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Potential flow Analysis to Model Lifting Devices

Potential flow Analysis to Model Lifting Devices. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi. In search of A Mathematical Model for Invention of Amazing Fluid Muscle……. Computation of Velocity Field Generated due to Interaction Function.

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Potential flow Analysis to Model Lifting Devices

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  1. Potential flow Analysis to Model Lifting Devices P M V Subbarao Professor Mechanical Engineering Department I I T Delhi In search of A Mathematical Model for Invention of Amazing Fluid Muscle……

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

  3. Stagnation Points on Cylinder Surface Stagnation points, S: u & v @x=R &y=0.

  4. Maximum velocity Points on Cylindrical Surface Identify the locations of Maximum Stream-wise Velocity Profiles

  5. Cartesian and Cylindrical Coordinate Systems

  6. 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.

  7. Creation of Pressure Distribution by the Interaction Function The pressure field is obtained from the Bernoulli equation Define coefficient of Pressure:

  8. No Net Upwash Effect ?!?!?!? Non-productive zero weight Balloons !?!?!

  9. 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.

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

  11. Visualization of Multilevel Interaction Function

  12. The Non-living Genius : Lifting Machine

  13. Computation of Velocity Field The radial and tangential velocities are given by: On the surface of the cylinder (r=R):

  14. Creation of Zero Weight Balloon

  15. Angle of Attack Unbelievable Flying Objects

  16. Computation of Surface Pressure Field Find the pressure field over the surface of the cylinder from Bernoulli’s equation:

  17. Computation of Lift Lift per unit span, (i.e. per unit distance normal to the plane of the paper) is given by: On the surface of the cylinder, x = R Cosθ. Thus, dx = -Rsinθdθ. The above integrals may be thought of as integrals with respect to θ. For the lower surface, θ varies between π and 2π. For the upper surface, θ varies between π and 0.

  18. The Kutta – Joukowski Lift Theorem • This is an important result. • It says that clockwise vortices will produce positive lift that is proportional to  and the free stream speed with direction 90 degrees from the stream direction rotating opposite to the circulation. • Kutta and Joukowski generalized this result to lifting flow over any general body. • This Equation is known as the Kutta-Joukowski theorem.

  19. Spindle Rotors take the Place of Wings • Flettner (1924) used rotating cylinder to produce forward motion.

  20. Further Observation of Natural Geniuses • At very low Reynolds numbers (<10,000 based on chord length) efficient airfoil sections can look rather peculiar as suggested by the sketch of a dragonfly wing. • The pigeon wing is thin and highly cambered

  21. Geometrical Knowledge of Pigeons

  22. Change In Perspective on Imagination Consider hallow Cylinder in Polar Coordinates Polar to Cartesian Mapping New Object in Cartesian Coordinates

  23. The Art of Transformation/Mapping

  24. Transformation for Inventing a True Flyer • A large amount of airfoil theory has been developed by distorting flow around a cylinder to get flow around an airfoil. • The essential feature of the distortion is that the potential flow being distorted ends up also as potential flow.

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