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By Tetsuro Ohashi, Tooru Matsumiya, Yoshio Abe

"The three-dimensional deformation of a continuously cast slab was modeled into two-dimensional deformation by developing the solidified shell of the slab. The developed solidified shell was divided into rectangular elements. The thermal strain produced as the slab is wi thdrawn over one roll spacing in the casting direction was calculated from the temperature change during that time and the increment of the geometrical unbending strain during the time was calculated from the change in the radius of curvature of the slab by assuming that the neutral axis of bending is located at the mid-thickness of the slab and that the transverse section of the slab is kept in a plane during unbending. These strains were imparted to each element as initial strains. The interaction between the elements and the overall deformation of the solidified shell were analyzed by the finite element method.The analysis was performed on a slab being cast on a machine of the circular arc type with progressive unbending. The following findings were obtained as a result. The effect of unbending is spread in the upstream and downstream directions of the slab by the shear deformation of the narrow and wide faces. As the shear deformation increases, the strain in the unbending zone decreases and the strain outside of the unbending zone increases. The effects of secondary cooling conditions, slab size, radius of caster circular arc section, compression casting, etc., were also analyzed. IntroductionTo develop a method for preventing the internal cracking of continuously cast slabs, it is important to acurately analyze the deformation of the slab and this subject has been extensively investigated. Many researchers, including the present authors, have analyzed slab bulging. (1)- (11) Analysis has also been made of thermal deformation that assumes importance in continuous casting of small-section blooms.(12)-(18) However, unbending deformation, an extremely important subject for continuous casters of the circular arc type, has not been fully analyzed."

Jan 1, 1986

By M. Rosales

By a physical and mathematical modeling, the behavior of the tri-dimensional waving, and the movement of the gases at the Teniente Converter was studied. The mathematical model considers the condensed phases of white metal and slag, along the gas phase, and includes the k-e model for the turbulence description. Both the physical model and the mathematical model allow to conclude that from a fluidynamic stand point the Teniente Converter clearly can melt 3000 tpd of concentrates. Also, both models are suitable to predict the slag fluidynamics and its spacial distribution inside the Teniente Converter, and the splashing in the tuyere zone as well.

Jan 1, 2006

By J. W. Evans

Mathematical modeling has now become a standard technique in the development of new technology and the improvement of existing technology in the processing industries. Physical modeling has a longer history but a smaller following at present. The paper reviews some examples of the application of both types of modeling in non-ferrous metal extraction, particularly within the copper and aluminum industries. The objective is to show that well founded models can lead to results that have practical consequence in scaleup, design and operation.

Jan 1, 1993

By H. H. Kellogg

The thermochemical properties of molten solutions in the binaries Cu-Bi, Cu-Sb and Bi-Sb, as well as the ternary Cu-Bi-Sb, have been correlated and described in mathematical form by use of the associated species concept combined with the three-suffix Margules equations to account for the non-idea 1 behavior of the solution species. Agreement of the correlations with experimental data is excellent (relative deviation of less than 2.5% in the values of the activity coefficients) in most cases. The correlations are applicable over the entire composition range of each system, and in the temperature range 700°-1250°C.

Jan 1, 1985

By W. G. Davenport

The remainder of this book develops and uses mass and heat balances to describe steady"state flash smelting. Its objectives are to: a) describe the many ways a flash furnace operator can produce specified products, e,g. 65% eu matte, 35% SiOz slag, 1500 K (b) determine the oxygen, air, flux and hydrocarbon fuel requirements of each method (c) show how the flash furnace can be controlled to give specified products with varying feed compositions (d) suggest how the flash furnace operator can maximize profitability while producing specified products. This chapter develops the basiC heat and mass balance equations of steady-state ?flash smelting. It then adapts the equations to industrial feed materials .and products. Lastly it determines the amounts of oxygen and flux needed to produce molten matte and 35% SiOz slag from chalcopyrite concentrate in an Inco oxygen flash furnace,

Jan 1, 2001

By Pascal Gardin

The purpose of the paper is the mathematical modelling of flows inside steel continuous casting mould. For CFD validation of flow oscillation prediction, unsteady calculations with a realizable k- model were performed in a billet caster with rectangular section. Self sustained and regular oscillations were obtained. Calculated flapping frequency is very close to what is mentioned in literature. For slab caster configuration, flow oscillation is influenced both by lower roll, which creates very small frequency oscillation (0.012 Hz for our water model), and upper roll, which creates slightly higher frequency oscillation (0.05 Hz). The two rolls interact and it is possible to detect both frequencies in the nozzle jet region. Numerical results are in good agreement with measurements for fluctuating velocity spectra and provide explanation for interaction of rolls. To improve flow stability inside the mould, it is established that gas injection in the nozzle has a very positive effect.

Jan 1, 2006

By Jing Zhong, Yugang Li, Chen Yan, Shaoda Zhang, Qian Wang

Online surface quenching technology has been developed for the hot charging process to prevent the surface cracks in high strength low-alloy steel slabs. In this paper, a two-dimensional heat transfer model of surface quenching process was presented. This finite element model includes nonlinear thermodynamic properties, by which the slab temperature distributions were computed. The model predicted temperatures show reasonable agreement with the measurements. The effects of the water flow rate and slab movement velocity on temperature variation during the quenching and subsequent tempering process were investigated. The result shows that the temperature drop increases but the tempering temperature changes slightly with increasing water flow rate and decreasing slab velocity. Keeping the slab movement velocity at 1.2-2.1m/min and the water flow rate at 55-70m3/h, the slab surface experiences a temperature drop of 400-600 firstly, then recovers above 650, the quenching and energy-saving effect are remarkable.

Jan 1, 2015

By Manuel Pérez-Tello

A mathematical model to represent the expansion and fragmentation of copper matte particles oxidized under flash converting conditions is presented. The model assumes the particles to be initially nonporous, have a constant mass prior to fragmentation, and travel at a constant velocity throughout the reaction chamber. The model requires the specification of five parameters: the particle expansion rate, a fragmentation diameter factor, a fragmentation size distribution parameter, and the fractions of the finest and the coarsest particles in the feed that undergo fragmentation. The model predictions show good agreement with experimental data collected in a laboratory flash converting furnace over a wide range of experimental conditions. The evolution of the size distribution of the particles along the reactor length was computed, and the model parameters were correlated with the experimental operating variables. Model predictions indicate that particle residence time is an important factor in the generation of dust. The presence of two maxima in the particle density function may be attributed to turbulent conditions prevailing in the furnace, which cause particles to follow very different trajectories within the furnace even if they are injected at the same location.

Jan 1, 2006

By Gennady I. Gulyayev

A mathematical model of plastic deformation occurring in cold plug drawing of mother tubes with initial cross-sectional wall thickness variations (CSWTV) has been developed. The main provision of the model is that eccentricity em is of such value that projection of all forces acting upon the plug in the deformation zone along the axis perpendicular to the drawing axis equals to zero. Calculations have proven that with other conditions being equal increase in the die cone angle and the deformation cycle number reduces CSWTV. Theoretical findings were confirmed by practical results. Keywords: cold, drawing, plug, die cone, plastic deformation.

Jan 1, 2003

By H. Saint-Raymond, F. Gruy, P. Gardin, M. Cournil

"The control of inclusion elimination is getting more and more important to obtain clean steel. This paper presents a methodology under development for predicting cluster growth and elimination in ladle - RH system. The first key point is to express the collision efficiency, which is very specific for alumina cluster due to the non-wetting fluid. Second, a description of the two-phase flow in the system is necessary. In our calculations with Fluent CFD package and Lagrangian approach for bubbles, bubble growth is implemented, which improves the predictions. Using global reactor decomposition makes possible the prediction of the time evolution of cluster distribution. Important effect of fractal dimension is demonstrated.IntroductionElaboration of new steel grades requires not only to have a high purity in terms of C, O and N content but also to eliminate particles such as alumina or slag droplets. Flow optimisation making easier inclusion elimination is then a key figure to satisfy cleanliness requirements. Mathematical models of flow and inclusion behaviour are widely used for this purpose (1, 2). But having a predictive tool is still a challenge, because the number of phases is important in steelmaking industry: liquid steel, slag layer, bubbles and inclusions (with a large range of composition and rheology). The paper presents the methodology which is developed at IRSID to predict oxygen content evolution during RH degassing.The main mechanisms which have to be considered are :-inclusion growth by turbulent aggregation of elementary inclusions (keeping in mind that liquid steel is a non-wetting medium for inclusions); the difficulty is to express collision efficiency for alumina particles,-inclusion removal by flotation; the difficulty for alumina clusters stems from the complex morphology of particle; fortunately, the use of fractal concept makes it possible to cope with this problem.The paper describes the general modelling of inclusion removal taking into account the previous mechanisms. Hydrodynamic parameters are obtained by means of Fluent CFD package and a specific coding is developed for cluster growth."

Jan 1, 2001

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 Mamoru Kuwahara, Tomohito Taki, Masamichi Sano

"Theoretical basis and experimental results on ultrasonic separation of dispersed inclusions from molten metal are outlined. Transitional formation of an ultrasonic standing ·wave field in a liquid bath is numerically predicted based .on the wave equations. Numerical solution of the equation of motion of a fine particle in a standing wave field indicates that the inertia term can be neglected during conventional ultrasonic separation of fine particles: Analytical solutions for the position at which particles are coagulated the minimum power for separation, and the ultrasonic separation time are derived to incorporate such key process parameters as the density difference and the acoustic energy density exerted. Cold model experiments have been carried out to observe ·transitional coagulation of polystyrene particles in an aqueous sugar solution with the incidence of standing ultrasonic plane wave. Experimental results agree well with the theoretical predictions.IntroductionDespite of recent progress of fundamental and applied researches in metallurgical systems, advanced materials· with less inclusions and better properties may demand more innovative processing in a: molten state. It may be realized by applying electromagnetic and/or ultrasonic external fields to the systems. The present authors1)·2) have been proposing : new methods of ultrasonic processing of materials based on such phenomena as acoustic streaming, acoustic radiation pressure on dispersed phase in a standing wave field, and the cavitation in liquid associated with use of high-intensity ultrasound and so on. Taking account of common physical natures between ultrasound and sound wave, we call such · a processing assisted by acoustic wave as ""sonoprocessing"". This report ·deals with some theoretical and technological aspects on the ultrasonic separation of fine particles from liquid, which could become an important operation to produce clean materials. Fundamental theory and ·supporting experimental results will be given below to give an insight into the liquid metal sonoprocessing."

Jan 1, 2000

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 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 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