The development and validation of computational MHD techniques for the modelling of metal production processes

Magnetic fields are used in a number of processes related to the extraction of metals, production of alloys and the shaping of metal components. Computational techniques have an increasingly important role to play in the simulation of such processes, since it is often difficult or very costly to conduct experiments in the high temperature conditions encountered and the complex interaction of fluid flow, heat transfer and magnetic fields means simple analytic models are often far removed from reality. In this paper an overview of the computational activity at the University of Greenwich is given in this area, covering the past ten years. The overview is given from the point of view of the modeller and within the space limitations imposed by the format it covers the numerical methods used, attempts at validation against experiments or analytic procedures; it highlights successes, but also some failures. A broad range of models is covered in the review (and accompanying lecture), used to simulate (a) A-C field applications: induction melting, magnetic confinement and levitation, casting and (b) D-C field applications such as: arc welding and aluminium electroloysis. Most of these processes involve phase change of the metal (melting or solidification), the presence of a dynamic free surface and turbulent flow. These issues affect accuracy and need to be address by the modeller.

Modeling the dynamics of electromagnetically agitated metallurgical flows: levitation, cold crucible, aluminium electrolysis, etc.

We present practical modelling techniques for electromagnetically agitated liquid metal flows involving dynamic change of the fluid volume and shape during melting and the free surface oscillation. Typically the electromagnetic field is strongly coupled to the free surface dynamics and the heat-mass transfer. Accurate pseudo-spectral code and the k-omega turbulence model modified for complex and transitional flows with free surfaces are used for these simulations. The considered examples include magnetic suspension melting, induction scull remelting (cold crucible), levitation and aluminium electrolysis cells. The process control and the energy savings issues are analysed.

Evaluation of distortions in laser welded shipbuilding parts using local-global finite element approach

In recognition of the differences of scale between the welding pool and the heat affected zone along the welding line on one hand, and the overall size of the components being welded on the other, a local-global finite element approach was developed for the evaluation of distortions in laser welded shipbuilding parts. The approach involves the tandem use of a 'local' and a 'global' step. The local step involves a three-dimensional finite element model for the simulation of the laser welding process using the Sysweld finite element code, which takes into account thermal, metallurgical, and mechanical aspects. The simulation of the laser welding process was performed using a non-linear heat transfer analysis, based on a keyhole formation model, and a coupled transient thermomechanical analysis, which takes into account metallurgical transformations using the temperature dependent material properties and the continuous cooling transformation diagram. The size and shape of the keyhole used in the local finite element analysis was evaluated using a keyhole formation model and the Physica finite volume code. The global step involves the transfer of residual plastic strains and the stiffness of the weld obtained from the local model to the global analysis, which then provides the predicted distortions for the whole part. This newly developed methodology was applied to the evaluation of global distortions due to laser welding of stiffeners on a shipbuilding part. The approach has been proved reliable in comparison with experiments and of practical industrial use in terms of computing time and storage.

A mixed Eulerian-Lagrangian approach for metal extrusion

In this paper a mixed Eulerian-Lagrangian approach for the modelling metal extrusion processes is presented. The approach involves the solution of non-Newtonian fluid flow equations in an Eulerian context, using a free-surface algorithm to track the behaviour of the workpiece and its extrusion. The solid mechanics equations associated with the tools are solved in Lagangrian context. Thermal interactions between the workpiece are modelled and a fluid-structure interaction technique is employed to model the effect of the fluid traction load imposed by the workpiece on the tools. Two extrusion test cases are investigated and the results obtained show the potential of the model with regard to representing the physics of the process and the simulation time.

Modeling of ingot development during the start-up phase of direct chill casting

Direct chill (DC) casting is a core primary process in the production of aluminum ingots. However, its operational optimization is still under investigation with regard to a number of features, one of which is the issue of curvature at the base of the ingot. Analysis of these features requires a computational model of the process that accounts for the fluid flow, heat transfer, solidification phase change, and thermomechanical analysis. This article describes an integrated approach to the modeling of all the preceding phenomena and their interactions.

Macro-segregation of multi-component alloys in shape casting simulation

The objective of this work is to present a new scheme for temperature-solute coupling in a solidification model, where the temperature and concentration fields simultaneously satisfy the macro-scale transport equations and, in the mushy region, meet the constraints imposed by the thermodynamics and the local scale processes. A step-by-step explanation of the macrosegregation algorithm, implemented in the finite volume unstructured mesh multi-physics modelling code PHYSICA, is initially presented and then the proposed scheme is validated against experimental results obtained by Krane for binary and a ternary alloys.

A comprehensive copper stockpile leach model: background and parameter sensitivity

The design and development of a comprehensive computational model of a copper stockpile leach process is summarized. The computational fluid dynamic software framework PHYSICA+ and various phenomena were used to model transport phenomena, mineral reaction kinetics, bacterial effects, and heat, energy and acid balances for the overall leach process. In this paper, the performance of the model is investigated, in particular its sensitvity to particle size and ore permeability. A combination of literature and laboratory sources was used to parameterize the model. The simulation results from the leach model are compared with closely controlled column pilot scale tests. The main performance characteristics (e.g. copper recovery rate) predicted by the model compare reasonably well with the experimental data and clearly reflect the qualitiative behavior of the process in many respects. The model is used to provide a measure of the sensitivity of ore permeability on leach behavior, and simulation results are examined for several different particle size distributions.

Computational modelling of freeze layers in smelting processes

The use of computational modelling in examining process engineering issues is very powerful. It has been used in the development of the HIsmelt process from its concept. It is desirable to further water-cool the HIsmelt vessel to reduce downtime for replacing refractory. Water-cooled elements close to a metal bath run the risk of failure. This generally occurs when a process perturbation causes the freeze and refractory layers to come away from the water-cooled element, which is then exposed to liquid metal. The element fails as they are unable to remove all the heat. Modelling of the water-cooled element involves modelling the heat transfer, fluid flow, stress and solidification for a localised section of the reaction vessel. The complex interaction between the liquid slag and the refractory applied to the outside of thewater-cooled element is also being examined to model the wear of this layer. The model is being constructed in Physica, a CFD code developed at the University of Greenwich. Modelling of this system has commenced with modelling solidification test cases. These test cases have been used to validate the CFD code’s capability to model the solidification in this system. A model to track the penetration of slag into refractory has also been developed and tested.

Demonstration thermo-electric and MHD mathematical models of a 500 kA A1 electrolysis cell

In the present study, a 3D full cell quarter thermo-electric model of a 500kA demonstration cell has been developed and solved. In parallel, a non-linear wave MHD model of the same 500 kA demonstration cell has been developed and solved. A preliminary study of the impact of the interactions between the cell thermo-electric and MHD models will be presented.

Using computer models to identify optimal conditions for flip-chip assembly and reliability

Flip-chip assembly, developed in the early 1960s, is now being positioned as a key joining technology to achieve high-density mounting of electronic components on to printed circuit boards for high-volume, low-cost products. Computer models are now being used early within the product design stage to ensure that optimal process conditions are used. These models capture the governing physics taking place during the assembly process and they can also predict relevant defects that may occur. Describes the application of computational modelling techniques that have the ability to predict a range of interacting physical phenomena associated with the manufacturing process. For example, in the flip-chip assembly process we have solder paste deposition, solder joint shape formation, heat transfer, solidification and thermal stress. Illustrates the application of modelling technology being used as part of a larger UK study aiming to establish a process route for high-volume, low-cost, sub-100-micron pitch flip-chip assembly.

Micro-mechanical parameterisations for continuum modelling of granular material using the discrete element method

The present work uses the discrete element method (DEM) to describe assemblies of particulate bulk materials. Working numerical descriptions of entire processes using this scheme are infeasible because of the very large number of elements (1012 or more in a moderately sized industrial silo). However it is possible to capture much of the essential bulk mechanics through selective DEM on important regions of an assembly, thereafter using the information in continuum numerical descriptions of particulate processes. The continuum numerical model uses population balances of the various components in bulk solid mixtures. It depends on constitutive relationships for the internal transfer, creation and/or destruction of components within the mixture. In this paper we show the means of generating such relationships for two important flow phenomena – segregation whereby particles differing in some important property (often size) separate into discrete phases, and degradation, whereby particles break into sub-elements, through impact on each other or shearing. We perform DEM simulations under a range of representative conditions, extracting the important parameters for the relevant transfer, creation and/or destruction of particles in certain classes within the assembly over time. Continuum predictions of segregation and degradation using this scheme are currently being successfully validated against bulk experimental data and are beginning to be used in schemes to improve the design and operation of bulk solids process plant.