Brinkman-Forchheimer equation
 

Dear All,

How can I model a porous medium in Fluent by using Brinkman-Forchheimer equation.

Many thanks,

Abdul

Re: Brinkman-Forchheimer equation
 

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

Re: Brinkman-Forchheimer equation
 

Dear Amir,

Could you be more specific, or can you direct me to a published on the approach you indicated.

Many Thanks,

Abdul

Re: Brinkman-Forchheimer equation
 

ok, I have been working on the same subject in my thesis and I found out there are different interpretations on Brinkman-Forchheimr 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, Springer-Verlag, 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. 195-203.

Re: Brinkman-Forchheimer equation
 

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

Regards,

Abdul

Re: Brinkman-Forchheimer equation
 

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 Brinkman-Forchheimer 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

Re: Brinkman-Forchheimer equation
 

Thank you Amir

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?

Requests for help
 

Dear Amir
I am trying to model a porous medium in Fluent by using Brinkman-Forchheimer 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. 195-203.

So I need your help, the more specific. Thanks a lot.
Best wishes!

How to add inertial parameter in Fluent
 

Hello
Nowadays I'm just working on modeling the heat transfer in a channel using porous media with a constant wall temperature.
First of all, I'm validating an article before starting my project. In the article, it has mentioned the inertial parameter and inertial coefficient of porous media by these equations:
AE= (CE*H*e)/[(K)^(0.5)]
CE=(1.75*e)/[(150*(e^5))^(0.5)]

AE=inertial parameter
CE=inertial coefficient of porous media
H=channel height(m)
e=porosity
K=permeability of the porous medium (m^2)

The value of AE=16.5 and H=1 and e=0.75 and K=10^(-4) has been considered.

This is my question. How can I add inertial parameter in porous zone area in the fluent?

( Fluent -> Cell Zone Conditions -> porous zone area )

Thanks.