[CellZone]

Hi,

I am wondering if I can use the RANS for transient simulations? Because I take the average of the velocity component over time? But if I can take a very small time step for RANS, then it should be possible to use it for transient simulations? But when I reduce Delta t -- > then the sense of RANS (to not calculate all fluctuations) would be lost?

There is already a thread RANS and URANS. but I do not understand why RANS should not be a time average method?

By the way, how can I picture out "ensemble average" comparing to "time average"?

Thank you guys

[FMDenaro]

It is somehow diffult to give a clear explanation of what URANS formulation means... It makes sense (in my opinion) only if an external time-dependent force exists. Therefore, the statistical averaging for URANS has its sense when formulated as

<f>(x,t)= 1/N Sum (i=1...N) f_i(x,t)

formally for N->Inf.

Of course, a question is that if using the ensemble averaging on the equations, the model of the unresolved terms should differ from those in RANS.

A different meaning in URANS can be when the time-averaging is performed over a finite time interval and the averaged function remains time-dependent. But that has some similarity with the time-filtered LES.

[BlnPhoenix]

Hi,

By the way, how can I picture out "ensemble average" comparing to "time average"?

Check this thread:

RANS modelling and URANS methods in unsteady flow simulations

In short: RANS does not concider time at all in the equations, it's always steady state. The ensemble-averaging sits in the turbulence model you use, which was actually calibrated by performing multiple experiments with DNS solvers and then ensemble-averaged to get mean parameters to account for transient effects. Therefore you do not need a time dependent RANS formulation to account for the transient effects rising from turbulent effects on very small and larger time scales.

On the other hand RANS can not always approach a steady state, because the underlying physics are of inherent transient behaviour on a larger time scale. For this you need URANS, where time is concidered in the NS equations. Then you can choose a time step which actually captures the transient nature of the flow, e.g. ociliations behind a cylinder. The frequencies of the oscillations can be captured with a sufficiently small time step.

Please take this explantion with a grain of salt, i'm also still no expert in RANS/URANS territory.

Edit: To make it more clear. Time averaging in RANS is done by Reynolds averaging velocities and modelling the time dependency by the turbulence model. So there is in fact no time-averaging over time steps or similar involved.

[juliom]

I agree with professor Denaro opinion. I found a very nice paragraph in one text book I love from professor Tappan, where he magically explains this difference. Since I don't have the textbook with me now I will paraphrase that amazing paragraph. Turbulence is transient by nature. However there are cases where the transient behavior is due to transient boundary conditions, as professor Denaro explained. However, the transient behavior of turbulence goes far beyond the boundary conditions because it relies on the "fluctuation". Therefore, no mater how small your time step is in z(URANS) your time step is killing or masking the turbulent fluctuations. Thus, you need something different from RANS or URANS. URAND is nothing more but a RANS model but with a transient approach, that does not have anything to do with the transient behavior proper of turbulence flows. Nonetheless, mathematically URANS models are less stiff and therefore easier to converge to a "steady state". I use "" because that steady state is from a statistical point of view.

[FMDenaro]

The main lack I see in the common URANS is that it is nothing else but a RANS where the time derivatives are simply added. That has the consequence that the turbulence model remains formally as same as it should contribute to a statistically steady field not an unsteady.

Have a look to the introduction in this paper
https://www.researchgate.net/publica...LIKE_BEHAVIOUR

[CellZone]

Thank you guys for all your comments. I'm trying to understand them step by step.

In short: RANS does not concider time at all in the equations, it's always steady state.

When I simulate a transient behaviour (like Karman Vortex street) with RANS, I should get after my solution has converged a steady state solution, so that there shouldn't be any changes in this video - but there are, so you clearly see the vortex shedding:

https://www.youtube.com/watch?v=Gv-CPKlFJeI

I would have expected a static "picture" after enough time.

Thank you for your reply!

[FMDenaro]

In fact, that is not a RANS solution../

[BlnPhoenix]

Originally Posted by FMDenaro

In fact, that is not a RANS solution../

Yes. It's probably a URANS solution. Large transient phenomena (Vortex Street) is captured with adding the variable time to the NS equations. Smaller transient phenomena (small turbulent velocity fluctuations) are accounted for by a RANS turbulence model, e.g. you don't see them in the solution as velocity fluctuations but they are accounted for.

But as Prof. Denaro pointed out, using a turbulence model which is calibrated for RANS in a URANS solution may be questionable.

[Altomare]

Originally Posted by CellZone

Hi,

I am wondering if I can use the RANS for transient simulations? Because I take the average of the velocity component over time? But if I can take a very small time step for RANS, then it should be possible to use it for transient simulations? But when I reduce Delta t -- > then the sense of RANS (to not calculate all fluctuations) would be lost?

There is already a thread RANS and URANS. but I do not understand why RANS should not be a time average method?

By the way, how can I picture out "ensemble average" comparing to "time average"?

Thank you guys

The RANS equations are derived using the first order statiatical momentum operator. As the probability densite can change in time and space, you can have transient RANS equations.

Your confusion can be explained by the ergodic theory, that tells the evarage calculated by probability densities converges into a temporal evarege to a very large time. What makes the flow in permanent state.

You can read more about this in Pope's book, second chapter.

Sent from my Moto G (4) using CFD Online Forum mobile app

[FMDenaro]

Originally Posted by Altomare

The RANS equations are derived using the first order statiatical momentum operator. As the probability densite can change in time and space, you can have transient RANS equations.

Your confusion can be explained by the ergodic theory, that tells the evarage calculated by probability densities converges into a temporal evarege to a very large time. What makes the flow in permanent state.

You can read more about this in Pope's book, second chapter.

Sent from my Moto G (4) using CFD Online Forum mobile app

Unfortunately, the general symbol of averaging makes the RANS/URANS equations similar to LES/TLES equations and one unused reader cannot appreciate the different meanings in those averaging, hidden by symbols like brackets, overbar, etc.

Hystorically, the Reynolds decomposition is v(x,t)=U(x)+v'(x,t) implying the adoption of a time-averaging operator for T->+Inf, for which U is steady. But, as I wrote above, one can use an ensemble averaging (or a time-averaging over a finite time) such that v(x,t)=V(x,t)+v''(x,t).

As you can see, the fluctuations fields are different and therefore different turbulent models should be adopted. Unfortunately, very often the RANS model is used and one simply switches the software to do a transient simulation. What is the physical meaning of the solution is not always clear...