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## Defining porosity using Darcy law

/*--------------------------------*- C++ -*----------------------------------*\ | ========= | | | \\ / F ield | OpenFOAM: The Open Source CFD Toolbox | | \\ / O peration | Version: 2.3.x | | \\ / A nd | Web: www.OpenFOAM.com | | \\/ M anipulation | | \*---------------------------------------------------------------------------*/ FoamFile { version 2.2; format ascii; class dictionary; object fvOptions; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // porosity1 { type explicitPorositySource; active yes; explicitPorositySourceCoeffs { type DarcyForchheimer; selectionMode cellZone; cellZone heatExchanger; DarcyForchheimerCoeffs { d d [0 -2 0 0 0 0 0] (7.65e7 3e10 3e10); f f [0 -1 0 0 0 0 0] (255 1e5 1e5); coordinateSystem { type cartesian; // global co-ordinate system (redundant) origin (0 0 0); // redundant in this case coordinateRotation { type axesRotation; // local Cartesian co-ordinates e1 (0.998 0.061 0); e2 (0.016 -1.000 0); } } } } // ************************************************************************* //

*Darcy law*is based on the resistance characteristics, which is replaced by second order polynomial function, e.g.:

- where are the “flow resistance” vectors in local coordinates of the porous region. In most cases . For a flow without friction and confined strictly to the direction, the components would be , i.e. the resistance is zero in the direction and infinite in the other two perpendicular directions and .
- In the example listing above, the flow is weakly confined to the (local) direction, with some friction in this allowed direction and a much greater friction in other two directions.
- The local coordinate system is specified by the unit vectors
*e1*and*e2*in the section*coordinateSystem*. The remaining axis is computed as the cross product*e1 e2*. - The ith source term component for the momentum equation, provided that user has chosen the canonical basis, reads:

where Einstein notation is not applied