LES vs. RANS for Re > 1e6
Does anyone know of published material that compares LES vs. RANS for Res greater than 1e6 for airfoils or other 2D shapes (squares, rectangles, diamonds, etc.)? The LES results should be 3D of a 2D shape.

Not completely done by LES but the combination of both (LES and RANS) in same simulation. Google these words "LES nasa rotor 35" and you will find the relevant papers by NASA and Stanford. For 3D LES of 2D shape google "LES of T106A"
I dont see the importance of LES higher than the Re 5e05 
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I guess it might be true under 2 conditions: a) keep the grid size constant between RANS and LES, so no refinement with increasing Re b) if you talk about flows that are indead (quasi)steady, I can't see RANS predicting anything useful for large separation, regardless of RE Interesting discussion! 
[QUOTE=cfdnewbie;339490]I guess it might be true under 2 conditions:
b) if you talk about flows that are indead (quasi)steady, I can't see RANS predicting anything useful for large separation, regardless of RE /QUOTE] As the Reynolds number increases, the eddies, relative to the geometry, get smaller. The separation region will still be there, but will be filled with small eddies, i.e. turbulence. So I would think RANS becomes more appropriate. This is why RANS does well for blunt body separation at high Re. However, Re is a global metric and, for high Re flow, there are always regions of the geometry that experience lower Re flow. So, for complex geometries, how that low Re flow region affects the rest of the flow field is the big uncertainty. This stuff is very non linear and what happens at the front of the geometry can have a dramatic affect on what happens at the back. So for sub critical (in regards to Mach number) I expect RANS, for high Re flow, to do OK at 25 (i.e. somewhat past stall) degrees alpha and 90 degrees. That has been my experience when comparing to data. However, at 4070 degrees I have absolutely no idea. It is this region, in general and in my experience, where the RANS equations become sensitive/unsteady for high Re airfoils. There is also significantly less experimental data and the data becomes uncertain. From an engineers perspective, this is what makes fluid dynamics so challenging. And, (again from an engineers perspective) because of the lack of best/worst practices, a thorough understanding of flow features, and the focus of academia on specific flow features academia are trying to model, for qualitative (edit: oops, I meant to save quantitative) results, CFD is viewed in certain circles as an "ivory tower" tool. It would be nice to see that change. 
In this case embedded LES is the most suitable option, since you can turn on in the regions of LOW Re

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I did do the searches you recommended but didn't find anything suitable. The geometries were too complex, i.e. cascading rotor blades, and the flow conditions too specific. A high angle alpha sweep of an airfoil at different Res would have been nice. But, probably too basic of a geometry and too likely to find regions where results don't match data. LOL, that's probably too researchy. There is a saying, "If you don't want to know the answer, don't ask." Sorry, off topic. 
[QUOTE=Martin Hegedus;339572]
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I understand your point, but I'm not sure if one could not look at it from the other side: As Re increases, your large eddies (let's say the size of your chord) stay the same, i.e. their size is determined by the geometry. What indeed happens is that the small eddies become smaller, as dissipation acts at a smaller wavenumber. So from that perspective, with increasing RE, the main flow features are still determined by the large eddies, so by the unsteadiness of your flow. What happens in the extreme of Re towards infinity (Euler flow)? It becomes clearer here, I guess: For that type of flow, LES would resort to an unsteady computation, while RANS would be the steady equivalent.... From that point of view, I am convinced that RANS and LES are not equivalent for high Re..... but I admit there might be a flaw in my thoughts! Interesting discussion, folks! cheers! 
Ah, but the size of the eddies are not only decided by the geometry, but also the velocity of the flow.
However, first, TRUE 100% Euler flow has shear layers and entropy layers. In reality, as far as I know, that is very hard to model with CFD. Shear layers are mangled by gridding and artificial dissipation (or algorithm dissipation) And, it takes a very fine grid. Also, to a degree Reynolds number is undefined for Euler flow or maybe better to say meaningless. I'll get to that later. As the Reynolds number increases the large coherent structures seen in typical Karman streets near the body break down. The flow becomes a mess. This is why, as I see it, the LES grids for high Reynolds flow need to be so fine. High Reynolds number is obtained by large length scales, high velocity, or low viscosity. So this can be seen in different ways. As the geometry gets bigger (and keeping the velocity the same), the vortices near the body get smaller relative to the geometry. As the velocity increases (and keeping the geometry the same) the momentum of the flow powers through the flow thus not allowing big structures to form till later, and as viscosity decreases vortices have a hard time exerting their influence to become large. In all three cases, the vortices generated in the boundary layer need TIME to exert their influence. This is not to say that as the flow gets further away from the body that structures do not develop. Why? Because, Reynolds number is actually based on the DIFFERENCE of velocities. For example, the Reynolds number for a sphere is the velocity of the sphere RELATIVE to the free stream. So, once the flow goes significantly past the sphere, the velocity used for local Reynolds number is not the sphere's velocity. It is some other velocity. What that is, I don't know. And, it approaches zero. So, taking the previous paragraph into consideration, what is the physical local Reynolds number for Euler flow? I have no idea. All I can say is that viscous terms are zero and the Euler flow becomes potential flow because of the slip condition. The effect of increasing Reynolds number can also be seen with experiments. If I remember correctly. As the Reynolds number increases, the magnitude of the unsteadiness for the integrated loads decreases. But I can be corrected on this!! So I'm not saying that RANS can predict what happens aft of the airfoil in the flow field. I'm thinking about the integrated loads on the airfoil. So flow features in the vicinity of the geometry, in regards to influence. Hope I haven't I confused people too much! 
Hi Martin
Thumbs up man. You have described the very difficult concepts in easy words. You have also made it clear why fine mesh is needed in High Re, which I didn't know for long time and every time I asked this question to myself, I had no answer that "Why fine mesh is needed for high Re". PS. Although there is formula to calculate the mesh size in terms of Reynolds number, but it was pure maths 
I'm not sure I'm fully understand Martin's post, so here's another perspective on increasing RE:
If you increase the RE number, the effect of viscosity are pushed to smaller and smaller scales, i.e. more scales "survive" in the flow. In the limit of Re> \inf, so for Euler, infinitesimally small scales would exist, since there's no viscosity. So in that sense, Euler is a true limit of the NS equations for Re> \inf. If you take a look at a typical turbulent spectrum for increasing Re, you will see that the inertial subrange gets longer, and the dissipation is pushed to higher wave numbers. So in that sense, the higher Re, the more "unsteady" scales are present in your flow, and the less significant the viscous part becomes.... The RANS approach on the other hand can be seen as "hyperviscosity" approach, that leaves only the temporal mean intact...., so the opposite of unsteadiness These two facts contradict themselves in my mind, but I admit I can't make them any clearer....it is more of a feeling than hard facts :) Any thoughts? 
Friction forces are a function of mu*(dV/dy). So, for the NS equations, even though mu might get very small, (dV/dy) gets very large. For a symmetric 2D shape at zero alpha, for example a cylinder, vorticity must be generated for drag to exist. For Euler, using higher order methods and a refined grid, the drag on the cylinder or symmetric airfoil goes to zero. Therefore it has zero vorticity. On the other hand, the drag for high Reynolds number flow does not go to zero (it can not because of skin friction) and therefore must produce vorticity.

Another way to look at it. Higher Re flow have geometrically smaller vorticity spinning very fast so are packing a punch with velocity. Low Re flow has geometrically large vorticity spinning very slowly so are packing a punch with size. Euler just doesn't have any vorticity (assuming no shocks and lift).
Edit: OK, not quite as simple as I made it sound. But I hope a point has been made. 
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