Numerical studies of viscous incompressible flow between two rotating concentric spheres

摘要

The problem of determining the induced steady axially symmetricmotion of an incompressible viscous fluid confined between twoconcentric spheres, with the outer sphere rotating with constantangular velocity and the inner sphere fixed, is numericallyinvestigated for large Reynolds number. The governingNavier-Stokes equations expressed in terms of a streamfunction-vorticity formulation are reduced to a set of nonlinearordinary differential equations in the radial variable, one ofsecond order and the other of fourth order, by expanding the flowvariables as an infinite series of orthogonal Gegenbauerfunctions. The numerical investigation is based on a finite-differencetechnique which does not involve iterations and whichis valid for arbitrary large Reynolds number. Presentcalculations are performed for Reynolds numbers as large as 5000.The resulting flow patterns are displayed in the form of levelcurves. The results show a stable configuration consistent withexperimental results with no evidence of any disjoint closedcurves.