eddy viscosity
 

Hi,
I am using a LES code with a Deardorff subgrid model.
Is it usually possible in the commercial software to find somehow the eddy viscosity, or it is impossible to know which is the portion of added eddy viscosity?

If I calculate the viscosity by looking at the ouput temperature, and I subtract it to the total viscosity. Do I obtain the added eddy viscosity?

Which viscosity should I consider if I have to quantify the Reynolds number?

Thanks

Usually you do have some means of finding the eddy viscosity because it's really easy to swap out models by just changing the way the eddy viscosity is computed and keeping the same higher-level equations the same.

Eddy viscosity is a flow property, it does not affect the static fluid temperature. You can't back-calculate the total or eddy viscosity by just looking at the temperature of the fluid at a location.

Reynolds number can mean a lot of things.. But if you have a flow in a pipe and you're wondering if the "Reynolds number" in the pipe is greater than or less than 2300 to determine if it is laminar or turbulent, then you'd be using the molecular viscosity. Or if you have a flat plate and you're wondering what the Reynolds number based on plate length and coordinates are, you'd also still be using the molecular viscosity.

Eddy viscosity is not real. Eddy viscosity is a proportionality constant used to rewrite the Reynolds stresses (the statistical average of products of velocity fluctuations) in a way that makes it look similar to the diffusion term.

Does the energy spectrum depends on the Reynolds number with the effective viscosity which include the eddy viscosity?

If I remember correctly, in Fluent you can extract the eddy viscosity function computed in the dynamic model.



Paolo (sbaffini) can answer.

I don't know anything about this Deardorf model but the Smagorinsky or dynamic Smagorinsky sgs viscosity is a readily available field function you can retrieve whenever you feel like it.

The viscosity that goes into Reynolds number is always the molecular viscosity.

No one puts eddy viscosity into Reynolds number. The ratio of eddy viscosity to molecular viscosity is itself another Reynolds number. I hope the circular definition is clear.

Since the energy spectrum varies if the Reynolds number varies. I wanted to know if the subgrid scale can act as a filter itself because the change in the Reynolds (due to the added eddy viscosity) affects the spectrum?

Of course! If you perform a simple experiment, that is a LES run without any SGS model and compare the resulting spectra to the ones computed with the SGS model you will see the differences. But that is not related to the meaning of the LES filter. The filter enters into the SGS eddy viscosity by means of the characteristic filter width.

Okay I forgot actually that we are talking about LES and here we are talking about the subgrid scale eddy viscosity. So ignore my writing about Reynolds stresses and please replace them with the filtered velocities. Anyway...



Different LES models will certainly produce different spectrum. But we wouldn't say that it is due to a Reynolds number change. Let's say we have a pipe flow at 10,000 Reynolds number and we pick a point in the flow and obtain its spectrum. The Reynolds number is the flowrate non-dimensionalized, i.e. it's an operating condition or a boundary condition. When we say the energy spectrum depends on Reynolds number, we are referring to this 10,000 number which is calculated based on the flowrate. If I double the flowrate, I double the Reynolds number and get a new spectrum.


Now if I change my LES model but keep the same flowrate, I keep the same Reynolds number. I can get a different spectrum because I use a different model. But any differences I observe in my LES result, I wouldn't say that it caused a change in Reynolds number. The same would be the case if I switched RANS models (say from k-epsilon to k-omega). Yes, the eddy viscosity would be different for each model. I could (but I wouldn't) say that it caused a Reynolds number change or is caused by a change in Reynolds number.

I understand what you said. The Reynolds of the flow is the same, indipendently from the SGS. I agree with this. But I think that is possible that adding an eddy viscosity with a SGS model modifies the spectrum as a change of fictitius (let's call in this way) occurs.

Sorry. I didn't understand what you mean with this?

There is a characteristic lenght to be used in the evaluation of the eddy viscosity model and this lenght is the filter width. This is the way the filter enters into the SGS term.

Yes, ok, but depending on the SGS model used, the shape of the Energy spectrum can change and this can be because the Re is different depending on the quantity of added viscosity. Isn't it?

Consider the ideal DNS spectrum. There are different effects in LES to produce modification in the spectrum:


1) The grid cut-off, that is the truncation of the DNS energy content at the Nyquist wavenumber pi/h

2) The smooth transfer function, that is the effect of filters such as the top-hat in FV/FD methods. The effect is in a smoothing of the DNS spectrum, not related to the SGS model. That effect is not present in spectral method.
3) The action of the SGS model that is active mainly at the resolved wavenumbers close to the pi/Delta wavenumber.


If you consider an eddy viscosity model and define a Reynolds number depending on the total viscosity, you have a "local" Re number and you can see the zones where the SGS mainly acts. There you can expect that there is a dissipation of the energy. But in general, all effects are combined in a mix of numerical and physical effects.


The best way to understand the specific effect of the SGS model is simply to compare the spectra for the LES no-model and the LES with model cases.

This sgs Reynolds number is way too novel of an interpretation of a turbulence model for my liking. Sorry. I just don't like it.

Different calculations will produce different results and produce different energy spectra. Okay we are good up to here. But you already could have different filter lengths, which begs the question of what your effective length scale is when you go to calculate this effective Reynolds number. And then there is the implied filter function which is different. We haven't even gotten yet to the eddy viscosity and already there are too many other things to consider. It's soooo convoluted.

But now I (personally) am a bit confused what even is this eddy viscosity we are talking about. In LES you solve for filtered velocities and there are some subgrid stress terms that need to be modeled (and this is where the sgs viscosity appears). Both influence the energy spectrum. The former is what we actually care about and responsible for most of the spectrum. The latter influence is a tiny contribution and undesirable in a good LES.

If you are talking about the sgs eddy viscosity and adding this contribution to your Reynolds number...

1) Keep in mind there isn't an sgs eddy viscosity in the general form of the governing equations. You are modeling a subgrid stress term. Yes we use (by popularity) a Boussinesq approach involving an sgs eddy viscosity but we inserted this eddy viscosity via our closure model. It wasn't already there. What was already there are subgrid stresses (the LES version of Reynolds stresses in RANS). Today you have a sgs viscosity because you model sgs stresses in LES a certain way. Tomorrow, someone else comes up with a different closure model that might not have an eddy viscosity in it.

2) Well you can just turn off the sgs term and effectively do a DNS, or you could do an actual DNS. Now you have an energy spectrum but no effective sgs eddy viscosity at all.