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Fluid Dynamic Characterization of Turbo-machinery

P M V Subbarao

Professor

Mechanical Engineering Department

Understanding the Role of Vectorial analysis !!

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The thermodynamic Variations

IncompressibleFluid

CompressibleFluid

Power GeneratingMachines

Hydraulic Turbines Steam/Gas/windTurbines

Power ConsumingMachines

Pumps Fan/blowers/Compressors

Two main categories of turbo-machine are identified: Firstly, those which absorb power to increase the fluid

pressure or head (fans, compressors and pumps); Secondly, those that produce power by expanding fluid to

a lower pressure or head (hydraulic, steam and gasturbines).

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Fluid Dynamics of A Turbo-machine

A Turbo-machine

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The Ancient Design : Undershot Water Wheel : 4000BC

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SOME TYPES OF WIND TURBINES: VAWT

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SOME TYPES OF WIND TURBINES: HAWT

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Various Types of Modern Turbomachine

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Why so many different types of either pumps(compressors) or turbines are in use ?

Is it due to (almost) infinite range of service requirements?

As a fact, for a given set of operating/resourcerequirements ,

there should be only one type of pump or turbine which is best suited to provide best/optimum performance.

Why So Many?

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Classification of Turbo-machines

Two main categories of turbo-machine are identified: Firstly, those which absorb power to increase the fluid

pressure or head (fans, compressors and pumps); Secondly, those that produce power by expanding fluid to

a lower pressure or head (hydraulic, steam and gasturbines).

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Classification : Flow Path

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Solid Fluid Interaction Level

Open flow No casing or enclosure for the rotating device

Propeller is an open flow power consuming

device. Windmill is an open flow power generating

device.

Enclosed or encased flow devices

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Any Unified Theory?

Developed by the Father of Turbo- machines

The Mathematics of Turbo-machinery

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Leonhard Euler

Leonhard Euler (1707-1783) wasarguably the greatest mathematician ofthe eighteenth century.One of the most prolific writer of alltime; his publication list of 886 papersand books fill about 90 volumes.

Remarkably, much of this output datesfrom the last two decades of his life,when he was totally blind.Euler's prolific output caused atremendous problem of backlog: the St.Petersburg Academy continued

publishing his work posthumously formore than 30 years.

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Theoretical and Rigorous Work of French

Bernoulli and Leonhard Euler. 1750:Euler offered a memoir containing analysis and

equations for hydraulic turbines. 1754: An idealized theoretical application of Newtons

Law to centrifugal impellers. Known as Euler Equation.

Did much to help the development of hydraulic machinery. 1767: Relation between Torque and Change in moment of

momentum of the fluid as it passed through the machine.

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Applications of Eulers Equation

Euler equation applies to all kinds of turbomachines. Wind turbines ---- Pumps --- Gas turbines. Axial flow machines to Radial flow to Mixed flow.

Energy extraction machines Energy consumingmachines. For a turbine the value of Equation is negative. For pumps, fans, blowers and compressors it is positive.

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The Superiority of Vector Parameters

k V jV iV V z r

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