LOW-REYNOLDS-NUMBER FLOW-FIELDS IN IMPERFECT FIBER ARRANGEMENTS

In the first part a new theoretical approach is described, which yield s an approximate analytical representation of the Stokes flow passing perpendicular through an isolated infinite grating of parallel, unequa lly 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 di ssipation theorem, for which an extended formulation is presented here . The analytical results are compared with velocity profiles and strea mline patterns, calculated with the help of a commercial finite-elemen t program. In the second part of this paper an experimental method is described, which allows the determination of the flow forces exerted o n individual cylinders by measuring the elastic deflexions, the cylind ers experience when being exposed to the flow. The theoretical and exp erimental results are compared. For the two-dimensional measurement of the deflexions, a new realization of the laser-triangulation techniqu e is employed, whose absolute accuracy substantially surpasses that of conventional instruments.