[MikeBravo]

Hello,

I am struggling to make sense of a grid sensitivity study that is diverging.

I am simulating a flat plate film cooling experiment that is inherently unstable, so I do not expect RANS to be adequate and am using LES. However, many journals require a grid sensitivity study and don't make exceptions for LES. The experiment has a very low Reynolds number, so the LES is already near DNS scales (length scale < 1X and time scale < 10X Kolmogorov). I have also performed a TKE spectrum analysis that shows that >99% of the turbulence is resolved and that it is well into the dissipation range of the energy cascade.

So the RANS grid sensitivity study does not converge across a range of block-structured meshes from much coarser to finer than the employed LES mesh. I interpreted this to be due to the inherent instability of the flow, but received the following feedback:

"As the grid is resolved, and for a RANS solution, there should be no sensitivity to the unsteadiness of the flow. This is mainly because the production term for kinetic energy is controlled by the strain rate tensor, which increases in value as the gradients are better resolved. As a result, the turbulent viscosity, which scales as the square of kinetic energy, becomes higher until convergence is reached. Under no circumstance should an increase in grid resolution for a transported RANS model formulation should lead to unsteadiness - this by itself is an indication that the software is not reliable."

Can anyone help make sense of this? This is a near-wall mixing problem with large, medium, and small eddies that RANS is not capturing, so I am struggling to understand this.

Thanks in advance!

[sbaffini]

There is a mix of statements here and is difficult to clearly understand what is going on.

Considering that, in any case, you would have little fortune in defending yourself from a reviewer if you're not in full command of the matter, here is my point of view (mixed with questions/hypotheses, because I haven't really understand what exactly you are doing and where the issue arose):

1) I assume you are doing RANS (as in steady solver used to solve a steady problem with a RANS turbulence model) and LES (unsteady solver used to solve an unsteady, 3D problem with an LES model) of a given flow.

2) Somebody (a reviewer I guess) asked to make a grid refinement study for both (LES and RANS). It's unclear how was this performed for LES, if it worked or not and the rule itself used to determine if that worked or not... but it seems to me that we shouldn't really care at all of the LES part here, except for the fact that the finer RANS grid was finer than (one of ?) the LES ones.

3) What I understood is that the problem is with the RANS one. Your grid refinement study does not converge. That is, you get converged steady solutions on all the grids but the quantity you use to assess the grid convergence (say, a pressure drop, an integral of something, a point value of some quantity, etc.) doesn't actually converge as expected for the given set of grids. Note that this is different from saying that one or more of the RANS calculations don't actually converge on a single grid.

4) If what I understood is correct, there might be several reasons for this but you provide no detail to ascertain what the problem might be.

So, lack of convergence in a quantity used for a grid convergence study, has nothing to do with the underlying flow, as long as you get a rock solid, converged steady solution.

However, and this is what puzzles me, the feedback you had seems relative to a situation where you were discussing about a lack of convergence of a single RANS computation on a single grid. That is, being unable to reach the steady state for a given run on a given grid.

In both cases, you received a very "misleading" (cough bullshit cough) feedback, at least according to the way you reported the thing. But I won't go into the details until you clarify exactly what was the issue.

[vesp]

May I ask who gave you this feedback ? It seems to disregard the fact that convergence issues / unsteadiness can be triggered by finer grids: the simple explanation is that a finer grids reduces the amount of numerical dissipation. One might argue that model dissipation should be sufficient to stabilize the solution, but that is often not enough. Many RANS simulations are stabilized by the numerical dissipation error in time and space. So while the statement might be true from a modeling standpoint, it disregards numerics.

If I had to guess I would say it was made by an older prof...

[FMDenaro]

RANS is by definition a steady model, it is suitable for flow having a statistical energy equilibrium (Production=Dissipation). The equations can converge or not but that is a typical model issue.
URANS is the unsteady counterpart but the theoretical basis for a flow developing unsteadness is not clear.


Considering the grid convergence, it has the aim of reducing the effect of the local truncation error. However, in RANS the turbulence model does not depend on the grid size as it is usual in LES. That makes sense for a grid independent solution in RANS. And this solution must be steady.

[MikeBravo]

Thanks for the reply Paolo, and I appreciate your point of view.

Responding accordingly,
1) I am focused on LES.
2) The reviewer asked for a grid refinement, which was done in RANS since I do not have the resources to do it in LES or do a DNS. And yes, the finest RANS grid was finer than the LES grid used.
3) Yes, the RANS grid sensitivity is what diverges, the RANS calculations themselves converge.
4) I'd be happy to elaborate on any details, here is a conference paper on the work: https://arc.aiaa.org/doi/abs/10.2514/6.2019-4089

The feedback was supposed to be in response to the grid convergence study, not a single RANS calculation...

Here is the plot in question, the value is effectively the area-average temperature on a surface as that is the result of interest. Average skin friction on the surface and TKE in the region of itnerest also show divergence.


Thanks for the insight.

[FMDenaro]

First of all, skin-friction is a post-processed variable and does not say directly what you get from the grid convergence analysis. What about the analysis on the computed variable?

Second, the dependence of the skin friction on the grid resolution in the BL is relevant but what about your type of BCs?

[MikeBravo]

vesp,
Thanks for the reply, it was a journal reviewer actually...
I noticed unsteadiness being triggered by the grid refinement early on for this problem while stile using URANS.

[MikeBravo]

FMD, I'm happy to get your input,

To be clear, synthetic turbulence is generated at the inlet and turbulence is generated in the mixing region where the injected cooling flow enters the mainstream, and that is not all being dissipated.

The computed variable shown in the plot is derived from the average temperature on the cooled surface. This is ultimately what we are trying to match in the experiment and seems to vary greatly depending on the setup. It is post-processed as well. Looking at solver variables, the streamwise momentum residual RMS, for example, does not exhibit convergence, though it does tend downward for the 3 finer grids. I am open to looking at any recommended solver variables as well.

For the BCs:
Inlet: Velocity inlet with a velocity and turbulence profiles applied
Outlet: Static pressure opening, backflow allowed
Sides: Periodic interfaces

[sbaffini]

Originally Posted by MikeBravo

Thanks for the reply Paolo, and I appreciate your point of view.

Responding accordingly,
1) I am focused on LES.
2) The reviewer asked for a grid refinement, which was done in RANS since I do not have the resources to do it in LES or do a DNS. And yes, the finest RANS grid was finer than the LES grid used.
3) Yes, the RANS grid sensitivity is what diverges, the RANS calculations themselves converge.
4) I'd be happy to elaborate on any details, here is a conference paper on the work: https://arc.aiaa.org/doi/abs/10.2514/6.2019-4089

The feedback was supposed to be in response to the grid convergence study, not a single RANS calculation...

Here is the plot in question, the value is effectively the area-average temperature on a surface as that is the result of interest. Average skin friction on the surface and TKE in the region of itnerest also show divergence.
[IMG][/IMG]

Thanks for the insight.

Well, for sure I would disregard for now the "feedback". I think the question here is very simple: is this supposed to happen? I think that an honest answer here is NO. If the points on your curve only differ by the grid and all of them are properly converged (which means that no signs of unsteadiness are allowed), this is not supposed to happen.

My first tought is that the difference you see in the result for 42 M elements is so large that you should be even able to spot it from the contour of the quantity you are averaging. If this is the case, this might be a first shot to give, to understand what is going on.

My second tought is on wall functions... are you sure you are not crossing any relevant boundary? Consider that, if you use thermal wall functions, a Pr different from 1 means that the velocity wall function and the thermal wall function will have different y+.

In more general terms, while it makes me laugh when people from academia criticize the major commercial codes (which in most cases are far more reliable than any randomly picked research code), I also have to say that I am not a fan of CFX and, for example, wall functions in node based/finite element frameworks are much less standard and open to baroque implementations.

[sbaffini]

Originally Posted by MikeBravo

FMD, I'm happy to get your input,

To be clear, synthetic turbulence is generated at the inlet and turbulence is generated in the mixing region where the injected cooling flow enters the mainstream, and that is not all being dissipated.

The computed variable shown in the plot is derived from the average temperature on the cooled surface. This is ultimately what we are trying to match in the experiment and seems to vary greatly depending on the setup. It is post-processed as well. Looking at solver variables, the streamwise momentum residual RMS, for example, does not exhibit convergence, though it does tend downward for the 3 finer grids. I am open to looking at any recommended solver variables as well.

For the BCs:
Inlet: Velocity inlet with a velocity and turbulence profiles applied
Outlet: Static pressure opening, backflow allowed
Sides: Periodic interfaces

Ok, admittedly, I haven't read the paper you linked, but I still don't understand if your RANS are actually steady RANS or URANS, that is unsteady? This makes a great difference here, and from your previous answer I understood you were doing steady RANS.

[FMDenaro]

I don’t think that a wall modelled BC is prescribed... that would not make sense for computing the skin friction

[sbaffini]

Originally Posted by FMDenaro

I don’t think that a wall modelled BC is prescribed... that would not make sense for computing the skin friction

The fact that his grid is finer than the LES one also suggests that this is not the case. But we don't know if its Pr number is around unity nor the turbulence model used for the RANS computation (for example, if for some reason he is using a model of the k-eps family, than wall functions are not avoidable).

[MikeBravo]

Sorry for the confusion,
The sensitivity study is just steady RANS, k-omega shear stress transport.
And the wall is adiabatic, I should have mentioned.

[FMDenaro]

Originally Posted by MikeBravo

Sorry for the confusion,
The sensitivity study is just steady RANS, k-omega shear stress transport.
And the wall is adiabatic, I should have mentioned.

Have you tried if the convergence is reached using a different turbulent model?
Just to understand better, what about the LES-based skin friction on the finest grid?

[sbaffini]

Originally Posted by MikeBravo

Sorry for the confusion,
The sensitivity study is just steady RANS, k-omega shear stress transport.
And the wall is adiabatic, I should have mentioned.

Ok, then this excludes the thermal wall function part. Maybe you should give more details (turbulence mode, y+, solver, schemes, etc.) and a picture of the contours whose average leads to the quantity that jumps in the convergence for 42 M elements. Without further details it is difficult to say anything.

However, if everything is done correctly, this doesn't obviously point to a code problem... not more than a RANS problem at least. As vesp pointed out, it is totally possible that the numerical viscosity played a role, progressively marginal, but sufficiently strong on all but the finest grid. But this also inevitably means that you are not converged yet, at least not for the quantity you are monitoring and the grid used to capture it.

I don't know, maybe you should have invested those 42 M cells differently, but at some point you must see convergence, otherwise there is obviously something that is changing and you don't know what it is, which is bad. For example, I see that the last passage is 5:4 while the others were of the form 1:4. Does this imply different directions of refinement or something similar? And does it mean that the last refinement was in a totally different direction than the previous ones? This would probably explain the behavior in the picture and the non optimal refinement.

[MikeBravo]

Ok, so looking at the skin friction for the LES, though it is just for the last timestep since I didn't save the time-average of that, it is well below all of the RANS mesh predictions:


Looking at temperature contours on the plate, the finer 42M element mesh just carries the cool film on the surface longer, the contour shape are very similar, but stretched out further for teh finer mesh:


To give more details:

• y+ = 4 (adiabatic mixing only, and enough points in the boundary layer for WMLES)
• x+= z+ = 12 (attempting to minimize aspect ratio of first layer for the LES)
• k-omega SST
• 'high-resolution' CFX advection scheme (2nd order)
• the mesh is block structured, and the different refinement levels are obtained by scaling the base length by 1:8, 1:4, 1:2, 1:1, and 1.25:1, so all the meshes are structured the same. So, as an example, if the number of nodes along the centerline were 100 for the 1:1 scale mesh, there would be 125 for the 1.25:1 scale mesh
  I would have kept going to 1.5:1 and 2:1, but I'd have to send that to the HPC

I can get a run started for the 1.25:1 mesh using a different RANS model pretty quickly to see if there is any impact there. I'll see if I can get the 1.5:1 and 2:1 meshes to the HPC, just limited resources on that. But would there be any value to refining the RANS so much to see the convergence? The mesh meets the requirements for WMLES (see paper), which is the aim of this work. I'd like to see it converge for my own satisfaction now though.

[FMDenaro]

First, you need to resolve the BL. That means you have to refine the grid to ensure 3-4 nodes (at least) are within y+<1.

[sbaffini]

Originally Posted by FMDenaro

First, you need to resolve the BL. That means you have to refine the grid to ensure 3-4 nodes (at least) are within y+<1.

Indeed, if y+ =4 is relative to the finest grid, it is confirmed to be a wall function problem. I can't double check now, but I'm pretty sure that the k-omega sst model in CFX uses an all y+ wall function, which means that a wall function is always active. While, in theory, such wall functions should be insensitive to the specific y+ value, they are not perfect and your case is very far from the typical wall function scenario (equilibrium boundary layer), so what you obtain is actually expected.

The only viable solution here, and I suggest you to investigate it also for your other models, is to redistribute cells in your grid to be always within y+ = 1-2, but no more. In any case, the important thing is that you can't have y+ changing between the grids when doing a grid refinement.

EDIT: I know, it sucks...

[gnwt4a]

A numerical scheme is supposed to have two analytical properties: convergence and consistency. The first says that the numerical method should reach *a* unique solution independently of the refinement path. The second says that the converged solution should be an approximation of the the equations of motion u started with. With nonlinear models neither is known a priori so there will always be doubt. This is accepted by most referees.

rans calculations that diverge with grid refinement are completely unacceptable.

the bit that u did a rans convergence study as replacement for the les is not clear to me. i am probably missing something because it sounds so bizarre.

use of the Kolmogorov scale as proof of good resolution is in principle and in practice (when using low order fds) for bounded flows, wrong. Moreover, calculating the dissipation rate from a simulation which uses 2nd order fds gives values that are already unreliably distorted. this method is, however, meaningful for fully spectral codes.

Here is what u can try with yr les calculation. Calculate the ratio of the eddy viscosity to the molecular one. If that hovers around one, then you are probably doing well though this is not conclusive. If u cannot refine the grid, then reduce it to (say) 80% in *one direction only* and then to 60% in the same direction. You should see decreasing gaps between adjacent simulation with increasing refinement. Repeat for the other two directions while the remaining ones are on the finest grid.

that thing about the spectra: best avoid using spectral arguments derived from fd calculations.

submitting a paper that shows divergence with grid refinement may have seriously damaged your standing with this particular referee. it should have never been submitted.
--

[sbaffini]

Originally Posted by gnwt4a

A numerical scheme is supposed to have two analytical properties: convergence and consistency. The first says that the numerical method should reach *a* unique solution independently of the refinement path. The second says that the converged solution should be an approximation of the the equations of motion u started with. With nonlinear models neither is known a priori so there will always be doubt. This is accepted by most referees.

rans calculations that diverge with grid refinement are completely unacceptable.

the bit that u did a rans convergence study as replacement for the les is not clear to me. i am probably missing something because it sounds so bizarre.

use of the Kolmogorov scale as proof of good resolution is in principle and in practice (when using low order fds) for bounded flows, wrong. Moreover, calculating the dissipation rate from a simulation which uses 2nd order fds gives values that are already unreliably distorted. this method is, however, meaningful for fully spectral codes.

Here is what u can try with yr les calculation. Calculate the ratio of the eddy viscosity to the molecular one. If that hovers around one, then you are probably doing well though this is not conclusive. If u cannot refine the grid, then reduce it to (say) 80% in *one direction only* and then to 60% in the same direction. You should see decreasing gaps between adjacent simulation with increasing refinement. Repeat for the other two directions while the remaining ones are on the finest grid.

that thing about the spectra: best avoid using spectral arguments derived from fd calculations.

submitting a paper that shows divergence with grid refinement may have seriously damaged your standing with this particular referee. it should have never been submitted.
--

I agree that doing a grid refinement in RANS as a mean to show, somehow, grid convergence in LES is as flawed as it sounds (and in this very case it only caused addtional problems in the end).

And, as a matter of fact, there might have been additional flaws in the submitted work, so it is probably pointless to discuss here anything different from the reasons that might have drived the observed behavior in the RANS grid convergence (which is an issue in itself that has nothing to do with the original submitted work)

But for grid convergence in LES, unless we are talking about explicitly filtered LES, the scientific relevance is that of the word of mouth, because:

1) If you change the grid, you are changing the underlying filtered equations (actually in a way that is unknown). Not more relevant than doing the exercise in RANS and pretending it has some link with the LES on the same grids.

2) If you don't change the grid (and at this point I don't know if it actually makes sense to mention grid convergence anymore), all the informations you have on what your grid is missing is your SGS model, which is just that... a model, whose interplay with the numerics is, at this point, unknown.

Nonetheless, it certainly has great practical relevance the comparison of the resolved and modeled dissipation on multiple grids as a mean to assess that the given experiment actually is an LES. But if it is on grid 0 and it is confirmed to be on the first refinement of this grid, I don't see the relevance of actually exploring the space of possible resolutions when it isn't the actual topic of the research.

But I also agree on the fact that the whole exercise might have no meaning when performed on low order codes, where the numerical scheme might always cover up any missing dissipation from the model (so that it always looks like you are doing an LES experiment). But this sort of reasoning inevitably leads to the fact that spectral codes are the only ones amenable of doing LES (at this point not even all of them, only those with certain filter properties, something that would affect also most explicitly filtered LES done today). This is something that I could agree in principle with, but that is away from the general consensus in the community (especially the ILES one).