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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……. THE DOUBLET. Consider a source-sink pair with strengths ± m , located at (∓ℓ/2, 0).

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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. THE DOUBLET Consider a source-sink pair with strengths ±m, located at (∓ℓ/2, 0). Let the separation distance ℓ approach zero, while simultaneously increasing the source and sink strengths such that the product κ  ℓ remains constant. The resulting flow is a doublet with strength, 

  3. Uniform Flow Past A Doublet : Perturbation of Uniform Flow The superposition of a doublet and a uniform flow gives the complex potential + - Streamlines-Doublet - Streamines – Uniform Flow

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

  5. Visualization of Interaction Function Note that one of the streamlines is closed and surrounds the origin at a constant distance equal to    

  6. The Shape of Zero Value Stream Line • There exist a circular stream line of radium R, on which value of stream function is zero. • Important Hypothesis: Any stream function of zero value is an impermeable solid wall. • Plot shapes of iso-streamlines of all values.

  7. Fascinating Vortex Phenomena : Kutta-Joukowski Theorem

  8. 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.

  9. Invention of Two Important Locations in Interaction Function • 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.

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

  11. The velocity Field due to Flow Past A Cylinder

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

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

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

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