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By Michael Zinigrad

The quality of metallic materials depends on their composition and structure and these are determined by various physico-chemical and technological factors. To effectively prepare materials with required composition, structure and properties it is necessary to carry out a research in two parallel directions: Comprehensive analysis of thennodynamics, kineties and mechanisms of the processes taking place at the solid-liquid-gaseous phase interface during welding processes and development of mathematical models of the specific welding technologies. We have developed unique method of mathematical modeling of phase interaction at high temperatures. This method allows us to build models taking into account the thennodynamic characteristics of the processes, the influence of the initial composition and temperature on the equilibrium state of the reactions, the kinetics of heterogeneous processes, the influence of the temperature, composition, hydrodynamic and thennal factors on the velocity of the chemical and diffusion processes. The model can be implemented in the optimization of various technological processes in welding, surfacing, casting as well as in manufacturing of steels and non-ferrous alloys, materials refining, alloying with special additives, removing of non-metallic inclusions.

Jan 1, 2003

By Michael Zinigrad

The quality of metallic materials depends on their composition and structure and these are determined by various physico-chemical and technological factors. To effectively prepare materials with required composition, structure and properties it is necessary to carry out a research in two parallel directions: Comprehensive analysis of thermodynamics, kinetics and mechanisms of the processes taking place at the solid-liquid-gaseous phase interface during welding processes and development of mathematical models of the specific welding technologies. We have developed unique method of mathematical modeling of phase interaction at high temperatures. This method allows us to build models taking into account the thermodynamic characteristics of the processes, the influence of the initial composition and temperature on the equilibrium state of the reactions, the kinetics of heterogeneous processes, the influence of the temperature, composition, hydrodynamic and thermal factors on the velocity of the chemical and diffusion processes. The model can be implemented in the optimization of various technological processes in welding, surfacing, casting as well as in manufacturing of steels and non-ferrous alloys, materials refining, alloying with special additives, removing of non-metallic inclusions.

Jan 1, 2003

By Y. M. Shneerson, V. M/ Shpaer, E. E. Zhmarin, A. Y. Lapin, E. M. Vigdorchik

This paper describes studies of zinc concentrate oxidizing pressure leaching using the method of mathematical modeling. The concept of a kinetic function was taken as a basis for mathematical modeling of the leaching process. The kinetic function describes dependence of the unreacted component share OJ on the relative time x (the relative time is the ratio of the test duration and the time of complete dissolution). This kinetic function is determined in accordance with the results of batch laboratory tests. The laboratory tests have been carried out on zinc concentrate produced from Kazakhstan zinc-copper ores. Zinc concentrate consisted mainly of three types of minerals: sphalerite (70%), pyrite (13%) and chalcopyrite (10%). Oxidation reactions of sphalerite, pyrite and chalcopyrite have been considered as principal ones. The kinetic characteristics of the process (kinetic function, reaction order, activation energy, duration of complete dissolution of the concentrate components) have been calculated in the course of laboratory tests. The mathematical model was used for estimation of the main technological leaching process parameters (such as process rate, degree of metals extraction, autoclave capacity, heat balance, etc.). Mathematical modeling based on the kinetic function concept allows safe designing of metallurgical equipment and scaling the technology to industrial capacity.

Jan 1, 2004

Sedimentation is used to clarify process effluents or to thicken process slurries. The sedimentation cycle of a suspension is presented as a settling curve. This curve is simply a plot of the height of the interface between the settled suspension and clear liquor versus time. Figure 1 shows a series of graduate cylinders which contain a suspension at various stages in its settling cycle. Cylinder 1 shows the suspension completely mixed at time zero. After a brief period of time (see cylinder 2), the suspension is observed to settle from its initial height Ho to height H1, leaving behind a volume of clear (or turbid) liquor, called the supernatant. The interface between the supernatant and suspension is termed the mud line. It is also possible to distinguish at the bottom of the cylinder a layer of sludge representing solids which have settled from the suspension. The interface between it and the suspension is called the sludge line. The sludge line moves upward in the cylinder.

Jan 1, 1992

By Mike Trovant, Stavros A. Argyropoulos

"A fixed grid numerical model for phase change problems is proposed. The model solves for heat transfer and fluid flow, via the coupled solution of the energy, continuity and momentum equations. In addition, the numerical scheme accounts for temperature varying thermophysical properties and determines the shrinkage profile resulting from phase and density change. Simulations are run to determine the effect of varying model parameters and wall cooling rates on the location and shape of the shrinkage void formation in cylindrical casts. Results are shown for both aluminum and magnesium.IntroductionThe mathematical modeling of phase change processes (be they solidification or melting problems) entails solving for many interrelated phenomena. A comprehensive numerical simulation of the casting of a metal, for example, would have to account for: (a) heat transfer in both the solid and liquid portions of the metal and in the mold, (b) the release of latent heat during phase change, (c) fluid flow behavior in the liquid portion of the metal, (d) temperature induced shrinkage caused by liquid contraction and solidification contraction, and (e) the development of thermal stresses with accompanying shrinkage in the solid portion of the cast and mold. A schematic of the relationships that exist between the coupled equations which govern solidification is shown in Figure 1."

Jan 1, 1994

By Xiaolin Wu

Most coal bump occurrences in the U.S. are directly related to mining operations under strong roofs. An understanding of the behavior of bridging or cantilevering strong roofs over working longwall faces is a key to a safe and productive longwall operation. In this paper, an attempt has been made to study the behavior of strong roof beds using the elastic beam theories. Four structural models are formulated to simulate the locations of strong roofs and their distinct weighting stages. For each model, analytical solutions for the deflection, bending moment, stress, and the strain energy stored in both the coal scam and the strong roof are obtained. Solutions for the critical spans, which are controlled by the caveability of the strong roof beds, are developed. The effects of rocks' differing elastic moduli, under tension and compression, on the actual flexural rigidity, and stress redistribution are analyzed.

Jan 1, 1993

By B. Abedian, L. M. Racz, S. R. Berry, R. W. Hyers

"The presented work represents an effort to improve understanding and prediction of turbulent flow inside electromagnetically-levitated droplets. We show that the flow field in a test case, a nickel droplet levitated under microgravity conditions, is a low Reynolds number turbulent flow, i.e. in the transitional regime between laminar and turbulent. Past research efforts have used laminar, enhanced viscosity, and k - E turbulence models to describe these flows. In our study, we compare the RNG algorithm to laminar and k - E turbulence model results. We show that accurate description of the turbulent eddy viscosity µr is critical in order to obtain realistic velocity fields, and that µr cannot be uniform in levitated droplets. In the RNG method there are no characteristic length or time scales associated with the flow, thus allowing such anisotropic features to be captured. We perform calculations and analyses for two cases (1) a small, non-deforming, spherical nickel droplet and (2) a deforming, oscillating droplet. In addition to flow field calculations, we compare numerically-obtained surface tension and viscosity values to those obtained experimentally by the oscillating drop technique.IntroductionElectromagnetic levitation (EML) is a containerless processing technique for conductive materials. Its advantages are the avoidance of contamination or chemical reaction at container walls and the ability to perform long-term experiments in a metastable state. Because of its current limitation to small sample sizes, its primary use is in the laboratory. One application of interest is the measurement of thermophysical properties of undercooled liquid metals [1, 2, 3, 4]. In EML, a sample weighing approximately 1 gram is positioned inside an electromagnetic field generated by alternating currents flowing through an axisymmetric water-cooled copper coil. The coil must be designed appropriately so that thesample levitates in a stable manner.Traditionally, mathematical modeling has been performed in tandem with both earth-and spacebound electromagnetic levitation experiments, in order to determine the effect of the magnetic field on material and flow characteristics [5, 6, 7, 8]. These calculations are important because they allow design, planning, and correct interpretation of experiments. In addition, the calculations are of fundamental scientific interest, as they can be applied to other electromagnetic materials processing applications [9]."

Jan 1, 1999

By A. Navarra

Within conventional copper and nickel-copper sulfide smelters, ladles of molten matte are fed into converters. These converters blast oxygen-enriched air into the matte, thereby eliminating iron and sulfur. The converting reactions are exothermic and, indeed, the converter heat balance is often a limiting consideration on the smelter throughput. If a portion of the matte were fed in solidified (granulated) form, this would support higher oxygen enrichment, and lower volumes of converter offgas, allowing higher throughput. This approach is not applied in conventional smelters, partly because of the copious amounts of water that must be evaporated in typical granulators, as in the Kennecott-Outotec process. The current paper recalls a waterless matte granulator that had been pioneered in the 1990’s, and is applicable to conventional smelters. A mathematical formulation is presented that can be used in the context of simulation-based optimization, to estimate the size and impact of waterless matte granulation.

By Elliot Schwartz, Julian Szekely

"In this paper we describe an experiment that was recently performed on the IML-2 Space Shuttle mission in which the thermophysical properties of molten metals were measured using electromagnetic levitation. In the planning of these experiments calculations had to be performed to predict the levitation and stirring forces, heating rates, sample deformation, and internal flows within the sample. These predictive calculations were essential for both the planning of the experiments and for the re-planning of experimental runs during the actual Space Shuttle mission.Introduction""Materials Processing in the Computer Age"" involves the use of mathematical modeling to obtain a quantitative understanding of the phenomena that govern materials processing operations. Microgravity, or space shuttle experimentation represents a specific case in point here; the very high cost of the space shuttle flights, the very limited flight opportunities that are available, and the tight resources aboard a shuttle clearly mandate that these experiments be very precisely planned and that all possible opportunities for mathematical modeling be fully exploited.The purpose of this paper is to present the results of calculations performed for the planning of a space shuttle experiment involving electromagnetic levitation and wherever possible present a comparison of the computational predictions with both experimental measurements and asymptotic analyses. Finally we shall seek to discuss the practical implications of both the computational methodologies and the potential experimental findings."

Jan 1, 1994

By Eren H

For a hydrocyclone of fIXed geometry, DC, Di, DO and ? are constants, the variable parameters affecting the performance are Qi, Fi, Du and H. (See Appendix 2 for definition of symbols).The relationship between d50c, Qi, Fi, Du and H gives models which can effectively be used for performance predictions. Such models have already been established by Lynch et al and by Plitt.These models have been tried in a limited manner under continuous operating conditions for on-line cowol. For on-line control effective and accurate instrumentation is required for which a new set up is proposed. Using this set up, a new model was established. A feature in this model is that deviations from the norm of operational parameters affecting d50c were considered. It is shown that these deviations generated by the disturbance of one or more of variations in the parameters, can be monitored by a computer and suitable signals generated to control servo mechanisms for restoring the required d50c value.The logic followed in developing the computer software is described and the application of the model is indicated.

Jan 1, 1990

By Gemei Yang, Pierre Mousset-Jones, Felipe Calizaya, Malcolm J. McPherson

Laboratory tests on controlled airflow recirculation have shown the development of transient states in response to changes in system prevailing conditions such as those generated by a sudden start-up and stoppage of fans. Researchers in many European countries have developed various models to explain these phenomena. However, these models failed to consider some important factors such as diffusion and dispersion of gas in turbulent flows. For both in-line and cross-cut recirculation, tests have shown that after the start- up of a booster fan, the gas concentration in the system fluctuates, reaching high levels at the initial states and slowly dying out with time. These fluctuations cannot be represented adequately by simple step-wise functions but rather by smooth, albeit complex equations. In this paper, the phenomena are explained by the convection-dispersion theory, and represented by a mathematical model. Based on a few simplifications and applying Fourier's Transform Method to the differential equations of the flow recirculation model, an integral form of gas concentration function was derived. The Simpson Integration Method was used to compute numerical results for two laboratory tests. The paper also discusses the range of the dispersion coefficient to improve the accuracy of the model.

Jan 1, 1989

By M. Moys

The use of temperature measurements for unusual applications in the analysis and control of column flotation and milling is discussed. This is followed by a review of some of the authors current research in the application of the discrete element method to the modelling of particulate processes, specifically milling, fluidized beds and chute flow.

Jan 1, 2005

By Y. Y. Sheng

Plume flows created by gas injection into liquid metals have been studied extensively, however the dynamics of bubbles within the plume have not received adequate attention, particularly for large, irregular bubbles, characteristic of the processing of liquid metals. The present model uses a combined Eulerian-Lagrangian approach in which an estimated void fraction distribution is used to calculate the liquid flow field with a conventional Eulerian scheme. The trajectories of bubbles are then computed in a Lagrangian manner using the estimated flow field, and experimentally measured information on bubble drag coefficients', lateral migration due to lateral lift forces and interaction with turbulent eddies, and variation in bubble size due to break-up. Turbulence in the two-phase zone is modeled with a modified k-e model with extra source terms to account for the second phase which have been recently determined by the present authors. The computed void fraction and turbulent liquid flow field distributions are in good agreement with experimental measurements.

Jan 1, 1993

By J. Zou

With the increasing applications of the Chinese metal magnetic liners, the requirement for their technical specifications has become stricter and stricter. It is necessary to deeply analyse the metal magnetic liners in order to improve their reliability and economics. The key issue of metal magnetic liners is magnetic forces: their attractions to mill shell and protection layer. Mathematical models were developed using finite-element analysis software and systematic simulation analyses of the two most critical indexes of magnetic liners were performed to find out the most important parameters and their effect on the liner?s characteristics. The relationships between magnetic forces and installation gaps, thickness of permanent magnets and thickness of protection layer may be used to guide the design of metal magnetic liners for ball mills in order to achieve good economic indexes.

Jan 1, 2014

By Saikat Chatterjee, Xintong (Brett) Liu, Kinnor Chattopadhyay

Magnesia carbon bricks are commonly used in BOFs and are generally pre-heated before the BOF goes into service. Owing to very stringent emission regulations, the BOF pre-heating process need to be controlled and optimized so that, the emission standards are met. One of the major concerns in organic emissions are its stringent limits on emission rates and total volatile emissions. In the present work, an attempt has been made to integrate CFD and Thermodynamic models to predict the emission rate of volatile organics during the pre-heating process. A one dimensional heat transfer model was developed using visual basic and then integrated with thermodynamics calculations using FactSage 6.4. The parameters that affected organic emissions were the pre heating procedure, gas composition of the burner, heating rate and type of the burner. Typical composition of MgO-C bricks and binder materials were obtained from literature and vendor data sheets. Chemical reactions between organic materials, refractory and burner gasses were considered. The model predictions indicated that certain burner conditions could destroy all organics before it exits the vessel while other conditions needed the use of an after burner at the mouth of the vessel. The model was also able to predict the organic emission rates based on the chosen pre-heating profile. This kind of predictive model will be very useful for the steel industry and enable them to justify permit limit applications and stick to the limits by fine tuning their pre-heating process.

Jan 1, 2015

By Taylor R. N

Flow simulations have been performed on the flash-smelting burners currently used at KNS. This paper presents studies of the heat transfer between gas and particles at the burner exit. Gas and particle temperatures, velocity and concentration profiles of the two-phase flow are calculated by the mathematical model. The predicted gas temperatures have been favourably compared against values measured by thermocouples placed near the burners in the flash furnace. The predicted particle temperatures are also reasonable when compared with the measured temperatures.

Jan 1, 1992

An efficient and portable mathematical model has been developed for simulating heat transfer in six-in-line slag-resistance-heating electric furnaces for smelting sulphide ores to produce base metals and platinum group metals. This model is a steady-state one relating furnace conditions and performances to various control and input parameters. Some transient effects occurring in electric furnaces are neglected for computation efficiency. This article describes the model development and modelling results. The present model is capable of predicting: (i) temperatures at various locations in a six-in-line furnace, such as slag bath, matte bath, solid charge, freeboard space, freeze lining, cooling water, and air gaps between solid material components, etc. (ii) freeze lining thickness, (iii)smelting rate, and (iv) heat loss rate, etc. A typical feature of the model is that it is easily portable to different application platforms and sufficiently efficient with execution times less than a few seconds. Therefore, it is possible to apply the model for online prediction and control of heat transfer and freeze lining thickness in industrial electric furnaces.

Jan 1, 2011

By M. I. Kalashnikova, Y. M. Shneerson, E. E. Zhmarin, Y. V. Degtiarev, E. M. Vigdorchik

Separation of a magnetic fraction from nickel concentrate following matte flotation, and its treatment in a separate circuit enable reduces precious metals losses. The magnetic fraction is treated in two stages of oxidative leaching: atmospheric and pressure leaching. A study of the atmospheric stage, using mathematical modelling, is described in this paper. The mathematical model and experimental data were used to carry out industrial process calculations. The model enabled extrapolation of the results of batch laboratory test to industrial-scale continuous processing and the selection of optimal process conditions and large-scale equipment. In December 2004, commercial oxidative leaching tests were performed on the magnetic fraction at the Severonickel Plant (Monchegorsk, Russia). A comparative analysis of the mathematical modelling results and the actual process parameters is presented.

Jan 1, 2005

By Pattinaja MA

Mathematical modelling was carried out to determine the probable convergence and vertical stress patterns around a retreating longwall panel in an underground coal mine in New South Wales. An 'Electrical Resistance Analogue' and a program called 'THREED' based on the displacement discontinuity method were used for the modelling. Parts of the obtained results are presented here and compared with some measurements of convergence at the site. The modelled and measured data agree better qualitatively, than quantitatively.

Jan 1, 1986

By P. A. Bahri, D. G. Dixon, T. M. Woodward

A comprehensive mathematical model of the Sherritt-Gordon ammoniacal pressure leaching process at K winana Nickel Refinery has been constructed. The process is comprised of six autoclaves functioning as a three-stage leach circuit, operating over the temperature and pressure ranges of 85-95°C and 750-1000 kPa, respectively. The process chemistry forms a complex series-parallel reaction network, characterised by: (1) the gas-liquid mass transfer and reduction of oxygen, (2) the oxidation of eight distinct minerals, (3) the oxidation of sulphur, and successive reactions involving various intermediately oxidised sulphur species, and (4) the oxidation of Fe(II) to Fe(III), and subsequent precipitation as a hydrated ferric oxide. Material balances were developed for species in all three phases, and an energy balance to account for all reactions and phase conversions. The multiple convolution integral (MCI) statistical reactor model was employed for the scale-up of particle kinetics. The model has been validated against plant data, and simulation results are in agreement with plant performance.

Jan 1, 2005