A computational model of coupled heat and moisture transfer with phase change in granular sugar during varying environmental conditions

As part of a comprehensive effort to predict the development of caking in granular materials, a mathematical model is introduced to model simultaneous heat and moisture transfer with phase change in porous media when undergoing temperature oscillations/cycling. The resulting model partial differential equations were solved using finite-volume procedures in the context of the PHYSICA framework and then applied to the analysis of sugar in storage. The influence of temperature on absorption/desorption and diffusion coefficients is coupled into the transport equations. The temperature profile, the depth of penetration of the temperature oscillation into the bulk solid, and the solids moisture content distribution were first calculated, and these proved to be in good agreement with experimental data. Then, the influence of temperature oscillation on absolute humidity, moisture concentration, and moisture migration for different parameters and boundary conditions was examined. As expected, the results show that moisture near boundary regions responds faster than farther away from them with surface temperature changes. The moisture absorption and desorption in materials occurs mainly near boundary regions (where interactions with the environment are more pronounced). Small amounts of solids moisture content, driven by both temperature and vapour concentration gradients, migrate between boundary and center with oscillating temperature.

Unstructured staggered mesh methods for fluid flow, heat transfer and phase change

Unstructured grid meshes used in most commercial CFD codes inevitably adopt collocated variable solution schemes. These schemes have several shortcomings, mainly due to the interpolation of the pressure gradient, that lead to slow convergence. In this publication we show how it is possible to use a much more stable staggered mesh arrangement in an unstructured code. Several alternative groupings of variables are investigated in a search for the optimum scheme.

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.

Heat and mass transfer in two-phase porous materials under intensive microwave heating

Computational results for the intensive microwave heating of porous materials are presented in this work. A multi-phase porous media model has been developed to predict the heating mechanism. Combined finite difference time-domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of both temperature and moisture fields as well as energy penetration as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

A new computational approach to microwave heating of two-phase porous materials

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent on both temperature and moisture content. The model was able to reflect the evolution of both temperature and moisture fields as well as energy penetration as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

A unified 3D model of the VAR process

A 3D time-dependent model of the VAR process has been developed using CFD techniques. The model solves the coupled field equations for fluid flow, heat transfer (including phase change) and electromagnetic field, for both the electrode and the ingot. The motion of the electic arc 'preferred spot' can be specified based on observations. Correlations are sought between the local gap height, resulting from instantaneous liquid pool surface shape and electrode tip shape, and the arc motion. The detailed behaviour of the melting film on the electrode tip is studies using a spectral free surface technique, which allows investigation of the drops' detachment and drip shorts.

A computational modelling framework to predict macroscopic phenomena in solder joint formation

A computational model of solder joint formation and the subsequent cooling behaviour is described. Given the rapid changes in the technology of printed circuit boards, there is a requirement for comprehensive models of solder joint formation which permit detailed analysis of design and optimization options. Solder joint formation is complex, involving a range of interacting phenomena. This paper describes a model implementation (as part of a more comprehensive framework) to describe the shape formation (conditioned by surface tension), heat transfer, phase change and the development of elastoviscoplastic stress. The computational modelling framework is based upon mixed finite element and finite volume procedures, and has unstructured meshes enabling arbitrarily complex geometries to be analysed. Initial results for both through-hole and surface-mount geometries are presented.

Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

Computational issues in the modelling of materials-based manufacturing processes

The manufacture of materials products involves the control of a range of interacting physical phenomena. The material to be used is synthesised and then manipulated into some component form. The structure and properties of the final component are influenced by both interactions of continuum-scale phenomena and those at an atomistic-scale level. Moreover, during the processing phase there are some properties that cannot be measured (typically the liquid-solid phase change). However, it seems there is a potential to derive properties and other features from atomistic-scale simulations that are of key importance at the continuum scale. Some of the issues that need to be resolved in this context focus upon computational techniques and software tools facilitating: (i) the multiphysics modeling at continuum scale; (ii) the interaction and appropriate degrees of coupling between the atomistic through microstructure to continuum scale; and (iii) the exploitation of high-performance parallel computing power delivering simulation results in a practical time period. This paper discusses some of the attempts to address each of the above issues, particularly in the context of materials processing for manufacture.

Modeling the dynamics of Magnetic Semilevitation Melting

In semilevitation melting, a cylindrical metal ingot is melted by a coaxial a.c. induction coil. A watercooled solid base supports the ingot, while the top and side free surface is confined by the magnetic forces as the melting front progresses. The dynamic interplay between gravity, hydrodynamic stress, and the Lorentz force in the fluid determines the instantaneous free surface shape. The coupled nonstationary equations for turbulent flow, heat with phase change, and high-frequency electromagnetic field are solved numerically for the axisymmetric time-dependent domain by a continuous mesh transformation, using a pseudospectral method. Results are obtained for the two actually existing coil configurations and several validation cases.

Finite volume methods applied to the computational modelling of welding phenomena

This paper presents the computational modelling of welding phenomena within a versatile numerical framework. The framework embraces models from both the fields of computational fluid dynamics (CFD) and computational solid mechanics (CSM). With regard to the CFD modelling of the weld pool fluid dynamics, heat transfer and phase change, cell-centred finite volume (FV) methods are employed. Additionally, novel vertex-based FV methods are employed with regard to the elasto-plastic deformation associated with the CSM. The FV methods are included within an integrated modelling framework, PHYSICA, which can be readily applied to unstructured meshes. The modelling techniques are validated against a variety of reference solutions.

Coupled 3-D finite difference time domain and finite volume methods for solving microwave heating in porous media

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of temperature and moisture fields as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

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.

Modelling the fluid dynamics and coupled phenomena in arc weld pools

A 3D model of melt pool created by a moving arc type heat sources has been developed. The model solves the equations of turbulent fluid flow, heat transfer and electromagnetic field to demonstrate the flow behaviour phase-change in the pool. The coupled effects of buoyancy, capillary (Marangoni) and electromagnetic (Lorentz) forces are included within an unstructured finite volume mesh environment. The movement of the welding arc along the workpiece is accomplished via a moving co-ordinator system. Additionally a method enabling movement of the weld pool surface by fluid convection is presented whereby the mesh in the liquid region is allowed to move through a free surface. The surface grid lines move to restore equilibrium at the end of each computational time step and interior grid points then adjust following the solution of a Laplace equation.

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.