Search Documents

By John C. Edwards

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

Jan 1, 1990

By F. Chabchoub

A mathematical model has been developed to study the influence of process variables on the horizontal Ohno continuous casting process. The model simulates the heat transfer and fluid flow in a wide plate ingot of pure tin. A two dimensional numerical analysis based on a control-volume finite difference approach, the Semi-Implicit Method for Pressure-Linked Equations algorithm (SIMPLER), and an Enthalpy Transforming Model was used. The shape and position of the solid-liquid interface were calculated at different casting speeds, ingot thicknesses, and cooling device characteristics, as well as various mould temperatures. Results of the mathematical model were compared with

Jan 1, 1992

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 A. Navarra

Within conventional copper and nickel-copper sulfide smelters, ladles of molten matte are fed into converters. These converters blast oxygen-enriched air into the matte, thereby eliminating iron and sulfur. The converting reactions are exothermic and, indeed, the converter heat balance is often a limiting consideration on the smelter throughput. If a portion of the matte were fed in solidified (granulated) form, this would support higher oxygen enrichment, and lower volumes of converter offgas, allowing higher throughput. This approach is not applied in conventional smelters, partly because of the copious amounts of water that must be evaporated in typical granulators, as in the Kennecott-Outotec process. The current paper recalls a waterless matte granulator that had been pioneered in the 1990’s, and is applicable to conventional smelters. A mathematical formulation is presented that can be used in the context of simulation-based optimization, to estimate the size and impact of waterless matte granulation.

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 Edmond Donovan, O&apos

With the increase in complexity of conveyor systems and the inexorable demand for more capacity and availability, the ability of designers to accurately predict performance is becoming increasingly important. Dynamic analysis techniques for modelling wave mechanics in conveyors are finding increased applications. Unfortunately, the reliability of these modelling techniques is dependent on a thorough understanding of the performance characteristics of the components that make up the system. These characteristics include such things as response rate, hysteresis and efficiency. Some parameters such as idler rolling resistance can be easily quantified by measurement. More complicated drive parameters are difficult or impossible to measure, particularly in large horse-power equipment. One method of quantifying or at least bracketing the performance envelope of complicated pieces of equipment is to construct a mathematical model. This can be done quickly and economically, and the influence of various parameters can be determined. This paper sets out to demonstrate by example the usefulness of this technique in gaining an understanding of complicated systems. The model is developed and the influence of a number of variables are examined.

Jan 1, 1996

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 Y. Y. Sheng

Plume flows created by gas injection into liquid metals have been studied extensively, however the dynamics of bubbles within the plume have not received adequate attention, particularly for large, irregular bubbles, characteristic of the processing of liquid metals. The present model uses a combined Eulerian-Lagrangian approach in which an estimated void fraction distribution is used to calculate the liquid flow field with a conventional Eulerian scheme. The trajectories of bubbles are then computed in a Lagrangian manner using the estimated flow field, and experimentally measured information on bubble drag coefficients', lateral migration due to lateral lift forces and interaction with turbulent eddies, and variation in bubble size due to break-up. Turbulence in the two-phase zone is modeled with a modified k-e model with extra source terms to account for the second phase which have been recently determined by the present authors. The computed void fraction and turbulent liquid flow field distributions are in good agreement with experimental measurements.

Jan 1, 1993

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

The paper presents an algorithm for calculating the natural air distribution in a ventilation network (sub-network) on the basis of following data: - for each network branch: labels of starting and ending nodes, label of the branch, resistance and natural depression; - for each fan: the characteristic in the form of a second order equation and initial flow.

Jan 1, 1977

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 M. I. Kalashnikova, Y. M. Shneerson, E. E. Zhmarin, Y. V. Degtiarev, E. M. Vigdorchik

Separation of a magnetic fraction from nickel concentrate following matte flotation, and its treatment in a separate circuit enable reduces precious metals losses. The magnetic fraction is treated in two stages of oxidative leaching: atmospheric and pressure leaching. A study of the atmospheric stage, using mathematical modelling, is described in this paper. The mathematical model and experimental data were used to carry out industrial process calculations. The model enabled extrapolation of the results of batch laboratory test to industrial-scale continuous processing and the selection of optimal process conditions and large-scale equipment. In December 2004, commercial oxidative leaching tests were performed on the magnetic fraction at the Severonickel Plant (Monchegorsk, Russia). A comparative analysis of the mathematical modelling results and the actual process parameters is presented.

Jan 1, 2005

By K. Kabezya

A study on slag dispersion in a model of bottom-blown bath smelting converter was undertaken at room temperature. The aim was to investigate the behaviour of the dispersed slag phase at various operating conditions with very high gas flow rates in low slag volume (10%) systems. For simulation purposes water, paraffin-oil, and air were used to represent the bulk steel, molten slag, and gases respectively in a one-fifth cold model of the commercial 100 t Creusot-Loire-Uddeholm (CLU) converter used in the manufacture of stainless steel in South Africa. Dimensional analysis was done to correlate mathematically the dispersed phase holdup with the operating conditions and the modified Froude number. The overall expression of the holdup revealed that the dispersed slag phase decreased with the vertical distance from the original interface between the liquid phases. The dispersed phase also decreased with the radial distance in the water plume zone toward the sidewall. The holdup was apparently much higher on the side of the reactor where there were no tuyeres. The modified Froude number ensured the correlation between the model and the prototype.

Jan 1, 2014

By J. M. Czaplicki

The problems connected with deep mine hoisting and the increasing complexity of this process can be analysed through the application of such mathematical tools as stochastic modelling to study the effectiveness, reliability or safety of hoist methods. To relate these theoretical investigations to real practice, knowledge about components, their stochastic nature and stochastic order of appearance is necessary. This paper presents results obtained during the ten-year (1976-85) period of research undertaken in the Polish mining industry by the Mining Mechanisation Institute of the Silesian Technical University, Gliwice, Poland.

Jan 1, 1987

By P. A. Bahri, D. G. Dixon, T. M. Woodward

A comprehensive mathematical model of the Sherritt-Gordon ammoniacal pressure leaching process at K winana Nickel Refinery has been constructed. The process is comprised of six autoclaves functioning as a three-stage leach circuit, operating over the temperature and pressure ranges of 85-95°C and 750-1000 kPa, respectively. The process chemistry forms a complex series-parallel reaction network, characterised by: (1) the gas-liquid mass transfer and reduction of oxygen, (2) the oxidation of eight distinct minerals, (3) the oxidation of sulphur, and successive reactions involving various intermediately oxidised sulphur species, and (4) the oxidation of Fe(II) to Fe(III), and subsequent precipitation as a hydrated ferric oxide. Material balances were developed for species in all three phases, and an energy balance to account for all reactions and phase conversions. The multiple convolution integral (MCI) statistical reactor model was employed for the scale-up of particle kinetics. The model has been validated against plant data, and simulation results are in agreement with plant performance.

Jan 1, 2005

By Vladimir Panjkovic, Ostrovski. Oieg, Campbell Cripps Clark, John Truelove

"Effects of properties of raw materials and blast on the performance of an iron bath reactor have been examined by a mathematical model. The model consists of three modules: 1) chemical reactions in the gas phase and heat transfer from gas to droplets ejected from the bath; 2) heat losses from the vessel and radiative heat transfer from the freeboard to the bath; and 3) heat and mass balances for the bath. The following parameters of the process are calculated: coal, ore, flux and oxygen consumption, post-combustion ratio and heat-transfer efficiency, temperature and composition of the off-gas, and slag and metal chemistry.IntroductionOne of the anticipated advantages of smelting reduction over conventional ironmaking is the use of lower-grade raw materials. In this work, the effect of-properties of raw materials on the performance of an iron-bath reactor is examined with a numerical model. The model is also used to assess the effect of properties of the blast (flowrate, temperature and oxygen enrichment) and ejected droplets (generation rate, size and ratio of total weights of slag and iron droplets) on the key parameters of the process. In the process coal, oxygen, ore (which may be partly prereduced) and fluxes for specified slag composition are charged to the bath. Slag and iron droplets are ejected from the bath into the gas phase, where they are heated before returning to the bath. Iron droplets undergo decarburisation and reoxidation with CO2 and H2O. Dust is also generated from the bath, and oxygen or preheated air for post combustion is injected from the top of the vessel.The model consists of three modules: 1) reactions in the gas phase and heat transfer from gas to droplets ejected from the bath; 2) heat losses from the vessel and radiative heat transfer from the freeboard to the bath; and 3) heat and mass balances for the bath. The structure of the model and the data exchange between the modules are shown in Fig. 1. The following parameters of the process are calculated: coal, ore, flux and oxygen consumption, postcombustion ratio (PCR), heat transfer efficiency (HTE), off-gas temperature and composition, slag and metal chemistry, and rates of decarburisation and reoxidation of the iron droplets."

Jan 1, 1996

By Isobe K, Muchi I, Hsieh YS

Theoretical and experimental studies have been made-to clarify the physical and chemical behavior of the tuyere combustion zone of blast furnace. Gas streamlines around this zone were visualized by the use of the two-dimensional equip- ment. Close agreement between the observed stream- lines and the calculated ones is found. The three- dimensional experimental studies have revealed that there exists a so-called dry zone in the neighbor- hood of the raceway and the trickling liquid be- haves approximately like a continuum. A kinetic model is develdped to describe the behavior of coke combustion in the tuyere zone. The model is based on the reaction kinetics, the differential balances of heat and mass, and the mechanics of gas flows. Regarding-the-axial distribution of gas composition in the tuyere zone, good agreement is obtained be- tween the model prediction and the data observed in a working furnace by the other investigators. Cal- culated results-show that the maximum consumption of coke occurs at the intermediate region of the raceway. For the blowing of oxygen-enriched or high -humidity blast, the position at which the maximum consumption of coke occurs is shifted toward the tuyere nose. Similar effect is found when the par- ticle diameter of coke in the tuyere zone is de- creased. The solid flow pattern around the tuyere combustion zone was visualized by the use of the two-dimensional equipment in which the sublimation of dry ice particles in front of the tuyere was

Jan 1, 1981

By Bruno Alves Resende, Antonio Adel dos Santos

Temperature, microstructure and dimensions are the main material parameters to be controlled during hot rolling of steel. Although thermal mathematical models have long been developed and applied for hot strip rolling, each Hot Strip Mill (HSM) must have its own model adapted to its facilities. Thus, a mathematical model for temperature evolution during rough rolling has been developed for the Usiminas HSM at Ipatinga Plant. The model achieved a high level of accuracy, which was assessed by comparing measured values of temperature at the hot strip mill entry with the calculated ones, the difference ranging from 9°C to 17°C. Application examples have shown that the slab can be occasionally stopped before start of rolling for as long as a couple of minutes without compromising its further processing. On the other hand, if the transfer bar stops after rough rolling even for short time, further processing in the HSM can be hindered, due to excessive temperature drop. In case of such abnormal line stop, the model can be used as a tool for decision-making to either continuing the planned rolling schedule or to changing the route, thus improving the overall rolling process.

Oct 1, 2019