Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

Computational modelling of bubbles, droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.

A computational study of segregation in granular material during heaping

A continuum model of the flow of granular material during silo filling using a viscoplastic constitutive relation is presented in this paper. The constitutive model is based on the Drucker-Prager plasticity yield function. The simulation results give a realistic representation of complex features of granular flows during filling processes, such as heap formation and non-zero inclination angle of the material-air interface. The model is also coupled within the same framework with novel micro-mechanical parametrisations and the process of segregation during filling of granular mixtures can also be modelled.

Time dependent electric, magnetic and hydrodynamic interaction in aluminium electrolysis cells

The waves in commercial cells for electrolytic aluminium production originate at the interface between the liquid aluminium and electrolyte, but their effect can spread into the surrounding busbar network as electric current perturbation, and the total magnetic field acquires a time dependent component. The presented model for the wave development accounts for the nonuniform electric current distribution at the cathode and the whole network of the surrounding busbars. The magnetic field is computed for the continuous current in the fluid zones, all busbars and the ferromagnetic construction elements. When the electric current and the associated magnetic field are computed according to the actual electrical circuit and updated for all times, the instability growth rate is significantly affected. The presented numerical model for the wave and electromagnetic interaction demonstrates how different physical coupling factors are affecting the wave development in the electrolysis cells. These small amplitude self-sustained interface oscillations are damped in the presence of intense turbulent viscosity created by the horizontal circulation velocity field. Additionally, the horizontal circulation vortices create a pressure gradient contributing to the deformation of the interface. Instructive examples for the 500 kA demonstration cell are presented.

Multiscale modelling of dendrite growth during vacuum arc remelting

Vacuum Arc Remelting (VAR) is the accepted method for producing homogeneous, fine microstructures that are free of inclusions required for rotating grade applications. However, as ingot sizes are increasing INCONEL 718 becomes increasingly susceptible to defects such as freckles, tree rings, and white spots increases for large diameter billets. Therefore, predictive models of these defects are required to allow optimization of process parameters. In this paper, a multiscale and multi-physics model is presented to predict the development of microstructures in the VAR ingot during solidification. At the microscale, a combined stochastic nucleation approach and finite difference solution of the solute diffusion is applied in the semi-solid zone of the VAR ingot. The micromodel is coupled with a solution of the macroscale heat transfer, fluid flow and electromagnetism in the VAR process through the temperature, pressure and fluid flow fields. The main objective of this study is to achieve a better understanding of the formation of the defects in VAR by quantifying the influence of VAR processing parameters on grain nucleation and dendrite growth. In particular, the effect of different ingot growth velocities on the microstructure formation was investigated. It was found that reducing the velocity produces significantly more coarse grains.

The study of flow and temperature fields in conducting droplets suspended in a DC/AC combination field

Electromagnetic Levitation (EML) is a valuable method for measuring the thermo-physical properties of metals - surface tensions, viscosity, thermal/electrical conductivity, specific heat, hemispherical emissivity, etc. – beyond their melting temperature. In EML, a small amount of the test specimen is melted by Joule heating in a suspended AC coil. Once in liquid state, a small perturbation causes the liquid envelope to oscillate and the frequency of oscillation is then used to compute its surface tension by the well know Rayleigh formula. Similarly, the rate at which the oscillation is dampened relates to the viscosity. To measure thermal conductivity, a sinusoidally varying laser source may be used to heat the polar axis of the droplet and the temperature response measured at the polar opposite – the resulting phase shift yields thermal conductivity. All these theoretical methods assume that convective effects due to flow within the droplet are negligible compared to conduction, and similarly that the flow conditions are laminar; a situation that can only be realised under microgravity conditions. Hence the EML experiment is the method favoured for Spacelab experiments (viz. TEMPUS). Under terrestrial conditions, the full gravity force has to be countered by a much larger induced magnetic field. The magnetic field generates strong flow within the droplet, which for droplets of practical size becomes irrotational and turbulent. At the same time the droplet oscillation envelope is no longer ellipsoidal. Both these conditions invalidate simple theoretical models and prevent widespread EML use in terrestrial laboratories. The authors have shown in earlier publications that it is possible to suppress most of the turbulent convection generated in the droplet skin layer, through use of a static magnetic field. Using a pseudo-spectral discretisation method it is possible compute very accurately the dynamic variation in the suspended fluid envelope and simultaneously compute the time-varying electromagnetic, flow and thermal fields. The use of a DC field as a dampening agent was also demonstrated in cold crucible melting, where suppression of turbulence was achieved in a much larger liquid metal volume and led to increased superheat in the melt and reduction of heat losses to the water-cooled walls. In this paper, the authors describe the pseudo-spectral technique as applied to EML to compute the combined effects of AC and DC fields, accounting for all the flow-induced forces acting on the liquid volume (Lorentz, Maragoni, surface tension, gravity) and show example simulations.

Effect of adding 0.3 wt% Ni into the Sn–0.7 wt%Cu solder: part I: wetting behavior on Cu and Ni substrates

Comparative wetting behavior of Sn-0.7Cu and Sn-0.7Cu-0.3Ni solders on Cu and Ni substrates were assessed through the wetting balance test. No-clean (NC), non-activated (R) and water soluble organic acid (WS) fluxes were used to assess the wetting behavior for three different solder bath temperatures of 255, 275 and 295 °C. Experimental results unveiled that adding of 0.3 wt% Ni into Sn-0.7Cu solder can improve the wetting on Cu substrate when NC and WS fluxes are used. However, such addition of Ni did not improve the wetting of Sn-0.7Cu solder for R-type flux. In the case of Ni substrate, addition of Ni helped to improve the wetting for all three types of fluxes as higher wetting forces were documented for Sn-0.7Cu-0.3Ni solder compared to the Sn-0.7Cu solder. Among the fluxes, worst performance was observed for R-type flux. Very large contact angles were recorded for both solders with this kind of flux. Experimental results also revealed that higher solder bath temperature played an important role to lower the contact angle, to increase the wetting force and to enhance the wetting. Computer modeling of wetting balance test also revealed that both the wetting force and meniscus height are inversely proportional to the contact angles. Besides, solder bath depth and radius do not affect significantly on the wetting behavior.

Effect of adding 0.3wt% Ni into the Sn-0.7wt% Cu solder - Part II: Growth of intermetallic layer with Cu during wetting and aging

The growth behavior of intermetallic layer with or without adding 0.3 wt% Ni into the Sn-0.7Cu solder was studied during the wetting reaction on Cu-substrate and thereafter in solid-state aging condition. The Cu-solder reaction couple was prepared at 255, 275 and 295 °C for 10 s. The samples reacted at 255 °C were then isothermally aged for 2-14 days at 150 °C. The reaction species formed for the Sn-0.7Cu/Cu and Sn-0.7Cu-0.3Ni/Cu soldering systems were Cu6Sn5 and (CuNi)6Sn5, respectively. The thickness of the intermetallic compounds formed at the solder/Cu interfaces and also in the bulk of both solders increased with the increase of reaction temperature. It was found that Ni-containing Sn-0.7Cu solder exhibited lower growth of intermetallic layer during wetting and in the early stage of aging and eventually exceeded the intermetallic layer thickness of Sn-0.7Cu/Cu soldering system after 6 days of aging. As the aging time proceeds, a non-uniform intermetallic layer growth tendency was observed for the case of Sn-0.7Cu-0.3Ni solder. The growth behavior of intermetallic layer during aging for both solders followed the diffusion-controlled mechanism. The intermetallic layer growth rate constants for Sn-0.7Cu and Sn-0.7Cu-0.3Ni solders were calculated as 1.41 × 10-17 and 1.89 × 10-17 m2/s, respectively which indicated that adding 0.3 wt% Ni with Sn-0.7Cu solder contributed to the higher growth of intermetallic layer during aging. © 2006 Elsevier B.V. All rights reserved.

Droplet oscillations in high gradient static magnetic field

In high intensity and high gradient magnetic fields the volumetric force on diamagnetic material, such as water, leads to conditions very similar to microgravity in a terrestrial laboratory. In principle, this opens the possibility to determine material properties of liquid samples without wall contact, even for electrically non-conducting materials. In contrast, AC field levitation is used for conductors, but then terrestrial conditions lead to turbulent flow driven by Lorentz forces. DC field damping of the flow is feasible and indeed practiced to allow property measurements. However, the AC/DC field combination acts preferentially on certain oscillation modes and leads to a shift in the droplet oscillation spectrum.What is the cause? A nonlinear spectral numerical model is presented, to address these problems.

Dynamic model for metal cleanness evaluation by melting in a cold crucible

Melting of metallic samples in a cold crucible causes inclusions to concentrate on the surface owing to the action of the electromagnetic force in the skin layer. This process is dynamic, involving the melting stage, then quasi-stationary particle separation, and finally the solidification in the cold crucible. The proposed modeling technique is based on the pseudospectral solution method for coupled turbulent fluid flow, thermal and electromagnetic fields within the time varying fluid volume contained by the free surface, and partially the solid crucible wall. The model uses two methods for particle tracking: (1) a direct Lagrangian particle path computation and (2) a drifting concentration model. Lagrangian tracking is implemented for arbitrary unsteady flow. A specific numerical time integration scheme is implemented using implicit advancement that permits relatively large time-steps in the Lagrangian model. The drifting concentration model is based on a local equilibrium drift velocity assumption. Both methods are compared and demonstrated to give qualitatively similar results for stationary flow situations. The particular results presented are obtained for iron alloys. Small size particles of the order of 1 μm are shown to be less prone to separation by electromagnetic field action. In contrast, larger particles, 10 to 100 μm, are easily “trapped” by the electromagnetic field and stay on the sample surface at predetermined locations depending on their size and properties. The model allows optimization for melting power, geometry, and solidification rate.

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.

Shallow water model for aluminium electrolysis cells with variable top and bottom

The MHD wave instability in commercial cells for electrolytic aluminium production is often described using ‘shallow water’ models. The model [1] is extended for a variable height cathode bottom and anode top to account for realistic cell features. The variable depth of the two fluid layers affects the horizontal current density, the wave development and the stability threshold. Instructive examples for the 500 kA cell are presented.

Modelling metal powder production by the gas atomisation process

Metal powder in the range of 10-100 microns is widely employed in the production of Raney nickel type catalysts for hydrogenation reactions and hydrogen fuel cell manufacture. In this presentation we examine the modelling of powder production in a gas atomisation vessel using CFD techniques. In a fully coupled Lagrangian-Eulerian two phase scheme, liquid meal particles are tracked through the vessel following atomisation of a liquid nickel-aluminium stream. There is full momentum, heat and turbulence transport between particles and surrounding argon gas and the model predicts the position of solidification depending on particle size and undercooled condition. Maps of collision probability of particles at different stages of solidification are computed, to predict the creation of satellite defects, or to initiate solidification of undercooled droplets. The model is used to support experimental work conducted under the ESA/EU project IMPRESS.

Impact of the vertical potshell deformation on the MHD cell stability behavior of a 500 kA aluminium electrolysis cell

In previous publications [1,2], it was rationalized that a large vertical potshell deformation may have a negative impact on the operations of very high amperage cells. The MHD-Valdis non-linear Magneto-Hydro-Dynamic model was therefore extended to take into account the displacement of the potshell. The MHD cell stability behavior of a 500 kA cell with a 17.3 meters long potshell was then studied.

Time-dependent modelling and experimental validation of the metal/flux interface in a continuous casting mould

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.