Numerical investigation of laminar fluid flow in an oscillating sphere

Abstract

The laminar flow of a fluid in an oscillating sphere is a well known problem investigated in literature for Newtonian and non-Newtonian fluids. For a fully filled sphere the fluid oscillates in azimuthal direction with the frequency of excitation. In the meridian plane exists a stationary drift caused by the inertia of the fluid. In the case of viscoelastic fluids the inertia competes against the forces of normal stress differences. For certain parameter analyticall results based on calculation of perturbation show not only two vortices in form of a torus, two additional vortices are developed with opposite direction of rotation. But also in the case of the fully filled hemisphere and Newtonian fluids additional vortices are observed experimentally.