Permeability (K) and form coefficient (C) are the two main hydraulic properties that characterize any porous medium. To simultaneously measure (evaluate) both of these for a porous medium, the accepted practice is by using the Hazen-Dupuit-Darcy (HDD) model (also known as the Forchheimer extended Darcy model) to curve-fit the longitudinal global pressure-drop versus the average fluid speed (seepage velocity) data from an isothermal, steady flow, hydraulic experiment across a test section of the porous medium and evaluating the K and C from the curve-fit, for known fluid thermo-physical properties.
The K and C thus measured are global parameters, i.e., valid for the entire porous medium. Under isothermal conditions, they are independent of the properties and flow conditions of the fluid flowing through the porous medium. Consequently, they can be used with the HDD model on all subsequent occasions in the determination of the unknown global pressure-drop for a particular flow speed across a configuration using that porous medium.
However, the above considerations are valid only for the flow throughout the porous medium, across which the hydraulic experiment is conducted to determine the K and C, is of slug flow nature. For instance, as the form coefficient (C) is dependent on the u(y) profile at every x along the porous medium test section, it can be different for the same porous medium, encountering non-slug flow like profiles at the inlet of the test section.
Experimental evidence from our project, presented in  and , delineates the effect of inlet velocity profiles on the permeability (K) and form coefficient (C) measured experimentally across a porous medium duct of square cross section. While the variation in permeability (K) for different inlet velocity profiles is minimal (which is expected), we find the form coefficient (C) to change as much as 11% when going from a fully developed velocity profile to a slug flow profile at the inlet to the porous medium.
Here is a summary of results from the measurements reported in . The numbers in the gray boxes indicate the percentage variation in the measurement of K and C, when the inlet velocity profile is altered between plug flow and fully developed flow.
Alteration in the inlet velocity profile is an effect that could be countered by the effect of porous medium test section length variation (increase). More experiments with suitable porous media to amplify the effects noticed in this paper are required to delineate appropriate correction factors to standardize K and C measurements.
- Protocol for Permeability Measurement
- Flow Through Porous Media Summary — Chapter 3 of Essentials of Heat and Fluid Flow in Porous Media.
- Wilson, L., Narasimhan, A. and Venkateshan, S. P., (2004), “Effect of Inlet Velocity Profile on the Permeability and Form Coefficient of Porous Medium Ducts,” Proc. 2nd Int. Conf. on Applications of Porous Media, Evora, Portugal, May 24-27.
- Wilson, L., Narasimhan, A. and Venkateshan, S. P., (2006), “Permeability and Form Coefficient Measurement of Porous Inserts with Non-Darcy Model using Non-Plug Flow Experiments,” ASME J. Fluids Engineering, 128, 638 – 642.