[sjwon1991]

Hi, I have a question about comparing SGS models for LES.

I simulate 3d turbulent channel flow to validate my code.

This code is normalized by central velocity (initially imposed as laminar profile) and channel half-width. And mass flow rate is constant.

I inputted Re_c and calculate Re_tau after the simulation.

To set same Re_tau, I should use different Re_c for each SGS models.

However, if I used different Re_c, I get different <u+> profile.

But when I plot u/u_c profile, all of mean velocity profile looks similar.

So I guess that the discrepancy is caused by u_tau value.

One thing that I want to know is "Should I use different Re_c value to set same Re_tau for each SGS models?"

Then how can I overcome the problem caused by different u_tau value for each sgs model which can cause some discrepancy in plot?

Thanks for your help!

[FMDenaro]

Yes, what you observed is quite normal and documented in literature...

A possible alternative way to use a different method to make the equations non-dimensional:
Given the forcing pressure gradient fixed and normalized to 1, means that the non diemnsional velocity in the momentum is directly the u+ field and the diffusive terms have (1/Re_tau) as coefficients.

You can find similar posts in cfd-online as well as seraching in the literature.

[sbaffini]

Dear Sungjin,

that, in practice, is the very essence of any turbulence model, not only LES (even if LES might somehow extremize that).

The system you are analyzing, the channel flow with a SGS model, has only one input, the driving pressure gradient, and one output, the mass flow rate in the channel (derived from the velocity profile). At the equilibrium, the driving pressure gradient of the channel, by construction, has to equilibrate your overall flux contribution on the walls.

Now there are two possible approaches. One is to directly fix the driving pressure gradient. Then, the wall fluxes will have to balance that specific value, and all SGS models will end up having the same but with different velocity profiles (and different mass flow rates), as each model will adapt differently at the specified wall flux (balancing the pressure gradient).

You can also fix the mass flow rate (as you did) but, again, as each SGS model has a different flux contribution at the walls, you end up with different values.

In practice, whatever approach you use, you should end up having differences. If you fix the pressure gradient, the differences show up away from the wall in + variables. If you fix the mass flow rate they show up at the wall in outer variables. It would be interesting to see the whole set of 4 comparisons (+ and physical variables for both fixed pressure gradient and mass flow rate).

On why such differences exists among different models, it is a delicate matter. Basically, for a channel flow, what actually matters in determining the mean velocity profile, is the <u'v'> term.

This has, first of all, a numerical contribution. So that, doing a no model LES you can see if the numerics (including the pure lack of resolution a la LES) has an effect.

Once that effect is established, your hope for a SGS model is that it will, somehow, overcome any deficiency in the <u'v'> term for the no model case. What, in my experience, happens for low order codes is that the celebrated y^3 near wall behavior is such that these SGS models have no effect at all. Their effect turns out to be just too small at the wall, which might or not be ok, depending on what you could achieve without model.

In practice, also because of implementation aspects, different models will adapt differently to the near wall dynamics and numerics, producing the different behaviors you notice.

Another relevant issue not properly investigated in the literature is related to the non-dimensionalization when a SGS model is in place. If a SGS model has a non null contribution at the wall for <u'v'>, is the common definition still relevant? It seems to be the case, but i suspect that the numerics and implementationton play a role in this which is not yet completely understood. Also, in my experience, strong differences exist between pure eddy viscosity models and mixed or scale-similar models, the latter introducing a much higher contribution at walls than the former.

Note that, in theory, no SGS model typically introduces a direct contribution exactly at the wall (in a FV context, for example, the relative fluxes are just 0). Still, in practice, what determines your is the mean velocity in the first cell off the wall which, in turn, sees the SGS model contribution from the opposite face (with respect to the wall) and, somehow, also from the remaining wall normal faces. Again, implementation/numerics aspects might play a relevant role here.

[FMDenaro]

I would highlight what Paolo said: see first the effects of the numerics in your scheme by performing a no-model LES. This way you will be able to understand what the SGS adds to the U+ profile.