
[Sponsors] 
Why are there different definitions for cell Reynolds number? 

LinkBack  Thread Tools  Search this Thread  Display Modes 
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.cfdonline.com/Forums/mai...dsnumber.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 nondimensional computational parameter involving a lenght characteristic of the scale of the mesh. 

September 4, 2016, 10:21 

#4 
Senior Member

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.


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 

#8 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71 

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 

#10  
Senior Member

Your question:
Quote:
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 
Thread Tools  Search this Thread 
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
decomposePar allRegions  stru  OpenFOAM PreProcessing  2  August 25, 2015 03:58 
[OpenFOAM.org] OF2.3.1 + OS13.2  Trying to use the dummy Pstream library  aylalisa  OpenFOAM Installation  23  June 15, 2015 14:49 
SigFpe when running ANY application in parallel  Pj.  OpenFOAM Running, Solving & CFD  3  April 23, 2015 14:53 
Stable boundaries  marcoymarc  CFX  33  March 13, 2013 06:39 
DecomposePar unequal number of shared faces  maka  OpenFOAM PreProcessing  6  August 12, 2010 09:01 