Pelton Wheel Water Turbine

Portions of text and figures on this page provided by G. Cussins Ltd, Manchester, UK

photo by Joe Turcio

TABLE OF CONTENTS

1. INTRODUCTION

2. DESCRIPTION

3. THEORY

3.1 List Of Symbols

3.2 Velocity Analysis

3.3 Nozzle Flow Coefficient

3.4 Power Output

3.5 Variation of Power Output With Speed

3.6 Efficiency

4. EXPERIMENTS

4.1 Experimental Program

4.2 Experimental Procedure

4.3 Speed Measurement

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1. INTRODUCTION

The Pelton Wheel is the only form of impulse turbine in common industrial use. It is a robust and simple machine which is ideal for the production of power from low volume water flows at a high head with reasonable efficiency.

Cussons P6240 Pelton Wheel, although a model, reproduces all the characteristics of full size machines and allows an experimental program to determine both the performance of the turbine and to verify design theory.

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2. DESCRIPTION

Cussons P6240 Pelton Wheel consists of a Degener 4717 model Pelton Wheel mounted on a base plate and fitted with a friction dynamometer as illustrated in Figure 2 overleaf. The design of the Degener Pelton Wheel follows typical industrial practice with a horizontal shaft, single horizontal jets produced by a single nozzle fitted with a needle or spear regulator, and a wheel fitted with multiple (16) elliptical ridged buckets at a mean diameter of 100mm.

The nozzle is positioned in the same plane as the wheel and arranged so that the jet of water impinges tangentially on to the buckets. The nozzle and a single bucket are illustrated in Figure 1 below. Each "bucket" is divided by a "splitter" ridge which divides the jet into two equal parts. The buckets are shaped so as to prevent the jet to the preceding bucket being intercepted too soon. After flowing round the inner surface of the bucket, the fluid leaves with a relative velocity almost opposite in direction to the original jet. The desired maximum deflection of the jet (180) cannot be achieved without the fluid leaving one bucket striking the following one, and so in practice the deflection is limited to approximately 155 (i.e. see Figure 1 below 180-25). The bottom of the casing is open to allow the water leaving the buckets to drain away. The front face of the casing is transparent Perspex allowing easy observation of the behaviour of the water jet and assessment of exit angles.

The nozzle is controlled by movement of the spear regulator along the axis of the nozzle which alters the annular space between the spear and the housing, the spear being shaped so as to induce the fluid to coalesce into a circular jet of varying diameter according to the position of the spear. A static pressure tapping is provided to allow measurement of the inlet water pressure.

The friction dynamometer consists of a 60mm diameter brake wheel fitted with a fabric brake band. The brake band is tensioned by a weight hanger and masses with the fixed end being secured via a spring balance to the support frame.

The speed of the turbine can be measured using Cussons P4740 Optical Tachometer which is available as an optional accessory.

 

Figure 1. Details of Pelton Wheel Buckets.

 

 

Figure 2 General Arrangement of Cussons Pelton Wheel note that our setup does not have the friction brake.

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3. THEORY

3.1 list of symbols

Ar

area of incident jet

m2

C

loss coefficient

 

Cv

coefficient of velocity for jet

 

F

force exerted on bucket

N

g

acceleration due to gravity

9.806 m/s2

H

inlet head

m

k1

frictional resistance coefficient

 

mass flow rate

kg/s

rate of flow of jet

m/s

R

radius of turbine rotor

m

U

tangential velocity of wheel

m/s

V1

incident jet velocity

m/s

Vr1

incident jet velocity relative to bucket

 

Vr2

emergent jet velocity relative to bucket

 

power output

watts

h

wheel efficiency

%

q

angle between incident and emergent jets

rads

r

density of water torque

kg/m3

t

torque

Nm

w

angular velocity

rads/s

3.2 Velocity Analysis

Consider a Pelton Wheel rotating in an anti-clockwise direction with an angular velocity w due to the combined action of an incident water jet of velocity V1 and a clockwise resisting torque t as shown in Figure 3a. The velocity analysis will use a bucket on the Pelton Wheel as a reference as shown in Figure 3b.

a) Absolute Velocities

b) Velocities Relative to Bucket

 

Figure 3. Velocity Analysis

 

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

Since the incident and emergent jets are both exposed to atmospheric pressure the magnitude of the emergent jet velocity will be only slightly less than the incident jet velocity due to frictional resistance which can be allowed for by introducing a frictional resistance coefficient k1 so that

The jet will be deflected so that the emergent jet is at an acute angle q to the incident jet. The change in the component of velocity in the plane of the wheel (i.e. in the line of the incident jet) will be

which can be written as

3.3 Nozzle Flow Coefficient

The discharge through the nozzle form the inlet head H is given by

3.4 Power Output

The force exerted on the bucket by the water jet is obtained from Newton's second law as the rate of change of momentum between the incident and emergent jets in the plane of the wheel.

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

and the power output is

substituting for and

3.5 Variation of Power Output With Speed

For a given head and nozzle area the power output will be a maximum if Cv and k1 have their highest obtainable values, if cos q = 1 and if U (V1 U) is a maximum.

U (V1 U) will be a maximum when V1 = 2U, that is, when the incident jet velocity is twice the Pelton Wheel bucket speed. For cos q =1 then q = 0 and relative to the buckets the incident jet is deflected through 180, furthermore if k1 = 1 then Vr1 = Vr2.

With V1 = 2U the Vr1 = U (and ignoring friction across the buckets Vr2 = U) the absolute velocity of the emergent jet in the plane of the wheel will then be zero, the whole of the velocity head of the incident jet will have been converted into useful work and the water will effectively fall off the trailing edge of the buckets. The maximum power output is given by

If resisting torque is reduced then wheel will accelerate, D V will reduce and the limiting case which would not be obtainable in practice would be when U = V1, for this condition the torque and power output would both be zero. If the resisting torque is increased the wheel can become stalled so that U = 0 and the stall torque will be

3.6 Efficiency

The input hydraulic power to the Pelton Wheel is the product of the inlet pressure and flow rate.

and the efficiency of the Pelton Wheel is

Since the input hydraulic power depends only on the head and the nozzle area and is independent of the Pelton Wheel speed then the efficiency is directly proportional to the power output and thus maximum power and maximum efficiency occur at the same conditions

Substituting for D V

For maximum power V1 = 2U

Substituting for

 

In an ideal situation, Cv, k1 and cos q are all equal to 1.0 and hence the ideal maximum efficiency is unity.

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4. EXPERIMENT

4.1 Experimental Program

The fundamental experiment which can be carried out with Cussons Pelton Wheel is to investigate the performance of the machine for a range of flow rates and rotational speeds.

There are two controls which can be varied independently; the load applied to the brake and the position of the nozzle regulating spear. The position of the nozzle regulating spear controls the nozzle flow rate whilst varying the friction brake load will vary the speed of the turbine wheel.

4.2 Experimental Procedure

The easiest way to organise the experiment is to set the nozzle regulating spear and conduct a number of tests from zero load to maximum load. The speed is influenced by the torque applied by the electro-magnetic brake.

4.3 Speed Measurement

The Pelton Wheel speed in RPM is displayed on the control panel and recorded in the data set.

Experiment Pelton wheel

Aim To investigate the performance of a Pelton Wheel.

Equipment Preparation Set up the quipment as follows.

  1. Position the Pelton Wheel base plate on the working surface of the Hydraulics Bench straddling the weir channel so that the nozzle is at the left hand side and ensuring that the four location pegs engage in the four holes in the base plate.
  2. Connect the delivery hose from the Hydraulics Bench to the inlet pipe of the Pelton Wheel and secure the hose with the worm drive hose clip. Connect the hose from the inlet valve pressure tapping to the auxiliary pressure gauge connection on the front panel of the Hydraulics Bench.
  3. Start the Labview Pelton VI.
  4. Turn on the power supply to the brake.
  5. Turn on the power on the SCXI-1000 signal conditioning box.
  6. Start the pelton.vi in LabVIEW. (Double click on the VI icon on the desktop and LabVIEW will bes started.

Experimental Procedure

    Caution: Be careful not to jam the spear at the end of its travel. Doing so could cause the spear to disconnect from the knob requiring disassembly of the turbine an considerable time delay.

     

  1. Switch on the Hydraulics Bench pump(s) and fully open the bench regulating valve.
  2. Fully open the spear regulator to produce maximum flow rate. Remove all weights and the weight carrier and unhook the friction band from the Pelton Wheel shaft. Measure the water flow rate using the volumetric tank and the free unloaded rotational speed of the Pelton Wheel using the computer display. Observe the emerging jet from the Pelton Wheel and if required make an assessment of the angle between the incident and emergent jets.
  3. Regulate the applied torque by adjusting the electro-magnetic brake torque.
  4. Repeat step c) until the Pelton Wheel stalls. Record the measurements for each condition including the stalled condition.
  5. Repeat procedure for difference settings of the spear regulator. Close the spear regulator to obtain other flow rates.

Results and Analysis

Record the data using the LabVIEW VI. Set the number of runs to 5000 so the VI does not stop before all your data is recorded. Note that each time the VI is stopped the current data set is filed. Restarting the VI will cause a new data file to be generated. This is not a problem so long as you capture all your files before leaving.

a) Record the results on a copy of the result sheet.
b) Calculate the inlet head H, the flow rate Q, incident velocity V1, Pelton Wheel speed U, the torque t , power output W and efficiency.

 

c) Plot graphs of torque, power and efficiency against Pelton Wheel speed for each setting of the spear regulator (approx. constant flow rate).
d) Plot graphs of torque, power and efficiency against U/V1 for each setting of the spear regulator (approx. constant flow rate).

Results Sheet

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