Numerical simulation of flow induced by a spinning sphere using spectral methods

Abstract

A direct numerical simulation, based on spectral methods, has been used to investigate viscous, incompressible, steady, rotationally symmetric flow due to a sphere rotating with a constant angular velocity about a diameter. The equations of motion have been reduced to a set of three nonlinear second order partial differential equations in terms of the vorticity, the stream function and the azimuthal velocity. The calculations have been carried out for Reynolds numbers (Re) from the Stokes flow regime (low Re) to the boundary layer regime (high Re). The numerical results clearly show how the Stokes flow behavior for low Reynolds numbers, and the boundary layer behavior for high Reynolds numbers, are approached in the appropriate limits. Besides showing the flow streamlines, results have been presented for the torque and the skin friction behavior. It is shown that the present results are in excellent agreement with both available experimental data, and previously obtained numerical data. The radial equatorial jet which develops with increasing Reynolds numbers has been observed as expected from boundary layer collision behavior. No separation was observed for the range of Reynolds numbers considered, even near the equator