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RANS Grid Sensitivity Divergence on LES Grid

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Old   May 14, 2020, 09:27
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Filippo Maria Denaro
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Actually, the discussion touched now several issues based on theoretical misconception.


1) There is no classical grid convergence in LES but only filter convergence in case of the use of explicit filtering
2) Comparing RANS and LES would make sense if the LES solution (for a gven filter width) is statistically averaged until a steady state. However, the filter effect can be present.
3) There is no theoretical reason to assess that LES requires only the cut-off filter. And there is no theoretical reason to think that the differential filtered equations are suitable for LES.
4) The numerics in RANS is much less relavant than in LES.
5) It makes no sense to compute the skin friction as convergence parameter to control while using wall modelled BCs.





I general I suppose that the submitted paper has also some relevant flaw...
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Old   May 14, 2020, 13:00
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I would like to add an issue that - although I doubt that it applies here - might help you with the reviewer. The stability of the RANS equations is not necessarily given, see e.g.

https://arxiv.org/abs/1803.05581

The research shows that the equations, closed by a perfect closure, might blow up due to being ill-conditioned. I do not know how the grid spacing comes into this, but at least it gives you some ammunition against the „if rans blows up, it is your fault“ argument.
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Old   May 14, 2020, 15:22
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Really appreciate all the help!
Ok, so y+ = 4 is not sufficient, I should have started there. I will get that below 1 for the RANS grid sensitivity for all the mesh levels. I kept the first layer thickness larger to preserve a lower aspect ratio for the LES to avoid a grid resolution-induced anisotropy, and that the documentation warns against high aspect ratios for LES.

Since this is using this 2nd-order code, and the Kolmogorov scales should not be used, here is the viscosity ratio. It is for the last timestep of the LES run on the 1:1 mesh. Mostly the eddy viscosity is below dynamic viscosity except for in the hole area, the mesh could use refinement there as the velocities are higher.


I will be careful with the spectral arguments as well. I did get a good match with the Pope spectral model for this though, and I can look at the resolved vs modeled energy for different LES grids for a practical comparison.
I would love to run this on a higher order code, but haven't found any with all the features we'll need (and I'm nowhere near the ability building these features), so the commercial products were the choice. I was hoping to chow the utility of the commercial options, but maybe I'm showing the futility...

Thanks for the comments that the diverging grid refinement should not be submitted, that is clear to me now!
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Old   May 14, 2020, 15:46
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Some suggestions:


1) In order to compute accurately the skin friction, the grid for LES requires the same care near a wall: no wall model and at least 3-4 nodes at y+<1 (viscous sublayer). Are you using periodic condition in spanwise direction?

2) Spatial central discretization with no bound (no flux limiter) and second order time integration is the lowest acceptable accuracy for LES. The implicit filter can be assumed to be smooth in wavenumber space. That should be considered in performing the spectral analysis.

3) Always compare your LES solution obtained with the eddy viscosity model to a case on the same grid but without any SGS model.
4) Ensure that the initial condition is totally disregarded.
5) Be careful in the inflow condition for LES, they are totally different from that you prescribe in RANS.
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Old   May 14, 2020, 16:12
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Thanks for all the advice FMD, here are my replies:

Quote:
1) In order to compute accurately the skin friction, the grid for LES requires the same care near a wall: no wall model and at least 3-4 nodes at y+<1 (viscous sublayer). Are you using periodic condition in spanwise direction?
Agreed. Please not the skin friction is not of interest though, the temperature is really the variable we're interested in, not that y+ is any less important even with the adiabatic condition. It was just a practical balance between aspect ratio and y+ and overall mesh size that drove it up.
And yes, the spanwise faces have a periodic interface specified.

Quote:
2) Spatial central discretization with no bound (no flux limiter) and second order time integration is the lowest acceptable accuracy for LES. The implicit filter can be assumed to be smooth in wavenumber space. That should be considered in performing the spectral analysis.
This is bounded CDS. I'm afraid I don't understand what you mean by the implicit filter being smooth though. But here is the spectrum at a point over the hole leading edge.


Quote:
3) Always compare your LES solution obtained with the eddy viscosity model to a case on the same grid but without any SGS model.
I ran this with the Smagorinsky coefficient set to zero and with laminar equations, though the laminar did not allow for synthetic turbulence at the inlet.[QUOTE]

Quote:
4) Ensure that the initial condition is totally disregarded.
Multiple flow-throughs were not sampled as the LES developed, and the sampled LES was for 6 flow-throughs to obtain stability in the variables.

Quote:
5) Be careful in the inflow condition for LES, they are totally different from that you prescribe in RANS.
True, this is actually using a feature in CFX that specifies a RANS inlet like a synthetic turbulence interface for zonal LES.
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Old   May 14, 2020, 16:36
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The thermal BL requires the same care about the y+ values for the first cells. I suppose you are working using air (Pr=0.71) therefore the dynamic and thermal BL are comparable.


The spectra you showed has two characteristics: a) a smothing at the high wavenumbers, this is a combined effect of the smooth transfer function implicitly induced by the second order central discretization and the eddy viscosity model. But, and that is a problem, a bounded scheme introduces a further artificial dissipation, like a supplementaru SGS model. That should be avoided and a pure central discretization should be used.
However, I don't understand what do you mean for resolved and modelled part of the spectrum. In LES you have a range of resolved wavenumbers and the SGS model acts on those.


What about the spectrum for the no-model LES? You can simply set the LES formulation by setting Cs=0.


Finally, are you able to use the dynamic Smagorinsky model?
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Old   May 14, 2020, 18:38
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Yes this is air, so agreed the y+ should be lower.

What I mean by that is that the grid is not sufficient to resolve those wavenumbers, and that is where it flattens out. The timestep size was small enough to go beyond that transition, up to nearly a wavenumber of 1E3, but the grid (or rather 3 times the grid size for the CDS scheme) could not resolve beyond. Here is a diagram of the spectrum to show it better.
[IMG][/IMG]

Also, I've overlaid the spectrum with a range of experiments with varying Retheta from Pope to show where it sits.
[IMG][/IMG]

The Cs=0 spectrum is very similar but has about 18% higher total energy (resolved + unresolved). The Laminar case (no synthetic turbulence), looks similar as well but is half the total energy. Plots of those are available in that conference paper, I'll spare the space here, but here's the link again:
https://arc.aiaa.org/doi/abs/10.2514/6.2019-4089

I am currently running dynamic Smagorinsky, not in CFX though as that precludes the synthetic turbulence feature unfortunately. This is on a much finer trimmed cell mesh as well. A constant Smagorinsky coefficient is definitely not ideal for this problem, we expect backscatter with the near-wall mixing.

I hope I'm explaining this well, I really appreciate all the help!
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Old   May 14, 2020, 19:11
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To tell the truth, I don't agree.
The sketch you posted is not what happens in LES. The general idea of LES is that you do not solve the dissipative range, the filter cuts away that part that is modelled. You have a spectrum extending up to the filter width wavenumber (describing only the inertial range) and all the considered components are resolved and are affected by the SGS model.

That last flat part of the spectrum has no physical meaning, it appears a numerical issue.

Assuming that you LES grid is so fine to solve the dissipative range you would have a DNS-like spectrum and the energy would drop
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Old   May 14, 2020, 20:15
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I should clarify, that is the total kinetic energy spectrum, so it's resolved + modeled. The flat part is then purely modeled. Does that make sense?
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Old   May 15, 2020, 04:10
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Quote:
Originally Posted by MikeBravo View Post
I should clarify, that is the total kinetic energy spectrum, so it's resolved + modeled. The flat part is then purely modeled. Does that make sense?
No. If you perform the Spectral analysis of the SGS term it is results having components in the same range of the resolved one.
You cannot add nothing behind the filter wavenumber.
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Old   May 15, 2020, 20:24
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Ok, hey this is probably getting off topic from the original post, so I don't know if I should start a new thread about the spectrum, but for now...

So here are the equations for resolved and unresolved TKE I am using:

Code:
resTKE = 0.5*((u-u.Trnavg)^2 + (v-v.Trnavg)^2 + (w-w.Trnavg)^2)
unresTKE = ((Cs*delta*Shear Strain Rate)^2)/0.3
    where delta = (Volume of Finite Volumes)^(1/3)
So the resolved TKE requires velocity, which is solved for using the 2nd order CDS advection scheme, requiring 3 elements in each direction (CFX is an element-based solver). So the highest frequency or the highest wavenumber I can get there is limited by the length of the 3 elements. Smaller elements would allow for higher frequencies. If I plotted just the resolved TKE, you would see a sharp drop off instead of a flattening out. Perhaps this is the more common way of showing the spectrum, but I think it is interesting to show the complete spectrum which shows how much energy is being modeled.

The unresolved TKE is limited by the timestep size instead. In the case of a 1st order time scheme (I know this is not ideal for LES, and lower order codes should not be trusted) the limiting frequency is 1/(2dt). I could use a larger timestep size to make the limiting frequencies for the resolved and unresolved TKE align with each other.

So is there something wrong with the equations I am using to calculate the resolved and unresolved TKE? I don't really see why the SGS TKE would be cut off by the upstream explicit filter. Shouldn't the subgrid energy be independent of the grid size since it is sub grid? Then the timestep size would be the only limiting factor.

I think I've got a good direction for my original question and have a good idea where to go, so thanks everyone for the help! I still welcome the expanded discussion and expertise on this spectrum and LES validation though, so thanks!
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Old   May 16, 2020, 04:35
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Dear @MikeBravo


I will try to give you some more rigorous answers.


First consider the physics in terms of the general energy spectrum, it will extend up to the Kolmogorov characteristic lenght eta, that is up to the wavenumber kc=pi/eta. That is the real total energy spectrum one ideally would see. If you perform a DNS that is obtained if you solve using a grid size h=O(eta), that is your DNS energy spectrum extends up to the Nyquist wavenumber pi/h=pi/O(eta).



Now consider the LES formulation in which the filter (implicit or explicit) introduce a cut-off at kf=pi/delta. Let us assume (approximatively) that the filter width delta corresponds to the grid size h. That means that your resolved filtered velocity field produces an energy spectrum that is represented up to the wavenumber kf. Be careful that in the filtered velocity field is already present the effect of the SGS model and the energy spectrum will show such effect (superimposed to the shape of the transfer function that can be smooth). Then in LES you can represent nothing for wavenumebers k>kf.

You can see the spectrum of the modelled term, always in the wavenumber range [0,kf], but you should represent that in a different plot.

In other terms it appears not correct to assume that the spectrum you would see in DNS can be compared to the spectrum obtained by summing the spectrum of the filtered velocity field with the spectrum of the modelled term. Note that some comparisons between DNS and LES use to post-filter the DNS data to get a filtered velocity to compare to the LES solution. However, this is also a questionable approach (that, however, I used, too).



I hope that would make sense for you and yes, maybe a new post for this specific topic would be better.




PS: why do you considered the time step? Isn't the spectrum obtained from the FFT along spatial directions?
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Old   September 15, 2020, 16:03
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Quote:
Originally Posted by sbaffini View Post
...
In any case, the important thing is that you can't have y+ changing between the grids when doing a grid refinement.
I'd like to revisit the remark in this post from a few months ago. I have since completed a grid refinement of the LES solution keeping the first layer thickness the same, and the solution exhibits grid insensitivity at the higher refinement levels.

However, I haven't found any references on keeping a constant y+ for grid sensitivity studies. I've just been seeing a y+ that varies with the grid resolution. Would anybody be able to recommend a resource on this?

Thanks!
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Old   September 16, 2020, 00:53
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Quote:
Originally Posted by MikeBravo View Post
I'd like to revisit the remark in this post from a few months ago. I have since completed a grid refinement of the LES solution keeping the first layer thickness the same, and the solution exhibits grid insensitivity at the higher refinement levels.

However, I haven't found any references on keeping a constant y+ for grid sensitivity studies. I've just been seeing a y+ that varies with the grid resolution. Would anybody be able to recommend a resource on this?

Thanks!



You would not find anything on it but it would save you lots of pain.

The main reason is that wall function is an inexact science specially when it comes to blending between high reynolds number formulation to low reynolds number formulation. Every software does it its way.

By keeping the nearest grid to the same size you try to fix this wall treatment to constant between various grids (fixing a BC) and then if you do the mesh refinement you are very likely to see the effects of grid refinements.

By changing the near wall grid you are now on mercy of how the behaviour of that particular software is with regard to the change you brought in.
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