Electrically Induced Vortical Flows

ISBN-13: 9789401070171 / Angielski / Miękka / 2011 / 400 str.

V. Bojarevi S.; YA Freibergs; E. I. Shilova

Opis

Every scientific subject probably conceals unexplored or little investigated strata, which may show up at the proper time when favourable conditions coincide (practical demands, a circle of scientists prepared to recognize the novelty and capable of giving impetus to the development of a new theory, etc.). Something like this occurred in early seventies for magnetohydrodynamics, which at the time was considered to be a relatively complete branch of hydro dynamics with no apparent broad, unexplored areas. It was unexpectedly realized that, in addition to the traditional methods of affecting an electrically conducting medium, there is yet another way, one which subsequently lead to a new direction in magnetohydrodynamics. In the Soviet scientific literature this direction has been termed 'electrically induced vortex flows', the essence of which are hydrodynamic effects due to the interaction of an electric current passing through the fluid with its own magnetic field. It cannot be said that this direction was created ex nihilo: individual studies related to the flows driven in a current-carrying medium in the absence of external magnetic fields appeared in the sixties; in the thirties the flows them selves were known to take place within electrical arcs; and yet the first observa tions on the behaviour of liquid current-carrying conductors were made at the beginning of this century."

Spis treści

1/Basic Properties of Axially Symmetric Motions in Magnetohydrodynamics.- 1.1. Magnetohydrodynamic Equations.- 1.2. Some Facts about Orthogonal Curvilinear Coordinates.- 1.3. Differential Operators in Orthogonal Curvilinear Coordinates.- 1.4. The Most Commonly Used Rotational Coordinate Systems.- 1.5. Axisymmetric Motions.- 1.6. Relation between Stokes Stream Function and Self-Magnetic Field of an Electric Current in Problems with Axial Symmetry.- 1.7. Feasible Schemes for Axially Symmetric Electric Current Distributions.- 1.8. Magnetic Field in Axisymmetric Flow.- 1.9. Electric Field in Axisymmetric Flow.- 1.10. Full Set of Equations for Axisymmetric Motion.- 2/Solutions in Spherical Coordinates.- 2.1. Definition of the Class of Exact Solutions.- 2.2. Low Magnetic Reynolds Number Approximation. Electric Current and External Magnetic Fields.- 2.3. Integral Flow Characteristics and Dimensionless Criteria.- 2.4. Review of the Class of Exact Solutions in Spherical Coordinates.- 2.5. Electrically Induced Vortex Flow in a Cone.- 2.6. Gas Flow in an Electrical Arc.- 2.7. Problems of the Nonlinear Solution.- 2.8. Landau-Squire Flows in the Presence of a Radially Diverging Electric Current.- 2.9. Effect of the Induced Electric Current on the Flow at a Point Current Source.- 2.10. Electrically Induced Flows at Finite Size Electrodes.- 3/Electrically Induced Vortex Flow at a Point Electrode and Azimuthal Rotation.- 3.1. Integral Properties of the Flows Driven by Rotational Electromagnetic Forces.- 3.2. A Model Demonstrating the Effect of Viscosity.- 3.3. Flow at an Immersed Electrode.- 3.4. Asymptotic Solution for High S.- 3.5. Electrically Induced Flow with Differential Rotation.- 3.6. Growth of Azimuthal Disturbance in the Electrically Induced Flow at a Point Electrode.- 3.7. Intensification of Rotation in a Closed Volume.- 3.8. Mechanism of Rotation Intensification in an Axisymmetric Vortex.- 4/Flows with Cylindrical Symmetry.- 4.1. External Electric Current and Magnetic Field in Cylindrical Coordinates.- 4.2. Similarity Solutions.- 4.3. Electrically Induced Flow between Two Parallel Walls.- 4.4. Flow with Line Source in a Circular Cone.- 4.5. Magnetohydrodynamic Model of Tornado.- 4.6. EVF in a Cylindrical Container.- 4.7. Effect of Electric Current Configuration on Flow in a Cylindrical Container.- 5/Periodic Electrically Induced Flows.- 5.1. Periodic Distributions of Current and Magnetic Field in Cylindrical Coordinates.- 5.2. Integral Action of Electromagnetic Force.- 5.3. A Method Used to Construct Linear Solution of Periodic EVF in Tubes.- 5.4. EVF in a Tube with Radial Current Supply.- 5.5. EVF in a Tube with Longitudinal Electric Current.- 5.6. EVF in an Annular Tube.- 5.7. Periodic EVF in a Longitudinal Magnetic Field.- 5.8. Longitudinal Magnetic Field Effect on Integral Features of EVF.- 5.9. Nonlinear Interaction of Periodic EVF with Through-Flow.- 5.10. Electrically Induced Flow in a Loosely Coiled Tube.- 6/Bodies in a Current-Carrying Fluid.- 6.1. Effect of Potential Forces on a Body in a Current-Carrying Fluid.- 6.2. Effect of the Rotational Electromagnetic Forces on Axisymmetric Bodies.- 6.3. Flow at a Stationary Sphere.- 6.4. Drag of a Sphere in the Flow of Current-Carrying Fluid.- 6.5. Flows at Spheroids.- 6.6. Discharge between Electrodes of Hyperboloidal Form.- 6.7. Flow at a Cone with an Electric Current Source in the Apex.- 6.8. Motion of a Sphere with a Current-Source.- 7/Heat and Mass Transfer in Electrically Induced Vortical Flows.- 7.1. Equations of Heat and Mass Transfer, and the Nondimensional Numbers.- 7.2. Mass Transfer from a Stationary Spherical Particle in Current-Carrying Fluid.- 7.3. Mass Transfer from a Translating Spherical Particle in a Current-Carrying Fluid.- 7.4. Mass Transfer from a Stationary Sphere in a Longitudinal Magnetic Field.- 7.5. Heat and Mass Transfer in a Cylindrical Container.- 7.6. Thermal Convection in Electrically Induced Flows.- 8/Experimental Investigations of EVF and Applications.- 8.1. Electroslag Welding.- 8.2. Electroslag Remelting.- 8.3. Electric-Arc Furnaces.- 8.4. Hydrodynamics of Furnaces with Multiple Electrodes.- 8.5. Electrical Jet Thrusters.- 8.6. Induction Channel Furnaces.- 8.7. Electrically Induced Flows in a Flat Layer between Ferromagnetic Masses.- 8.8. Electrolytic Aluminium Production.- References.