Rotation Of Endwall Research Articles

Thermocapillary instabilities in a laterally heated liquid bridge with end wall rotation

The effect of rotation on the stability of thermocapillary driven flow in a laterally heated liquid bridge is studied numerically using the full-zone model of the floating-zone crystal growth technique. A small Prandtl number (0.02) fluid, relevant for semiconductor melts, is studied with an aspect ratio (height to diameter of the melt) equal to one. Buoyancy is neglected. A linear stability analysis of three-dimensional perturbations is performed and shows that for any ratio of angular velocities, a weak rotation rate has the surprising effect of destabilizing the base flow. By systematically varying the rotation rate and ratio of angular velocities, the critical threshold and azimuthal wave number of the most unstable mode is found over a wide range of this two parameter space. Depending on these parameters, the leading eigenmode is a wave propagating either in the positive or negative azimuthal direction, with kinetic energy typically localized close to one of the end walls. These results are of practical interest for industrial crystal growth applications, where rotation is often used to obtain higher quality crystals.

Response to “Comment on ‘Surface switching of rotating fluid in a cylinder”' [Phys. Fluids 19, 069101 (2007)

In our Letter [T. Suzuki, M. Iima, and Y. Hayase, “Surface switching of rotating fluid in a cylinder,” Phys. Fluids 18, 101701 (2006)], we reported a surface switching phenomenon of fluid in a cylinder driven by the endwall rotation. In the Comment by Vatistas [G. Vatistas, “Comment on ‘Surface switching of rotating fluid in a cylinder',” Phys. Fluids 19, 069101 (2007)], the author claims that a periodic sloshing phenomenon reported by Vatistas in 1990 is the same phenomenon as the surface switching. We clarify the difference between these phenomena in terms of the parameters, the phenomena, the boundary condition, and the physical mechanism.

Confined flow vortex breakdown control using a small rotating disk

As part of a program to investigate the effectiveness of vortex breakdown in bioreactors for cell and tissue growth, a nonintrusive method of flow control is presented. A small rotating disk flush-mounted opposite to the rotating lid in a confined cylindrical vessel is found to precipitate or delay the onset of vortex breakdown depending on whether it is corotating or counterrotating, respectively. Furthermore, corotation increases the bubble radial and axial dimensions while shifting the bubble in the upstream direction. By contrast, counterrotation tends to reduce the size of the bubble, or completely suppress it, while shifting the bubble in the downstream direction. It has also been shown that corotating swirl addition using the small disk is orders of magnitude more energy efficient in manipulating the vortex breakdown bubble than using end wall rotation.

Effects on vortex breakdown due to an abrupt change in the rotation of endwall in a disk-cylinder system

The transient flow in a cylindrical enclosure with fixed sidewall is studied numerically. The initial motion due to uniform rotation of the lower endwall is disturbed by setting the top endwall to corotate impulsively with a small angular velocity. The flow parameter values are chosen so as to induce a vortex breakdown in the initial steady state. The unsteady rotationally-symmetric Navier-Stokes equations are solved iteratively using a combination of second-order and fourth order compact difference schemes. At higher values of the Reynolds number, upwind differencing is used in the convective terms. The breakdown bubble in the initial steady state occurs between the stationary top end wall and the mid-plane. The numerical soulution shows that at the early stage of the transient flow the breakdown bubble enlarges in size, and in subsequent time the bubble occurs between the mid-plane and the faster rotating endwall. The role of the azimuthal component of vorticity in the breakdown phenomena is analysed. The torque on the lower endwall is obtained at several values of non-dimensional time during the transient flow.

Boundary layer separation in a rotating container

The flow field induced in a cylindrical container by the rotation of the container and/or the end wall(s) about the axis of symmetry is highly vortical. If the container and the end walls are rotated at different angular velocities, a meridional flow develops due to the tilting and stretching of the axial vorticity created by the rotation of the bounding surfaces. In the present study, the flow field induced by the differential rotation of the container and one end wall while the other end wall remains fixed is numerically studied for a range of Reynolds numbers and ratios of the container to the end wall rotation rate. It is shown that the production of azimuthal vorticity by the tilting and stretching of axial vorticity causes the container side wall boundary layer to separate for a range of Reynolds numbers and ratios of the container to the end wall rotation rate.