Taylor-Couette Flow

A rotating filter separator consists of a cylindrical porous membrane filter rotating within a concentric outer cylinder. A suspension enters the annulus between the filter and the outer cylinder. The filtrate passes through the porous inner cylinder while the concentrate remains in the annulus. The fundamental basis for a rotating filter is the appearance of toroidal vortices in the annulus of the device, known as Taylor vortices. We have studied Taylor-Couette flow with particular interest in the appearance of these vortices for conditions similar to those in a rotating filter.

• "Azimuthal velocity in supercritical circular Couette flow," with S. Wereley, Experiments in Fluids, 18:1-9, 1994. Although a vast amount of research on circular Couette flow has been published since Taylor's pioneering work, nearly all of the research has been related to the stability problem with very little attention paid to the supercritical velocity field between the rotating inner cylinder and a concentric, fixed outer cylinder. We extended and expanded Davey's analytic approach to the problem and were able to predict the theoretical supercritical flow field. We found that this theoretical velocity field matched the flow field that we measured using laser Doppler velocimetry as shown in the figure below. Although previous experimental work suggested that the amplitudes of individual Fourier coefficients of the disturbed velocity field increase with the Taylor number, our measurements of the azimuthal velocity field were the first to confirm that supercritical Taylor vortices increase in strength as the Taylor number increases. Our measurements of the velocity field were the first for wavy and modulated wavy vortex flow. In these cases the radial transport of high azimuthal momentum fluid away from the inner cylinder and low azimuthal momentum fluid away from the outer cylinder increases as the Taylor number increases, resulting in a nearly uniform azimuthal velocity in the annulus with steep velocity gradients near the walls of the annulus. Furthermore, as the Taylor number increases, the outflow regions between adjacent vortices become jet-like. See Figure
  

• "Stability of axial flow in an annulus with a rotating inner cylinder," with A. Docter and K. Min, Physics of Fluids A: Fluid Dynamics, 4:2446-2455, 1992. This study focused on identifying the flow regimes that result from the combination of circular Couette flow and axial pressure-driven flow in the annulus between a rotating inner cylinder and a fixed outer cylinder. This flow was studied experimentally using flow visualization and an optical detection method based on the spectral analysis of the intensity of laser light reflected from seed particles carried with the Taylor vortices in the flow. The study revealed a rich variety of flow regimes depending on the flow conditions, several of which were not previously identified. Seven types of toroidal vortices and three types of helical vortices were observed. All toroidal vortices and two types of helical vortices translated axially with the axial fluid flow, but in one situation the helical vortices remained stationary. Previous researchers studying rotating filtration have not appreciated that the vortices travel axially, nor have they realized the large number of flow regimes that can result for different flow conditions.

• "Hydrodynamic stability of viscous flow between rotating porous cylinders with radial flow, " with K. Min, Physics of Fluids, 6:144-151, 1994. An unusual complication to the base circular Couette flow is a pure radial flow through a pair of differentially-rotating concentric porous cylinders. Our linear stability analysis, which is the first for the wide annular gap case, indicates that weak radially outward flow destabilizes the circular Couette flow resulting in the appearance of Taylor vortices at a lower Taylor number. Any radially inward flow and strong radially outward flow stabilize the flow. This result can be explained as follows. The fluid motion leading to supercritical vortices first appears near the inner rotating cylinder and propagates radially outward as the Taylor number increases. Weak radial outflow washes the incipient motion from near the inner cylinder outward across the annulus resulting in the supercritical transition at a lower rotational speed. Radial inflow and strong radial outflow wash the fluid where the incipient motion appears out of the annulus increasing the critical Taylor number. The vortices in the annulus are shifted in the direction of the radial flow, with the largest shifts for the largest magnitudes of radial flow.

  
  

• "Circular Couette flow with pressure-driven axial flow and a porous inner cylinder," with K. Min, Experiments in Fluids, 17:190-197, 1994. This experimental work represents the first study of combined circular Couette flow, axial flow, and radial suction at the inner cylinder. Both the transition to Taylor vortex flow and the transition to wavy vortex flow are stabilized by the radial flow. The mechanism for the delay of the first transition is the same as that for pure radially inward flow described above. The delay of the second transition occurs since a radial inflow weakens the outflow jet between vortices delaying the onset of waviness. A suction boundary condition applied at the inner cylinder results in a multitude of flow regimes that were not identified prior to our work, although the azimuthal velocity profiles measured using laser Doppler velocimetry are similar for the various flow regimes as long as the flow is supercritical. This is because the vortices transport high momentum fluid from near the inner cylinder and low momentum fluid from near the outer cylinder toward the center of the annulus, resulting in a region at the center of the annulus with a relatively flat azimuthal velocity profile and steep velocity gradients near the walls.