Interception efficiency in two-dimensional flow past confined porous cylinders

Abstract

The flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector, is an important parameter in applications such as particle capture, filtration, and sedimentation. In this work, flow permeation through a porous circular cylinder located symmetrically between two impermeable parallel plates is investigated numerically under different flow and geometrical conditions. A flow interception efficiency is defined and calculated based on the flow permeation rate for a wide range of system parameters. The dependencies on all physical variables can be captured in three dimensionless numbers: the Reynolds number, the Darcy number (ratio of permeability to the square of cylinder diameter), and the plate separation relative to the cylinder size. The flow interception efficiency is very low in the limit of unbounded cylinders but significantly increases by restricting the flow domain. The fluid permeation rate through the porous cylinder varies nonlinearly with the relative plate/cylinder spacing ratio, especially when the gap between the cylinder and the confining plates is small compared to the cylinder size. In general, the effects of the Reynolds number, the Darcy number, and confinement on the flow interception efficiency are coupled; however, for most practical cases it is possible to factorize these effects. For practical ranges of the Darcy number (Da<10[superscript −4], which means that the pore size is at least one order of magnitude smaller than the porous cylinder diameter), the interception efficiency varies linearly with Da, is independent of the Reynolds number at low Reynolds numbers (Re[subscript D]<10), and varies linearly with Reynolds number at higher flow rates. In addition to numerical solutions, theoretical expressions are developed for the flow interception efficiency in two limiting cases of confined and unbounded flow, based on modeling the system as a network of hydrodynamic resistances, which agree well with the numerical results. Furthermore, an expression for the drag coefficient on the porous cylinder is proposed as a function of the Darcy number which can be used in the limit of large plate/cylinder relative spacing.