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.

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.

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.

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.

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 tilt casting of titanium aluminides

TiAl castings are prone to various defects including bubbles entrained during the turbulent filling of moulds. The present research has exploited the principles of the Durville tilt casting technique to develop a novel process in which the Induction Skull Melting (ISM) of TiAl alloys in a vacuum chamber has been combined with controlled tilt pouring to achieve the tranquil transfer of the metal into a hot ceramic shell mould. Practical casting equipment has been developed to evaluate the feasibility of this process in parallel with the development of novel software to simulate and optimize it. The PHYSICA CFD code was used to simulate the filling, heat transfer and solidification during tilt pouring using a number of free surface modelling techniques, including the novel Counter Diffusion Method (CDM). In view of the limited superheat, particular attention was paid to the mould design to minimize heat loss and gas entrainment caused by interaction between the counter-flowing metal and gas streams. The model has been validated against real-time X-ray movies of the tilt casting of aluminium and against TiAl blade castings. Modelling has contributed to designing a mould to promote progressive filling of the casting and has led to the use of a parabolic tilting cycle to balance the competing requirements for rapid filling to minimize the loss of superheat and slow filling minimize the turbulence-induced defects.

Rapid solutions for application specific IGBT module design

The electric car, the all electric aircraft and requirements for renewable energy are prime examples of potential technologies needing to be addressed in the world problem of global warming/carbon emission etc. Power electronics are fundamental for the underpinning of these technologies and with the diverse requirements for electrical configurations and the range of environmental conditions, time to market is paramount for module manufacturers and systems designers alike. This paper presents a 'virtual' design methodology together with theoretical and experimental results that demonstrate enhanced product design with improved reliability, performance and cost value within competitive schemes.

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.

Advanced microwave oven for rapid curing of encapsulant

The curing of a thermosetting polymer materials utilized on micro-electronics packaging applications can be performed using microwave systems. The use of microwave energy enables the cure process to be completed more rapidly than with alternative approaches due to the ability to heat volumetrically. Furthermore, advanced dual-section microwave systems enable curing of individual components on a chip-on-board assembly. The dielectric properties of thermosetting polymer materials, commonly used in microelectronics packaging applications, vary significantly with temperature and degree of cure. The heating rate within a material subjected to an electric field is primarily dependant on the dielectric loss properties of the material itself. This article examines the variation in dielectric properties of a commercially available encapsulant paste with frequency and temperature and the resulting influence on the cure process. The 'FAMOBS' dual section microwave system and its application to microelectronics manufacture are described. The measurement of the dielectric properties of 'Henkel EO1080' encapsulant paste uses a commercially available 'dielectric probe kit' and is described in this paper. The FAMOBS heating system is used to encapsulate a small op-amp chip. A numerical model formulated to assess the cure process in thermosetting polymer materials under microwave heating is outlined. Numerical results showing that the microwave processing systems is capable of rapidly and evenly curing thermosetting polymer materials are presented.

Three-dimensional simulation of the influence of convection on dendritic solidification

Bulk and interdendritic flow during solidification alters the microstructure development, potentially leading to the formation of defects. In this paper, a 3D numerical model is presented for the simulation of dendritic growth in the presence of fluid flow in both liquid and semi-solid zones during solidification. The dendritic growth was solved by the combination of a stochastic nucleation approach with a finite difference solution of the solute diffusion equation and. a projection method solution of the Navier-Stokes equations. The technique was applied first to simulate the growth of a single dendrite in 2D and 3D in an isothermal environment with forced fluid flow. Significant differences were found in the evolution of dendritic morphology when comparing the 2D and 3D results. In 3D the upstream arm has a faster growth velocity due to easier flow around the perpendicular arms. This also promotes secondary arm formation on the upstream arm. The effect of fluid flow on columnar dendritic growth and micro-segregation in constrained solidification conditions is then simulated. For constrained growth, 2D simulations lead to even greater inaccuracies as compared to 3D.

Thermoelectric effects on alloy solidification microstructure

Thermoelectric currents in the presence of a magnetic field generate Lorentz forces which can drive fluid flow. In the case of dendritic growth a naturally occurring thermoelectric current exists and in the presence of a high magnetic field micro convections are generated. Experimental evidence has attributed changes in microstructure to this effect. A numerical model has been developed to study the flow field around an unconstricted equiaxed dendrite growing under these conditions. The growth is modeled in 2D and 3D by an enthalpy based method and a complex flow structure has been predicted. Using a pseudo-3D approximation for economy, realistic 2D simulations are obtained where a fully coupled transient scheme reveals significant changes to the dendrite morphology reflecting experimental evidence. There is a rotation of the preferred direction of growth and increased secondary branching.

Application of accelerated carbonation with a combination of Na2CO3 and CO2 in cement-based solidification/stabilization of heavy metal-bearing sediment

The efficient remediation of heavy metal-bearing sediment has been one of top priorities of ecosystem protection. Cement-based solidification/stabilization (s/s) is an option for reducing the mobility of heavy metals in the sediment and the subsequent hazard for human beings and animals. This work uses sodium carbonate as an internal carbon source of accelerated carbonation and gaseous CO2 as an external carbon source to overcome deleterious effects of heavy metals on strength development and improve the effectiveness of s/s of heavy metal-bearing sediment. In addition to the compressive strength and porosity measurements, leaching tests followed the Chinese solid waste extraction procedure for leaching toxicity - sulfuric acid and nitric acid method (HJ/T299-2007), German leaching procedure (DIN38414-S4) and US toxicity characteristic leaching procedures (TCLP) have been conducted. The experimental results indicated that the solidified sediment by accelerated carbonation was capable of reaching all performance criteria for the disposal at a Portland cement dosage of 10 wt.% and a solid/water ratio of 1: 1. The concentrations of mercury and other heavy metals in the leachates were below 0.10 mg/L and 5 mg/L, respectively, complying with Chinese regulatory level (GB5085-2007). Compared to the hydration, accelerated carbonation improved the compressive strength of the solidified sediment by more than 100% and reduced leaching concentrations of heavy metals significantly. It is considered that accelerated carbonation technology with a combination of Na2CO3 and CO2 may practically apply to cement-based s/s of heavy metal-bearing sediment. (C) 2008 Elsevier B.V. All rights reserved.

Immobilisation of heavy metal in cement-based solidification/stabilisation: a review

Heavy metal-bearing waste usually needs solidification/stabilization (s/s) prior to landfill to lower the leaching rate. Cement is the most adaptable binder currently available for the immobilisation of heavy metals. The selection of cements and operating parameters depends upon an understanding of chemistry of the system. This paper discusses interactions of heavy metals and cement phases in the solidification/stabilisation process. It provides a clarification of heavy metal effects on cement hydration. According to the decomposition rate of minerals, heavy metals accelerate the hydration of tricalcium silicate (C3S) and Portland cement, although they retard the precipitation of portlandite due to the reduction of pH resulted from hydrolyses of heavy metal ions. The chemical mechanism relevant to the accelerating effect of heavy metals is considered to be H+ attacks on cement phases and the precipitation of calcium heavy metal double hydroxides, which consumes calcium ions and then promotes the decomposition Of C3S. In this work, molecular models of calcium silicate hydrate gel are presented based on the examination of Si-29 solid-state magic angle spinning/nuclear magnetic resonance (MAS/NMR). This paper also reviews immobilisation mechanisms of heavy metals in hydrated cement matrices, focusing on the sorption, precipitation and chemical incorporation of cement hydration products. It is concluded that further research oil the phase development during cement hydration in the presence of heavy metals and thermodynamic modelling is needed to improve effectiveness of cement-based s/s and extend this waste management technique. (C) 2008 Elsevier Ltd. All rights reserved.

Thermoelectric MHD in dendritic solidification

The effects of a constant uniform magnetic field on dendritic solidification were investigated using an enthalpy based numerical model. The interaction between thermoelectric currents on a growing crystal and the magnetic field generates a Lorentz force that creates flow. The need for very high resolution at the liquid-solid boundary where the thermoelectric source originates plus the need to accommodate multiple grains for a realistic simulation, make this a very demanding computational problem. For practical simulations, a quasi 3-dimensional approximation is proposed which nevertheless retains essential elements of transport in the third dimension. A magnetic field normal to the plane of growth leads to general flow circulation around an equiaxed dendrite, with secondary recirculations between the arms. The heat/solute advection by the flow is shown to cause a change in the morphology of the dendrite; secondary growth is promoted preferentially on one side of the dendrite arm and the tip velocity of the primary arm is increased. The degree of approximation introduced is quantified by extending the model into 3-dimensions, where the full Navier-Stokes equation is solved, and compared against the 2-dimensional solution.