Slow viscous flow past two rotating cylinders

Abstract

An earlier paper (1) treated the flow produced by the slow rotation of two parallel circular cylinders in a viscous fluid at rest at infinity. The present work deals with the flow of a uniform stream past the cylinders. The principal feature of interest is that the rotation of the cylinders leads, in general, to a lift force on the cylinders of the same order as the drag. The second-order Oseen approximation to the flow therefore involves the product of lift and drag and the square of the lift, as well as the square of the drag. The case of equal contra-rotating cylinders is considered first, with the stream either normal or parallel to the plane containing the axes of the cylinders. The components of the resultant force on the cylinders link the inner Stokes solution with the outer Oseen solution, and are determined by matching these solutions. The general case of arbitrary radii and angular velocities of the cylinders, and any direction of the stream, is also treated