Search Documents

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 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 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 G. F. Friel, J. C. Edwards, C. C. Hwang

In the implementation of a mine fire alarm and location strategy, the Interpretation of the fire signature Is Important. Smoke and CO are the two dominant fire signatures, and many mine fire detection systems utilize sensors which respond to smoke or CO through a diffusion mode or a mechanical pump mode. The fire signature may be modified during its transport along airways and at crosscuts. The modification occurs through dilution of the contaminants. In this Investigation, computer codes were employed to compute the effects of contaminant dilution on the contaminant signature when a straight flow passage has one dead-end crosscut. The model predicted the airflow within always and the entrainment of contaminants into the crosscut from the airway. One application of the model is to determine the most suitable location for CO detectors for early mine fire detection.

Jan 1, 1995

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 Robert C. Bates

Background is given on the various equations used to describe diffusion and convective flow of radon in porous media. Bureau-developed equations for modeling diffusion and Darcy flow through multilayered porous media are described briefly, and examples of their use are given. Analysis results discussed include: The transient effect of pressure changes in different length models, time dependent flux changes in multi-layered models, and radon flux through pinholes in sealants

Jan 1, 1980

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 Eren H

For a hydrocyclone of fIXed geometry, DC, Di, DO and ? are constants, the variable parameters affecting the performance are Qi, Fi, Du and H. (See Appendix 2 for definition of symbols).The relationship between d50c, Qi, Fi, Du and H gives models which can effectively be used for performance predictions. Such models have already been established by Lynch et al and by Plitt.These models have been tried in a limited manner under continuous operating conditions for on-line cowol. For on-line control effective and accurate instrumentation is required for which a new set up is proposed. Using this set up, a new model was established. A feature in this model is that deviations from the norm of operational parameters affecting d50c were considered. It is shown that these deviations generated by the disturbance of one or more of variations in the parameters, can be monitored by a computer and suitable signals generated to control servo mechanisms for restoring the required d50c value.The logic followed in developing the computer software is described and the application of the model is indicated.

Jan 1, 1990

By Batterham RJ

A 'research model' can be used to investigate cause and effect relations and generally improve the understanding of extractive metallurgical processes. As such, it is a useful research technique which complements the traditional methods of laboratory and plant measurement. The procedure of model development is iterative and involves observation of the process, hypothesis of phenomena, prediction using mathematical descriptions of the phenomena and comparison of predictions with real-world measurements. Lack of agreement of predictions with real-world measurements usually indicates an inadequacy in the hypotheses and necessitates revision. Experimentation has an integral role in the process of model development but its emphasis is different from that when experimentation alone is used to study processes. Since a process as a whole is investigated by using a model, experimentation is restricted to the study of specific phenomena to aid the description of these in the model, to the characterisation of the raw materials (for initial values of the model parameters) and to the measurement of physical and chemical constants required in the model equations. Similarly, plant measurements are made for the purpose of comparison with the model predictions not to establish cause and effect relations. This makes plant experimentation much simpler and cheaper'since most measurements-can be taken during normal operation.

Jan 1, 1984

By Gemei Yang, Pierre Mousset-Jones, Felipe Calizaya, Malcolm J. McPherson

Laboratory tests on controlled airflow recirculation have shown the development of transient states in response to changes in system prevailing conditions such as those generated by a sudden start-up and stoppage of fans. Researchers in many European countries have developed various models to explain these phenomena. However, these models failed to consider some important factors such as diffusion and dispersion of gas in turbulent flows. For both in-line and cross-cut recirculation, tests have shown that after the start- up of a booster fan, the gas concentration in the system fluctuates, reaching high levels at the initial states and slowly dying out with time. These fluctuations cannot be represented adequately by simple step-wise functions but rather by smooth, albeit complex equations. In this paper, the phenomena are explained by the convection-dispersion theory, and represented by a mathematical model. Based on a few simplifications and applying Fourier's Transform Method to the differential equations of the flow recirculation model, an integral form of gas concentration function was derived. The Simpson Integration Method was used to compute numerical results for two laboratory tests. The paper also discusses the range of the dispersion coefficient to improve the accuracy of the model.

Jan 1, 1989

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 V. P. Kolosyuk, A. M. Bryukhanov

Occurrences of hazardous events (explosions of methane or coal dust, fires, outbursts) have been investigated and presented as a flow of events in time. It has been shown that flows of hazardous events in a long time span are homogeneous, stationary and no-after effect flows and can be considered as stationary Poisson flows. A flow of CH4/coal dust explosions that had happened for the last 27 years in Ukraine was analyzed. The explosions have been statistically processed. Practicability of agreement of statistical and theoretical data on mathematical expectation and mean square deviation of time interval between explosion and the explosion intensity has been stated. Probability of an emergency event in time is expressed through an exponential function, while mathematical expectation of an accident and mean square deviation of time interval between successive explosions are in inverse proportion to the accident intensity. Accident probability for practical purposes can be determined as a product of accident intensity by calculated time interval.

Jan 1, 2003

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