Evolution of Wind Turbines

1. Evolution of Wind Turbines P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Physics is experience, arranged in economical order. — Prof. Ernst Mach Growth of Wind mill into A Wind turbine ….

2. The Fundamental Realization • The power in the wind is proportional to: • the area of windmill being swept by the wind • the cube of the wind speed • the air density - which varies with altitude • The formula used for calculating the power in the wind is shown below: where, P is power in watts (W) ρ is the air density in kilograms per cubic meter (kg/m3) A is the swept rotor area in square meters (m2)

3. Modern Wind Turbine as A Musical Instrument

4. Lift Replaces Drag • A revolutionary change from the simple, straightforward push of the wind on the face of the sail was replaced by the action of the wind in flowing smoothly around the sail (blade). • A change from providing a force tangential to the direction of the wind to providing a force normal to the direction of the wind. • This is a sophisticated 20th century concept. • Developed only after the advent of the airplane and the engineering science of aerodynamics

5. Class 1 Type of Wind Turbines Level 1 Innovation: Level 2 Innovation:

6. Class 1 Type of Wind Turbines Level 3 Innovation: Unnecessary

7. CLASS 2 TYPE OF WIND TURBINES Level 1 Innovations:

8. CLASS 2 TYPE OF WIND TURBINES Level 2 Innovations:

9. CLASS 2 TYPE OF WIND TURBINES Level 3 Innovations: Unnecessary

10. CLASS 2 TYPE OF WIND TURBINES Level 4 Innovations: ?????

11. Thermodynamics of A Fluid-machine A Fluid-machine Fluid in Fluid out

12. 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.

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. • Designated 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. The Superiority of Vector Parameters

15. Euler’s Vision of Vector

16. 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.

17. Euler Theory: Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid = t