Linear stability of cylindrical Couette flow in the convection regime

2005 ◽  
Vol 17 (5) ◽  
pp. 054112 ◽  
Author(s):  
Mohamed E. Ali ◽  
G. B. McFadden
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Convection Regime ◽  
Cylindrical Couette Flow

Generalized hydrodynamics and linear stability analysis of cylindrical Couette flow of a dilute Lennard–Jones fluid

1993 ◽  
Vol 71 (11-12) ◽  
pp. 518-536 ◽  
Author(s):  
Roger E. Khayat ◽  
Byung Chan Eu
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Couette Flow ◽  
Linear Stability Analysis ◽  
Hydrodynamic Theory ◽  
Navier Stokes ◽  
Marginal Stability ◽  
Lennard Jones ◽  
Stability Point ◽  
Cylindrical Couette Flow

Linear stability analysis is carried out for cylindrical Couette flow of a Lennard–Jones fluid in the density range from the dense liquid to the dilute gas regime. Generalized hydrodynamic equations are used to calculate marginal stability curves and compare them with those obtained by using the Navier–Stokes–Fourier equations for compressible fluids and also for incompressible fluids. In the low Reynolds or Mach number regime, if the Knudsen number is sufficiently low, the marginal stability curves calculated by the generalized hydrodynamic theory coincide, within numerical errors, with those based on the Navier–Stokes theory. But there are considerable deviations between them in the regimes beyond those mentioned earlier, since nonlinear effects manifest themselves in the laminar mean flow through the nonlinear dissipation term and normal stresses. There are three marginal stability curves obtained in contrast to the Navier–Stokes theory, which yields only two. The previously observed phase-transition-like behavior in fluid variables and the slip phenomenon are found to occur beyond the hydrodynamic stability point. The disturbance entropy production associated with the Taylor–Couette vortices is calculated to first order in disturbances in flow variables and is found to decrease as the number of vortices increases and thereby the dynamic structure is progressively more organized.

On the linear stability of cellular spiral Couette flow

1993 ◽  
Vol 5 (5) ◽  
pp. 1188-1200 ◽  
Author(s):  
Mohamed E. Ali ◽  
P. D. Weidman
Keyword(s):  
Linear Stability ◽  
Couette Flow

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 On the linear stability of compressible plane Couette flow

1994 ◽  
Vol 258 ◽  
pp. 131-165 ◽  
Author(s):  
Peter W. Duck ◽  
Gordon Erlebacher ◽  
M. Yousuff Hussaini
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Small Amplitude ◽  
Reynolds Numbers ◽  
Inviscid Limit ◽  
Plane Couette Flow ◽  
Moving Wall ◽  
Type Boundary ◽  
The Stability ◽  
Radiation Type

The linear stability of compressible plane Couette flow is investigated. The appropriate basic velocity and temperature distributions are perturbed by a small-amplitude normal-mode disturbance. The full small-amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in some detail. It is found that instabilities can occur, although the corresponding growth rates are often quite small; the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wave speed of the disturbances approaches the velocity of either of the walls, and these regimes are also analysed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

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

Turbulent momentum transfer in two-phase cylindrical Couette flow

AIChE Journal ◽  
1971 ◽  
Vol 17 (2) ◽  
pp. 349-352 ◽  
Author(s):  
Ravi Gandhi ◽  
Joseph Estrin
Keyword(s):  
Momentum Transfer ◽  
Couette Flow ◽  
Two Phase ◽  
Cylindrical Couette Flow ◽  
Turbulent Momentum
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