Jean-François Bilodeau

A Mathematical Model for Ultrafine Iron Powder Growth in a Thermal Plasma

ABSTRACT A two-dimensional model is developed for the growth of ultrafine metal powders in a thermal plasma reactor. The model accounts for particle formation by nucleation, and growth by condensation and Brownian coagulation. Transport of particles occurs by convection, thermophoresis, and Brownian diffusion. The conservation equations for the moments of the particle size distribution are solved, coupled to the equation for the conservation of metal vapor. Elliptic conservation equations result from the consideration of both axial and radial diffusion of the particles. This allows for simulations in complex, recirculating flows, which are likely to occur for numerous reactor configurations and parameters. A progressive grid refining technique is used to accelerate convergence. The model is applied to the case of a typical thermal plasma reactor for the production of ultrafine iron powders. The fields of the macroscopic properties of the aerosol population and the contribution of the different mechanisms ...

A model for ultrafine powder production in a plasma reactor

A model is proposed for the analysis of the production of ultrafine particles in thermal plasma reactors. The model initially solves the fluid flow, temperature, and concentration fields using a classical control volume approach. The nucleation and growth of ultra fine particles are then solved along each streamline. The evolution of the particle distribution is described by a statistical approach, using the first moments of the distribution as the dependent variables. Brownian coalescence is considered in the free molecular regime. In the discussion, the model is used to demonstrate the effects of some important parameters, such as the initial concentration of metal vapor, its radial distribution, and the radial injection of a cooling gas, on the particle size distribution.

Gasification of Residual Biomass via the Biosyn Fluidized Bed Technology

A series of gasification experiments of waste wood, waste wood and plastic mixtures and municipal solid waste have been performed in a 50 kg/h nominal throughput air blown fluidized bed reactor. The state of constant sand bed temperature (±3°C) was usually maintained for 1.5-2 hours. Small fluctuations in process parameters, especially biomass feed rate, resulted in some variations of the composition of the gas. Between 1.7 and 2.4 Nm3 of dry gas were obtained per 1 kg of dry feedstock. The heating value of the gas depended mostly on the feed composition and the amount of air used for gasification. It ranged from 5.2 to 8.2 MJ/Nm3. The carbon conversion rate from biomass to gas in most of the cases exceeded 95% while char yield was less than 3% of dry feed. The material balances were close to 100% with some deficit of carbon and some excess of oxygen accounting for the observed deviations.

Mixing Characteristics of an Axial-Flow Rotor: Experimental and Numerical Study

In the metallurgical industry, various types of rotors are used for the injection and distribution of gas and for homogenizing molten metal. In the present work, the liquid-gas two-phase flow around an axial type impeller is studied in a water model, in order to analyze the bubble break-up and coalescence and metal mixing. Details like primary and secondary vortex structure, gas flooding between the blades and gas dispersion are recorded by using high speed photography.A mathematical model that takes into account the combined effect of bubble break-up and coalescence is implemented in the commercial computational fluid dynamics (CFD) software FLUENT. In the proposed work, the impeller is explicitly described in three dimensions using Multiple Reference Frame Model. Dispersed gas and bubbles dynamics in the turbulent water are modeled using an Eulerian-Eulerian approach with dispersed k-epsilon turbulent model. The model predicts spatial distribution of gas hold-up, average bubble size and flow structure. Good qualitative agreement between physical model and simulation is achieved when comparing the bubble size distribution, flow structure and mixing.

Advanced numerical simulation of the thermo-electro-chemo-mechanical behaviour of hall-héroult cells under electrical preheating

In today’s context, aluminum producers strive to improve their position regarding energy consumption and production costs. To do so, mathematical modeling offers a good way to study the behavior of the cell during its life. This paper deals with the numerical simulation of the electrical preheating of a Hall-Heroult cell using a quarter model of the cell. The fully coupled thermo-electro-mechanical model includes material non linearities and multiphysical behavior at interfaces allowing accurate evaluation of the stress distribution in the cathode blocks and surrounding components. The baking of the ramming paste as well as the evolution of its thermo-electro-mechanical properties are updated via the baking index computed using a kinetic of reaction. The model is initially calibrated with in situ measurements and then used to estimate the effect of preheating on the behavior of the cell including temperature, current, deformations as well as the contact conditions at critical interfaces.

Thermal conductivity of the sideledge in aluminium electrolysis cells: Experiments and numerical modelling

During aluminium electrolysis, a ledge of frozen electrolytes is generally formed, attached to the sides of the cells. This ledge acts as a protective layer, preventing erosion and chemical attacks of both the electrolyte melt and the liquid aluminium on the side wall materials. The control of the sideledge thickness is thus essential in ensuring a reasonable lifetime for the cells. The key property for modelling and predicting the sideledge thickness as a function of temperature and electrolyte composition is the thermal conductivity. Unfortunately, almost no data is available on the thermal conductivity of the sideledge. The aim of this work is to alleviate this lack of data. For seven different samples of sideledge microstructures, recovered from post-mortem industrial electrolysis cells, the thermal diffusivity, the density, and the phase compositions were measured in the temperature range of 423 K to 873 K. The thermal diffusivity was measured with a laser flash technique and the average phase compositions by X-ray diffraction analysis. The thermal conductivity of the sideledge is deduced from the present experimental thermal diffusivity and density, and the thermodynamically assessed heat capacity. In addition to the present experimental work, a theoretical model for the prediction of the effective thermal transport properties of the sideledge microstructure is also proposed. The proposed model considers an equivalent microstructure and depends on phase fractions, porosity, and temperature. The strength of the model lies in the fact that only a few key physical properties are required for its parametrization and they can be predicted with a good accuracy via first principles calculations. It is shown that the theoretical predictions are in a good agreement with the present experimental measurements.

Modeling the Behavior of Alumina Agglomerate in the Hall‐Héroult Process

During the feeding of the Hall-Heroult cell, cold alumina comes into contact with the electrolyte bath and tends to agglomerate due to the formation of a frozen bath layer that holds physically the alumina together. This agglomeration, producing alumina agglomerates, called also lumps or sludge, affects both the rate of alumina dissolution and the stability of the cell. In this paper, all the physical phenomena (heat and mass transfer) between the formation and the complete dissolution of agglomerate will be described and are defined by a set of equations. This mathematical model allows observing the strong coupling between the mechanisms of heat and mass transfer e.g. the solidification with diffusion of chemical species, the infiltration of the bath in the porous agglomerate and the dissolution of sintered alumina. A parametric study using this model might identify the most important factors related to the lifespan and behavior of alumina agglomerates.

Experimental Determination of the Thermal Diffusivity of α-Cryolite up to 810 K and Comparison with First Principles Predictions

In aluminum electrolysis cells, a ledge of frozen electrolyte is formed on the sides. Controlling the side ledge thickness (a few centimeters) is essential to maintain a reasonable life span of the electrolysis cell, as the ledge acts as a protective layer against chemical attacks from the electrolyte bath used to dissolve alumina. The numerical modeling of the side ledge thickness, by using, for example, finite element analysis, requires some input data on the thermal transport properties of the side ledge. Unfortunately, there is a severe lack of experimental data, in particular, for the main constituent of the side ledge, the cryolite (Na3AlF6). The aim of this study is twofold. First, the thermal transport properties of cryolite, not available in the literature, were measured experimentally. Second, the experimental data were compared with previous theoretical predictions based on first principle calculations. This was carried out to evaluate the capability of first principle methods in predicting the thermal transport properties of complex insulating materials. The thermal diffusivity of a porous synthetic cryolite sample containing 0.9 wt % of alumina was measured over a wide range of temperature (473–810 K), using the monotone heating method. Because of limited computational resources, the first principle method can be used only to determine the thermal properties of single crystals. The dependence of thermal diffusivity of the Na3AlF6 + 0.9 wt % Al2O3 mixture on the microstructural parameters is discussed. A simple analytical function describing both thermal diffusivity and thermal conductivity of cryolite as a function of temperature is proposed.

Study of the Impact of Anode Slots on the Voltage Fluctuations in Aluminium Electrolysis Cells, Using Bubble Layer Simulator

There is a constant effort from aluminium producers to reduce energy consumption of the Hall-Heroult cells in order to decrease cost and environmental fingerprint. Among others, slotted anodes were introduced in order to promote faster evacuation of the electrically isolating anode gas bubbles and thus diminish their contribution to the total cell voltage. A bubble layer simulator was developed to reproduce cell voltage fluctuations, caused by the dynamics of anode bubbles. Results of simulations show that the slots cut in the right position and direction can reduce both the amplitude of fluctuations and the average cell voltage. This impact is even higher for new, almost horizontal flat anode bottoms. It is also revealed that the slots are acting mainly as a simple bubble sink, but they also contribute to the acceleration of the bubble layer as well and thus their role in the momentum exchange between liquid and gas must be taken into account.

Spreading of Alumina and Raft Formation on the Surface of Cryolitic Bath

It is a well-known phenomenon in aluminum industry that alumina powder, fed into the electrolyte, tends to stay afloat on the surface of the bath. This hinders dispersion and direct contact of most of the powder with the electrolyte, therefore delays dissolution. In addition, large clusters of alumina particles sintered together during raft formation might lead to the agglomerate piercing through the bath-aluminum interface, which should be avoided. Since the interference between raft formation and alumina dissolution is significant, it deserves more attention. Several experiments were conducted in a small carbon crucible in which cryolitic bath was melted and alumina of different properties was fed. The injections were recorded by a video camera above the bath. The spreading of the powder on the surface, the infiltration of powder by the bath as well as the disintegration or the sinking of the raft was observed and the results analyzed.