Harvesting of the Useful Energy of the Bountiful Fluid

1. Harvesting of the Useful Energy of the Bountiful Fluid P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Creation of A Better Energy Harvester !!!?!?!?!

2. Wild Solutions to Utilize Available Energy

3. The Family of Steam Engines

4. The definition of Work • The term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as "weight liftedthrough a height“. • This is based on the use of early steam engines to lift buckets of water out of flooded ore mines.

5. The Basic & Essential Cause for Generation of motive work • The experts advocate an approach to action by Newton's laws. • Any solid body that can generate an action on the continuously flowing fluid clearly implies that there will be a reaction on the solid body as a Newton's 3rd law reaction. • From the conservation of momentum for control Volume: • If an exiting stream from a solid body is given a downward component of momentum by the solid body, • To conserve momentum, something must be given an equal upward momentum to solid body. • Only those bodies which can give downward momentum to exiting fluid can experience reactive force !

6. Reaction leading to Torque • The concept of torque, also called moment or couple, originated with the studies of Archimedes on levers. • The rotational analogues: • Force – Torque • Mass – Inertia • Acceleration -- angular acceleration

7. Simple Turbine : Harvester of Useful Fluid Energy in T out

8. Acquisition of Work from Riverine Bounty

9. Hydraulic Turbine : Harvester of Kinetic Energy

10. The Hydro Power House

11. Wind Turbine : Harvester of Kinetic Energy

12. SOME TYPES OF WIND TURBINES

13. Macro Analysis of A Turbine A Turbine Fluid in Fluid out

14. Leonhard Euler • Leonhard Euler (1707-1783) was arguably the greatest mathematician of the eighteenth century. • One of the most prolific writer of all time; his publication list of 886 papers and books fill about 90 volumes. • Remarkably, much of this output dates from the last two decades of his life, when he was totally blind. • Euler's prolific output caused a tremendous problem of backlog: the St. Petersburg Academy continued publishing his work posthumously for more than 30 years.

15. 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.

16. 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.

17. The Superiority of Vector Parameters in A Cylindrical Coordinate System

18. Order of Velocity Vectors The real flow through any turbomachine is three dimensional. Axial, Radial and Circumferential. Axi-symmetry: Inter blade row space. Axi-symmetry assumes an average value to represent the state of working fluid in the blade-to-blade plane.

19. The Reference Plane of Euler Equation : Meridional Plane The momentum balance is considered in a plane constructed through axis of rotation and radial axis. This Plane is called Meridional Plane.

20. Euler’s Vision of Vector

21. Macro Analysis of A Steam Turbine Fluid in Fluid out

22. Euler’s Version of Newton’s Second Law • In turbo-machines much useful information is obtained by employing Newton’s second law in the form where it applies to the moments of forces. • This form is of central importance in the analysis of the energy transfer process in turbo-machines.

23. Euler’s Statement for Second Law • For a system of mass m, the vector sum of the moments of all external forces acting on the system about some arbitrary axis A--A fixed in space is equal to the time rate of change of angular momentum of the system about that axis, i.e.

24. Euler Theory: Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid = t Angular momentum is moment of linear momentum of angular velocity, Vq Define, L as Angular momentum :

25. For a steady flow through a turbo-machine: Inlet rate of angular momentum : Exit rate of angular momentum at exit: Change in Rate of angular momentum:

26. Euler Turbine Equation Euler Theory: Power : A change in Whirl Velocity of fluid is essential to establish Power Exchange between fluid and rotor in a turbo-machine !

27. Infinitesimal Euler Turbine Equation

28. Conservation of Energy for An Ideal Turbine Euler Turbine Power Equation.

29. Combination of Euler and SFEE For a Turbomachine: Over an ideal turbomachine blade along flow direction rothalpy remains constant