Search Documents

By John J. Jonas, Sang-Hyun Cho, Ki-Bong Kang

"The recrystallization behavior of Nb micro alloyed steels containing Cr, Mo, Ni and Ti. was studied using hot torsion testing with the aim of modeling the recrystallization processes and the mean flow stress taking into account the microstructural behavior during hot rolling. The kinetics of static and metadynamic recrystallization were characterized and appropriate expressions were formulated for the recrystallization kinetics. These are shown that the recrystallization kinetics depend on steel composition and the processing conditions. The stress-strain curves were determined in order to derive new equations for the peak stress, peak strain, mean flow stress and softening kinetics. The peak strain is influenced by the presence of alloying elements; their addition, which has a solute drag effect, retards the rate of grain boundary motion, shifting the peak to the right. The addition of Nb to the steel results in a significant increment in the activation energy for hot deformation, and Mo has smaller effect than Nb, but Cr has the opposite effect. It was also found that the deformation activation energy in these steels was not altered by the addition of Ni. The rate of metadynamic recrystallization increases with strain rate and temperature and is observed to be independent of strain, in contrast to the observations for static recrystallization.The mean flow stress (MFS) calculations, based on the Sims analysis, are then compared with the predictions of a model based on an improved Misaka mean flow stress equation in which solute effects, strain accumulation, as well as the kinetics of static and metadynamic recrystallization are accounted for. Good agreement between the measured mean flow stresses, which is obtained from the mill logs of POSCO Kwangyang #3 HSM (hot strip mill), and 'predicted ones is obtained over the whole range of rolling temperatures. The results demonstrate that dynamic recrystallization followed by metadynamic recrystallization, supported by the unexpected load drops, sometimes occurs for the rolling schedules studied in the present analysis."

Jan 1, 2001

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 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

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 Zden[e]k P. Bažant

Due to their heterogeneity, most rocks fracture with a zone of distributed cracking ahead of the fracture front. This makes linear elastic fracture mechanics inapplicable. The present study describes a mathematical model in which the progressive microcracking is taken into account by strain-softening stress-strain relation. In a simpler version of the model, the triaxial strain-softening stress- strain relation is obtained by direct adjustment of the elements of the compliance matrix. This formulation is rigorous only if the principal stress directions do not rotate during fracture formation within the fracture process zone. As a more sophisticated and generally applicable model, the so-called microplane model which is an analogue of the slip theory of plasticity is outlined. Comparison with fracture data for various rocks are given.

Jan 1, 1984

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 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 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 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 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