Mathematical modelling of the solidification of liquid tin with electromagnetic stirring

It is well known that during alloy solidification, convection currents close to the so-lidification front have an influence on the structure of dendrites, the local solute concentration, the pattern of solid segregation, and eventually the microstructure of the casting and hence its mechanical properties. Controlled stirring of the melt in continuous casting or in ingot solidification is thought to have a beneficial effect. Free convection currents occur naturally due to temperature differences in the melt and for any given configuration, their strength is a function of the degree of superheat present. A more controlled forced convection current can be induced using electro-magnetic stirring. The authors have applied their Control-Volume based MHD method [1, 2] to the problem of tin solidification in an annular crucible with a water-cooled inner wall and a resistance heated outer one, for both free and forced convection situations and for various degrees of superheat. This problem was studied experimentally by Vives and Perry [3] who obtained temperature measurements, front positions and maps of electro-magnetic body force for a range of superheat values. The results of the mathematical model are compared critically against the experimental ones, in order to validate the model and also to demonstrate the usefulness of the coupled solution technique followed, as a predictive tool and a design aid. Figs 6, refs 19.

The multiphysics modeling of solidification and melting processes

Solidification and melting processes involve a range of physical phenomena and their interactions (i.e., multiphysics). Computational modeling of such processes presents a significant challenge, both in representing the physics involved and in handling the resulting coupled behavior. Two methods for the computational modeling of multiphysics processes in complex geometries are highlighted in the context of four challenging applications

Assessing the scalability of multiphysics tools for modeling solidification and melting processes on parallel clusters

A comprehensive solution of solidification/melting processes requires the simultaneous representation of free surface fluid flow, heat transfer, phase change, nonlinear solid mechanics and, possibly, electromagnetics together with their interactions, in what is now known as multiphysics simulation. Such simulations are computationally intensive and the implementation of solution strategies for multiphysics calculations must embed their effective parallelization. For some years, together with our collaborators, we have been involved in the development of numerical software tools for multiphysics modeling on parallel cluster systems. This research has involved a combination of algorithmic procedures, parallel strategies and tools, plus the design of a computational modeling software environment and its deployment in a range of real world applications. One output from this research is the three-dimensional parallel multiphysics code, PHYSICA. In this paper we report on an assessment of its parallel scalability on a range of increasingly complex models drawn from actual industrial problems, on three contemporary parallel cluster systems.

PHYSICA - A software environment for the modelling of multi-physics phenomena

A brief description of a software environment in FORTRAN77 for the modelling of multi-physics phenomena is given. The numerical approach is based on finite volume methods but extended to unstructured meshes (ie. FV-UM). A range of interacting solution procedures for turbulent fluid flow, heat transfer with solidification/melting and elasto-visco-plastic solid mechanics are implemented in the first version of PHYSICA, which will be released in source code form to the academic community in late 1995.

Computational magnetohydrodynamics - Application

There are many processes, particularly in the nuclear and metals processing industries, where electromagnetic fields are used to influence the flow behaviour of a fluid. Procedures exploiting finite volume (FV) methods in both structured and unstructured meshes have recently been developed which enable this influence to be modelled in the context of conventional FV CFD codes. A range of problems have been tackled by the authors, including electromagnetic pumps and brakes, weirs and dams in steelmaking tundishes and interface effects in aluminium smelting cells. Two cases are presented here, which exemplify the application of the new procedures. The first case investigates the influence of electromagnetic fields on solidification front progression in a tin casting and the second case shows how the liquid metals free surface may be controlled through an externally imposed magnetic field in the semi-levitation casting process.

Multiphysics modelling of the metals casting process

Metals casting is a process governed by the interaction of a range of physical phenomena. Most computational models of this process address only what are conventionally regarded as the primary phenomena-heat conduction and solidification. However, to predict the formation of porosity (a factor of key importance in cast quality) requires the modelling of the interaction of the fluid flow, heat transfer, solidification and the development of stress-deformation in the solidified part of a component. In this paper, a model of the casting process is described which addresses all the main continuum phenomena involved in a coupled manner. The model is solved numerically using novel finite volume unstructured mesh techniques, and then applied to both the prediction of shape deformation (plus the subsequent formation of a gap at the metal-mould interface and its impact on the heat transfer behaviour) and porosity formation in solidifying metal components. Although the porosity prediction model is phenomenologically simplistic it is based on the interaction of the continuum phenomena and yields good comparisons with available experimental results. This work represents the first of the next generation of casting simulation tools to predict aspects of the structure of cast components.

A computational model for defect prediction in shape castings based on the interaction of free surface flow, heat transfer, and solidification phenomena

High-integrity castings require sophisticated design and manufacturing procedures to ensure they are essentially macrodefect free. Unfortunately, an important class of such defects—macroporosity, misruns, and pipe shrinkage—are all functions of the interactions of free surface flow, heat transfer, and solidication in complex geometries. Because these defects arise as an interaction of the preceding continuum phenomena, genuinely predictive models of these defects must represent these interactions explicitly. This work describes an attempt to model the formation of macrodefects explicitly as a function of the interacting continuum phenomena in arbitrarily complex three-dimensional geometries. The computational approach exploits a compatible set of finite volume procedures extended to unstructured meshes. The implementation of the model is described together with its testing and a measure of validation. The model demonstrates the potential to predict reliably shrinkage macroporosity, misruns, and pipe shrinkage directly as a result of interactions among free-surface fluid flow, heat transfer, and solidification.

Parallel performance in multi-physics simulation

A comprehensive simulation of solidification/melting processes requires the simultaneous representation of free surface fluid flow, heat transfer, phase change, non-linear solid mechanics and, possibly, electromagnetics together with their interactions in what is now referred to as "multi-physics" simulation. A 3D computational procedure and software tool, PHYSICA, embedding the above multi-physics models using finite volume methods on unstructured meshes (FV-UM) has been developed. Multi-physics simulations are extremely compute intensive and a strategy to parallelise such codes has, therefore, been developed. This strategy has been applied to PHYSICA and evaluated on a range of challenging multi-physics problems drawn from actual industrial cases.

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.

An explicit scheme for coupling temperature and concentration fields in solidification models

A numerical scheme for coupling temperature and concentration fields in a general solidification model is presented. A key feature of this scheme is an explicit time stepping used in solving the governing thermal and solute conservation equations. This explicit approach results in a local point-by-point coupling scheme for the temperature and concentration and avoids the multi-level iteration required by implicit time stepping schemes. The proposed scheme is validated by predicting the concentration field in a benchmark solidification problem. Results compare well with an available similarity solution. The simplicity of the proposed explicit scheme allows for the incorporation of complex microscale models into a general solidification model. This is demonstrated by investigating the role of dendrite coarsening on the concentration field in the solidification benchmark problem.

Modelling the metal arc weldpool

Traditionally, before flip chips can be assembled the dies have to be attached with solder bumps. This process involves the deposition of metal layers on the Al pads on the dies and this is called the under bump metallurgy (UBM). In an alternative process, however, Copper (Cu) columns can be used to replace solder bumps and the UBM process may be omitted altogether. After the bumping process, the bumped dies can be assembled on to the printed circuit board (PCB) by using either solder or conductive adhesives. In this work, the reliability issues of flip chips with Cu column bumped dies have been studied. The flip chip lifetime associated with the solder fatigue failure has been modeled for a range of geometric parameters. The relative importance of these parameters is given and solder volume has been identified as the most important design parameter for long-term reliability. Another important problem that has been studied in this work is the dissolution of protection metals on the pad and Cu column in the reflow process. For small solder joints the amount of Cu which dissolves into the molten solder after the protection layers have worn out may significantly affect solder joint properties.

Computational modeling techniques for reliability of electronic components on printed circuit boards

This paper describes modeling technology and its use in providing data governing the assembly and subsequent reliability of electronic chip components on printed circuit boards (PCBs). Products, such as mobile phones, camcorders, intelligent displays, etc., are changing at a tremendous rate where newer technologies are being applied to satisfy the demands for smaller products with increased functionality. At ever decreasing dimensions, and increasing number of input/output connections, the design of these components, in terms of dimensions and materials used, is playing a key role in determining the reliability of the final assembly. Multiphysics modeling techniques are being adopted to predict a range of interacting physics-based phenomena associated with the manufacturing process. For example, heat transfer, solidification, marangoni fluid flow, void movement, and thermal-stress. The modeling techniques used are based on finite volume methods that are conservative and take advantage of being able to represent the physical domain using an unstructured mesh. These techniques are also used to provide data on thermal induced fatigue which is then mapped into product lifetime predictions.

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.

Computational modeling of mold filling and related free-surface flows in shape casting: an overview of the challenges involved

Accurate representation of the coupled effects between turbulent fluid flow with a free surface, heat transfer, solidification, and mold deformation has been shown to be necessary for the realistic prediction of several defects in castings and also for determining the final crystalline structure. A core component of the computational modeling of casting processes involves mold filling, which is the most computationally intensive aspect of casting simulation at the continuum level. Considering the complex geometries involved in shape casting, the evolution of the free surface, gas entrapment, and the entrainment of oxide layers into the casting make this a very challenging task in every respect. Despite well over 30 years of effort in developing algorithms, this is by no means a closed subject. In this article, we will review the full range of computational methods used, from unstructured finite-element (FE) and finite-volume (FV) methods through fully structured and block-structured approaches utilizing the cut-cell family of techniques to capture the geometric complexity inherent in shape casting. This discussion will include the challenges of generating rapid solutions on high-performance parallel cluster technology and how mold filling links in with the full spectrum of physics involved in shape casting. Finally, some indications as to novel techniques emerging now that can address genuinely arbitrarily complex geometries are briefly outlined and their advantages and disadvantages are discussed.

The effects of thermo-electrically induced convection in alloy solidification

The effects of a constant uniform magnetic field on thermoelectric currents during dendritic solidification were investigated using a 2-dimensional enthalpy based numerical model. Using an approximation of the dendrite growing in free space it was found that the resulting Lorentz force generates a circulating flow influencing the solidification pattern. As the magnetic field strength increases it was found that secondary growth on the clockwise side of the primary arm of the dendrite was encouraged, while the anticlockwise side is suppressed due to a reduction in local free energy. The preferred direction of growth rotated in the clockwise sense under an anti-clockwise flow for both the binary alloy and pure material. The tip velociy is significantly increased compared to growth in stagnant flow. This is due to a small recirculation that follows the tip of the dendrite; bringing in colder liquid and lower concentrations of solute. The recirculation being not normally incident on the tip is most likely the cause for the rotation. Grain growth consisting of multiple seeds with the same anisotropy growing in the same plane, gives a competition to release latent heat resulting in stunted growth. The initial growth for each dendrite is very similar to the single seed cases indicating that dendrites must become before the thermoelectric interactions are significant.