MODELLING THE EFFECT OF HEAD AND BUCKET …eaas-journal.org/survey/userfiles/files/v5i305...

Aug. 2014. Vol. 5. No. 03 ISSN2305-8269

International Journal of Engineering and Applied Sciences © 2012 - 2014 EAAS & ARF. All rights reserved www.eaas-journal.org

26

MODELLING THE EFFECT OF HEAD AND BUCKET SPLITTER

ANGLE ON THE POWER OUTPUT OF A PELTON TURBINE

1UJAM J. A.,

2*CHUKWUNEKE J. L.,

2ACHEBE C. H.,

2IKWU G. O. R.

1Mechanical/Production Engineering, Enugu State University of Science & Technology, Enugu, Nigeria

2Department of Mechanical Engineering, Nnamdi Azikiwe University, P.M.B. 5025 Awka, Nigeria

E-mail: 1*[email protected]

ABSTRACT

This work investigates the effect of head and bucket splitter angle on the power output of a pelton turbine

(water turbine), so as to boost the efficiency of Hydro-electric power generation systems. A simulation

program was developed using MatLab to depict the force generated by the bucket as the water jet strikes

the existing splitter angle (100 to 15

0) and predicted (1

0 to 25

0) splitter angles. Result shows that in addition

to the existing splitter angle, six more angles have been investigated for the two operating conditions to

give maximum power. The angles are 250, 6

0 and 19

0 for high head and low flow with increased pressure

while low head and high flow with decreased pressure are 230, 21

0 and 3

0 in order of the maximum

generating power. The Turbine power output for simulation was more than that of the experiment. This was

as a result of their head conditions and the bucket splitter angle.

Keywords: Bucket Splitter Angle, Force, Head, Modelling, Pelton Turbine, Power Output, Shaft Output

1. INTRODUCTION

The high demand for a clean source of energy

continues to increase as indicated by the increase in

distributed generation technologies and adoption of

renewable energy resources. Climate change and

global warming have made renewable energy the

most appropriate and fitting means of answering all

these changes in our environment. Micro-hydro

power plant (MHPP) is considered as one of the

most reliable renewable energy technologies in the

world according to Newman, [1] in his article on

renewable energy. It is also one of the earliest

small scale renewable energy technologies and is

still an important source of energy today. MHPPs

are appropriate in most cases for individual users or

groups who are independent of the electricity

supply grid. MHPP is generally a hydroelectric

power installation that can produce up to 100kW of

power. It does not encounter the problem of

population displacement and is not expensive as

solar or wind energy.

Currently the highest cost in a small hydro site is

the penstock. Penstocks are generally pipes or

conduits and their material costs depend on

regional manufacturing capabilities and supply.

Generators are difficult to make locally, but they

can be replaced by lower cost alternatives such as

car alternators or induction motors, both of which

are fairly abundant in Nigeria. Usually turbines for

hydro systems are imported into Nigeria from

Europe and America at high costs, thus making it

difficult for a small scale hydro technology to

spread with foreign aid. However, Nigeria is

blessed with abundant resources which if properly

used, will aid local manufacture of turbines,

thereby reducing the material cost and increasing

money flow within the rural communities.

The aim of this paper is to model the effect of head

and bucket splitter angle on power output of a

Pelton turbine, using the velocity triangle to

consider the flow interaction mathematically in a

pelton bucket to determine the effect of bucket

splitter on the power output, and to investigate

through simulation, the effect of head and bucket

splitter angle on the power output of a pelton

turbine. The introduction of pelton turbines in

power generation will not only provide energy but

will reduce air pollution and diseases from the use

of biomass. Some parameters are important when

considering the pelton turbine as a technology for

power generation. These parameters are the head,

flow rate from nozzle and bucket shape. These are

considered in this work, with the objective of

helping to improve power generation in Nigeria.

http://www.eaas-journal.org/

Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


27

2. FLOW INTERATION IN A PELTON

BUCKET:

2.1. Bucket Geometry

Fig.1. A 3-D model showing the geometry of the

Pelton turbine “bucket”.

The shape of the bucket on the turbine is crucial

to extracting the most energy from the jet. The

development of the shape of the bucket came from

Lester Allan Pelton while he was observing a

paddle wheel with cupped buckets being propelled

by a water stream. The paddle wheel had slipped

over on its shaft causing the water stream to strike

the edge of the curved buckets. When this occured

the speed of the wheel increased, as nothing else in

the system had changed. Pelton had deduced that

the curved slope the water was following into the

bucket was harnessing more of the stream’s energy.

This is the primary principle in the design of the

buckets for modern pelton turbines. Fig.2 shows

that the water entering the bucket is forced to curve

around and exit the side of the bucket. The curving

slopes of the bucket work to remove as much

energy from the fluid jet as possible by forcing it to

change direction and create vector forces which act

on the bucket (see fig.2). The most efficient bucket

would have the exit velocity of the fluid relative to

the housing of the turbine to be zero. Unfortunately

having the exit velocity being zero would result in

the fluid not properly exiting the bucket. The 165

degree angle on the edge of the bucket surfaces

insures that the fluid will have enough velocity to

exit the bucket and clear the bucket above it. This

velocity represents a loss in energy and is called the

discharge loss. In addition to discharge loss there

are multiple frictional losses which all reduce the

efficiency of the turbine.

The bucket is designed to maximize power

transfer from the water to the turbine. To increase

the momentum transfer [2, 3], the water should

have as little residual velocity as possible once it

leaves the buckets. To do this the pelton bucket

splits the jet and directs it around the edge of the

bucket, essentially reversing its direction. The

bucket is designed to maximize power transfer from

the water to the turbine.

Fig.2. Entry position of the fluid jet and the path

it follows within the bucket.

The general expression for the energy transfer

between the bucket and the fluid based on the one

dimensional theory usually referred to as Euler’s

equation, can be obtained using the velocity

triangle of the pelton wheel turbine.

2.2. Bucket Vector Diagram

Fig.3. Basic bucket vector diagrams

In order to produce no axial force on the wheel,

the flow is divided equally by the shape of the

bucket. This produces a zero net change in

momentum in the axial direction, and then water is

deflected over each half of the bucket by an angle

degree. Since the change in momentum is the

same for both halves of the flow, the vector

diagram for one half only needs to be considered.

The initial velocity is and the bucket velocity U

is in the same direction. The relative velocity of the

water at inlet (in the middle) is and is also in the

same direction so the vector diagram is a straight

line as shown in fig.5. If the water is not slowed


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


28

down as it passes over the bucket surface, the

relative velocity will be the same as . In

reality, friction slows it down slightly and we

define a blade velocity coefficient as;

K = / (1)

The exact angle at which the water leaves the sides

of the bucket depends upon the other velocities but

as always the vectors must add up so that;

= U + (2)

But, = = U since the bucket has a uniform

velocity everywhere.

The pelton wheel being a parallel flow turbine, the

peripherical velocities at inlet and outlet are equal.

2.3. Velocity Triangle of a Pelton Wheel

Fig.4: 2D velocity triangle of a pelton bucket

2.4. Pelton wheel

If the frictional resistance along the vanes is

ignored then relative velocities at inlet and outlet

are equal (i.e. = ). Let be the outlet vane

angle.

Fig.5. Shows the inlet and outlet velocity triangle

of a pelton bucket

Then, the velocity diagram at inlet is a horizontal

straight line, as shown in fig.4 and fig.5.

At inlet; = – U (3a)

= = √ (3b)

At exit; = K* (4a)

= U – Cos (180 - ) (4b)

Therefore; = U – K * Cos (180 - ) (4c)

= 180 -

2.5. Turbine Power Output

Kinetic momentum theorem: Since the runner

is rotating about a shaft then only the force in the

circumferential direction performs useful work,

hence we need to find the change in angular

momentum in this direction. Changes of

momentum in the radial direction have no effect

because they do not generate a moment about the

axis of rotation of the runner. From fig.4, the fluid

enters with a velocity then flows through the

runner and leaves with a velocity . In the process

of passing through the runner, energy is transferred

from the fluid to the runner. Most of this performs

useful work; a small amount is lost in friction.

Using conservation of momentum to analyze the

system, Newton’s second law of motion can be

applied to rotational as well as linear systems, and

thus “torque is equal to the rate of change of

angular momentum and is expressed as;T =

(5)

Where; T is the torque, is the angular

momentum and t is the time. In linear motion, force

is equal to the rate of change of momentum in the

system. Applying Eq.5 to the flow through a turbo

machinery passage as shown in fig.6, with an entry

at station1 and exit at station 2.The passage varies

in radius from station1 to station 2 and can be of

any shape. The passage is bounded by a hub and a

casing so mass flow is conserved through the turbo

machinery passage. The velocity through this

passage may differ between entry and exit but at

either of those stations is uniform.


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


29

Fig.6. Velocity of a water particle in a runner

channel

Angular momentum is given by the moment of

momentum [4, 5]: L = ṁ r (6)

Where; represents the flow rate, L is the angular

momentum or angular momentum flow rate and

is the whirl velocity of the system, so at entry to the

turbo machinery passage the angular momentum is

r and at exit the angular momentum is

r. The rate of change in angular momentum

between entry and exit is: ṁ - ṁ .

Since; r, The rate of change in angular

momentum between entry and exit is;

ṁ (7)

Since ( = ); ṁ r r ( ) (8)

The time rate of angular momentum is equal to the

torque we have; T = ṁr( ) (9)

From basic mechanics the power is torque times

rotational speed;

P = Tω = ṁrU/r ( - ) = ṁU( ) (10)

Where; = = U/r, is the rotational speed of the

device.

P = ṁ = ṁgE (11)

If = gE, Therefore; E = /g, E is called specific

energy.

Thus; E = U ( - )/g (12)

Eq.12 is known as Euler’s Equation. This is also

called Euler’s head which can also be determined

from the elevation of pelton wheel from river bed.

A. Velocity Diagram:

Since, = ;

= U – cos (180 - ) = U + cos (13)

K = / (14)

Where; K represents the reduction of the relative

velocity due to friction.

Therefore; E = U/g [ – U – K ( - U)Cos ] =

U/g ( - U)(1 - KCos ) (15)

But; ṁ = ρ x Q, Therefore the total power output

from the flowing fluid delivered to the Pelton wheel

is given as [4, 5]: P = ṁgE = P = ρQgE (16)

Where; P is the power delivered to the wheel by the

jet, Q is the volumetric flow rate through the

nozzle, g is the gravitational acceleration, E is the

energy the fluid delivers to the wheel.

For maximum power output ρ,Q,g is constant, E

is varying. Maximum power output will occur at

some intermediate value of the vane velocity.

This may be obtained by differentiation as follows:

= 0. [(1 - Kcos )/g]( - 2U) = 0. Hence, -

2U = 0, U = 1/2 .

Therefore; = (

) =

(1 - kcos ) (17)

=

(1 - kcos ) (18)

The Energy arriving at the wheel is in the form

of kinetic energy of the water jet and is given by

1/2 . The Efficiency of the wheel is;

(Max) =

(19)

(Max) = 1 - kcos /2 [6] (20)

is the efficiency of the wheel, K is the velocity

coefficient, is the exit angle. Note that the

splitter angle is given as = (180 - ). [Eq.18 to

Eq.20 is valid according to BREKKE, H. A. [6].

Considering the speed of turbine [7]:

(Ft/s) = (rad/s) x

(ft) (21)

B. In metric form:

0.5 X (m/s) = 5.235 x x (rpm) x

(mm) (22)

= 0.5 x 1.91 x x

(23)

Eq.23 [7] is the rotational velocity or speed of the

turbine

2.6. Force Generated by the Bucket

Flow forces and energy conversion: The energy

conversion in pelton turbines takes place through

the jet of water onto the rotating bucket, to show

the principle of this type of energy conversion the

impact of the jet onto the moving bucket is assumed

to take place in a straight line (see fig.4 and fig.5).

The constant jet and bucket velocities are and U

respectively.

In reality the interaction between the jet and the

bucket is considered in the system of the moving

bucket and is express as: = – U. Because the

bucket moves in a straight line, this relative

velocity remains constant through the flow period

within the bucket ( = = , if the friction is

neglected. The interaction force between the jet and


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


30

the bucket is considered in the U-direction and is

calculated according to the momentum law which is

expressed as: Force applied by the bucket to the

water stream as in Eq.24 [8]:

= ṁ ( cos - ) (24)

Assuming = , (elastic collision in bucket)

F = ṁ ( cos - ) = ṁ (cos - 1)[8] (25)

Since; = 180 -

Force of water on bucket is equal and opposite;

= ṁ (1 - cos ) (26)

Substituting Eq.3a ( into Eq.26 to get Eq.27

which is the force generated by the bucket as a

result of the splitter

= ṁ ( - U) (1 - cos ) (27)

Where; =is the force generated by the

bucket (N), ṁ = is the mass flow rate (kg/s), = is

the velocity of the fluid jet before striking the

bucket (m/s), U = is the velocity of the bucket

(m/s), = is the splitter angle and is always given

or express as = (180 - ) ( .).

U (velocity of the bucket) can be obtained as

follows: For a turbine with a single nozzle, the

optimal; (28)

This constrains the pitch circle diameter (PCD).

The PCD is the diameter of the runner which is

measured from where the center of the jet hits the

bucket as shown in Fig.3 [9]:

PCD = √

(29)

Therefore; U =

(30)

For most designs the jet diameter is 10-11% of

the PCD, but due to the Pelton’s versatile operating

characteristics, it is possible to have a jet as large as

20% of the PCD. All other dimensions relate to the

pitch diameter (PCD) or jet diameter (d). For

manufactured turbines, this has been optimized

over decades of design and there is very little

variation among different manufacturers. This

statement and Eqs.28, 29 & 30 according to [9] is

valid.

2.7. Shaft Output ( )

The torque on the shaft is; = (31)

Substituting Eq.27 into Eq.31 to get Eq.32

= ṁ ( - U) (1 – cos ) (32)

The rate of shaft work being done (on the fluid,

note sign change) [10]:

= (33)

Substituting Eq.32 into Eq.33 to get:

= ṁ ( - U) (1 – cos ) (34)

But; = U/r and ṁ = .

= ( - U) (1 – Cos ) U/r (35)

Eq.35 is reduced to Eq.36 after eliminating r.

= ρ Q U ( - U) (1 - cos ) = 2ρQ

( )[10] (36)

Where; = is the shaft output (kW), ρ = is

the fluid density (kg/ ), Q = is the volumetric

flow rate from the nozzle , = is the

velocity of the fluid just before striking the bucket

(m/s), U = is the velocity of the bucket (m/s), =

is the splitter angle ( ) Since U, shaft

work being done is negative; the pelton wheel

extracts energy from the fluid by the splitter

angle and = 180 - . Typically which is the

exit angle is equal to 165 , so cos (165) = -0.966,

the (1 – cos ) factor is 1.966, the torque is

maximum when U = 0. But work is being done

when the wheel is turning. The maximum power

output occurs when U(U - ) is maximum.

The turbine overall power output is expressed as;

P (kW) =

[10] (37)


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


31

3. RESULTS AND DISCUSSION

Force Generated by the Bucket Due To the Splitter Angles obtained through Simulation

Fig.7. Graph of head Vs force generated by the bucket at 1° & 3° splitter angle

Fig.8: Graph of head Vs force generated by the bucket at 5° & 6° splitter angle


0.00E+00

2.00E+07

4.00E+07

6.00E+07

8.00E+07

1.00E+08

1.70E+09

1.71E+09

1.71E+09

1.72E+09

1.72E+09

1.73E+09

0 200 400 600 800 1000 1200

Fb @

1°

and

3°

Head (m)

1°

3°

2.17E+09

2.17E+09

2.17E+09

2.17E+09

2.17E+09

1.42E+09

1.42E+09

1.43E+09

1.43E+09

1.44E+09

1.44E+09

1.45E+09

1.45E+09

0 2 4 6 8 10 12

Fb @

5°

and

6°

Head (m)

5°

6°

1.94E+09

1.94E+09

1.94E+09

1.94E+09

1.95E+09

1.95E+09

1.95E+09

9.40E+08

9.50E+08

9.60E+08

9.70E+08

9.80E+08

9.90E+08

1.00E+09

0 2 4 6 8 10 12

Fb@

7°

and

8°

Head (m)

8°

7°


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


32



Fig.12: Graph of head Vs force generated on bucket at 21° & 23° splitter angle

1.11E+09

1.12E+09

1.13E+09

1.14E+09

1.15E+09

1.16E+09

0.00E+00

5.00E+07

1.00E+08

1.50E+08

2.00E+08

2.50E+08

3.00E+08

0 2 4 6 8 10 12

Fb@

10

° an

d 1

1°

Head (m)

10°

11°

2.1974

2.1975

2.1976

2.1977

2.1978

2.1979

2.198

2.10752.108

2.10852.109

2.10952.11

2.11052.111

2.11152.112

0 200 400 600 800 1000 1200

Fb@

13

° an

d 1

9°

Head (m)

13°

19°

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

0 200 400 600 800 1000 1200

Fb @

21

° an

d 2

3°

Head (m)

21°

23°


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


33

Fig.13: Graph of head Vs force generated by the bucket at 25° splitter angle

Using predicted and existing Pelton bucket

splitter angle to determine the force generated by

the bucket as a result of the energy delivered by the

head to the fluid. The following angleswere used

for the simulation 1°, 3°, 5°, 6°, 7°, 9°, 10°, 11°,

13°, 15°, 17°, 19°, 21°, 23°, 25°. From the

simulation performed, a graph of force generated

by the bucket Versus splitter angle was plotted and

the following results were obtained.

For Predicted Splitter Angles: At 1° splitter

angle, the force generated by the bucket increases

as the head was increasing from 1.7039 x at

100m to 1.7231 x at 1000m.At 3° splitter

angle, the force generated by the bucket increased

from 1.9338 x at 100m to 9.3853 x .

At 5° splitter angle, the force generated by the

bucket was 1.4214 x at 100m and increased

to 1.4482 x at 1000m.At 7° splitter angle,

the force generated increased from 1.9390 x

at 100m to 1.9483 x .At 8° splitter angle, the

force generated at 100m was 9.4861 x while

that of 1000m was 9.9186 x .At splitter

angles 17°, 19°,21°,23°,25°, the force generated by

the bucket as a result of the splitter angle forcing

the jet to change direction and exiting at the side of

the bucket, thereby extracting energy from the

fluid. The forces generated at 100m vary as follows

8.0623 x , 2.1975 x 5.0619 x

5.0619 x and 2.2003 x . While

that of 1000m vary as follows

8.5398 2.1979 2.1076

5.6414 , 5.7998 x and

2.2006 All the forces generated were

increasing from 100m head to 1000m at different

rate for each splitter angle.

For Existing Angles: At 10° splitter angle, the

force generated by the bucket at 100m was

1.8547x to 2.5434 x at 1000m head.

At 11° splitter angle, the force generated increased

from 1.1140 x at 100m to 1.1513 x at

1000m head. At 13° splitter angle, the force

generated was 2.1081 x at 100m and

increased to 2.1115 at 1000m.At 15°, the

force generated increased from 2.7286 at

100m to 3.3875 . The forces generated

using predicted parameters had the highest force at

25 while that of the existing angle

was 13°.

Fig.14: Shows graph of force generated at 1000m Vs splitter angle

2.20E+09

2.20E+09

2.20E+09

2.20E+09

2.20E+09

2.20E+09

2.20E+09

2.20E+09

2.20E+09

0 200 400 600 800 1000 1200

25°

0.00E+00

5.00E+08

1.00E+09

1.50E+09

2.00E+09

2.50E+09

1° 3° 5° 6° 7° 8° 10° 11° 13° 15° 17° 19° 21° 23° 25°Forc

e g

en

era

ed

@ 1

00

0m

splitter Angle in Degree

Fb


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


34

Fig.14 shows the summation of forces generated

at 1000m head using both the predicted and already

existing splitter angles for pelton bucket. From the

reading we can conclude that the bucket generated

greater force at 25° followed by 6° 19° and 13°,

showing that the predicted angle could give a better

result compared to that of the existing angle, with

this some other splitter angles are recommended to

improve the power output of a pelton turbine.

3.1. Shaft Output due to the Existing and Predicted Splitter Angles obtained through Simulation

Fig.15: Shows shaft output at 1000m head Vs splitter angle

Fig.16: Shows force generated by the bucket & shaft output at 1000m head Vs splitter angle

Fig.15 and fig.16, show the force generated at

1000m head using both the predicted and already

existing splitter angles to estimate the shaft output.

This was calculated using

.

. Recall

U, shaft work being done is negative since

work is done on the system and torque is maximum

when U = 0, also work is being done when the

wheel is not turning therefore shaft output is

maximum when = 0. The shaft output

was maximum at 25° followed by 6°, 19° and 13°

and the lowest was 3° and also

the shaft output increases as the force generated by

the bucket was increasing with increased head and

varied splitter angle.

3.2. Turbine Power Output due to the Force

generated at 1000m Head for both the

Existing and Predicted Splitter Angles

obtained through Simulation

-6.00E+05

-5.00E+05

-4.00E+05

-3.00E+05

-2.00E+05

-1.00E+05

0.00E+00

6.0

0E+

05

-4.0

7E+

06

-1.1

9E+

06

2.7

9E+

06

4.2

0E+

06

-2.3

1E+

06

-4.2

5E+

06

1.7

9E+

06

2.7

6E+

06

-4.0

9E+

06

6.3

7E+

05

3.5

5E+

06

-3.6

0E+

06

-5.6

2E+

06

Ẇ

shaf

t @

max

He

ad

10

00

m

Splitter angle

ẇshaft

-6.00E+05

-5.00E+05

-4.00E+05

-3.00E+05

-2.00E+05

-1.00E+05

0.00E+00

0.00E+00

5.00E+08

1.00E+09

1.50E+09

2.00E+09

2.50E+09

1°

3°

5°

6°

7°

8°

10

°

11

°

13

°

15

°

17

°

19

°

21

°

23

°

25

°

Forc

e o

n b

uck

et

& s

haf

t o

utp

ut

@1

00

0m

splitter Angle

Fb

ẇshaft


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


35

Fig.17: Graph of overall power output Vs bucket splitter angle

As the force generated by the bucket increases the

turbine power output also increases at different

splitter angles.

3.3. Turbine Power Output due to the Energy

delivered by the head to the Bucket Splitter

at 25 obtained through Simulation

Fig.18: Graph of Turbine power output Vs Head at 25 bucket splitter angle

As the head increases from 100 to 1000m, the

energy delivered to the turbine system also

increases thereby causing the turbine power output

to increase. Finally the investigation on the effect of

Head and bucket splitter angle on the power output

of a pelton turbine shows that angles 25°, 6°, 19°

and some other predicted splitter angle gave a

better result compared to that of the existing angle.

4. CONCLUSION

The pelton turbine operating on high head and

low flow with increased pressure condition

generated a power output which could be applied in

sitting a large hydro power plant while that of the

low head and high flow with decreased pressure

generated a lesser output and could be applied in

sitting a small MHPP.

Comparing the forces generated by the bucket for

both the existing splitter angle (10° - 15°) and

predicted splitter angle (1° -25°) operating on high

head and low flow head conditions, the result

shows that in addition to the existing splitter angle

(10° - 15°) three more angles have been

investigated to give maximum power. The angles

are 25°, 6°, and 19° in order of their maximum

generating power. Thus combining the existing and

predicted values, the following angles (25 , 6 ,

19 , 13 and 11 ) can be said to be suitable for

maximum power generation in a hydro turbine

application, in their order of maximum generating

power.

0

50000

100000

150000

25° 6° 19° 13° 11°

P(kW)@ 1000m

P(kW)@ 1000m

114000115000116000117000118000119000120000121000

0 200 400 600 800 1000 1200

Po

we

r o

utp

ut

fro

m t

urb

ine

(k

W)

Head (m)

P(kW)

P(kW)


Aug. 2014. Vol. 5. No. 03 ISSN2305-8269


36

The operating condition for the pelton turbine in

the lab was low head and high flow with decreased

pressure, the force generated on the bucket surface

as the jet strike the splitter angle was maximum at

23° followed by 21° 15° 10° 3°. This result shows

that in addition to the existing splitter angle (10° -

15°) three more angles have been investigated to

give maximum power. The angles are 23°, 21°, and

3° in order of their maximum generating power.

For maximum efficiency, there is no reduction of

the relative velocity over the wheel and the bucket

deflection angle should not be more than 155 to

170 . To avoid the interference between the

oncoming and out coming jet and hence overall

efficiency would decrease.

REFERENCE

[1] Newman, Mark (2006). Study on a Renewable

Energy for sustainable future. Oxford: Oxford

university press.

[2] Thapa Bhola., Upadhyay Piyus, Gautem

Prakash (2006). Performance Analysis of

pelton turbine buckets Using Impact testing

and flow visualization techniques NHE.

Katthmandu University Journal of science,

Engineering and Technology Vol 5, No 2. Sept

2009, page 42 – 50.

[3] Zoppe B.J pellone C. (2006). Flow Analysis

inside pelton turbine bucket’’ Journal of turbo

machinery, Vol 4, page 128.

[4] Ainley, D.G and Matheson (1957).A Method

of performance Estimation G. C. R

for Axial flow turbines, Aero, Res.Council and

m. 2974.

[5] Rajput, R.K (1998). Fluid mechanics and

hydraulic Machines New Delhi S.Chend and

co. Ltd.

[6] Brekke, H. A general study of the design of

vertical pelton turbines. In turboinstitut (B.

Velensek and M. Bajd, 13-15 September

1984), B. Velensek and M. Bajd, Eds., vol. 1,

pp.383–397. Proceedings of the conference on

hydraulic machinery and flow measurements.

[7] Perrig, A., Farhat, M., Avellan, F., Parkinson,

E., Garcin, H., Bissel, C.,Valle, M., and Favre,

J. Numerical flow analysis in a pelton turbine

bucket. In Hydraulic Machinery and Systems

[49]. Proceedings of the 22nd IAHR

Symposium.

[8] Zhang, Zh., Muggli, F., Parkinson, E., and

Scha¨rer, Ch.(2000), Experimental

investigation of a low head jet flow at a model

nozzle of a Pelton turbine. Proceedings of the

11th International Seminar on Hydropower

Plants, Vienna, Austria, pp. 181–188.6.

[9] Ben M. Koons (2008).Mechanical Design on

pelton turbine for Rwanda Pico Hydro- Hydro

Project (Thayer School of Engineering

Dartmouth College.

[10] Richard L. Roberts on (August 8 2008).Ocean

Energy. Wentworth Institute of Technology

Senior Design Project, Mechanical

Engineering.


MODELLING THE EFFECT OF HEAD AND BUCKET …eaas-journal.org/survey/userfiles/files/v5i305...

Documents

Transcript of MODELLING THE EFFECT OF HEAD AND BUCKET …eaas-journal.org/survey/userfiles/files/v5i305...