Effects of Geometrical Structure on Flows Around a Rotating Disk in an Enclosure

Flows around a rotating disk in a cylindrical enclosure are typical models of flows found in fluid machinery and chemical reactors. They have their practical applications and draw engineering interests. When the radius of the disk is infinite, it is known that circular rolls, spiral rolls, turbulent spirals and turbulent spots appear. In this case, the parameters governing the flows are the Reynolds number based on the angular velocity of the disk and the axial gap between the disk surface and the end wall of the enclosure. We consider, in this paper, a more practical configuration. The disk has its thickness comparable with the axial height of the enclosure, and the radial gap between the disk rim and the side wall of the enclosure is not negligible. Vortex flows are driven by the centrifugal force around the disk rim, and they are expected to have effects on the entire flow. We performed numerical and experimental studies and investigated the unsteady three-dimensional behaviors. A new criterion to identify flow patterns is introduced and the Hopf bifurcation points from the axisymmetric flows to the three-dimensional flows are determined. The phase velocity of the spiral rolls are measured by a time-dependent analysis. The influence of the geometrical structure on the phase velocity is estimated. New types of flows are found, where bead-like vortices appear and spiral rolls with positive and negative front angles coexist.