Thanks for this precise answer Bernhard!

Indeed, I want to show the -5/3 energy cascade. So let me rephrase to be sure I understood everything:

First, I have to choose a location where the turbulence is developed. Then, I take the temporal signal of the velocity at this specific location and apply the pwelch function to it. And I will obtain my spectra.

So it implies that I have sufficient time steps with developed turbulence at the chosen location.

Some more question come to me:

- To do a complete study, I should reproduce this method to other locations to be sure that the -5/3 cascade is verified all over the jet, right?

Thanks

It's been a while but finally, here is some feedback from this work on the spectra. By the way, I think there is to much topic left without a feedback from the initial author, to see it worked or to see if the author satisfaction regarding to the answers.

So, back to the main topic, I used the method using the pwelch function, as you suggested Bernhard, an it worked pretty well and pretty fast compared to the other methods I saw overthere.

I also tried to tune the overlap and the window parameters to see their effect on the response. Just as Bernhard said it, I would recommend to not modify them unless you have real knowledge of it, because you can make the function pretty much everything... (I used the function for two different cases and obtained exactly the same spectra, very clean, too clean...)

Thanks again for the precious help

Summary of the first steps of a spectra:

EDIT 2016-03-30:

I would like to add something which came to my knowledge recently on this topic. The method described in the original message gives a temporal spectrum which is a function of the frequency. However, it was explained to me that the comparison with the -5/3 line can be done only using a the Taylor or frozen-turbulence hypothesis. The later assumes that the fluctuations are convected only by the average flow which establishes the link between frequency and spacial wavenumbers. And thus we can actually compare to the -5/3 line. For more precisions, you can take a look at "Turbulent flow" by Pope, section 6.5 or the following references.

http://glossary.ametsoc.org/wiki/Taylor's_hypothesis

http://www.atmos.washington.edu/academics/classes/2013Q2/547/lect2.pdf

 Dear Jonathan; I have a question regarding your previous post. Were you working with 3D data, because from different textbooks and paper I have read that the Kinetic Energy Spectrum is the volume integral of the E(k).  I also need to do some spectrum analysis from a LES code. So far what I have read is that the Kinetic energy is the FFT of the Correlation tensor.. Hence, somehow you need to compute this tensor at each node. Maybe I am wrong, because I have read so many things that now I am more confused. Let say that I have my velocity vector (u,v,w) at each node. How may I proceed?

Thanks  

Don't worry, I also was confused by all I had read at that time. In fact, there is different way to produce the spectrum depending on your application.

But basically, in my case which is a spacial round jet, I took my velocity field at one node in the mixing layer versus the time. Then, I used the pwelch function on this temporal signal which gave me the spectrum. This function is based on the FFT but with some modifications to damp fluctuations of the spectrum.

Concerning the volumic integral, it would correspond to do an average over the volume. But you can not use this method in all cases. I saw this type of average for a channel flow for exemple, but i would not use it on a spacial turbulent jet.

Could you tell me which type of application you are studying?

Thanks Jonathan; I did not expected your reply that fast.!!! At this stage I am doing verification of the LES code with a channelf flow. Your approach seems to be very interesting and easy to grasp from a physical point of view. It is like a temporal spectrum. I have read,from different resource, and they basically ended up doing the spatial average. Lets say. we have u_i(x,y,z,t) and at a fixed time you compute the FFT of each componenet along 'x' and 'z'. It means that you fixed an specific height (y+ = 10.11) Then you take the average of the coefficients... However, I am still confused!!! My work is based on hydro kinetic horizontal turbines. But I am interested of comparing the energy spectrum with the power spectrum of the machine. I am also "applying a novel averaging technique for the forces" but I need to make sure the LES code is working fine! 

Hi Julio,

I am really sorry for the delay but I have been pretty busy lately...

In the case you're exposing, I don't really understand what you call "coefficients" that you average. Could you tell me more about it or send me the reference DOI/link?

Further, concerning you application, if I understand well, you would like to apply this same method to obtain your energy spectrum of your flow in the turbine. Am I right? 

Hi Jonathan, 

Sorry for my late answer. When I mention the average of the coefficient is because, Based on Pope's book you have triple integral (equation 6.116). Somehow you need to take the average over the volume. Hence, every time you compute the FFT, indeed what you get are the Fourier Coefficients at an specific wavenumber. That is why you have to compute the volume average or the average over a plane if you fixed the other plane. 

I am really sorry, I completly forgot to answer...

So I took a look at the equations you're refering to and I have been thinking about your application. However, I am not sure that it is possible to do a volumic average in your case... Indeed, whether  you take the flow close to the wall or far from it, you will not find the same flow at all (i.e. smallest structures close to the wall), thus the coefficients will be really different I think. It would work for a turbulence decaying case as the flow would behave the same way in the 3 direction, which is not the case for the channel flow.

Thus, I think it would be better to go back to the method you suggested at constant distance from the wall. At a constant distance from the wall, take several points where you compute the temporal spectrum, and then do an average of all those spectra (still at constant distance from the wall). I think it should work

Dear All,

Is it possible to generate an energy spectrum for a pressure time Signal? How would it differ when I use velocity signals to generate the energy spectrum? The turbulent kinetic energy is a function of the velocities? How does it denote the pressure fluctuations?

I am doing an LES Simulation of Francis turbine. In my case, the pressure fluctuations on the blades are the most important studies.

Thanks.

Hi Mr. Juzer, this is a very good question. But; according to my experience this is not possible because the energy spectrum is related to the velocity field via the two point correlation (which is defined by the velocity). However; I am sure there has to be some way to relate velocity and pressure but I do not have experience doing so. 

Nonetheless your questions is very important, let's what other members add!!

Hello all,

I have a confusion between RANS and URANS (ensemble averaging).

Can anyone comment on the time scales of the URANS model as usually in the RANS derivation one assumes infinite averaging time, thus the question is: what drives the time scales in the numerical solution which appears as transient?

Regards,

Juzer

In URANS indeed you are not solving (integrating in time) based on the time scale. Indeed you only consider the stability condition criteria to march in time. Hence, there is not time scale restriction in the time marching space.  I hope that this answers your question.!!! 

Thanks for your answer.

However, I still don't get the Picture clear.

How do we distinguish the time scales and turbulent scales in RANS and URANS?

In URANS, we take into account the unsteady term in the momentum equation. Don't we?

Thanks and Regards,

Juzer Rangwala

Dear Juzer; 

Since your are not using the time scale for integrate the equation, this information is not 'relevant' for the computation; as long as the computation is stable. 

The time scale from URANs and RANS might be the same, because both represents the same physics but with diffirent solving technique. 

Imagine this; think about an eddy that which dimension is constant in time and space. In the steady state solution, the eddy in RANS and URANS will be the same (theoretically) and you can compute or obtain the scales from that eddy. You will realize that the time scale for both is the same; because the model is the same. Both model have the same physics. Both are eddy viscosity model and neither space nor time (both are averaged equations) differ. 

I did precisely what Bernhard suggested but this is using experimental data and the data is from the development region but i am wondering about the second peak.

The reynolds based on the diameter of the nozzle is about 21000.

Id appreciate any help

Just by looking at the spectrum it clearly shows that you have something, maybe a source in your system, that is injecting energy to the cascade at that specific wavenumber. I have had those spectrum in old computation when I was using a source term in my computation to drive the flow, but in my case I was introducing that force I used to check the spectrum to verify that my force was introducing the energy at the right wavenumber. If you have no source, then you are in the presence of energy pile-up.

M. Kapoor,

Could you just describe step by step the method you used? With the detailed parameter of the function you used. 

Also, are you measuring a turbulent round jet? With no special features? 

Have a nice day

I agree with Jonathan, you should give more details about your problem and BC too. Are you computing the time spectrum ?