Pressure Distributions in Porous Ducts of Arbitrary Cross Section

Abstract

A general analytical method has been developed to approximate the pressure distribution along a porous duct of an arbitrary cross section with uniform fluid extraction or addition through the wall. Application of this method is made to a variety of cross sections including circular tubes, parallel plate channels, elliptical ducts, rectangular ducts, annular ducts, and isosceles triangular ducts. Comparisons have been made with results from existing literature on cases of the circular porous tube and the parallel porous plate channel in which exact solutions are available. A numerical solution for the case of a parallel channel consisting of an impermeable wall on one side and a porous wall on the other side is also presented. One important filter duct design criterion has been found for each of the above cases. At a critical wall Reynolds number, defined by flow velocity normal to the wall and the equivalent diameter of the duct, the pressure gradient along the filter duct approaches zero. The zero pressure gradient in a filter duct ensures uniform filtration of solid particles.