FINITE-ELEMENT ANALYSIS OF THE AXIALLY-SYMMETRICAL MOTION OF AN INCOMPRESSIBLE VISCOUS-FLUID IN A SPHERICAL ANNULUS

This paper presents results obtained by employing a modified Galerkin finite element method to analyse the steady state flow of a fluid cont ained between two concentric, rotating spheres. The spheres are assume d to be rigid and the cavity region between the spheres is filled with an incompressible, viscous, Newtonian fluid. The inner sphere is cons trained to rotate about a vertical axis with a prescribed angular velo city while the outer sphere is fixed. Results for the circumferential function OMEGA, streamfunction PSI vorticity function zeta and inner b oundary torque T1 are presented for Reynolds numbers Re less-than-or-e qual-to 2000 and radius ratios 0.1 less-than-or-equal-to alpha less-th an-or-equal-to 0.9. The method proved effective for obtaining results for a wide range of radius ratios (0.1 less-than-or-equal-to alpha les s-than-or-equal-to 0.9) and Reynolds numbers (0 less-than-or-equal-to Re less-than-or-equal-to 2000). Previous investigators who employed th e finite difference method experienced difficulties in obtaining resul ts for cases with radius ratios alpha less-than-or-equal-to 0.2, excep t for small Reynolds numbers (Re less-than-or-equal-to 100). Results f or OMEGA, PSI, ZETA and T1 obtained in this study for radius ratios 0. 8 < alpha < 0.9 verified the development of Taylor vortices reported b y other investigators. The research indicates that the method may be u seful for analysing other non-linear fluid flow problems.