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.

The development of magnetohydrodynamic flow due to an electric current discharge

1975 ◽  
Vol 70 (3) ◽  
pp. 509-517 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Flow Field ◽  
Electric Current ◽  
Stagnation Point ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Magnetohydrodynamic Flow ◽  
Dimensionless Variable ◽  
Closed Loops ◽  
Developing Flow ◽  
Set Up

The development of the magnetohydrodynamic flow field due to the discharge of an electric current J0 from a point on a plate bounding a semi-infinite viscous incompressible conducting fluid is considered. The flow field is the response of the fluid to the Lorentz force set up by the electric current and the associated magnetic field. The problem is formulated in terms of the dimensionless variable (vt)½/r and solved numerically. Here ν is the coefficient of kinematic viscosity, t the time from the application of the electric current and r the distance from the discharge. It is shown that the streamlines of the developing flow field in a cross-section through the axis of the discharge are closed loops about a stagnation point. As the flow field develops, the stagnation point moves to infinity along a ray emanating from the discharge with a speed proportional to t−½. The steady state, within a distance r from the discharge, is practically established when t = r2/ν.

Towed Underwater SPIV Measurement of Flow Fields Around a Surface-Piercing Cylinder With Free Surface Effects

2015 ◽  
Author(s):  
Jeonghwa Seo ◽  
Bumwoo Han ◽  
Shin Hyung Rhee
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Surface Wave ◽  
Flow Field ◽  
Cross Section ◽  
Surface Effects ◽  
Flow Fields ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Wave Induced

Effects of free surface on development of turbulent boundary layer and wake fields were investigated. By measuring flow field around a surface piercing cylinder in various advance speed conditions in a towing tank, free surface effects were identified. A towed underwater Stereoscopic Particle Image Velocimetry (SPIV) system was used to measure the flow field under free surface. The cross section of the test model was water plane shape of the Wigley hull, of which longitudinal length and width were 1.0 m and 100 mm, respectively. With sharp bow shape and slender cross section, flow separation was not expected in two-dimensional flow. Flow fields near the free-surface and in deep location that two-dimensional flow field was expected were measured and compared to identify free-surface effects. Some planes perpendicular to longitudinal direction near the model surface and behind the model were selected to track development of turbulent boundary layer. Froude numbers of the test conditions were from 0.126 to 0.40 and corresponding Reynolds numbers were from 395,000 to 1,250,000. In the lowest Froude number condition, free-surface wave was hardly observed and only free surface effects without surface wave could be identified while violent free-surface behavior due to wave-induced separation dominated the flow fields in the highest Froude number condition. From the instantaneous velocity fields, Time-mean velocity, turbulence kinetic energy, and flow structure derived by proper orthogonal decomposition (POD) were analyzed. As the free-surface effect, development of retarded wake, free-surface waves, and wave-induced separation were mainly observed.

scholarly journals Simultaneous Measurement of Free Surface Elevation and Three-Component Velocity Field Around a Translating Surface-Piercing Foil

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
James Schock ◽  
Jason Dahl
Keyword(s):  
Particle Image Velocimetry ◽  
Free Surface ◽  
Velocity Field ◽  
Numerical Methods ◽  
Flow Field ◽  
Particle Image ◽  
Laser Sheet ◽  
Three Dimensional ◽  
Dynamic Mode ◽  
Image Velocimetry

Two methods are investigated to simultaneously obtain both three-dimensional (3D) velocity field and free surface elevations (FSEs) measurements near a surface piercing foil, while limiting the equipment. The combined velocity field and FSE measurements are obtained specifically for the validation of numerical methods requiring simultaneous field data and free surface measurements for a slender body shape. Both methods use stereo particle image velocimetry (SPIV) to measure three component velocities in the flow field and both methods use an off the shelf digital camera with a laser intersection line to measure FSEs. The first method is performed using a vertical laser sheet oriented parallel to the foil chord line. Through repetition of experiments with repositioning of the laser, a statistical representation of the three-dimensional flow field and surface elevations is obtained. The second method orients the vertical laser sheet such that the foil chord line is orthogonal to the laser sheet. A single experiment is performed with this method to measure the three-dimensional three component (3D3C) flow field and free surface, assuming steady flow conditions, such that the time dimension is used to expand the flow field in 3D space. The two methods are compared using dynamic mode decomposition and found to be comparable in the primary mode. Utilizing these methods produces results that are acceptable for use in numerical methods verification, at a fraction of the capital and computing cost associated with two plane or tomographic particle image velocimetry (PIV).

The nonlinear flow field induced by a point force in the presence of a plane wall

1981 ◽  
Vol 376 (1766) ◽  
pp. 435-450 ◽  
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Plane Wall ◽  
Point Force ◽  
Nonlinear Flow ◽  
Unit Force ◽  
Closed Loops ◽  
Meridian Section ◽  
Continuous Application ◽  
Section Form

A nonlinear solution is constructed representing the steady flow field generated by the continuous application of a constant point force of magnitude F 0 in an incompressible fluid that is bounded by a fixed plane wall. The force is applied at a fixed distance from the wall, is perpendicular to the wall and directed towards it. The streamlines in a meridian section form closed loops which nest at a stagnation point and it is found that as F 0 increases this stagnation point is displaced towards the wall. It is also found that as F 0 increases the total volume flow per unit force decreases.

The Pattern of Plastic Deformation in a Deeply Notched Bar With Semicircular Roots

1956 ◽  
Vol 23 (1) ◽  
pp. 56-58
Author(s):  
L. Garr ◽  
E. H. Lee ◽  
A. J. Wang
Keyword(s):  
Plastic Deformation ◽  
Free Surface ◽  
Velocity Field ◽  
Plastic Strain ◽  
Plane Strain ◽  
Cross Section ◽  
Finite Deformation ◽  
Large Plastic Strain ◽  
Step Method ◽  
Square Grid

Abstract The plastic deformation in a notched bar with deep semicircular roots pulled in plane strain is determined theoretically. The finite deformation is analyzed according to plastic-rigid theory. The motion is unsteady, and the velocity field at any instant is given in terms of the current geometry of the deformed free surface. A graphical step-by-step method is used to determine the deformation of a square grid scribed on the undeformed cross section. The deformed pattern details the regions of large plastic strain, and may be useful in considering the initiation of fracture cracks.

The axisymmetric flow field induced by a point force in the presence of a plane wall

1982 ◽  
Vol 380 (1779) ◽  
pp. 349-357 ◽  
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Axisymmetric Flow ◽  
Plane Wall ◽  
Point Force ◽  
Nonlinear Flow ◽  
Volume Flux ◽  
Closed Loops ◽  
Meridian Section ◽  
Section Form

In this paper we consider a numerically constructed solution concerning the steady nonlinear flow field generated by a point force of magnitude F 0 in an incompressible fluid bounded by a plane wall. The force is applied at a fixed distance from the wall and is perpendicular to it. The streamlines in a meridian section form closed loops which nest at a stagnation point and it is found that as F 0 increases this stagnation point is displaced towards or away from the wall depending on whether the force is pointing towards or away from it. It is also found that as F 0 increases the total volume flux per unit force decreases when the force is pointing towards the wall and increases when the force is pointing in the opposite direction. For instance when F 0 is 150 v 2 ρ , where v denotes the coefficient of kinematic viscosity and ρ the fluid density, the total volume flux for the case where the force points away from the wall is several times that for the case where the force points towards the wall.

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.

Development of the flow field of a point force in an infinite fluid

1979 ◽  
Vol 91 (3) ◽  
pp. 541-546 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Flow Field ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Point Force ◽  
Linear Flow ◽  
Closed Loops ◽  
Stagnation Points ◽  
Dipole Structure ◽  
Field Lines ◽  
Set Up

By means of similarity principles an analytical solution is constructed for the development of the linear flow field due to the instantaneous application of a constant point force in an infinite liquid. If the force is applied at the origin O and if ν denotes distance from O, ν denotes the coefficient of kinematic viscosity of the fluid and t the time from the application of the force, the solution constructed exhibits the following features. Initially the flow field set up has a dipole structure with centre at O and axis along the direction of the impressed force. At a station r this dipole structure persists so long as 4νt [Lt ] r2. In an axial cross-section the field lines form two sets of closed loops about two stagnation points in the equatorial plane. The stagnation points occur at r = 1.76(νt)½ and thus propagate to infinity with speed 0.88(ν/t)½. The steady state is reached algebraically.

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.

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.

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