© 2003 by Oxford University Press
On Secondary Flow Due to the Coaxial Rotation of Two Spheres: Low Reynolds Number Theory and Finite Reynolds Number Experiment
( 1 Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA 2 University of Applied Sciences, 77652 Offenburg, Germany 3 Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA )
The structure of the separation bubble that appears in the secondary meridional flow between two coaxially rotating spheres at low and finite Reynolds number (Re) is considered. The low Re analytical study was motivated by recognizing some errors in the analytical work on this problem by Arunachalam and Majhi (1987, Q. Jl Mech. Appl. Math., 40, 47) whilst the finite Re experimental study was motivated by the desire to observe the separation bubble in the laboratory. Though the finite Re experiments were performed in a confined apparatus, they exhibit the qualitative features of the low Re theoretical predictions for the axisymmetric separation bubble that encloses two toroidal vortices symmetrically disposed above and below the mid-plane of sphere separation, but strong effects of confinement are apparent. The flows observed include (i) a wall-attached bubble symmetric about the mid-plane at low Re, (ii) symmetric free-standing bubbles at moderate Re, and (iii) an asymmetric bubble with flow separating from one sphere and attaching to the support shaft between the spheres at sufficiently high Re.
Received 7 March 2002. Revised 19 November 2002 and 20 March 2003.