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August 5, 2013, 20:25 
spectra peaks in freestream

#1 
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Sheyda
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Hello there. Could anybody help me out to understand my spectral data... see pictures pls.
The case is a bluff body LES with the white noise random disturbances at the inlet to impose a freestream turbulence on the simulation. Power spectra in the separated and wake regions show some frequency peaks which are associated with the vortex shedding and flapping motion of the separated shear layer, no problems here. What I cannot understand is the additional presence of two unusually large frequencies everywhere in the freestream, far upstream and above the body and vortex regions. This does not make sense to me because the white noise disturbances are generated at the inlet and hence no distinct frequency would be expected in the freestream, right? I am wondering could this be due to numerical effects (reflections from boundaries??) or anything else?? Thanks shedding (2).jpg freeStream (2).jpg
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August 6, 2013, 02:02 

#2 
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Some details are missing:
 numerical method (time and space)  courant number (maximum and in the locations where spectra are extracted)  specific implementation of the random number generator However, the two pictures don't have the same scale, which might be confusing. First try having the same scale on both pictures. 

August 6, 2013, 03:36 

#3 
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Filippo Maria Denaro
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did you perform FFT of velocity components at some fixed position x for some time interval, right?
1) what about the temporal window? 2) what about u,v,w at same location? 3) did you average over several timewindows? 4) Has the flow reached an energy equilibrium? From your figure I don't see an energy pileup suggesting numerical instability 

August 6, 2013, 03:36 

#4  
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cfdnewbie
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Quote:
May I ask, out of curiosity, why you are interested in the local CFL number at the sampling positions? I see how a CFL number might impose a minimum frequency, is that the reason for your question? 

August 6, 2013, 06:26 

#5 
Senior Member

Dear cfdnewbie,
my line of reasoning is that, the spectra being temporal (extracted in slected space locations), the adopted numerical method will certainly be sensitive the the courant number, which is clearly a local variable. As a consequence, the local spectral features might be numerically affected in different ways according to the local courant number. Even if (but we don't know) he is using a finer grid in the wake (where everything looks fine) than at the inlet (where something looks wrong), hence excluding a possible courant number effect, i guess you never know and it is better to ask. However, before any other comment, i would like to first see the images with the same scale and/or somehow normalized with the inlet velocity (or something meaningful). This would also help detremining any possible effect of the sampling as, in both pictures, i can't clearly see the cut in the spectrum (maybe its just me). As a first guess, i would say it is not relevant. 

August 7, 2013, 21:58 

#6 
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Sheyda
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Thanks for the inputs.
 FFT is performed for time series of velocities taken at some fixed positions. I attach plots of u,v,w spectra at two points; a point in the vortex shedding region (black line) and a point in the free stream (blue line).  Not sure about details of FFT procedure, but as far as i can read the FFT code, there is averaging over a few time windows.  How could we see if the flow reached energy equilibrium? As for the numerical aspects, Grid is colocated with standard RhieChow pressure smoothing. Spatial discretisation is second order central differencing. Time discretization is a single stage backwards scheme with time step size 5.0×1006 seconds. For spectral analysis, after flow reached a statistically stationary state, 20,000 samples taken every 20 time steps at each point. Maximum CFL was monitored at each block and it is not higher than 0.15. Looking forward for your views. Thanks Untitled.png
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August 8, 2013, 03:45 

#7 
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Filippo Maria Denaro
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energy equilibrium is in your case equivalent to a statistical steady state.
However I have somehow the feeling that you are using the FFT in a wrong way. For example, if your time step is dt = 5.0×1006 seconds, then your spectra should extend up to the Nyquist frequency pi/dt = 6.28 x 10^5 s^1 that does not appear from your figures. Furthermore, what about the window period T? 

August 12, 2013, 20:19 

#8 
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Sheyda
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Thanks Filippo. I cannot see what is wrong
I have tried different window sizes 4096, 2048, 1024 and I get similar spectra peaks. 

August 13, 2013, 04:52 

#9  
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Filippo Maria Denaro
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Quote:
Assuming that your dt is fixed, your spectra should extend until the Nyquist frequency pi/dt, could you check that your FFT extends up to such frequency? Changing the temporal window, only the time period T is affected. Then, each frequency is K = n*2*pi/T , n being the integer wavenumber 

August 13, 2013, 16:15 

#10 
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Sheyda
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Sorry I am confused. dt is the time between samples? or the time step used in the simulation?
I have stored time history for the velocities every 20 time steps, and as seen in the pictures my spectra extends up to frequency almost 5 x 10^3 s^1 

August 13, 2013, 16:22 

#11  
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Filippo Maria Denaro
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Quote:
Therefore, your FFT does not work on the whole frequency range 

August 14, 2013, 04:29 

#12 
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Filippo Maria Denaro
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just did a test on your data file that contains 20000 values of u,v,w sampled each 20*dt = 10^4 s.
I used my FFT code, first on the window [1:500], then on the full sampled window [1:20000]. You can see the spectra of the w component. The Nyquist frequency is correct at 3,14*10^4 Hz, changing only the assumed period T and the first wavenumber 2*pi/T. You can also see the difference in the spectra. That can be explained by the fact that the chosen windows does not ensure that the function is periodic and therefore an approximation is introduced. 

August 14, 2013, 04:30 

#13 
Senior Member

I can see three things from your pictures and additional details:
1) One of the three components in the free stream region has a very different spectrum. While this may indicate an effect of different cell Reynolds number in that direction (mean flow direction?), it is also possible that it is the effect of enforcing the continuity, which maybe is also affecting strangely the other components. You may want to check the spectra in a point further away from the inlet but on the same direction coming from the inlet face. 2) I still think that the order of magnitude of the free stream spectra is sufficiently low to be somehow an acceptable behavior, considering the fact you are actually imposing random numbers at inlet. Does flow visualization tell you that something strange is happening there? 3) Your sampling of the velocity signal implies some aliasing. Have you tried without sampling? 

September 3, 2013, 08:11 

#14 
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Sheyda
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Thank you guys for the tips.
Flow visualization shows everything normal and velocity and stress profiles match the experimental data. I am trying to use different FFT codes to see the effect
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frequency, les, spectral density, white noice 
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