Pressure Drop through Structured Porous Media. Inlet and Outlet Effects

Abstract

Inlet and outlet pressure drop effects can contribute significantly to the total pressure drop in porous media if thin solid matrices are used. However, these effects are usually ignored and few are the studies that focus on this topic. This paper uses a numerical simulation approach to determine the importance of the inlet and outlet pressure drop effects on the total pressure drop in a staggered arrangement of square cylinders with equal sizes, dc. The Navier-Stokes equations are solved at the pore level for several matrix lengths (from dc to 34dc) and for several Reynolds numbers based on dc and maximum velocity of the velocity inlet profile (from 36 to 120). Accurate results of the velocity and pressure fields are obtained through the use of the immersed boundary method in combination with the finite differences method, 4th-order compact schemes for spatial discretization and 4th-order Runge-Kutta temporal discretization. The results presented in this paper confirm that the classical models (e.g., Hazen-Dupuit-Darcy model) are only valid when the solid matrix has a length above a certain value, called the critical length. For shorter porous media, the pressure drop does not vary linearly with the matrix length. The deviations to the model that occur at the shortest porous media are explained by the entrance and exit contributions to the total pressure drop that, in these cases, are not negligible when compared to the bulk pressure drop. For the staggered array of square cylinders and range of Reynolds numbers considered, the critical porous medium length is 16dc. A practical outcome of the present study is the quantification of the influence of the pressure tap locations on the measurements of pressure drop in porous media. When the matrix is short when compared to the particle diameter, care must be taken with the pressure taps placement: they should be located outside the porous matrix and not too close to its inlet and outlet sections. If the matrix is thick enough when compared to the particle diameter, the taps can be placed either inside or outside the matrix. Also, if the influence of the side walls on the total pressure drop is not high (i.e., the walls are at a relative large distance when compared to the particle diameter), there is no practical need to correct the measured pressure values to account for the influence of the walls. This correction should be considered for the shortest matrices though.