1. Invention of Geometries to Generate Lift
P M V Subbarao
Professor
Mechanical Engineering Department
Device to generate Net Downwash in Exiting Flow.....

2. Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

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

4. Diagnosis of the Stream Function
Find out a stream line corresponding to a value of steam function is zero

5. The Zero Value & Other Stream Lines
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.
Note that one of the streamlines is closed and surrounds the origin at a constant distance equal to    

6. Fluid Dynamics of the Selected Interaction Function
Recall the fact that, by definition, a streamline cannot be crossed by the fluid.
Hence 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.
Compute the velocity at (two) intersections of the x-axis with the =0 stream line.
These velocities will be found to be zero !?!?
These two points are thus called stagnation points.

7. Computation of Velocity Field Generated due to Interaction Function
To obtain the velocity field, calculate dw/dz.

8. The velocity Field due to Flow Past A Cylinder

9. Diagnosis of Velocity Field
Equation of zero stream line:
with

10. Stagnation Points on Cylinder Surface
Stagnation points, S:
u & &y=0.

11. Generation of Vorticity (Down Wash)
Identify the locations of Maximum Stream-wise Velocity Profiles

12. Cartesian and Cylindrical coordinate systems

13. V2 Distribution on the surface of Cylinder (=0)
The velocity of the fluid is zero at = 0o and = 180o. Maximum velocity occur on the sides of the cylinder at = 90o and = -90o.

14. Creation of Pressure Distribution
The pressure field is obtained from the Bernoulli equation
Define coefficient of Pressure:

15. No Net Upwash Effect

16. THE VORTEX FUNCTION
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 .
If the closed curve does not include the origin, the circulation will be zero.

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

18. Visualization of Multilevel Interaction Function

19. The Non-living Genius : Lifting Machine

20. Creation of Zero Weight Balloon

21. Angle of Attack
Unbelievable Flying Objects

22. The Strange Natural Genius : The Wright Brothers