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March 7, 2011, 12:34 
Laminar vs Turbulent NavierStokes

#1 
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Truman Ellis
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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, 13:27 

#3 
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Truman Ellis
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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, 13:42 

#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 15:55. 

March 7, 2011, 13:51 

#5 
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Truman Ellis
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Ok, but then how do you solve a laminar flow problem at high Reynolds number, say a highspeed laminar boundary layer?


March 7, 2011, 14:22 

#6  
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Quote:
To get insight why it happens take a look at OrrSommerfeld theory. Last edited by truffaldino; March 7, 2011 at 15:54. 

March 7, 2011, 14:44 

#7 
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Truman Ellis
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All of my undergrad aerodynamics just came back to me. Thank you, it all makes a lot more sense now.


Tags 
cfd, laminar, navierstokes, turbulence 
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