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Tom Brown February 6, 2002 12:50

time and frequency domain

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

Jongdae Kim February 6, 2002 17:43

Re: time and frequency domain
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

Tom Brown February 7, 2002 09:59

Re: time and frequency domain
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.

Jongdae Kim February 11, 2002 17:51

Re: time and frequency domain
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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