A small confusion regarding terminology of turbulence modeling
Whenever, someone talks about Low-Re turbulence modeling, I assume that the `Low-Re`refers to the low value of turbulent Reynolds number ( friction velocity*distance from wall/ kinematic viscosity of fluid) which in turn means near wall region. In other words I assume that Low-Re turbulence modeling means integrating the turbulence equations upto solid wall without the use of wall functions.
It becomes slightly confusing when in some publications, authors refer to Low Re as being the low Re of flow and not low turbulent Re.
Am I messed up in the understanding of this terminology?
Sorry, I mentioned incorrect definition of turbulent Re (Re_t). Its correct definition is :
k: turbulent kinetic energy
epsilon: rate of dissipation of k
neu: fluid kinematic viscosity
To take my confusion a bit forward, is the commonly denominated 'Low- Re' formulation of turbulence models (i.e. where turbulence equations are integrated all the way to wall), also good for low flow Re (say in the range <4000)? I think it is if I understand correctly from my previous discussions here with Glen.
But I might be wrong as this confusion in terminology still persists for me. A confirmation and clarification will be greatly helpful.
The terminology does need to be read in context - for instance the first metre of flow over a supertanker is low Re flow, but the flow over the whole thing is very high Re.
In my other post I was referring to flows which are only just above turbulence transition. That could be a pipe flow, boundary layer, jet, anything - the characteristics of the turbulence are what I was talking about.
You can integrate to the wall in high Re flows. In some flows this is required. But be aware you will need a really fine mesh! So integration to the wall does not imply low Re flow, it is just easier in low Re flows.
So if I understand correctly I should draw the following conclusions from your comment here & before and from literature for my as well as other readers' benefit :
1. 'Low-Re Turbulence models' in literature refer to the 'Low -Re formulation' of turbulence models. This formulation means that wall functions are not used and turbulence equations are integrated upto the solid wall.
2. This formulation can be used in both low and high flow Re. However, it is easier to use in low Re flows as for the same y+ requirement, actual mesh required near the wall is coarser in low Re flow than in high Re flow due to larger boundary layer thickness in low Re flow.
3. Apart from its ease of use in low Re flows, the 'Low-Re formulation' is also more accurate than wall function approach in low Re flows. It can handle transitional flows better than wall-functions.
4. The 'Low-Re formulation' is available in both k-epsilon and k-omega equations based models. However, the latter performs more accurately in low Re flows . Hybrid models like SST which combine the 'Low-Re formulation' of k-omega based model near wall with k-epsilon model in bulk flow are the best bet in low-Re and transitional flows if the low-Re flow cannot be simulated with laminar flow assumption.
Please correct me if I am wrong anywhere.
1. Not quite. Turbulence models are applied across the whole fluid region, but something needs to be done at the boundaries. The turbulence model and the boundary treatment are separate - there are turbulence models suitable for low or high Re (eg k-w/SST is good for low and high Re, k-e is only good for high Re), and there are wall treatments which use coarser meshes (ie wall functions) and finer meshes (ie integrating to the wall). Do not confuse turbulence models and wall treatments.
2. Not quite sure what you mean here, but if you are saying it is easier (ie coarser mesh) to integrate to the wall in a low Re flow than a high Re flow then that is correct.
3 and 4. You are getting confused between turbulence models and boundary treatments again.
1. Yes, I meant the same what you said. Turbulence model equations are used throughout the flow. But for wall treatment there are two seperate approaches:
a) wall function approach in which turbulence model equations are used only upto a distance from the wall (y+ >30 in case of conventional wall functions) and boundary conditions to these equations are applied at this distance from the wall and not at the wall
b) in the other approach, turbulence equations are integrated upto the wall, boundary conditions are applied at the wall and hence no wall function is used. This approach requires very fine mesh near the wall. It is this approach that is sometimes named as the 'Low-Re formulation'. I have seen this nomenclature in literature and also in CFX manual. I think this name comes from the fact that the turbulent Re (i.e. Re_t and not the overall Re of the flow) is small near the wall. The difference between the two Reynolds numbers is :
Re_t = k^2/(epsilon*neu). This number is high in the bulk of the turbulent flow but is small near the wall.
Re=average velocity * hydraulic diameter/ neu. This is the overall Reynolds number of the flow . This is what I was referring to as 'flow Re'.
Additionally, approach (b) is better if flow Re is low as this approach performs better at predicting transitional flows as well as relaminarization. Wall-functions i.e. approach (a) is suited only at high flow Re and are not capable for predicting transitional and relaminarization.
2. Yes, I meant the same. Approach (b) can be used at any overall flow Re as long as there is some turbulence in flow. However, at higher flow Re, finer mesh is required due to smaller boundary layer thickness. For example:
If we need y+<2
this implies yu*/neu<2 where u* is friction velocity and y is the location of first mesh node from wall
hence y<2neu/u*. At low flow Re, u* is smaller as compared to at high flow Re. Thus for same y+ requirement, low flow Re situation requires a coarser mesh near wall.
3. I meant that approach (b) is more accurate than approach (a) at low flow Re.
4. I meant that both approaches ((a) i.e wall functions and (b) i.e. Low-Re formulation) can be used with any type of two-equation turbulence model. But the k-omega based models are more suited to approach (b) than k-epsilon models due to simpler near wall treatment .
And among the k-omega based models, the hybrid SST model is best .
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