Hello Ghassan. AbuSultanah ,
Sorry for the delayed response. Upon reviewing your calculations and simulations I have noticed some discrepancies, which could be my misunderstanding or incorrect assessment. Please feel free to address them, if necessary.
The calculation sheet mentions k-factor which is used to calculate the analytical pressure drop values for given velocities. I was not sure what this k-factor is, the formula used to calculate this k factor is Where e is the porosity of the medium, this k-factor does not have any unit. It is then used to calculate pressure drop for a given velocity and uses a quadratic formula as , which means that k is the unitless entity called inertial loss factor, which is used to calculate the inertial resistance C2. Again the pressure calculated with the quadratic formulation is curve fitted with a trendline with power 2, and it gives zero as the linear S term, which would mean zero viscous losses. This seems to be incorrect for laminar flow.
This same k seems to be also divided by the thickness to calculate C1 (viscous resistance), which actually should be C2 (inertial resistance).
Since it is said that the flow is laminar and you have considered C2 to be zero, the calculations are still done for C2 or inertial resistance. The calculations are required to be done for Viscous losses, and for which you will need to calculate the permeability factor (α).
The values calculated in the excel sheet and the ones used in the simulation, also do not match up. Unless the calculations and input values are correct the results will not be of any significance. Please refer to the Fluent documentation on porous media to understand which formulae and equations to use.
Another small suggestion would be to cross-check the unit conversion or use the same units in the calculation as well as simulation, to avoid unnecessary confusion.