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Time scale and frequency of small eddies

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Old   July 8, 2015, 09:43
Default Time scale and frequency of small eddies
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Hello dear users,

I have the following problem: Air at standard conditions is flowing through a rectangular pipe. The needed data is:

> Hydraulic diameter \delta = 0,24 m
> Flow speed \vartheta= 30 m/s
> Kintematic viscosity \nu = approx. 2e-7 mē/s

I now want to determine the time-scale and frequency of the smallest eddies, that occur in the flow.
According to Kolmogorov's energy cascade the time scale of the smallest eddies is:
\tau ~ T*Re^{(-1/2)}

With T being the Time scale of the largest eddies (as an assumption I take \delta / \vartheta = 0,008 seconds).
The Reynolds Number is calculated from the given hydraulic diameter, flow speed and viscosity - giving me a value of 27*10^6.

This gives me a time scale \tau of about 1,5*10^-6 seconds.

Now I want to get the frequency which is 1/time scale and gives me 650 kHz.
According to several sources in the literature (e.g.: Versteeg and Malalasekera) the frequency of those small eddies is in the range of 10 kHz for most engineering flows.

I do see, that the assumption of taking the full amount of the mean velocity is not correct. Could anyone tell me which percentage (in this case the turbulence intensity) would be a good start? Any help or useful critic is highly appreciated!

Last edited by Edeluc; July 8, 2015 at 11:38.
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Old   July 8, 2015, 11:22
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Filippo Maria Denaro
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you could also check in this way:

at the Kolmokorov scale Re_delta=O(1), therefore the reference velocity at the smallest scale is u = ni/delta.


1/tau = ni/delta^2

and, for a known kinematic viscosity, you have just to estimate the spatial Kolmogorov scale.
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