
[Sponsors] 
March 7, 2011, 11:34 
Laminar vs Turbulent NavierStokes

#1 
New Member
Truman Ellis
Join Date: Mar 2011
Location: Austin, TX
Posts: 5
Rep Power: 15 
I am trying to wrap my head around the practical considerations of solving laminar vs turbulent NavierStokes. I understand that the plain Navier Stokes equations describe the most general case and that if they were solved at sufficient spatial and time resolution (as in DNS) they would describe the appropriate laminar or turbulent flow for whatever application that you were considering. I also understand that Reynolds (or Favre) averaging seeks to average out the turbulent fluctuating terms so that such high resolution is not necessary.
Referring to http://www.cfdonline.com/Wiki/Favre_averaged_NavierStokes_equations, the Favre averaged equations (30)  (32) look just like the original NavierStokes equations (1)  (3) with some additional turbulent terms that need to be modeled via a turbulent closure model like komega or kepsilon. So, assuming laminar flow and neglecting the turbulence terms, it looks like we are back to the original NavierStokes except each instantaneous variable has been replaced with its averaged equivalent. This leads me to my point of confusion, if you attempt to solve the full NavierStokes equations without sufficient spatial and time resolution, are you just assuming laminar conditions and solving for the laminar solution? Will this solution approach the full turbulent solution as you refine in space and time? A related question: if you neglect all time derivatives in equations (1)  (3), what are you actually solving for some pseudo Reynolds or Favre averaged solution or will you arrive at a steadystate laminar solution? None of these conclusions feel right to me, but I can't quite put my finger on what is wrong. Any help is appreciated. Thank you. 

March 7, 2011, 12:27 

#3 
New Member
Truman Ellis
Join Date: Mar 2011
Location: Austin, TX
Posts: 5
Rep Power: 15 
But if you make the assumption that your flow is laminar, the eddy viscosity goes to zero and you are only left with the molecular viscosity and the original NavierStokes equations. I guess part of my question comes down to: what is the difference between assuming laminar flow and solving the full NavierStokes equations, aside from resolution?


March 7, 2011, 12:42 

#4 
Senior Member

Sorry I have not read your question carefully.
Here is the answer: Turbulence exists on large scales too, this is not the problem of resolution, rather it is problem of stability of solution of NS equation which can be broken at large scales too, depending on Reynolds number. If you take NS equation on more coarse grid, solution will also become unstable after reynolds number will exceed critical value. In other words at certain reynolds numbers laminar solution is not stable and chaotic solution you will get does not approach turbulent solution, as this is a chaotic systems where limit does not exists (unless you are going to DNS scale). Last edited by truffaldino; March 7, 2011 at 14:55. 

March 7, 2011, 12:51 

#5 
New Member
Truman Ellis
Join Date: Mar 2011
Location: Austin, TX
Posts: 5
Rep Power: 15 
Ok, but then how do you solve a laminar flow problem at high Reynolds number, say a highspeed laminar boundary layer?


March 7, 2011, 13:22 

#6  
Senior Member

Quote:
To get insight why it happens take a look at OrrSommerfeld theory. Last edited by truffaldino; March 7, 2011 at 14:54. 

March 7, 2011, 13:44 

#7 
New Member
Truman Ellis
Join Date: Mar 2011
Location: Austin, TX
Posts: 5
Rep Power: 15 
All of my undergrad aerodynamics just came back to me. Thank you, it all makes a lot more sense now.


July 8, 2017, 12:45 

#8  
Member
Min Zhang
Join Date: Mar 2017
Posts: 81
Rep Power: 9 
Quote:
I am just a beginner for OpenFOAM and I want to talk about my thinking. But I am not sure whether it is correct. 1. If you choose to use the Reynolds averaged equations, you can not neglect the turbulence terms, that is to say, you cannot assume laminar flow. This is because if you neglected the turbulence terms, that equations will be invalid. I mean the averaged values won't satisfy the NavierStokes equations. 

July 10, 2017, 07:20 

#9  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,839
Rep Power: 73 
Quote:
Actually, if you would solve the RANS equations without modelling the unresolved stress you would have formally no difference with a laminar steady solver. The steady state would have a deterministic meaning, not a statistical one. The key is that at low Reynolds number that will drive to a physically relevant steady solution whilst, by increasing the Re number, you will get no longer convergence towards a steady state. 

Tags 
cfd, laminar, navierstokes, turbulence 
Thread Tools  Search this Thread 
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
CFX Treatment of Laminar and Turbulent Flows  Jade M  CFX  18  September 15, 2022 07:08 
Laminar doesn't converge; Turbulent models do?  Amit  FLUENT  11  April 23, 2015 22:55 
LBM Vs navier stokes equations in turbulent fluid flow modeling.  sharad_shevate  Main CFD Forum  0  August 3, 2009 01:25 
Half laminar and turbulent model trying to solve  Andrew Clarke  FLUENT  5  May 19, 2008 13:40 
Newbie:Viscoelasticity and Navier stokes equation  Rajil Saraswat  Main CFD Forum  2  June 9, 2003 07:21 