Exp 1 Pelton Wheel Turbine

MEHB221 Fluid Mechanics Lab 2012

1

Experiment No. 1

PERFORMANCE OF PELTON WHEEL TURBINE

Objective

To investigate the performance of the Pelton Wheel turbine with different range of flow

rates and rotational speeds.

Summary of theory

Pelton Wheel turbine is an impulse type of hydraulic turbine. The total drop in pressure

of the fluid takes place in stationary nozzles. A proportion of the kinetic energy of a high

velocity jet is converted into mechanical work delivered to the shaft, the remainder being

dissipated by fluid friction and partly retained as kinetic energy of fluid leaving the cups.

The fluid transfers its momentum to buckets mounted on the circumference of a wheel.

Pelton Wheel or impulse type hydraulic turbine is used in hydroelectric scheme when the

head available exceeds about 300m. The turbine is supplied with water under high head

through a long conduit called penstock. The water is then accelerated through a nozzle

and discharge at high-speed free jet at atmospheric pressure, which then impinges the

cascade of impulse buckets.

Control Volume

Consider Pelton Wheel rotating in an anti-clockwise direction (refer to figure 2) with an

angular velocity, ω, due to the combined action of an incident water jet and a clockwise

resisting moment τ. We take a control volume that is moving at a constant velocity with

the bucket on the Pelton Wheel as shown in figure 3.

The velocity of the incident jet relative to the bucket is given by: -

Vr1 = V1 - U

= V1 - ωR

Where R is the mean radius of the wheel.

Since the incident and emergent jets are both exposed to atmospheric pressure, the

magnitude of the emergent jet will be only slightly less than the frictional resistance

which can be allowed for by introducing a frictional resistance coefficient k1 so that: -

Vr2 = K1Vr1


2

The jet will be deflected so that the emergent jet is at an acute angle θ to the incident jet.

The change in the component of relative velocity in the plane of the wheel (i.e. in the line

of the incident jet) will be: -

∆Vr = Vr1 + Vr2 Cos θ

= Vr1 (1 + k1 Cos θ)

= (V1 – U) (1 + k1 Cos θ)

Which can be written as:

∆Vr = (V1 – U) (1 + c)

Flow Discharge

The discharge through the nozzle, Q from an inlet height H at pressure P is given by:

H = P/ρg

Q = AnV1

Where An is the nozzle opening area. But,

Hence,

Where Cv is the nozzle flow coefficient.

Power Output

Using the force-momentum equation, the force, F exerted on the bucket by the water jet

is given by:

F = ρQ∆Vr

The torque acting on the shaft of the Pelton Wheel is then:

τ = FR

= ρQ∆VrR

gH2CV v1 =

gH2CAQ vn=


3

And the power output, Wout is:

Wout = τω

= ρQ∆VrU

Substituting for ∆Vr gives:

Wout = ρUQ (V1 – U) (1 + k1 Cos θ)

Efficiency

The input hydraulic power, Win to the Pelton Wheel is the product of the inlet pressure

and flow rate.

Win = PQ

= ρgHQ

and the efficiency of the Pelton Wheel is

η = Wou t/ Win

= U∆V / gH

Procedures

In this experiment, we will fix the flow rate and gradually varying the brake load from

zero load to a maximum load. The speed is influenced by the coefficient of friction

between the band and the shaft pulley, which is influenced by temperature; therefore, it is

necessary at each condition to wait for the speed to stabilize before taking readings. The

torque produced can be then determined knowing the force applied and the wheel speed.

The experiment will be repeated for 3 different flow rates (3 different pressure values).

1. Zero the tension gauge at no load.

2. Prepare the friction band and weight hanger (weighing 350g) of the friction

dynamometer.

3. Make sure that the suction valve and volumetric measuring valve are open (in line).

4. Fully open the bench flow-regulating valve.

5. Switch on the Hydraulic Bench pump.

6. Slowly increases the pump speed regulator until maximum (the ‘white-line’ pointed

to the downward direction).

7. Adjust the nozzle spear valve until the inlet pressure reads approximately 0.8 bar.

8. Wait until the condition has stabilized.

9. Record the weight (i.e. 350g) and the reading of the tension gauge.

10. Using the non-contact optical tachometer, measure the speed of rotation of the wheel

in rpm. Point the light beam to a position least affected by the water in order to obtain


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better accuracy. At low speed, the variation in the reading will be quite significant.

(call the instructor to use the optical tachometer)

11. Add another 100 grams weight and repeat steps 8 to 10.

12. Repeat 11 in the step of 100 grams until the wheel stall (the wheel stop rotating).

13. Remove all the weight from the hanger.

14. Measure the flow rate. To measure the flow rate, close the volumetric measuring

valve and note the time taken for the water to fill a certain volume using the scale

(take 10 liters).

15. Open back the volumetric measuring valve.

16. Adjust the nozzle spear valve until the inlet pressure is approximately 1.0 bar and

repeat steps 8 to 15.

17. Adjust the nozzle spear valve until the inlet pressure is approximately 1.2 bar and

repeat steps 8 to 15.

18. Switch off the hydraulic bench pump.

Data, Observation and Results

• Record the results of the experiment on the results sheet provided.

• Calculate the inlet head (H), the discharge or flow rate (Q) and the power input (Win).

Where ρ = 1000 kg/m3

g = 9.81 m/s2

• Calculate the measured torque (τm), the measured power output (Wout,m) and the

measured efficiency (ηm).

Where W = Applied weight in grams

S = Tension gauge reading in grams

Rd = Radius of dynamometer wheel

= 0.03 meter

60xt

VolQ =

[ ]dm gRx1000

)SW( −=τ

WattQxPx

Win

60

)10)(10( 35 −

=

mg

)10Px(H

5

ρ=


5

ηm = Wout,m / Win

• Calculate the theoretical values of output torque (τth), power output (Wout,th) and

efficiency (ηth).

Where K1 = 0.8

θ = 25o

ηth = Wout,th / Win

• Calculate the velocity ratio U/V1.

Where R = 0.05m

Cv = 0.94

• Plot the graph of measured power against wheel speed for all conditions. (All three

conditions on the same graph – Graph 1)

• Plot the graph of measured efficiency against wheel speed for all conditions. (All

three conditions on the same graph – Graph 2)

Analysis and Discussion

• Explain the working principle of Pelton Wheel Turbine.

• Comment on Graph 1 and Graph 2.

• Discuss the performance of the Pelton Wheel turbine with respect to different range

of flow rates and different range of rotational speeds.

• List the possible sources of errors and safety precaution.

Watt60

2W

mm,out

πωτ=

( )Rcosk160

2R)gH2(C

60

10Qx1v

3

th θ+

πω−

ρ=τ

−

WattWth

thout

60

2,

πωτ=

[ ] Watt60

2x

gH2C

R

V

U

v1

πω=

MEHB221

Figure 1:

Figure 3:

Fluid Mechanics Lab

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Figure 1: Detail of Pelton Wheel Buckets

Figure 2: Absolute Velocities

Figure 3: Velocities Relative to Bucket

2012

MEHB221

Figure 4: General Arrangement of Cussons Pelton Wheel

Fluid Mechanics Lab

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General Arrangement of Cussons Pelton Wheel

2012


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Example of Result Table

Inlet pressure P = ___________bar

Inlet Head H = ___________ m

Volume of water collected Vol = ___________ liter

Time taken t = ___________ s

Discharge Q = ___________ liter/min

Power Input Win = ___________ Watt

Weight

W

(g)

Tension

S

(g)

Speed

ω (rpm)

Measured

Torque

τm (Nm)

Measured

Power Out

Wout,m

(Watt)

Measured

Efficiency

ηm

Theoretical

Torque

τth (Nm)

Theoretical

Power Out

Wout,th

(Watt)

Theoretical

Efficiency

ηth

U/V1

350

450

550

650

750

850

950

1050

1150

1250

1350

Documents

Exp 1 Pelton Wheel Turbine