Instability Vortex and Mesh Choice
 

I wasn't sure whether to post this in the main forum or the OpenFOAM sections, but regarding the fundamental nature of my question I thought it would be a good idea to post it here. Sorry if this turns out to be OpenFOAM bug or something.

Calculation description: I was trying to model a system depicted in the attached file "0_configuration.jpg" (sizes and boundary conditions shown). It is a system where silicon is melted in a water-cooled crucible with electron beam radiating from the top. Crucible is cooled in such a way that thin solid silicon layer forms on the crucible walls. It is a proposed system for purifying metallurgical-grade silicon to obtain solar-grade silicon.

So I was using OpenFOAM to model this system. Solver "buoyantBoussinesqSimpleFoam" and k-omega SST turbulence model is used. As these are just very first calculations, I was using different meshes and experimenting both with the boundary conditions and gmsh mesh generation program. I'm fairly new to modelling so playing around is what I do :) Some of you might say that the mesh is not good because there is no mesh adaptation at the solid walls and laminar sub-layer is not considered correctly (large y+ values), but I believe that doesn't consider the problem below.

Problem: I noticed that when I use unstructured mesh ("2_instability_mesh.jpg") OpenFOAM calculates a vortex in the melt ("1_instability.jpg"). But when I use structured mesh ("4_stability_mesh.jpg"), vortex is not present ("3_stability.jpg"). Votex is also not present regardless of the mesh choice when symmetry boundary conditions is used i.e. only one-fourth of the melt is modelled with two symmetry planes.

Question: Which result is more likely to occur in reality? Is this calculation error or maybe even visualisation error when using streamline tool in paraFoam?

My current undergraduate-level explanation bound to be corrected: I believe that the situation I'm considering is in fact unstable. Just like water going down the sink, there always will be a vortex. When I'm forcing a competely symmetrical calculation (by mesh or by symmetry boundary conditions) I'm limiting the result to a unstable situation which doesn't occur in the reality. Unstructured mesh simulates fluctuations and disturbances which will definitely occur in the reality. Thus the result with the vortex is a more realistic one.

Additional question (also very important for me): My colleagues (all experienced modelers) say that structured meshes are the way to go. They are good because next to a solid wall you can expect a flow which is parallel to the wall, and it is good to have flow perpendicular to cell borders (thus structured, square cells are good). Why is it so good? How does the result gets degraded when flow is happening non-parallel to the cell normals?

The solution with structured mesh is most likely to be correct. Here is the reason:

On unstructured grids, the gradients are not nice. To understand this, imagine that you want to take gradient of simple thing as X or Y.

Now what you shall have is this

dXdX = 1
dXdY = 0
dXdz = 0

This is very simple and basic thing, but it turns out that on unstructured grids even this simple thing could give you results like say for example


dXdX = 1.23
dXdY = 0.2
dXdz = -0.05

(this is just an example).


So these imperfect gradients could give rise to source in flow that otherwise shall not be there.

On structured grids this is not there and hence solution is most likely to be true.

About your symm condition case, the symm boundary makes sure that there is no flow across it and hence you can not create vortex even in unstrutured mesh.

Yes, sounds quite clear for me. Thanks!

Only now I could ask this: if somebody would try to model water flowing out from the sink in situation I mentioned in my previous post... if using symmetrical sink geometry and structured mesh he would get a result with no whirlpool (at least I think so). But nevertheless it doesn't correspond to reality as there always be fluctuations that will lead to a development of a whirlpool.

So is the modeler right or wrong when he/she has obtained a result that does not occur in reality?

I hope I'm not getting too philosophical here :) I'm just trying to figure out whether or not my whirlpool-ish result is worth something or just doomed to be deleted.