2. 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….

3. Conservation of Rothalpy 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. or

4. Ideas for creation of a variety in turbo-machine. Novel Idea for Creation of Variety

5. Blade Velocity Vs Tangential Component of Fluid Velocity UbUb UbUb V wi V ai V fi V ri In maridional plane at mean radius of rotor

6. UbUb V wi V ai V fi V ri UbUb V wi V ai V fi V ri Vwi UbUb V ai V fi V ri

7. Relative Angular Velocity Constant in an ideal turbo-machine

8. For stator U blade =0 For rotors : For a true axial flow machines: U blade constant

9. Complex Geometrical Features of A Turbo- Machinne

10. A turbomachine working with incompressible fluid will be isothermal and hence U(T) is constant throughout the machine. For an Ideal Hydro Power Plant :

11. A Two-Way Welfare for the Globe

12. Hydro Electric Plant with High Heads p atm H

13. Option for High Head Hydro Station In an ideal Penstock In an ideal Nozzle In an ideal turbo-machine

14. U V ri V re V ai UV ri V ai Inlet Velocity Triangle U V re V ae Exit Velocity Triangle V ri

15. More Ideas For an Ideal Hydro Power Plant :

16. Turbo-machines working with Vapors/Gas For an ideal gas:

17. For simple compressible fluid: Like Inert Gas

18. The Fourth Generation Nuclear Power Plants

19. An Advanced Nuclear Power Plant

20. 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.

21. 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.

22. 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 ….

23. Radial Variation Blade Geometry

24. 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.

25. Radial Equilibrium Analysis The centrifugal force = (  rdrd  )  2 r V  = r  The centrifugal force is The pressure force on the element

26. If the two forces are the only ones acting (viscous and other effects neglected), the particle will move at constant radius if:

27. 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?

28. Total Energy Equation for A Rotating Fluid Stagnation enthalpy should conserve, as there are not interactions with rotor at inlet or exit.

30. Radial component of velocity should be constant (zero) along radial direction for radial equilibrium of flow.

31. Constant in a turbo-machine along meridonial Plane Stagnation enthalpy is Constant in a turbo-machine along radial direction at intake and discharge.

32. Twisted Blades for Large Turbines

33. Lessons from Nature In the case of a vortex, the flow field is purely tangential. The complex potential function: THE VORTEX

34. Free Vortex Whirl: Forced Vortex Whirl : General Rules for Selection of Whirl Component

35. More complex Models Weighted mean of free and forced vortices General Whirl Distribution Inlet Exit

36. Radial Variation of Flow Velocity in Real Machine Intake Discharge

37. Radial Variation of Whirl Velocity Intake Discharge

38. Radial Variation of Mass flow rate Intake Discharge

39. Design of Compact Machine

40. Kaplan Turbine

41. DESIGN OF THE BLADE Two different views of a blade 90% or better in efficiency

43. Basic Rules for Design of An Ideal Turbo- machine

44. Enumerate the details of source or demand. Calculate Specific speed and identify the fundamental concept of operation. X 1 (Impulse)+X 2 (Reaction)+(1-X 1 -X 2 )(centrifugal) Y 1 (Radial)+(1-Y 1 )(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 ……

45. 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.