Turbulent Taylor Vortex Research Articles

A study on dynamic separation of silica slurry using a rotating membrane filter 1. Experiments and filtrate fluxes

The microfiltration performance of an axially rotating filter was in vestigated experimentally with an aqueous slurry containing fine silica particles. The effects of the rotating speed of the inner filter, gap size, feed concentration and feed rate on the filtrate flux were examined. Since Taylor vortices generated in its annular gap reduce the cake formation on the surface of the inner filter medium, an efficient removal of water from the slurry was achieved to a certain degree. The results show that continuous filtration is possible in turbulent Taylor-vortex regimes. By dividing the experimental data into two groups, transient and pseudosteady, empirical correlations for the dimensionless filtrate flux were obtained in terms of the Taylor number and the ratio of the annular gap to the inner cylinder radius, respectively.

Influence of quantized vortex lines on the stability of Taylor-Couette flow in He II

Taylor-Couette flow between two concentric cylinders with rotating inner cylinder and fixed outer cylinder has been investigated in the temperature range from 1.5 K to 2.1 K. The formation of quantized vortex lines in the gap between the cylinders has been measured by analyzing the amplitude of azimuthal second-sound resonances. The damping of these resonances as a function of the rotational rate of the inner cylinder shows discontinuities at certain critical angular velocities which can be identified with the appearance of the quantized vortex lines and with the onset of the Taylor instability. The obtained results show that the presence of the quantized vortex lines leads to an additional stabilization of the flow field which is in agreement with recent theoretical results. The visualization of the local flow field was achieved using hollow glas spheres of appropriate average density. This allowed the observation of the structure of the turbulent Taylor vortices at high Reynolds numbers.

Numerical solution of turbulent Taylor-vortex flow

The numerical solution of mean turbulent Taylor-vortex flow is shown. The azimuthal-invariant, cylindrical, Navier-Stokes equations are solved to steady-state for the case of inner cylinder rotation with radius ratio 0.5 and Taylor cell wavelength 2.3. Closure is obtained via a Prandtl-Van Driest turbulence model. Subject to no-slip conditions at radial boundaries and periodic conditions at axial boundaries, the turbulent solution was obtained for a critical Taylor number multiple of 700. The vorticity-velocity method relies on a second-order accurate alternating-direction implicit (ADI) scheme with logarithmic grid clustering. Convective terms are differenced by a hybrid method that is central-preferred/upwind. Azimuthal velocity and wall shear stress are compared to the experiments of Taylor.

Phase dynamics in the Taylor–Couette system

The phase dynamics of flows in the Taylor–Couette system have been studied by applying a forced modulation to the upper boundary of a large aspect ratio concentric cylinder system. In a one phase variable case, the Taylor vortex flow, the perturbations diffuse along the axial direction and the pattern’s response is well described by a simple diffusion model. In a two phase variable case, the wavy vortex flow, the perturbations either propagate as traveling waves or diffuse, depending on the coupling between the axial and azimuthal phase variables. In the turbulent Taylor vortex flow, where spatial coherence coexists with the turbulent flow, the phase dynamics of the coherent structure are described by a diffusion model with a diffusion coefficient an order of magnitude larger than for the laminar Taylor vortex flow.

Turbulent flow between concentric rotating cylinders at large Reynolds number.

Turbulent Taylor vortex flow is studied in experiments for Reynolds numbers ${10}^{3}$R${10}^{6}$. Simple scaling of the torque with Reynolds number is m/Inot observed for any range of R, although the characteristic time scales and the transport of passive scalars are found to scale with the global torque measurements. Above a nonhysteretic transition observed at R=1.3\ifmmode\times\else\texttimes\fi{}${10}^{4}$, the torque has a Reynolds number dependence similar to the drag observed in wall-bounded shear flows such as pipe flow and flow over a flat plate.

An Experimental Study on Turbulent Taylor Vortex Flow between Concentric Cylinders

Mean flow properties, including turbulent stresses, were fully measured in a turbulent Taylor vortex flow between stationary outer and rotating inner cylinders with a radius ratio of 1/0.92. The static pressure distribution on the outer wall confirmed that many turbulent Taylor vortex pairs about twice as high as the channel width continued to exist over a wide range of Taylor numbers varying by more than one digit. A new technique using a grid was effectively applied to fix a vortex pair to be measured at the required position during the velocity field measurements. In the core region extending over 60% of the channel width, the secondary flow contributed to the angular momentum transfer by about 90%. The turbulent stress distributions were characterized by production and convection due to the secondary flow.

An analytical study on the turbulent taylor vortex flow between concentric cylinders. Prediction of the flow field by using the .KAPPA.-.EPSILON. model.

The flow accompanied with turbulent Taylor vortices between inner-rotating and outer-stationary cylinders is analytically treated by using two kinds of κ-e models. The results obtained with both models are generally in good agreement with the existing experimental results. No marked tendency for the secondary flow to disappear with increasing rotating speed is found within the range of the calculation. For a fixed value of Reynolds number, there exists a certain radius ratio which makes the intensity of the vortex maximum. The more this intensity decreases, the more the turbulence energy increases. As the radius ratio approaches unity, the intensity of the vortex decreases monotonously. Conversely, the intensity of the circumferential component of the secondary flow continues to increase until a radius ratio very close to unity. The hypothesis that the vortex determines its shape so that the total amount of the dissipation rate becomes maximum is substantially consistent with the experimental evidence.

An experimental study on turbulent taylor vortex flow between concentric cylinders.

Mean flow properties, including turbulent stresses, were fully measured in a turbulent Taylor vortex flow between outer stationary and inner rotating cylinders with a radius ratio of 1/0.98. The static pressure distribution on the outer wall confirmed that many turbulent Taylor vortex pairs about twice as high as the channel width continued to exist over a wide range of Taylor numbers varying by more than one digit. A new technique using a grid was effectively applied to fix a vortex pair to be measured at the required position during the velocity field measurements. In the core region extending over 60% of the channel width, the secondary flow contributed to the angular momentum transfer by about 90% . The turbulent stress distributions were characterized by production and convection due to the secondary flow.

Flow regimes in a circular Couette system with independently rotating cylinders

Our flow-visualization and spectral studies of flow between concentric independently rotating cylinders have revealed a surprisingly large variety of different flow states. (The system studied has radius ratio 0.883, aspect ratios ranging from 20 to 48, and the end boundaries were attached to the outer cylinder.) Different states were distinguished by their symmetry under rotation and reflection, by their azimuthal and axial wavenumbers, and by the rotation frequencies of the azimuthal travelling waves. Transitions between states were determined as functions of the inner- and outer-cylinder Reynolds numbers, Ri and Ro, respectively. The transitions were located by fixing Ro and slowly increasing Ri. Observed states include Taylor vortices, wavy vortices, modulated wavy vortices, vortices with wavy outflow boundaries, vortices with wavy inflow boundaries, vortices with flat boundaries and internal waves (twists), laminar spirals, interpenetrating spirals, waves on interpenetrating spirals, spiral turbulence, a flow with intermittent turbulent spots, turbulent Taylor vortices, a turbulent flow with no large-scale features, and various combinations of these flows. Some of these flow states have not been previously described, and even for those states that were previously described the present work provides the first coherent characterization of the states and the transitions between them. These flow states are all stable to small perturbations, and the transition boundaries between the states are reproducible. These observations can serve as a challenge and test for future analytic and numerical studies, and the map of the transitions provides several possible codimension-2 bifurcations that warrant further study.

Turbulent Taylor vortex flow

The wavelength of turbulent Taylor vortices at very high Taylor numbers up to 40000Tc, has been measured in long fluid columns with radius ratios η = 0·896 and η = 0·727. Following slow acceleration procedures the wavelength (in units of the gap width) of turbulent axisymmetric vortices was found to be λ = 3·4 ± 0·1 with the small gap and about λ = 2·4 ± 0·1 with the larger gap, and thus in both cases substantially larger than the critical wavelength of laminar Taylor vortices. In the narrow and wide gap the wavelength was, within experimental error, independent of the Taylor number for T > 100Tc. In the experiments with the narrow gap a clear dependence of the value of the wavelength of the turbulent vortices on initial conditions was found. After sudden starts to Taylor numbers > 700Tc the wavelength of steady axisymmetric turbulent vortices was only 2·4 ± 0·05, being then the same as the wavelength of the vortices after sudden starts in the wide gap, and being, within the experimental error, independent of the Taylor number. In the narrow gap all values of the wavelength between λmax = 3·4 and λmin = 2·4 can be realized as steady states through different acceleration procedures. In the wide gap the dependence of the wavelength on initial conditions is just within the then larger experimental uncertainty of the measurements.