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By A. K. Fallaw, D. L. Taylor, G. Wang, L. R. Moore, S. Dobson, C. B. Parkinson

"Over the years, the decline of high grade ores have become an increasing problem in the global mining industry. As such, techniques and chemistries must change in order to continue to meet the market demand and quality. Reverse cationic flotation of quartz and silicates is one of the most important techniques for generating the industry standard product from minerals such as iron and phosphate ores. Amine collectors are the global standard in such processes. However, as the ore quality continues to decline so must the chemistry change to meet the change in ore composition. This paper will focus on the introduction and full scale application of a novel amine collector towards a cleaner flotation process in phosphate beneficiation with Crago process. The results suggests the collector is capable of improving the phosphate recovery, in this cleaner circuit, to approximately 94% with minimal sensitivity to the everyday changes in feed grade.INTRODUCTION The days of mining high grade minerals are long gone, but the demand continues to increase. Phosphate ore, for example, is most dominantly demanded from the agriculture industry as a fertilizer component (i.e. diammonium phosphate, DAP) (FAO, 2014). Some literature suggests that global food production must increase by approximately 70% by 2050 (Cordell, 2009). It is also suggested that the peak global phosphorus production will occur around the year 2033, which is the period at which the easily accessible reserves have been depleted. Currently, phosphorus is commonly mined with a BPL (Bone Phosphate of Lime) concentration of 12-20% and a remainder typically being gangue minerals such as silica, clays, metal oxides, calcareous minerals, and carbonaceous minerals. These gangue components can lead to various negative processing and utilization consequences. Calcium, from carbonaceous minerals, is problematic due to the elevated levels of sulfuric acid required to convert the phosphate rock to the acid form (SRI Consulting, 2009). Calcium can also lead to elevated dosages of flotation reagents due to the desire of the fatty acid to coordinate to calcium minerals. Carbonate leads to increased levels of foam during the wet acid process. Silica is associated with the level of insols (acid insolubles), which must be less than 10% in the final concentrate that will be transferred to the chemical plant for acidification. Phosphate ore can generally be classified as carbonaceous or siliceous (El-Shall, 2003). Siliceous ores are commonly processed through various sizing steps followed by multi-staged flotation (Figure 1) (FIPR, 2014 & Güven, 2010). Though the higher grade phosphate pebble is declining, many mines are still able to size good enough to produce some amount of such pebble. Unlike most metal flotation processes where grinding is a necessity for an optimal process, Florida phosphate flotation does not generally require aggressive grinding and can typically operate at 0.1-1.0 mm. The rougher flotation step applies pH modification to achieve the optimal pH of 8.8-9.3 followed by conditioning with a fatty acid type collector, which builds a hydrophobic waxy layer on the surface of the particle to assist in the flotation. This generally achieves higher than 85% recovery of a product with 50-60% BPL and 15-30% insols. Unfortunately, DAP production generally requires 3.5 tons of phosphate rock containing greater than 63% BPL to produce 1 ton of phosphoric acid (ArgusMedia, 2014). Thus, further purification is required to achieve the grade by the chemical plant for fertilizer production. After the fatty acid is scrubbed off the phosphate particles using sulfuric acid (pH 2.5-3.5), the pH is generally operationally readjusted to 6.5-7.2 by washing with “fresh” water. A second collector is applied prior to the cleaner, which is a reverse cationic flotation process. This collector is typically a cationic amine based reagent, which should have an affinity for silica containing mineral"

Jan 1, 2015

By C. R. Breck

THERE has been a running discussion over the past several years with respect to the life and adequacy of our natural gas reserves. Some of the experts agree on one phase of the subject at least-that eventually it will be necessary to augment deliveries of natural gas in the northern markets by the development of a more or less comparable synthetic gas made from coal. The purpose of this paper is to point out: 1. It may be later than a good many people think-the demand for addi¬tional domestic and commercial pipeline gas in at least one section of the North will probably be felt rather keenly before an adequate synthetic pipe¬line-gas project, developed on economic lines, could be completed, even if initiated in the near future. 2. The evidence is considerable that such a project would be technically sound and economically self-supporting, although the margin of profit at first might be so small and the magnitude of an economic enterprise so great -that financing would be impossible without Government aid in some form or other. The part of the country referred to is the heavily populated section in the northeast of the United States. To simplify an examination of the situa¬tion, let us take the potential marketing areas within range to the north and east of the three pipelines: 1. Tennessee Gas Transmission Co. as it enters Erie County, New York state. 2. Texas Eastern Transmission Corporation just before the tap that sup¬plies the general Philadelphia area. 3. Transcontinental Gas Pipe Line Corporation as it enters the state of New Jersey. The sources of gas for these three pipelines are in Texas and Louisiana. The ultimate maximum combined capacity of the three lines at the points stated is approximately 1,200,000,000 cu ft per 24 hr at the maximum load factor probable of attainment in normal operation. The areas supplied by the three lines north and east of the points stated, or assumed as eventual markets, are: 1. Central New York state, from Buffalo to Albany (both inclusive).

Jan 1, 1953

By Jesse White, Arlin Olson

"An Engineering Scale Technology Demonstration (ESTD) unit utilizing the THOR fluidized bed steam reforming technology was built and operated by Hazen Research, Inc. for the purpose of denitrating and solidifying various Department of Energy (DOE) radioactive tank waste surrogates into granular products. The ESTD offered the opportunity to investigate the operational characteristics of two fluidized beds in series to test process system designs such as those for fluidization, feeding, and product collection. Operational characteristics that were evaluated included bed attrition rate, particle growth, and elutriation; and the effects that variations in process parameters (e.g., fluidizing gas flow rate, feed composition, feed injection method, and gas distributor design) had upon these characteristics were observed. Testing of the process systems on this scale allowed for design changes to be made where the cost in time and money were significantly less by comparison to those same modifications being made on the commercial scale.IntroductionFluidized bed steam reforming (FBSR) offers a moderate temperature (620-750°C) continuous method by which various liquid wastes can be processed irrespective of whether they contain organics, nitrates, sulfates/sulfides, chlorides, fluorides, volatile radionuclides or other aqueous components. The FBSR technology has exhibited the potential to process these wastes into either a carbonate or crystalline ceramic (mineral) granular product.Pilot scale testing was performed using the THOR Treatment Technologies, LLC (ITT) FBSR process, as it offered the opportunity to evaluate multiple aspects in an environment more conducive to experimentation. Process changes and system modifications could be made faster and with less cost impact as compared with changes to an assembled commercial plant. These aspects include verification of process chemistry and kinetics, evaluation of materials of construction, equipment sizing and design, and the interactions of the systems. Evaluation of process chemistry allowed for the verification of thermodynamic and kinetic models, and was used in conjunction with these models to improve the database and modeling assumptions. It also allowed for the reevaluation of data from earlier bench scale testing with the opportunity for long-term operations. These long-term effects may include the buildup of one or more elements that results in the formation of eutectics leading to the destabilization of a fluidized bed, or the shift in particle size as a result of attrition or agglomeration. The pilot plant also provided an environment to evaluate materials of construction."

Jan 1, 2014

By Jun Xiao, Jianwen Yang, Yanhong Dong, Daixiong Chen

"MANGOTE Surface oxidizied mine is a gold-bearing deposit in Congo's Mai-Ndombe Province. In the past decades, the ore has been exploited in a crude way by local farmers, which directly causes the severe processing difficulty and lack of economy of cyanide leaching. Hunan Research Institute for Non-ferrous metals (HRIM) is currently investigating options to recover gold through understanding the mineralogical characteristics of MANGOTE surface oxidized ore. Chemical analysis , X-ray diffraction(XRD) and Quantitative Evaluation of Minerals by SCANing electron microscopy (QEMSCAN ) were conducted on samples from mine site. The bulk analysis results showed that gold separation of gold from gangue minerals was feasible after grinding the ore samples to 86.53% -74µm and adjusting the pulp specific weight at 100g/L, and gravity separation was conducted with using spiral chute after grading of fine particles. The research results highlight relationship between mineralogical characteristics of abandoned ore and economy of comprehensive utilization that might be directive experience to similar cases. INTRODUCTION The occurrence state of gold in natural gold minerals determines the basic recovery and recovery effect of gold(Komnitsas, C., & Pooley, F. D. 1989). The occurrence of gold in the ore refers to the form of gold in the ore.Generally the existing state of gold can be divided into four major categories according to the viewpoint of the dispersion system: independent minerals and gold, a coarse dispersed system;colloidal gold, a colloidal dispersion; solid solution gold, is atomic ion dispersion; adsorptive gold, according to the adsorbed particle is the micelle or ion, respectively is a colloidal dispersion or ion dispersion(Mao, S. D., & Yang, R. S. 2009; Liu, J. J. et al. 2007; Horisberger, M., & Rosset, J. 1977; Li, Y., & Audétat, A. 2013).With the increasing technology of comprehensive utilization of resources,varied plants can now process different gold ores with various occurrence states(Neesse, T. 2014; 7. Ogundare. et al.2014)."

Jan 1, 2018

By T. Fraszczak, U. A. Peuker, T. Mütze, T. Leißner, A. Wikedzi

The present paper highlights on the comminution and liberation properties of two greisen-type lithium bearing-mica ore blends (L1, L2) subjected to different breakage devices; cone crusher (CC), roller crusher (RC), rotor beater mill (RBM) and a screen mill (SM). The particle size distribution (PSD) of the products from each device were evaluated to search for an appropriate PSD model using Gates-Gaudin-Schuhmann (GGS) and Rosin-Rammler (RR) functions. In order to determine an appropriate function that could better describe the PSDs from the devices used, the coefficient of determination (R2) was used as a criterion. In terms of mineral liberation studies, due to costs, only products from rotor beater mill (RBM) were examined through an automated scanning electron microscope (SEM) technique. It was found that RBM, RC and SM products were better described by the RR model than the GGS model with higher R2 values (0.97-1.0). However, cone crusher products for L1 were better described by GSS model, while that for L2 were better described by RR model. In terms of the spread of size distribution as indicated by RR model parameters, RC products were more uniformly distributed compared to products from other devices, for both ore blends. Also the RBM products were more scattered than products from other devices. The results indicate that the composition of individual ore blends affected the comminution products PSDs since different PSD model parameters were obtained for samples comminuted by same devices. The modal mineralogy of the two ore blends indicate both to be rich in quartz, topaz, zinnwaldite and muscovite. Further, the result indicate that, for both ore blends, zinnwaldite phase is more enriched in the fraction < 250 µm. Moreover, better liberation of zinnwaldite is observed for L1 compared to L2. This could be explained by differences of the two ore blends in three aspects; the nature of mineral association, reduction ratio of the fractions analysed and the nature of spread of the size distribution.

Jan 1, 2018

By R. J. SHAW

Oil shale has been defined as, "a compact, laminated rock of sedimentary origin yielding over 35 percent of ash and containing organic matter that yields oil when distilled but not appreciably when extracted with the ordinary solvents for petroleum." The oil-yielding organic matter in oil shale, commonly called kerogen, decomposes upon application of heat to form bituminous materials that are soluble in organic solvents and may be extracted from the inorganic residue. However, separation usually is accomplished by continuing the heating and thereby cracking the primary bitumens to gas and oil, which distill, leaving a carbonaceous material on the mineral residue. It has been suggested that this conversion takes place only at relatively high temperatures - 750°F or higher. On the other hand, other workers have found that transformation may take place to some extent at temperatures as low as 400°F. In either a solvent extraction or a destructive distillation process for separating organic material from the inorganic portion of oil shale, the quantity of heat required to raise the temperature of the oil shale sufficiently to induce a satisfactory rate of conversion of kerogen to oil is important in determining the design of an economical process. Likewise, the quantity of heat recoverable from a spent shale is important in determining the overall heat balance of the process. Published data on the specific heat of American oil shales are meager. Gavin and Sharp present data for two samples of Colorado oil shale, one from near DeBeque and one from Parachute Creek, and for a sample of spent shale over a temperature range of 68°F to 1940°F. McKee and Lydor present data on the specific heat of two samples of oil shale from near DeBeque, Colorado. Additional thermal data on various grades of oil shale over a wider range of temperature are needed in order to apply sound engineering practices to the design of equipment for processing oil shale.

Nov 1, 1947

By Oliver W. Keener

The operation described herein differs from the usual practice in the Tri-State district in two important respects: (1) the ore is loaded into cars which are tramped to the shaft and hoisted on self-dumping cages, and (2) about 30 per cent of the ore is loaded by power shovels. The four-month period covered by the cost data appended at the end of the paper immediately followed a period of about one year during which the mine was shut down, and the expense incident to the resumption of operations is reflected in the costs. The author acknowledges the assistance of C. F. Jackson, mining engineer, U. S. Bureau of Mines, in the preparation of this paper and the compilation of the data.

Jan 1, 1929

By B. Konda, R. Lauer, D. Camilucci, D. Gladwin

"Income based taxes are significant cost elements to be considered in evaluating investment in new mine development. This paper presents the results of comparative analysis of effective income-based tax rates for mining in the Northwest Territories (NWT), selected Canadian provinces and international jurisdictions. The study was done as background to a review of royalty regulations for the NWT. ObjectiveThis paper presents results of comparative analysis of effective mining royalty1 rates, and combined effective mining royalty and income tax rates on selected mine models for the Northwest Territories (NWT), with those for several other jurisdictions in Canada and abroad which compete with the NWT for mining investment.BackgroundThe February 27, 1995 federal budget directed the Department of Indian Affairs and Northern Development (DIAND) to proceed with a comprehensive review and amendments to northern natural resource management legislation in order “to increase revenues and ensure a fair return to the Crown.” DIAND is responsible for the administration of the Territorial Lands Act, and its regulations.The Territorial Lands Act gives the Governor-in-Council the authority to “… make regulations for the leasing of mining rights in, under or on territorial lands and the payment of royalties therefor,…”. In the NWT, the Canada Mining Regulations (CMR) provide for the disposition of mineral rights for most minerals, other than coal, petroleum and related hydrocarbons, in return for the payment of a royalty to the Crown.As part of this review of the NWT mining royalty regime, several computer mine models were developed and tax regimes in a number of jurisdictions were analyzed. Effective mining royalty rates, and the combined effective mining royalty and income tax rates were compared across the jurisdictions. The results presented in this paper are a part of the background work done in preparing a discussion paper on proposed changes to the NWT mining royalty that is expected to be released for public consultation in the very near future."

Jan 1, 1997

By Jianhang Hu, Li Yang, Yonggang Wei, Kongzhai Li

"In this paper, the pyrolysis of biomasses including bamboo, sawdust and walnut shell were performed in a tube furnace under temperatures between 400? and 600? to obtain biomass carbon, gas, and tar. Textural parameters analysis revealed the caloric value of biomass carbons between 32 MJ/kg and 34 MJ/kg. It also indicated that the surface of biomass carbon consists of mesopore and macropore structures. By using GC analysis, it was determined the main ingredients of pyrolysis gas are CO, H2, CO2, CH4, C2H4 and C2H6. Calculation states that the density of pyrolysis gas is roughly between 1.0 kg/m3 and 1.7 kg/m3, while the calorific value of pyrolysis gas is between 12000 kJ/m3 and 16500 kJ/m3, illustrating that pyrolysis gas is a median gas. The calorific value of biomass tar was found to be between 32 MJ/kg and 34 MJ/kg, with more than 80 compounds in the biomass tar identified by GC-MS method.IntroductionBiomass as a renewable source is the world's largest and most sustainable energy resource [1].The conversion of biomass has the potential to be a renewable and carbon neutral method of producing fuels and chemicals [2-4]. Pyrolysis is a thermo-chemical process defined as applying heat to degrade biomass in an inert atmosphere. It transforms unstable biomass and other organic materials into biomass carbon, gas, and tar [5]. Biomass carbon can be stored or transported much easier as compared to parent biomass or be converted to value added products such as activated carbons[6]; gas is a relatively low-energy-density fuel; tar can be considered as a source of useful chemicals[7].The characterization of biomass pyrolysis will lead to its increased understanding and utilization as a source of solid, liquid and gaseous products which can be used as fuels and petrochemical feedstock[8,9].In recent years, many researchers studied the effect of temperature on biomass pyrolysis product distribution characteristics in a variety of pyrolysis reactor[10]. Ramin Azargohar's paper [11] presents the results of characterization for biomass and investigates the effects of pyrolysis temperature on the pyrolysis products obtained by fast pyrolysis of four different types of biomass."

Jan 1, 2014

By J. G. Donaldson

Binary alloys of molybdenum and tungsten were prepared by the Bureau of Mines in laboratory-scale experiments by hydrogen reduction of their vaporized hexafluorides. Near-optimum deposition parameters were determined, and the nature of the deposited alloys was investigated. Dense, homogeneous alloys were codeposited between 650° and 750° C with a reduction efficiency of more than 75 percent. The alloy composition was uniform when the hydrogen ratio in the gas feed mixture did not exceed 3 times the stoichiometric requirement. Regulating the proportions of the metal hexafluorides in the gas feed provided a large degree of control over the composition of the deposit. Hardness of the deposits varied directly with the proportion of excess hydro,,,, in the gas feed and with the weight-percent of tungsten in the alloy. Hardness was not affected by deposition temperature over the range 650° to 750° C for specimens of similar composition. Extreme brittleness and unsuitable physical shapes of the alloys prevented tensile strength measurements.

Jan 1, 1966

By K. Lang

The use of high-efficiency electrical submersible pumps (ESPs) for large scale, open pit mine dewatering operations provides a good example of how technology, products and services from the oil and gas industry can be adapted to the mining industry. In this case, the mine is Goldcorp?s Peñasquito in the Zacatecas state of Mexico, at the Peñasco and Chile Colorado open pit deposits. The technology, products and services are from Schlumberger artificial lift (AL) and Schlumberger industrial water services (IWS). Overview of high-efficiency ESPs This section provides a brief description of the basic components, specifications and operating capacity ranges for the ESPs compared with traditional or conventional dewatering well pumps. This information helps to establish how ESPs provide certain functional and economic advantages over conventional pumps in a mine dewatering application. A schematic of a high-efficiency ESP in an oil and gas (O&G) application is shown in Fig. 1.

Sep 1, 2013

By T. J. White

Xtaltite is the trade name for a generic technology which exploits the well known insolubility of some minerals, which naturally incorporate toxic waste elements, to consolidate and immobilise a range of inorganic waste products. It is a specific case of synthetic mineral immobilisation technology (SMITE) which is already used to immobilise high level nuclear wastes (HLW. Although HLW is highly toxic, it exists in relatively small volumes, occurs in central facilities and may be stabilised at low waste loading (< 10 wt%). In contrast, heavy metal wastes are of considerable volume, therefore Xtalitite waste forms must routinely accommodate high waste loadings (usually in excess of 30 wt% for a particular toxic oxide or combination of oxides) and be suitable for fabrication in remote locations using relatively simple technology. This paper details the methodology underlying Xtaltite, with particular emphasis given to the interplay between solid state chemistry, durability and economic considerations. Specific reference is made to the treatment of arsenious and mercurial wastes.

Jan 1, 1994

By L. BENEDICT

COMMENTING on the report of the latest Royal Commission for India, the September, 1926, issue of the National City Bank&apos;s monthly letter states, among other things, that "The decision of the Royal Commission is against the proposal for a gold coinage, but in favor of placing the silver coins and paper currency now redeemable in silver on a gold basis." Also, it quotes the following from the Royal Commission&apos;s report: The essence of the proposal * * * * * is that the ordinary medium of circulation in India should remain as at present the currency note and the silver rupee, and that the stability of the currency in terms of gold should be secured by making the currency directly convertible into gold for all purposes, but the gold should not circulate as money. It must not circulate at first, and it need not circulate ever. In this connection it may be stated that during the last one hundred and fifty years or so unsuccessful attempts have been made by the governments of different nations of the world to devise a plan or plans by which gold and silver could be used concurrently for money purposes and, particularly, as standard money; such, for example, as bimetallism, which, of course, is impracticable. But, since none of such plans has been adopted generally it is logical to conclude that their proponents did not shape them so as to conform to the basic principle of standard money, or else political issues were deemed to be dominant, or, perhaps, it was partly due to each.

Jan 1, 1926

By Brandon Fryman, Josh Hoffman, Rhys Baker

A post-detonation debris collection project was led in conjunction with a large ammonium nitrate (AN) railcar detonation conducted by the Department of Homeland Security-Transportation Security Administration, Department of Defense-Combating Terrorism Technical Support Office, Sandia National Laboratories, and the U.S. Army Dugway Proving Grounds. This important work will aid in underpinning algorithms used in a Quantitative Risk Assessment (QRA) tool.

Feb 1, 2020

By Paul Laforest, Michael Moats, Daniel Majuste

The interaction of anode and electrolyte chemistry in copper electrorefining is complex. This is especially true with regard to the behavior of Group 15 elements (As, Sb, and Bi). To better understand this system, laboratory electrorefining experiments were conducted using commercial anodes with As/(Sb + Bi) molar ratios of 0.54 and 3.8 and an electrolyte collected from a commercial refinery. The effect of adding thiourea during plating was also examined. Twenty-one hour copper deposits were produced in the laboratory to simulate starter sheet production. The mechanical properties of the electrodeposited copper as measured by an industrially relevant empirical bend test and a one-point bend test developed by UFMG are reported. The crystal structures of the samples were also examined.

Mar 1, 2017

By LefTvre Y

In May 1991, AZSA commissioned a new conventional Cell House. This paper focuses on the major improvements introduced in the design and the construction of the equipment, machinery and control. An effective control system together with good reporting and routine operation has resulted in quality control of the Cell House at the highest possible level. Consequently the monthly current efficiency consistently averages above 93 per cent with a total energy usage of 3000 AC kWh/t of cathode zinc. The new concept for the year 2000 and beyond is introduced.

Jan 1, 1993

By Cris Sideco

This paper describes the concentration processes of the Sullivan. Concentrator, including crushing , transportation, sink-float, grinding , flotation and dewatering. Handling of hot muck has had a deleterious effect on most of the processes, resulting in significant operating problems and poorer metallurgy. These problems are described -in detail. THE SULLIVAN CONCENTRATOR is situated in Kimberley, high up in the Purcell Range of the Selkirk Mountains, at an elevation of 3,600 feet, approximately 4 miles from the Sullivan Mine (see Fig. 1). The original plant went on stream on August 23, 1923 at a designed capacity of 2,500 tons per day. This has been increased in stages to its present rated capacity of 11,000 tons per day. The latest stage was in 1949, when several major projects, including the underground crushing plant, the sink-float plant and the installation of a rod mill, were completed. Some 112,800,000 tons of ore have been treated in this concentrator to November 1975. The plant started on a 48-hour/ week schedule, but was reduced to 44 hours/week in October 1946 and down to 40 hours/week by the end of 1949. Except for a 6-month period in 1952 when the mill operated continuously, the 40-hour/week, Monday to Friday schedule was in effect.

Jan 1, 1977

By R. J. Traill

Introduction Following the discovery of high-grade deposits of pitchblende in the Great Bear Lake area of the Northwest Territories by Mr. Gilbert LaBine in May, 1930, samples were submitted to the Mines Branch for examination and investigation as to suitable methods of treatment (1). The purpose of this paper is to present, briefly, the results of the investigative work conducted on the ores and an outline of the methods developed for the extraction of the radium content and recovery of the by-products. The paper is presented in two parts. Part I gives a review of the history of radium production and of the principal processes used in other countries. Part II describes the work and gives the results of the Mines Branch investigation. Part 1-Radium Production In Other Countries Historical Outline Uranium was discovered in 1789, and more than a century later Madame Curie, while studying the physical properties of this element, observed that the ore of uranium exhibited greater activity than the pure uranium com-pounds she had prepared and traced the cause to the presence of a new element which she named radium. Eventually, research proved radium to be a disintegration product of uranium, and always present in uranium ores.

Jan 1, 1933

By E. Onal

Mining operators are faced with complex information delivered by technology-centric rather than user-centric systems. The ability to achieve high situation awareness (SA) in the face of this data overload is a key challenge for effective decision making and information exploitation. Incidents that result in loss of revenue and even life, and compromise safety that are attributed to human error are often the result of system designs that overload human cognitive capabilities. This paper focuses on defining SA as it relates to mining operations and presents methods for improving SA through a scientific approach for electric shovel operator user interface development.

Aug 1, 2013

By S. Viswanathan, Q. Han, A. S. Sabau

"In spite of recent advances in the mathematical modeling of fluid dynamics for materials processing applications, no significant advances have been made in the numerical discretization of these equations. In this work, the application of two-step projection methods for the numerical simulation of interdendritic flows is discussed. Unlike previous methods, the methods presented here are constructed for the exact equations which are characterized by variable density and volumetric fraction of the liquid. The drag terms, which describe the momentum loss due to the flow around and through the dendrite structures, are treated implicitly. Numerical examples for shrinkage-induced flow during solidification of an Al-4.5% Cu alloy bar is used to illustrate the effectiveness of the proposed algorithm.IntroductionLiquid contraction during solidification plays an important role in the formation of casting defects such as shrinkage voids, microporosity, and macrosegregation. Owing to their importance, the study of transport processes during solidification have received considerable attention during the past years [1, 2]. By the use of volume-averaging techniques, the mass and momentum equations for flow through a stationary dendritic structure were derived [3]. By using the volume-averaging techniques for multi-phase systems, two-phase transport equations for solidification problems were derived [4]."

Jan 1, 1999