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Developing temperature fields in frozen cheese sauce undergoing microwave heating were simulated and measured. Two scenarios were investigated: a centric and offset placement on the rotating turntable. Numerical modeling was performed using a dedicated electromagnetic Finite Difference Time Domain (FDTD) module that was two-way coupled to the PHYSICA multiphysics package. Two meshes were used: the food material and container were meshed for the heat transfer and the microwave oven cavity and waveguide were meshed for the microwave field. Power densities obtained on the structured FDTD mesh were mapped onto the unstructured finite volume method mesh for each time-step/turntable position. On heating for each specified time-step the temperature field was mapped back onto the FDTD mesh and the electromagnetic properties were updated accordingly. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Detailed comparisons were carried out for the centric and offset placements, comparing experimental temperature profiles during microwave thawing with those obtained by numerical simulation.

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.

Induction Skull Melting (ISM) is used for heating, melting, mixing and, possibly, evaporating reactive liquid metals at high temperatures when a minimum contact at solid walls is required. The numerical model presented here involves the complete time dependent process analysis based on the coupled electromagnetic, temperature and turbulent velocity fields during the melting and liquid shape changes. The simulation is validated against measurements of liquid metal height, temperature and heat losses in a commercial size ISM furnace. The often observed limiting temperature plateau for ever increasing electrical power input is explained by the turbulent convective heat losses. Various methods to increase the superheat within the liquid melt, the process energy efficiency and stability are proposed.

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.

Induction skull melting (ISM) is a widely used process for melting certain alloys that are very reactive in the molten condition, such as those based on Ti, TiAl, and Zr, prior to casting components such as turbine blades, engine valves, turbocharger rotors, and medical prostheses. A major research project has been undertaken with the specific target of developing improved techniques for casting TiAl components. The aims include increasing the superheat in the molten metal to allow thin section components to be cast, improving the quality of the cast components and increasing the energy efficiency of the process. As part of this, the University of Greenwich (United Kingdom) has developed a dynamic, spectral-method-based computer model of the ISM process in close collaboration with the University of Birmingham (United Kingdom), where extensive melting trials have been undertaken. This article describes in detail the numerical model that encompasses the coupled influences of turbulent flow, heat transfer with phase change, and AC and DC magneto-hydrodynamics (MHD) in a time-varying liquid metal envelope. Associated experimental measurements on Al, Ni, and TiAl alloys have been used to obtain data to validate the model. Measured data include the true root-meansquare (RMS) current applied to the induction coil, the heat transfer from the molten metal to the crucible cooling water, and the shape of the semi-levitated molten metal. Examples are given of the use of the model in optimizing the design of ISM furnaces by investigating the effects of geometric and operational parameter changes.

Sound waves are propagating pressure fluctuations and are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier-Stokes (RANS) equations do not resolve the acoustic fluctuations. Direct numerical simulation of turbulent flow is still a prohibitively expensive tool to perform noise analysis. This paper proposes the acoustic correction method, an alternative and affordable tool based on a modified defect correction concept, which leads to an efficient algorithm for computational aeroacoustics and noise analysis.

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 loca...

Software technology that predicts stress in electronic systems and packages, developed as part of TCS Programme, is described. The software is closely integrated within a thermal design tool providing the ability to simulate the coupled effects of airflow, temperature and stress on product performance. This integrated approach to analysis will help decrease the number of design cycles.

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: • a single mesh covering the entire domain, • a Navier–Stokes flow, • a single FV-UM discretisation approach for both the flow and solid mechanics procedures, • an implicit predictor–corrector version of the Newmark algorithm, • a single code embedding the whole strategy.

This paper describes work performed at IRSID/USINOR in France and the University of Greenwich, UK, to investigate flow structures and turbulence in a water-model container, simulating aspects typical of metal tundish operation. Extensive mean and fluctuating velocity measurements were performed at IRSID using LDA to determine the flow field and these form the basis for a numerical model validation. This apparently simple problem poses several difficulties for the CFD modelling. The flow is driven by the strong impinging jet at the inlet. Accurate description of the jet is most important and requires a localized fine grid, but also a turbulence model that predicts the correct spreading rates of jet and impinging wall boundary layers. The velocities in the bulk of the tundish tend to be (indeed need to be) much smaller than those of the jet, leading to damping of turbulence, or even laminar flow. The authors have developed several low-Reynolds number (low- Re ) k – e model variants to compute this flow and compare against measurements. Best agreement is obtained when turbulence damping is introduced to account not only for walls, but also for low- Re regions in the bulk – the k – e model otherwise allows turbulence to accumulate in the container due to the restricted outlet. Several damping functions are tested and the results reported here. The k – ω model, which is more suited to transitional flow, also seems to perform well in this problem.

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, P hysica , which can be readily applied to unstructured meshes. The modelling techniques are validated against a variety of reference solutions.

Sound waves are propagating pressure fluctuations, which are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier–Stokes equations do not resolve the acoustic fluctuations. This paper discusses a defect correction method for this type of multi-scale problems in aeroacoustics. Numerical examples in one dimensional and two dimensional are used to illustrate the concept. Copyright (C) 2002 John Wiley & Sons, Ltd.

The effects of a slow rotating magnetic field on thermoelectric magnetohydrodynamics during alloy solidification were investigated using a micro-scale numerical model. For conventional directional solidifcation it was shown that in general the time-dependent acceleration force on the fluid flow is negligible. Using an undercooled growth model with directional solidification approximations the effect on dendritic morphology is predicted, suggesting thermoelectric induced flows will create a significant increase in secondary branching and preferential growth directions on one side of the primary trunk. The extent of macro-segregation under these conditions was also estimated.

Ultrasound treatment of molten metals is used for degassing, to refine microstructure, or disperse immersed particles. The process is most effective when vibrations lead to cavitation. A contactless method of generating sound waves is investigated using electromagnetic (EM) induction. Advantages over an immersed sonotrode would be lack of contamination in reactive melts, strong induced stirring due to Lorentz forces and application to high temperature materials. The induction coil surrounding the crucible — also used to melt the alloy — may be adopted for this purpose with suitable tuning. Numerical simulations of the sound generation have been performed for various cases, with and without resonance in the melt volume, with and without an auxiliary DC field. A computational acoustics approach is coupled with Maxwell’s equations, and likely cavitation zones are identified using the Rayleigh-Plesset equation. Near-resonance conditions are most likely to produce cavitation without mechanically endangering the crucible.

A mathematical model and a numerical scheme for the inverse determination of heat sources generated by means of a welding process is presented in this paper. The accuracy of the heat source retrieval is discussed.

Numerical solutions of realistic 2-D and 3-D inverse problems may require a very large amount of computation. A two-level concept on parallelism is often used to solve such problems. The primary level uses the problem partitioning concept which is a decomposition based on the mathematical/physical problem. The secondary level utilizes the widely used data partitioning concept. A theoretical performance model is built based on the two-level parallelism. The observed performance results obtained from a network of general purpose Sun Sparc stations are compared with the theoretical values. Restrictions of the theoretical model are also discussed.

An electrolytic cell for Aluminum production contains molten metal subject to high currents and magnetic flux density. The interaction between these two fields creates electromagnetic forces within the liquid metal and can generate oscillations of the fluid similar to the waves at the free surface of oceans and rivers. The study of this phenomenon requires the simulation of the current density field, of the magnetic flux density field and the solution of the equations of motion of the liquid mass. An attempt to analyze the dynamical behavior of this problem is made by coupling different codes, based on different numerical techniques, in a single tool. The simulations are presented and discussed.

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.

Aerodynamic generation of sound is governed by the Navier–Stokes equations while acoustic propagation in a non-uniform medium is effectively described by the linearised Euler equations. Different numerical schemes are required for the efficient solution of these two sets of equations, and therefore, coupling techniques become an essential issue. Two types of one-way coupling between the flow solver and the acoustic solver are discussed: (a) for aerodynamic sound generated at solid surfaces, and (b) in the free stream. Test results indicate how the coupling achieves the necessary accuracy so that Computational Fluid Dynamics codes can be used in aeroacoustic simulations.

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.

This paper describes a method for the retrieval of discontinuous heat sources involved in a metal cutting process. Two smoothing techniques were used in the present study in order to smooth noisy sensor data recorded by temperature sensors. The two smoothing techniques are a least squares polynomial fit and a Lagrangian smoothing. These data are then used to recover the heat source. It is found that the least squares polynomial provides over-smoothed results and the Lagrangian smoothing produces phyically acceptable results of the retrieved heat source.

This work is concerned with the development of a numerical scheme capable of producing accurate simulations of sound propagation in the presence of a mean flow field. The method is based on the concept of variable decomposition, which leads to two separate sets of equations. These equations are the linearised Euler equations and the Reynolds-averaged Navier–Stokes equations. This paper concentrates on the development of numerical schemes for the linearised Euler equations that leads to a computational aeroacoustics (CAA) code. The resulting CAA code is a non-diffusive, time- and space-staggered finite volume code for the acoustic perturbation, and it is validated against analytic results for pure 1D sound propagation and 2D benchmark problems involving sound scattering from a cylindrical obstacle. Predictions are also given for the case of prescribed source sound propagation in a laminar boundary layer as an illustration of the effects of mean convection. Copyright © 1999 John Wiley & Sons, Ltd.

International audience; The present article treats different phenomena taking place in a steelmaking converter through the development of two separate models. The first model describes the cavity produced at the free surface of the metal bath by the high-speed impinging oxygen jet. The model is based on a zonal approach, where gas compressibility effects are taken into account only in the high velocity jet region, while elsewhere the gas is treated as incompressible. The volume of fluid (VOF) method is employed to follow the deformation of the bath free surface. Calculations are presented for two- and three-phase systems and compared against experimental data obtained in a cold model experiment presented in the literature. The influence on the size and shape of the cavity of various parameters and models (including the jet inlet boundary conditions, the VOF advection scheme, and the turbulence model) is studied. Next, the model is used to simulate the interaction of a supersonic oxygen jet with the surface of a liquid steel bath in a pilot-scale converter. The second model concentrates on fluid flow, heat transfer, and the post-combustion reaction in the gas phase above the metal bath. The model uses the simple chemical reaction scheme approach to describe the transport of the chemical species and takes into account the consumption of oxygen by the bath and thermal radiative transfer. The model predictions are in reasonable agreement with measurements collected in a laboratory experiment and in a pilot-scale furnace.

A mathematical model to analyse some key aspects of the metal cast process is described involving the filling of the mould by liquid metal and simultaneously, undergoing both cooling and solidification (re-melting) phase change. A computational solution procedure based upon a finite volume discretisation approach, on both structured and unstructured meshes, is described. The overall flow solution procedure is based on the pressure correction algorithm SIMPLE suitably adapted to: (a) solve for the free surface with minimal smearing by the SEA algorithm, and (b) solve for the solidification/melting phase change using an enthalpy conservation algorithm developed by Voller, but with its root in the work of Crank many years ago.

In fluid mechanics, it is well accepted that the Euler equation is one of the reduced forms of the Navier-Stokes equation by truncating the viscous effect. There are other truncation techniques currently being used in order to truncate the Navier-Stokes equation to a reduced form. This paper describes one such technique, suitable for adaptive domain decomposition methods for the solution of viscous flow problems. The physical domain of a viscous flow problem is partitioned into viscous and inviscid subdomains without overlapping regions, and the technique is embedded into a finite volume method. Some numerical results are provided for a flat plate and the NACA0012 aerofoil. Issues related to distributed computing are discussed.

A new general cell-centered solution procedure based upon the conventional control or finite volume (CV or FV) approach has been developed for numerical heat transfer and fluid flow which encompasses both structured and unstructured meshes for any kind of mixed polygon cell. Unlike conventional FV methods for structured and block structured meshes and both FV and FE methods for unstructured meshes, the irregular control volume (ICV) method does not require the shape of the element or cell to be predefined because it simply exploits the concept of fluxes across cell faces. That is, the ICV method enables meshes employing mixtures of triangular, quadrilateral, and any other higher order polygonal cells to be exploited using a single solution procedure. The ICV approach otherwise preserves all the desirable features of conventional FV procedures for a structured mesh; in the current implementation, collocation of variables at cell centers is used with a Rhie and Chow interpolation (to suppress pressure oscillation in the flow field) in the context of the SIMPLE pressure correction solution procedure. In fact all other FV structured mesh-based methods may be perceived as a subset of the ICV formulation. The new ICV formulation is benchmarked using two standard computational fluid dynamics (CFD) problems i.e., the moving lid cavity and the natural convection driven cavity. Both cases were solved with a variety of structured and unstructured meshes, the latter exploiting mixed polygonal cell meshes. The polygonal mesh experiments show a higher degree of accuracy for equivalent meshes (in nodal density terms) using triangular or quadrilateral cells; these results may be interpreted in a manner similar to the CUPID scheme used in structured meshes for reducing numerical diffusion for flows with changing direction.

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.

The interaction of an externally imposed magnetic and electric field on the laminar flow of a conducting fluid in a channel is studied using computational techniques. The Navier-Stokes equations and the equations describing the electromagnetic field are solved simultaneously in a single control volume-type computational fluid dynamic code, in a moderate Hartmann number and interaction parameter regime. The flow considered is two-dimensional, with an imposed magnetic field acting in the third dimension over the central region of the channel and decaying exponentially in the remainder. A pair of electrodes placed at right angles to the magnetic field exercises control over the resultant Lorentz force and hence the velocity profile shape. This configuration has application in direct-current electromagnetic pumps or, conversely, electromagnetic brakes. The initial parabolic flow profile acquires an M-shape / W-shape mode in the magnetic field fringe regions, corresponding to a pump / brake. A novel coupled procedure is described to model magnetohydrodynamic phenomena and is used to explore the effects of the Reynolds number, interaction parameter, and applied voltage on the pump / brake configuration.

This study concerns the mathematical modeling of heat transfer and free surface motion under gravity, in cavities partially filled with a liquid. This two-phase flow problem is solved using a single-phase technique that assumes the air and liquid occupying the volume of the cavity can be treated as a single fluid with a sharp property discontinuity at the interface. A two-valued scalar advection equation is solved to mark the extent of each fluid. This idea is simple in concept, but requires careful application for two reasons: (1) The interface must remain sharp throughout the simulation; and (2) the equations of motion have to be expressed in a way that prevents the numerical “smothering” of the lighter fluid by the heavy one during the iteration process. To satisfy (1), the Van Leer TVD differencing scheme is adopted for the scalar advection equation, with appropriate flux corrections in the momentum and enthalpy equations. To satisfy (2), the continuity equation is expressed in volumetric form. The te...

A technique is described for the adaptation of a structured control volume mesh during the iterative solution process of the Navier-Stokes equations. The scalar equidistribution method is adopted, in conjunction with a Laplace-like grid solver to make a curvilinear body-fitted grid sensitive to local flow gradients. Hence, whilst the total number of grid nodes remains constant during a computation, their relative position is continuously adjusted to promote clustering of cells in regions where gradients are high. The focus of this work is in compressible aerodynamics, where such clustering would be desirable in regions containing shocks but also in boundary layers. The technique is three-dimensional and operates in a series of user-defined grid subdomains or patches. These patches act as reference frames within which grid activity takes place. Bi-cubic splines are extensively used to define the aerodynamic surfaces forming the calculation boundaries and to ensure that grid movement does not compromise surface integrity. The technique is applied to aerofoils, wing surfaces, transonic ducts and nozzles and a supersonic wedge cascade. Significant sharpening of both normal and oblique shock discontinuities is demonstrated over static grid simulations and with fewer overall grid nodes. The technique is successful in both inviscid and viscous (turbulent) simulations.

The analysis of semi-levitation melting is extended to account for the presence of particles (impurities, broken metal dendrite agglomerates, bubbles) during the full melting cycle simulated numerically using the pseudo-spectral schemes. The AC coil is dynamically moving with the melt front progress, while the generated Joule heat serves to enhance the melting rate. The electromagnetic force is decomposed into the time average and the oscillating parts. The time average effects on the particle transport are investigated previously using approximations derived for a locally uniform magnetic field. This paper presents expressions for the skin-layer type of the AC force containing also the pulsating part which contributes to the particle drag by the 'history' and 'added mass' contributions. The intense turbulence in the bulk of molten metal additionally contributes to the particle dispersion. The paper attempts to demonstrate the importance of each of the mentioned effects onto the particle transport during the melting until the final pouring stage. The method could be extended to similar AC field controlled melting/solidification processes.

The application of ultrasound to industrial casting processes has attracted research interest during the last 50 years. However, the transfer and scale-up of this advanced and promising technology to industry has been hindered by difficulties in treating large volumes of liquid metal due to the lack of understanding of certain fundamentals. In the current study experimental results on ultrasonic processing in deionised water and in liquid aluminium (Al) are reported. Cavitation activity was determined in both liquid environments and acoustic pressures were successfully measured using an advanced high-temperature cavitometer sensor. Results showed that highest cavitation intensity in the liquid bulk is achieved at lower amplitudes of the sonotrode tip than the maximum available, suggesting nonlinearity in energy transfer to the liquid, while the location of the sonotrode is seen to substantially affect cavitation activity within the liquid. Estimation of real-time acoustic pressures distributed inside a crucible with liquid Al was performed for the first time. EPSRC

High speed compressible jets are used in a number of steel-making applications. In the case of the BOF, a compressible oxygen jet reacts with a carbon-rich iron bath to reduce carbon levels and produce steel. The intensity of the process is governed by the speed of the jet and by the size and shape of the depression created in the metal and slag by the force of the jet, i.e. by the corresponding free surface. This is a difficult CFD problem, since there are compressible and incompressible regions in the flow domain, which need to be handled differently in a finite volume (FV) pressure-correction scheme. Also, standard turbulence models do not account for compressibility, or the large difference in density between the cold oxygen jet and the hot reacting surroundings. Corrections are introduced to the k-e model to remedy this deficiency and the results are validated against experimental data. The compressible/incompressible boundary is handled through a transition region, based on Mach number.

The future trading of carbon credits and increased financial cost necessitates substantial cuts in incidental CO2 emissions in the production of metals (iron, steel, aluminum, zinc, lead). Although greener methods of production are being developed, in the short term the use of point-source CO2 extraction using existing technology remains attractive. Accelerated natural carbonation, in a fluidized bed is a feasible technological route investigated in this research. CFD modelling has been used to study the efficiency of CO2 capture in a fluidized bed reactor containing a CaO solid sorbent. A Lagrangian/Eulerian scheme describes CaO particle trajectories and exchange of mass, momentum and energy with the carrier gas, with a typical off-gas composition. Different reactor geometries are considered (with uniform, stepped and gradually expanding cross-section), to maximize conversion for a given particle loading and size distribution (100-200 microns). Removal efficiencies of up to 80% are demonstrated, making this a viable process.

Numerical models are used to analyze the complex behaviour of magnetically levitated droplets in the context of determining their thermophysical properties. We focus on a novel method reported in Tsukada et al. [4] which uses periodic laser heating to determine the thermal conductivity of an electromagnetically levitated droplet in the presence of a static DC field to suppress convection. The results obtained from the spectral-collocation based free surface code SPHINX and the commercial package COMSOL independently confirm and extend previous findings in [4]. By including the effects of turbulence and movement of the free surface SPHINX can predict the behaviour of the droplet in dynamic regimes with and without the DC magnetic field. COMSOL is used to investigate arbitrary amplitude axial translational oscillations when the spherical droplet is displaced off its equilibrium. The results demonstrate that relatively small amplitude oscillations could cause significant variation in Joule heating and redistribution of the temperature. The effect of translational oscillations on the lumped circuit inductance is analysed. When a fixed voltage drive is applied across the terminals of the levitation coil, this effect will cause the coil current to change and a correction is needed to the electromagnetic force acting on the droplet.

The flow development and heat transfer in a differentially heated cavity containing a non‐Newtonian fluid is studied using CFD techniques. Investigations are made for a fluid obeying a power‐law type behaviour, for a nominal Rayleigh number of 105. Both dilatant and pseudoplastic regimes are considered and the Nusselt number is obtained for a range of power‐law index values. The results, given in a graphical and tabular form, suggest that deviations from Newtonian stress‐strain behaviour can lead to large changes in overall heat transfer. These changes are due to the behaviour of the wall boundary layers. In the dilatant, or shear‐thickening regime, the isothermal wall layers are thick and slow‐moving; as a consequence, buoyancy induced flow affects the whole of the cavity volume. In contrast, the pseudoplastic (or shear‐thinning) regime leads to thin, fast‐moving wall layers whose effect does not propagate to the core of the cavity which remains stagnant. This behaviour, which is directly attributable to the local value of the fluid viscosity, causes the average Nusselt number to decrease with the power‐law index, n. Pseudoplastic fluids are therefore better at conducting heat than Newtonian fluids, and conversely dilatant fluids are worse. The information contained in this paper is of general interest to workers in heat transfer, but is more specifically relevant to researchers in non‐Newtonian fluids. Example applications include biotechnology, where close temperature control of bio‐cultures in enclosed vessels is required, the food processing industry, the metals casting industry and areas where heat transfer in fine suspensions is required.

Models for three interesting magnetohydrodynamic (MHD) flows have been considered, whereby predicted numerical solutions are compared with their analytical counterparts. Predicted solutions were obtained from simulations carried out using the CFD code PHOENICS, with a Fortran attachment supplying momentum sources to the equations of motion to model the effect of an externally imposed magnetic field. The mathematical formulations adopted and the analytical solutions obtained are described together with the results of the computations.

Quantum-behaved particle swarm optimization was proposed from the view of quantum world and based on the particle swarm optimization, which has been proved to outperform the traditional PSO. The Expansion-Contraction coefficient is the only parameter in QPSO, which has great influence on the global search ability and convergence of the particles. In this paper, two parameter control methods are proposed. Numerical experiments on the benchmark functions are presented.

Microgravity provides ideal experimental conditions for studying highly reactive and under-cooled materials where there is no contact between the sample and the other experimental apparatus. The non-contact conditions allow material properties to be measured from the oscillating liquid droplet response to perturbations. This work investigates the impact of a strong magnetic field on these measurement processes for weakly viscous, electrically conducting droplets. We present numerical results using an axisymmetric model that employs the pseudo-spectral collocation method and a recently developed 3D model. Both numerical models have been developed to solve the equations describing the coupled electromagnetic and fluid flow processes. The models represent the changing surface shape that results from the interaction between forces inside the droplet and the surface tension imposed boundary conditions. The models are used to examine the liquid droplet dynamics in a strong DC magnetic field. In each case the surface shape is decomposed into a superposition of spherical harmonic modes. The oscillation of the individual mode coefficients is then analysed to determine the oscillation frequencies and damping rates that are then compared to the low amplitude solutions predicted by the published analytical asymptotic theory.

The development of the multi-phase flow algorithm MIPSA (Multi-InterPhase Slip-Algorithm) within a two-dimensional Computational Fluid Dynamics (CFD) code called CASCADE is summarized with its application to the modelling of lean phase circulating fluidized beds. The well-known interPhase Slip Algorithm (IPSA) technique for handling the presence of particles in an air stream is modified and extended, to handle explicitly a range of particle sizes simultaneously. The salient features of IPSA are retained; hence each size family is treated as a separate “phase” and its motion governed by its own momentum equations. The MIPSA algorithm is embedded within CASCADE, in a framework which ensures overall conservation of mass, momentum and energy. In this paper, the MIPSA algorithm is used to model the hydrodynamic behaviour of Circulating Fluidized Beds (CFB). CFB's are increasingly being employed by a wide range of process industries and their design for a specific application can be problematic. The ob...

A high DC magnetic field can be used to levitate liquid droplets in terrestrial conditions, as is known from experiments [1,2]. The DC magnetic levitation mechanism is considerably different from the AC case [3], where an intense turbulent flow is generated as a consequence of the rotational nature of the electromagnetic force. In DC magnetic levitation the force distribution is a potential function, which permits analytical solutions in particular cases [4]. The dynamic interactions of the flow with the oscillating interface, confined by the magnetic force, are analysed using a multi-physics numerical model for simulating the time dependent liquid metal and the magnetic field generated by currents in the coil system [5]. The numerical simulations demonstrate the possibility of levitating diamagnetic droplets in strictly controllable conditions permitting the material properties measurement from experimental observations.\ud \ud Two different coil arrangements are analysed using the numerical code to model the DC magnetic levitation of a water droplet. The levitation of liquid in controllable conditions is achievable but requires careful optimisation of the electromagnetic and gravity force balance. The fluid velocities, generated by the magnetic force modification due to the liquid surface oscillation in the strong gradient field, are small in magnitude and remain in the laminar regime.

The focus of this paper is to provide an insight into the complex nature of the flow fields that develop through the application of a magnetic field at different orientations to the direction of dendritic growth. Through the use of linear superposition and exploiting symmetry planes the results show that a variety of different flow fields can be achieved. Some of the features exhibited are a global circulation around the dendrite and circulations at the dendrite tips. How these circulations effect the morphology of the dendrite is investigated when the magnetic field is orientated in the (001) direction. Rotation of the preferential direction of growth and an increase in secondary branching are observed and are a consequence of circulations altering surface free energy. A qualitative agreement of these morphological changes is found between a full 3-dimensional model using a moving mesh and a 2-dimensional model using quasi 3-dimensional approximations.

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.

A finite volume computer model of the continuous casting process for steel flat products has been developed. In this first stage, the model concentrates on the hydrodynamic aspects of the process and in particular the dynamic behavior of the metal/slag interface. The model was validated against experimental measurements obtained in a water model apparatus.

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.

Ultrasound Treatment (UT) is commonly used in light alloys during solidification to refine microstructure, or disperse immersed particles. A sonotrode probe introduced into the melt generates sound waves that are strong enough to produce cavitation of dissolved gases. The same method cannot be used in high temperature melts, or for highly reactive alloys, due to probe erosion and melt contamination. An alternative, contactless method of generating sound waves is proposed and investigated theoretically in this paper, using electromagnetic (EM) induction. In addition to strong vibration, the EM induction currents generate strong stirring in the melt that aids distribution of the UT effect to large volumes of material. In a typical application, the same induction coil surrounding the crucible used to melt the alloy may be adopted for UT with suitable frequency tuning. Alternatively - or in addition - a top coil may be used. For industrial use, instead of multiple sonotrodes as has been the practice in scaling up, modelling shows that one simply has to alter the coil geometry and current to suit. To reach sinusoidal pressure fluctuations suitable for cavitation it may be necessary to tune the induction coil frequency for resonance, given the crucible dimensions.

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Ultrasonic cavitation treatment of melt significantly improves the downstream properties and quality of conventional and advanced metallic materials. However, the transfer of this technology has been hindered by difficulties in treating large volumes of liquid metal. To improve the understanding of cavitation processing efficiency, the Full Cavitation Model, which is derived from a reduced form of the Rayleigh-Plesset equation, is modified and applied to the two-phase problem of bubble propagation in liquid melt. Numerical simulations of the sound propagation are performed in the microsecond time scale to predict the maximum and minimum acoustic pressure amplitude fields in the domain. This field is applied to the source term of the bubble transport equation to predict the generation and destruction of cavitation bubbles in a time scale relevant to the fluid flow. The use of baffles to limit flow speed in a launder conduit is studied numerically, to determine the optimum configuration that maximizes the residence time of the liquid in high cavitation activity regions. With this configuration, it is then possible to convert the batch processing of liquid metal into a continuous process. The numerical simulations will be validated against water and aluminium alloy experiments, carried out at Brunel University. The UK Engineering and Physical Sciences Research Council (EPSRC) for financial assistance for this research in contract numbers: EP/K00588X/1 and EP/K005804/1.

This paper is intended to provide a general review of the current capabilities of turbulence models within the specific area of electronic cooling. The work discussed in this paper is aimed at examining currently available turbulence models and the formulation of a new two-layer hybrid k/spl epsiv//kl model which is specifically designed for electronic application areas. A classic backward facing step configuration was used to evaluate the performance of the turbulence models in the prediction of separated flows. The preliminary results suggest that the hybrid k/spl epsiv//kl turbulence model is a promising zonal model to pursue.

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.