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September 23, 2012, 14:56 
Does 2d turbulence modelling have any significance?

#1 
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Arijit Hazra
Join Date: Apr 2011
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In my bachelor thesis, I am working with a twodimenional NavierStokes equation with a eddyviscosity turbulence model for turbomachinery applications(turbine to be specific).I have a 2d Solver only and results for that.
If turbulence is always three dimensional is there any justificattion can I forward for using a two dimensional NS eqn with an eddyviscosity model? Is it generally used even in conceptual design phase in industry or anywhere? though it will not properly capture the physics of the flow will it be able to capture the physics too some extent? how can I defend my postion actually?Becos I do not have time to develope a 3d model with turbulence and I have to give some justification actually. 

September 23, 2012, 15:11 

#2 
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Francesco Capuano
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Although turbulence is inherently threedimensional, there might be cases in which the socalled mean flow is 2D, because in the third direction turbulence is said to be 'homogeneous' (i.e., statistically invariant under translations of the reference frame). In those cases, if you solve for the mean flow variables  namely you use a RANS approach  you make no mistake in solving 2D equations. On the other hand, if you solve for instantaneous, fluctuating variables (as in LES or DNS), then you have to solve the fully 3D system of equations.
You said your solver uses an eddy viscosity turbulence model, so I guess it's a RANS code, is it right? In this case you don't have to worry: RANS turbulence modeling is used by the overwhelming majority of industries for design phase purposes. 

September 23, 2012, 15:47 

#3 
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Arijit Hazra
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Thanks a lot for your reply.I just want to clarify the last point  did you mean to say 2D RANS turbulence modeling is used by the overwhelming majority of industries for design phase purposes ?
another question, is this 2D turbulence modelling actually diffrent from 2d Turbulence where there is no vortex streching term? 

September 23, 2012, 16:52 

#4  
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Francesco Capuano
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Quote:
I'm not sure I have fully understood your question. What do you mean by 2d turbulence where there is no vortex stretching term? Strictly speaking, turbulence is always threedimensional  in fact, the vortex stretching term appears only in 3D equations, the correspondent mechanism being fundamental in the turbulent energy cascade process. As far as I know, it does have a sense to speak about '2D turbulence' only for very largescale motions (e.g. atmosphere and oceans). 

September 24, 2012, 16:26 

#5 
Senior Member

The 2D approach Francesco is referring to has nothing in common with 2D turbulence (except the 2D concept itself).
2D turbulence is a mathematical concept related to the 2D instantaneous NavierStokes equations. These equations exhibit a chaotic nonlinear behaviour also known as 2D turbulence; obviously, a very strong difference in this theoretical system (with respect to reality) comes from the fact that the vortex stretching term is missing. In practice, in 2D, a lot of degrees of freedom and energy modes are missing so the system obviously evolves differently. Still, very large scale phenomena in the atmosphere have a lot of similarities with this 2D system, due to the very different sizes of the horizontal and vertical length scales usually involved. The possibility of using a 2D RANS approach comes instead from the 3D NavierStokes equations when Reynolds averaged. I don't know if there is any sound proof for this but, the general idea is that if the boundary conditions (intended in the most general sense) have symmetries then these are also shared by the time averaged flow field, laminar or turbulent. So yes, 2D RANS is fully applicable; actually, it is a feasible choice every time the 3D effects can be assumed to be negligible. Nonetheless, this tells you a lot about the tremendous task the RANS models have to face (2D, 3D, someone also asks for unsteadiness in 2D/3D... it is really a lot) Of course this is just part of the story as i'm pretty sure there are some specific cases where, even with symmetric boundary conditions, a stable symmetric flow field can't be achieved (or, put differently, the symmetric solution is not stable). This is true for the real flow situations, the 3D mathematical model we call N.S. equations and sometimes also for the 2D version of the model. However, once you put an eddy viscosity model in your equations everything changes 

September 24, 2012, 16:57 

#6  
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Filippo Maria Denaro
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Quote:
I agree, the concept of the 2D RANS implies the use of a statistical average on the 3D NS equations and the hypotesis that the flow is statistically 2D. 

September 25, 2012, 12:25 

#7 
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Arijit Hazra
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Thanks a lot for your reply.


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