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porousSimpleFoam: A fundamental inconsistency to formula in Fluent

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Old   May 18, 2018, 07:13
Default porousSimpleFoam: A fundamental inconsistency to formula in Fluent
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Kai
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Hi, Foamers

The formulation in solver porousSimpleFoam is based on the articles: Porous Media in OpenFOAM - Chalmers
http://www.tfd.chalmers.se/~hani/kur...ukurReport.pdf

in the article, the invicid Navier-Stokes Eqn is written down as
\frac{\partial}{\partial t}(\gamma \rho u_i)+u_j \frac{\partial}{\partial x_j}( \rho u_i)=-\frac{\partial p}{\partial x_i} +S_i \:\:\:[1]

I think the velocity here refers to the superficial velocity.

However, according to the formulation in Fluent and other ref:
[1]http://www.afs.enea.it/project/neptu...ug/node233.htm
[2]Novel porous media formulation for multiphase flow conservation equations, by Sha and Chao 2007
the Navier-Stokes Eqn should be
\frac{\partial}{\partial t}(\gamma \rho u_i)+\frac{\partial}{\partial x_j}( \gamma \rho u_i u_j )=-\gamma \frac{\partial p}{\partial x_i}+S_i
and here the velocity is physical velocity. The formula are derived according to time/volume averaging.

And if we substitute the above Eqn with u_{\rm superficial } = \gamma u_{\rm physical }, we have
\frac{\partial}{\partial t}(\gamma \rho u_i)+\frac{\partial}{\partial x_j}(  \rho u_i u_j )=-\gamma^2 \frac{\partial p}{\partial x_i}+ \gamma S_i \:\:\:[2]
how to explain the inconsistency of the coefficient in pressure term between Eqns [1] and [2]?
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Last edited by kaifu; May 18, 2018 at 07:15. Reason: something wrong with solver's name
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Old   May 18, 2018, 10:32
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One of the possibilities may come from the temporal/spatial inertial term. Both of them may be negligible, compared to the pressure and viscous resistance in the pore. But still sounds something is wrong..
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