Numerical Studies of the Flow between Two Concentric Rotating Spheres in the Range of Great Reynolds Numbers

Abstract

The steady, nonlinear motion of a viscous, incompressible fluid between two concentric rotating spheres is numerically studied at some great Reynolds numbers. Several numerical methods are compared on the same boundary condition in which the outer sphere rotates and the inner one is stationary. The variation of the velocity profiles in the θ-direction in the clearance between the spheres and the effects of Reynolds number increase on the velocity profiles are considered. Although the velocity distributions near the pole in the clearance between the spheres are similar to those of the enclosed rotating disks, those at the equator are found to be markedly different from those of the concentric cylinders, one of which rotates, because the secondary flow in the clearance still has a great effect at the equator. In the case where both the inner and outer spheres rotate, contour lines of stream function, velocity profiles and the coefficient of viscous frictional moment are considered numerically in relation to some rotating angular velocity ratios α and the value of |1-α|.