Cylindrical Couette flow with fixed outer cylinder: Rarefied effects

2021 ◽  
Vol 33 (9) ◽  
pp. 097111
Author(s):  
A. A. Abramov ◽  
V. Yu. Alexandrov ◽  
A. V. Butkovskii ◽  
O. G. Buzykin
Keyword(s):  
Couette Flow ◽  
Outer Cylinder ◽  
Cylindrical Couette Flow

Stability of modulated finite-gap cylindrical Couette flow: linear theory

1981 ◽  
Vol 108 ◽  
pp. 19-42 ◽  
Author(s):  
S. Carmi ◽  
J. I. Tustaniwskyj
Keyword(s):  
Unsteady Flow ◽  
Couette Flow ◽  
Floquet Theory ◽  
Analytic Solution ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Linear Perturbation ◽  
Cylindrical Couette Flow ◽  
The Stability ◽  
The Galerkin Method

The linear stability of an extensively modulated cylindrical Couette flow is investigated in the finite-gap range. A closed form analytic solution is obtained for the basic unsteady flow after modulation is introduced through the boundary conditions. The general linear perturbation equations for three-dimensional disturbances are then derived and subsequently solved using the Galerkin method with the stability analysed by the Floquet theory. Modulation is found to destabilize the flow in most cases and results compare very favourably with the ones obtained experimentally. Stabilization is possible only for some cases of outer cylinder modulation.

Modeling of Cylindrical Couette Flow of Rarefied Gas. The Case of Rotating Outer Cylinder

2009 ◽  
Author(s):  
P. Gospodinov ◽  
D. Dankov ◽  
V. Roussinov ◽  
S. Stefanov ◽  
Michail D. Todorov ◽  
...  
Keyword(s):  
Couette Flow ◽  
Rarefied Gas ◽  
Outer Cylinder ◽  
Cylindrical Couette Flow

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

scholarly journals A frictional Cosserat model for the slow shearing of granular materials

2002 ◽  
Vol 457 ◽  
pp. 377-409 ◽  
Author(s):  
L. SRINIVASA MOHAN ◽  
K. KESAVA RAO ◽  
PRABHU R. NOTT
Keyword(s):  
Angular Velocity ◽  
Granular Material ◽  
Shear Layer ◽  
Granular Materials ◽  
Layer Thickness ◽  
Couette Flow ◽  
Velocity Fields ◽  
Cosserat Continuum ◽  
Cosserat Model ◽  
Cylindrical Couette Flow

A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.

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.

Cylindrical Couette flow of Laponite dispersions

2018 ◽  
Vol 162 ◽  
pp. 83-89 ◽  
Author(s):  
Marguerite Bienia ◽  
Cyril Danglade ◽  
André Lecomte ◽  
Julien Brevier ◽  
Cécile Pagnoux
Keyword(s):  
Couette Flow ◽  
Cylindrical Couette Flow

scholarly journals Exploring the phase diagram of fully turbulent Taylor–Couette flow

2014 ◽  
Vol 761 ◽  
pp. 1-26 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Phase Diagram ◽  
Reynolds Number ◽  
Couette Flow ◽  
Parameter Space ◽  
Coriolis Force ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Aspect Ratios ◽  
Cylinder Rotation

AbstractDirect numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to $3\times 10^{5}$, corresponding to Taylor numbers of $\mathit{Ta}=4.6\times 10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.

Sign in / Sign up

Export Citation Format

Share Document