A numerical method for solving the motion of an incompressible viscous fluid between two rotating and precessing spheres
The main purpose of this research is to study the use of a numerical method which has been developed by this investigator to solve unsymmetric fluid flow problems which are formulated in terms of the primitive variables; i.e., pressure and velocity. The numerical solution of these equations presents several difficulties due to (a) coupling of nonlinear equations, (b) lack of prescribed boundary conditions for the pressure and (c) the fact that the continuity equation does not contain an explicit time-derivative term. The investigator's method, which overcomes all of these difficulties, is demonstrated by applying it to a problem involving the flow of a viscous fluid contained in an annulus between two concentric spheres spinning about a common axis which is rigidly attached to a rotating platform. It is assumed that the spin axis of the two spheres with prescribed torques is inclined to the platform and that the platform is undergoing constant rotation about a vertical inertial axis, thus resulting in unsymmetric flow in the annulus. Results are obtained which demonstrate the effects of the nutation angle and precession rate on the fluid flow.