Turbomachinery - Turbines
Mashilo Nkgoeng
November 9, 2021
Contents
1 Introduction 1
2 Classification of Turbines 2
2.1 Pelton wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.1 Parts of a Pelton Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.2 Advantages of a Pelton wheel turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.3 Disadvantages of a Pelton Wheel Turbine . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.4 Velocity Triangle Diagram of a Pelton Wheel Turbine . . . . . . . . . . . . . . . . . . 4
2.1.5 Design Consideration of Pelton Wheel Turbines . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Reaction Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Parts of Reaction Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Types of Reaction Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Radial Flow Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Axial Flow Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Mixed Flow Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Tutorial Problems due 13th November 2021 10
Abstract
A Pelton wheel turbine was named after an American famous engineer in 1870, Lester Allan Pelton. It
is an impulse turbine in which the flow of water is tangential to the runner and the available energy at the
entrance is completely kinetic energy. The pressure available at the inlet and the outlet is atmospheric.
The conversion of pressure energy into kinetic energy takes place through a nozzle. This forms a high
velocity jet that is used for the driving wheel by changing its velocity on the buckets.
1 Introduction
A machine that is designed to add energy to the fluid or removes energy from the fluid by virtue of a rotating
system of blades is referred to as a turbo machine. Hydraulic turbines and pumps are good example of turbo
machines.
Turbine: removes energy from a fluid.
Pump: adds energy to the fluid.
The rotating part in a pump is called an impeller and in a hydraulic turbine it is called a runner. So, when
dealing with hydraulic power, we are talking about power that has been developed by hydraulic turnines
that converts hydraulic energy into mechanical energy. This mechanical energy is used for running electric
generators directly coupled to the shaft of turbines. Turbines unlike pumps are operated at a constant speed.
In the US, 60 - cycle system (cycles/sec or Hz) electric current is commonly used, and under such con-
ditions, the rotating speed of a turbine denoted by N rpm is given by n = 7200/N , where n is the number of
poles in the generator and must always be an even integer. Most 60 Hz generators have between 12 − −96
poles. In many parts of the world, 50 − cycle current is used, in which case n = 6000/N
1
, 2 Classification of Turbines
Hydraulic turbines are classified based on hydraulic actions, i.e. Impulse or Reaction. There is a drop in
static pressure and a drop in velocity head across the runner of a reaction turbine during energy transfer. A
turbine is said to be purely impulsive if the static pressure is constant across the runner.
2.1 Pelton wheel
A pelton wheel turbine is a tangential flow impulse turbine. The water strikes the bucket along the tangent
of the runner. The energy available at the inlet of the turbine is only kinetic energy. The pressure at the inlet
and outlet of the turbine is atmospheric. This type of turbine is used for high heads at low flow rates, and
it can handle a gross head greater than 250 m. In a hydroelectric power plant, this is used to drive the gen-
Figure 1: Pelton Wheel
erator of the turbine and that generator generates the mechanical energy of the turbine into electrical energy.
This turbine was named after LA Pelton, an American Engineer.
p
If the turbine is working under a net head, hfl (gross head-pipe friction loss), the jet velocity Vj = Cv 2ghfl .
Usually, Cv values ranges between 0.97 to 0.99. The bucket speed can be obtained from the equation:
U = ωr (1)
At inlet, Vj = Vw1 = Vr1 + U .
The energy transferred per unit weight of the fluid is given by the following equation:
U
E= [(Vj − U )(1 − K cos θ)] (2)
g
where K is the reduction in relative velocity and the value is usually between 0.8 to 0.9 and θ is the angle
through which the bucket deflect the jet and it usually ranges from 160◦ to 170◦ . The maximum energy
transferred will always occur at some point where dE/dU = 0 and this occurs at U = 0.5Vj .
See how this turbine work on YouTube: https://youtu.be/rf9meqw2SQA
2.1.1 Parts of a Pelton Wheel
Refer to Figure 2 for the different components making up the pelton wheel turbine. Check out the YouTube
video on its operation.
Nozzle - The amount of water striking the buckets of the runner is controlled by providing a spear in the
nozzle. The speed is a conical needle which is operated either by a hand wheel or automatically in an
2
Mashilo Nkgoeng
November 9, 2021
Contents
1 Introduction 1
2 Classification of Turbines 2
2.1 Pelton wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.1 Parts of a Pelton Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.2 Advantages of a Pelton wheel turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.3 Disadvantages of a Pelton Wheel Turbine . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.4 Velocity Triangle Diagram of a Pelton Wheel Turbine . . . . . . . . . . . . . . . . . . 4
2.1.5 Design Consideration of Pelton Wheel Turbines . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Reaction Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Parts of Reaction Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Types of Reaction Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Radial Flow Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Axial Flow Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Mixed Flow Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Tutorial Problems due 13th November 2021 10
Abstract
A Pelton wheel turbine was named after an American famous engineer in 1870, Lester Allan Pelton. It
is an impulse turbine in which the flow of water is tangential to the runner and the available energy at the
entrance is completely kinetic energy. The pressure available at the inlet and the outlet is atmospheric.
The conversion of pressure energy into kinetic energy takes place through a nozzle. This forms a high
velocity jet that is used for the driving wheel by changing its velocity on the buckets.
1 Introduction
A machine that is designed to add energy to the fluid or removes energy from the fluid by virtue of a rotating
system of blades is referred to as a turbo machine. Hydraulic turbines and pumps are good example of turbo
machines.
Turbine: removes energy from a fluid.
Pump: adds energy to the fluid.
The rotating part in a pump is called an impeller and in a hydraulic turbine it is called a runner. So, when
dealing with hydraulic power, we are talking about power that has been developed by hydraulic turnines
that converts hydraulic energy into mechanical energy. This mechanical energy is used for running electric
generators directly coupled to the shaft of turbines. Turbines unlike pumps are operated at a constant speed.
In the US, 60 - cycle system (cycles/sec or Hz) electric current is commonly used, and under such con-
ditions, the rotating speed of a turbine denoted by N rpm is given by n = 7200/N , where n is the number of
poles in the generator and must always be an even integer. Most 60 Hz generators have between 12 − −96
poles. In many parts of the world, 50 − cycle current is used, in which case n = 6000/N
1
, 2 Classification of Turbines
Hydraulic turbines are classified based on hydraulic actions, i.e. Impulse or Reaction. There is a drop in
static pressure and a drop in velocity head across the runner of a reaction turbine during energy transfer. A
turbine is said to be purely impulsive if the static pressure is constant across the runner.
2.1 Pelton wheel
A pelton wheel turbine is a tangential flow impulse turbine. The water strikes the bucket along the tangent
of the runner. The energy available at the inlet of the turbine is only kinetic energy. The pressure at the inlet
and outlet of the turbine is atmospheric. This type of turbine is used for high heads at low flow rates, and
it can handle a gross head greater than 250 m. In a hydroelectric power plant, this is used to drive the gen-
Figure 1: Pelton Wheel
erator of the turbine and that generator generates the mechanical energy of the turbine into electrical energy.
This turbine was named after LA Pelton, an American Engineer.
p
If the turbine is working under a net head, hfl (gross head-pipe friction loss), the jet velocity Vj = Cv 2ghfl .
Usually, Cv values ranges between 0.97 to 0.99. The bucket speed can be obtained from the equation:
U = ωr (1)
At inlet, Vj = Vw1 = Vr1 + U .
The energy transferred per unit weight of the fluid is given by the following equation:
U
E= [(Vj − U )(1 − K cos θ)] (2)
g
where K is the reduction in relative velocity and the value is usually between 0.8 to 0.9 and θ is the angle
through which the bucket deflect the jet and it usually ranges from 160◦ to 170◦ . The maximum energy
transferred will always occur at some point where dE/dU = 0 and this occurs at U = 0.5Vj .
See how this turbine work on YouTube: https://youtu.be/rf9meqw2SQA
2.1.1 Parts of a Pelton Wheel
Refer to Figure 2 for the different components making up the pelton wheel turbine. Check out the YouTube
video on its operation.
Nozzle - The amount of water striking the buckets of the runner is controlled by providing a spear in the
nozzle. The speed is a conical needle which is operated either by a hand wheel or automatically in an
2
