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April 9, 2005, 17:12 
BrinkmanForchheimer equation

#1 
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Dear All,
How can I model a porous medium in Fluent by using BrinkmanForchheimer equation. Many thanks, Abdul 

April 10, 2005, 09:50 
Re: BrinkmanForchheimer equation

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If you mean equation 2.143 of Kaviany's book. What I did, I multiplied both sides of the equation with porosity factor and updated the source terms and calculated them accordingly.
Amir 

April 10, 2005, 13:07 
Re: BrinkmanForchheimer equation

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Dear Amir,
Could you be more specific, or can you direct me to a published on the approach you indicated. Many Thanks, Abdul 

April 10, 2005, 13:22 
Re: BrinkmanForchheimer equation

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ok, I have been working on the same subject in my thesis and I found out there are different interpretations on BrinkmanForchheimr equations. Some researchers use an extra porosity factor in the denominator of the convection term (Neild and Bejan) and some not (Vafai and Kaviany). I personally use the work of Vafai and Kaviany. I give you a couple of publications by them at the end of this message. Take a look at them and see if you still have problem with the form of the equaitons and then I will conduct you to how implement that into FLUENT.
Amir 1. Kaviany, M., 1991, Principles of Heat Transfer in Porous Media, SpringerVerlag, New York. 2. Vafai, K. and Tien, C. L., 1980, "Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media," International Journal of Heat and Mass Transfer, 24, pp. 195203. 

April 14, 2005, 11:27 
Re: BrinkmanForchheimer equation

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Yes, I still have problem with the form of the equaitons. Please, show me how to implement that into FLUENT.
Regards, Abdul 

April 16, 2005, 12:33 
Re: BrinkmanForchheimer equation

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Well, if you are convinced to use the form of equation recommended by Vafai and Chen, you can easily multiply both sides of the equation by porosity factor. then the momentum equation solved by FLUENT would be as close as possible to the form of BrinkmanForchheimer equation presented by Vafai and Kaviani. you just need to treat the source terms properly which I beleive would be as following:
C1 = mu*epsilon/K C2 = rho*F*epsilon^2 / K^.5 in which mu = density K = permeability rho = density epsilon = porosity factor F = Forchheimer coefficient and F = 1.75/sqrt(150*epsilon^5) based on the packed bed model Hope it helps Amir 

April 17, 2005, 16:22 
Re: BrinkmanForchheimer equation

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Thank you Amir


July 2, 2010, 04:20 

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Hi Amir,
I am having the exact same problem in modeling Vafai's equation in Fluent. Your answer is indeed very helpful. However, I have a question: What do you do with the pressure gradient term on RHS? If we multiply that too, by porosity factor, the solution diverges. Is it good to neglect multiplication to pressure gradient term, and multiply all the other terms with porosity? Will this give huge errors? 

November 8, 2011, 22:52 
Requests for help

#9  
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Yongsheng Tian
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Quote:
I am trying to model a porous medium in Fluent by using BrinkmanForchheimer equation. I am a Chinese students, so I have a difficulty to find that publication that you mentioned:Vafai, K. and Tien, C. L., 1980, "Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media," International Journal of Heat and Mass Transfer, 24, pp. 195203. So I need your help, the more specific. Thanks a lot. Best wishes! 

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