Models for magnetohydrodynamics of aluminium electrolysis cells

The electric current and the associated magnetic field in aluminium electrolysis cells create effects limiting the cell productivity and possibly cause instabilities: surface waving, ‘anode effects’, erosion of pot lining, feed material sedimentation, etc. The instructive analysis is presented via a step by step inclusion of different physical coupling factors affecting the magnetic field, electric current, velocity and wave development in the electrolysis cells. The full time dependent model couples the nonlinear turbulent fluid dynamics and the extended electromagnetic field in the cell, and the whole bus bar circuit with the ferromagnetic effects. Animated examples for the high amperage cells are presented. The theory and numerical model of the electrolysis cell is extended to the cases of variable cell bottom of aluminium layer and the variable thickness of the electrolyte due to the anode non-uniform burn-out process and the presence of the anode channels. The problem of the channel importance is well known Moreau-Evans model) for the stationary interface and the velocity field, and was validated against measurements in commercial cells, particularly with the recently published ‘benchmark’ test for the MHD models of aluminium cells [1]. The presence of electrolyte channels requires also to reconsider the previous magnetohydrodynamic instability theories and the dynamic wave development models. The results indicate the importance of a ‘sloshing’ parametrically excited MHD wave development in the aluminium production cells

Numerical modelling of liquid droplet dynamics in microgravity

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

Bubble transport by electro-magnetophoretic forces at anode bottom of aluminium cells

Electrically conducting and nonconducting particles and bubbles experience additional forcing in a liquid which carries electric current. These so called electro-magnetophoretic forces are well known in metallurgical applications, like metal purification in vacuum-arc remelting, electro-slag processes, impurity removal or concentration change in special castings. However, the effect of electro-magnetophoretic forces has never been considered for aluminium cells where the gas bubbles evolving in the liquid electrolyte are surrounded by an electric current and significant magnetic fields. We present models to estimate the effect of electric current flow in the vicinity of the bubbles and the additional pressure distribution resulting from the magnetic forces in the surrounding liquid electrolyte. According to the estimates, this force becomes important for bubbles exceeding 2 mm in size, and could be sufficient to overcome the typical drag force associated with electrolyte flow thereby opposing motion of the bubble along the base of the anode when it is inclined at a slight angle. The effect could explain certain features of the anode effect onset. Mathematical models and numerical results are presented and a further implementation in the general MHD code for the aluminium cell design is discussed

Liquid Droplet Dynamics in Gravity Compensating High Magnetic Field

Numerical models are used to investigate behavior of liquid droplets suspended in high DC magnetic fields of various configurations providing microgravity-like conditions. Using a DC field it is possible to create conditions with laminar viscosity and heat transfer to measure viscosity, surface tension, electrical and thermal conductivities, and heat capacity of a liquid sample. The oscillations in a high DC magnetic field are quite different for an electrically conducting droplet, like liquid silicon or metal. The droplet behavior in a high magnetic field is the subject of investigation in this paper. At the high values of magnetic field some oscillation modes are damped quickly, while others are modified with a considerable shift of the oscillating droplet frequencies and the damping constants from the non-magnetic case

Numerical modelling of silicon melt purification in induction directional solidification system

Solar grade silicon production is an energy intensive and harmful to the environment process. Yet 40% of this valuable product material is lost into sawdust (kerf loss) during wafering. The kerf waste from Fixed Abrasive Sawing of PV silicon wafers is pelletized and then remelted in an induction furnace. The furnace has a square cross-section quartz crucible, surrounded by graphite susceptors and heated by an induction coil that enables directional solidification of the new ingot. Top and bottom 'pancake' coils provide additional temperature control. Once melted, silicon becomes electrically conductive and subject to stirring by induction. To recycle the silicon, particulate impurities (due to the sawing, condensed silicon oxides or carbides) need to be removed. Flow control and the electromagnetic Leenov-Kolin force are used to expel particulates, through a novel dual frequency induction scheme. Three-dimensional, multi-physics numerical modelling captures the electromagnetic, fluid-flow and heat-transfer effects in this process. The presented results show it is possible to retain the impurity particles on the sides of the solidified ingot where they can be sliced off and removed

Droplet Formation with Electromagnetic Pulse Force

Abstract Methods for serial generation of droplets from a liquid jet are shortly reviewed. A method of liquid metal droplet generation based on AC high frequency magnetic field is considered in detail. Numerical model for direct simulation of the time dependent droplet generation process is presented. Computed examples demonstrate the liquid silicon droplet formation for the cases of 500-1500 µm diameter

Finite volume solutions for electromagnetic induction processing

A new method is presented for numerically solving the equations of electromagnetic induction in conducting materials using native, primary variables and not a magnetic vector potential. Solving for the components of the electric field allows the meshed domain to cover only the processed material rather than extend further out in space. Together with the finite volume discretisation this makes possible the seamless coupling of the electromagnetic solver within a multi-physics simulation framework. After validation for cases with known results, a 3-dimensional industrial application example of induction heating shows the suitability of the method for practical engineering calculation

MHD stability of large scale liquid metal batteries

The aim of this paper is to develop a stability theory and a numerical model for the three density-stratified electrically conductive liquid layers. Using regular perturbation methods to reduce the full 3d problem to the shallow layer model, the coupled wave and electric current equations are derived. The problem set-up allows the weakly non-linear velocity field action and an arbitrary vertical magnetic field. Further linearisation of the coupled equations is used for the linear stability analysis in the case of uniform vertical magnetic field. New analytical stability criteria accounting for the viscous damping are derived for particular cases of practical interest and compared to the numerical solutions for variety of materials used in the batteries. The new criteria are equally applicable to the aluminium electrolysis cell MHD stability estimates

Magneto-hydrodynamic stability of a liquid metal battery in discharge

All liquid three layer batteries are intended as large scale electrical energy storage. The paper investigates long wave interfacial instabilities driven by the electromagnetic forces during dynamic phases of the battery charging/discharging. The liquid metal battery of 20 cm size with sodium metal anode, which is a candidate for experimental and commercial implementation, is shown to be unstable at the discharge state when the top metal layer depth is reduced below a critical level. The numerical model includes the effects of viscous friction and the horizontal wave velocities. The instability does not depend on the initial interface perturbation type

Anode bottom burnout shape and velocity field investigation in a high amperage electrolysis cell

Long term burnout shape of the anode bottom is believed to reflect the quasi-stationary liquid metal interface dome-shaped deformation. The shape profiles and their interplay affect the MHD stability, the velocity fields, set up of new anodes and electrical efficiency of the cell. Spent prebake anode bottom profiles were systematically measured at Rusal 309 kA cell to obtain the overall view of the liquid metal deformation. The magnetic field distribution and velocities of liquid metal flow were measured in order to obtain a more complete characterization of the cell. The results are compared to the modelling results using the specialised MHD-VALDIS software giving the insight to the cell dynamics