An%20Exclusive%20Conservation%20Equation%20for%20Ideal%20Turbo-machines

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An Exclusive Conservation Equation for Ideal
Turbo-machines

• P M V Subbarao
• Professor
• Mechanical Engineering Department

Invention of New Property for CVs with Work
Transfer.
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Conservation of Rothalpy
or

• A cornerstone of the analysis of steady, relative
  flows in rotating systems has, for many years,
  been the immutable nature of the fluid mechanical
  property rothalpy.
• "In a moving passage the rothalpy is therefore
  constant provided
• the flow is steady in the rotating frame
• no friction from the casing
• there is no heat flow to or from the flow.

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Novel Idea for Creation of Variety
Ideas for creation of a variety in turbo-machine.
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Blade Velocity Vs Tangential Component of Fluid
Velocity
In maridional plane at mean radius of rotor
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Relative Angular Velocity
Constant in an ideal turbo-machine
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For stator Ublade 0
For rotors
For a true axial flow machines Ublade constant
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Complex Geometrical Features of A Turbo-Machinne
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A turbomachine working with incompressible fluid
will be isothermal and hence U(T) is constant
throughout the machine.
For an Ideal Hydro Power Plant
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A Two-Way Welfare for the Globe
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Hydro Electric Plant with High Heads
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Option for High Head Hydro Station
In an ideal Penstock
In an ideal Nozzle
In an ideal turbo-machine
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Vri
Vri
U
Vre
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More Ideas
For an Ideal Hydro Power Plant
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Turbo-machines working with Vapors/Gas
For an ideal gas
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For simple compressible fluid Like Inert Gas
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The Fourth Generation Nuclear Power Plants
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An Advanced Nuclear Power Plant
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Geometrical Details along the Third Direction

• True flow through a turbo-machinery is
  three-dimensional.
• Flow and tangential flow velocities are very
  important for better operation of a
  turbo-machine.
• The third component, which is normal to flow and
  tangential direction is in general of no use.
• This direction can better represented as blade
  height direction.

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Third Direction of an Axial Flow Turbo-Machines

• The third direction in an axial flow machine is
  the radial direction.
• The direction of Centrifugal forces!
• Strong centrifugal forces are exerted on blades
  fluid in radial direction.
• The centrifugal field distorts the flow velocity
  profiles considerably.
• Fluid particles tend to move outwards rather
  than passing along cylindrical stream surfaces as
  classically assumed.

• Particularly in tall blade (low hub tip) ratio
  designs.
• An approach known as the radial equilibrium
  method, widely used for three-dimensional design
  calculations in a an axial flow machine.

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Radial Equilibrium Theory of Turbo-machines

• P M V Subbarao
• Professor
• Mechanical Engineering Department

A Model for Stable Operation of A Machine A
guiding equation for distribution of load along
blade length .
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Radial Variation Blade Geometry
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Radial Equilibrium Theory

• Assumes that flow is in radial equilibrium before
  and after a blade row.
• Radial adjustment takes place through the row.
• More important for Axial Flow Machines.

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Radial Equilibrium Analysis
The centrifugal force (rrdrdq)w2r Vq rw
The centrifugal force is
The pressure force on the element
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If the two forces are the only ones acting
(viscous and other effects neglected), the
particle will move at constant radius if
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Equilibrium Condition for A Rotating Fluid
An equivalent equation for compressible flow can
be developed by using the following
thermodynamic relation
The radial variation of whirl velocity should be
according to above equation. How to implement on
a machine?
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Total Energy Equation for A Rotating Fluid
Stagnation enthalpy should conserve, as there are
not interactions with rotor at inlet or exit.
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Radial component of velocity should be constant
(zero) along radial direction for radial
equilibrium of flow.
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Constant in a turbo-machine along meridonial
Plane
Stagnation enthalpy is Constant in a
turbo-machine along radial direction at intake
and discharge.
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Twisted Blades for Large Turbines
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Lessons from Nature
THE VORTEX

• In the case of a vortex, the flow field is purely
  tangential.

The complex potential function
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General Rules for Selection of Whirl Component

• Free Vortex Whirl

• Forced Vortex Whirl

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More complex Models

• Weighted mean of free and forced vortices

Inlet
Exit

• General Whirl Distribution

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Radial Variation of Flow Velocity in Real Machine
Discharge
Intake
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Radial Variation of Whirl Velocity
Intake
Discharge
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Radial Variation of Mass flow rate
Intake
Discharge
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Design of Compact Machine
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Kaplan Turbine
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DESIGN OF THE BLADE
90 or better in efficiency
Two different views of a blade
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Basic Rules for Design of An Ideal Turbo-machine
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Basic Rules for Design of An Ideal Turbo-machine

• Enumerate the details of source or demand.
• Calculate Specific speed and identify the
  fundamental concept of operation.
• X1 (Impulse)X2(Reaction)(1-X1-X2)(centrifugal)
• Y1 (Radial)(1-Y1 )(Axial)
• Design of Flow Path using Conservation of
  rothalpy.
• Design blade cascade using conservation of mass
  and momentum.
• Design of Radial Geometry using Radial
  Equilibrium Theory.
• A design of an Ideal Machine..
• Real Performance will be lower

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Basic Rules for Design of A Real Turbo-machine

• More customized rules along with the general
  rules.
• Customized rules are specific to application
• Power consumption Vs Power Generation.
• Radial Vs Axial.
• Incompressible flow Vs Compressible.
• In Reality
• Design analysis of A Real Machine is an Exclusive
  Scientific Art.