Vacuum arc remelting time dependent modelling

Newly developed numerical modelling tools are described, which address the 3-dimensional (3D) time-dependent magnetohydrodynamic and thermal behaviour in the liquid pool zone in the adjacent ingot, electrode and crucible. The melting electrode film flow and the droplet detachment initiation are simulated separately by an axisymmetric transient model.

Levitated droplet oscillations: effect of internal flow

The numerical model for electrically conducting liquid droplets levitated in AC magnetic field is applied to demonstrate various factors affecting the accuracy of material property value measurements in microgravity conditions. The included effects are the electromagnetic force induced stirring and the resulting turbulence, the thermo-capillary convection, and the droplet rotation. The results are validated against available analytical solutions.

Convection-diffusion in MHD: Comparison of primitive variable and vector potential solutions of the magnetic induction equation

Abstract not available

Finite volumes simulations in magnetohydrodynamics

Abstract not available

A finite-volume shallow layer method for the MHD instabilities in an aluminium production cell

An electrolytic cell for Aluminium production contains molten metal and molten electrolyte, which are subject to high dc-currents and magnetic fields. Lorentz forces arising from the cross product of current and magnetic field may amplify natural gravity waves at the interface between the two fluids, leading to short circuits in extreme cases. The external magnetic field and current distribution in the production cell is computed through a detailed finite element analysis at Torino Polytechnic. The results are then used to compute the magnetohydrodynamic and thermal effects in the aluminium/electrolyte bath. Each cell has lateral dimensions of 6m x 2m, whilst the bath depth is only 30cm. the electrically resistive electrolyte path, which is critical in the operation of the cell, has layer depth of only a few centimetres below each carbon anode. Because the shallow dimensions of the liquid layer a finite-volume shallow-layer technique has been used at Greenwich to compute the resulting flow-field and interface perturbations. The information obtained from this method, i.e. depth averaged velocities and aluminium/electrolyte interface position is then embedded in the three-dimensional finite volume code PHYSICA and will be used to compute the heat transfer and phase change in the cell.

Investigation of the cold crucible melting process: experimental and numerical study

The dynamic process of melting different materials in a cold crucible is being studied experimentally with parallel numerical modelling work. The numerical simulation uses a variety of complementing models: finite volume, integral equation and pseudo-spectral methods combined to achieve the accurate description of the dynamic melting process. Results show the temperature history of the melting process with a comparison of the experimental and computed heat losses in the various parts of the equipment. The free surface visual observations are compared to the numerically predicted surface shapes.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

Cold crucible melting of reactive metals using combined DC and AC magnetic fields

Cold crucible furnace is widely used for melting reactive metals for high quality castings. Although the water cooled copper crucible avoids contamination, it produces a low superheat of the melt. Experimental and theoretical investigations of the process showed that the increase of the supplied power to the furnace leads to a saturation in the temperature rise of the melt, and no significant increase of the melt superheat can be obtained. The computer model of theprocess has been developed to simulate the time dependent turbulent flow, heat transfer with phase change, and AC and DC magnetohydrodynamics in a time varying liquid metal envelope. The model predicts that the supermimposition of a strong DC field on top of the normal AC field reduces the level of turbulience and stirring in the liquid metal, thereby reducing the heat loss through the base of the crucible and increasing the superheat. The direct measurements of the temperature in the commercial size cold crucbile has confirmed the computer redictions and showed that the addition of a DC field increased the superheat in molten TiAl from ~45C (AC field only) to ~81C (DC+AC fields). The present paper reports further predictions of the effect of a dDC field on top of the AC field and compares these with experimental data.

Numerical modelling for electromagnetic processing of materials

Electromagnetic processing of materials (EPM) is one of the most widely practiced and fast growing applications of magnetic and electric forces to fluid flow. EPM is encountered in both industrial processes and laboratory investigations. Applications range in scale from nano-particle manipulation to tonnes of liquid metal treated in the presence of various configurations of magnetic fields. Some of these processes are specifically designed and made possible by the use of the electromagnetic force, like the magnetic levitation of liquid droplets, whilst others involve electric currents essential for electrothermal or electrochemical reasons, for instance, in electrolytic metal production and in induction melting. An insight for the range of established and novel EPM applications can be found in the review presented by Asai [1] in the EPM-2003 conference proceedings.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Levitated droplet oscillations: effect of internal flow

The numerical model for electrically conducting liquid droplets levitated in AC magnetic field is extended to demonstrate various factors affecting the accuracy of material property value measurements. The effects included are the electromagnetic force induced stirring and the resulting turbulence, thermo-capillary convection, and the droplet rotation. The results are validated against available analytical solutions.

Effects of magnetic fields on crystal growth

The effects of a constant uniform magnetic field on dendritic solidification were investigated using a 2-dimensional enthalpy based numerical model. The interaction between thermoelectic currents and the magnetic field generates a Lorentz force that creates a flow. This flow causes a change in the morphology of the dendrite; secondary growth is promoted on one side of the dendrite arm and the tip velocity of the primary arm is increased.

Shallow water model for aluminium electrolysis cells with variable top and bottom

The MHD wave instability in commercial cells for electrolytic aluminium production is often described using ‘shallow water’ models. The model [1] is extended for a variable height cathode bottom and anode top to account for realistic cell features. The variable depth of the two fluid layers affects the horizontal current density, the wave development and the stability threshold. Instructive examples for the 500 kA cell are presented.