Nonlinear fluid motions in a container due to the discharge of an electric current

1984 ◽  
Vol 148 ◽  
pp. 285-300 ◽  
Author(s):  
O. O. Ajayi ◽  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Electric Current ◽  
Equatorial Plane ◽  
Critical Value ◽  
Electromagnetic Stirring ◽  
Series Form ◽  
Point Electrode ◽  
Point Discharge ◽  
Nonlinear Fluid

The nonlinear electromagnetic stirring induced in a hemispheroidal container by the axisymmetric discharge of an electric current is investigated. The electric current is discharged into the fluid from a circular electrode which is at the centre of the equatorial plane of the container, the remaining part of the equatorial plane being a free surface. The equations of the problem are solved semi-analytically and results are presented for several sets of data. In the case of a point electrode when the current exceeds a critical value we have velocity breakdown. Here it is shown that, as the size of the area through which the current is discharged increases, the intensity of the flow field decreases, and thus for a larger electrode a larger amount of current can be discharged without velocity breakdown. When, however, the current is sufficiently large the solution becomes unstable, and this indicates velocity breakdown. Finally in an Appendix the solution for the case of a point discharge in a semi-infinite fluid is expressed in analytic (series) form.

Magnetohydrodynamic flow in a container due to the discharge of an electric current from a finite size electrode

1978 ◽  
Vol 362 (1711) ◽  
pp. 509-523 ◽  
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Electric Current ◽  
Stokes Flow ◽  
Equatorial Plane ◽  
Finite Size ◽  
Magnetohydrodynamic Flow ◽  
Point Electrode ◽  
Equatorial Radius ◽  
Constant Potential

In this paper we consider the Stokes flow field generated in a hemispheroidal container by the axisymmetric discharge of an electric current. The current is discharged from a circular electrode which is at the centre of the equatorial plane of the spheroid. The electrode is assumed to be at a constant potential. The equatorial radius of the spheroid is a and that of the electrode is k , the annulus k ≼ r ≼ a being a free surface. For a given container depth it is shown that as k increases the intensity of the flow field decreases and when the depth of the container is comparable to k the intensity of the flow field is only a small fraction of that associated with the point electrode case. As one might expect, the vorticity has a singularity at the rim of the electrode. When the width of the annulus forming the free surface is small, relative to the radius of the electrode, an eddy is formed about the rim of the electrode. As the annulus increases the eddy decreases in size until it eventually disappears.

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

1976 ◽  
Vol 73 (4) ◽  
pp. 641-650 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Flow Field ◽  
Electric Current ◽  
Cross Section ◽  
Analytic Solution ◽  
Closed Loops ◽  
Slow Viscous Flow ◽  
Axial Cross Section ◽  
Section Form

In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.

On magnetohydrodynamic flows generated by an electric current discharge

1974 ◽  
Vol 63 (4) ◽  
pp. 665-671 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Electric Current ◽  
Critical Value ◽  
Conducting Fluid ◽  
Infinite Plane ◽  
Current Discharge ◽  
Practical Applications ◽  
Magnetohydrodynamic Flows ◽  
Theory And Experiment

Magnetohydrodynamic flows generated in a semi-infinite viscous incompressible conducting fluid by the discharge of an electric current J0 from a point on the infinite plane bounding the fluid develop singularities when J0 exceeds a certain critical value. In practical applications sometimes currents much in excess of the critical value of J0 may be passed between electrodes before singularities appear in the velocity field. In this paper we consider the flow field associated with some current distributions and attempt to provide an explanation for the discrepancy between theory and experiment.

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

scholarly journals Sediment and Cavitation Erosion Studies through Dam Tunnels

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Muhammad Abid ◽  
Jamal Saeed ◽  
Hafiz Abdul Wajid
Keyword(s):  
Flow Field ◽  
Flow Rate ◽  
Erosion Rate ◽  
Cavitation Erosion ◽  
Critical Value ◽  
Sudden Increase ◽  
Sediment Erosion ◽  
Sediment Flow ◽  
Particulate Mass ◽  
Tarbela Dam

This paper presents results of sediment and cavitation erosion through Tunnel 2 and Tunnel 3 of Tarbela Dam in Pakistan. Main bend and main branch of Tunnel 2 and outlet 1 and outlet 3 of Tunnel 3 are concluded to be critical for cavitation and sediment erosion. Studies are also performed for increased sediments flow rate, concluding 5 kg/sec as the critical value for sudden increase in erosion rate density. Erosion rate is concluded to be the function of sediment flow rate and head condition. Particulate mass presently observed is reasonably low, hence presently not affecting the velocity and the flow field.

scholarly journals Size Effect on Mechanical Properties and Deformation Behavior of Pure Copper Wires Considering Free Surface Grains

Materials ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 4563
Author(s):  
Yu Hou ◽  
Xujun Mi ◽  
Haofeng Xie ◽  
Wenjing Zhang ◽  
Guojie Huang ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Free Surface ◽  
Size Effect ◽  
Single Crystal ◽  
Deformation Behavior ◽  
Pure Copper ◽  
Critical Value ◽  
Wire Diameter ◽  
Surface Model

The size (grain size and specimen size) effect makes traditional macroscopic forming technology unsuitable for a microscopic forming process. In order to investigate the size effect on mechanical properties and deformation behavior, pure copper wires (diameters range from 50 μm to 500 μm) were annealed at different temperatures to obtain different grain sizes. The results show that a decrease in wire diameter leads to a reduction in tensile strength, and this change is pronounced for large grains. The elongation of the material is in linear correlation to size factor D/d (diameter/grain size), i.e., at the same wire diameter, more grains in the section bring better plasticity. This phenomenon is in relationship with the ratio of free surface grains. A surface model combined with the theory of single crystal and polycrystal is established, based on the relationship between specimen/grain size and tensile property. The simulated results show that the flow stress in micro-scale is in the middle of the single crystal model (lower critical value) and the polycrystalline model (upper critical value). Moreover, the simulation results of the hybrid model calculations presented in this paper are in good agreement with the experimental results.

scholarly journals Prediction of flow around a sharp-nosed bridge pier: influence of the Froude number and free-surface variation on the flow field

2019 ◽  
Vol 58 (4) ◽  
pp. 582-593
Author(s):  
Recep Kahraman ◽  
Matthew Riella ◽  
Gavin R. Tabor ◽  
Mohsen Ebrahimi ◽  
Slobodan Djordjević ◽  
...  
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Froude Number ◽  
Bridge Pier ◽  
Surface Variation
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