Theory of Large Turbines

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Theory of Large Turbines

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• I I T Delhi

An Appropriate proportion of Impulse and Reaction
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Vri
U
Vre
Exit Velocity Triangle
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Vai Inlet Absolute Velocity Vri Inlet Relative
Velocity Vre Exit Relative Velocity VaeExit
Absolute Velocity ai Inlet Nozzle Angle. bi
Inlet Blade Angle. be Exit Blade Angle. ai Exit
Nozzle Angle.
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Need for Multi Staging
Mean Peripheral Speed of the Blade 825 m/s
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Strategy for Multi Staging
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Current Practice

• Purely multistage impulse turbines are mainly
  preferred in medium capacities of power
  generations.(30 60 MW units).
• The main advantages are simplicity of
  construction, low costs, reliability and
  convenience of operation.
• The height of blades in last stages of multistage
  turbine rapidly increase.
• It is difficult to obtain tall, smooth and
  streamlined shape for the turbine.
• Turbines of compound impulse stages are
  considered obsolete at present.
• It is current practice for multistage turbines
  to allow for some amount enthalpy drop to take
  place in the moving blades as well.

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HP Turbine Rotor
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LP Turbine Rotor
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Impulse-Reaction turbine

• This utilizes the principle of impulse and
  reaction.
• There are a number of rows of moving blades
  attached to the rotor and and equal number of
  fixed blades attached to the casing.
• The fixed blades are set in a reversed manner
  compared to the moving blades, and act as
  nozzles.
• The fixed blade channels are of nozzle shape and
  there is a some drop in pressure accompanied by
  an increase in velocity.
• The fluid then passes over the moving blades and,
  as in the pure impulse turbine, a force is
  exerted on the blades by the fluid.
• There is further drop in pressure as the fluid
  passes through the moving blades, since moving
  blade channels are also of nozzle shape.
• The relative velocity increases in the moving
  blades.

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The reaction effect is an addition to impulse
effect.
The degree of reaction
p
va
vr
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First law for fixed blades
2
0
1
First law for moving blades
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• The steam is delivered to the wheel at an angle
  a1 and velocity Va1.
• The selection of angle ai is a compromise.
• An increase in a1, reduces the value of useful
  component (Absolute circumferential Component).
• This is also called Inlet Whirl Velocity, Vw1
  Va1 cos(a1).
• An increase in a1, increases the value of axial
  component, also called as flow component.
• This is responsible for definite mass flow rate
  between to successive blade.
• Flow component Vf1 Va1sin(a1) Vri sin(b1).
• The absolute inlet velocity can be considered as
  a resultant of blade velocity and inlet relative
  velocity.
• The two points of interest are those at the inlet
  and exit of the blade.

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• If the steam is to enter and leave the blades
  without shock or much losses, then relative
  velocity should be tangential to the blade inlet
  tip.
• Vr1 should enter at an angle b1, the inlet blade
  angle.
• Similarly, Vr2 should leave at b2, the exit blade
  angle.
• In an impulse reaction blade, Vr2 gt Vr1

• The flow velocities between two successive blade
  at inlet and exit are Vf1 Vf2.
• The axial (basic useful) components or whirl
  velocities at inlet and exit are Vw1 Vw2.

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Newtons Second Law for an Impulse-reaction
Blade The tangential force acting of the jet
is F mass flow rate X Change of velocity in
the tangential direction Tangential relative
velocity at blade Inlet Vr1 cos(b1). Tangential
relative velocity at blade exit -Vr2
cos(b2). Change in velocity in tangential
direction -Vr2 cos(b2) Vr1 cos(b1). -
(Vr2 cos(b2) Vr1 cos(b1)). Tangential Force,
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The reaction to this force provides the driving
thrust on the wheel. The driving force on wheel
Power Output of the blade
Diagram Efficiency or Blade efficiency
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2
0
1
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Nozzle blade factor, f
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For a given shape of the blade, the efficiency is
a strong function of U/Vfitc.
For maximum efficiency
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Stage Sizing
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Selection of Degree of Reaction
L increasing
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Turbine Inlet
Turbine Outlet
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PRESSURE VARIATION ALONG THE STAGES
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Temperature variation along the
stages
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Stator (h0-h1)
Rotor (h1-h2)
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Degree of Reaction
R
Stage No.
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VARIATION OF INTERNAL POWER ALONG THE STAGES
210MW
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