Mechanically driven circulation in a rotating cylinder/disk device

Abstract

The circulation flow of a viscous incompressible fluid in the cylindrical containers bounded by the ends with the rotating and fixed disks are explored. The main goal of the research is aimed to study influence of rotation of casing and end disk on a circulation flow in a cylinder/disk device. This problem relates to inducing a circulation flow in a mechanical centrifuge for mixture separation. To solve this complex problem, an approximate calculation approach is proposed. It is based both on the integral relationships reducing to the balance of the azimuthal moment friction forces acting on the rotating volume and continuity of a circulation flow. To evaluate the friction forces at the ends of a cylinder, the case of infinitely extended disks is considered. For this case, the approximate analytical solutions of the hydrodynamic problem for the turbulent boundary layers on the rotating and fixed extended disks are obtained. In contrast to the previously published works, the inertial convective term associated with the angular momentum transfer from the external flow to the boundary layer in the equations of motion and the symmetrical radial velocity profile are taken into account.