Flow around a confined rotating cylinder at small Reynolds number

Abstract

A numerical finite-volume technique to solve the two-dimensional Navier-Stokes equations is applied to the rotation of a rigid circular cylinder between parallel plane walls. In this confined situation, the torque exerted on the cylinder is a function of both the distance between the two walls and the position between them. In the absence of experimental results for this problem, we propose here new data of the torque in a wide range of confinements and we study the influence of the eccentricity of the cylinder. When the cylinder rotates close to a wall, there is also a fall of pressure that is likely to create cavitation in the fluid, in accordance with experimental results. Finally, a force parallel to the plane parallel boundaries is numerically obtained, whereas it is theoretically found to be equal to zero in the presence of a single wall. This phenomenon is studied in detail and an explanation is proposed here. The same results could be obtained for the torque experienced by a cylinder translating parallel to the parallel walls.