: Radial und Axialpumpen, 2. Aufl. Springer, Berlin (1959)

SÃ©dille, M.: TurboMachines Hydrauliques et Thermiques. Masson & Cie (1967).

Busemann, A.: Das FÃ¶rderverhalten radialer Kreiselpumpen mit logarithmischspiraligen Schaufeln. ZAMM 8(5), (1958)

Kaewnai S, Chamaoot M and Wongwises S 2009. Predicting performance of radial flow type impeller of centrifugal pump using CFD J. Mech. Sci. Techno. 23, pp 16201627.

Anagnostopoulos J, 2006. CFD Analysis and Design Effects in a Radial Pump Impeller WSEAS Transactions on Fluid Mechanics,1,pp 763770

Mentzos M, Filios A, Margaris P and Papanikas D 2005. CFD predictions of flow through a centrifugal pump impeller. Proceedings of International Conf. Experiments/Process/System Modelling/ Simulation/Optimization. Athens, pp. 18.

Paeng, K.S., Chung, M.K., A new slip factor for centrifugal impellers, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Vol.215, 2001, pp.645649.

Bronshtein, I.N., Semendyayef, K.A., Musiol, G., MÃ¼hlig, H., Handbook of Mathematics, sixth edition, SpringerVerlag, 2015.

Samani, Z., 1991, Performance estimation of closecoupled centrifugal pumps. American Society of Agricultural Engineers, 7, pp.563565.

A & M Emami,Design and Implementation of an Online Precise Monitoring and Performance Analysis System for Centrifugal Pumps IEEE Transactions on Industrial Electronics 2017

ANDRZEJ WILK, The Analysis of the Influence of the Initial Impeller on the Discharge and the Delivery Head of High Speed Pump with Radial Blades Volume 4, October 2009

A. J. Acosta R. D. Bowerman AN EXPERIMENTAL STUDY OF CENTRIFUGAL PUMP IMPELLERS Report No. E19. 8 August 1955 – Office of Naval Research Department of the Navy

Angela Gerlach The Influence of Impeller Designs on the Performance of a Vortex Pump, Berlin thesis 2018.

Hayder Kareem Sakran, NUMERICAL ANALYSIS OF THE EFFECT OF THE NUMBERS OF BLADES ON THE CENTRIFUGAL PUMP PERFORMANCE AT CONSTANT PARAMETERS International Journal of Mechanical Engineering and Technology (IJMET) Volume 6, Issue 8, Aug 2015, pp. 105117

E. Korkmaz, M. GÃ¶lcÃ¼ and C. Kurbanolu Effects of Blade Discharge Angle, Journal of Applied Fluid Mechanics, Vol. 10, No. 2, pp. 529540, 2017.

Amin Habibi Sarbanani, A numerical study on the influence of the blade number and rotational speed on the centrifugal pump performance under twophase flow Journal of Engineering (IOSRJEN)
International organization of Scientific Research ,2016

K.M. Pandey, A.P. Singh and Sujoy Chakraborty , NUMERICAL STUDIES ON EFFECTS OF BLADE NUMBER VARIATIONS ON PERFORMANCE OF CENTRIFUGAL PUMPS AT 2500 RPM, Journal of Environmental Research And Development Vol. 6 No. 3A,
JanMarch 2012863

Hydraulic design method for low specic speed overload free centrifugal pump impeller, google patent ,20141126 CN 201410712052

Ashish Bowade, Charu Parashar , A Review of Different Blade Design Methods for Radial Flow Centrifugal Pump , International Journal of Scientific Engineering and Research (IJSER) : 23473878, 2014

Menny , K Stroemungsmaschinen , TeunerVerlag 1985

Sigloch ,H Stroemungsmaschinen , HanserVerlag 1984

Adel Pourtaghia, Heidar Pouladib , Numerical Investigation of the Effect of the Number of the Blades of the Impeller on the Performance of Centrifugal Pumps Mapta Journal of Mechanical and Industrial Engineering (MJMIE), Vol. 2, No. 1, April, 2018

LIU Houlin, WANG Yong, YUAN Shouqi, TAN Minggao, and WANG Kai, Effects of Blade Number on Characteristics of Centrifugal Pumps ,CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol.23, 2010

Sujoy Chakraborty , K.M. Pandey , Bidesh Roy , Numerical Analysis on Effects of Blade Number Variations on Performance of Centrifugal Pumps with Various Rotational Speeds International Journal of Current Engineering and Technology 2012 INPRESSCO.

Hassan, Mohamed Izzedin DOCTORAL THESIS 1946 Der Einfluss der Schaufelzahl des Laufrades auf den Wirkungsgrad bei Kreiselradmaschinen eth ZUERICH.

http://www.globalpumps.in/beacon.html

Mohammed Ahmed ElNaggar, A OneDimensional Flow Analysis for the Prediction of Centrifugal Pump Performance Characteristics, International Journal of Rotating Machinery, Volume 2013, pp.119