Showing papers on "Hartmann number published in 1969"

Electrohydrodynamic Charge Relaxation and Interfacial Perpendicular‐Field Instability

Abstract: The small‐amplitude motions of a plane interface between two fluids stressed by an initially perpendicular electric field are investigated. The fluids are modeled as Ohmic conductors and the convection of the surface charge caused by the dynamic interplay of interfacial electric shear stresses and the viscous stresses is highlighted. The influence of viscosity on instability growth rates in the zero‐shear stress limits of perfectly conducting and perfectly insulating interfaces is described and compared to cases involving electrical shear stresses. Detailed attention is given to the instability of an interface between fluids having electrical relaxation times long compared to times of interest. It is shown that, for many common liquids, even a slight amount of surface charge makes the interface unstable at a considerably lower voltage than would be expected from theories based on the dielectrophoretic limit of no interfacial free charge. Experiments, performed using high‐frequency ac stresses, gradually increased dc fields, and abruptly applied dc fields, support the theoretical model. In the general case, the electric Hartmann number is identified as an index to the dominance of the electric shear stresses over the viscous shear stresses in determining the interfacial convection of free charge.

Magnetohydrodynamic flow between rotating coaxial disks.

Abstract: This is a study of the magnetohydrodynamic flow of an incompressible viscous fluid between coaxial disks, with a uniform axial magnetic field B. The fluid has density ρ, viseosity η and electrical conductivity σ. The flow is assumed to be steady, and to be similar in the sense that the radial and tangential components of velocity increase linearly with radial distance from the axis of rotation. Most of the work is concerned with disks which are electrical insulators, one of which rotates while the other remains stationary. The imposed conditions can then be represented by the Reynolds number R = ρΩad2/η and the Hartmann number M2 = σB2d2/η, where Ωa is the angular velocity of the rotating disk and d is the gap between the disks. Asymptotic solutions are given for R [Lt ] M2, and numerical solutions are obtained for values of R and M2 up to 512. Experimental measurements are presented which are in general agreement with the theoretical flows, and the results for small values of the Hartmann number provide the first known experimental support for the purely hydrodynamic solutions in the range 100 < R < 800.

Hydromagnetic stability of dissipative flow between rotating permeable cylinders. Part 2. Oscillatory critical modes and asymptotic results

Abstract: In considering the onset of instability of an electrically conducting fluid between rotating permeable perfectly conducting cylinders in an applied axial magnetic field, it is found that oscillatory axially symmetric modes occur at large values of Hartmann number, in addition to the usual stationary modes. Results are presented showing the effect of the oscillatory modes on the criterion of onset of instability.The asymptotic behaviour of the stability criterion is considered in the limit of very large radial Reynolds number, and also in the limit where both the radial Reynolds number and the Hartmann number are large.

Flow of a Conducting Fluid between Porous Disks for Large Suction Reynolds Number

Abstract: The magnetohydrodynamic laminar flow between two parallel porous disks is examined for large suction Reynolds number and arbitrary Hartmann number. The equations of motion are solved using the singular perturbation technique and the expressions for the velocity, pressure and shear stress distributions are obtained. The results of this analysis are compared with the case of large injection Reynolds number.

Inertia Effect in Hydromagnetic Slider Bearing

Abstract: A theoretical investigation of inertia effects in an inclined slider bearing with an electrically conducting lubricant in the presence of azimuthal magnetic field is presented. It is shown that the load supporting capacity of bearing is increased for short circuit case if the lubricant inertia effects are taken into account. However, the inertia effect becomes smaller when the strength of magnetic field increases. In open circuit case for Hartmann number M≤4 the load capacity increases due to inertia and for M≥5 the load capacity decreases due to inertia. Further it is seen that the effect of inertia is rather small at Hartmann numbers 4.1, 4.2, 4.2 and 4.4 for Reynolds numbers .01, .1715, .25 and 1.39 respectively.

Hartmann flow in annular channels. Part 2. Numerical solutions for low to moderate Hartmann numbers

Abstract: Flow of a conducting fluid along the annular channel between two non-conducting circular cylinders is examined by a numerical method for concentric and eccentric cases. Solutions have been obtained for Hartmann numbers ranging from 0·1 to 40 and, for some of these, details of velocity distribution and of induced current are given. The results obtained enable the development of the patterns of velocity and of current flow to be traced as the Hartmann number increases. The details of the development of the current flow patterns for eccentric cylinders are particularly interesting and are discussed in detail. At the higher values of Hartmann number studied the solutions are in excellent agreement with the results of Todd's (1967) high Hartmann number analysis and it is possible to determine at what value of Hartmann number Todd's analysis becomes applicable within a specified accuracy. The effect of eccentricity of the cylinders on the flow rate at a fixed pressure gradient is shown to diminish rapidly with increasing Hartmann number. The net flow of current around the annulus, which occurs when the cylinders are eccentric, has a maximum value for each case studied at a Hartmann number of 3, approximately.

Experiments on Hartmann Channel Flow in Plasmas

Abstract: An experimental study of subsonic Hartmann channel flow of a plasma is described. A partially ionized gas, consisting of high‐temperature atmospheric‐pressure potassium‐seeded combustion products, was passed through an insulated rectangular channel in the presence of a transverse magnetic field. The influence of the electrical‐conductivity profile within the plasma was studied by systematically varying the wall temperature with respect to the mean plasma temperature. The effect of the magnetic field was found to be sensitive to this temperature difference. Only situations where the wall temperature is less than the mean plasma temperature have been investigated. With wall temperatures several hundred degrees below the mean plasma temperature, an increase in wall‐shear stress of about 30% is observed, as compared with a factor‐of‐2 increase found in the corresponding uniform conductivity, liquid metal experiments. The experimental data for laminar flow agree well with the results of an approximate analysis. Turbulence‐damping effects, Hall‐parameter effects and fluid‐property‐variation effects are discussed. The turbulence‐damping effect is smaller in the present experiments than in the mercury‐flow experiments. No pressure gradients were observed in the u × B direction. A complete correlation of the data is proposed.

Hydromagnetic Noncyclic Squeeze Films in Journal Bearing with Radial Magnetic Field

Abstract: A theoretical study is made of noncyclic squeeze films in full and half journal bearings of infinite length between two insulating surfaces in the presence of radial magnetic field. It is shown that the time of approach increases with the large Hartmann number. Further it is seen that the increase in the time of approach is much for large values of the Hartmann number whereas the increase in the time of approach is very small for small Hartmann numbers.

On the steady rotation of an axisymmetric solid in a conducting fluid at high Hartmann numbers

Abstract: In an earlier paper [Shail, 1] one of the present authors considered the effect of a magnetic field on the frictional couple experienced by an axisymmetric solid insulator which rotates slowly in a bounded viscous conducting fluid, the applied magnetic field being parallel to the axis of rotation. Results for the couple in various geometrical configurations were obtained in the form of power series expansions in the Hartmann number M , and hence are valid only for M ≪ 1. However, because of the increased rigidity given to the fluid by the applied field, it is physically evident that the magnetic field will have a more dramatic effect on the flow pattern for large values of M . Thus one object of this paper is to investigate the frictional couple on a solid insulator rotating in an unbounded fluid for values of M ≫ 1.

A rotating field mhd hydrostatic thrust bearing.

Abstract: It is found that the load capacity of a magnetohydrodynamic thrust bearing with a rotating disk can be increased by rotating the axial magnetic field at a suitable speed in a direction opposite to that of the disk rotation. This method of improving the bearing performance is considered to be efficient if the Hartmann number is not too large. Thus for a given load, the size and weight of the magnet to be used in a thrust bearing with rotating field can be reduced considerably.

The Effect of Variable Fluid Properties on the Sensitivity of MHD Flowmeters

Abstract: For ducts operated as MHD flowmeters, it is demonstrated that the sensitivities are substantially affected by variable fluid viscosity and electrical conductivity. The analysis considers a mathematical model based on fully developed laminar MHD flows with constant heat flux boundary conditions. By considering the pertinent equations in dimensionless form and assuming a power law dependency of the fluid properties on temperature, flowmeter sensitivities are calculated as functions of the Hartmann number, duct aspect ratio, and the magnitude of the property variations. It is shown that, even for small property variations, the flowmeter sensitivities deviate significantly from constant property values. For larger variations, they can be as much as 60% below ideality for heated walls and 30% above for cooled walls.