scholarly journals On the stability of compressible differentially rotating cylinders

1987 ◽  
Vol 225 (2) ◽  
pp. 227-255 ◽  
Author(s):  
W. Glatzel
Keyword(s):  
Rotating Cylinders ◽  
The Stability

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

The stability of viscous flow between rotating cylinders in the presence of a magnetic field. II

1961 ◽  
Vol 262 (1311) ◽  
pp. 443-454 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Rotating Cylinders ◽  
Counter Rotation ◽  
Angular Velocities ◽  
The Stability

The theory developed in an earlier paper (Chandrasekhar 1953) is extended to allow for counter-rotation of the two cylinders. Explicit results are given for the case when the two cylinders rotate in opposite directions with equal angular velocities.

The stability of elastico-viscous flow between rotating cylinders Part 3. Overstability in viscous and Maxwell fluids

1966 ◽  
Vol 24 (2) ◽  
pp. 321-334 ◽  
Author(s):  
D. W. Beard ◽  
M. H. Davies ◽  
K. Walters
Keyword(s):  
Viscous Flow ◽  
Couette Flow ◽  
Taylor Number ◽  
Linear Perturbation ◽  
Rotating Cylinders ◽  
Initial Value ◽  
Viscous Liquids ◽  
Maxwell Fluids ◽  
Newtonian Liquids ◽  
The Stability

Consideration is given to the possibility of overstability in the Couette flow of viscous and elastico-viscous liquids. The relevant linear perturbation equations are solved numerically using an initial-value technique. It is shown that over-stability is not possible in the case of Newtonian liquids for the cases considered. In contrast, overstability is to be expected in the case of moderately-elastic Maxwell liquids. The Taylor number associated with the overstable mode decreases steadily as the amount of elasticity in the liquid increases, and it is concluded that highly elastic Maxwell liquids can be very unstable indeed.

The effect of a radial magnetic field on the stability of Couette flow

1994 ◽  
Vol 72 (5-6) ◽  
pp. 258-265 ◽  
Author(s):  
M. A. Ali
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problem ◽  
Incompressible Fluid ◽  
Couette Flow ◽  
Wave Number ◽  
Rotating Cylinders ◽  
Radial Magnetic Field ◽  
Electrically Conducting ◽  
Angular Velocities ◽  
The Stability

The effect of a radial magnetic field on the stability of an electrically conducting incompressible fluid between two concentric rotating cylinders is considered. The eigenvalue problem for determining the critical Taylor number TC and the corresponding wave number aC is solved numerically for different values of ±μ(= Ω2/Ω1), (where Ω1, and Ω2 are me angular velocities of the inner and outer cylinders, respectively) and for different gap sizes. It is observed that the radial magnetic field stabilizes the flow. This effect is more pronounced for cylinders that are corotating as compared with counter-rotating cylinders or the situation where only the inner one is rotating.

The stability of Couette flow of certain anisotropic fluids

1964 ◽  
Vol 60 (4) ◽  
pp. 949-955 ◽  
Author(s):  
F. M. Leslie
Keyword(s):  
Steady State ◽  
Couette Flow ◽  
Steady State Solution ◽  
State Solution ◽  
Rotating Cylinders ◽  
Important Conclusion ◽  
Preferred Direction ◽  
The Stability ◽  
Anisotropic Fluids

AbstractThe stability of the flow between concentric, rotating cylinders is discussed when the gap is small and the cylinders are rotating in the same direction for a class of anisotropic fluids in which the fluid has a preferred direction. An important conclusion of the analysis is that a steady-state solution of the equations has previously been considered unstable on false grounds.

On the stability of viscous flow between rotating cylinders Part 2. Numerical analysis

1964 ◽  
Vol 20 (1) ◽  
pp. 95-101 ◽  
Author(s):  
D. L. Harris ◽  
W. H. Reid
Keyword(s):  
Numerical Analysis ◽  
Eigenvalue Problem ◽  
Viscous Flow ◽  
Numerical Method ◽  
Couette Flow ◽  
Stream Function ◽  
Oscillatory Behaviour ◽  
Rotating Cylinders ◽  
The Stability

A simple numerical method is presented for solving the eigenvalue problem which governs the stability of Couette flow. The method is particularly useful in obtaining the eigenfunctions associated with the various modes of instability. When the cylinders rotate in opposite directions, these eigenfunctions exhibit an exponentially damped oscillatory behaviour for sufficiently large values of − μ, where μ = Ω2/Ω1. In terms of the stream function which describes the motion in planes through the axis of the cylinders, this means that weak, viscously driven cells appear in the outer layes of the fluid which, according to Rayleigh's criterion, are dynamically stable. For μ = − 3, for example, four cells are present, the amplitudes of which are in the ratios 1·0:0·0172:0·013:0·00125.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

On flow between counter-rotating cylinders

1982 ◽  
Vol 120 ◽  
pp. 433-450 ◽  
Author(s):  
C. A. Jones
Keyword(s):  
Radius Ratio ◽  
Rotating Cylinders ◽  
The Stability ◽  
Axisymmetric Disturbances

Axisymmetric flows between counter-rotating cylinders of varying radius ratio are examined. The stability of these flows to non-axisymmetric disturbances is considered, and the results of these calculations are compared with experiments.

Stability of spiral flow between concentric circular cylinders at low axial Reynolds number

1965 ◽  
Vol 21 (4) ◽  
pp. 635-640 ◽  
Author(s):  
Subhendu K. Datta
Keyword(s):  
Reynolds Number ◽  
Perturbation Theory ◽  
Viscous Liquid ◽  
Axial Flow ◽  
Circular Cylinders ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
The Stability

The stability of a viscous liquid between two concentric rotating cylinders with an axial flow has been investigated. Attention has been confined to the case when the cylinders are rotating in the same direction, the gap between the cylinders is small and the axial flow is small. A perturbation theory valid in the limit when the axial Reynolds number R → 0 has been developed and corrections have been obtained for Chandrasekhar's earlier results.

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