CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Reynolds stresses and second law

Register Blogs Members List Search Today's Posts Mark Forums Read

Like Tree1Likes
  • 1 Post By scicomex

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   May 9, 2005, 17:08
Default Reynolds stresses and second law
  #1
JF
Guest
 
Posts: n/a
Hi all,

I wonder if there is a mathematical proof showing that the Reynolds stresses follows the second principle of thermodynamic. Of course, I know that the unsteady Navier-Stokes follows the second pricinciple. But if we (Reynolds) average these equations and that we look directly at the Reynolds stresses, can we state that the conservation of entropy won't be violated ? In fact, this question should arise when you model the Reynolds stresses. In this case, how to be sure that the model is consistent with the second law ?

Thank you for your enlightment.

JF

  Reply With Quote

Old   May 9, 2005, 18:41
Default Re: Reynolds stresses and second law
  #2
noName
Guest
 
Posts: n/a
All turbulence models that approximate the Reynolds stress tensor using an eddy viscosity model generally end up defining a positive eddy viscosity. This is simply the proof of second law. It is easy to prove that entropy only increases with a positive diffusion constant and can never decrease. (e.g. the first integral of the heat equation).

E.g.

Constant Eddy visc model: nu_T > 0

Mixing Length models: nu_T = l_m^2 * abs(dU / dy) > 0

One equation models: nu_T = C * k^(0.5) * l_m > 0

k-epsilon model and other two equation models: nu_T = c_mu * k^2 / epsilon > 0

And the list can go on ...
  Reply With Quote

Old   May 10, 2005, 03:38
Default Re: Reynolds stresses and second law
  #3
Jean-François
Guest
 
Posts: n/a
Thank you for responding.

All turbulence models that approximate the Reynolds stress tensor using an eddy viscosity model generally end up defining a positive eddy viscosity. This is simply the proof of second law.

I agree with that, the proof is similar to the (laminar) Navier-Stokes equations one's. But what happens if you don't take the eddy viscosity assumption and that you directly look at the Reynolds stresses. What is the condition that must fullfill the Reynolds stresses to follow the conservation of entropy. Do you know a reference dealing with this ?
  Reply With Quote

Old   May 10, 2005, 12:45
Default Re: Reynolds stresses and second law
  #4
noName
Guest
 
Posts: n/a
I admit, I don't know any restrictions on the Reynolds stress tensor that are required for second law satisfaction. If you do come across something, please let the forum know!
  Reply With Quote

Old   May 11, 2005, 05:36
Default Re: Reynolds stresses and second law
  #5
scicomex
Guest
 
Posts: n/a
I have measured Reynolds stresses in a flow in the lab, and what I found was related to this question. It seems the Reynolds stresses can take both signs (positive and negative) for some flow configurations (for some components of the Reynolds stress tensor at least)!! That would imply transfer of mom. energy from fluctuations (disordered motion) to mean flow (order). I have read some articles that speak of "negative turbulent energy production" (???). I am also trying to find out more about this issue, so if someone has any ideas, they are wellcome!!
chegdan likes this.
  Reply With Quote

Old   May 11, 2005, 10:20
Default Re: Reynolds stresses and second law
  #6
noName
Guest
 
Posts: n/a
I think it is fairly well known that energy transfer can take place in both directions (forward = cascade & backward = backscatter). However, both such energy transfers should result in entropy increase. I think a proof of that is lacking...
  Reply With Quote

Old   June 2, 2005, 22:57
Default Re: Reynolds stresses and second law
  #7
MASDINAR GINTING
Guest
 
Posts: n/a
Dear Sirs,

  Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On



All times are GMT -4. The time now is 00:37.