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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 G. Babut

The restructuring of mining operations in Valea Jiului coal basin imposed by the transation to the market economy calls for an increased coal production. Under the circumstances, the role of drainage networks grows ever more important. The paper describes an original mathematical model and software developed on its basis, with enables the ventilation engineer to assess the configurations of different systems, as well as to test their reliability and prognose their future performance before conceiving another methane drainage system or changing the existing one. The paper also includes the underlying principles of an optimization program for methane drainage networks, which will enable the detection of the optimal methane drainage system, both from a technical and an economic point of view.

Jan 1, 1996

By G. T. Lapidus, J. Trejo-Gallardo

A phenomenological model is presented for leaching silver from silver sulfide contained in mineral particles with ammoniacal thiosulfate solutions of copper in stirred reactors. Experimental results were used to adjust the kinetic parameters of the model, such as the reaction order and velocity. The incorporation of the cuprous sulfide-silver sulfide equilibrium at the reaction interface allowed the prediction of the conversion limits for different reagent concentrations. The information obtained from the reactor model was later integrated into a heap leaching simulation, whose results adequately describe tendencies observed in column tests, with respect to variations in copper and thiosulfate concentrations. Comp

Jan 1, 2005

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 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 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 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

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

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

Jan 1, 2001

By Paul M. Bommer

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

Jan 1, 1979

By Baozhong Zhao

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

Jan 1, 1994

By M. E. Huckman

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

Jan 1, 1996

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

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

Jan 1, 1996

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

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

Oct 3, 2019

By Barda K. Mishra, Surya P. Mehrotra

"INTRODUCTIONIn a jig, which is primarily a coarse mineral concentration device, the bed of mineral particles is pulsated with a stream of water resulting in the particles of different specific gravities. It operates in a cyclic manner – the jig cycle consists of four stages, namely, inlet, expansion, exhaust and compression. In the inlet stage the bed lifts up en masse. Near the end of the lift stroke the particles at the bottom of the bed start falling resulting in the loosing of the bed which, in turn, causes its expansion or dilation. During the third and fourth stages the particle resettle through the fluid, and the bed collapses back to its original volume. The pulsation and suction are repeated to bring about stratification with respect to specific gravity across the bed height. Various parameters affecting the stratification process include amplitude and frequency of pulsation, bed thickness, rate of hutch water flow, and feed characteristics. This paper first presents a review of various jigging theories and then describes a new approach to mathematical modeling of jigging employing the discrete element method.JIG MODEL BASED ON DISCRETE ELEMENT METHOD (DEM) APPROACHThe jig models based on DEM essentially involve tracking the position of each particle incrementally, applying Newton’s law of motion and a force displacement law at the contact. The model presented here is based on a three dimensional mathematical description of solid-solid and fluid-solid interactions. In this model, the force balance on a particle is extended to account for the effect of continuously varying fluid on the particle. The total force on each particle is made up of a known external body force, fluid particle interaction force and particle-particle and/or particle-wall interaction force. The fluid-particle interactive force is primarily made of drag and buoyancy. Di Felice’s correlation is used to evaluate the drag force. Solid-solid interaction is described by treating particles as discrete elements that are indestructible but interact with each other and any other elements present, such as walls, when they make physical contacts. A pair of spring and dashpot represents a contact The contact forces are computed from the amount and the rate of overlap of the particles at the contact. The motion of the particle is due to movement of the fluid, which transmits its energy through the particle-particle contacts. A computer program incorporating both the contact and the fluid model has been developed. It takes the operating parameters such as amplitude and frequency of the pulsating fluid, pertinent data concerning particle properties and the geometry of the jig bed as inputs."

Jan 1, 2003

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