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Isotropic Turbulence Flow

  1. Oct 23, 2015 #1
    1. The problem statement, all variables and given/known data
    Hello everyone, I am having a problem whether or not a turbulence at a specific location (let's say A) is isotropic or not.

    I have calculated the two root mean square values of velocity fluctuations measured at the point A in a fully developed turbulent pipe flow.

    the first rms= 7.55, which is the velocity component parallel to the pipe axis
    the second rms= 0.335, which is the velocity component along the radius
    These two components are simultaneously measured.

    The question is, is the turbulence isotropic at A?

    Do I need a formula to calculate whether the turbulence is isotropic at A?
    I am given the density (1.2) and the dynamic viscosity of the fluid (1.8*10^-5).

    Any help would be greatly appreciated. Thank you.
     
  2. jcsd
  3. Oct 23, 2015 #2
    What does the word "isotropic" mean to you?

    Chet
     
  4. Oct 24, 2015 #3
    That it is uniform in all directions?

    I read in wikipedia that "Fluid flow is isotropic if there is no directional preference (e.g. in fully developed 3D turbulence). An example of anisotropy is in flows with a background density as gravity works in only one direction. The apparent surface separating two differing isotropic fluids would be referred to as an isotrope."

    Since my flow has two velocity components, does this mean it is not isotropic?

    Thank you very much for the help.
     
  5. Oct 24, 2015 #4
    You are trying to determine whether the turbulence is isotropic, not the overall flow. If the rms velocity fluctuations do not match in two directions, then the turbulence is not isotropic.

    Chet
     
  6. Oct 24, 2015 #5
    You have measurements of two velocity components, but of course, there are three velocity components.
    So, if your measured values were u'u'=0.1 and v'v'=0.1, then you still don't know if the flow is isotropic or not, because the tangential component could be w'w'=0.5 or w'w'=0.0.

    Also, turbulent pipe flow is not isotropic, but it becomes more isotropic if you measure further away from the walls.
     
  7. Oct 24, 2015 #6
    Well, you would know that it's at least transversely isotropic in the plane that contains u and v. In order for it to be fully isotropic w'w' would have to be equal to 0.1 also.
    Yes, and....?
     
  8. Oct 25, 2015 #7
    He could have answered the question on isotropy without any measurements.
     
  9. Oct 25, 2015 #8
    Okay, is it possible to calculate the tangential component from the two rms velocity measurements? Is it by Pythagoras theorem?

    The measurements were done at 3 points actually, A, B, and C. But only at A that the two components of velocity were measured. Will it help if I calculate the rms at point B and C?

    Thank you very much, as you can see, I'm quite clueless.
     
  10. Oct 25, 2015 #9
    Thank you, Chet.

    I have two different rms values of fluctuations at A (one parallel to the pipe axis and another one along the radius) and thus the turbulence is not isotropic at A.

    Is my statement correct? or do I miss something?

    Thank you very much.
     
  11. Oct 25, 2015 #10
    Another question that has been bothering me is that:
    Is the rms fluctuation measured parallel to the pipe is actually the rms fluctuations in the circumferential (tangential)?
    Which thus also means the rms fluctuations along the radius is the fluctuations in the radial direction?

    Thank you again.
     
  12. Oct 25, 2015 #11
    In my judgement, your answer is correct.
     
  13. Oct 25, 2015 #12
    The fluctuations in measured parallel to the pipe are in the axial direction, and the fluctuations along the radius are in the radial direction. The fluctuations in the circumferential direction were not measured. That's the best I can judge from the wording.

    Chet
     
  14. Oct 25, 2015 #13
    Thank you Chet!

    Ah I see, is it possible to calculate the fluctuations in the circumferential direction?
    The question says, "assuming the rms fluctuations in the circumferential (i.e. tangential) direction to be similar to that of the fluctuations in the radial direction, estimate the turbulent energy at A."

    Which is why I was wondering whether the question is referring to the rms values I have already obtained, or I have to calculated another rms value.

    Thank you again!
     
  15. Oct 25, 2015 #14
    They already said that the fluctuations in the circumferential direction are similar (I interpret this as essentially the same) as the fluctuations in the radial direction.

    Chet
     
  16. Oct 26, 2015 #15
    Thus Chet,
    Do you mean that the flow's turbulent kinetic energy at A is thus:

    k = 0.5 * (0.3352 +0.3352)
    k = 0.112225?

    *the rms fluctuations along the radius is 0.335.

    Thank you very much.
     
  17. Oct 26, 2015 #16
    No. You need to include the contribution from the fluctuation in the circumferential direction.

    Chet
     
  18. Oct 26, 2015 #17
    The question says that 'assuming the rms fluctuations in the circumferential (i.e. tangential) direction to be similar to that of the fluctuations in the radial direction, estimate the turbulent energy at A'.

    Thus I assume that the rms fluctuations in the circumferential direction = rms fluctuations in the radial direction = 0.335.

    I don't understand where I went wrong. Would you please explain?

    Thank you very much.
     
  19. Oct 26, 2015 #18
    k = 0.5 * (0.3352 +0.3352+0.3352)
     
  20. Oct 26, 2015 #19
    I'm really sorry, Chet, but I don't quite understand.

    If turbulent kinetic energy = 0.5 * (rms u12+rms u22+rmsu32)

    where
    u1 is the velocity component parallel to the pipe axis (axial)
    u2 is the velocity component along the radius (radial)
    u3 is the velocity component in the circumferential (tangential)

    and u2=u3
    Then why isn't the kinetic energy equals to
    k = 0.5 * (7.55 +0.3352+0.3352)?

    Once again, thank you very much for all the help.
     
  21. Oct 26, 2015 #20
    No. Not the velocity components. The time-dependent fluctuations in the velocity components.

    Chet
     
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