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By Bruno Lebon, Koulis Pericleous, Georgi Djambazov, Mayur Patel

"High speed compressible jets are used in a number of steel-making applications. In the case of the BOF, a compressible oxygen jet reacts with a carbon-rich iron bath to reduce carbon levels and produce steel. The intensity of the process is governed by the speed of the jet and by the size and shape of the depression created in the metal and slag by the force of the jet, i.e. by the corresponding free surface. This is a difficult CFD problem, since there are compressible and incompressible regions in the flow domain, which need to be handled differently in a finite-volume (FV) pressure-correction scheme. Also, standard turbulence models do not account for compressibility, or the large difference in density between the cold oxygen jet and the hot reacting surroundings. Corrections are introduced to the k-E model to remedy this deficiency and the results are validated against experimental data. The compressible/incompressible boundary is handled through a transition region, based on Mach number.IntroductionThe deformation of a free surface by a compressible high speed jet is of paramount engineering interest, particularly for understanding the physical processes within a Basic Oxygen Furnace (BOF). In a BOF, a supersonic oxygen jet impinges on a molten iron surface, thereby creating a cavity. Oxygen penetrates the bath and removes carbon, resulting in low carbon steel [1].The challenges in modelling such a process lie in coupling a solution domain with distinct compressible and incompressible regions and in dealing with large density differences between the modelled gas and liquid. The modelling of compressibility within the jet is crucial, since the correct velocity profile in the jet is required to determine the cavity depth with accuracy."

Jan 1, 2012

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 Marco A. Ramírez-Argáez

A 2D mathematical model was developed for the plasma arc welding process. Computational simulations based on mass and momentum conservation equations as well as Maxwell equations were performed by using the commercial software PHOENICS. The model predicts the electric characteristics of the arc column, flow patterns, temperature contours and electrical potential, by varying the composition of the cover gas, in this case, argon and nitrogen. It was found that an arc of nitrogen with respect to one of argon generates more intense jets, greater voltages, and lower temperatures in the arc column for welding arcs current of 150 A and 10 mm arc length.

Oct 30, 2017

By Erich Hovestädt, Hans-Jürgen Odenthal, Christian Wuppermann, Herbert Pfeifer, Antje Rückert

"During the argon oxygen decarburization (AOD) process high-chromium steel melts are decarburized by oxygen and inert gas injection through sidewall nozzles and a top-lance. Due to the large amount of the injected processing gas, low frequency oscillations of the vessel can be observed. It is suspected that these oscillations can influence the converter's structure. The exchange of forces between fluid and the surrounding vessel is the focus of this study. An oscillation model was developed and tested, one objective being to limit the computational effort which is necessary for fully coupled and time resolved CFD and FEM simulations. Experimental results obtained from water-model studies as well as from on-sight measurements are available and were used in order to validate the numerical results. The authors' intention is a contribution towards a more in depth understanding of the factors influencing vessel vibration during the AOD process.IntroductionDuring the last four decades the AOD process has been established as a reliable and efficient refining process in stainless steel making. The injection of process gases (O2, N2, Ar) through sidewall nozzles shows advantages in mixing effectiveness compared to other injection geometries e.g. bottom blowing [1]. Stainless steel grades contain usually more than 10% chromium. With decreasing carbon content during the decarburization periods the tendency of chromium oxidation increases according to the varying chemical equilibrium which depends on the partial pressure of carbon-monoxide (CO) in the gas phase. That's why oxygen is gradually replaced by inert gases, usually argon or nitrogen, in order to lower the CO partial pressure and thus to minimize chromium oxidation. Despite the high injection velocity of approximately Ma = 1, the kinetic energy of the gas jets is consumed within a short distance from the nozzle exits due to the large density ratio between gas and melt of approximately 1:8000. With increasing distance to the nozzle exit, the initial horizontal velocity of the gas jet decreases and due to buoyancy force motion of the detached bubbles turns into a vertical direction. Subsequently a gas plume develops with its typical conical shape described by various authors [1-4]. Due to the drag force between gas bubbles and melt also the liquid phase is forced into a vertical motion. Near the free surface and the wall regions the melt flow is deflected in different directions. Subsequently, the typical flow pattern in the AOD vessel arises, as sketched in Figure 1 and described in literature [5-9]."

Jan 1, 2012

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 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 Edgar E. Vidal, Patrick R. Taylor

Standard textbook equations for heterogeneous kinetics typically utilize a constant driving force to solve for rates and times of reactions. In order to more closely model real systems, equations and solutions are presented for particle leaching kinetics in which the driving force is decreased as the reactions proceeds. In addition, models for continuous co-current and continuous counter current aqueous-solid reactions are presented.

Jan 1, 2005

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 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

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

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 John C. Edwards

To have the capability to predict the development of localized spontaneous heating within a porous coalbed that is subjected to forced air ventilation or in an otherwise quiescent environment in which buoyancy develops, the Bureau of Mines developed three time-dependent mathematical models, which were used to calculate the temperature increase associated with chemisorption of oxygen by the coal. In each model, spontaneous heating is driven by an Arrhenius first-order reaction between the oxygen and coal. Two models are two-dimensional, and one is one-dimensional. In the first two-dimensional model, a constant-velocity forced convection airflow is specified; and in the other, buoyant flow is allowed to develop in the absence of forced convection. The third model evaluates the airflow from Darcy's law and a specification of the pressure at the surface of a one-dimensional porous coalbed. Numerical computations demonstrated how each model could be used to predict the onset of spontaneous heating when the porous coalbed was subjected to constraints of an imposed internal heat source or a high- temperature airflow. The effects of particle size and coalbed compaction upon spontaneous heating were examined with the third model.

Jan 1, 1990