Finite element analysis of the axially symmetric motion of an incompressible viscous fluid in a spherical annulus
W. Ni, Nicholas J. Nigro · International Journal for Numerical Methods in Fluids · 1994
Abstract This paper presents results obtained by employing a modified Galerkin finite element method to analyse the steady state flow of a fluid contained between two concentric, rotating spheres. The spheres are assumed to be rigid and the cavity region between the spheres is filled with an incompressible, viscous, Newtonian fluid. The inner sphere is constrained to rotate about a vertical axis with a prescribed angular velocity, while the outer sphere is fixed. Results for the circumferential function Ω, streamfunction ψ, vorticity function ζ and inner boundary torque T1 are presented for Reynolds numbers Re ⩽ 2000 and radius ratios 0.1 ⩽ α ⩽ 0.9. The method proved effective for obtaining results for a wide range of radius ratios (0.1 ⩽ α ⩽ 0.9) and Reynolds numbers (0 ⩽ Re ⩽ 2000). Previous investigators who employed the finite difference method experienced difficulties in obtaining results for cases with radius ratios α ⩽ 0.2, except for small Reynolds numbers (Re ⩽ 100). Results for Ω, Ψ, ζ and T1 obtained in this study for radius ratios 0.8 ≤ α ≤ 0.9 verified the development of Taylor vortices reported by other investigators. The research indicates that the method may be useful for analysing other non‐linear fluid flow problems.