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TurbinesSteam and Gas Units
Ch 5 in El-Wakil
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Turbines
Consider the following schematic of a vapour power plant.
Until now, we have focused most of our attention onsubsystems A and B
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Turbines
Within subsystem B is the turbine, which merits special
attention. We will now consider steam and gas turbines inmore detail.
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Steam Turbines
Before 1900, steam power plants werereciprocating engines to convert enthalpy to work
1909: Steam turbines started to get implemented
with 12 MW units being installed
siemens.com
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Steam Turbines
1929: A 208 MW unit is installed in NYC
1950s: 450 MW steam turbines were being
installed
Capacities have now risen to over 1000 MW
siemens.com
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Gas Turbines
1903: The first successful gas turbine was built in
France (with = 3% it was not practical)
1939: First flight of a jet plane powered by a gas
turbine
flightglobal.com
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Gas Turbines
WWII: Swiss engineers develop gas turbines for
power generation that are efficient enough for use
After WWII, jet fighters and passenger jets became
widespread in many countries
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Turbine Uses for Power
Steam turbines are used for municipal power
generation, normally providing base load power from
large installations
Gas turbines: Used as peaking units
Power isolated locations such as oil rigs
Power oil pipeline routes
Used with steam turbines in combined cyclepower plants
To understand the physics of blade motion, we
revisit the Impulse Principle
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The Impulse Principle
Consider a horizontal jet impinging in the +x
direction on a flat plate.
The fluid imparts a horizontal force, called an
impulseto the plate
F= the force of the impulse (N)
= mass flow rate of the jet (kg/s)
= velocity of the jet in the x-direction (m/s)
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The Impulse Principle
If the plate is moving as the jet hits it, than the
velocity of the jet relativeto the plate is Vs- V
b
Now:
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The Impulse Principle
Work is being done on the plate, because the force
is being applied over a distance (recall W=Fd.
Power is work done per unit time =Fd/t
Alternatively:
Or:
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The Impulse Principle
The efficiency of the transfer or power from the jet
to the plate, can be found by dividing the power
by the power of the water jet
to get the efficiency
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The Impulse Principle
In a gas turbine with a steam jet impinging on a
blade, maximizing power transfer is an objective
This can be done by differentiating w/r/t and
setting it equal to zero (see El-Wakil 5.2).
This gives:
Note that this is50% of the power
in the incoming
water
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The Impulse Principle
Turbine blades are rounded. Consider a surface
that is rounded instead of flat, which causes the jet to
change direction.
The fluid velocity, relative to the surface is still
Vs - Vb. The fluid exit velocity, relative to the surface isalso V
s- V
b.
This will increase the impulse that is imparted to
the rounded surfaces
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The Impulse Principle
Using the same analysis as with the flat plate,
impulse, power, and blade efficiency are:
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The Impulse Principle
Again, the blade velocity which maximizes power
transfer can be found by differentiating power and
setting the expression equal to zero.
Note that this is100%of the
power in the
incoming water
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Example 14
A jet of water with a mass flow rate of 0.84 kg/s and
a velocity of 0.66 m/s impinges on a curved surfaces
and propels it forward. The efficiency with which
power is transferred from the jet to the surface is
78%.A) Calculate the velocity of the surface
B) Calculate the power transferred from the jet to
the surface
C) Calculate the velocityof the surface and power
transferred as functions of
varying efficiency
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The Impulse Principle
In a turbine, the blades are rotating away from a jet,
so there must be a continuous series of blades.
Turbines typically have 30 - 60 blades per rotor.
In the confined space of a gas turbine, it is
impossible to have the jet impinging directly on theblades
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The Impulse Principle
The jet impinges at an angle
The jet also exits at an angle close to so that it
can be redirected to another row of blades
General FlowDirection
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