Flow through and particle interception by an infinite array of closely-spaced circular cylinders

Abstract

Steady two-dimensional laminar flow through an infinite array of parallel circular cylinders is computed numerically for values of the Reynolds number Re, based on oncoming velocity and cylinder diameter, up to 40, and for values of the spacing parameter, W (the ratio of the distance between cylinder axes to the cylinder radius), ranging from 2.3 to 10. The method used is that of Fornberg (1991). Results are presented for the dimensionless drag on a cylinder, D (or, equivalently, the dimensionless permeability of the array, β = W/D) and are compared with previous analytical results for very small Re and either wide or very narrow gaps. Results are also presented for the efficiency with which a filter consisting of such an array would capture spherical particles of radius b by direct interception, assuming that particle centres follow streamlines and that a particle is captured whenever it touches a cylinder. Such results are applicable to the study of filter feeding by small aquatic organisms.