Which turbulence model can be applied in the modelling of cyclone behaviour in stead of the isotropic k-e turbulence model ? Need comments about the accuracy of similar simulations.

Regards Günther

salut guenther,

you are right, an isotropic k-e model can not work correctly for strongly rotating flows. since almost one year i plan to make a les on a cyclone flow. unfortunately i never found the time to start this activity. if you are interested in a les on a cyclone flow please contact me, maybe we can cooperate on this topic

regards

ulrich

" Modeling Flow and Heat Transfer in Vortex Burners" Anatoly Borissov, Vladimir Shtern and Fazle Hussain University of Houston, Houston, Texas 77204-4792 AIAA Journal, Vol. 36, No. 9, September 1998

This is an excellent research paper about the mathematical modeling of turbulent vortex flow. Modeling of cyclone behaviour is similar to artificial tornadoes. I would strongly recommend you to read this research paper.

We're having the same problem. We're using CFX 4.2 for solving and calculations, this isotropic profile givven by k-e model is a big problem. Our doubt here is how can we use an anisotropic model which could be used on CFX...

Thanks, Kasper.

The main problem with the cyclon is that it is swirling. Classical k-epsilon models are notoriously bad at swirling flows. You can do several different things to improve things.

The classical solution is to add a Richardson number correction to the k-epsilon model - see for example Launder, Priddin Sharma - "The calculation of Turbulent Boundary Layers on Spining and Curced Surfaces" ASME Journal of Fluids Engineering, 1977, vol 99. This kind of correction usually improves things significantly, but it is a bit of ad-hoc. I think Patel wrote a nice summary paper of different curvature corrections, let me know if you want me to dig out the reference.

You can also use other variants of the k-epsilon model. The RNG formulation is said to be better at swirling flows, but I haven't tried that myself. Most non-linear models will also behave much better. If you are using k-omaga there is also a curvature correction (Wilcox-Chambers), which works quite well.

However, for strongly swirling flows I think that you should use a differential Reynolds stress model. I usually don't use these models, but in cases when you have strong swirl I think that it can be warranted. This kind of flows are inherently very difficult to solve correctly with an eddy-viscosity model and RSM captures much more physics without any ad-hoc corrections.

Hi.

I did my PhD research on LES of developing turbulence in trailing vortices. Theses vortices are modelled using common models which are also applicable to cyclones, i.e. the 2D Lamb-Oseen model, and the 3D Batchelor vortex (also known as q-vortex) with axial flow. It is a well-known fact that k-epsilon models greatly overpredict turbulence levels in vortical flows, even if you add corrective terms for curvature. O.Zeman from CTR did an interesting study in which he compared k-e and RSM in a Lamb-Oseen vortex : Zeman, O. : The persistence of trailing vortices: A modeling study. Phys. Fluids 7, 135, (1995 ?).

My opinion is that the only way to correctly study turbulence in vortices is to use LES with a good subgrid-scale (SGS) model, i.e. not the Smagorinsky which is far too dissipative. Some people use a dynamic Germano model but I find it CPU-consuming and unstable.

Feel free to email me if you have specific questions.

Fabien

I would suggest the differential stress model. For a very recent article about the Second-moment turbulence closure model DSM, I would refer to Int. J. Comp. Fluid Dyn. 1999, Vol 12, 67-97 from K. Hanjalic. DSM is also applied in a study on swirling flows by M.Ohtsuka in Int. J. Heat Mass Transfer, 1995, Vol 38, No. 2, 331-337.

Good luck, Gert-Jan van der Gulik

My opinion is also that the only way to correctly study turbulence in vortices is to use LES with a good subgrid-scale (SGS) model. Incompressible Navier-Stokes equations along with swirl terms can be applied. Please see if you can get hold of the references I have mentioned. There are also lot of latest research papers on LES. I would recommend you to read those too. I think it may be hard to solve this kind of complex problem with Fluent or Star-CD due to their limited application capabilities.

I still believe that Reynolds stress models overpredict turbulence levels for strongly swirling flows. In the Zeman paper cited in my previous message, you can get a really good analysis of the pros/cons of the application of RSM to vortices. A good idea would be to run comparisons between an LES and a RSM model for a given vortical flow. For typical vortex models like Lamb and Batchelor, the linear amplification phases of non-axisymmetric disturbances (eigenmodes) are well documented in the literature and you could use that as a basis for comparison. Also, commercial codes like Fluent and StarCD now include LES options, although they only have the Smagorinsky SGS model which will have a tendency to dampen your disturbances.

(1). Almost all existing turbulence models require further adjustment when used for a new problem. (2). In early 80's, I did some modeling using two-equation k-epsilon model as the starting point for turbulent, swirl flow in dump combustor type configuration. (3). I think, it is fun to do the turbulence modeling or adjustment, when you have your own code and can easily change the model. But, you need a good set of data to do the modeling. (4). Once the model is adjusted, you can use it for the similar types of flow. (5). In the modeling, it is hard to say which model is more right or accurate than others. (6). We know that there is no universal model and constants, so each problem requires its own set of constants and model.

Hi there,

You don't give much details of the problem you wish to solve so I am not quite sure if the flow is 2D 3D etc...

Spectral methods are high order accuracy methods and have been used to model turbulent planetary atmosphere (actually DNS - Direct Numerical Simulations). I have myself used spectral method to model 2D compressible turbulence in a rotating system. And vortices are well modelled (cyclonic and anticyclonic vortices). There can be several approaches to the problem, here are some of the ones I know:

Under certain conditions (purely 2D, incompressible) you can just solve for the vorticity equation (one equation), this of course will make sure the potential vorticity is a conserved quantity, and vortex dynamic will also be well represented (however with an infinite interaction range).

The next approach is the Shallow Water Equations, where a 3D incompressible (vertically thin) flow is represented by 2 equations for the velocity field and one equation for the vertical thickness of the flow. This is used in Planetary and terrestrial atmosphere modeling (again using spectral methods, though not restricted to this method only).

You can also just solve the equations for a compressible (or incompressible) flow in 2D or 3D using the spectral methods.

The spectral method are high order accuracy methods and therefore don't have much numerical dissipation. You can resolve the fine structure of the flow as well as the 'gross' structure.

IN all these cases, you implement the method with the use of a hyperviscosity, to make sure that you cut off the high wave number. IN 3D this is used to model the dissipation of the small scales, and it avoids numerical instability. So that the energy spectrum of the turbulence is well modeled. For example for a 3D rotating flow, the large scale are affected by the rotation and the energy spectrum in the largest scale has a slope characteristic of 2D turbulent flows (with an inverse cascade of energy), on the small scale the turbulence is 3D homogeneous (with a Kolmogov spectrum) and on the smallest scale the hyperviscosity should cut off sharply the slope of the energy spectrum. A good model should not only get the vortices and their dynmical interaction right, but also the energy spectrum should be correctly represented.

Patrick

Dear mr. Larsson

Thanks for your advice about this problem. I would be most grateful If you could direct me to the summary of Patel about different curvature corrections.

Regards Günther Hasse

Not Smagorinsky and not Dynamic model a'la Germano... What kind of subgrid model would you recommend? Is this choice important for the prediction of the special charateristics of a swirling flow? I imagine that the rotation would also effect the subgrid model. Are there any subgrid models with curvature corrections?

If the Reynolds number is so high that a proper LES is not possible, do you still think that it is better to do a VLES than to use a RSM model? - An impossible question to answer I guess, but any speculation is interesting. In industrial cyclone flows I'd guess that it is an important question.

I dont't see a code related problem here. All commercial codes privide some "well known" models but it is also possible to implement your own model via user-subroutines or to adjust the implemented models.

For daily calculation of cyclones the RMS model seems to provide at least some accuracy.

Here it is - Patel, Sotiropoulus, "Logitudinal Curvature Effects in Turbulent Boundary Layers", Progress in Aerospace Sciences, 1997, vol. 33., p 1

In Fluent's experience, Reynolds-stress transport models (or differential Reynolds stress models), among all RANS-based turbulence models, "consistently" give best predictions of all the salient features of cyclone flows. The cost of using RSTM is not as high as some people love to quote in the literature. If you want, I can send you our recent RSM results for several different cyclone flows.

And I must say in passing that LES seems to be another useful approach, since we've recently done nicely reproduced characteristic features of cycolne flows. But it takes far more time and effort as you know.

Interesting, I have one question - how important do you think that it is that you also use a real RSTM model in the low-Re regions of the bounday layers? Many implementations of RSTM-models use a very simplified boundary layer handling and I'm wondering if this is an important issue for cyclone flows. The same question of course also applies to LES, where you also often see simplifed boundary layer approaches.