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By S. R. Krogh, T. O. Olsen

Analytical expressions for the breakage rate as functions of mill charge, mill speed, particle size, ball diameter, and ball load are derived, using idealized models for probability of breakage (Gaudin and Meloy), energy distribution (Mempel), and arithmetic mean of effective ball energy (Langemanns). Computational results using the theoretical equations are compared to experiments. The equations enable simulation of ball mill grinding at different grinding conditions.

Jan 1, 1973

By T. Fabritius, L. Hekkala, J. Härkki

The Outokumpu steel belt sintering technology is used for manufacturing chromite pellets that are charged into smelting furnace for ferrochromium production. Hot air is blown through the moving bed of raw pellets. Direct temperature and flow measurements are difficult to do in the bed of a real scale belt sintering process. Therefore, a tested and reliable mathematical model would be a valuable help for optimising operational parameters of the process and designing new constructional improvements. The aim of this work is to present a mathematical model that calculates the gas flow and temperature distribution in the bed of pellets and the atmosphere. Computational fluid dynamics program FLUENT is used to calculate the gas flow, composition and temperature of the gas in the sintering bed during processing. Energy equation for the bed, containing the effects of evaporation of water and oxidation of carbon and iron oxide, will be added to the model to obtain the temperature of the pellets. The porous media model used for pressure drop calculations in the bed is shortly discussed. A comparison between CFD-calculations and experiments with a pilot scale batch-sintering reactor are also presented. The final model can be used as an engineering tool when developing the process and the equipment further. Different designs can be easily tested with the model and the effects of the changes to the flow pattern and temperature distribution can be studied.

Jan 1, 2004

By Karel SPIRKO

The one-dimensional mathematical model of unsteady-state heat conduction through semi-infinite homogeneous and isotropic airway walls with convective heat and moisture transfer between their wet or dry naked surfaces and mine air with time variable temperature and humidity has been developed on the basis of introduction of acceptable simplifications of description of heat and moisture transfer between rock mass and mine air. The analytical solutions for computation of the temperature distribution and surface temperature of the airway walls and floor and for calculation of water vapour pressure near the wet surfaces at given time are obtained by means of the model presented. The presented solutions are derived for general conditions and they could be easily adapted to the actual ones. Results of the model represent basis for balancing heat and moisture transfer between mine air and its surrounding in deep mines under time variable temperature and humidity of the air and enable us to solve complicated dynamic changes of mine air temperature and humidity in an airway system by relatively simple mathematical tools. INTRODUCTION The importance of unfavourable influences and the costs of condition arrangements increases with mine depth. Precision demands on the methods which predict the environmental condition changes and by which it is possible to optimize condition arragements are still increasing. Environmental conditions in deep mines are determined especially by flow velocity, barometric pressure, temperature, and humidity of mine air. Therefore new and more exact mathematical models of mine air flow through airway system and those of heat and moisture transfer between mine air and individual important sources of heat and moisture are developed. The paper presented deals with description and solution of problems of heat and moisture transfer between mine air and airway walls as the rock mass is one of the important heat and moisture sources in deep mines. There are several different approaches to the problem. In some models the moisture transfer between mine air and airway walls is not considered at all. In other models the moisture transfer is described only by certain empirical coefficients. Simultaneous heat and moisture transfer is described seldom. This paper tries to describe in a simple way simultaneous convective heat- and mass-transfer processes taking place on wet naked surface of airway walls by means of corresponding

Jan 1, 1993

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 G. T. Lapidus, R. M. Luna-Sánchez

In the present study, a series of cyanidation experiments were performed on a bulk sulfide concentrate which contained silver in four distinct phases, to determine its extraction rate, varying the oxygen concentration. The results showed that three of the four phases were refractory, aguilarite (Ag,iSeS) being the only leachable phase, and that the effect of the oxidant concentration is minimal. Mathematical simulations were performed, adjusting only the Damkohler number to adequately fit the experimental data. This model, and the mechanism implied, was compared with that found for acanthite (Ag2S) in a previous study, and the differences between the two discussed.

Jan 1, 2005

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 R. V. Ramani, V. T. Burgos, J. A. McClay

The systems contributing to the cost analysis, and the flow of data input and output related to these systems, are brought into focus in Figure 6. The various sub-systems of the Master Design Simulator provide the raw operating data basic to the cost model which, operating independently, accumulates the raw input, assigns costs to this data by standard or modified costing procedures, manipulates the costs into standard formats and outputs the data for managerial evaluation. Cost Modeling Direct costing methods are not complex in the sense that elemen¬tary arithmetic is employed using the same basic relations for each cost category. The basic cost model relations described above are illustrated in Figure 7. The greatest difficulty encountered in the transition from a dy¬namic systems simulation model to a costing model is the time frame of the input and output data. Dynamic simulation models utilize a small time increment, on the order of seconds or fractions of seconds, to analyze system operations and interactions. On the other hand, for cost computation and reporting, the smallest relevant time unit is the shift, with reporting periods expanding to days, weeks, months, and years. Complications arise in the accumulation of data for the various report periods due to the use of the Gregorian calendar by modern so¬ciety. The potential for simulation for the life of the mine, possibly in excess of 50 years, increases the complexity of the costing process

Jan 1, 1975

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 Kevin D. Lofftus

This paper presents a dynamic model for column flotation. The model equations are normalized and the dimensionless groups that are directly responsible in determining the column flotation behavior are identified. The resulting model equations are incorporated for computer simulation. Numerical results from computer simulations are analyzed to gather information about design and operation of column flotation devices.

Jan 1, 1988

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 E. J. Freech

In this part of the two-part paper we discuss briefly the adaptation of the comminution model to describe the observed behavior of an industrial grinding circuit. Although reported verification of comminution models for continuous systems is limited, some interesting work has been reported 1,2 recently. The data acquisition and modeling efforts are described first, followed by discussion of some of the simulation results. Observations pertinent to steady-state operation are presented followed by a description of the application of a dynamic model of the grinding circuit for synthesis and evaluation of grinding-circuit control. The pilot-scale work indicated the comminution model should be capable of describing an industrial size-reduction process. Recognizing the broad utility of a process model based on first- principles, the Industrial Nucleonics Corporation of Columbus, Ohio, embarked on a joint program with the Duval Corporation of Tucson, Arizona, to evaluate the industrial applicability of the models described in Part I. This program was conducted in a grinding circuit, which included a rod mill 12.5 feet in diameter and 16 feet long and a ball mill 12.5 feet in diameter and 14 feet long, at Duval Corporation's Esperanza property3. The rod mill was operated in open circuit and the ball mill in closed circuit with cyclone classifiers.

Jan 1, 1970

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 E. J. Freeh, W. E. Horst

Mathematical models of a continuous comminution process are developed as an extension of the batch grinding model. Pilot-scale experimental work is described and the results are used to demonstrate the capability of the comminution models to simulate observed behavior over a relatively wide range of process variables.

Jan 1, 1973

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 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