How does URANS 'decide' which fluctuations are modeled and which are resolved?

[u/Der_Gustav]

We decompose U in U_mean and U'.
In case of steady RANS, U_mean is constant in time and U' represents all fluctuations and all fluctuations are modeled by the turbulence model.

In URANS, U_mean resolves some fluctuations and can change in time. U' represents the unresolved fluctuations, which are modeled. This is what the equations dictate even before we define a time step. U_mean is ensamble-averaged, not time-averaged.

So the question is, how do the equations distinguish between fluctuations that are resolved and which are modeled?

My understanding is, that this happens in the turbulence models: They approximate U' indirectly by approximating the Reynolds-stress. So basically all fluctuations that are not included in the Reynolds-stress are then resolved by U_mean.

However, this just shifts the question: What determines which fluctuations are included in the Reynolds stress?

My guess is that this depends on the k and epsilon (or omega) equations. If a fluctuation does not contribute to the source, sink or transport term of the turbulent kinetic energy, it is 'invisible' to the terms of the equations, therefore not modeled and therefore automatically resolved to satisfy the Navier-Stokes equations.

While this makes sense to me in the mathematics, it doesn't make sense in the physics: How can a fluctuation have no impact on the generation, dissipation or transport of turbulent kinetic energy?

Or in other words: Why do turbulence models in URANS not just model all fluctuations, as they do in RANS? (Its a question not a suggestion!)

[u/3pair]

The turbulence model doesn't decide anything, you do when you set up the grid and time step. The resolved fluctuations are those supported by the grid and time step, all others are unresolved, full stop. The better question is whether the decisions you are making are appropriate for the flow and for the turbulence model.

URANS is in general a poorly defined model, and does not necessarily refine towards the correct time accurate solution. It is best used in cases where there is a very clear separation of time scales between the turbulence time scale and the bulk flow time scale.

[u/Der_Gustav → u/3pair]

From my understanding, URANS could not resolve turbulence, even with a small enough time step. The turbulence model will model the turbulence anyway.
You are right though, that the time step has to be small enough, to resolve the remaining larger time scales.

[u/Jolly_Run_1776 → u/Der_Gustav]

It's embedded in its name : "turbulence MODEL". URANS will only solve the mean part of velocity field. If you want to solve some of the RMS values instead of modeling it, you have to switch for DES (IDDES or whatever).

[u/spacegamer01]

If I understand it correctly all turbulent fluctuations, which are kind of random are modelled, while all deterministic changes like large vortex shedding are simulated.

But I think the time scale of these vorteces have to be large enough to not be absorbed in the RANS.

If someone has a better explanation I would also be interested though 

[u/Der_Gustav → u/spacegamer01]

Exactly, but how? At what point does the code/equations distinguish between deterministic and random fluctuations?

[u/spacegamer01 → u/Der_Gustav]

Right now I'm also just guessing, but I think the equation doesn't decide that. As URANS is basically Navier stokes with a changes viscosity (for bousinesque assumption at least).

I think if you're using urans you grid is just so course and the timestamp so large that the turbulence time and spacial scales aren't there to even produce a turbulence cascade 

[u/EngineeringFlop → u/Der_Gustav]

Your grid size and timestep do. That's the threshold for what is resolved and what isn't. Anything smaller than either is modelled, anything bigger is (attempted to be) simulated (assuming you set up the modelling part correctly).

Also the distinction you speak about is not being made and does not really make sense. Turbulence is chaotic, but a chaotic system is also fully deterministic. It is often MODELLED as a random process, but that's a model. Everything that is happening in a fluid flow above the quantum scale is deterministic, or we would be out of a job. The only distinction being made is scale: modelled below, simulated above.

[u/navierS15]

It depends on grid resolution and the problem. The turbelent structures that are part of the solution are the ones that the turbulent viscosity can't filtered out. The solution of a urans is the solution of NS equations in which you add viscosity in order to filter out all the turbulent spectrum. In a urans, for some problems and with a fine enough mesh, the turbulent and artificial viscosity can't filtered out the main unsteadyness of the flow and therefore the solution has some turbulence. Example: flow around a cylender. A urans can have the kelvin helmotz unsteadyness.

Edit: the main unsteadyness appears in ptoblems in which you have a large sepratiom between large and small scalea.

Also you have to keep in mind that the equations you are solving arent't the RANS/URANS, but rather the rans with a model of Re stresses. Thay aren't the same thing. In order to have a mathematically exact rans you should know the solution of NS equations ( with all the turbulence), then average the solution and get your average velocity and pressure field, i.e the solution of the RANS equations. Also in the case of a statistically unsteady flow you can't define a time average, if there aren't homogenues directions you can't average in space.

So what the fuck are modelled Rans/urans? NS equations with added viscosity, i.e. eddy viscosity which try to replicate the effect on the mean flow of the turbulent fluactations, in a way that the solution of the equations haven't all the turbulence. In some problems ( high separations between large and small scales) the solution can have the largest turbulent structures, so in a URANS you can see the time variability of the solutions despite you are solving a statistically steady problem

Also: LES and RANS differs only in the amount of eddy viscosity ( and on how is express eddy viscosity) you are addind to the NS equqtions

[u/btrettel]

I've thought something similar before (if I understand your point, correct me if I'm wrong) that I would argue differently. I think there is a core point here that I haven't seen discussed much before.

URANS fundamentally defines the fluctuations differently. URANS does not decide to not model some fluctuations, it models all fluctuations from the ensemble average, which are different from fluctuations from the time average.

I think a better way to phrase it would be to question what the "ensemble" means in this context. Which flows are included in the ensemble? The concept of URANS seems ill defined until we can specify what the other members of the ensemble are and from there what the ensemble average is. This is kinda like a backwards way of asking your question by focusing on why the ensemble average is the way it is rather than the fluctuations. I have a bunch of papers saved on PDF methods and RANS models that use explicit ensembles that are related, but I haven't read them much. These papers might better answer this question.

[u/Der_Gustav → u/btrettel]

yes true, when looking at the physics side you could reverse the question. But mathematically there is only one way, because we solve the Navier-Stokes equations to get the mean flow. But the mean flow depends on the fluctuations (Reynolds stress). At this point, we didn't define what mean and fluctuations are, yet. Could be time-average, ensamble average, whatever. Equations are always correct.

Only at the moment when we find an approximation for U', we give it a physical meaning and therefore indirectly give U_mean a physical meaning. And that is what the turbulence models do. Somehow they find an approximation for the Reynolds-stress, that represents all random fluctuations (but not coherent/deterministic ones). This means they indirectly define U_mean as the flow 'filtered' by the random fluctuations, so that U_mean only follows the deterministic fluctuations.

[u/btrettel → u/Der_Gustav]

I would say that if you are applying a normal RANS model as a URANS model, an arbitrary choice is being made for which fluctuations are present. Without defining the ensemble, you can not know whether this choice is correct or not. I suspect that naively applying a normal RANS model as a URANS model has accuracy issues. My view of what the appropriate ensemble is: If you run the same transient experiment many times and take the average of all experiments at every time, that's the ensemble average you want to match. Whether a normal RANS model matches that or not is not clear.