THE INFLUENCE OF SLIP AND JUMP BOUNDARY CONDITIONS ON THE CYLINDRICAL COUETTE FLOW

2002 ◽  
Vol 12 (03) ◽  
pp. 445-459 ◽  
Author(s):  
LILIANA M. GRAMANI CUMIN ◽  
GILBERTO M. KREMER ◽  
FELIX SHARIPOV
Keyword(s):  
Angular Velocity ◽  
Boundary Conditions ◽  
Couette Flow ◽  
Rarefied Gas ◽  
Thermodynamic Force ◽  
Heat Conducting ◽  
Field Equations ◽  
Viscous Stress Tensor ◽  
Heat Flux Vector ◽  
Cylindrical Couette Flow

The solution of the field equations of the cylindrical Couette flow problem for a rarefied gas is found when the state of equilibrium between the cylinders is perturbed by the following small thermodynamic forces: (i) a pressure difference; (ii) an angular velocity difference; and (iii) a temperature difference. The flow is analyzed within the framework of continuum mechanics by using the field equations that follow from the balance equations of mass, momentum and energy of a viscous and heat conducting gas. These equations are solved analytically by considering slip and jump boundary conditions. The fields of density, velocity, temperature, heat flux vector and viscous stress tensor are calculated as functions of the Knudsen number and of the angular velocity of the rotating cylinders for each thermodynamic force. The asymptotic behaviors of these fields are compared with those obtained from a kinetic model of the Boltzmann equation. The influence of the slip and jump boundary conditions on the solutions is also discussed.

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.

Cylindrical Couette Flow of a Rarefied Gas

1967 ◽  
Vol 10 (6) ◽  
pp. 1200 ◽  
Author(s):  
Carlo Cercignani
Keyword(s):  
Couette Flow ◽  
Rarefied Gas ◽  
Cylindrical Couette Flow

The cylindrical couette flow of a rarefied gas consisting of charged particles inside walls with arbitrary reflection coefficients

1991 ◽  
Vol 69 (12) ◽  
pp. 1429-1440
Author(s):  
M. A. Mahmoud ◽  
G. A. Shalaby
Keyword(s):  
Shear Stress ◽  
Distribution Function ◽  
Reflection Coefficient ◽  
Couette Flow ◽  
Method Of Moments ◽  
Rarefied Gas ◽  
Charged Particles ◽  
Reflection Coefficients ◽  
Model Kinetic Equation ◽  
Cylindrical Couette Flow

A kinetic-theory treatment of the cylindrical Couette flow is considered. A generalization of the case of a surface with an arbitrary reflection coefficient that depends on the nature of the surface. In this paper we consider that the reflection coefficients of the inner and outer walls are different. A model kinetic equation of the BGK (Bhatnger–Gross–Krook) type is solved using the method of moments with a two-sided distribution function. The dependence of the velocity and shear stress on the reflection coefficient is obtained.

Upper bounds on the torque in cylindrical Couette flow

1969 ◽  
Vol 38 (4) ◽  
pp. 807-815 ◽  
Author(s):  
E. C. Nickerson
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Couette Flow ◽  
Qualitative Agreement ◽  
Upper Bounds ◽  
Parameter Dependence ◽  
Rotating Cylinders ◽  
Cylindrical Couette Flow ◽  
Asymptotic Parameter

Upper bounds on the torque are derived for a fluid that is contained between two concentric rotating cylinders. Absolute upper bounds are obtained by requiring that the fluid satisfy the boundary conditions and the dissipation integral. Improved bounds are then found by requiring that the fluid satisfy continuity conditions. These bounds are in qualitative agreement with the data in that they reflect the asymptotic parameter dependence in the range of experimental data.

Cylindrical Couette Flow of Rarefied Gas: Comparison between Navier-Stokes and DSMC Computations

2010 ◽  
Author(s):  
P. Gospodinov ◽  
D. Dankov ◽  
V. Roussinov ◽  
S. Stefanov ◽  
Michail D. Todorov ◽  
...  
Keyword(s):  
Couette Flow ◽  
Rarefied Gas ◽  
Navier Stokes ◽  
Cylindrical Couette Flow
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