Numerical Simulation of Steady Liquid-Metal Flow in the Presence of a Static Magnetic Field

2004 ◽  
Vol 71 (6) ◽  
pp. 786-795 ◽  
Author(s):  
Amnon J. Meir ◽  
Paul G. Schmidt ◽  
Sayavur I. Bakhtiyarov ◽  
Ruel A. Overfelt
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Metal Flow ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Dissipative Heat ◽  
Novel Approach ◽  
Liquid Metal Flow

We describe a novel approach to the mathematical modeling and computational simulation of fully three-dimensional, electromagnetically and thermally driven, steady liquid-metal flow. The phenomenon is governed by the Navier-Stokes equations, Maxwell’s equations, Ohm’s law, and the heat equation, all nonlinearly coupled via Lorentz and electromotive forces, buoyancy forces, and convective and dissipative heat transfer. Employing the electric current density rather than the magnetic field as the primary electromagnetic variable, it is possible to avoid artificial or highly idealized boundary conditions for electric and magnetic fields and to account exactly for the electromagnetic interaction of the fluid with the surrounding media. A finite element method based on this approach was used to simulate the flow of a metallic melt in a cylindrical container, rotating steadily in a uniform magnetic field perpendicular to the cylinder axis. Velocity, pressure, current, and potential distributions were computed and compared to theoretical predictions.

Velocity, Potential, and Temperature Distributions in Molten Metals During Electromagnetic Stirring: Part II — Numerical Simulations

1999 ◽  
Author(s):  
Amnon J. Meir ◽  
Paul G. Schmidt ◽  
Sayavur I. Bakhtiyarov ◽  
Ruel A. Overfelt
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Metal Flow ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Molten Metals ◽  
Dissipative Heat ◽  
Novel Approach ◽  
Thermally Driven

Abstract We describe a novel approach to the mathematical modeling and computational simulation of fully three-dimensional, electromagnetically and thermally driven liquid-metal flow. The phenomenon is governed by the Navier-Stokes equations, Maxwell’s equations, Ohm’s law, and the heat equation, all nonlinearly coupled via Lorentz and electromotive forces, buoyancy forces, and convective and dissipative heat transfer. Employing the electric current density rather than the magnetic field as the primary electromagnetic variable, it is possible to avoid artificial or highly idealized boundary conditions for electric and magnetic fields and to account exactly for the electromagnetic interaction of the fluid with the surrounding media. A finite-element method based on this approach was used to simulate the flow of a metallic melt in a cylindrical container, rotating steadily in a uniform magnetic field perpendicular to the cylinder axis. Velocity, pressure, current, and potential distributions were computed and compared to theoretical predictions.

Liquid-metal flow in an insulated rectangular expansion with a strong transverse magnetic field

1995 ◽  
Vol 305 ◽  
pp. 111-126 ◽  
Author(s):  
John S. Walker ◽  
Basil F. Picologlou
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Boundary Layers ◽  
Applied Magnetic Field ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Metal Flow ◽  
Constant Area ◽  
Large Expansion ◽  
The Magnetic Field

This paper concerns a steady liquid-metal flow through an expansion or contraction with electrically insulated walls, with rectangular cross-sections and with a uniform, transverse, externally applied magnetic field. One pair of duct walls is parallel to the applied magnetic field, and the other pair diverges or converges symmetrically about a plane which is perpendicular to the field. The magnetic field is assumed to be sufficiently strong that inertial effects can be neglected and that the well-known Hartmann-layer solution is valid for the boundary layers on the walls which are not parallel to the magnetic field. A general treatment of three-dimensional flows in constant-area ducts is presented. An error in the solution of Walker et al. (1972) is corrected. A smooth expansion between two different constant-area ducts is treated. In the expansion the flow is concentrated inside the boundary layers on the sides which are parallel to the magnetic field, while the flow at the centre of the duct is very small and may be negative for a large expansion slope. In each constant-area duct, the flow evolves from a concentration near the sides at the junction with the expansion to the appropriate fully developed flow far upstream or downstream of the expansion. The pressure drop associated with the three-dimensional flow increases as the slope. increases.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

Numerical Simulation of Three-Dimensional Molten Pool Temperature Field and Flow Field for Laser Melt Injection Based on Fluent

2012 ◽  
Vol 538-541 ◽  
pp. 1837-1842 ◽  
Author(s):  
Long Zhi Zhao ◽  
Zi Wang ◽  
Xin Yan Jiang ◽  
Jian Zhang ◽  
Ming Juan Zhao
Keyword(s):  
Temperature Field ◽  
Liquid Metal ◽  
Molten Pool ◽  
Metal Flow ◽  
Three Dimensional ◽  
Transient Temperature ◽  
Transient Temperature Field ◽  
Liquid Metal Flow ◽  
Fluent Software ◽  
Thermo Physical Properties

According to the characteristics of laser melt injection, a numerical model for a simplified 3D transient temperature field in molten pool was established using FLUENT software in this paper. In the model, many factors were considered such as liquid metal turbulence, latent heat of phase transformation and material thermo physical properties depending on temperature. The results show that the model can be developed well by FLUENT software. And the results also show that the driving force of the liquid metal flow mechanism.

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