Laminar Taylor-Couette Flow Research Articles

Elastic turbulence in two-dimensional Taylor-Couette flows

We report the onset of elastic turbulence in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model generated with the program OpenFOAM®. Beyond a critical Weissenberg number, an elastic instability causes a supercritical transition from the laminar Taylor-Couette flow to a turbulent flow. The order parameter, the time average of secondary-flow strength, follows the scaling law with and . Additionally, the flow resistance increases beyond Wic. The temporal power spectra of the velocity fluctuations show a power-law decay with a characteristic exponent in the range , which strongly depends on the radial position. The characteristic exponent β for the spatial power spectra obeys the necessary condition , associated with elastic turbulence, for all .

Transition to magnetorotational turbulence in Taylor–Couette flow with imposed azimuthal magnetic field

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experiments of Taylor–Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI. We here report on a numerical investigation of the MRI with an imposed azimuthal magnetic field. We show that the laminar Taylor–Couette flow becomes unstable to a wave rotating in the azimuthal direction and standing in the axial direction via a supercritical Hopf bifurcation. Subsequently, the flow features a catastrophic transition to spatio-temporal defects which is mediated by a subcritical subharmonic Hopf bifurcation. Our results are in qualitative agreement with the PROMISE experiment and dramatically extend their realizable parameter range. We find that as the Reynolds number increases defects accumulate and grow into turbulence, yet the momentum transport scales weakly.

Azimuthal velocity profiles in Rayleigh-stable Taylor–Couette flow and implied axial angular momentum transport

We present azimuthal velocity profiles measured in a Taylor–Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of ${\it\eta}=0.716$, an aspect ratio of ${\it\Gamma}=11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. This regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $\mathit{Re}_{S}\sim O(10^{5})$, for both ${\it\Omega}_{i}>{\it\Omega}_{o}>0$ (quasi-Keplerian regime) and ${\it\Omega}_{o}>{\it\Omega}_{i}>0$ (sub-rotating regime), where ${\it\Omega}_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles match the non-vortical laminar Taylor–Couette profile. The deviation from that profile increases as solid-body rotation is approached at fixed $\mathit{Re}_{S}$. Flow super-rotation, an angular velocity greater than those of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that are larger than the torques for the case of laminar Taylor–Couette flow. The quasi-Keplerian profiles are composed of a well-mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor–Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.

Ghost hunting—an assessment of ghost particle detection and removal methods for tomographic-PIV

This paper discusses and compares several methods, which aim to remove spurious peaks, i.e. ghost particles, from the volume intensity reconstruction in tomographic-PIV. The assessment is based on numerical simulations of time-resolved tomographic-PIV experiments in linear shear flows. Within the reconstructed volumes, intensity peaks are detected and tracked over time. These peaks are associated with particles (either ghosts or actual particles) and are characterized by their peak intensity, size and track length. Peak intensity and track length are found to be effective in discriminating between most ghosts and the actual particles, although not all ghosts can be detected using only a single threshold. The size of the reconstructed particles does not reveal an important difference between ghosts and actual particles. The joint distribution of peak intensity and track length however does, under certain conditions, allow a complete separation of ghosts and actual particles. The ghosts can have either a high intensity or a long track length, but not both combined, like all the actual particles. Removing the detected ghosts from the reconstructed volume and performing additional MART iterations can decrease the particle position error at low to moderate seeding densities, but increases the position error, velocity error and tracking errors at higher densities. The observed trends in the joint distribution of peak intensity and track length are confirmed by results from a real experiment in laminar Taylor–Couette flow. This diagnostic plot allows an estimate of the number of ghosts that are indistinguishable from the actual particles.

Study on Performance of Laminar Taylor-Couette Flow with Different Developed Procedures

The performance of laminar Taylor-Couette flow with different developed procedures is studied by the way of computational fluid dynamics (CFD) in steady state. In order to gain a group of developed procedure in CFD, a set of convergent solutions are used as the initial value of next boundary condition, and the new set of convergent solutions are regarded as developing from the previous steady state. Three groups of developed procedures are gained from the rotating speed series of inner cylinder, respectively from the gradual increase procedure (GIP), the gradual decrease procedure (GDP) and the sudden increase procedure (SIP). It is proved that the convergent solutions of fluid control equations are different when they are solved from laminar state with the same boundary condition, the same fluid property, the same mesh grid in CFD and the same business software except that the flow states have developed from the procedures of GDP, GIP and SIP. It is shown that the developed procedure could leave behind some information in the performance of the flow. In other words, the flow between concentric rotating cylinders has somewhat memory for the procedure of its history.

Numerical flow visualization of the formation of taylor cells in a laminar taylor-couette flow

Numerical flow visualization of the formation of taylor cells in a laminar taylor-couette flow

UV Disinfection of E. coli Between Concentric Cylinders: Effects of the Boundary Layer and a Wavy Wall

UV inactivation of E. coli in a plug flow reactor between concentric cylinders was investigated. The concentration boundary layer thickness was computed for laminar, turbulent and Taylor-Couette flow in terms of the respective mass transfer Sherwood number. It is demonstrated that the concentration boundary layer is thin and that the mass transfer coefficient is large and comparable in size for both turbulent and laminar Taylor-Couette flow in contrast to laminar flow. Computation of the fluence distribution for each flow pattern indicate that turbulent and especially Taylor-Couette flow subject E. coli to an equal flux of photons corresponding to ideal plug flow. However, experiments with turbulent flow that require large axial velocities indicate that very long reactor lengths are necessary to inactivate E. coli. Finally, rotor wavy wall modifications are explored to increase the inactivation of microorganisms in Taylor-Couette flow.

Temporal evolution of a localized weak vortex in viscous circular shear flows

The evolution of a weak, highly localized, initial vortex in a steady circular flow is addressed. The effect of basic flow curvature, characterized by the ratio between the Coriolis and inertial forces, on the evolution of the initial vortex is studied. It is shown that the vortex remains weak throughout its entire evolution, although in a certain range of orientation angles of the initial vortex plane there occurs a transient algebraic growth of intensity of the vortex characterized by the value of its total enstrophy. Special attention is devoted to comparison of the results obtained with the experimental results reported by Malkiel, Levinski, and Cohen (1999) where the evolution of artificially synthesized localized vortices in a laminar Taylor–Couette flow was investigated. In particular, it was found that the orientation of the plane of vortex localization predicted by the theoretical model differs from the one observed in the experiment. However, the agreement between the theoretical model and experimental results is expected to be sufficiently better for strong initial vortices. The results of direct numerical simulation of the vortex evolution in a plane flow with constant velocity shear, reported recently by Suponitsky et al. (2003, 2004) show promise of achieving this objective. The analytical expression, obtained in this paper for a weak vortex, may serve as a good test for such a numerical simulation of the evolution of strong vortices in a circular flow.

CFD simulation of aggregation and breakage processes in laminar Taylor–Couette flow

An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of ∼ 10 μm latex spheres suspended in an aqueous solution undergoing laminar Taylor–Couette flow was carried out according to the following program. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method) and with predictions using spatial average shear rates. The mean particle size evolution predicted by CFD and QMOM using appropriate kinetic expressions that incorporate information concerning the particle morphology (fractal dimension) and the local fluid viscous effects on aggregation collision efficiency match well with the experimental data.

Flow between two coaxial rotating cylinders with a highly water‐repellent wall

AbstractThe torque and velocity profile of a flow between two coaxial cylinders with a highly water‐repellent wall were measured experimentally. Two kinds of highly repellent wall were tested to clarify the surface condition effect of the cylinder on laminar drag reduction with fluid slip. The results of torque measurement showed that laminar drag reduction does not occur for a highly water‐repellent wall with no fine grooves at the wall surface. Fluid slip of Newtonian fluids was clarified by measuring the velocity profile close to the highly water‐repellent wall in a Couette flow by a tracer method for flow visualization. The maximum slip velocity is less than 20% of the wall velocity of the rotating inner cylinder. The result of the drag reduction ratio for the torque was calculated by applying to the slip velocity, and agrees with the experimental result quantitatively. Consequently, the gas trapped in the fine grooves plays an important role in laminar drag reduction with respect to fluid slip. From the flow visualization of laminar Taylor–Couette flow, the intervals of Taylor cells become slightly irregular in the case of the cylinder with a highly water‐repellent wall. The calculation result for the Taylor cell applying the fluid slip boundary condition agrees with the experimental result.

Détermination expérimentale de l'efficacité de coalescence

An experimental method is presented to determine the coalescence efficiency of a liquid-liquid dispersion. A laminar Taylor-Couette flow is choised as reference flow. The Sauter diameter of the dispersion is measured with a turbidimetric probe. The coalescence efjiciency is deduced of a physical code. The hydrodynamic diffusivity of dispersed population is calculed with complementaries video experiments.

Stokes Modes in Taylor-Couette Geometry

Abstract The eigenvalue problem of the Stokes operator is solved for an incompressible fluid contained between two coaxial cylinders of infinite height. Flow field patterns and spectra of the eigenmodes ("Stokes modes") are offered. Furthermore, in finite dimensional subspaces generated by these Stokes modes, the eigenproblem for the Navier-Stokes operator linearized about the laminar Taylor-Couette flow is studied. Although the spectrum's qualitative features are still correct, we quantitatively obtain wrong results. We trace this back to a Gibbs like phenomenon of higher order derivatives of the flow field as probable source, since the Stokes modes do not reflect the discontinuity arising from different velocities at both cylinders

The appearance of vortices in the flow of helium II between rotating cylinders

We argue that the appearance of quantized vortices in laminar Taylor-Couette flow of helium II is a problem for which free energy minimization should give valid results even in the presence of dissipation. We (approximately) reduce the problem to an equivalent problem in solid-body rotation, for which the solution for the low-lying states has been obtained by Fetter. We then use approximations to the solution for solid-body rotation to predict the appearance of vortices for the general Taylor-Couette problem. These results compare moderately well with the existing data, which now seem relatively incomplete.