1. Blades for Wind Turbines
P M V Subbarao
Professor
Mechanical Engineering Department
An extra-ordinary Fluid Device.....

2. Roles of Blade in Wind Turbine

3. Flow past an airfoil

4. Effect Based Description

5. Definition of lift and drag
Lift and drag coefficients Cl and Cd are defined as:

6. Can We Identify the Cause?

7. The Natural Genius & The Art of Generating Lift

8. Hydrodynamics of Prey & Predators

9. The Art of C-Start

11. The Art of Complex Swimming

12. Development of an Ultimate Fluid machine

13. 19th Century Inventions
H F Phillips
Otto Lilienthal

14. History of Airfoil Development

15. The Basic & Essential Cause for Generation of Lift
The experts advocate an approach to lift by Newton's laws.
Any solid body that can force the air downward clearly implies that there will be an upward force on the airfoil as a Newton's 3rd law reaction force.
From the conservation of momentum for control Volume
The exiting air is given a downward component of momentum by the solid body, and 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 lift !
Kutta-Joukowski theorem for lift.

16. Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

17. Fascinating Vortex Phenomena : Kutta-Joukowski Theorem
The Joukowsky transformation is a very useful way to generate interesting airfoil shapes.
However the range of shapes that can be generated is limited by range available for the parameters that define the transformation.

18. Three Basic Elements in Creation of Thin Aerofoil Theory

19. THE COMPLEX POTENTIAL
Invscid Flow field and perturbing solid(s) can be represented as a complex potential.
In particular we define the complex potential
In the complex plane every point is associated with a complex number
In general we can then write

20. Now, if the function f is analytic, this implies that it is also differentiable, meaning that the limit
so that the derivative of the complex potential W in the complex z plane gives the complex conjugate of the velocity.
Thus, knowledge of the complex potential as a complex function of z leads to the velocity field through a simple derivative.

21. Elementary fascination Functions
To Create IRROTATIONAL PLANE FLOWS
The uniform flow
The perturbation objects
The source and the sink
The vortex

22. THE UNIFORM FLOW : Creation of mass & Momentum in Space
The first and simplest example is that of a uniform flow with velocity U directed along the x axis.
In this case the complex potential is

23. THE SOURCE OR SINK: The Perturbation Functions
source (or sink), the complex potential of which is
This is a pure radial flow, in which all the streamlines converge at the origin, where there is a singularity due to the fact that continuity can not be satisfied.
At the origin there is a source, m > 0 or sink, m < 0 of fluid.
Traversing any closed line that does not include the origin, the mass flux (and then the discharge) is always zero.
On the contrary, following any closed line that includes the origin the discharge is always nonzero and equal to m.

24. Iso f lines
Iso y lines
The flow field is uniquely determined upon deriving the complex potential W with respect to z.

25. A Combination of Source & Sink

26. THE DOUBLET
The complex potential of a doublet

27. Uniform Flow Past A Doublet : Perturbation of Uniform Flow
The superposition of a doublet and a uniform flow gives the complex potential

28. Find out a stream line corresponding to a value of steam function is zero

29. There exist a circular stream line of radium R, on which value of stream function is zero.
Any stream function of zero value is an impermeable solid wall.
Plot shapes of iso-streamlines.

30. Note that one of the streamlines is closed and surrounds the origin at a constant distance equal to    

31. Recalling the fact that, by definition, a streamline cannot be crossed by the fluid, this complex potential represents the irrotational flow around a cylinder of radius R approached by a uniform flow with velocity U.
Moving away from the body, the effect of the doublet decreases so that far from the cylinder we find, as expected, the undisturbed uniform flow.
In the two intersections of the x-axis with the cylinder, the velocity will be found to be zero.
These two points are thus called stagnation points.

32. To obtain the velocity field, calculate dw/dz.

33. Equation of zero stream line:
with

34. Cartesian and polar coordinate system

36. V2 Distribution of flow over a circular cylinder
The velocity of the fluid is zero at = 0o and = 180o. Maximum velocity occur on the sides of the cylinder at = 90o and = -90o.

37. Creation of Flow Past A Cylinder

38. Generation of Vorticity

39. Creation of Pressure Distribution

40. No Net Up wash Effect

41. THE VORTEX
In the case of a vortex, the flow field is purely tangential.
The picture is similar to that of a source but streamlines and equipotential lines are reversed.
The complex potential is
There is again a singularity at the origin, this time associated to the fact that the circulation along any closed curve including the origin is nonzero and equal to g.
If the closed curve does not include the origin, the circulation will be zero.

42. Uniform Flow Past A Doublet with Vortex
The superposition of a doublet and a uniform flow gives the complex potential

46. Angle of Attack
Unbelievable Flying Objects

47. Kate Carew Interviews the Wright Brothers
“Are you manufacturing any racing machines?”
“Not just now, but we intend to.”
“How much can I buy one for?”
“Seven thousand five hundred-dollars.”
“Is that all? It doesn’t seem like an outside price for a perfectly good airship?”
“Airship!” shouted the Wright brothers indignantly.
“Is that the wrong word?”
“An airship,” said Wilbur contemptuously, “is a big, clumsy balloon filled with gas.”
“Well, I don’t see why your biplane shouldn’t be called an airship, too.”
“It’s a flying machine,” said Wilbur.
“The name we prefer is ‘flyer,’” said Orville.
“An airship would cost $50,000,” said Wilbur.
“More like $150,000,” said Orville, and they argued the question.