Time scale and frequency of small eddies

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 July 8, 2015, 09:43 Time scale and frequency of small eddies #1 New Member   Lucas Join Date: Jun 2015 Posts: 11 Rep Power: 2 Hello dear users, I have the following problem: Air at standard conditions is flowing through a rectangular pipe. The needed data is: > Hydraulic diameter = 0,24 m > Flow speed = 30 m/s > Kintematic viscosity = 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: ~ * With being the Time scale of the largest eddies (as an assumption I take / = 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 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.

 July 8, 2015, 11:22 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 1,775 Rep Power: 23 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. Thus 1/tau = ni/delta^2 and, for a known kinematic viscosity, you have just to estimate the spatial Kolmogorov scale.

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