NUMERICAL SOLUTION OF THE SLOW TRANSLATION OF A SPHERE MOVING ALONG THE AXIS OF A ROTATING VISCOUS FLUID

The motion of a sphere along the axis of rotation of an incompressible viscous fluid that is rotating as a solid mass is investigated by means of numerical methods for small values of Reynolds numbers and moderate values of Taylor numbers. The Navier-Stokes equations governing the steady, axisymmetric, viscous flow can be written as three coupled, nonlinear, elliptic partial differential equations for the stream function, vorticity and rotational velocity component. Finite difference method is used for solving the governing equations. Second order derivatives are approximated by central differences and nonlinear terms are approximated by upwind differences. Results are presented mostly in the form of graphs of the streamlines and vorticity lines. When 1/ Ro > 2.2, separation occurs and reverse flow is obtained.