Stokes Flow Through a System of Parallel Infinite Cylinders with Axes Oriented at an Angle to the Direction of Mean Flow

摘要

The three-dimensional Stokes equation for creeping, incompressible flow through a doubly periodic, infinite lattice of infinite circular cylinders is considered when there is a constant mean flow whose direction makes an acute angle with the axes of the cylinders. It is shown that the problem can be resolved into a two dimensional equation for the component of flow transverse to the cylinders and a one dimensional problem for the parallel component. The velocity field for the transverse problem can be represented by a stream function and the parallel problem reduces to a Poisson problem with a constant nonhomogeneous term. The natural periodicity associated with this problem leads to the specification of periodicity as a boundary condition. Following the lead of S. Kuwabara, these boundary conditions are replaced by considering an imagined cell of fluid surrounding one of the cylinders and assuming that the vorticity is zero on the outside boundary of this cell. The resulting problems can be solved in closed form and give an approximation of the flow through the periodic lattice. 6 refs., 2 figs. (ERA citation 11:005919)