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.

The shallow water approximation applied to the aluminium electrolysis process

The industrial production of aluminium is an electrolysis process where two superposed horizontal liquid layers are subjected to a mainly vertical electric current supplied by carbon electrodes. The lower layer consists of molten aluminium and lies on the cathode. The upper layer is the electrolyte and is covered by the anode. The interface between the two layers is often perturbed, leading to oscillations, or waves, similar to the waves on the surface of seas or lakes. The presence of electric currents and the resulting magnetic field are responsible for electromagnetic (Lorentz) forces within the fluid, which can amplify these oscillations and have an adverse influence on the process. The electrolytic bath vertical to horizontal aspect ratio is such, that it is advantageous to use the shallow water equations to model the interface motion. These are the depth-averaging the Navier-Stokes equations so that nonlinear and dispersion terms may be taken into account. Although these terms are essential to the prediction of wave dynamics, they are neglected in most of the literature on interface instabilities in aluminium reduction cells where only the linear theory is usually considered. The unknown variables are the two horizontal components of the fluid velocity, the height of the interface and the electric potential. In this application, a finite volume resolution of the double-layer shallow water equations including the electromagnetic sources has been developed, for incorporation into a generic three-dimensional computational fluid dynamics code that also deals with heat transfer within the cell.

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].

Water privatisation

The article examines the expansion of private water companies since 1989 the withdrawal from developing countries from 2003 onwards, and the economic impact of privatisation. The analysis is set in the context of the historical development of water services in the north and the south, showing that the role of private water companies since the start of the 20th century has been historically limited and exceptional. The impact of water privatisation is considered in relation to the issues of investment, prices, and efficiency, drawing on empirical evidence from the north and developing countries in Asia, Africa and Latin America. Particular attention is given to France and the UK, where private water companies, for different reasons, are most established. The evidence from both north and south shows systematic underinvestment, monopoly pricing, regulatory gaming, and no significant efficiency differences between public and private sector operators. In conclusion, the article identifies institutional policies including fiscal constraints and lending conditionalities as key drivers of privatisation, and questions whether these can sustain privatisation in the water sector where historical experience indicates it is an inappropriate solution.

Finance for water and sanitation as a public service

Drawing on empirical evidence gathered through the PSIRU database, this contribution aims at addressing the potential of public finance to enhance the provision of water supply and sanitation as a public service. It highlights the problems associated with (and the disappointing results obtained from) resort to Private Sector Participation and private finance, both historically and in the last 15-20 years, in developed and developing countries. It also addresses the advantages of using public finance as a more cost-effective and equitable instrument to achieve developmental objectives such as the expansion of service coverage and development of water and sanitation infrastructure. The potential of public operations in maximising developmental impact from the social, economic and environmental points of view is then explored referring to specific examples from a variety of countries and regions. These include the in-house restructuring of public operations to enhance transparency, accountability and effectiveness, as well as the use of Public-Public Partnerships (PUPs) to build capacity. Attention is devoted to the specific financial requirements of expanding sewerage services at global level to achieve MDGs or broader developmental goals. These requirements are revisited in light of a regional breakdown of coverage gaps, available resources and development aid flows. These findings challenge the established view among international and bilateral agencies that expanding sewerage services in developing countries is excessively costly and should be abandoned as a priority because unaffordable. This contribution draws on a number of PSIRU Reports, and particularly the following. - http://www.psiru.org/reports/2008-03-W-sewers.pdf - http://boell-latinoamerica.org/download_es/agua08_privatizacion_LA_2007.pdf - http://boell-latinoamerica.org/download_es/agua08_agua_un_servicio_publico.pdf - http://www.psiru.org/reports/2006-03-W-investment.pdf All PSIRU Reports are accessible at http://www.psiru.org/publicationsindex.asp.