Low Reynolds number flow fields in imperfect fibre arrangements

Abstract

In the first part a new theoretical approach is described, which yields an approximate analytical representation of the Stokes flow passing perpendicular through an isolated infinite grating of parallel, unequally spaced circular cylinders in a periodic arrangement. The method is based on a well-known analytical solution for the case of equidistant parallel cylinders and, moreover, on the Helmholtz minimum rate of dissipation theorem, for which an extended formulation is presented here. The analytical results are compared with velocity profiles and streamline patterns, calculated with the help of a commercial finite-element program. In the second part of this paper an experimental method is described, which allows the determination of the flow forces exerted on individual cylinders by measuring the elastic deflexions, the cylinders experience when being exposed to the flow. The theoretical and experimental results are compared. For the two-dimensional measurement of the deflexions, a new realization of the laser-triangulation technique is employed, whose absolute accuracy substantially surpasses that of conventional instruments.