Rotating-frame nuclear magnetic relaxation of spins diffusing on a disordered lattice: a Monte Carlo model

The rotating-frame nuclear magnetic relaxation rate of spins diffusing on a disordered lattice has been calculated by Monte Carlo methods. The disorder includes not only variation in the distances between neighbouring spin sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent spin correlation functions which translate into asymmetry in the characteristic peak in the temperature dependence of the dipolar relaxation rate. The results may be used to deduce the average hopping rate from the relaxation but the effect is not sufficiently marked to enable the distribution of the hopping rates to be evaluated. The distribution, which is a measure of the degree of disorder, is the more interesting feature and it has been possible to show from the calculation that measurements of the relaxation rate as a function of the strength of the radiofrequency spin-locking magnetic field can lead to an evaluation of its width. Some experimental data on an amorphous metal - hydrogen alloy are reported which demonstrate the feasibility of this novel approach to rotating-frame relaxation in disordered materials.

Magnetic modelling and magneto-hydro-dynamic simulations of an aluminium production electrolytic cell

A simulation of the motion of molten aluminium inside an electrolytic cell is presented. Since the driving term of the aluminium motion is the Lorentz (j × B) body force acting within the fluid,this problem involves the solution of the magneto-hydro-dynamic equations. Different solver modules for the magnetic field computation and for the fluid motion simulation are coupled together. The interactions of all these are presented and discussed.

Magnetic levitation fluid dynamics

This work is concerned with the accurate computation of flow in a rapidly deforming liquid metal droplet, suspended in an AC magnetic field. Intense flow motion due to the induced electromagnetic force distorts dynamically the droplet envelope, which is initially spherical. The relative positional change between the liquid metal surface and the surrounding coil means that fluid flow and magnetic field computations need to be closely coupled. A spectral technique is used to solve this problem, which is assumed axisymmetric. The computed results are compared against a physical experiment and "ideal sphere" analytic solutions. A comparison between the "magnetic pressure" approximation and the full electromagnetic force solutions, shows fundamental differences; the full electromagnetic force solution is necessary for accurate results in most practical applications of this technique. The physical reason for the fundamental discrepancy is the difference in the electromagnetic force representation: only the gradient part of the full force is accounted for in the "magnetic pressure" approximation. Figs 9, Refs 13.

Nonlinear MHD stability of aluminium reduction cells

An industrial electrolysis cell used to produce primary aluminium is sensitive to waves at the interface of liquid aluminium and electrolyte. The interface waves are similar to stratified sea layers [1], but the penetrating electric current and the associated magnetic field are intricately involved in the oscillation process, and the observed wave frequencies are shifted from the purely hydrodynamic ones [2]. The interface stability problem is of great practical importance because the electrolytic aluminium production is a major electrical energy consumer, and it is related to environmental pollution rate. The stability analysis was started in [3] and a short summary of the main developments is given in [2]. Important aspects of the multiple mode interaction have been introduced in [4], and a widely used linear friction law first applied in [5]. In [6] a systematic perturbation expansion is developed for the fluid dynamics and electric current problems permitting reduction of the three-dimensional problem to a two dimensional one. The procedure is more generally known as “shallow water approximation” which can be extended for the case of weakly non-linear and dispersive waves. The Boussinesq formulation permits to generalise the problem for non-unidirectionally propagating waves accounting for side walls and for a two fluid layer interface [1]. Attempts to extend the electrolytic cell wave modelling to the weakly nonlinear case have started in [7] where the basic equations are derived, including the nonlinearity and linear dispersion terms. An alternative approach for the nonlinear numerical simulation for an electrolysis cell wave evolution is attempted in [8 and references there], yet, omitting the dispersion terms and without a proper account for the dissipation, the model can predict unstable waves growth only. The present paper contains a generalisation of the previous non linear wave equations [7] by accounting for the turbulent horizontal circulation flows in the two fluid layers. The inclusion of the turbulence model is essential in order to explain the small amplitude self-sustained oscillations of the liquid metal surface observed in real cells, known as “MHD noise”. The fluid dynamic model is coupled to the extended electromagnetic simulation including not only the fluid layers, but the whole bus bar circuit and the ferromagnetic effects [9].

Droplet generation with modulated AC electromagnetic field at nozzle exit

A method of droplet generation based on applying a modulated AC high frequency magnetic field in the localized region of capillary breakup is considered as ans alternative to traditional methods for high temperature liquid melt droplet serial production by pressure variation. The method is based on a pseudo-spectral approximation with a coordinate transformation adaptin to the developing free surface. The electromagnetic field is recomputed continuously with the domain shape change. Practical application cases for liquid silicon droplets of 0.5 - 2 mm diameter are considered in detail.

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.

Levitated droplet oscillations: effect of internal flow

The numerical model for electrically conducting liquid droplets levitated in AC magnetic field is extended to demonstrate various factors affecting the accuracy of material property value measurements. The effects included are the electromagnetic force induced stirring and the resulting turbulence, thermo-capillary convection, and the droplet rotation. The results are validated against available analytical solutions.

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.

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.

Levitated droplet oscillations: effect of internal flow

The numerical model for electrically conducting liquid droplets levitated in AC magnetic field is applied to demonstrate various factors affecting the accuracy of material property value measurements in microgravity conditions. The included effects are the electromagnetic force induced stirring and the resulting turbulence, the thermo-capillary convection, and the droplet rotation. The results are validated against available analytical solutions.