Hi,

I am currently finishing my engineering studies, I am making some CFD analysis with Fluent for plasma simulation.

Anyway, I have a few questions about turbulence models.

I am using the k-e RANS model, but I am doing unsteady simulations.

And I know that RANS model are based on the fact that we are simplifying turbulence by looking only for the time averaged flow.

So, how can we use it for UNsteady simulations? RANS shouldn't only be used in steady analysis? I have seen that RANS is very commonly and widely used for unsteady simulations but I don't really understand that. I'm not very comfortable with this.

I know there are U-RANS (unsteady RANS) methods but I don't have them with my version of Fluent and, anyway, I am very curious on how this could work?

I mean, how can we pretend that we are only seeking for the time-averaged flow but making unsteady calculus.

I think these RANS model are merging volumic and time average, so may be we are calculating volumic average instead of time average? I could understand that but, really, I am a bit confused.

Could someone help me by explaining this?

Thanks a lot!

What actually change between RANS and URANS is the time over which you perform the average (infinity for RANS, a critical period for URANS)

Because of its commutative property with derivative operators, the time average of RANS and URANS does not appear anywhere in the equations so the URANS can just be performed with the extra time derivative and nothing else, the same is for the turbulence models (so URANS model are present in Fluent, they are the same as for RANS)

A very important issue is the significance of this kind of simulation. URANS has a sense only when the critical period is very different from the turbulent time scale. The other issue is the implicit time filtering associated with the grid you are using (a sort of volume average).

It's a very complex argument (in the sense of physical interpretation of your simulation) and the late time, my poor english, my personal comprension of the argument and the place (a forum) are not the right conditions to explain this in the right way.

However i think that the most meaningful approach to this is the LES approach with a general time-space filter; in this case RANS and URANS are just a subset of the general case. In the LES framework is more easy to understand the roles of your grid, your numerical time step, the assumed critical period for the time average and how each of these parameters influences each other

Thanks for your answers.

I know that LES is much better than RANS, but it also needs more computational effort.

Anyway, I am using RANS and I am not supposed to change it for LES, I am supposed to keep RANS.

I just wanted to know what U-RANS exactly is, and from what I understood I would say this is exactly the same as RANS but running unsteady, right? And this approach has a physical meaning only if the time step is good. You say that the critical period should be very different from the turbulence time scale? What's the critical period?

In fact, I have a teacher very tough in turbulence and I am pretty sure he will ask me precise and difficult questions about this.

That is why I wanted to know how I could explain to him that I could use RANS in unsteady calculations without doing anything stupid.

Mathematically speaking, RANS and U-RANS are exactly the same?

I'm sorry maybe i was not so clear, but i didn't mean that you should switch your simulation from URANS to LES.

What i said is that the theoretical framework of LES is much more general and is very useful for understanding (really and deeply) also the RANS and URANS approach.

You could start giving a look to the Amazon excerpt of the book of Sagaut: Large Eddy Simulation of Incompressible Flows

In the very first pages (that are present on the amazon site, you have to click on "look inside" in the book page) there is a very easy to follow explanation of the differences between RANS, URANS and LES.

Resuming:

Computationally speaking, the URANS is just an unsteady RANS; that's all. All the turbulence RANS models are actually the same with the additional time derivative.

Physically speking, what this kind of simulation is? This is somehow still an open question. The right approach is to use it when there is a known external time scale (what i called "critical period") very different from the turbulent ones. Two right cases are vortex shedding in some situations and low frequency pulsatile flows in ducts.

In all the other cases it's very difficult to say what the result actually means due to the interactions between different time scales and time and grid scales (anyway it wiil actually be something wrong).

As stated in the other post, this is the much i can say about a so general and complex argument; if you have some more specific questions about your exam maybe i can be of much more help.

However, what is usually enough in exams is that you say that (maybe in a more correct english, because this is not my original language) "the period over which you perform the average in the URANS approach has to be large compared to that of the turbulent fluctuations and small compared to that of the external forcing" (it is usually assumed that the need for URANS comes from the presence of a known unsteady external forcing field; in the case of vortex shedding the period is that of the shedding).

I hope i've been much more clear now

Thank you for these details.

Don't worry about your english, I am french, so english isn't my native langage either

I will go and have a look at the book you mentioned.

Where do I select the period of averaging in Fluent? I have never seen this parameter. All I can do is selecting the turbulence model, and I don't think this is possible at all to give any period like this. Is it?

Thanks!

You can't select it in Fluent or other codes; the only place where it emerges in the URANS equations is the Reynolds stress tensor.

In fact when you time averages the N.S. equations (it doesn't mean what period you uses) every single term will transform linearly with the original variable replaced by it's time-averaged counterpart. This is due to the commutative property of the time-average operator (but this is an other story).

However, the only term for which this doesn't happen is the nonlinear convective term, due to it's nonlinearity. So, in it, the time average operator, and so the time period choosed, is still formally visible.

But, actually, because you are going to change this term with some turbulence model, this is not going to be, in practice, true.

That is, the only way the time period could be apparent is that the turbulent model explicitly treats it as a model parameter.

Today, in my knowledge (which is not so deep, so you could check this by yourself) there is no turbulent model which actually contains the time-average period as an explicit parameter.

As stated before the only difference between RANS and URANS turbulence models is the presence of a time derivative.

In theory, if you would like to develops your own turbulence model for URANS, an idea would be that you decide to implement the time-average period as a parameter.

The reason for which this has never been done is that in your URANS simulation there are two more subtle effects, the time and space discretization, which acts as a sort of time and space average but they acts and interacts with each other in a non trivial way.

So, in the end, the pratical approach is:

1) Use URANS where an external unsteady forcing field is present; this is correct only if the caracteristic frequency of the external field is low and however far from the turbulent ones

2) Use a time step for your simulation that can accurately represents the time evolution of the external unsteady forcing field

3) Use RANS criteria for the grid

That's all.

Ok, thank you very much for these explanations. I'll check this out!

http://publications.onera.fr/exl-doc/320539.pdf

Bonne lecture