Three-dimensional velocity field for wavy Taylor–Couette flow

Abstract

The stability of wavy supercritical cylindrical Couette flow has been studied extensively, but few measurements of the velocity field in flow have been made. Particle image velocimetry was used to measure the azimuthal and radial velocities in latitudinal planes perpendicular to the axis of rotation for wavy cylindrical Couette flow in the annulus between a rotating inner cylinder and a fixed outer cylinder. These measurements were matched to previous measurements of the axial and radial velocity measured in several meridional planes resulting in an experimentally measured, time-resolved, three-dimensional, three-component velocity field for wavy cylindrical Couette flow. Using this complete velocity field it is possible to evaluate details of the flow field. The vortical motion transports azimuthal momentum radially while the axial exchange of fluid between vortices in wavy flow transports azimuthal momentum axially. As the Reynolds number increases, these effects strengthen. Streams of net axial flow stretch axially along the length of the annulus and wind around the vortices from the inner cylinder to the outer cylinder and back while also winding azimuthally in the annulus. The azimuthal velocity measured at the center of a vortex is similar to the azimuthal wave speed. Measurements of the azimuthal velocity in cylindrical surfaces concentric with the axis of rotation suggest that the origin of the waviness is related to a jet-like azimuthal velocity profile rather than the radial outflow jet. Near both cylinder walls, the shear stress is quite large, decreasing to near zero at the middle of the annular gap.

Dynamics of axially localized states in Taylor-Couette flows

“…The frequency of the LJ remains around 56% of the rotation frequency of the inner cylinder. All these observations coincide with previously reported descriptions of this flow pattern [14,42,43]. The LJ preserves the same discrete symmetry group Z 2 as the SJ.…”

“…For this reason it is referred to as large jet LJ, although most authors call it just wavy vortex flow (WVF) [42,43]. In order to compare the SJ and LJ states, Fig.…”

Preferential accumulation of bubbles in Couette-Taylor flow patterns

“…12͒. This feature was clearly emphasized experimentally by Akonur and Lueptow, 32 who observed these axial flows in the WVF regime using particle image velocimetry. Such streams turn out to be strong enough to drive bubbles outside the vortices and to disperse them more evenly than in the TVF regime.…”

Wavy Taylor vortices in molecular dynamics simulation of cylindrical Couette flow

“…The streamlines in Fig. 5 show that an additional mixing between the vortices, a phenomenon that is also observed in experiments [14], is another feature of the wavy-vortex flow that is absent from the pure Taylor vortex. The two states are also differentiated by the radial positions of the vortex centers.…”

“…At this point, a waviness develops and the new state is described as a "wavyvortex" flow. The waves are convected around the azimuth at a constant speed that is approximately linear in i [13], and the streamlines are no longer confined to a single vortex [14]. Progressively increasing the Reynolds number even further results in a series of new bifurcations which eventually lead to a fully turbulent regime.…”