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Andrew Hayes July 24, 2006 11:17

Porous media Brinkman extension
is the brinkman extension in porous media the same term that is originally in the NS equation with the only difference being that it uses the effective viscosity


Does it just take into acount the shear at the wall in the porous media?


Boorgloo July 24, 2006 16:09

Re: Porous media Brinkman extension
Hello Andrew,

How's Isaac? (hihihi!)

The most knowledgeable people with cfd + porous are fluent according to fluent forum. You might try to contact fluent support or ask in the forum.


Andrew Hayes July 24, 2006 16:24

Re: Porous media Brinkman extension
I just need to know this in order for me to explain it in a presentation for the darcy-brinkman-forchheimer equation. I am hoping to explain each of the additional terms of the momentum equation and what they represent. I was just making sure that I understood the brinkman addition correctly. There is a lot of mention of it, but not much explanation.

opaque July 24, 2006 16:43

Re: Porous media Brinkman extension
Dear Andrew,

The Brinkman extension is completely empirical, and very difficult to justify w/o doing a careful volume averaging of the equations at the pore level to obtain the macroscopic level equations such Darcy, or Darcy-Forcheimer..

Some of the best works on this subject include the following authors:

- Dr. Stephen Whitaker at University of California at Davis.

He has done more than plenty of theoretical development of the porous media equations since 1966, including multiphase flow, electromagnetics, and other effects in porous media flow

- Dr. William Gray at University of Notre Dame..

He has several publications on theoretical development of the macroscopic equations..

- Dr. Kambiz Vafai at The Ohio State University.

He has worked for quite a while on porous media.. He has a publication titled:

"An Analysis of Variants Within the Porous Media Transport Models" ASME Journal of Heat Transfer , 2000, V 122, p 303..

I am sure that they will be more than happy to point you in the right direction in regard of the "best publications to spent your spare time"

Good luck,


Andrew Hayes July 24, 2006 16:53

Re: Porous media Brinkman extension
thanks, I have been reading Whitaker's book and have spoken with him directly. I also have read most of vafai's papers. Neither explain exactly what it is. They just say "and the third term is the brinkman extension" Jiang also did/does a lot of porous media work. Both Jiang and Vafai explain that it is the effective viscosity that is being considered, but in my case the viscosity is constant. I was just trying to derive it so I better understood where it came from. I just end up with the term that is already in the NS equation except when I take into consideration the 'effective' viscosity. I think I have an understanding. Thanks for the help. I will have to check the Notre Dame guy.

opaque July 25, 2006 09:57

Re: Porous media Brinkman extension
Dear Andrew,

There are two ways to view the porous media equations:

- From the practical point of view and experimental evidence, you can measure pressure drop, and realize that there is a linear relationship, i.e Darcy's law.. Then, under certain regimes that linear relation tends to fail and can be correlated by an expression that is second order in velocity, i.e Forchheimer correction.. None of those account for the viscous effects and possible wall effects, and "ad hoc" term can be added similar to the NS equations, i.e "the Brinkman extension"..

- Another view is to try to generalize the understanding of fluid flow by studying the porous media as an average of all the pores at a higher level (similar to transient averaging for turbulent flow).. Following all the mathematics of volume averaging and starting from the local NS equations (which already have the viscous term) you will end up with a viscous term similar to the Brinkman extension.. I say similar because is not the same term since include the effect of volume fraction (porosity) and depends on how you write the rest of the equation, it may include other corrections.

The papers from Gray have a lot of details of the averaging process.

Good luck,


wei rong July 28, 2006 12:01

Re: Porous media Brinkman extension
Andrew, I think you are right about brinkman term. It is analogous to the flow friction term in the N-S. The term presents the application of no-slip B.C. along the solid wall that bounds the porous media. During the volume averaging and scale analysis, brinkman term is negligible compared to bulk viscous force inside porous media. However , one would like to leave it as when permeability approaches infinity, the volume averaged equation could be restored to N-S.

Opaque, I would like to add 2 professors in your porous media transport research guru list:

Prefessor MASSOUD KAVIANY from University of Michigan.

Prefessor Josť L. Lage from Southern Methodist University.

Andew, I met them in NASA GLENN regenerator workshop in 2004 and was impressed by their presentation. I think talking with either one of them will be very instructive.

Prefessor T.W Simon from University of Minnesota. He is active in regenerator experimental work.

Hope it will help.

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