Time scale and frequency of small eddies

Edeluc · July 8, 2015, 09:43

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 m²/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:
$\tau$ ~

* $Re^{(-1/2)}$

With

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!

FMDenaro · July 8, 2015, 11:22

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.

thomas. · September 23, 2016, 09:13

Hello Edeluc,

I know the post is old, but I am struggling with a similar problem. Did you solve yours?

Thanks in advance.

July 8, 2015, 09:43	Time scale and frequency of small eddies	#1
Edeluc New Member Lucas Join Date: Jun 2015 Posts: 20 Rep Power: 10	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 m²/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: $\tau$ ~ * $Re^{(-1/2)}$ With 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 2710^6. This gives me a time scale $\tau$ of about 1,510^-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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July 8, 2015, 11:22		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	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.

September 23, 2016, 09:13		#3
thomas. Member thomas Join Date: Jul 2014 Posts: 50 Rep Power: 11	Hello Edeluc, I know the post is old, but I am struggling with a similar problem. Did you solve yours? Thanks in advance.