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Old   July 10, 2009, 03:33
Default About the physics of turbulence...
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I still would like to have some further explanations about the formula I=0.16 \cdot Re^{-1/8} (turbulence intensity in a fully developped pipe flow) which I quoted in my previous post.

- How comes the turbulence intensity decreases when mean velocity gets bigger? Would it be that fluctuations are smoothed when a flow becomes faster?

- What range of Re this expression if valid for? I cannot believe turbulence intensity exceeds 6% for laminar flows....!

Thank you in advance
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Old   July 10, 2009, 05:28
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I guess I won't be more successful than this poster whose question was asked more than a year ago.......

Question on Turbulence Intensity

Please, make an effort, I cannot believe that nobody here is able to answer that simple question
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Old   July 10, 2009, 16:55
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The formula is an approximation of turbulent intensity from pipe flow empirical correlations, and is valid only for developed turbulent flow. The Re is actually Re_Dh:
http://www.cfd-online.com/Wiki/Hydraulic_diameter

The actual definition of turbulent intensity is velocity fluctuation divided by the mean flow velocity. So, to answer your first question, the empirical correlations tell us that velocity fluctuation growth is small compared to the increase in mean flow velocity.
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Old   July 11, 2009, 05:15
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in other words:

I=\frac{u'}{u} = 0.16\left(\frac{uD_h}{\nu}\right)^{-1/8}
u' = 0.16 \left(\frac{D_h}{\nu}\right)^{-1/8} u^{7/8}

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Old   July 11, 2009, 05:18
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Hello f-w

I'm okay with this correlation valid for fully developped turbulent flows only, I just wondered how low could the Reynolds actually get. The transition is known to occur between 2000 and 3000, so I guess I can still use the formula for Re_ {D_{h}}=7000 ? Anyway, my simulation is rather not sensitive to turbulent boundary conditions, so I may use the formula without commiting too much error. I was just surprised such a low Re could yield to 5% turbulence intensity...

You're right, that is just the competition between <u'> and U0 turning in favor of U0 when Re grows. My question was kind of metaphysical: why?


Thank you for your precisions!
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Old   July 11, 2009, 05:26
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Thank you henrik

Actually f-w had made me realized my dumb mistake in confusing <u'> and I..... Your formula clearly shows <u'> grows with u (thus Re), which seems logical. But after all, this still does not answer what is the physical reason for I decreasing with u... Are the fluctuations "smoothed" when flow goes faster, as I said in my first post?
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Old   July 11, 2009, 18:33
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As long as your Re_Dh is two times the expected transitional value (~2300 for pipes), you're fine. Otherwise, some additional considerations must be taken for an accurate analysis, where transition might be delayed.

Turbulent intensity is undefined for laminar flows, so careful how you use it. It does grow with decreasing Re, and can get pretty large with complex geometries where you can have large fluctuations with low mean velocities (like in forest flows).

As henrik pointed out, fluctuations can be rewritten (with the help of a correlation) as a function of mean velocity. At higher mean velocities, you can imagine having more powerful eddies, which in turn mix all the gradients (velocity, pressure, temperature, ...) to a greater degree.
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