permeability setup

I have a problem with the permeability tutorial. In practice I’ve taken this example as a base case and I have adapted it to my different geometries.
First of all, as someone else has written previously, we can not determine the Reynolds number before the simulation and this sound a bit tricky to me because we se just a deltaP between inlet and outlet and so we don’t have a characteristic velocity. Actually I’ve thought that a choice of thise velocity might be Uo=(deltaP/rho)^(1/2), but I’ve not found it in literature. Then we can of course compute a Reynolds number with this velocity. My problem is that I’m not sure that these procedure is correct. In fact I’m not sure that the equality of this Reynolds number in 2 different cases guarantees the hydrodynamic similarity, i.e. the same adimensional solution.
I also wonder if palabos automatically set neumann boundary condition on velocity on inlet and outlet. Isn’t a condition on velocity necessary in this case?
Moreover, I have problems in the choice of the initial time step, i.e. the choice of the relaxation parameter. I know that this choice influences the permeability of the porous media because of the pour representation of geometry (and in fact it is what I’ve obtained), but if omega is to low I think there are also problems because the physical time step is too long.
Thank you all!