When doing a turbulent simulations with models such as LES, how can I compute the ensemble average of the instantaneous velocities. I know that there is an option for calculating "time statistics" in Fluent, but I think that option just calculate the time average between the initial and final time points (1 value for the whole simulation). What I am looking for is unsteady ensemble average. Actually, I am not completely sure how it is supposed to be done, since velocity fluctuations do not have a single wavelength. So the more general question would be: If I have u(t) how can I calculate U_bar (t) (assuming: u(t)=U_bar(t)+u'(t))?
Any help will be appreciated.
It sounds to me like you are interested in a statistically stationary flow, if this is the case I think you would want to proceed as follows:
1. Iterate your solution forward in time tracking some variable such as a velocity or an integrated force such that you integrate past the initial transient.
2. This is the point at which you will "check the box" for time statistics. If you had already been collecting time statistics, you can reinitialize them with the command "Solve/Initialize/Reset Statistics".
3. Then you will iterate over the desired sampling time. Typically this is done by iterating over a set number of characteristic times defined as a characteristic length/characteristic velocity. I typically use the time it would take for a single particle to traverse the entire domain.
4. After you have completed these iterations you will now see variables such as "Mean X Velocity" and "RMS X Velocity". Assuming your statistics are converged, this would be your U_bar and u'.
Hope that helps, good luck!
Stuart,
Thanks for your reply and helpful tips.
So, what is the definition of statistically stationary flow in turbulence. I mean, if I track the fluctuations in velocity at one point, how can I differentiate the initial transient state from turbulent fluctuations? How would you decide if your flow reached that point in time?
From your 3rd point, are you saying that the period over which the ensemble averaging is done should be based on a characteristic time that you mentioned? In that case, How can one obtain U_bar as a function of time (and not just one value at the end of period).
Take the attached figure for example. lets say that velocity fluctuations at one point in different cycles (which have a period based on a characteristic time as you said?) are shown in colors. The ensemble average that I am looking for is the black bold line. So it is a fiction of time.
Ah, so statistically stationary refers to turbulence in which the mean flow and statistics are not functions of time.
I think what you are trying to do will be somewhat empirical. Defining a mean flow as a function of time is more of a low pass filtering procedure which will be dependent on your choice of window size. You might consider looking into triple-decomposition approaches using POD, possibly. This sometimes does a good job of separating out stochastic turbulence from large scale structures and low frequency changes.
Are you able to provide more details about your flow? Is it the case that if you simply continue to iterate that your flow will reach a statistically stationary state?
Stuart,
This is exactly my question, how can I monitor mean flow and statistic without activating "time statistics" option in fluent?
My case, for now is very simple: flow inside a tube and it will reach a statistically stationary state(SSS). My questions are mostly about basic turbulent theories and they way that they are being implemented in fluent.
So, if I understood correctly, you are saying that there is no built-in function in Fluent for obtaining mean properties as a function of time, right?
Now, I know that I can compare LES SSS results as they are reported by fluent at the end of the simulation, with the results obtained from a steady state RANS model. But what if I want to compare with unsteady RANS model...?
Thanks.
I'm not sure that FLUENT has any built in options for any of these methods. You would likely need to program it into a UDF or post process your velocity data separately.
I think you will have to write UDF's for this kind of post processing. Just like a turbulent flow experimental researcher processing an instantaneous hot wire output.
Hello Stuart,
I have a question which is similar to what you were trying to do. I have an LES file and I would like to read fluctuating velocities there. Is there any way like a UDF function to put into fluent and get fluctuating velocities?
Thank you
Dear colleagues, I know that my comments (and my question) is late compared to the other questions. I will try to make my questions easy.
I am doing DNS of the 1D Burger equation with and without force. The computation without force is expect to have a flow field that is influenced only by the Boundary conditions and the initial condition. Somehow it will tends toward zero since there is no other force "inducing perturbations" the flow field. Thus, this problem is not statistically stationary or as Wilcox defined this is a non-stationary turbulence flow. How can I compute the mean of the velocity and the fluctuation of the velocity if the flow field is always changing until the viscous forces consumes all the energy.
The other case is more straight forward because the force, although is random, it will force the solution to a "steady state" thus the mean, and hence, the fluctuation of the velocity is very straight forward, once the computation is done.
What are your thoughts and comments??
Respectfully
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