## Defining porosity using Darcy law

• Porosity could be modeled using so called Darcy law
• The file system/fvOptions defining porous zone named porosity1 should contain following lines (this setup is used for the training case):+
• /*--------------------------------*- 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.:
• The pressure drop depends on the speed of the fluid.
• The parameters d and f can be expressed as
• 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