# Why are there different definitions for cell Reynolds number?

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 September 3, 2016, 18:12 Why are there different definitions for cell Reynolds number? #1 New Member   carl jung Join Date: Mar 2016 Posts: 15 Rep Power: 10 Hi all, I'm trying to understand the cell Reynolds number(or grid Reynolds number), but I found several different definitions about it. 1) ch/, where c = mean velocity, h = length of a cell, and is a positive number (Kellogg's Uniqueness and Cell Reynolds Number, 1980) 2) Re*Δx, where Re = Reynolds number and Δx = length of a cell in X (Cheng's ￼Computational Accuracy and Mesh Reynolds number, 1977) I also found a paper about invalidity of cell Reynolds number restriction (Thompson's The Cell Reynolds Number Myth, 1985) Could anyone please explain the concept and equation of the cell Reynolds number? FYI, I'm working on a aerodynamics of a small revolving plate. Thank you,

 September 4, 2016, 02:29 #2 New Member   Ehsan Mahravan Join Date: Dec 2014 Location: Tehran, Iran Posts: 9 Rep Power: 11 take a look at http://www.cfd-online.com/Forums/mai...ds-number.html Are you sure about the second relation? It is dimensional.

 September 4, 2016, 04:04 #3 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,777 Rep Power: 71 Maybe the second relation is Re*h/L? However the cell Re number is always a non-dimensional computational parameter involving a lenght characteristic of the scale of the mesh.

 September 4, 2016, 10:21 #4 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,152 Blog Entries: 29 Rep Power: 39 Well, a possible answer is: because it really is a matter of definition. When you discretize a physical equation, the same non dimensional numbers show up also in their discrete counterpart. According to the way you perform the discretization, different discrete spatial scales will show up. For example, the implicit finite volume discretization of diffusion operators on unstructured cell centered grids typically involve the distance between adjacent cell centers. Other discretizations might involve different length scales. fredericgaillard likes this.

 September 4, 2016, 18:09 #5 New Member   carl jung Join Date: Mar 2016 Posts: 15 Rep Power: 10 Thank you all for the answers. For the second one, That paper is about finite difference equation rather than actual CFD. So, I think the Δx is already nondimensionalized. I read the old post about Cell Reynolds Number that EhsanMh referenced. So, is it the "local Reynolds number based on the velocity in the calculation cell"? It makes sense to me, but not the detailed explanations below that first answer. I'd like make sure the cell Reynolds number is "local Reynolds number based on the velocity in the calculation cell." Can it be understood in the same context of CFL condition? FYI, I'm working on a Cartesian grid. Thank you again,

 September 4, 2016, 18:18 #6 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,777 Rep Power: 71 The cell Re number has a velocity and a lenght scale that depend on the computation and can be local. In principle, you can also define cell Reynolds number for each direction. The way you select them depend on the scope... see for example http://www.bakker.org/dartmouth06/en...ocabulary.html

 September 4, 2016, 18:54 #7 New Member   carl jung Join Date: Mar 2016 Posts: 15 Rep Power: 10 Thanks, FMDenaro, It's becoming much more clear in my head. Can anyone give me an example that would have a cell Reynolds number other than "Local velocity * Cell dimension / Kinematic viscosity?" Thank you!

September 5, 2016, 03:23
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Filippo Maria Denaro
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Quote:
 Originally Posted by carl jung Thanks, FMDenaro, It's becoming much more clear in my head. Can anyone give me an example that would have a cell Reynolds number other than "Local velocity * Cell dimension / Kinematic viscosity?" Thank you!

This is the general definition...

 September 5, 2016, 07:23 #9 New Member   carl jung Join Date: Mar 2016 Posts: 15 Rep Power: 10 Yes, I know, but sbaffini mentioned that it could be a matter of definition.

September 5, 2016, 08:57
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Paolo Lampitella
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Quote:
 Originally Posted by carl jung Hi all, I'm trying to understand the cell Reynolds number(or grid Reynolds number), but I found several different definitions about it.
Each of the definitions you quoted has a different length scale only.

Than my answer was:

"According to the way you perform the discretization, different discrete spatial scales will show up".

So, my logics would sum up as follows:

I have different "definitions" of cell Re number because different length scales can show up in a discretization, according to the chosen method. So, if a choose a method i will get a certain definition, if i switch to another method i will get another definition. So, if there isn't one single definition (except for the dimensional ground on which any Re number can be based), i guess "it is just a matter of definition" the reason for which several forms show up. Intending that different people can give different definitions just beacause different quantities show up in their discretizations.

The matter is different if you don't know why such numbers actually show up (in practice they don't unless you force them to).

 September 5, 2016, 09:51 #11 New Member   carl jung Join Date: Mar 2016 Posts: 15 Rep Power: 10 Thanks for the explanation. I guess I fully understnand it now. Thank you all for the answers!

 Tags cartesian grid, cell reynolds number, grid

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