Stagnation points for flow around a cylinder

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SUMMARY

To find stagnation points for incompressible flow around a cylinder using the stream function, identify representative nodes and solve the Navier-Stokes equation using finite differences. The velocity components can be derived from the stream function with the equations u = dψ/dy and v = -dψ/dx. Stagnation points occur where both velocity components, u and v, equal zero, typically at the surface of the cylinder.

PREREQUISITES
  • Understanding of the Navier-Stokes equation
  • Familiarity with stream functions in fluid dynamics
  • Knowledge of finite difference methods for solving PDEs
  • Basic concepts of incompressible flow
NEXT STEPS
  • Study the application of finite difference methods in fluid dynamics
  • Learn how to derive velocity components from stream functions
  • Explore the characteristics of incompressible flow around various geometries
  • Investigate advanced techniques for solving the Navier-Stokes equations
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Fluid dynamics engineers, researchers in computational fluid dynamics, and students studying incompressible flow phenomena will benefit from this discussion.

SaveFerris
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i was just wondering how you'd go about finding the location of stagnation points for an incompressible flow around a cylinder if you know what the stream function is?

Thanks!
 
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You have to come up with representative nodes to solve ur equation for velocity and then see which points have no flow velocity. I usually use finite differences at each node to solve the PDE (Navier-Stokes equation). Remember that molecules on the surface have zero velocity.
 
If you know the stream function, it's easy. Just look for points on the surface of the cylinder with zero velocity. Typically, the velocity components can be found from the streamfunction in a fairly straightforward way:

<br /> u = d\psi/dy<br />
<br /> v = -d\psi/dx<br />

At the stagnation point, u and v will be zero.
 
Thank you so much.
This is a great help!
 

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