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By P. J. Baguley

The model has been developed on the basis of the observation that the partitioning behaviour of a particle is related to its calculated terminal velocity. It utilises a theoretical calculation of the terminal velocity of each particle class. This is then correlated with the observed partition data for a plant separator using empirically-derived functions of operating conditions which take into account effects such as bath turbulence, holes in drum lifters and feed arrangements. The model successfully decouples the effects of medium density and viscosity and is appropriate for any bath-type separator. The correlation between calculated terminal velocity and actual partitioning behaviour was established and modelled using data obtained from two Wemco drums treating Fe and Mn ores. The model can be used to predict the prevailing size-by-size partition curves and the separation (product grades/recoveries) given the washability of the feed and operating conditions. Simulations are used to show that, for the treatment of Fe ore, there is a maximum medium density beyond which product grades fall and that this maximum decreases as the proportion of magnetite in the medium increases. This is attributed to the dominant effect of viscosity at higher medium solids concentrations

Jun 18, 1905

By Jianhua Xin, Min Chen, Lei Xu, Haohua Deng, Nan Wang

A mathematical model of converter slagging and steelmaking process by replacing part of lime with limestone is established. The rate equations of oxidation reactions and lime dissolution in converter under the limestone substitution proportion increasing from 25 to 50% can be obtained and the effects of limestone substitution proportion on the variations of the composition of hot metal, slag and converter gas during the steelmaking process are investigated. In the process of converter slagging and steelmaking by replacing part of lime with limestone, increasing the hot metal temperature and the lance height could be favor to increase the content of FeO in the slag and accelerate the limestone decomposition and dissolution. With the limestone substitution proportion increasing from 25 to 50%, the maximum of oxygen supply ratio increases from 10.7 to 19.7% and the temperature drop of converter bath is 8–60 °C.

Mar 1, 2018

By Pietro Navarra

Cooling of critical furnace equipment to produce freeze lining is of particular interest as many metallurgical processes are intensified while attempting to prolong campaign life. This idea was combined with high-capacity heat pipes in the design of a copper slag launder. The design methodology of the launder and heat pipe cooling system is examined in this paper. With reliable material properties and operating conditions, CFD was used to quantitatively predict the skull thickness and the corresponding heat load applied to the slag launder. The operational limitations of heat pipe technology were considered and an appropriate cooling system was incorporated into the model. Parametric modeling was used to simulate several launder and heat pipe configurations. The generated results were then used to optimize the design of the launder, which was built and tested in August of 2005. The experimental performance of the cooling system is evaluated and compared with the model results.

Jan 1, 2006

By Stavros A. Argyropoulos, Henry H. Hu

"The assimilation of exothermic additions in liquid metals exhibit an array of unique coupled heat, mass and momentum transport phenomena. These phenomena are further complicated by the presence of a moving boundary.This paper describes a) A mathematical model which simulates the complex phenomena, and b) An extensive verification of the mathematical model. The SIMPLER algorithm was employed to solve numerically the pertinent partial differential equations. The computational results indicated that the exothermic heat of mixing led to a rapid increase in temperature around the moving boundary, which produced an enhanced convective flow in the liquid phase. The intensification of fluid flow around the moving boundary resulted in an acceleration of the melting process.Verification of the model was carried out in two contexts. The first was, in a low temperature physical model consisting of ice immersion in different sulfuric acid solutions. In this physical model, both temperature and velocity measurements were carried out. The model results were compared with experimental measurements and they were found to be in excellent agreement. The second context employed high temperatures, involving the assimilation of silicon in high carbon liquid iron. The model was also applied to predict fluid flow, heat and mass transfer for these high temperature experiments and a good agreement was obtained.In addition new dimensionless heat transfer correlations that quantify these complex phenomena will be presented."

Jan 1, 2001

By W. E. Horst

In Part I of this paper we describe two techniques that were employed in the development of mathematical descriptions of the size reduction process which takes place in a ball mill. In Part II we show how the comminution model was imbedded in a process model to effect steady-state and dynamic simulation of a closed-circuit grinding operation. Increasing emphasis is being placed on development of approaches whereby the essential characteristics of a process can be succinctly represented in terms of a mathematical description of the relationships that exist among important process variables. This activity, commonly known as mathematical modeling, predates modern electronic computers: however, these computers with their tremendous computational capability have given new impetus to the whole field. Although the computer is quite helpful in the development of mathematical models, the real value to the engineer lies in the fact that computers represent such a powerful tool for simulating systems described by mathematical models. As a consequence, engineers may simulate and thereby study the behavior of complex. interacting, systems over a broad range of process variables and configurations once appropriate process models have been developed for the sequence of steps comprising the process.

Jan 1, 1970

By Roberto Parreiras Tavares, Frederico da Costa Fernandes, Guilherme Antonio Defendi, Vangleik Ferreira da Cruz, Júlio César de Sousa Pena

"Near-net-shape casting is an important area of research in the iron and steel industry today. Among the near-net-shape casting processes, the single-belt caster seems to be the most promising, since it is the only one that can achieve levels of productivity similar to those obtained with conventional continuous casting machines. One of the most important aspects in the single-belt casting is the feeding system used to deliver liquid metal over the belt. This system determines the velocity distribution and the levels of turbulence of the liquid metal and affects the quality of the strips. In the present work, a metal delivery system having a simple geometry was proposed. Using the CFD code CFX 5.6, a mathematical model to simulate three-dimensional turbulent fluid flow and heat transfer in that system has been developed. This model was used to analyze different configurations of the metal delivery system and the free surface shape of the fluid was also determined. A physical model of the feeding system was built and used to validate the predictions of the mathematical model. The fluid flow calculations have been validated by dye injection experiments and laser doppler anemometry. Measurements of the free surface levels have also been performed. These experiments provided supporting evidence for the predictions of the mathematical model.IntroductionTo maintain its competitiveness in the present market, the metallurgical sector, particularly the steelmaking companies, are developing new techniques of production. Some of these new processes are focussed on the strip casting technologies. Among these technologies, the SingleBelt process is considered the most interesting option, reducing the number of rolling steps and, consequently, the final cost of the product, especially the part associated to the energy consumption (fuel and/or electric energy). This process can also reach levels of productivity that can not be matched by other strip casting methods(1). One of the most important aspects concerning these new processes is related to the liquid metal delivery system. This system can have a significant effect on the final quality of the strips, since it determines the velocity distribution and the levels of turbulence of the liquid metal."

Jan 1, 2004

By Naiyi Li, Henry Hu, Alfred Yu

"In the past few years, various squeeze cast aluminum components have been developed and successfully implemented in various vehicles by the automotive industry because of their superior engineering performance. However, fundamental understanding of the formation of air gap during squeeze casting processes is still very limited despite of its significant influence on the extent of heat transfer between the casting and mould. In this paper, a mathematical model has been developed to simulate phenomena of air gap between the casting and mold' during squeeze casting of aluminum alloys. The model considers the effect of process parameters such as applied pressures and mold temperatures on the events of air gap formation. The predication indicates that the occurrence of highly enhanced heat transfer in squeeze casting of aluminum alloys primarily results from the presence of excess applied pressures.IntroductionA number of squeeze cast Al components has been developed and used in mass-produced vehicles in the past few years, such as steering knuckles, Road wheel, Engine Block etc. This is attributed to their superior engineering performance. In squeeze casting, the cooling rate can be increased by applying high pressure during solidification which results in the noted refinement in the micro structure scale leading to better casting properties. However, the excessive pressure increased interfacial heat transfer coefficient is affected during the solidification by air gap formation and die surface condition etc., which is believed to increase thermal resistance at the casting/die interface [l - 4]."

Jan 1, 2004

By K. Oraee

Excessive emissions of methane from the coal seams can have a serious adverse effect on both safety and productivity of longwall coal faces. Mechanization of coal faces has increased production possibilities to the extent that normal ventilation systems may not be able to ventilate coal face areas in order to lower methane content in the air to within legal limits. Production increases may therefore be prohibited for this reason, especially in gassy seams. Methane drainage from the coal seam by means of long holes and before production starts can act as a useful remedial action. In this paper a two dimensional mathematical model has been produced. The model that is based on finite elements, simulates a methane drainage system where the resultant risk is linked to the coefficient of diffusion, coal permeability, holes pattern and the duration for which the seam is subject to drainage. It is concluded that methane drainage of this type can assist in achieving production increases in many coals seems, especially where high gas content is a virtue of the seam.

Jan 1, 2010

By C. Hennesmann, D. Maijer, S. L. Cockcroft, P. Yo

"Die cast aluminum wheels are one of the most difficult automotive castings to produce because of stringent cast surface and internal quality requirements. As part of a collaborative research agreement between researchers at the University of British Columbia and Canadian Auto Parts Toyota Incorporated, work has been underway to predict heat transport and porosity formation in die cast A356 wheels. The basic heat transfer equations have been solved using the commercial finite element package ABAQUS to which specialized routines have been added to predict porosity. Preliminary work on predicting porosity formation focused on using the Niyama parameter as a measure of the probability of porosity. The latest version of the model incorporates a new fundamentally based porosity criterion, which takes into account the effect of hydrogen concentration. The development of this model together with its application to a series of cylindrical test castings as well as a production cast wheel are presented.I. IntroductionDie cast aluminum wheels are one of the most difficult automotive castings to produce because of stringent cast surface and internal quality requirements. Microporosity, in particular, is a common defect that can adversely affect wheel quality. The mechanism of microporosity formation in aluminum alloys is complex owing to its dependence on the interaction of a number of phenomena occurring during solidification including the decrease in hydrogen solubility, the decrease in volume, the development of the solidification structure, and the increase in difficulty in interdendritic feeding [1]. As a result, the amount, size, and distribution of microporosity is affected by a large number of casting parameters including thermal variables, melt composition, grain structure, modification, and inclusion content, making optimization by trial-and-error methodologies difficult.The use of criteria functions, based on thermal conditions during casting, offers a relatively simple approach to predicting microporosity. In practical terms, they are useful because they provide a straightforward method of assessing the impact of varying casting parameters on porosity through various thermal parametersl21 such as thermal gradient, cooling rate, solidification time, and solidus velocity. Drawbacks of criteria functions include insensitivity to varying hydrogen concentration and the limitation to qualitative predictions. Consequently, in aluminum alloys, attempts have been made to develop models incorporating the effects of hydrogen gas and microstructure evolution. However, these types of models represent a significant increase in complexity and sacrifice the simplicity and ease of application of the thermally based criteria functions."

Jan 1, 2001

By Paul M. Bommer

Abstract. This cater presents the development of and results from a computer model of in-situ uranium leaching. This model uses a streamline-concentration balance approach and is useful with a vide range of reservoirs. It can be used with any type of veil system, in a reservoir with or without boundaries, and with any form of descriptive kinetics. The model also includes the effects of dispersion and consumption of oxidant by minerals other than uranium. The effects of areal sweep, variable uranium concentrations, variable permeability, and the presence of oxidant consumers on uranium production are shown and discussed.

Jan 1, 1979

By Baozhong Zhao

In-situ vitrification (ISV) is a new technology used for treating radioactive, organic and inorganic contaminated soils. In this process, electricity is applied through electrodes buried in the contaminated soil to melt it and form an environmentally stable glass-like solid. The organic contaminants and volatile metals are vaporized during heating up, the non-volatile inorganic elements are dissolved and incorporated into the melt. In present full-scale operation, the ISV process can treat 4 to 6 tons of soil per hour at consumption of about 1000 kwh per ton of soil. In this study, various configurations of electrodes were examined in a mathematical model. The results may be used to optimize the ISV process.

Jan 1, 1994

By M. E. Huckman

In this paper, we review the equations needed to construct an ion exchange column model. These models contain three major components: 1) a differential material balance around the colunm, 2) a differential material balance around an ion exchange particle, and 3) a constitutive equation for diffusive flux We then examine the ability of a fairly simple mathematical model to predict ion exchange column experimental data. This model contains the traditional absorption theory equations and is used to predict the behavior of a column filled with a hydrous crystalline silico-titanate and which is removing trace amounts of Cs+ from a high pH, complex electrolyte solution. Finally, we propose replacing Fick's law with the Nernst-Planck equation as the constitutive equation for diffusive flux We use a Nernst-Planck type model to predict batch experimental data, then evaluate it by comparing it's ability to predict experimental data to that of a more traditional Fick's law type model? The data from this comparison suggests that the Nemst-Planck type model yields better results.

Jan 1, 1996

By D. Gu, R. G. Anthony, C. V. Philip, M. E. Huckman

"In this paper, we review the equations needed to construct an ion exchange column model. These models contain three major components: 1) a differential material balance around the column, 2) a differential material balance around an ion exchange particle, and 3) a constitutive equation for diffusive flux. We then examine the ability of a fairly simple mathematical model to predict ion exchange column experimental data. This model contains the traditional absorption theory equations and is used to predict the behavior of a column filled with a hydrous crystalline silico-titanate and which is removing trace amounts of Cs+ from a high pH, complex electrolyte solution. Finally, we propose replacing Fick's law with the Nemst-Planck equation as the constitutive equation for diffusive flux. We use a NemstPlanck type model to predict batch experimental data, then evaluate it by comparing it's ability to predict experimental data to that of a more traditional Fick's law type model. The data from this comparison suggests that the Nemst-Planck type model yields better results.IntroductionMillions of gallons of strongly basic, radioactive waste are currently stored in underground storage tanks at Hanford and Savannah River and several locations within the United States. Due to the limited life expectancy of the tanks, there is a pressing need to remediate these wastes. This need has prompted the recent development of new ion-exchange materials for removing radioactive elements from aqueous solutions. A novel material called TAM-5 has been developed jointly by Texas A&M University and Sandia National Laboratories. TAM- 5, a crystalline silico-titanate, is highly selective for Cs + in the complex electrolytic solutions typical of these wastes. It is stable in very basic solutions and in radioactive environments [1, 2 ,3]. In laboratory testing to determine the selectivity of various materials, TAM-5 was superior to other candidate ion exchangers [4, 5]. The selectivities were determined by measuring a distribution coefficient, Kd, which is defined as the concentration, gig or mmols/g of Cs in the solid phase divided by the concentration, mg/L or mmols/mL, of Cs in the liquid phase. The units of Kd are ml/g or L/kg. Table 1 shows Kd values for TAM-5 compared to 9 other candidate materials in a typical waste solution [6]."

Jan 1, 1996

By Luís Marcelo Tavares, Henrique Dias Gatti Turrer, Luciana Pereira Alves

Desliming is a method of classifying mineral particles, which aims at removal of slimes so as to prepare the slurry to downstream concentration processes. It is a common item in mineral processing flowsheets, being mostly carried out in hydrocyclones, in which separation is result of complex fluid flow and its interaction with the mineral particles. When dealing with particles contained in size ranges relevant to desliming, the challenge in describing the process is even greater. The work deals with the fitting of the Narasimha-Mainza model of classification in hydrocyclones to data from desliming an itabirite iron ore, for prediction of feed slurry flowrate, corrected cut size and short-circuit to the underflow. As such, tests were conducted at both pilot and industrial plants in KREBS 2.7” and 4” cyclones operating under a variety of conditions. In the validation of the model, deviations between the predicted and measured values were lower than 34% for feed slurry flowrate, less than 22% for corrected cut size and less than 18% for short-circuit for underflow.

Oct 3, 2019

By A. McLean, L. Gao, Z. Shi, Y. D. Yang, K. Chattopadhyay, G. F. Zhang

Levitation melting of metals is one of the emerging applications of magnetic and electric fields in liquid metal refining. The varying magnetic field generates induced current inside the metal droplet and leads to the Joule heating effect and Lorentz force against gravity. This contactless process can avoid contamination from the crucible and can be used to produce high-purity materials. Visualization of the levitation melting process is difficult, and thus generally investigated by mathematical modeling. In the present study, a three-dimensional mathematical model of metal levitation was developed using finite element method for proper understanding of the levitation process. The effects of harmonic magnetic field frequency, coils power input, and sample size on levitation nickel droplet were investigated. Temporal evolution of temperature fields were predicted directly though the model. Levitation and balance condition of the droplet were investigated as well.

Jan 1, 2015

By J. R. Bhamidipati, Nagy EI-Kaddah

"Over the years, mathematical modeling has been established as a viable tool for design and analysis of melting and solidification processes. Modeling of electromagnetic casting and melting systems involves three coupled problems -- determination of the containment field, the shape of the meniscus, and the temperature field -- which have to be solved simultaneously. One of the difficulties in numerical simulation of these systems is in defining and gridding the solution domain as the meniscus shape of the liquid region is not known a priori. This paper describes a methodology for solving these coupled problems in a two-dimensional electromagnetic containment field. This method is based on the solution of the electromagnetic, free surface dynamic, and heat transfer equations in a fixed domain in computational space by mapping the physical space into an invariant computational space during the search for the equilibrium shape using a variable non-orthogonal coordinate transformation. This approach, also, eliminates the need for regridding the liquid and solid regions during phase change. This methodology is demonstrated for two electromagnetic confinement systems -- the Magnetic Suspension Melting process and the electromagnetic casting of aluminum. The model predictions are in good agreement with available data for these systems. It is suggested that the methodology presented here is likely to provide a useful tool in the design, analysis, and optimization of electromagnetic confinement systems. IntroductionDuring the past decade, mathematical modeling has emerged as a viable tool for the design, analysis, and optimization of casting and melting processes /1-2/. It is generally recognized that the usefulness of modeling to study the interplay between the various process parameters without resorting to extensive experimentation relies heavily on accurate representation of the physical phenomena in these systems. In modeling electromagnetic confinement casting and melting systems, it is important that the model address all aspects of electromagnetic field interaction with the metal, if accurate predictions are to be obtained /3/. The electromagnetic field affects the heat transfer phenomena primarily through joule heating. In addition, the electromagnetic forces play a key role in heat redistribution in the molten pool via melt stirring, and, in confinement systems, support the molten metal pool."

Jan 1, 1994

By Olusegun J. Ilegbusi

"A two-fluid model is used to calculate flow and heat transfer characteristics of a plasma jet. This model accounts for both gradient-diffusion mixing and unmixing that may result from pressure-gradient-body-force imbalance in the system. The unmixedness is considered to be essentially a Rayleigh-Taylor kind instability. Separate transport equations are solved for the plasma and ambient gas velocities, temperatures and volume fractions. The two fluids allowed to exchange mass, momentum and energy through empirical interaction parameters. The empirical coefficients are first established by comparison of predictions with available experimental data for shear flows. The model is then applied to an Argon plasma jet ejecting into stagnant air. The predicted results show the significant build-up of unmixed air within the plasma gas, even relatively far downstream of the plasma torch. By adjusting the inlet condition, the model adequately reproduces the available experimental data on the temperature profile.IntroductionPlasma jets have important applications in materials processing, some of which include spray deposition, melting and refining, heat treatment and materials synthesis. In a typical reactor, the hot plasma stream entrains a surrounding gas and the resulting heat and mass transfer and the condition of operation of the torch, determines to a large extent, the performance of the unit. The entrainment may prevent uniform mixing and produce regions of unmixed hot/cold gases and non-uniform deposits as a result of insufficient melting of deposit in cold regions. This phenomenon may also affect chemical reaction rate in plasma systems for NOx reduction in exhaust gases.The study of plasma phenomena is often conveniently divided into three parts namely, the plasma torch, the plasma jet and analysis of the particles carried in the jet. The present work concerns processes occuring in the near-field of the plasma jet i.e. just downstream of the torch."

Jan 1, 1994

By Amjad Asad, Boyd Davis, Kinnor Chattopadhyay, Rüdiger Schwarze, Christoph Kratzsch, Donghui Li, Lei GAO

Sodium (Na) and Lithium (Li) are produced using molten salt electrolysis. The electrochemistry of the electrolyte is well-researched; however, there are benefits to understanding the melt flow and implications on it for cell design modifications. The basic configuration of alkali metal cells is the Downs cell. This consists of a central anode surrounded by a cathode, and this geometry was the basis for this mathematical modeling study. The behavior of gas bubbles in molten electrolyte was studied in both Na and Li cells through the use of computational fluid dynamics (CFD) techniques. The distance between the anode and the cathode was varied in the CFD model to ascertain whether strong circulatory flows would change significantly in the cell. The standard k-ε turbulence model was used to mimic turbulent flow, and a two-way coupled Discrete Phase Model (DPM) was adopted to simulate flotation behavior of chlorine bubbles and liquid metal droplets. The liquid metal distribution on the free surface was predicted using the Volume of Fluid (VOF) multi-phase model.

Mar 1, 2017

By Han-Tao Hu

Keywords: RH refining process, flow of molten steel, two-phase flow, gas holdup, circulation rate, mathematical modeling A three-dimensional mathematical model for the flow of the molten steel in the whole degasser during the RH refining process has been proposed and developed with considering the physical characteristics of the process, particularly the behaviors of gas-liquid two-phase flow in the up-snorkel and the momentum exchange between the two phases. The fluid flow fields and the gas holdups of liquid phases and others respectively in a 90 t RH degasser and its water model unit with a 1/5 linear scale have been computed using this model. The results showed that the flow pattern of molten steel in the whole RH degasser could be well modeled by the model. The liquid can be fully mixed during the refining process except the area close to the free surface of liquid and zone between the two snorkels in the ladle, but there is a boundary layer between the descending liquid stream from the down-snorkel and its surrounding liquid, which is a typical liquid-liquid two phase flow, and the molten steel in the ladle is not in a perfect mixing state. The lifting gas blown is rising mostly near the up-snorkel wall, which is more obvious under the conditions of a practical RH degasser, and the flow pattern of the bubbles and liquid in the up-snorkel is closer to an annular flow. The calculated circulation rates for the model unit at different lifting gas rates are in good agreement with the determined values.

Jan 1, 2005

By Rodríguez M. Esperanza

The efficient performance of Pachuca tanks is strongly linked to the suspension of mineral particles, which results from the motion of the liquid caused by injected gas rising, in general, through a central draft tube. This study reports a computational investigation on the effect of operating and design parameters on the suspension of particles. By extending the classical 2-phase drift-flux model to compute the gas hold-up, the three-phase (water-air-particles) system was simulated as consisting of a variable-density liquid plus the solid particles. These two phases were treated as interpenetrated continua using an Eulerian approach to set a turbulent recirculating flow model in 2-D and transient state. The model predicted adequately the measured critical superficial air velocity, uc, needed for maintaining particle suspensions, in pulps with 10-50 wt% solids. Additionally, the model was used to investigate the operation of industrial size reactors, obtaining results that agree well with the general trends reported in the literature, and highlighting important differences with respect to laboratory-scale reactors.

Jan 1, 2009