1. Design 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 power in the wind 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 metre (kg/m3)
A is the swept rotor area in square metres (m2)

3. History of Wind Power
The use of wind power in sailing vessels appeared in antiquity.
The earliest mentions of the use of wind power come from the East: India, Tibet, Afghanistan, Persia.
the widespread use of wind power for grinding grain and pumping water was delayed until
the 7th century in Persia,
the 12th century in England, and
the 15th century in Holland.
17th century, Leibniz proposed using windmills and waterwheels together to pump water from mines in the Harz Mountains.
Dutch settlers brought Dutch mills to America in the 18th century.
This led to the development of a multiblade wind turbine that was used to pump water for livestock.

4. The First Record of a Windmill
The first accepted establishment of the use of windmills was in the tenth century in Persia.
It is documented by reliable writers and reinforced by ancient drawings that correspond to the remains of old mills and to modern ones still in use.
The region is Sıstan in eastern Persia (in presentday Iran), which bordered on Afghanistan.
About A.D. 1300, a Syrian cosmographer who provided a detailed description and a drawing.

5. A Persian vertical-axis windmill in Sıstan
The two storied, walled structure had millstones at the top and a rotor at the bottom.
The latter consisting of a spoked reel with 6 to 12 upright ribs, each covered with cloth to form separate sails.
The sketch shows the bellying of the cloth coverings as they catch the wind and push the reel around.
Each wall had an offset opening the height of the rotor, with its perimeter beveled to decrease the free area through the thickness of the wall and hence accelerate the wind from any direction.

6. The Windmills of Neh

7. Performance of Persian Mills : 1963
In 1963, 50 mills were still operating.
Each milled an average of a ton of grain in 24 hours, so in a 120day windy season, they were said to produce a total output of 6,000 tons.
Based on a wind speed of about 30 m/s, an effective exposure at any time of 1.5 blades
The mill efficiency was of 50 percent, with a power output of about 75 hp per mill.
It is difficult to accept this high figure!!!
The basic design of these primitive vertical axis mills has lasted at least 1,000 years

8. The vertical-axis Chinese windmill

9. The Horizontal-Axis European Windmill
Conversion of the Roman watermill with its horizontal wheel shaft to the ordinary windmill with a horizontal shaft.
All the essentials of a windmill were ready to hand except the sails which replace the blades and rim on the water wheel.
The mechanism is is like that of an early watermill turned upside down,
The watermill drive being from below upwards and the windmill drive from above downwards.

10. A Musical Instrument

11. 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 concept, which was not fully developed until the advent of the airplane at the beginning of the twentieth century and the engineering science of aerodynamics

12. CLASS 1 TYPE OF WIND TURBINES

13. CLASS 2 TYPE OF WIND TURBINES

14. Fluid Dynamics of A Turbo-machine
Fluid in
Fluid out

15. Leonhard Euler
Leonhard Euler ( ) 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.

16. 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.

17. The Superiority of Vector Parameters

18. Euler’s Vision of Vector

19. 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.

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

21. Meridional Plane
The momentum balance is considered in a plane constructed through axis of rotation and radial axis.
This Plane is called Meridional Plane.
Euler Differential Turbine Equation.

22. Euler Wind Turbine Equation
Wind turbine is an axial flow machine.
For a SSSF Wind turbine
A change in Whirl Velocity of fluid can only establish Power Exchange between fluid and rotor in a turbo-machine !
Torque developed by a Wind turbine
Euler Theory:
Power :