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In a cylindrical chamber with a high diameter-to-height ratio; a fluid is tangentially injected. there is an axial exit to the cylinder.

how do I determine if the vortex so formed is laminar or turbulent? what parameter will indicate this?

(this is a simulation; so I can measure whichever velocity/turbulent KE that is needed.)

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If it is a simulation, how do you model turbulence? Or is it DNS? –  Bernhard Mar 8 '13 at 8:13
by RANS RNG k-epsilon. –  aditya kp Mar 8 '13 at 9:03
Easiest would be to check the value of the turbulent viscosity compared to the laminar viscosity. –  Bernhard Mar 8 '13 at 9:08
You could calculate the Reynolds number for the injection point. Also, realized that $k-\varepsilon$ does not perform that well for rotational flows. –  Bernhard Mar 8 '13 at 9:34
For future reference, note that we don't do computational questions here; use the Scientific Computation beta site for that. That said, I think this question is one mostly about physics (i.e. what properties can be used to distinguish the two states, without reference to the computational nature of the system) and do not propose to close it. –  dmckee Mar 8 '13 at 17:18
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1 Answer

up vote 1 down vote accepted

Firstly let us define what is meant by turbulent and laminar in a case such as the one you describe...

The Reynolds number of a flow gives a measure of the relative importance of inertial forces (associated with convective flow) and viscos forces. From experimental observations it is seen that for values of Re below the so-called critical Reynolds number the flow is smooth and adjacent layers of fluid slide past each other in an ordinary fashion. If the applied Boundary Conditions (BC) do not change with time the flow is steady and this is Laminar flow.

At values of Re above the critical Reynolds number a complicated series of events takes place which leads to a radical change in the flow character. In the final state the flows behaviour is random and chaotic. The motion in this case is intrinsically unsteady event with constant BCs - all flow characteristics vary in an random way and this is Turbulent flow.

Okay, now to address your problem directly. From what you have asked (I believe you have asked this in the right place) and from reading the comments, I think you have miss-understood what the Reynolds Average Navier-Stokes (RANS) models actually achieve. Taking first the standard $\mathrm{k}-\epsilon$ RANS model; this model (and all other RANS models based upon Reynolds Decomposition) provides a model for all turbulent length scales, even to the Komglarov scale (large eddies cascading down to smaller and smaller eddies until the dissipation length scale is reached). This is the same for the RNG $\mathrm{k}-\epsilon$ RANS model.

Asside: the Renormalisation Group [$\mathrm{k}-\epsilon$] Model (RNG) uses statistical mechanics and a limited number of assumptions regarding the statistic of small-scale turbulence, to provide a rigorous basis for extension of eddy viscosity models.

The flow that you describe is a rotating flow with a curved Boundry Layer (BL). Now:

  1. The $\mathrm{k}-\epsilon$ RANS model is very poor at resolving the turbulence generated in such flows, where the curved BL and swirling flow induces large extra strains (I would use a $\mathrm{k}-\omega$-type RANS model).

  2. Secondly, in the flow that you describe the large scale rotational flow (vortex flow) could happily be resolved using a purely convective model (advection equation alone) and the dynamics of the flow will be dominated by advection, not (relatively small scale) turbulence.

So, to answer your question:

How do I determine if the vortex so formed is laminar or turbulent?

The flow in your case will have some 'lamina' features and be fully turbulent. To establish the dominating factor in this case should be obvious. It is the bulk motion of the flow that drives the type of vortex you describe, not turbulence.

What paremeter will indiacate this?

For a case where you wanted to establish the length scale of turbulent eddys (relatively small-scale flow (possibly sub-grid level)), then with $\mathrm{k}-\epsilon$-type models we can define the velocity scale ($\vartheta$) and length scale ($l$) of the largest turbulent eddies via:

$$\vartheta = k^{1/2}, \;\; l=\frac{k^{3/2}}{\epsilon}$$.

You could question the validity of using the 'small eddy' variable $\epsilon$ to define the 'large eddy' scale $l$. This is reasonable because for large Re the rate at which large eddies extract energy from the mean flow is roughly matched to the rate of transfer of energy accross the energy-spectrum to small dissipating eddies if the flow is not changing rapidly (assuming you are doing steady-state simulations). if this is not the case then the energy at some turbulent scale could grow or deminish with out limit.

Finally, I would be careful in your selection of RANs model. The advantages and disadvantage for each one is well documented and should be addressed before selection. For your flow I would suggest the Menter SST $\mathrm{k}-\omega$ model, which uses $\mathrm{k}-\omega$ near wall and $\mathrm{k}-\epsilon$ in the free stream (with appropriate wall function treatment depending on your code).

I hope this helps.

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The term "sub-grid scale" is usually not used for RANS-type models. This is LES, where you are especially filtering, normally based on the grid. In RANS it is ensemble average, and you model the Reynolds stress tensor, which includes larger then grid scales as well –  Bernhard Mar 18 '13 at 13:12
Although you are right in what you say about LES, it is wrong to say that RANs is not a sub-grid scale model. Of course these models are focused on the mean flow and the effects of turbulence on that mean flow, but the mixing length scale for many flow simulations is smaller than the grid-resolution. This does not mean that turbulent KE and the vicious dissipation is not well represented by the RANs model at these scales. My main point in the above, is that he is seeing bulk vortex flow, and this will have little to do with the turbulence model employed... –  Killercam Mar 18 '13 at 15:47
However, I will edit the answer to take into account that the RANs does not just model sub-grid scale turbulence. To see that RANs can and does model sub-grid scale turbulence you only have to look at the turbulence length scales involved in typical pipe flow. –  Killercam Mar 18 '13 at 15:54
LES: Only the “Large” turbulent scales are resolved. The “smaller” scales are modelled. RANS : All the turbulent scales are modelled. In LES, you solve a filtered version of the Navier-Stokes Equations along with another equation to represent the turbulent small scales In RANS, you solve the averaged version of the Navier-Stokes equation along with another equation to represent all the turbulent scales. –  Killercam Mar 18 '13 at 15:56
Thank you for your replies! @Killercam, I did not understand what you mean by "To establish the dominating factor in this case should be obvious." I know that it is the bulk-flow that drives the vortex; I wish to find if any particular region in this vortex is laminar. Even if I do have the values of the velocity and length-scales; how do I know if the flow is turbulent there? Is there a threshold value? if yes, how do I determine it? Also, I have seen a lot of validations for confined vortex flows with RNG-K-eps models. Keeping the turbulence model aside, I wish to understand this physically. –  aditya kp Mar 19 '13 at 10:58
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