Subcritical transition and spiral turbulence in circular Couette flow

2012 ◽  
Vol 709 ◽  
pp. 106-122 ◽  
Author(s):  
M. J. Burin ◽  
C. J. Czarnocki
Keyword(s):  
Velocity Profile ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Transition To Turbulence ◽  
Coupling Mechanism ◽  
Rotation Rates ◽  
Circular Couette Flow ◽  
Flow Curvature ◽  
Gap Width

AbstractWe present new observations of a controlled transition to turbulence in a fundamental but little-studied regime: circular Couette flow with only the outer cylinder rotating. Our apparatus consists of an outer cylinder of fixed radius and three inner cylinders having different radii that are used interchangeably to study the effect of flow curvature. With the smallest inner cylinder the end-cap configuration (vertical boundary conditions) may also be varied. The turbulent transition is found to be sensitive to both gap width and end-cap configuration, with wider gaps transitioning at higher rotation rates. All configurations are observed to transition with hysteresis and intermittency. A laser Doppler velocimetry (LDV)-based study of the azimuthal velocity profile as a function of gap width and rotation rate reveals that turbulence, once initiated, is confined to regions of significant shear. For wider gap widths, the radial location of these shear layers is determined by the chosen end-cap configuration. This, in turn, affects the transition Reynolds number, which we posit to be radially dependent. The narrow-gap case in particular features spiral turbulence, whose properties are found to be similar to observations of the phenomenon in related shear flows. The velocity profile in this case is correlated with overlapping boundary layers, suggesting a coupling mechanism for the origin of laminar-turbulent banding phenomena.

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

2015 ◽  
Vol 774 ◽  
pp. 342-362 ◽  
Author(s):  
Freja Nordsiek ◽  
Sander G. Huisman ◽  
Roeland C. A. van der Veen ◽  
Chao Sun ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Velocity Profiles ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Angular Momentum Transport ◽  
Taylor Couette ◽  
Taylor Couette Flow

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.

Velocity profiles, flow structures and scalings in a wide-gap turbulent Taylor–Couette flow

2017 ◽  
Vol 831 ◽  
pp. 330-357 ◽  
Author(s):  
A. Froitzheim ◽  
S. Merbold ◽  
C. Egbers
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Cylinder Wall ◽  
Taylor Vortices ◽  
Wide Gap ◽  
Taylor Couette ◽  
Taylor Couette Flow

Fully turbulent Taylor–Couette flow between independently rotating cylinders is investigated experimentally in a wide-gap configuration ($\unicode[STIX]{x1D702}=0.5$) around the maximum transport of angular momentum. In that regime turbulent Taylor vortices are present inside the gap, leading to a pronounced axial dependence of the flow. To account for this dependence, we measure the radial and azimuthal velocity components in horizontal planes at different cylinder heights using particle image velocimetry. The ratio of angular velocities of the cylinder walls $\unicode[STIX]{x1D707}$, where the torque maximum appears, is located in the low counter-rotating regime ($\unicode[STIX]{x1D707}_{max}(\unicode[STIX]{x1D702}=0.5)=-0.2$). This point coincides with the smallest radial gradient of angular velocity in the bulk and the detachment of the neutral surface from the outer cylinder wall, where the azimuthal velocity component vanishes. The structure of the flow is further revealed by decomposing the flow field into its large-scale and turbulent contributions. Applying this decomposition to the kinetic energy, we can analyse the formation process of the turbulent Taylor vortices in more detail. Starting at pure inner cylinder rotation, the vortices are formed and strengthened until $\unicode[STIX]{x1D707}=-0.2$ quite continuously, while they break down rapidly for higher counter-rotation. The same picture is shown by the decomposed Nusselt number, and the range of rotation ratios, where turbulent Taylor vortices can exist, shrinks strongly in comparison to investigations at much lower shear Reynolds numbers. Moreover, we analyse the scaling of the Nusselt number and the wind Reynolds number with the shear Reynolds number, finding a communal transition at approximately $Re_{S}\approx 10^{5}$ from classical to ultimate turbulence with a transitional regime lasting at least up to $Re_{S}\geqslant 2\times 10^{5}$. Including the axial dispersion of the flow into the calculation of the wind amplitude, we can also investigate the wind Reynolds number as a function of the rotation ratio $\unicode[STIX]{x1D707}$, finding a maximum in the low counter-rotating regime slightly larger than $\unicode[STIX]{x1D707}_{max}$. Based on our study it becomes clear that the investigation of counter-rotating Taylor–Couette flows strongly requires an axial exploration of the flow.

Energy stability of modulated circular Couette flow

1977 ◽  
Vol 79 (3) ◽  
pp. 535-552 ◽  
Author(s):  
Peter J. Riley ◽  
Robert L. Laurence
Keyword(s):  
Couette Flow ◽  
Nonlinear Stability ◽  
Energy Analysis ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Initial Energy ◽  
Critical Parameters ◽  
Narrow Gap ◽  
Circular Couette Flow ◽  
The Stability

The stability of circular Couette flow when the outer cylinder is at rest and the inner is modulated both with and without a mean shear is examined in the narrow-gap limit. Disturbances are assumed to be axisymmetric. Two criteria are used to determine conditions for stability; the first requires that the motion be strongly stable, the second only that disturbances of arbitrary initial energy decay from cycle to cycle. The behaviour of critical parameters as a function of frequency is similar for the linear and the energy analysis. The range of Reynolds numbers bounded above by certain instability and below by conditional nonlinear stability is enlarged by modulation.

Azimuthal velocity in supercritical circular Couette flow

1994 ◽  
Vol 18-18 (1-2) ◽  
pp. 1-9 ◽  
Author(s):  
S. T. Wereley ◽  
R. M. Lueptow
Keyword(s):  
Couette Flow ◽  
Azimuthal Velocity ◽  
Circular Couette Flow

Cylindrical Couette Flow of a Rarefied Gas From Macro- to Micro-Scales

2009 ◽  
Author(s):  
Sheng Wang ◽  
Kangbin Lei ◽  
Xilian Luo ◽  
Kiwamu Kase ◽  
Elia Merzari ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Velocity Profile ◽  
Couette Flow ◽  
Knudsen Number ◽  
Rarefied Gas ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Flow Field Characteristics ◽  
Dimensional Parameters

The cylindrical Couette flow of a rarefied gas from macro- to micro-scales, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest, is extensively investigated by direct simulation Monte Carlo (DSMC) code incorporated with a Volume-CAD software. The generalized soft sphere (GSS) model is applied to an intermolecular collision calculation. The diffuse reflection model and Cercignani-Lampis-Lord (CLL) model are used to model the molecule-surface interaction by considering the accommodation coefficients on inner cylinder (ACI hereafter) and outer cylinder (ACO hereafter) separately. The contents in this paper include following three aspects: I the flow field characteristics and force and torque on inner cylinder for eccentric Couette flow between different scales with same non-dimensional parameters (accommodation coefficients, eccentricity-clearance ratio, Knudsen number and Reynolds number) are compared; the flow field characteristics for different scales are same; with the increase of the scale, the total force on the inner cylinder increases slightly, while the torque is proportional to the scale; II the velocity profiles in concentric Couette flow under different non-dimensional parameters are studied; the result shows that the phenomenon of inverted velocity profile in the concentric Couette flow is only induced by a smooth outer cylinder; the non-dimensional tangential velocity, as well as its gradient is high at low Reynolds number; the Knudsen number has great impact on the tangential velocity profile, and the velocity profile may not be inverted in the case of low Knudsen number; III the flow field characteristics in eccentric Couette flow under different non-dimensional parameters are obtained; the recirculation zone may not appear when Knudsen number is high; the position of its center may be different depending on Reynolds number; with the increase of Reynolds number, the compressibility effect becomes important; stratified distribution of the density becomes obvious at low Knudsen number.

Stratified circular Couette flow: instability and flow regimes

1995 ◽  
Vol 292 ◽  
pp. 333-358 ◽  
Author(s):  
B. M. Boubnov ◽  
E. B. Gledzer ◽  
E. J. Hopfinger
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Couette Flow ◽  
Flow Instability ◽  
Buoyancy Frequency ◽  
Vertical Wavelength ◽  
Taylor Vortices ◽  
Circular Couette Flow ◽  
Vortex Size ◽  
Gap Width

The stability conditions of the flow between two concentric cylinders with the inner one rotating (circular Couette flow) have been investigated experimentally and theoretically for a fluid with axial, stable linear density stratification. The behaviour of the flow, therefore, depends on the Froude number Fr = Ω/N (where Ω is the angular velocity of the inner cylinder and N is the buoyancy frequency of the fluid) in addition to the Reynolds number and the non-dimensional gap width ε, here equal to 0.275.Experiments show that stratification has a stabilizing effect on the flow with the critical Reynolds number depending on N, in agreement with linear stability theory. The selected, most amplified, vertical wavelength at onset of instability is reduced by the stratification effect and is for the geometry considered only about half the gap width. Furthermore, the observed instability is non-axisymmetric. The resulting vortex motion causes some mixing and this leads to layer formation, clearly visible on shadowgraph images, with the height of the layer being determined by the vertical vortex size. This regime of vertically reduced vortex size is referred to as the S-regime.For larger Reynolds and Froude numbers the role of stratification decreases and the most amplified vertical wavelength is determined by the gap width, giving rise to the usual Taylor vortices (we call this the T-regime). The layers which emerge are determined by these vortices. For relatively small Reynolds number when Fr ≈ 1 the Taylor vortices are stable and the layers have a height h equal to the gap width; for larger Reynolds number or Fr ≈ 2 the Taylor vortices interact in pairs (compacted Taylor vortices, regime CT) and layers of twice the gap width are predominant. Stratification inhibits the azimuthal wavy vortex flow observed in homogeneous fluid. By further increasing the Reynolds number, turbulent motions appear with Taylor vortices superimposed like in non-stratified fluid.The theoretical analysis is based on a linear stability consideration of the axisymmetric problem. This gives bounds of instability in the parameter space (Ω, N) for given vertical and radial wavenumbers. These bounds are in qualitative agreement with experiments. The possibility of oscillatory-type instability (overstability) observed experimentally is also discussed.

Spontaneous layering in stratified turbulent Taylor–Couette flow

2013 ◽  
Vol 721 ◽  
Author(s):  
R. L. F. Oglethorpe ◽  
C. P. Caulfield ◽  
Andrew W. Woods
Keyword(s):  
Couette Flow ◽  
Outer Cylinder ◽  
Buoyancy Frequency ◽  
Number Of Layers ◽  
Asymptotic Constant ◽  
Inner Radius ◽  
Velocity Scale ◽  
Taylor Couette ◽  
Gap Width ◽  
Taylor Couette Flow

AbstractWe conduct a series of laboratory experiments to study the mixing of an initially linear stratification in turbulent Taylor–Couette flow. We vary the inner radius, ${R}_{1} $, and rotation rate, $\Omega $, relative to the fixed outer cylinder, of radius ${R}_{2} $, as well as the initial buoyancy frequency ${N}_{0} = \sqrt{(- g/ \rho )\partial \rho / \partial z} $. We find that a linear stratification spontaneously splits into a series of layers and interfaces. The characteristic height of these layers is proportional to ${U}_{H} / {N}_{0} $, where ${U}_{H} = \sqrt{{R}_{1} { \mathrm{\Delta} }_{R} } \Omega $ is a horizontal velocity scale, with ${ \mathrm{\Delta} }_{R} = {R}_{2} - {R}_{1} $ the gap width of the annulus. The buoyancy flux through these layers matches the equivalent flux through a two-layer stratification, independently of the height or number of layers. For a strongly stratified flow, the flux tends to an asymptotic constant value, even when multiple layers are present, consistent with Woods et al. (J. Fluid Mech., vol. 663, 2010, pp. 347–357). For smaller stratification the flux increases, reaching a maximum just before the layers disappear due to overturning of the interfaces.

Linear stability of modulated circular Couette flow

1976 ◽  
Vol 75 (4) ◽  
pp. 625-646 ◽  
Author(s):  
P. J. Riley ◽  
R. L. Laurence
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Floquet Theory ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Narrow Gap ◽  
Circular Couette Flow ◽  
Steady Rotation ◽  
The Stability ◽  
Axisymmetric Disturbances

The linear stability of modulated circular Couette flow to axisymmetric disturbances is examined in the narrow-gap limit. The outer cylinder is assumed stationary, while the inner is modulated both with and without a mean rotation. The equations governing the disturbance motion are solved by a Galerkin expansion with time-dependent coefficients, and the stability of the motion determined by Floquet theory. Modulation is found, in general, to destabilize the flow due to steady rotation, although weak stabilization is found for some modulation amplitudes at intermediate frequencies.

On the stability of circular Couette flow with radial heating

1990 ◽  
Vol 220 ◽  
pp. 53-84 ◽  
Author(s):  
Mohamed Ali ◽  
P. D. Weidman
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Boussinesq Approximation ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Critical Stability ◽  
Circular Couette Flow ◽  
Prandtl Numbers ◽  
The Stability

The stability of circular Couette flow with radial heating across a vertically oriented annulus with inner cylinder rotating and outer cylinder stationary is investigated using linear stability theory. Infinite aspect ratio and constant fluid properties are assumed and critical stability boundaries are calculated for a conduction-regime base flow. Buoyancy is included through the Boussinesq approximation and stability is tested with respect to both toroidal and helical disturbances of uniform wavenumber. Symmetries of the linearized disturbance equations based on the sense of radial heating and the sense of cylinder rotation and their effect on the kinematics and morphology of instability waveforms are presented. The numerical investigation is primarily restricted to radius ratios 0.6 and 0.959 at Prandtl numbers 4.35, 15 and 100. The results follow the development of critical stability from Taylor cells at zero heating through a number of asymmetric modes to axisymmetric cellular convection at zero rotation. Increasing the Prandtl number profoundly destabilizes the flow in both wide and narrow gaps and the number of contending critical modes increases with increasing radius ratio. Specific calculations made to compare with the stability measurements of Snyder & Karlsson (1964) and Sorour & Coney (1979) exhibit good agreement considering the idealizations built into the linear stability analysis.

Circular Couette Flow between Porous Cylinders

2005 ◽  
Vol 219 (8) ◽  
pp. 743-747 ◽  
Author(s):  
V. D. Djordjevic
Keyword(s):  
Couette Flow ◽  
Effective Viscosity ◽  
Stokes Equations ◽  
Outer Cylinder ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Circular Couette Flow ◽  
Special Case ◽  
Porous Boundaries ◽  
Porous Cylinders

Circular Couette flow between porous cylinders is treated in this paper. Exact solutions of Navier-Stokes equations for the flow in the gap between cylinders and of Darcy-Brinkman-Lapwood equations for the flow in porous rings are found analytically by matching velocities and stresses on the porous boundaries, without making any previous assumptions concerning the slip velocities. In the special case in which the inner cylinder is fully porous and stationary, and the outer cylinder is fully rigid and rotating, the torque exerted by the rotation of the outer cylinder on the inner one is found, and it is shown how the effective viscosity of the liquid can be determined in possible experiments.

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