A mixture model to take into account diluted gas in liquid flow: applications to aluminium electrolysis

Aluminium is a metal sought in the industry because of its various physical properties. It is produced by an electrolysis reduction process in large cells. In these cells, a large electric current goes through the electrolytic bath and the liquid aluminium. This electric current generates electromagnetic forces that set the bath and the aluminium into motion. Moreover, large quantities of carbon dioxide gas are produced through chemical reactions in the electrolytic bath: the presence of these gases alleviates the density of the liquid bath and changes the dynamics of the flow. Accurate knowledge of this fluid flow is essential to improve the efficiency of the whole process.The purpose of this thesis is to study and approximate the interaction of carbon dioxide with the fluid flow in the aluminium electrolysis process.In the first chapter of this work, a mixture-averaged model is developed for mixtures of gas and liquid. The model is based on the conservation of mass and momentum equations of the two phases, liquid and gas. By combining these equations, a system is established that takes into account the velocity of the liquid-gas mixture, the pressure, the gas velocity and the local gas concentration as unknowns.In the second chapter, a simplified problem is studied theoretically. It is shown that under the assumption that the gas concentration is small, the problem is well-posed. Moreover, we prove a priori error estimates of a finite element approximation of this problem.In the third chapter, we compare this liquid-gas model with a water column reactor experiment. Finally, the last chapter shows that the fluid flow is changed in aluminium electrolysis cells when we take into account the density of the bath reduced by carbon dioxide. These changes are quantified as being of the order of 30% and explain partially the differences between previous models and observations from Rio Tinto Aluminium engineers.

Méthodes numériques liées à la distribution d'alumine dans une cuve d'électrolyse d'aluminium

Thomas Frédéric Hilke

Metallic aluminium plays a key role in our modern economy. Primary metallic aluminium is produced by the transformation of aluminium oxide using the Hall-Héroult industrial process. This process, which requires enormous quantities of energy, consists in performing the electrolysis of an aluminium oxide solute in large pots and with hundreds of thousands of amperes of electrical current. The topic of this thesis is the study of some selected aspects of the modelisation of the electrolysis process from the point of view of numerical simulation. This thesis is divided in two parts. The first part is focused on the numerical modelisation of the alumina powder dissolution and transport in the electrolytic bath as a function of the bath temperature. We provide a mathematical model for the transport and dissolution of the alumina powder, followed by its time and space discretisation by means of a finite element method. Finally, we study the behavior of this numerical model in the case of an industrial electrolysis pot. The second part is devoted to the development of a numerical scheme for the approximation of the fluid flows in an electrolysis pot. The scheme relies on a Fourier basis decomposition of the unknowns. The amplitude of each Fourier component satisfies a partial differential equation which is explicitely derived. The solution of this equation is approximated by means of a finite element method. Finally, the approximate fluid flow obtained with this new method is compared with the solution provided by the reference model in an industrial

EPFL2019

Flow pattern observations and flow pattern map for adiabatic two-phase flow of carbon dioxide in vertical upward and downward direction

Rémi Revellin, Jürg Alexander Schiffmann, David Schmid

A test facility to investigate flow pattern transitions of vertical two-phase flow of CO2 has been built within the scope of the high-luminosity detector upgrades at the European Organization for Nuclear Research (CERN). Adiabatic flow pattern observations for both vertical up- and downflow are recorded with high-speed imaging in tubes of 8 mm inner diameter, with saturation temperatures in the range of −25◦C to +5◦C and mass velocities ranging from 100 kgm−2 s−1 to 450 kgm−2 s−1. A database of 431 flow pattern observations in upward and 123 in downward direction has been compiled. The recorded data have been analysed with machine learning techniques and a previously trained Frame- and Flow-Regime-Classifier is used for the flow regime classification. The observed two-phase flow pattern transitions did not match the transition lines of existing flow pattern maps. As a consequence, new transition lines for the bubbly-to-slug, slug-to-churn and churn-toannular transitions have been developed for both vertical upflow and downflow respectively and condensed into new flow pattern maps. It is concluded, that the flow regime transitions are strongly depended on vapour quality, mass velocity, the flow direction and the fluid properties. Compared to horizontal flow, a dryout region is not observed and the liquid film of the annular flow regime dries out symmetrically at vapour qualities close to 𝑥 = 1.

2022

Dynamic wetting in pressure-infiltration of ceramic particle preforms by molten metal

Gionata Schneider

This thesis investigates the interaction between mechanically induced flow of a liquid metal into a porous solid, and kinetic effects at the triple line. The approach is experimental and focuses on metal-ceramic systems for which the literature gives values of wetting and local kinetic parameters (Simga, SimgaLV, and interfacial phenomena near the triple line) at high temperature, gleaned by means of the sessile drop experiment. We investigate the infiltration with Al of Al2O3 preforms at 1000°C, 1050°C and 1100°C, and the infiltration with Cu-x (x=Si, Ti or Cr) of porous CGr between 1050°C and 1200°C. Those three alloys are known to form carbides better wetted by the liquid than is graphite. If measurements are taken at various values of applied metal overpressure, in the presence of thermally activated processes at the triple line, time intervenes in capillarity and the front does not stabilise. We observe that the metal continues to invade slowly the porous medium, gradually ¿creeping¿ into its pores under the action of local phenomena that take place at the triple line. We characterise such dynamic infiltration by measuring rates of steady isobaric infiltration, measuring also the variation of infiltration rates at Pth and Pth+0.05MPa. Saturation rates are then computed by means of a linear regression over 100s of the measured saturation for each pressure step. Data are interpreted using an analogy with high-temperature plasticity. This leads to assume that the applied pressure contributes a proportional reduction in the activation energy of the process that governs the rate of preform infiltration, the constant of proportionality defining an activation volume that characterises the thermally activated process. Cu-46at.pct.Si infiltrating carbon is a mildly reactive system that forms SiC at the interface. Isobaric saturation rates of infiltration and their dependence on variations in the applied pressure were conducted between 1050°C and 1200°C. It is found that an activation volume on the order of ~200nm3 makes the data compatible with the Arrhenius law, with an estimated activation energy value of ~400kJ/mol, which is realistic for a process limited by the rate of SiC growth along the interface. Aluminium infiltrating three different Al2O3 preforms shows similar behaviour as does the mildly reactive Cu-Si/C system if particles in the preform are highly angular, regardless of the presence or absence of Na impurities. Isobaric saturation rates measured between 1000°C and 1100°C give a similar activation volume as the Cu-Si/C system, on the order of ~200nm3, and an activation energy ~300kJ/mol, suggesting that the kinetics are likely limited by solid phase diffusion. It is also shown that sodium impurities in alumina serve to facilitate its infiltration by aluminium, likely because sodium alters the oxide skin that initially covers the melt. Finally, in the infiltration of Cu-1at.pct.Cr or Cu-10at.pct.Ti into CGr, one finds that interfacial reaction does not aid pressure infiltration. In the former, it is because initial reaction between melt and preform depletes the alloy in reactive Cr, leading to similar infiltration as with pure Cu. In the latter, initial carbide formation is so extensive that it blocks ingress of the metal into the preform. For alloying elements forming a better wetted interface to aid pressure infiltration, reaction must thus be sufficiently slow compared to the rate of metal flow.

EPFL2019

Dynamic wetting in pressure-infiltration of ceramic particle preforms by molten metal

Gionata Schneider

EPFL2019