Velocity Triangle for Moving Blade of an impulse Turbine
1.
2. Velocity triangle for Moving Blade of an impulse
turbine
1. Consider a steam jet entering
a curved blade after leaving
the nozzle at C.
2. Now let the jet glides over
the inside surface and leaves
the blade at D, as shown in
fig.
3. Now let us draw the velocity
triangles at inlet and outlet
tips of the moving blade, as
shown in fig.
4. The inlet triangle of velocities
represented by AEC and
outlet triangle by AFD.
5. The relations between inlet
and outlet velocity triangle is
Vr= Vr1.
Fig.: Velocity triangle of an impulse turbine
3. Velocity triangle for Moving Blade of an impulse
turbine
Let
Vb = Liner velocity of the moving
blade(AB)
V= Absolute velocity of steam
entering the moving blade(AC),
Vr= Relative velocity of jet to the
moving blade(BC). It is the vectorial
difference between Vb and V.
Vf= Velocity of flow at entrance of the
moving blade. It is the vertical
component of V.
Vw=Velocity of whirl at entrance of
the moving blade. It is horizontal
component of V.
θ= Angle which the relative velocity of
jet to the moving blade(Vr) makes
with the direction of motion of the
blade.
α= Angle with the direction of
motion of the blade at which the jet
enterns the blade.
V1, Vr1, Vf1, Vw1, β, ϕ = Corresponding
values at exit of the moving blade.
Fig.: Velocity triangle of an impulse
turbine
4. Power produced by an Impulse
Turbine
Consider an impulse turbine working under the action of a steam jet.
Let,
m = Mass of steam flowing through the turbine in Kg./s
Now, Change in the velocity of whirl in m/s = Vw+ Vw1 [Vw – (– Vw1 ), when Vw1 is
negative]
We know that according to the Newton’s second law of motion, force in the
direction of motion of the blades
Fx = Mass of steam flowing per second × Change in the velocity of whirl
= m(Vw+ Vw1)
and work done in the direction of motion of the blades
= Force × distance
= m(Vw+ Vw1)× Vb N-m/s
So,
Power produced by the turbine P= m(Vw+ Vw1)× Vb watts. [ 1 N-m/s = 1 watt]
5. Power produced by an Impulse
Turbine
Similarly, we can find out the axial thrust on the wheel is due to the
difference of velocities of flow at inlet and outlet.
So, axial thrust on the wheel
FY = Mass of steam flowing per second × Change in the velocity of flow
= m(Vf - Vf1)
* The value of Vw1 is taken as negative because of the opposite direction of
Vw with respect to the blade motion. If Vw1 is in the same direction with
respect to the blade motion, then Vw1 is taken as positive.
** The ratio of Vr1 to Vr is known as blade velocity coefficient or friction
factor, denoted by K
So, K =
6. Reaction Turbine
1. In a reaction turbine, the steam enters the wheel under
pressure and flows over the blades.
2. The steam, while gliding, propels the blades and make
them to move.
3. As a matter of fact, the turbine runner is rotated by the
reactive force of steam jets.
4. It has the following main components:
i. Casing
ii. Guide mechanism
iii. Runner
iv. Draft tube
7. 1. Casing
1. It is an air-tight metallic case.
2. In it the steam from the boiler, under a high pressure
and temperature, is distributed around the fixed
blades(guide mechanism).
3. It is designed in such a way that the steam enters the
fixed blades with a uniform velocity.
8. 2. Guide mechanism
It is a mechanism, made up with the help of guide
blades, in the form of a wheel and generally fixed to
the casing.
It is designed properly in order to:
1. Allow the steam to enter the runner without shock.
2. Allow the required quantity of steam to enter the
turbine.
9. 3.Runner
1. It is consists of runner blades fixed to a shaft or rings.
2. The blades, fixed to the runner, are properly
designed in order to allow the steam to enter and
leave the runner without shock.
3. The surface of the turbine runner is made very
smooth to minimise the frictional losses.
4. It is, generally, cast in one piece but sometimes made
up of separate steel plates welded together.
10. 4.Draft tube
The steam, after passing through the runner, flows
into the condenser through a tube called draft tube.
11.
12. Velocity triangle for moving blades of a reaction turbine
1. Consider steam, in the
form of a jet, entering
the curved blade at C.
2. Let the jet glides over
the inside surface and
leaves the blade at D as
shown in fig.
3. Now let us draw the
velocity triangles at
inlet and outlet tips of
the moving blade as
shown in fig.
Fig.: Velocity triangle for a reaction
turbine
13. Velocity triangle for moving blades of a reaction
turbine
Let
Vb = Liner velocity of the moving
blade(BA)
V= Absolute velocity of steam entering
the moving blade(BC),
Vr = Relative velocity of jet to the moving
blade(AC). It is the vectorial difference
between Vb and V.
Vf = Velocity of flow at entrance of the
moving blade EC. It is the vertical
component of V.
Vw =Velocity of whirl at entrance of the
moving blade BE. It is horizontal
component of V.
Θ = Angle which the relative velocity of
jet to the moving blade(Vr) makes with
the direction of motion of the blade.
α= Angle with the direction of motion of
the blade at which the jet enters the
blade.
V1, Vr1, Vf1, Vw1, β, ϕ = Corresponding
values at exit of the moving blade. Fig.: Velocity triangle for a reaction
turbine
14. Power produced by a Reaction Turbine
Consider a reaction turbine working under the action of a steam jet.
Let,
m= Mass of steam flowing through the turbine in Kg./s,
Change in the velocity of whirl in m/s = Vw+ Vw1 [Vw – (– Vw1 ), when Vw1 is
negative]
We know that according to the Newton’s second law of motion, force in the
direction of motion of the blades
Fx = Mass of steam flowing per second × Change in the velocity of whirl
= m(Vw+ Vw1)
and work done in the direction of motion of the blades
= Force × distance
= m(Vw+ Vw1)× Vb N-m/s
So,
Power produced by the turbine P= m(Vw+ Vw1)× Vb watts. [ 1 N-m/s = 1 watt]
15. Power produced by a Reaction Turbine
Similarly, we can find out the axial thrust on the wheel is due to the
difference of velocities of flow at inlet and outlet.
So, axial thrust on the wheel
FY = Mass of steam flowing per second × Change in the velocity of flow
= m(Vf - Vf1)
* The value of Vw1 is taken as negative because of the opposite direction of
Vw with respect to the blade motion. If Vw1 is in the same direction with
respect to the blade motion, then Vw1 is taken as positive.
** The ratio of Vr1 to Vr is known as blade velocity coefficient or friction
factor, denoted by K
So, K =
