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.

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.

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.

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.

scholarly journals Ion energy increase in laser-generated plasma expanding through axial magnetic field trap

2007 ◽  
Vol 25 (3) ◽  
pp. 453-464 ◽  
Author(s):  
L. Torrisi ◽  
D. Margarone ◽  
S. Gammino ◽  
L. Andò
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electric Fields ◽  
Axial Magnetic Field ◽  
Ion Beam ◽  
High Vacuum ◽  
Target Surface ◽  
Axial Direction ◽  
Ion Interactions ◽  
The Magnetic Field

Laser-generated plasma is obtained in high vacuum (10−7 mbar) by irradiation of metallic targets (Al, Cu, Ta) with laser beam with intensities of the order of 1010 W/cm2. An Nd:Yag laser operating at 1064 nm wavelength, 9 ns pulse width, and 500 mJ maximum pulse energy is used. Time of flight measurements of ion emission along the direction normal to the target surface were performed with an ion collector. Measurements with and without a 0.1 Tesla magnetic field, directed along the normal to the target surface, have been taken for different target-detector distances and for increasing laser pulse intensity. Results have demonstrated that the magnetic field configuration creates an electron trap in front of the target surface along the axial direction. Electric fields inside the trap induce ion acceleration; the presence of electron bundles not only focuses the ion beam but also increases its energy, mean charge state and current. The explanation of this phenomenon can be found in the electric field modification inside the non-equilibrium plasma because of an electron bunching that increases the number of electron-ion interactions. The magnetic field, in fact, modifies the electric field due to the charge separation between the clouds of fast electrons, many of which remain trapped in the magnetic hole, and slow ions, ejected from the ablated target; moreover it increases the number of electron-ion interactions producing higher charge states.

scholarly journals Thermal diffusion in a binary fluid mixture flows due to a rotating disc of uniform high suction in presence of a weak axial magnetic field

2010 ◽  
Vol 37 (3) ◽  
pp. 161-187
Author(s):  
B.R. Sharma ◽  
R.N. Singh
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Rotating Disc ◽  
Fluid Mixture ◽  
Suction Parameter ◽  
Electrically Conducting ◽  
Flow Parameters ◽  
Polar Coordinate ◽  
Dimensional Parameters ◽  
High Suction

The effect of a weak uniform axial magnetic field on separation of a binary mixture of incompressible viscous thermally and electrically conducting fluids flowing due to a rotating disc of uniform high suction is examined. Neglecting the induced electric field the equations governing the motion, temperature and concentration are solved in cylindrical polar coordinate by expanding the flow parameters as well as the temperature and the concentration in powers of suction parameter. The solution obtained for concentration distribution is plotted against the different axial distances from the disc for various values of non-dimensional parameters. It is found that the temperature gradient, axial magnetic field, Reynolds number, Schmidt number, Prandtl number and suction parameter effect the species separation significantly.

scholarly journals On the Hydromagnetic Stability of a Rotating Fluid Annulus

2010 ◽  
Vol 2 (2) ◽  
pp. 250-256
Author(s):  
H. A. Jasmine
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Velocity Component ◽  
Axial Direction ◽  
Inner Product ◽  
Rotating Fluid ◽  
Concentric Cylinders ◽  
Swirl Velocity ◽  
Product Method ◽  
Mhd Stability

The linear stability of a rotating fluid  in  the annulus  between two concentric cylinders is investigated in the presence of a magnetic field  which is  azimuthal as well as in axial direction. Several results of MHD stability have been derived by using the inner product method. It is shown that when the swirl velocity component is large, the hydromagnetic effects become small compared with those due to swirl. The presence of a velocity field and imposed magnetic field will lead to the basic state to more stability. Keywords: Hydromagnetic Stability; Rotating Fluid. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.3945                 J. Sci. Res. 2 (2), 250-256 (2010) 

Hydromagnetic spin-up of a fluid confined by two flat electrically conducting boundaries

1971 ◽  
Vol 50 (3) ◽  
pp. 609-623 ◽  
Author(s):  
David E. Loper
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Arbitrary Field ◽  
Plate Interface ◽  
Magnetic Diffusion ◽  
Electrically Conducting ◽  
Single Plate ◽  
Electrically Conducting Fluid ◽  
Special Cases ◽  
Plate Analysis

The prototype linear spin-up problem consisting of a homogeneous viscous electrically conducting fluid confined between two infinite flat rotating electrically conducting plates in the presence of an applied axial magnetic field is studied in an effort to understand better the strength and nature of the coupling between a fluid and its rotating conducting container. It is assumed that the response time of the bounding plates to a magnetic perturbation is much less than the fluid spin-up time and that the plate conductivity is an arbitrary function of distance from the fluid-plate interface. The general Laplace transform solution is inverted and discussed for three special cases: magnetic diffusion regions thick compared with fluid depth during spin-up, arbitrary magnetic field strength and boundary conductance; magnetic diffusion regions thin, weak conductance, arbitrary field; magnetic diffusion regions thin, strong conductance, arbitrary field. In each case conductance of the boundary strengthens the coupling between fluid and boundary, thereby decreasing the spin-up time. The corresponding single plate analysis of Loper (1970a) is found to predict spin-up accurately only if the boundary conductance is much smaller than that of the fluid. The fluid possesses an oscillatory mode of spin-up if the magnetic diffusion regions are thin and boundary conductance is large. That is, the inviscid current-free core of fluid rotates significantly faster than the boundaries during a portion of the spin-up process.

Stability of hydromagnetic dissipative Couette flow with non-axisymmetric disturbance

1998 ◽  
Vol 366 ◽  
pp. 135-158 ◽  
Author(s):  
CHA'O-KUANG CHEN ◽  
MIN HSING CHANG
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Hartmann Number ◽  
Axial Magnetic Field ◽  
Outer Cylinder ◽  
Numerical Procedure ◽  
Stationary Mode ◽  
Instability Modes ◽  
Wide Range ◽  
Axisymmetric Instability

A linear stability analysis has been implemented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field. The small-gap equations with respect to non-axisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of boundary conditions, conducting and non-conducting walls, are considered. A parametric study covering wide ranges of μ, the ratio of angular velocity of the outer cylinder to that of inner cylinder, and Q, the Hartmann number which represents the strength of axial magnetic field, is conducted. Results show that the stability characteristics depend on the conductivity of the cylinders. For the case of non-conducting walls, it is found that the critical disturbance is a non-axisymmetric mode as the value of μ is sufficiently negative and the domain of Q where non-axisymmetric instability modes prevail is limited. Similar results are obtained for conducting walls at low Hartmann number. In addition, the transition of the onset of instability from non-axisymmetric modes to axisymmetric modes for the case μ=−1 with increasing strength of magnetic field are discussed in detail. For high values of the Hartmann number, the critical disturbance is always the axisymmetric stationary mode for non-conducting walls but not for conducting walls. For −1[les ]μ<1, it is demonstrated that non-axisymmetric instability modes prevail in a wide range of Q for conducting walls and axisymmetric oscillatory modes may, in fact, become more critical than both of the non-axisymmetric and axisymmetric stationary modes at higher values of the Hartmann number.

The cut-off characteristic of the single anode magnetron

1939 ◽  
Vol 35 (4) ◽  
pp. 637-651
Author(s):  
A. F. Harvey
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Axial Magnetic Field ◽  
Present Discussion ◽  
A Value ◽  
Field Parallel ◽  
Concentric Cylinders ◽  
Image Position ◽  
The Magnetic Field

For the purpose of the present discussion the magnetron will be defined as a diode thermionic tube, having concentric cylinders as electrodes, in which there is a uniform magnetic field parallel to the axis of the electrodes. An electron emitted from the cathode travels towards the anode in a path which is bent by the action of the magnetic field. If the anode has radius a and is at potential V with respect to the cathode of radius b, then it is well known that electrons emitted without velocity from the cathode will just graze the anode when the uniform and axial magnetic field has a value H such that

scholarly journals Thermoelectric precession in turbulent magnetoconvection

2021 ◽  
Vol 930 ◽  
Author(s):  
Yufan Xu ◽  
Susanne Horn ◽  
Jonathan M. Aurnou
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Axial Magnetic Field ◽  
Liquid Gallium ◽  
Magnetic Field Direction ◽  
Thermoelectric Effects ◽  
Mixing Processes ◽  
Electrically Conducting ◽  
Precessional Motion ◽  
Cylindrical Volume

We present laboratory measurements of the interaction between thermoelectric currents and turbulent magnetoconvection. In a cylindrical volume of liquid gallium heated from below and cooled from above and subject to a vertical magnetic field, it is found that the large-scale circulation (LSC) can undergo a slow axial precession. Our experiments demonstrate that this LSC precession occurs only when electrically conducting boundary conditions are employed, and that the precession direction reverses when the axial magnetic field direction is flipped. A thermoelectric magnetoconvection (TEMC) model is developed that successfully predicts the zeroth-order magnetoprecession dynamics. Our TEMC magnetoprecession model hinges on thermoelectric current loops at the top and bottom boundaries, which create Lorentz forces that generate horizontal torques on the overturning large-scale circulatory flow. The thermoelectric torques in our model act to drive a precessional motion of the LSC. This model yields precession frequency predictions that are in good agreement with the experimental observations. We postulate that thermoelectric effects in convective flows, long argued to be relevant in liquid metal heat transfer and mixing processes, may also have applications in planetary interior magnetohydrodynamics.

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