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a,b ,alpha and beta in porousSimpleFom

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Old   August 23, 2013, 15:21
Default a,b ,alpha and beta in porousSimpleFom
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mohsen kh
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Hi dear foamers
I don't know how and where I can find a,b ,alpha and beta.and also I want to know if darcy and forchheimer coefficients effect on porosity or not?
the last question of mine is that if I must say somewhere in my case folder or source code for instant ( porosity = 0.5) or not?
I want to set my porosity 0.5 but I don't know how to do it.
please help me by your useful helps.

best regards
Mohsen
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Old   August 26, 2013, 08:21
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mohsen kh
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Hi

I found my answer.
darcy-Forchhiemer equation is:

delta P/delta x = -(mu/K)v + (beta*rho)v^2 (Eq. 1)

( see it in convection heat transfer by A. Bejan, chapter 12, page571)

the first term refers to friction and the second one refers to inertia.
in source code which would be find here

http://openfoam.org/mantisbt/view.php?id=42

this equation is something like this

deltaP= (mu * D * v + 0.5 * rho * F * v^2)*L (Eq. 2)

if the Darcy-Forchhiemer equation is simplified as follow:

deltaP= B*v + A*v^2 (Eq. 3)

so from Eq. 1 and Eq. 3, B= (mu/K)v and A=(beta*rho).

my case is a bed of packing spheres and as Ergun said:
(again see convection heat transfer by A. Bejan, chapter 12, page571)

K= [(d)^2 * (Porosity)^3]/[150*(1-porosity)^2]

beta= [1.75(1-porosity)]/[(porosity)^3*(d)]

d : diameter of particles

from Eq. 2 and Eq. 3 we have:

D=B/mu

F=2A/rho


d d[0 -2 0 0 0 0 0] (D D D)
f f[0 -1 0 0 0 0 0] (F F F)

so you can easily calculate your Darcy and Forchhiemer coefficients.


best regards
Mohsen
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