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 s3s4m October 26, 2011 10:38

Modelling capillary forces in porous media

Hi at all !

I have found this forum during my seemingly endless investigation of a solution to my problem in CFX. I hope there is someone here who can help.

I want to model the spreading of a liquid through a porous medium. Initially, there is air inside this porous medium. Than you inject some other liquid fluid in this p.m. The liquid spreads and the air is displaced.

So far, so good. I chose a multiphase approach, inhomogenous fluid model.
But the question is...how do I implement the capillary force, which acts on the gas-fluid interface ?
As a first step, I established a subdomain to the p.m. I can define a general momentum source there, when the volume fraction of the liquid exceeds a certain value. But this Source acts on both fluids, the air and the liquid. This is not physically correct, since the capillary force acts only on the liquid phase and "pulls" it towards the gaseous phase.

Basically, I should manipulate the term S_M,alpha of the phase alpha at the inhomogenous hydrodynamic equations for multiphase flow.
With S_M,alpha, I should be able to define the capillary force for the liquid at a certain position (i.e. the interface) as an external body force.
How do I do that ?

There is nothing described in the documentation to manipulate S_M,alpha :(

I would appreciate your help. And sorry for my rough english.

F.F.

 ghorrocks October 26, 2011 16:49

I cannot see how to do this.

Here's an idea which I am not sure will work:
Do a volume fraction source term which if there is a VF of 0 or 1 (with a small tolerance) then it does nothing, but if the VF is in the middle somewhere, that is the element is partly liquid and partly gas, it generates some VF.

This approach would not conserve VF and would not generate the correct flow behind the wetting front. Also I am not sure how you would tune it to give the correct wetting velocity. But it was an idea I thought I would put out there - hopefully somebody can come up with a better one.

 s3s4m October 27, 2011 02:55

I also thought of adding a mass source term to this interface region.
But I'm really not sure if this is physically correct.

Actually I try to do the modeling described here by Khlaifat:
http://www.apgindia.org/pdf/441.pdf
He used CFX-F3D and used different source terms in the momentum equations for the two phases (water and gas).

In CFX, I need to define S_M,alpha and give the constitutive equation for the pressure
p_c=p_g-p_w
But I don't know how to do that :(

Are there any other ideas ?

 ghorrocks October 27, 2011 06:12

Quote:
 I also thought of adding a mass source term to this interface region. But I'm really not sure if this is physically correct.
It is not. The reason is because the surface will advance through the porous region through the generation of new fluid with the source term. It will not draw fluid through the porous material, so you will not get the pressure drop this generates.

The momentum source term approach is better because you can then apply a "pull" on the fluid, which can be matched to the capillary pressure. This is more physically correct, but it means you need to work out the liquid surface orientation so you can pull in the correct direction. I cannot see how to do this.

A quick look through the paper you reference and I cannot see where they have put in the local free surface direction. I cannot see how this can be done without it, but I am no expert in this area.

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