Vortex Breakdown in an Enclosed Cylinder With a Partially Rotating Bottom-Wall

Abstract

A numerical study of the axisymmetric flow in a cylindrical chamber of height H is presented, which is driven by a bottom disk rotating at angular velocity Ω. However, unlike most previous studies, the present rotating disk is of smaller radius than the bottom-wall. The boundary curves for the onset of vortex breakdown are presented using different definitions of the nondimensional parameters, depending on whether the cylinder radius R or the disk radius rd is used as the length scale. The study shows that the boundary curves are best correlated when presented in terms of the Reynolds number Ωrd2∕υ, aspect ratio H∕R, and cylinder-to-disk ratio R∕rd. The cylinder-to-disk ratio R∕rd up to 1.6 is found to have noticeable effect on vortex breakdown; this is attributed to the change of effective aspect ratio. The contours of streamline, angular momentum, and azimuthal vorticity are presented and compared with those of whole bottom-wall rotation.