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Comparison of FEA and closed form solution for fluid velocity in a channel

  1. Oct 27, 2008 #1
    I am trying to compare the fluid velocity given by the closed form solution and FEA analysis for fluid flowing through a channel that is 800u long and 100u wide.

    I am using the equation vmax= (gradP)*(radius)^2/(4*viscosity)

    I got 8.4cm/s in the former compared to ~10cm/s in the latter.

    What could be the reason for the difference in both values. I thought of some like entrance length which is considerable compared, FEA has a square cross section instead of circular.

    Am I right? Are there any more reasons. If so can I compensate for any of them using, say an extra term or longer channel (though FEA could take more time) etc.

    Phew!!!Lot of questions
  2. jcsd
  3. Oct 27, 2008 #2


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    There are numerous reasons that the numeric solution could be off. People spend years verifying and validating codes to ensure accuracy. The simplest explanation could be mesh size, then you have numerical differencing error, truncation error, the list goes on and on.

    From what I hear, some of the guys here ran a simple pipe flow with our latest greatest CFX code, and it failed to get the analytic solution horribly.
  4. Oct 27, 2008 #3

    That is interesting. First of all, I am an Electrical Engineer, so I might be wrong in any of my statements.

    I thought that FEA analysis takes into account every detail in my structure (two of the differences I had already mentioned) and hence should be accurate. Though I know that a coarse mesh size will give a result which is slightly farther from the actual value. However, I thought that the closed form solution would be farther away from the actual value compared to FEA.

    From your feedback, I guess values of 8.4 and 10 are acceptable in this case.

  5. Oct 27, 2008 #4


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    There's a running joke that goes around between fluid dynamicists that the numerical ones (CFD) believe the experimental guys over their stuff, and the experimental guys believe the CFD over theirs.

    I don't think that CFD has gotten user-proof to the point that anyone can step in and get good results. It's still at a point where the person using it has a large (relative) effect on the answers, particularly with generating meshes.

    If the problem that you're testing has a closed form analytic solution then you can assume that to be correct. Simple invisid-incompressible pipe flow would be an example. You'll never get a more correct answer than what you have on paper.

    Now with that in mind, you are correct that numerical solutions give you the opportunity to add complexities such as viscous flows, pipe roughness, compressibility factors. However, trying to model a simple flow, you can easily see that these things aren't foolproof, and are by no way perfect.
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