Stagnation points for flow around a cylinder

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Discussion Overview

The discussion revolves around finding the location of stagnation points for incompressible flow around a cylinder, specifically using the stream function. The focus includes theoretical approaches and mathematical reasoning related to fluid dynamics.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant inquires about the method to find stagnation points given the stream function.
  • Another participant suggests using representative nodes to solve the velocity equations and identify points with zero flow velocity, mentioning the use of finite differences and the Navier-Stokes equation.
  • A third participant explains that if the stream function is known, stagnation points can be found by determining points on the cylinder's surface where the velocity components are zero, providing the equations for velocity components derived from the stream function.
  • A later reply expresses gratitude for the assistance provided in the discussion.

Areas of Agreement / Disagreement

Participants appear to agree on the approach of using the stream function to identify stagnation points, but there are different methods suggested for solving the equations involved, indicating some variation in perspectives.

Contextual Notes

There may be limitations regarding the assumptions made about the flow characteristics and the specific conditions under which the methods apply, as well as potential dependencies on the definitions of the stream function and velocity components.

Who May Find This Useful

This discussion may be useful for students and professionals interested in fluid dynamics, particularly those exploring the behavior of flow around cylindrical objects and the mathematical methods used to analyze such flows.

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:

[tex] u = d\psi/dy[/tex]
[tex] v = -d\psi/dx[/tex]

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

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