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Question: - How do I set resistance terms, such as the Ergun Equation?

Answer:

The ERGUN equation represents the pressure drop associated with flow through a packed bed, or more generally, a porous medium.

In PHOENICS, pressure drops are applied as sinks in the momentum equation. The units of the momentum equation are those of force, so the pressure drop must also be turned into a force.

The ERGUN equation can be written as:

dp/dx = a*U1 + b*U1²

where a=µ/K and b is an empirical constant. Here, µ is the dynamic viscosity of the fluid flowing through the porous media and K is an emprical constant called the permeability.

The pressure drop can be turned  into a force, as follows:

F_x = Area * dp

Now Area = dy * dz;

so dx * Area = Volume

Hence:

Fx = Volume * (a*U1 + b*U1²)

The velocities used in the equation are superficial velocities, so

This can be introduced as two patches:

Note that the -ve COefficient in patch ERGUN2 is activating a quadratic source - as stated in POLIS.