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International Journal of Mechanical Engineering and Technology (IJMET)Volume 8, Issue 6, June 2017, pp.
Available online at http://www.iaeme.com/IJME
ISSN Print: 0976-6340 and ISSN
© IAEME Publication
EXPERIMENTAL STUDY A
EROSIVE WEAR RATE PARAMETE
A NOVEL ENT
PELTON TURBINE
Robin Thakur, Anil Kumar
School of Mechanical & Civil E
Department of Mechanical Engineering, OM Institute of Technology, Juglan (Hisar)
AP Goyal Shimla University, Himachal Pradesh, India
ABSTRACT
In this article, the effect of differe
concentration, and jet velocity has been
silt size (�) = 90-450, silt concentration (
25.492 and operating time (
a multi criteria decision making
experimental values achieved
agreement. Depend upon the Entropy
that experimental parameters
25.492 and 12 provided an best parameter
Key words: Energy, silt size, erosion, stream velocity
Cite this Article: Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana,
Muneesh Sethi Experimental Study and Op
Using A Novel Entropy Vikor Approach in A Pelton Turbine Buckets
Journal of Mechanical Engineering and Technology
http://www.iaeme.com/IJME
NOMENCLATURE
� Average grain size coefficient of suspended sediment with a base of 0.05 mm
� Silt concentration
�� Fraction of silt by weight
� Particle size
� Jet diameter
IJMET/index.asp 27 [email protected]
International Journal of Mechanical Engineering and Technology (IJMET) 2017, pp. 27–43, Article ID: IJMET_08_06_004
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=6
6340 and ISSN Online: 0976-6359
Scopus Indexed
EXPERIMENTAL STUDY AND OPTIMIZING
E WEAR RATE PARAMETERS USING
A NOVEL ENTROPY VIKOR APPROACH
PELTON TURBINE BUCKETS
Robin Thakur, Anil Kumar and Rahul Nadda
School of Mechanical & Civil Engineering, Bajhol (Solan), (HP), India
Sourabh Khurana
Department of Mechanical Engineering, OM Institute of Technology, Juglan (Hisar)
Muneesh Sethi
AP Goyal Shimla University, Himachal Pradesh, India.
he effect of different experimental factors such as
jet velocity has been examined. The experimentation
450, silt concentration (�) = 2000 - 8000, jet velocity (
25.492 and operating time () = 9-12 respectively. Hybrid Entropy-VIKOR technique,
a multi criteria decision making method (MCDM) is consequently implimented
values achieved, which measures the variant responses
upon the Entropy-VIKOR analysis method, it has been
experimental parameters of �,�, and having mathematical value of 90, 8000,
an best parameter combination respectively.
Energy, silt size, erosion, stream velocity.
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana,
Muneesh Sethi Experimental Study and Optimizing Erosive Wear Rate Parameters
Using A Novel Entropy Vikor Approach in A Pelton Turbine Buckets
Journal of Mechanical Engineering and Technology, 8(6), 2017, pp. 27
aeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=6
verage grain size coefficient of suspended sediment with a base of 0.05 mm
Silt concentration
raction of silt by weight
T&VType=8&IType=6
ND OPTIMIZING
RS USING
ROPY VIKOR APPROACH IN A
BUCKETS
(HP), India.
Department of Mechanical Engineering, OM Institute of Technology, Juglan (Hisar)
.
such assilt size, silt
. The experimentation involves the
8000, jet velocity () = 25.436-
VIKOR technique,
implimented to the
s the variant responses as a common
method, it has been obtained
value of 90, 8000,
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana,
timizing Erosive Wear Rate Parameters
Using A Novel Entropy Vikor Approach in A Pelton Turbine Buckets. International
27–43.
asp?JType=IJMET&VType=8&IType=6
verage grain size coefficient of suspended sediment with a base of 0.05 mm
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
http://www.iaeme.com/IJMET/index.asp 28 [email protected]
�� Erosive wear
1 2 3 Coefficient of shape, hardness and abrasion resistance of base metal,
respectively
Normal component of particle impact velocity needed to initiate the erosion
� Silt size
�1 Coefficient of C
�2 Coefficient of silt hardness
�3 Coefficient of silt particle size
�4 Coefficient of silt particle shape
Operating time (h)
� Velocity of particle/Flow velocity (m/s)
Jet velocity
� Normalized wear rate (kg/h)
� Exponent for relative velocity
�, �, ����� Constants whose values depend on the properties of the erodent as well
as the target material
Greek Letters
�� Loss in runner efficiency due to sediment erosion, %/year
� Impact angle
� Abrasion rate (mm/h)
� Deformation factor
� Exponent for annual suspended sediments content
Exponent for average grain size coefficient
1. INTRODUCTION
Energy emergency and a worldwide temperature alteration, for example, depletion of fossils
powers, have made it noteworthy to utilize renewable energy sources like hydroelectric
energy adequately [1]. For satisfying the request of energy, a worldwide level activity is
required to use renewable energy. Hydro power has been considered as a standout among the
most dependable and flexible type of renewable energy source which can satisfy both base
and pinnacle request. Hydro turbines are heart of hydro power plants and working of hydro
power plants primarily rely on upon turbine effectiveness. The variable which influences the
execution of hydro turbines is residue disintegration. Sediment disintegration is for the most
part considered as steady evacuation of material created by disfigurement and cutting activity
[2-3].The fundamental driver of disintegration in hydro turbine parts is the mix of high
grouping of residue with a higher rate of quartz substance in water which is a to a great degree
hard material [4-5]. Erosion in hydro turbines for the most part rely on upon different
variables like sediment size, sediment concentration, working hours, stream velocity, jet
diameter, residue shape and nozzle angle [6-7]. In case of impulse turbines buckets, nozzle,
blades and needle are affected due to silt erosion and in case of reaction turbines runner
blades, face plates and guide vanes are prone due to sediment erosion [8]. Because of
sediment disintegration stream design changes, loss in effectiveness, vibration delivered lastly
breakdown of hydro turbine happen [9]. A various research has been attempted to foresee the
conduct and to decrease the impact of disintegration in hydro turbines because of sediment.
[10-16].Bain et.al [17] built up a relationship to explore the disintegration rate by gathering
broad data from a bench scale test rig. The connection can be spoken to in the given shape as,
W = KVβdγCφ (1)
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana, Muneesh Sethi
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where W is erosion rate, V is velocity of particle, d is particle size, C is solid
concentration, and K, β, γ and φ are constants whose values depend on the properties of the
erodent as well as the target material. Tsuguo [18] established a correlation of basic
parameters which are responsible for erosion of turbines based on erosion data of 18
hydropower plants of 8 years. He proposed following relation to estimate erosion in turbines.
W = β.Cx.a
y.k1.k2.k3.V
m [mm/year] (2)
Where W is loss of thickness per unit time, β is turbine coefficient at eroded part, V is
relative flow velocity. The term ! iscoefficient of average grain size on the basis of unit value
for grain size 0.05 mm. The terms k1 and k2 are coefficient of shape and hardness of sand
particles and k3 is abrasion resistant coefficient of material. The x, y are exponent values for
concentration and size coefficient respectively. Naidu [19] revealed a review that India is
confronting the issue of sediment in very nearly 22 substantial hydropower stations. These
power stations have been arranged into three classifications in view of level of harm:
impressive harm, which needs unmistakable endeavours and assets inside 15-20 years;
broadly high harm, which require change in at regular intervals; and serious harm which
requires repair each year. Thapa et al. [20] examined the impact of suspended residue in hydro
power ventures in view of a contextual analysis of 60MW Khimti hydro power plant. Because
of nearness of high measures of residue, the hydro power plant was composed with settling
bowls to screen 85% of all particles with a width of 0.13 mm and 95% of all particles with a
distance across of 0.20 mm. The plant was dispatched in July 2000 and the harm to the
turbine segments was explored in July 2003. The agents watched that a lot of disintegration
had showed up in the turbine bucket and needles. Chitrakar et al. [21] describes the
simultaneous nature of combine effect which contributes to vibration, losses, fatigue problems
and failure of Francis turbines. They have also discussed to minimize the combine effect by
controlling the erosion or secondary flow in the turbine.
The aim of this experimental study was to determine the normalized erosive wear for
Pelton turbine buckets made of Aluminium as a function of silt and operating parameters. In
current investigation Entropy-VIKOR technique has been used for calculating the best set of
experimental factors of erosive wear rate on Pelton turbine buckets which are designed with
Taguchi orthogonal array. Weight of responses i.e. W and efficiency has been determined via
Entropy weight production model and after that the alternatives of experimental sets have
ranked as per to VIKOR method.
2. EXPERIMENTATION ANALYSIS DETAILS AND GOVERNING
EQUATIONS
A trial set up has been composed and created by the Pelton turbine model design for 1 kW
control yield as appeared in Fig. 1. The runner of Pelton turbine having pitch circle diameter
145 mm, nozzle diameter 12 mm and having 20 quantities of buckets has been utilized for the
exploratory review. The heaviness of every basin is around 115 gm. The model of every
bucket and runner was made on AutoCAD and CREO version 2016 as appeared in Fig. 2. To
get the disintegration in limited ability to focus time, turbine buckets were made of
Aluminium. In this test work two tanks were made (650 mm × 520 mm × 800 mm). The
principal tank was utilized to store water and to flow sediment water blend to the runner of
Pelton turbine of various residue focuses. The second tank was utilized to quantify the release
by utilizing rectangular notch. Amid test work a stirrer was utilized constantly in order to
supply a uniform blend of sediment water to turbine runner. A penstock pipe having 70 mm
external width and 3 mm thickness was utilized for providing water to the turbine runner. A
monoblock having 40 m evaluated head and a release limit of 9 l/s was utilized to make hydro
potential. A computerized weight transducer of Yokogawa make having scope of 0.5 "� to
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
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14 #"� and having exactness ± 0.065 % was fitted with penstock pipe to quantify the net
head at bay of Pelton turbine. A generator was straight forwardly coupled to the turbine shaft.
Electric knobs of various wattages were utilized as resistive load. The electric load was
measured to decide the yield of the turbine. The weight reduction of Pelton basins were
measured previously, then after the fact experimentation with the assistance of electronic
weight adjust having minimum tally of 0.1$�. Distinctive sorts of sifters of 90, 150, 300 and
450 microns were utilized so that reviewing of sediment should be possible.
2.1. Experimental Procedure
Before beginning the investigation, a trial test was directed to check the best possible working
of the entire set up. Legitimate working of the considerable number of instruments was
additionally confirmed. At first administration pump drew water from the capacity tank and
provided it to the turbine. Water from the turbine was permitted to move through second fitted
with rectangular score for release estimation. The height of water over the crest of the notch
was recorded by a pointer gauge and the release of the pump relating to every head was
resolved. The figuring of release will be made based on the height of water (h) streaming over
the peak. To examine the impact of residue disintegration on containers of Pelton turbine,
silty water of known focus was set up in the principal tank. For providing a uniform blend of
sediment and water ceaselessly to turbine a stirrer was turned with the assistance of engine.
Amid tests head and stream were kept steady. One arrangement of readings was taken at four
estimations of time interim of 2 h by keeping one parameter as fix and other parameter as
variable.
Figure 1 Schematic of experimental setup
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana, Muneesh Sethi
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(a)
(b) PCD φ145mm (c)
Figure 2 Design details of Pelton turbine blades and runner
To assess disintegration qualities an aggregate 192 arrangements of readings were
recorded by taking distinctive estimations of residue size four arrangements of trials, also for
sediment focus four arrangements of examinations and four stream speed three arrangements
of tests were directed. To explore disintegration in containers they were destroyed after at
regular intervals of investigation. An advanced adjust of Tapson make with traverse go from
10 g to 210 g and least count of 0.1 mg were utilized to gauge loss of weight. Be that as it
may, because of course of silty water to turbine runner the impeller of the pump got
disintegrated after certain time of operation so the impeller was supplanted with new impeller.
3. RANGE OF PARAMETERS
In this test work residue measure, sediment focus, stream speed and working hours were
researched parameters. For this, specimen of sediment was gathered from Chameralake,
Chamba (HP, India) in which the sediment concentration amid storm season was around
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
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20000 ppm and the normal quartz substance was observed to be around 80%. Residue was
dried in the daylight for 3-4 days and sifters of various sizes were utilized to strainer the sand
before blending with water. The factors of experiment which has been studied contains four
values of �,four values of�, four values of and four values of respectively. The ranges of
different parameters are depicted in Table 1.
Table 1 Range of experimental parameters
Sr. No. Parameters Symbols Range
1. Silt size � 90-450
2. Silt Concentration � 2000-8000
3. Jet Velocity 25.436-25.492
4. Operational time 3-12
4. UNCERTAINTY ANALYSIS
Uncertainty in experimental measurements has been carried out. Let a set of measurement is
made and the uncertainty in each measurement may be expressed. These measurements are
then used to calculate some output of experiments. The result (R) is a given function of the
independent variables x1, x2, x3,………,xn. Hence,
),.......,,( 21 nxxxRR = (3)
Let WR be the uncertainty in the result and W1, W2, W3,……….,Wn be the uncertainties in
the independent variables. The resultant uncertainty (WR) is calculated as;
∂
∂++
∂
∂+
∂
∂=
22
2
2
2
1
1
............. n
n
R Wx
RW
x
RW
x
RW
(4)
Uncertainty calculation for S (S) is determined as follow:
21 SSS −=
Uncertainty of Particular size range is provided as follow:
( ) ( )[ ]S
WW
S
W SSS
5.02
2
2
1+
=
(5)
( ) ( )[ ]%57.10157.0
90
115.022
==+
=S
WS
The maximum possible measurement errors in the values of major parameters are given
below in Table 2:
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana, Muneesh Sethi
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Table 2 Uncertainty analysis of major Parameters
S.No. Parameters Range Uncertainty
1 Silt size 90, 150, 300, 450 µm 1.57%
2 Silt concentration 2000, 4000, 6000, 8000 ppm 0.25%
3 Jet velocity 115g 0.69%
4 Operating time 8 h 1.18%
5 Pressure 0.5 kPa to 14 MPa ± 0.065 %
6 Discharge H=45-90 mm 1.68%
5. OPTIMIZATION METHODOLOGY
VIKOR approach is one of the significant MCDM processes which ranks parameters and
conclude the optimal results. Results achieved are extremely nearer to optimal response and
away from the worst. Due to the fast raise in functioning of VIKOR, we have preferred this
approach for optimization in current study also.
5.1. HYBRID ENTROPY-VIKOR METHOD
In terms of combined entropy-VIKOR approach the weight of responses from entropy process
are combined among the other stages of VIKOR. The outline of process in form of flow chart
has presented in Fig. 3. Three steps of the process are as follow:
1. Step-1: Elementary formation
2. Step-2: Entropy weight creation method
3. Step-3: VIKOR
5.2. STEP-1: ELEMENTARY FORMATION
In current step, amount of alternatives and different responses employed in the performance
estimation of specified MCDM are calculated and a comparative result matrix is created.
Figure 3 Schematic of the estimation methodology for optimization
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
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If ‘O’ signify number of alternatives and ‘P’, signify number of responses then result
matrix having an order of O × P is characterized as:
=×
MNMM
N
N
PO
bbb
bbb
bbb
A
…
�…��
…
…
21
22221
11211
(6)
Here, a parameterijb (for i=1, 2... O; j = 1, 2... P),stands for real data of the i
th alternative
with respect jth
response.
After the generation of results matrix, benefit ( )maxijb and cost ( )
minijb response has obtained
as:
( ) [ ]Oibbb ijijiij ...2,1,maxmax
max===
( ) [ ]Oibbb ijijiij ...2,1,minmin
min===
(7)
5.3. STEP-2: ENTROPY WEIGHT CREATION METHOD
In this step the weights of different responses are calculated with the entropy process.
Primarily, projection value (ijπ ) for every alternative is determined as follow:
∑=
=O
i
ij
ij
ij
b
b
1
π
(8)
After the calculation of (ijπ ), entropy of all responses is determined as follow:
)ln(1
ij
P
j
ijj ππςε ∑=
−=
(9)
Here, ς is alteration constant and determined as,
)ln(
1
O=ς
After that the dispersion value (jλ ) of every response is determined as follow:
jj ελ −= 1 (10)
At last the weight of every response is determined as follow:
∑=
=P
j
j
j
j
1
λ
λω
(11)
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana, Muneesh Sethi
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5.4. STEP-3: VIKOR
Normalize the result matrix. The method of normalization is prepared with supposing
arithmetical alternatives jon every response:
�%& = ()*+∑ ()*-.*/0
(12)
In this step alternatives are measured and ranking is achieved. Method is expressed as
below: The data of utility measure ( jS ) and regret measure ( jR ) are determined as:
[ ][ ] criteriabenefitisjwhen
mm
mmS
P
j ii
ijij
j ,1
∑=
+•
•
−
−=
ω
(13)
[ ] criteriatisjifmm
mmwR
iii
ijij
j cos,][
max+•
•
−
−= , for j = 1, 2. . . O (14)
VIKOR index ( iϑ ) is calculated as:
)(
))((1(
)(
)(•+
•
•+
•
−
−−+
−
−=
RR
RRv
SS
SSv jj
iϑ (15)
Here, ν and ( ν−1 ) are established as weight for the highest value of utility and weight of
the particular regret respectively. The value of ν is used as 0.5. jS ,•
S , jR , •R are the highest
and lowest values of utility and regret calculations.
At last, with iϑ values the alternatives has been ranked and the alternative among the
lowest value of iϑ will be ranked as optimal alternative.
6. EXPERIMENTAL RESULTS AND DISCUSSION
Testing has been performed forerosive wear rate on Pelton turbine among combinations of
experimental factors as depicted in Table 3. After the examination of each alternative which is
parametric set of erosive wear rate on Pelton turbine, the results has been noted and calculated
for� and efficiency loss. Table 3 depicts� and efficiency lossresponsesachieved for all
alternatives combinations. The surface conditions of bucket after the investigation are shown
in Fig. 4. The results of Table 3 have been presented graphically in Fig. 5 so as to observe the
inclination of � and efficiency loss difference concurrently. It has been found that where the
efficiency loss is improved, at the same time the �value has also improved.
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
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Figure 4 Surface condition of bucket after experimentation
Table 3 Experimental results of variant parameters
Experimental Parameters Results
Alternatives S C V t W (C1) Efficiency loss
(C2)
A-1 90 2000 25.436 3 0.0002188 0.087
A-2 90 4000 25.452 6 0.0009835 0.314
A-3 90 6000 25.476 9 0.0025402 0.667
A-4 90 8000 25.492 12 0.0037861 1.129
A-5 150 2000 25.452 9 0.0008754 0.221
A-6 150 4000 25.436 12 0.0022773 0.594
A-7 150 6000 25.492 3 0.0007170 0.331
A-8 150 8000 25.476 6 0.0017790 0.758
A-9 300 2000 25.476 12 0.0013742 0.287
A-10 300 4000 25.492 9 0.0016786 0.505
A-11 300 6000 25.436 6 0.0016638 0.583
A-12 300 8000 25.452 3 0.0010410 0.477
A-13 450 2000 25.492 6 0.0006898 0.173
A-14 450 4000 25.476 3 0.0006130 0.225
A-15 450 6000 25.452 12 0.0038404 0.985
A-16 450 8000 25.436 9 0.0033419 1.082
7. NUMERICAL SIMULATION FOR OPTIMIZATION
The responses achieved from testing have been optimized by Entropy-VIKOR technique.
Variant steps of the evaluation processes are explained as below:
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana, Muneesh Sethi
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8. STEP-1: ELEMENTARY STRUCTURE
The set A-1 to A-16 are selected as alternatives and responses of W and efficiency loss are
considered as criterions (� as C-1 and efficiency loss as C-2) for performance estimation of
erosive wear rate on Pelton turbine.
Figure 5 Difference of experimental results with alternatives
A resultant matrix ( )POD × has been created in which alternatives stands for by O and criterions
for P. Concurrently, all constituents of the matrix are denoted by
( )PjOiford ij ....3,2,1;....3,2,1 == . Decision matrix is,
( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )
( ) ( )
=×
MNM
NM
dd
dd
dd
dd
dd
dd
D
1.0820.0033419
0.2210.0008754
1.1290.0037861
0.6670.0025402
0.3140.0009835
0.0870.0002188
1
5251
4241
3231
2221
1211
��
After generation of resultant matrix, benefit ( )maxijd and cost ( )
minijd responses have been
determined as follow:
( ) [ ]0.0002188,0.0038404max
max== ijiij dd
( ) [ ]0.087,1.129min
min== ijiij dd
8.1. STEP-2: ENTROPY WEIGHT DETERMINATION MODEL
After operating the data of benefit and cost responses, weights of these responses have been
calculated by Entropy weight determination model. Projection results of every response and
alternatives have determined by equation (8)and are depicted in Table 4.
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
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For determining entropy, alteration constant can be calculated as follow:
0.36067)16ln(
1==ς
Results of )ln(1
ij
N
j
ij ππ∑=
have been calculated in Table 4.
Table 4 Projection values of all alternatives and responses
Alternatives Projection Value, ijπ ( )
ijij ππ ln×
C-1 C-2 C-1 C-2
A-1 0.00798 0.010335 -0.03855 -0.04725
A-2 0.035868 0.037301 -0.11937 -0.12267
A-3 0.09264 0.079235 -0.22039 -0.20089
A-4 0.138078 0.134117 -0.27339 -0.26945
A-5 0.031926 0.026253 -0.10996 -0.09556
A-6 0.083053 0.070563 -0.20666 -0.18708
A-7 0.026149 0.039321 -0.09528 -0.12724
A-8 0.06488 0.090045 -0.17746 -0.21678
A-9 0.050117 0.034094 -0.15002 -0.11519
A-10 0.061218 0.05999 -0.171 -0.16879
A-11 0.060678 0.069256 -0.17003 -0.18491
A-12 0.037965 0.056664 -0.12419 -0.16266
A-13 0.025157 0.020551 -0.09264 -0.07984
A-14 0.022356 0.026728 -0.08497 -0.09681
A-15 0.140058 0.117011 -0.27531 -0.25105
A-16 0.121878 0.128534 -0.25652 -0.2637
Total 1 1 -2.56574 -2.58986
After that the entropy of all responses has been determined using equation (9):
( ) ( ) 0.92542.5657436067.01 =−×−=−Cε
Similarly,
( ) ( ) 0.93412.5898636067.02 =−×−=−Cε
Dispersive results of the all responses have been determined from equations (10) and after
that weights have been determined using equation (11)as follow:
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana, Muneesh Sethi
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0.5309580.14051
0.07461 ==−Cω
0.4690430.14051
0.06592 ==−Cω
The entropy, dispersion value and the weight particular response depend on Shannon
entropy model is depicted in Table 5. It has been obtained that the maximum disorder in
response means minimum weight and vice versa. In current examination, the W show s
minimum data of the entropy and hence it has higher weight as compared to efficiency loss.
Table 5 Response weight determined with entropy technique
Criteria C-1 C-2
Entropy 0.9254 0.9341
Dispersion
value 0.0746 0.0659
Weight 0.530958 0.469043
8.2. STEP-3: VIKOR
The method of normalization is prepared with supposing arithmetical alternatives jon every
response and determined by using equation (12) and presented in Table 6 respectively.
Table 6 Normalized decision matrix
Alternatives C-1 C-2
A-1 0.00798 0.010335
A-2 0.035868 0.037301
A-3 0.09264 0.079235
A-4 0.138078 0.134117
A-5 0.031926 0.026253
A-6 0.083053 0.070563
A-7 0.026149 0.039321
A-8 0.06488 0.090045
A-9 0.050117 0.034094
A-10 0.061218 0.05999
A-11 0.060678 0.069256
A-12 0.037965 0.056664
A-13 0.025157 0.020551
A-14 0.022356 0.026728
A-15 0.140058 0.117011
A-16 0.121878 0.128534
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
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The utility measure, regret measure and VIKOR index has been calculated using equation
(13-15 respectively and after that characterized among ranking of the alternatives in Table 7.
The alternative among maximum range of VIKOR index has been ranked the optimal. It
has been found that A-4 has maximum range of VIKOR index and A-1 has minimum range of
VIKOR index therefore A-4 the most suitable alternative among every one of alternative.
Table 7 Utility measure, regret measure, VIKOR index and ranking of parameters
Alternatives Utility measure
( jS )
Regret measure
( jR )
VIKOR index
( jϑ ) Ranking
A-1 0.000176 0.00163 0.00181 16
A-2 0.214166 0.111985 0.205756 11
A-3 0.601391 0.340312 0.605129 4
A-4 0.992094 0.523052 0.963098 1
A-5 0.156448 0.09613 0.163396 13
A-6 0.52997 0.301751 0.534824 6
A-7 0.18273 0.109833 0.188809 12
A-8 0.530705 0.302042 0.535447 5
A-9 0.259318 0.16929 0.281303 10
A-10 0.402095 0.213938 0.391214 8
A-11 0.435035 0.223268 0.415654 7
A-12 0.295972 0.175553 0.304609 9
A-13 0.107619 0.068907 0.114518 14
A-14 0.119761 0.062119 0.113867 15
A-15 0.935239 0.531016 0.943644 2
A-16 0.905786 0.4579 0.860612 3
The experimental parameters of erosive wear rate on Pelton turbineat alternative A-4 are:
S, silt concentration, and with relevant values of 90, 8000, 25.492 and 12 respectively.
The combination of alternatives in the descending order of their position are A-4>A-15>A-16
>A-3>A-8 > A-6>A-11>A-10>A-12>A-9>A-2>A-7>A-5>A-13>A-14 > A-1.
The erosive wear rate on Pelton turbine has been studied for W and efficiency loss
descriptions. Increase in both the performance estimation response has been obtained. The
entropy-VIKOR technique proposes that erosive wear rate on Pelton turbines with alternative
combination are� of 90, � of 8000, of 25.492 and of 12 provides the highest overall
performance as clearly observed IN Figure 6&7.
Robin Thakur, Anil Kumar and Rahul Nadda, Sourabh Khurana, Muneesh Sethi
http://www.iaeme.com/IJMET/index.asp 41 [email protected]
Figure 6 Normalized wear loss vs silt size and silt concentration
Figure 7 Efficiency loss vs silt size and silt concentration
8. CONCLUSIONS
In this paper, experimental analysis and parameters optimization Entropy-VIKOR techniques
has been carried out to investigate the effects of effect wear rate on silt size and silt
concentration in a Pelton turbine bucket. Based on the experimental results, the following
conclusions are drawn:
1. Entropy-VIKOR has been used in many engineering applications as a multi criteria decision
making (MCDM) approach. Where entropy measures the weights of each of the performance
evaluation criterion towards overall performance, the VIKOR method provides ranking of the
alternatives by providing the best compromise solution which is nearest to the real and farthest
from the worst. The results obtained from this study will be useful for the designers and
researchers in the field of Pelton turbine bucket for performance evaluation and optimization
with desired evaluation criteria for maximum overall performance.
2. Entropy technique has been used to the combination of experimental factors as designed with
Taguchi design of experiments on every of the performance responses. It was found that the
efficiency loss has maximum disorder of 0.9341 as compared the normalized weight loss
among a value of 0.9254. The equivalent weights of the responses are 0.530958 and 0.469043
respectively. This proposes that the efficiency loss response has higher influence on the whole
performance of erosive wear rate on Pelton turbine than that of normalized weight loss
response.
Experimental Study and Optimizing Erosive Wear Rate Parameters Using A Novel Entropy Vikor Approach
in A Pelton Turbine Buckets
http://www.iaeme.com/IJMET/index.asp 42 [email protected]
3. The best factors combination which gives the optimal normalized weight loss and efficiency
loss performance based upon VIKOR method with normalized weight loss and efficiency loss
at the higher end concurrently is alternative A-4. The ranking of whole factors combination
refers the order: A-4 > A-15 > A-16 > A-3 > A-8 > A-6 > A-11 > A-10 > A-12 > A-9 > A-2 >
A-7 > A-5 > A-13 > A-14 > A-1.
4. The entropy-VIKOR technique proposes that erosive wear rate on Pelton turbines with
alternative combination are� of 90, � of 8000, of 25.492 and of 12 provides the highest
overall performance.
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