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Variations of Turbo-Machines Development of a Macro Mathematical Model

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Variations of Turbo-Machines Development of a Macro Mathematical Model

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    1. Variations of Turbo-Machines & Development of a Macro Mathematical Model P M V Subbarao Professor Mechanical Engineering Department

    2. Fluid Dynamics of A Turbomachine

    3. The Ancient Design : Undershot Water Wheel : 4000BC

    4. Various Types of Turbomachine

    5. Why so many different types of either pump (compressor) or turbine are in use ? Due to (almost) infinite range of service requirements? As a fact, for a given set of operating/resource requirements there should be only one type of pump or turbine which is best suited to provide optimum performance. Why So Many?

    6. 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 gas turbines).

    7. Classification : Flow Path

    8. Classification : Flow Path Turbomachines are further categorised according to the nature of the flow path through the passages of the rotor. When the path of the through-flow is wholly or mainly parallel to the axis of rotation, the device is termed an axial flow turbomachine. When the path of the through-flow is wholly or mainly in a plane perpendicular to the rotation axis, the device is termed a radial flow turbomachine. Mixed flow turbomachines are widely used. The term mixed flow refers to the direction of the through-flow at rotor outlet when both radial and axial velocity components are present in significant amounts.

    9. 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.

    10. Further Classification of Turbomachines Compressibility of the fluid Incompressible The density is constant through the entire flow process; liquid pumps. Compressible; Gas flows: compressors.

    11. Any Unified Theory? The Father of Turbo-machines The Mathematics of Turbo-machinery

    12. Leonhard Euler

    13. 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 Newton’s 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.

    14. Applications of Euler’s 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 consuming machines. For a turbine the value of Equation is negative. For pumps, fans, blowers and compressors it is positive.

    15. The Superiority of Vector Parameters

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