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 Lance September 2, 2011 04:16

Eddy viscosity ratio and LES

Hi,
I've read a couple of papers where people have computed the eddy-viscosity ratio and used it to motivate the use of LES in their low-Re models. For example, if the eddy-viscosity ratio becomes 0.30, some authors claim that the subgrid scale dissipates 30% of the energy of the flow, which justifies their use of LES compared to a laminar solution.

Is this really true? And what happens when the eddy viscosity ratio becomes more than 1? Does that mean that the subgrid scale dissipate more energy than there is in the flow?

edit: on second thought, energy is also created in the subgrid scale. Is that why the ratio can become more than 1?

 ghorrocks September 2, 2011 06:39

The sub grid model is not limited (in my knowledge anyway) to a ratio of 0.3. These low ratioes of dissipation simply mean the turbulence dissipation is small relative to the viscous dissipation.

I think a better way of validating an LES model is by showing that you are in the right length and time scales, or by showing that the turbulence spectrum is correct.

Quote:
 And what happens when the eddy viscosity ratio becomes more than 1?
Nothing. It simply means there is more turbulent dissipation than viscous.

Quote:
 energy is also created in the subgrid scale.
No it isn't. It might put some energy into some frequencies in the turbulent spectrum, but it takes more out elsewhere. Overall it is dissipative..... Unless you like perpetual motion machines.

By the way, for the mathematically picky - It has not been proven mathematically that the Navier Stokes equations are dissipative (ie that flow always dies out in time and does not perpetually flow). This is such a physically obvious thing but diabolical to prove formally that it has been made a millenium problem (http://www.claymath.org/millennium/N...kes_Equations/) and anybody who can prove it will be award \$1 million.

 Lance September 2, 2011 07:16

Quote:
 Originally Posted by ghorrocks (Post 322636) No it isn't. It might put some energy into some frequencies in the turbulent spectrum, but it takes more out elsewhere. Overall it is dissipative..... Unless you like perpetual motion machines.
Im really into perpetual motion machines (my car violates the second law of thermodynamics every morning), but I agree that the total amount of energy does not increase. Was reading about backscatter (energy transfer from smaller to larger eddies) and got a bit confused. Never mind.

Quote:
 Originally Posted by ghorrocks (Post 322636) I think a better way of validating an LES model is by showing that you are in the right length and time scales, or by showing that the turbulence spectrum is correct.
I totally agree, a scale study or a turbulence spectrum would be a good way to validate the use of the LES model. That's why Im a bit confused about statements like "the eddy-viscosity ratio is 0.3, which means that the sub-grid scale dissipates 30% of the energy in the flow, which justifies the use of LES". Without a turbulence spectrum plot, is the eddy-viscosity ratio enough to motivate a (low-Re) LES simulation ?

 ghorrocks September 2, 2011 18:35

Quote:
 is the eddy-viscosity ratio enough to motivate a (low-Re) LES simulation ?
In my opinion (and it is only an opinion), showing the eddy viscosity ratio is low simply means that an LES model is likely to be easier than if it were high, as the length and time scales required are likely to be much larger and therefore easier. Whether LES is good idea compared to a RANS approach will depend on exactly what you are doing.

 M_Tidswell April 8, 2013 09:00

Related query

Dear All

I have been reading very similar papers I suspect, one of them suggests that a simple grid size estimator for an LES grid would be the SGS viscosity/ molecular viscosity, you would be looking to achieve approx 20 for a high Re flow.

Could this be applied to an SAS-SST model? Such as obtaining the eddy/turbulent viscosity in the fine near wall region where the SST model would have resolved the value? I can't see a way of extracting an SST specific term from Ansys CFX.

I have played with extracting the kolmogorov length scale from a previous SST simulation and using that as a measure for the required transient grid length but I'm not convinced by the results although it is early days

Mark

 ghorrocks April 8, 2013 18:21

The Kolmogorov length scale has little relevance to a LES simulation.

The Taylor length scale is a useful starting point for working out the mesh size required for LES: http://en.wikipedia.org/wiki/Taylor_microscale

 ghorrocks April 8, 2013 23:52

Energy is not created in the subgrid scale. In a turbulence model the turbulence just increases viscosity, so this is dissipative and cannot create energy -at least not in this universe, but if you can prove this you will win the \$1 million Millenium prize (http://planetmath.org/millenniumproblems see number 3).

Energy can move about on the turbulence frequency spectrum, but not be generated.

As I said previously the ratio being less than 1 simply means there is more viscous dissipation than turbulent dissipation. This is true for all laminar flows and turbulent flows at low Re number. There is nothing special about it.

 M_Tidswell April 9, 2013 05:27

Just goes to prove you shouldn't believe everything you read even if it is a journal! Hehe
Will look into the Taylor length scale

Many Thanks

 ghorrocks April 9, 2013 19:01

I am not saying the journal is wrong - you suggest it was saying you can estimate LES mesh size by when the viscous to turbulent dissipation ratio is one. This also sounds like a reasonable starting point for a LES mesh size. In most flows the turbulent dissipation is much bigger than the viscous, so if the ratio is 1 it means the mesh size has been reduced to the size where viscous dissipation is becoming important.

This is another independant way of estimating mesh size for LES.

This is one of the really tricky things about LES. The results are dependant on mesh size and the mesh size you can use depends on the SGS model you are using.

 M_Tidswell April 15, 2013 14:31

Hello

Sorry for taking so long to thank you I have been chasing a bug in some simulations and hadn't got round to having a think. It had struck me that as the Kolmogorov length scale relates to the smallest features it was going in the direction of a DNS simulation hence my initial post.

The results look really good, more inline with the experimental data, can i ask despite it being a slightly different subject - is there a way of exporting location settings from CFX post? I have 60 odd points/lines in a post file and I want to use them in another one, typing it in would be very dull. I export pre settings a lot as CCL files but I've never needed to do this before.

Thank you again

Mark

 ghorrocks April 15, 2013 19:08

If you intend to do DNS style simulations you need to consider things like numerical dissipation and related issues. It is critical that the mesh defines the dissipation, not the numerics.

You can both import and export CCL in CFX-Pre and when you run the solver on the command line. In CFX-Pre you can also edit the CCL of individual objects in the tree (right click on the tree item).

 oj.bulmer April 16, 2013 08:57

Some interesting discussion going on here. Not an expert in this area, but would like to venture some thoughts...

Quote:
 Originally Posted by Lance on second thought, energy is also created in the subgrid scale. Is that why the ratio can become more than 1?
The main difference between DNS and LES is that in LES the unresolved lengthscales are modelled using SGS models, while the DNS resolves lengthscales upto Kolmogorov's scales. Essentially, in the region of unresolved scales, the energy drain (in the cascade) should still be mimicked. Thus SGS models do not account for SGS stresses at every point of space/time but represent their overall global effect. Essentially, the energy from smallest resolved scale, when transferred to the lengthscale modelled by SGS models, appears as a source term in transport equations. Perhaps, this is what you were referring as "Production" of energy? This rather is a trick to have a consistent energy cascading, distributing the energy to upto smallest scales where it is eaten up by viscosity.

Quote:
 Originally Posted by Lance ...some authors claim that the subgrid scale dissipates 30% of the energy of the flow, which justifies their use of LES compared to a laminar solution.
I will take a wild guess to reason the choice of LES. In energy cascade, the energy is transferred from big length scales to immediate small lengthscales. But Kraichenan (1976) and Domaradzki et al (1993) showed that in the energy spectrum (divided between resolved and unresolved/modelled lengthscales) upto 25% energy transfer can happen between much larger scale eddies and the cut-off lengthscale eddies ( the ones modelled by SGS models). This might have been a motivation to do LES, which would still resolve these larger eddies and give a correct picture. In Low Re models, all the lengthscales are just modeled, and thus modelling errors do jeopardize prediction of this sensitive energy transfer. Laminar models abolish any turbulent lengthscales.

Quote:
 Originally Posted by M_Tidswell ... I have played with extracting the kolmogorov length scale from a previous SST simulation and using that as a measure for the required transient grid length...
Choosing Kolmogorov's lengthscale for grid, literally, would mean you are actually close to DNS than LES! The advantage of LES over DNS is that in LES you'd only resolve the larger lengthscales that are dependent on the boundary conditions, while the smaller lengthscales that are independent of BCs are modeled. In wall bounded flows, it would be important to resolve the near-wall eddies, so grid spacings in inner layer close to wall in terms of non-dimensionalised distances can be , x being streamwise direction (Ugo Piomelli, 2002).

Quote:
 Originally Posted by ghorrocks The Taylor length scale is a useful starting point for working out the mesh size required for LES
Indeed, but there are caveats. While Taylor lengthscales are situated in inertial sub-range (close to dissipation subrange end), they don't have a clear physical representation and their calculation is not always straightforward. Gaitonde (2008) predicts that for relatively high Reynolds number, the use of Taylor's lengthscale as a measure of LES grid size would result in an over-resolved LES. Hence the author recommends a cap on the cut-off lengthscale while filtering (smallest resolved lengthscale) as max(Taylor's lengthscale,L/10), where L is turbulent energy lengthscale.

OJ

 M_Tidswell April 29, 2013 09:32

Hi OJ

Yes my venturing into the realms of Kolmogorov length scale produced some rather interesting meshes and were essentially beyond the practical computational power I had available for any reasonable time step.
I'm currently attempting to emulate some experimental results for a back-step and I got some quite interesting results using the Taylor micro-scale which I calculated based on some semi-empirical formulas based on the RANS SST simulation I was using the trigger the transient simulation. The result do not however show any Brown-Roshko structures in the shear layer region between the recirculating fluid and the main flow which I was expecting to see at the Reynolds number I was considering. Clearly a bit more fiddling is need on my part!

Does anyone have an opinion on what type of plot would show these structures most effectively, I was using contour plots but unsurprisingly they have a rather defined contoured nature to them which I don't think is helping.

Many thanks

 ghorrocks April 29, 2013 19:02

First of all, is your model sufficiently accurate that you will get the structures you expect? You will need a low dissipation numerical scheme - use the LES settings with a central differencing advection scheme. You will also need second order time stepping. Are you using these?

There are some vortex visualisation tools in CFD-Post. Have a look at the additional variables available under the puzzlingly labelled "..." button.

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