Does anyone know of a turbulence model that describes the flow characteristics of a packed bed (porosity 40%) accurately? The optimal solution would of course be a k-epsilon model, modified for porous media with tuned constants.

Is there any literature on this subject available?

Any help would be appreciated!

Erwin

It's very difficult to calculate turbulence in a packed bed. Specially if a chemical reaction is included. Someone usually uses the velocity distribution along the radius introduced from Vortmeyer. The velocity distribution is surely much more influenced from the packed bed and less from transport phenomena and the chemical Reaction. By the way such a problem is very difficult to solve. One has to generate a randomly created packed bed. Then you have to generate a computational grid all over the packed bed, including a quite high resolution near the pellets of your katalyst. If you want to calculate a whole packed bed, including millions of pellets you should get enought memory. (turbulent flows are 3d flows!!). Then you might start with calculating the flow field including a k-e modell. then you must consider a chemical reaction. The chemical Reaction is very difficult, if you have diffusion in your katalyst so you must . . .

Anyway compare the difficulty of obtaining a "gut" approximation of the turbulent flow *around a single duct (carman)... Try to calculate only a small volume including few pallets. That could be a good start. Try to write down *all the equations that describe your flow. Try to generate an unstrucktured grid around your pellets. Don't include chemical reaction in the beginning. (Packed beds are usually used with chemical reactions.) This problem is very interesting, you can't eliminate any dimension you might get only a symmetry axis and that's all, you can't even implement a multigrid methods.

I don't think that you can get enough Memory in order to obtain a fine resolution around all your millions of pellets needed for a "gut" approximation. I don't even think that one really needs such a calculation, which is surelly not accurate enough for any reasonable use. Empirical equations and tests including upscaling techniques belong to the state of art.

Chemical reaction including such problems are probably not suitable for CFD.

There is a theoretical work about packed bed reactors, that uses a quite simple assumption: they calculate the free volume between the katalyst-pellets and they generate laminar flowed corridors. I think that they don't calculate the fluid flow in those small ducts, but use a general low-accuracy but fast-approximation technik in order to calculate the flow field. They don't use any turbulence modelling ( it's quite obvious that this assumption doesn't deserve and is not suitable for any turbulence modelling). I haven't seen any publications about this method and this is the research state of 1995 (?). I am afraid that nobody has calculated a turbulent flow in a packed bed.

* there might be few need for such calculations * the required computer power is not available * CFD Methods are not appropriate for such calculations.

Thanks for your suggestions, they are however a bit too complicated for me. I really don't intend to actually grid a large number of pellets. I was just planning on using simple porous media inside Fluent. Then I have the option to turn the generation of turbulence on or off. Turning it on using a standard k-epsilon model assumes negligible impact of the packed bed on turbulence generation and dissipation rates, which seems hardly realistic with porosities of 40%. Turning it off gives less accurate results in case where diffusion or thermal dispersion needs to be predicted. I would like to be able to turn the generation of turbulence on, but with a specific packed bed k-epsilon model.

I know that there are 0-equation models available ('Turbulence model for flow through porous media', Int. J. Heat Mass Tr. Vol.39 No.13), my question is if there are also k-epsilon models of this kind available?

Take a look at this PhD: Stroemungsverlaeufe in poroesen Medien , 1990 Peter W. Wagner Lehrstuhl B fuer Thermodynamik Tecnische Universitaet Muenchen

If I have time I will look for more works

There is just one k-e model on turbulent flow through porous medium that I know of. This is the model developed by Antohe and Lage and you will find the model in the October 1996 issue of Int. Journal of Heat and Mass Transfer. In what context are you studying packed bed systems? I am interested in similar systems. I would advice you to look at simpler models like 0 equation models which might be suitable for your specific case before jumping into a k-e model.

We are going to look at shallow packed beds and radial flow packed bed reactors. At this point we are looking at flow distribution problems only, but in time we will include heat transfer and chemical reactions to study diffusion and thermal dispersion.

I have checked all October issues of the Int. J. Heat Mass Transfer (http://www.elsevier.nl/inca/publicat....htt?menu=cont)

but I have not been able to locate the article you mentioned. Could you please check which volume/issue this article is in?

Thanks.

Hi,

I found this listing:

B.V. Antohe, J.L. Lage, A general two-equation macroscopic turbulence model for incompressible flow in porous media, International Journal of Heat and Mass Transfer 40 (13) (1997) pp. 3013-3024.

good Luck................................Duane

Hi, I am very sorry to give the wrong date. The paper can be found in the 1997 issue of IJHMT, vol.40, pp.3013-3024