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Old   February 6, 2002, 12:50
Default time and frequency domain
Tom Brown
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I am doing time-dependent compressible turbulent flow analysis where inflow boundary condition is time-dependent. In general, what (if anything) can be deduced from converting the solution from time to frequency domain? For example what can I say about frequency content of turbulent kinetic energy over my computational domain?

Thanks, Tom
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Old   February 6, 2002, 17:43
Default Re: time and frequency domain
Jongdae Kim
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step 1 : measure u,v,w,p,temperature (1 dimensional data, function of time)

step 2 : Apply 'psd' (matlab function of calculating power spectral density)to your signals. You can make your own source code based on the Fourier analysis.

step 3 : You can get powerspectrum of your signals which are function of frequncy.

Step 4 : You can see the dominant frequency of your signal.

************************************************** *

According to Reynolds decomposition scheme,


where U is time averaged (or mean) velocity. The fluctuating parts are expressed as follows ;

u'(t)=u(t)-U, v'(t)=v(t)-V

and now you can calculate the turbulent kinetic energy ' k ' as follows ;

k(t) = 0.5 * (u'*u' + v'*v')

and then you can calculate powerspectrum of 'k'. If you know how to apply two dimensional Fourier analysis, you can get two dimensional frequency map.

Jongdae Kim
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Old   February 7, 2002, 09:59
Default Re: time and frequency domain
Tom Brown
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Thank you. Indeed, I use Matlab to calculate PSD, Power Spectral Density. One can use either periodogram or spectrum commands in Matlab for that purpose.

My question goes a bit further. Based on PSD and dominant frequency what (if anything) can I say about the flow field, for example, transition from laminar to turbulant flow. Any references on Power Spectral Density analysis as applied to the time-dependent CFD analysis will be appreciated.

Thanks, Tom.
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Old   February 11, 2002, 17:51
Default Re: time and frequency domain
Jongdae Kim
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In my case, I'm using phase averaging. After applying the phase averaging technique to the turbulent flow from LES, I can visualize phase averaged flow field. I consider the flow as coherent structure of the turbulent flow.

The other approach of extracting coherent structure is as follows ( a kind of conceptual approach) :

1. Calculating PSD of the turbulent signal.

2. Taking high energy part with some threshold (for example, 10 % of the max. energy part) in the frequnecy domain.

3. Apply inverse FT to the signal and then you can get some high energy part of the signal. That could be a kind of coherent part of your data. (Actually I have not yet applied this method. But in the near future, I'll apply it to my turbulent flow to compare the coherent structures.)

If you want to discuss this part - coherent structures from the turbulent flow - please send mail to me.

Jongdae Kim
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