Stability of the Base Flow to Axisymmetric and Plane-Polar Disturbances in an Electrically Driven Flow Between Infinitely-Long, Concentric Cylinders

2000 ◽  
Vol 123 (1) ◽  
pp. 31-42
Author(s):  
J. Liu ◽  
G. Talmage ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Axial Magnetic Field ◽  
Normal Modes ◽  
Azimuthal Velocity ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Electrically Conducting ◽  
Concentric Cylinders ◽  
The Stability

The method of normal modes is used to examine the stability of an azimuthal base flow to both axisymmetric and plane-polar disturbances for an electrically conducting fluid confined between stationary, concentric, infinitely-long cylinders. An electric potential difference exists between the two cylinder walls and drives a radial electric current. Without a magnetic field, this flow remains stationary. However, if an axial magnetic field is applied, then the interaction between the radial electric current and the magnetic field gives rise to an azimuthal electromagnetic body force which drives an azimuthal velocity. Infinitesimal axisymmetric disturbances lead to an instability in the base flow. Infinitesimal plane-polar disturbances do not appear to destabilize the base flow until shear-flow transition to turbulence.

THE STAEILITY OF COUETTE FLOW IN AN AXIAL MAGNETIC FIELD

1958 ◽  
Vol 36 (11) ◽  
pp. 1509-1525 ◽  
Author(s):  
E. R. Niblett
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Theoretical Prediction ◽  
Viscous Flow ◽  
Rotation Speed ◽  
Axial Magnetic Field ◽  
Radioactive Isotopes ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability

Chandrasekhar's theory of the stability of viscous flow of an electrically conducting fluid between coaxial rotating cylinders with perfectly conducting walls is extended to include the case of non-conducting walls, and it is found that their effect is to reduce the critical Taylor numbers and increase the wavelength of the instability patterns by considerable amounts. An experiment designed to measure the values of magnetic field and rotation speed at the onset of instability in mercury between perspex cylinders is described. The radioactive isotopes Hg197 and Hg203 were used to trace the flow. The results support the theoretical prediction that the boundary conditions can have a large effect on the motion.

The stability of hydromagnetic Couette flow

1964 ◽  
Vol 60 (3) ◽  
pp. 635-651 ◽  
Author(s):  
P. H. Roberts
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Conducting Fluid ◽  
Theoretical Studies ◽  
Numerical Computations ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability ◽  
Gap Width

AbstractThe theoretical studies of Chandrasekhar on the stability of Couette flow in a viscous, electrically conducting, fluid in the presence of a uniform axial magnetic field are extended to include cases of finite gap width between the cylinders, and cases in which the conductivity of the walls of the containing cylinders is finite. In addition, the non-axisymmetric modes of instability are discussed, and the results of numerical computations are presented.

Hydromagnetic Stability of Current-Induced Flow in a Small Gap Between Concentric Cylinders

1999 ◽  
Vol 121 (3) ◽  
pp. 548-554 ◽  
Author(s):  
Min-Hsing Chang ◽  
Cha’o-Kuang Chen
Keyword(s):  
Magnetic Field ◽  
Secondary Flow ◽  
Axial Magnetic Field ◽  
Experimental Studies ◽  
Numerical Procedure ◽  
Axial Direction ◽  
Electrically Conducting ◽  
Concentric Cylinders ◽  
Weakly Conducting ◽  
Induced Flow

A linear stability analysis has been carried out for hydromagnetic current-induced flow. A viscous electrically conducting fluid between concentric cylinders is driven electromagnetically by the interaction of a superimposed radial current and a uniform axial magnetic field. The assumption of small-gap approximation is made and the governing equations with respect to nonaxisymmetric disturbances are derived and solved by a direct numerical procedure. Both of the two different types of boundary conditions, namely ideally conducting and weakly conducting walls, are considered. For 0 ≤ Q ≤ 5000, where Q is the Hartmann number, which represents the strength of magnetic field in the axial direction, it is found that the instability sets in as a steady secondary flow for the case of weakly conducting walls but not for ideally conducting walls. For ideally conducting walls, it is demonstrated that the onset mode is due to nonaxisymmetric rather than axisymmetric disturbances as Q exceeds a certain critical value. The transition of the onset of instability from axisymmetric modes to nonaxisymmetric modes is discussed in detail and the possibility of axisymmetric oscillatory modes is examined. The values of the radial current density required for the appearance of secondary flow are also determined. Furthermore, the predictions of present numerical results are found to be in agreement with previous experimental studies.

scholarly journals Thermal convection of dusty compressible Rivlin-Ericksen viscoelastic fluid with hall currents

2012 ◽  
Vol 16 (1) ◽  
pp. 177-192 ◽  
Author(s):  
Urvashi Gupta ◽  
Parul Aggarwal ◽  
Kumar Wanchoo
Keyword(s):  
Magnetic Field ◽  
Thermal Instability ◽  
Normal Modes ◽  
Suspended Particles ◽  
Stationary Convection ◽  
Viscoelastic Parameter ◽  
Electrically Conducting ◽  
Stabilizing Effect ◽  
The Stability ◽  
Rayleigh Numbers

An investigation is made on the effect of Hall currents and suspended particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico-viscous fluid. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of hydromagnetic equations. A dispersion relation governing the effects of viscoelasticity, magnetic field, Hall currents, compressibility and suspended particles is derived. For the stationary convection Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. Compressibility and magnetic field are found to have a stabilizing effect on the system whereas Hall currents and suspended particles hasten the onset of thermal instability. These analytic results are confirmed numerically and the effects of various parameters on the stability parameter are depicted graphically. The critical Rayleigh numbers and the wavenumbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, suspended particles and Hall currents which were not existing in the absence of these parameters.

Magnetohydrodynamic lubrication flow between parallel rotating disks

1962 ◽  
Vol 13 (1) ◽  
pp. 21-32 ◽  
Author(s):  
W. F. Hughes ◽  
R. A. Elco
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Load Capacity ◽  
Electrical Energy ◽  
Axial Current ◽  
Frictional Torque ◽  
Rotating Disks ◽  
Radial Magnetic Field ◽  
Electrically Conducting ◽  
Parallel Disks

The motion of an electrically conducting, incompressible, viscous fluid in the presence of a magnetic field is analyzed for flow between two parallel disks, one of which rotates at a constant angular velocity. The specific application to liquid metal lubrication in thrust bearings is considered. The two field configurations discussed are: an axial magnetic field with a radial current and a radial magnetic field with an axial current. It is shown that the load capacity of the bearing is dependent on the MHD interactions in the fluid and that the frictional torque on the rotor can be made zero for both field configurations by supplying electrical energy through the electrodes to the fluid.

scholarly journals High-speed shear-driven dynamos. Part 1. Asymptotic analysis

2019 ◽  
Vol 868 ◽  
pp. 176-211 ◽  
Author(s):  
Kengo Deguchi
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Solar Phys ◽  
Wave Interaction ◽  
Resonant Absorption ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Alfven Wave ◽  
Hydrodynamic Theory ◽  
Large Reynolds Number

Rational large Reynolds number matched asymptotic expansions of three-dimensional nonlinear magneto-hydrodynamic (MHD) states are the concern of this contribution. The nonlinear MHD states, assumed to be predominantly driven by a unidirectional shear, can be sustained without any linear instability of the base flow and hence are responsible for subcritical transition to turbulence. Two classes of nonlinear MHD states are found. The first class of nonlinear states emerged out of a nice combination of the purely hydrodynamic vortex/wave interaction theory by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) and the resonant absorption theories on Alfvén waves, developed in the solar physics community (e.g. Sakurai et al. Solar Phys., vol. 133, 1991, pp. 227–245; Goossens et al. Solar Phys., vol. 157, 1995, pp. 75–102). Similar to the hydrodynamic theory, the mechanism of the MHD states can be explained by the successive interaction of the roll, streak and wave fields, which are now defined both for the hydrodynamic and magnetic fields. The derivation of this ‘vortex/Alfvén wave interaction’ state is rather straightforward as the scalings for both of the hydrodynamic and magnetic fields are identical. It turns out that the leading-order magnetic field of the asymptotic states appears only when a small external magnetic field is present. However, it does not mean that purely shear-driven dynamos are not possible. In fact, the second class of ‘self-sustained shear-driven dynamo theory’ shows a magnetic generation that is slightly smaller in size in the absence of any external field. Despite its small size, the magnetic field causes the novel feedback mechanism in the velocity field through resonant absorption, wherein the magnetic wave becomes more strongly amplified than the hydrodynamic counterpart.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

An exact solution in the stability of m. h. d. Couette flow

1972 ◽  
Vol 327 (1569) ◽  
pp. 269-278 ◽  
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Couette Flow ◽  
Stability Problem ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Mhd Stability ◽  
Arbitrary Magnetic Field ◽  
The Stability ◽  
Conducting Cylinders

The MHD stability problem for dissipative Couette flow in a narrow gap between corotating, conducting cylinders with an axial magnetic field is solved exactly. Results are presented for an arbitrary magnetic field; in particular, previous results on the zero and infinite magnetic field limits are verified.

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.

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