2001 TMS Fall Extraction and Process Metallurgy Meeting: Computational Modeling of Materials, Minerals,

and Metals What follows is the final technical program of the 2001 TMS Fall Extracting and Process Metallurgy Meeting: Computational Modeling of Materials, Minerals, and Metals which was scheduled for Setpember 23-26, 2001. Following the events of September 11, 2001, the ongoing difficulties associated with U.S. and international air travel, and the cancellation of nonessential travel by the employers of many attendees and presenters, this meeting has been postponed until further notice. This technical program is being provided for archival purposes, and does not necessarily represent the planned symposia of the rescheduled conference.

Monday AMOpening Plenary Session

KeynoteMulti-Physics Simulation of Metal Processing:Mark Samonds

KeynoteComputing the Dynamic Interaction ofMagnetic Fields and Turbulent ConductingFluids in Metals Processing: Koulis Pericleous

10:30 AM Break

Track A - CFD Modelling - I10:45 AMSimulation of Turbulent Flow and ParticleTransport in the Continuous Casting of Steel:Q. Yuan; T. Shi; S. P. Vanka; B. G. Thomas

11:10 AMCFD Modeling of the Hydrodynamics ofFluidization in the Sand Surrounding a LostFoam Casting Pattern:Nathanael HarrisonHudson; Sushil Bhavnani; Ruel A. Overfelt

11:35 AMContinuum Modelling of Granular Flows usingPHYSICA, a 3-D Unstructured, Finite-VolumeModelling Framework: Nicholas Christakis;Mayur K. Patel; Mark Cross; John Baxter; HadiAbou-Chakra; Ugur Tüzün

12:00 PMMathematical Model of Inclusion Removalduring Steel Degassing: Michel Cournil; FrédéricGruy; Pascal Gardin; Hubert Saint-Raymond

12:25 PMApplication of Coupled Continuum-Mesoscopic Computational Methods for theSimulation of Complex Fluids in IndustrialProcesses: Greg Glinski; Chris J. Bailey; KoulisPericleous

Track B - Heat & Mass Transfer - I10:45 AMHeat Load Control of Blast Furnace Wall usingStatistical Optimization Techniques: Tae-hwaChoi; Yong-hwan Chu; Chonghun Han

11:10 AMMathmatical Modeling and ExperimentalVerification of Assimilation of ExothermicAdditions in Liquid Metals: Stavros A.Argyropoulos; Henry H. Hu

11:35 AMA Model of the Cathode Dynamics in ElectricField-Enhanced Smelting and Refining ofSteel: David Michael Dussault; Adam Powell

12:00 PMA Mathematical Model for the Control ofMetallurgical Properties of the Product Sinter:Ndabezinhle Manengi Dube; E. F. Vegman

12:25 PMModelling the Magnetostriction of TexturedFerromagnetic Materials with a CubicStructure: Ruben Decocker; Leo Kestens; YvanHoubaert

Monday PM Plenary SessionKeynoteModelling and Process Optimization forFunctionally Graded Materials: Dan Tortorelli

Track A - Optimization & NovelMethods

2:45 PMLattice Boltzmann Methods for MetallurgicalProcess Simulation: Christian Redl

3:10 PMViscosity Estimation Model for an OscillatingCup Viscometer: Deming Wang; R. A. Overfelt

3:35 PM Break

3:50 PMNumerical Optimization of MagnesiumReduction in a Modified Pidgeon Process: AlfredYu; Henry Hu

4:15 PMDeterministic and Regression Models of NickelOxide Reducing Roasting Process: V. M.Paretsky; A. V. Tarasov

4:40 PMIntegrating Computational Mechanics andNumerical Optimization for the Design ofMaterial Properties in Electronic Packages:Stoyan Stoyanov; C. Bailey; M. Cross

5:05 PMComputer-Aided Modeling and Control ofAutogenous Copper Smelting Process: A. V.Tarasov; V. M. Paretsky

Track B - Melting & Solidification - I2:45 PMA Marker Chain Front Tracking Method forModelling Meniscus Dynamics in the Al IngotCasting Process: Fionn Iversen; Jon Arne Bakken;Stein Tore Johansen

3:10 PMComputational Modeling of Heat Mass andSolute Transport in Directional SolidificationProcesses: Mohammed El Ganaoui; Patrick Bontoux

3:35 PM Break

3:50 PMComputational Modelling of Freeze Layers inSmelting Processes: Andrew P. Campbell; KoulisA. Pericleous; Mark Cross

4:15 PMMathematical Modeling of Heat Transfer andMicroporosity Formation in Die Cast A356Wheels: P. Vo; D. Maijer; S. L. Cockcroft; M. A.Wells; C. Hermesmann

4:40 PMModelling Filters in Metal Casting Processes:Mark R. Jolly; Jean-Christophe Gebelin

5:05 PMComputer Heat Transfer Model for DirectionallySolidified Castings: Deming Wang; R. A. Overfelt

Tuesday AM Plenary SessionKeynotePhase Field Methods for Modeling Microstruc-ture: James A. Warren

Track A - Structure9:45 AMMicroporosity Evolution and InterdendriticFluid Flows during Solidification: Adrian S.Sabau; Srinath Viswanathan

10:10 AMCellular Automata Computer Model ofPolycrystalline Plastic Deformation: AlexanderV. Spuskanyuk; Yakiv E. Beygelzimer; Victor M.Varyukhin

10:35 AM Break

10:50 AMSimulations of Microstructural Evolution:Martin E. Glicksman; Kegang Wang; P. Crawford

11:15 AMAb Initio Calculations of Theoretical TensileStrength in Metals and Intermetallics: MojmirSob; Ligen Wang; Martin Friak; Vaclav Vitek

11:40 AMModeling of Interdendritic Strain and Interden-dritic Cracking Phenomena during DendriticSolidification Processes: Mostafa El-Bealy

Track B -Melting & Solidification - II

9:45 AMWax Injection in the Investment CastingIndustry: Jean-Christophe Gebelin; AlexanderCendrowicz; Mark R. Jolly

10:10 AMMicro/Macro Modeling of Ingot CoolingProcesses for Ni-Cu-S Alloys: ApostleMouchmov; Mark Cross; Koulis Pericleous

10:35 AM Break

10:50 AMComparison of Numerical Models of Solidifica-tion Behavior in Direct Chill Casting withExperiments: Christopher J. Vreeman; DavidSchloz; Matthew John M. Krane

11:15 AMTwo-Phase Predictive Finite-Element FlowModel for Semi-Solid Slurries: Frédéric Pineau

11:40 AMCFD Simulation of Continuous Charging andMelting of Small Metallic Particles in a MeltingReactor: Stefan Pirker; Oszkar Biro; Philipp Gittler;Peter Mittag; Bernard Aigner

12:05 PMNumerical Simulation of Wax Pattern Dimen-sions in Investment Casting: Adrian S. Sabau;Srinath Viswanathan

Monday AM Monday PM Tuesday AM

At-A-Glance Technical Program

Tuesday PM Plenary SessionKeynoteComputational Modelling of Metals ReductionProcesses: Phil Schwarz

Track A - CFD Modelling - II2:45 PMModelling of Raceway Hysteresis: Govind S.Gupta; S. Sarkar; M. G. Basavaraj; P. D. Patil

3:10 PMLifetime Prediction of Pneumatic ConveyorBends with the Aid of Computational Models:Mayur K. Patel; Robert Hanson

3:35 PM Break

3:50 PMA Parametric Study of Oxy-Fuel Burners inSecondary Aluminum Melting: MadhuHuggahalli; Neeraj Saxena; Ken Grieshaber; JerryBernardski; David Stoffel

4:15 PMComputational Modelling of Vortex Formation inthe Lead Refining Kettle: Suman Kumar; Chris Bailey;Mayur Patel; A. W. Piper; M. Cowling; R. A. Forsdick

4:40 PMCFD Modeling of Solids Suspensions inStirred Tanks: Lanre Oshinowo; André Bakker

5:05 PMWater Model and Numerical Study on theSpout Height in a Gas Stirred Vessel: DiancaiGuo; G. A. Irons

Track B -Thermo-Mechanical Modelling - I

2:45 PMThick Yield Surface: An Approach to theProcessing of Computer Experiments onPolycrystalline Deformation: Yan E. Beygelzimer;Alexander V. Spuskanyuk; Victor Varyukhin

3:10 PMModel for Stress, Temperature and PhaseTransformation Behaviour of Steels on Run-Out Table in Hot Strip Mill: Heung Nam Han; JaeKon Lee; Hong Jun Kim; Young-Sool Jin

3:35 PM Break

3:50 PMThermo-Mechanical Coupling Finite ElementAnalysis of Sheet Metal Extrusion Process:Zhanghua Chen; C. Y. Tang; T. C. Lee

4:15 PMA Model for Calculating the Lankford Value inSheet Steels: Sihai Jiao; C. Isaac Garcia; AnthonyJ. DeArdo

4:40 PMInterfacial Modelling of Hot Rolling: AProbabilistic Approach: Sumitesh Das; Eric J.Palmiere; Ian C. Howard

5:05 PMComputational Experiment in the Mechanics ofMaterials: Leon Mishnaevsky; Ulrich Weber; NilsLippmann; Siegfried Schmauder

Wednesday AM Plenary SessionKeynoteMicro-Macro Modeling of SolidificationProcesses and Phenomena: Vaughan Voller

Track A - Heat & Mass Transfer - II9:45 AMA Steady State Electrothermic SimulationAnalysis of a Carbothermic Reduction Reactorfor the Production of Aluminium: Dimitrios I.Gerogiorgis; B. Erik Ydstie; Sridhar S. Seetharaman

10:10 AMThe Limitations of CFD Modelling for FurnaceAtmosphere Troubleshooting: Paul F. Stratton;Neeraj Saxena; M. Huggahalli

10:35 AM Break

10:50 AMSimulation of Internal Oxidation: Henrik Larsson;Martin Schwind; John Ågren

11:15 AMDynamic Model for a Vapor Recovery in Carbo-thermic Aluminum Process: Vianey Garcia-Osorio; Tor Lindstad; B. Erik Ydstie

11:40 AMComputer Simulation of the Structure-Energetical Transformations at CombustionSynthesis in the Systems NiAl and TiAl: MikhailD. Starostenkov; Gennadiy M. Poletayev; AlexandraS. Starostenkova

12:05 PMInfluence of Surface Pressure and Slag Layer onBubble Bursting in Degasser Systems: Julie Cranga;Pascal Gardin; Didier Huin; Jacques Magnaudet

Track B -Melting & Solidification - III

9:45 AMComputational Studies of the Control ofConvection in Diamagnetic Liquids duringSolidification with Magnetic Field Gradient: C.B. Seybert; J. W. Evans

10:10 AMMethods for Approximating Discontinuous orRapidly Changing Conductivity in NumericalCalculations: Vaughan Richard Voller

10:35 AM Break

10:50 AMModelling of the De-Waxing of Investment CastShells: Jean-Christophe Gebelin; Sam Jones; MarkR. Jolly

11:15 AMThe Swirling Effect in an Immersion Nozzle onthe Flow in a Continuous Casting Mold:Shinichiro Yokoya; Sigeo Takagi; Manabu Iguchi;Katsukiyo Marukawa; Shigeta Hara

11:40 AMComputational Modelling of Metals Extrusionand Forging Processes: A. J. Williams; T. N.Croft; M. Cross

12:05 PMThe Role of Orifice Shape in the Detection ofInclusions in Liquid Metals: Roderick I.L. Guthrie; Mei Li

Wednesday PM Plenary SessionKeynoteComputational Modeling of Thermo-Mechanical Phenomena: Christopher Bailey

Thermo-Mechanical Modelling II2:45 PMMathematical Modeling of Mean Flow Stressduring Hot Strip Rolling of Nb MicroalloyedSteels: Ki Bong Kang; Sang Hyun Cho; John J.Jonas

3:10 PMModeling of Residual Stresses and MechanicalBehavior of Glass-Infiltrated Spinel CeramicComposites: Anil Saigal; Edwin R. Fuller; SaidJahanmir

3:35 PM Break

3:50 PMSimulation of Fatigue Stress Life (S-N)Diagrams for Ti-6Al-4V Alloy by Application ofArtificial Neural Network: S. McShane; SavkoMalinov; J. J. McKeown; Wei Sha

4:15 PMPrediction of Lateral and Normal Force-Displacement Curves for Flip-Chip SolderJoints: Daniel Wheeler; Daniel Josell; James A.Warren; William E. Wallace

4:40 PMSimulation of the Plastic Behavior duringMechanical Testing of Galvanized Steel usingthe Finite Element Method: Adriana Salas;Martha Patricia Guerrero Mata; Rafael Colás; RenéGarza

Tuesday PM Wednesday AM Wednesday PM

At-A-Glance Technical Program

Technical Program Grid

Monday-September 24 Tuesday-September 25 Wednesday-September 26

AMPMAMPMAM PM

Track B -Heat &

Mass Transfer - I

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Track A -Optimization &Novel Methods

Track B -Melting &

Solidification - I

Track B -Melting &

Solidification - II

Track B -Thermo-

MechanicalModelling - I

Track B -Melting &

Solidification - III

Track A -Structure

Track A -CFD Modelling -II

Track A -Heat &

Mass Transfer - II

Thermo-Mechanical

Modelling - II

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Monday AMOpening Plenary

Session

Monday PMPlenary Session

Tuesday AMPlenary Session

Tuesday PMPlenary Session

Wednesday AMPlenary Session

Wednesday PMPlenary Session

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2001 FALL EXTRACTION AND PROCESS METALLURGY MEETING:COMPUTATIONAL MODELING OF

MATERIALS, MINERALS & METALS PROCESSING SYMPOSIUMSeptember 23–26, 2001San Diego, California

Monday AMOpening Plenary Session9:00 AM–10:30 AM

Monday AM Room: St. Tropez/Monte CarloSeptember 24, 2001 Location: Hilton San Diego Resort

Session Chairs: Mark Cross, The University of Greenwich, Centre forNumerical Modelling & Process Analysis, Old Royal Naval College, 30Park Row, Greenwich, London SE10 9LS UK; James W. Evans,University of California, Dept. of Matls. Sci. & Min. Eng., 585 EvansHall, Berkeley, CA 94720-1760 USA

KeynoteMulti-Physics Simulation of Metal Processing: MarkSamonds1; 1UES Software, Inc., 175 Admiral Cochran Dr.,Annapolis, MD 21401 USA Manufacturing processes which involve liquid to solidand solid state transformations in metals encompass a widevariety of physical phenomena. The past twenty years haveseen a steady evolution in the complexity and scope ofnumerical models of these processes, beginning with ther-mal analyses without phase change. Recently, a few soft-ware packages have become available which have truemulti-physics capabilities. This permits the treatment ofthermal, fluids, stress, electromagnetic, chemical reactionand microstructure development aspects altogether in afully coupled simulation. This paper will consider variousaspects of these types of models.

KeynoteComputing the Dynamic Interaction of Magnetic Fieldsand Turbulent Conducting Fluids in Metals Processing:Koulis Pericleous1; 1University of Greenwich, GreenwichMaritime Campus, Queen Mary Ct., Rm. 361, Greenwich,London SE10 9LS UK Magnetic fields have many actual applications in themetals processing industry. Externally applied magneticfields give rise to electromagnetic (Lorentz) forces formedby the cross product JxB, between the induced current den-sity J and the magnetic field density B. When the metal is inliquid form, the Lorentz force generates motion in the fluidwhich in applications of practical interest becomes turbu-lent. In modelling terms, the Lorentz force appears as asource in the momentum equations. In addition, the in-duced current generates heat (Joule heating) in the metal

that is in proportion to J2, with a corresponding souirceof heat in the energy equation. Whether as heat or as aforce, these effects represent action at a distance–a mostuseful attribute when dealing with hot metal. The Lorentzforce is used to stir solidifying alloys, pump liquid metal inconduits, dampen the flow in the meniscus of a continu-ous caster, levitate metal drops, induce artificial gravityconditions in suspensions or contain liquid metal. Else-where, the Lorentz force may be a by-product of some otheroperation, so leading to wave excitation in aluminium elec-trolysis cells, or altering the shape of the weld pool in arcwelding. Joule heating is most commonly used with ap-plied AC fields, to melt metal in induction furnaces. Theauthor and his colleagues have been involved in the mod-elling of most of these processes in the past decade. Model-ling is not however straightforward, since most of the ex-amples mentioned represent genuine multi-physics chal-lenges. There is a strong coupling between the flow fieldand electromagnetic field. The addition of a dynamicallyvarying metal free surface and the moving solidus frontmeans the flow, heat and electromagnetic fields need to becomputed simultaneously. In situations involving metalcontainment, the metal free surface position is governed bythe interplay of gravity, Lorentz force, surface tension andfluid inertia. Since all the interesting effects often happenin thin boundary layers at the surface due to the skin effect,mesh generation and mesh control during the computa-tion become non trivial problems that need to be addressed.This paper presents a review of numerical methods used tomodel droplet levitation, semi-levitation melting and coldcrucible induction melting of metals. The first method isbased on spectral collocation techniques and the second isthe traditional FV approach. Steps taken to validate thecomputations and typical transient results are also given.

10:30 AM Break

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Track A - CFD Modelling - I

Monday AM Room: St. TropezSeptember 24, 2001 Location: Hilton San Diego Resort

Session Chairs: Mark Samonds, UES Software, Inc., 175 AdmiralCochran Dr., Annapolis, MD 21401 USA; Mayur Patel, University ofGreenwich, Ctr. of Numcl. Modlg. & Proc. Analy., London SE10 9LSUK

10:45 AMSimulation of Turbulent Flow and Particle Transport inthe Continuous Casting of Steel: Q. Yuan1; T. Shi1; S. P.Vanka1; B. G. Thomas1; 1University of Illinois at Urbana–Champaign, Dept. of Mechl. & Indl. Eng., 1206 W. GreenSt., Urbana, IL 61801 USA The quality of continuous cast steel is greatly affected byfluid flow in the mold region, especially involving tran-sient phenomena. Mathematical models are being appliedto investigate many different aspects of these phenomena,but their accuracy must be validated before they can beapplied with confidence. As part of a long-term effort todevelop and apply comprehensive models of the continu-ous casting process, this work evaluates the relative accu-racy of models of three different fluid flow phenomena incontinuous casting through comparison with measure-ments. Firstly, transient flow simulations of velocities inthe mold region are compared with digital particle imagevelocimetry (PIV) measurements in a single phase watermodel. Large-eddy simulations (LES) are found to reason-ably match the flow measurements, including transient flowvariations, except at long time scales, which could not bemodeled owing to the excessive computation costs. Thestandard K-e model produced very good agreement withtime-averaged velocities for relatively little computationtime, although it is inaccurate at predicting the transientvariations. Secondly, particle trajectory calculations arecompared with water model measurements to study thedistribution and flotation removal of inclusion particles.The LES model was able to match the measurements bothqualitatively and quantitatively. Thirdly, steady, multiphaseflow computations are compared with flow patterns ob-served in both a water model and an operating steel casterwith argon gas injection. For the same conditions, the wa-ter model and steel caster produced very different flow be-havior. The computational model was able to match themeasured flow patterns in both cases. This work suggeststhat computational flow modeling has the potential tomatch real processes as well or better than water models,especially when complex related phenomena such as par-ticle motion and multiphase flow are involved. Much workis still needed to further improve the models and to applythem in parametric studies.

11:10 AMCFD Modeling of the Hydrodynamics of Fluidization inthe Sand Surrounding a Lost Foam Casting Pattern:Nathanael Harrison Hudson1; Sushil Bhavnani1; Ruel A.Overfelt1; 1Auburn University, Dept. of Mechl. Eng., 213Ross Hall, Auburn University, AL 36849 USA In the aerospace and automotive industries, shapes arisewhich require casting. The problem with these cast parts isthe empiricism and expense in developing an efficient cast-ing process. There has been an interest in using the fluid-ized bed to allow sand to better encapsulate the compli-cated surface geometry of a lost foam pre-casting mold.Fluidization helps to eliminate the voids in the sand andimproves the integrity of the casting. At issue is the hydro-dynamics of the sand and air around the pre-casting mold.The software PHOENICS, employing a two-fluid approach,is used to simulate the flow of sand and air as interpen-etrating continua. The kinetic theory of granular flow forthe sand phase is incorporated into the re-compilablePHOENICS code. The results of this study consist ofvoidage patterns and the velocity components of the re-spective phases around the pre-casting submerged in a two-dimensional fluidized bed. The model is benchmarkedagainst experimental voidage patterns without a foam pre-casting and to some trials with a pre-casting. The final testconsists of a series of computer runs with an obstacle sub-merged in the bed at various aspect ratios of length to width.

11:35 AMContinuum Modelling of Granular Flows using PHYSICA,a 3-D Unstructured, Finite-Volume Modelling Frame-work: Nicholas Christakis1; Mayur K. Patel1; Mark Cross1;John Baxter2; Hadi Abou-Chakra2; Ugur Tüzün2; 1Univer-sity of Greenwich, Ctr. of Numcl. Modlg. & Proc. Analy.,Sch. of Compg. & Mathl. Scis., 30 Park Row, London SE109LS UK; 2University of Surrey, Dept. of Cheml. & Proc.Eng., Guildford, GU2 5XH Surrey, UK In recent years significant effort has been put in usingContinuum Mechanics for the description of granularflows. Although these models are partially successful incapturing some flow characteristics, they lack essentialinformation on material properties, which are needed toaccount for the interactions between different particles.Thus, they are incomplete and can not be used to describeprocesses such as hopper filling/emptying and pneumaticconveying, where particle-particle interactions can lead tophenomena such as segregation, degradation and agglom-eration. In this paper, a 3-D unstructured Finite-Volumeframework is presented, which employs interface trackingtechniques (VOF/SEA algorithms) to determine the mate-rial-air interface. Separate routines are employed to per-form the tracking of the individual material components ofthe granular mixture in the bulk. Various transport pro-cesses, arising from the micro-mechanical properties of thedifferent particle species in the granular mixture, can beobtained through kinetic theory. The transport coefficient(s)of each of the individual species can be determined andanalysed in a micro-mechanical framework and the trans-port process parametrised in the form of constitutive model.These models provide the continuum theory with informa-tion on the micro-mechanics. This work describes in detailthe numerical schemes employed in the Continuum Me-chanics framework and the micro-mechanical

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parametrisations that are implemented in the transportequations. Model predictions for different flow conditionsand comparisons with experimental data are presented andconclusions are drawn on the model capability to realisti-cally predict and quantify the main characteristics of granu-lar flows.

12:00 PMMathematical Model of Inclusion Removal during SteelDegassing: Michel Cournil1; Frédéric Gruy1; PascalGardin2; Hubert Saint-Raymond3; 1Ecole des Mines deSaint-Etienne, SPIN Div., 158 Cours Fauriel, Saint-Etienne,Cedex 2 42023 France; 2IRSID, Themef, Voie Romaine, BP30320, Maizières-lès-Metz, Cedex 57283 France; 3IRSID,PCMO, Voie Romaine, BP 30320, Maizières-lès-Metz, Cedex57283 France The control of inclusion elimination is getting more andmore important to obtain clean steel. But having a predic-tive tool is still a challenge, because the number of phasesis important in steelmaking industry: liquid steel, slag layer,bubbles and inclusions (with a large range of compositionand rheology). The paper presents the methodology whichis developed at IRSID to predict oxygen content evolutionduring RH degassing. The main mechanisms which haveto be considered are: -inclusion growth by turbulent aggre-gation of elementary inclusions (keeping in mind that liq-uid steel is a non-wetting medium for inclusions); the diffi-culty is to express collision efficiency for alumina particles,-inclusion removal by flotation; the difficulty for aluminaclusters stems from the complex morphology of particle;fortunately, the use of fractal concept makes it possible tocope with this problem. The proposed paper describes thegeneral modelling of inclusion removal taking into accountthe previous mechanisms. Hydrodynamic parameters areobtained by means of Fluent CFD package and a specificcoding is developed for cluster growth. Influence of differ-ent parameters (fractal dimension, argon flow rate) on time-dependant inclusion size distribution is given.

12:25 PMApplication of Coupled Continuum-Mesoscopic Compu-tational Methods for the Simulation of Complex Fluids inIndustrial Processes: Greg Glinski1; Chris J. Bailey1; KoulisPericleous1; 1University of Greenwich, 30 Park Row, Green-wich SE10 9LS UK Recent advances in new computational modelling tech-niques such as Lattice-Boltzmann and Dissipative Particlemethods offer the prospect of simulating complex fluidssuch as colloidal and dense suspensions in industrial pro-cesses. These methods provide a means to overcome chal-lenges that arise in modelling such fluids due to the dis-parate temporal scales present. These methods are termedmesoscopic methods as they lie between computationalintense molecular dynamics and traditional macroscopicCFD methods. This paper will discuss the use of the meth-ods to simulate the movement and subsequent processingof solder paste material in electronic component manufac-ture. Results will be presented that show how these meth-ods are coupled within a macroscopic CFD code to providedetailed predictions of solder paste deposition onto aprinted circuit board. Comparisons between the model re-sults and experimental data will also be presented.

Track B - Heat & Mass Transfer - I

Monday AM Room: Portofino/MarseillesSeptember 24, 2001 Location: Hilton San Diego Resort

Session Chairs: Koulis Pericleous, University of Greenwich, Green-wich Maritime Campus, Greenwich, London SE10 9LS UK; Stavros A.Argyropoulos, University of Toronto, Dept. of Metall. & Matls. Sci., 184College St., Toronto, Ontario M5S 3E4 Canada

10:45 AMHeat Load Control of Blast Furnace Wall using StatisticalOptimization Techniques: Tae-hwa Choi1; Yong-hwanChu2; Chonghun Han2; 1Pohang Iron and SteelCompany(POSCO), Techl. Rsrch. Labs./Iron & Steel Mak-ing Rsrch. Grp., 1 Goedong-dong, Nam-gu, Pohang-shi,Gyungbuk 790-785 Korea; 2Pohang University of Scienceand Technology, Dept. of Chem. Eng., 31 san Houja-dong,Nam-gu, Pohang-shi, Gyungbuk 790-300 Korea In the blast furnace, various complex phenomena takeplace including mass transfers, heat transfers, a lot of reac-tions and phase equilibriums, but systems of these phe-nomena are not found out clearly even until now. Conse-quently, it is very difficult to make fundamental models onthese systems, which results in the operation based on theheuristics of industrial operators by changing operatingcondition little by little due to ignorance of the optimumpoint. However, since this method is not systematic, wepropose statistical optimization technique based on analy-sis of historical data and empirical model building. In thisapproach, we first find the variables which must be opti-mized and the manipulated variables to adjust those re-sponse variables. Next, we collect the necessary data forthese variables after preprocessing such as removal of noiseand outlier. Finally, we construct empirical models describ-ing the patterns of response variables in terms of manipu-lated variables by PLS regression method, and then thesemodels are used as objective functions for entire optimiza-tion problem. By using appropriate optimization algorithm,this multi-objective optimization problem is solved, whichgives us the compromising optimum operating conditionconsidering all response variables from the past operatingconditions.

11:10 AMMathmatical Modeling and Experimental Verification ofAssimilation of Exothermic Additions in Liquid Metals:Stavros A. Argyropoulos1; Henry H. Hu2; 1University ofToronto, Dept. of Metall. & Matls. Sci., 184 College St.,Toronto, Ontario M5S 3E4 Canada; 2University of Windsor,Dept. of Mech., Automot. & Matls. Eng., 401 Sunset Ave.,Windsor, Ontario N9B 3P4 Canada The assimilation of exothermic additions in liquid met-als exhibit an array of unique coupled heat, mass and mo-mentum transport phenomena. The phenomena are fur-ther complicated with the presence of a moving boundary.In this paper a mathematical model will be described whichsolves these coupled complex phenomena. The SIMPLERalgorithm was employed to solve numerically the perti-

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nent partial differential equations. The computational re-sults indicated that the exothermic heat of mixing leads toa rapid increase of temperature around the moving bound-ary, which produced an enhanced convective flow in theliquid phase. The intensification of fluid flow around themoving boundary resulted in an acceleration of the melt-ing process. An extensive verification of the mathematicalmodel was carried out and will be described in the paper.First, in a low temperature physical model consisting of iceimmersion in different sulfuric acid solutions. In this physi-cal model, both temperature and velocity measurementswere carried out. The model results were compared withexperimental measurements and they were found to be ingood agreement. Second, in a high temperature work in-volving assimilation of silicon in high carbon liquid iron.The model was also applied to predict fluid flow, heat andmass transfer for this high temperature experiments and areasonable agreement was obtained. In addition new di-mensionless heat transfer correlations that quantify thesecomplex phenomena will be presented.

11:35 AMA Model of the Cathode Dynamics in Electric Field-En-hanced Smelting and Refining of Steel: David MichaelDussault1; Adam Powell1; 1Massachusetts Institute of Tech-nology, Matls. Sci. & Eng., 77 Massachusetts Ave., Rm. 4-117, Cambridge, MA 02139 USA A mathematical model of coupled diffusion, electrochemi-cal reactions and fluid dynamics at the cathode in electricfield-enhanced smelting and refining of steel is developedusing the Navier-Stokes equations and the phase fieldmethod. Experimental evidence indicates that the reactionrate is limited by ferrous ion transport to the cathode, re-sulting in a Mullins-Sekerka instability at the slag-metalinterface and the growth of liquid iron fingers into the liq-uid slag. The differential equations are discretized usingfinite differencing with a uniform mesh, and the resultingsystem of nonlinear equations is solved using a multidi-mensional Newton-Krylov method. Presented are the for-mulation and two dimensional results, and issues expectedto arise on extension to three dimensions are discussed.

12:00 PMA Mathematical Model for the Control of MetallurgicalProperties of the Product Sinter: Ndabezinhle ManengiDube1; E. F. Vegman2; 1University of Zimbabwe, Fac. of Eng.,Dept. of Metall. Eng., PO Box MP167, Mount Pleasant,Harare, Zimbabwe; 2Institute of Steel and Alloys, Moscow,Russia In the conventional practice of sintering, the quality ofthe product sinter down the cross-section of the bed is quitevariable,with the top layer consisting of weak sinter andthe bottom layer, strong over-fused sinter of poor reducibil-ity. This points to a variable distribution of the heat bal-ance in the sintering process down the sinter bed. Thiscauses losses in the productivity of the sinter machine andthe blast furnace. The experienced phenomenon caused byvarying input of regenerated heat requires a zonal approachto the study of the sintering process with the aim of pro-ducing a uniform quality of the sinter cake. The currentwork includes a mathematical model that would make pos-sible optimization of multiple-layer sintering and segrega-tion technologies. It is based on a zonal heat balance. This

calculation method presents the following prospects: 1. Theminimum theoretically possible coke fines consumptionduring the sintering of any type of iron ore fines can beestablished. The optimum difference between the coke finesrates in the top and bottom layers during multiple-layersintering should be easily determined with the aid of thismodel. 2. On the basis of this model an automatic controlsystem for the coke rates in the top and bottom layers dur-ing two-layer sintering is possible. 3. The model can beused to control the quality (chemical, physical and metal-lurgical) of the sinter in any point down the sinter bedsince the data input includes basicity, combustion zonetemperature, and FeO content in the product sinter.

12:25 PMModelling the Magnetostriction of Textured Ferromag-netic Materials with a Cubic Structure: Ruben Decocker1;Leo Kestens1; Yvan Houbaert1; 1University Ghent, Metall.& Matl. Sci., Technologie-park 9, Ghent, East-Flanders 9052Belgium A magneto-elastic model is presented to calculate the ori-entation dependence of the magnetostrictive strain, ob-served at saturated magnetization in ferromagnetic mate-rials with a cubic crystal structure and an arbitrary crystal-lographic texture. The formula of Becker and Döring is usedto express the anisotropy of magnetostriction for a singlecrystal. In order to simulate the macroscopic average mag-netostriction of a polycrystalline aggregate (with an arbi-trary texture) the Reuss assumption of the elasticity theorywas applied. According to this assumption the variousorientations of the polycrystal can deform without con-straints, producing local strain incompatibilities in themicrostructure but observing a total stress equilibrium. Themacroscopic strain is calculated as the weighted averageof the individual strains of all orientations composing thepolycrystal. The weight factors are determined by the vol-ume fractions of the corresponding orientations of the giventexture, which can be measured by standard X-ray diffrac-tion techniques. The model is applied to simulate the varia-tion of magnetostriction (at saturation) with respect to therolling direction for a standard grade of non-oriented elec-trical steel. A brief comparison with experimental data al-lows validating the basic model assumptions.

Monday PM Plenary Session2:00 PM–2:45 PM

Monday PM Room: St. Tropez/Monte CarloSeptember 24, 2001 Location: Hilton San Diego Resort

Session Chair: Vaughan Voller, University of Minnesota, Saint AnthonyFalls Lab., Minneapolis, MN 55414-2196 USA

KeynoteModelling and Process Optimization for FunctionallyGraded Materials: Dan Tortorelli1; 1University of Illinois–Urbana, Dept. of Mechl. & Indl. Eng., 350 MEB, MC 244,1206 W. Green, Urbana, IL 61801 USA We optimize continuous quench process parameters toproduce functionally graded aluminum alloy extrudates.

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To perform this task, an optimization problem is definedand solved using a standard nonlinear programming al-gorithm. Ingredients of this algorithm include 1) the pro-cess parameters to be optimized, 2) a cost function: theweighted average of the precipitate number density distri-bution, 3) constraint functions to limit the temperature gra-dient (and hence distortion and residual stress) and exittemperature, and 4) their sensitivities with respect to theprocess parameters. The cost and constraint functions aredependent on the temperature and precipitate size whichare obtained by balancing energy to determine the tempera-ture distribution and by using a reaction-rate theory to de-termine the precipitate particle sizes and their distribu-tions. Both the temperature and the precipitate models aresolved via the discontinuous Galerkin finite element method.The energy balance incorporates nonlinear boundary con-ditions and material properties. The temperature field isthen used in the reaction rate model which has as many as105o of-freedom per finite element node. After computingthe temperature and precipitate size distributions we mustcompute their sensitivities. This seemingly intractable com-putational task is resolved thanks to the discontinuousGalerkin finite element formulation and the direct differen-tiation sensitivity method. A three-dimension example isprovided to demonstrate the algorithm.

Track A - Optimization & NovelMethods

Monday PM Room: St. TropezSeptember 24, 2001 Location: Hilton San Diego Resort

Session Chair: Dan Tortorelli, University of Illinois–Urbana, Dept. ofMechl. & Indl. Eng., Urbana, IL 61801 USA

2:45 PMLattice Boltzmann Methods for Metallurgical ProcessSimulation: Christian Redl1; 1Mining University Leoben,CD-Lab. Appl. Comptnl. Thermofluid-dyn., Franz-Josef-Strasse 18, Leoben 8700 Austria The Lattice Boltzmann Method (LBM) solves fluid dy-namics problems based on a discrete mesoscopic approach.It is based on the Lattice Boltzmann equation which is aspecial discretisation of the continuous Boltzmann equa-tion. Its principle advantage is that it can handle complexphysical phenomena (like interaction between differentcomponents and surface effects), complicated boundary andinitial conditions very well, free from many gridding andstability constraints that plague conventional numericalmethods used for fluid flow simulations. The LBM algo-rithm has a simple structure and acts locally, which isfavourable for parallel computing. Complex structures likeporous media can be resolved directly. Its potential for met-allurgical process simulations is demonstrated in thepresent study which is concerned with the simulation ofthe flow in a copper winning electrolysis cell. The electro-lyte is modelled as the carrier fluid and the oxygen is con-sidered via a so called active scalar equation. The model-ling of buoancy, momentum exchange and the free surface

requires special effort. The results of the simulation arevalidated against experimental data obtained by Laser-Dop-pler-Anemometry. Despite the simplifications made, goodagreement was found.

3:10 PMViscosity Estimation Model for an Oscillating Cup Vis-cometer: Deming Wang1; R. A. Overfelt1; 1Auburn Univer-sity, Dept. of Mechl. Eng., 201 Ross Hall, Auburn Univer-sity, AL 36849 USA Viscosity measurements of molten alloys become moreand more important in modern metallurgy engineering.Lack of the viscosity data of many new alloys hampersmany CAD computer codes to apply in casting manufac-tures. The oscillating cup viscometer has become a domi-nant technique to measure the viscosities of high tempera-ture molten metals. Unfortunately, the viscosity estimationmodel from the observed logarithmic decrement and pe-riod of the oscillation is very complicated. There are stilllarge discrepancies of viscosity estimation values betweenusing different measurement facilities or using differentviscosity estimation models for a same molten metal. Thepurpose of the paper is to evaluate the accuracy of an oscil-lating cup viscometer in Auburn University. Two wellknown viscosity estimation models, Roscoe’s and Torklep’sequations, are discussed and compared viscosity for dif-ferent alloys. The theoretical literature for the fluid flowinside an oscillating cup is reviewed and a more accurateworking equation for Auburn oscillating cup viscometer isdeveloped. Some design parameters of the oscillating cupviscometer which also directly affect the accuracy of vis-cosity estimation by using the working equation are dis-cussed. In addition, applications and experimental mea-suring data are presented in the paper for several differentcommercial alloys, such as aluminum alloys: A319, A356and A201, nickel-base super alloys: In713 and In718, andcasting irons, C40 Gray Iron and Ductile Iron.

3:35 PM Break

3:50 PMNumerical Optimization of Magnesium Reduction in aModified Pidgeon Process: Alfred Yu1; Henry Hu2;1Nanjing Welbow North America Office, 601-969 Felix Ave.,Windsor, Ontario N9C 4C7 Canada; 2University of Windsor,Mechl. & Matl., 401 Sunset, Windsor, Ontario N9B 3P4Canada A numerical model of heat and mass transfer in the retortwas set up to simulate and optimize the reduction phe-nomena in the process of Pidgeon magnesium reduction.The simulations were run to determine the effect of varyingprocessing parameters on the magnesium reduction time.The model predicted the temperature distributions, the heat-ing curves, the recovery ratio of magnesium, and the totalprocess time. The predictions were used to optimize themagnesium reduction process, the dimensions of retort, theshapes of materials, and reaction cycle. Demo operationshows that, with application of the optimizations, signifi-cantly production capacity increases in the same furnace,reduction period decreases, energy consumption decreases.

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4:15 PMDeterministic and Regression Models of Nickel OxideReducing Roasting Process: V. M. Paretsky1; A. V. Tarasov1;1State Research Center of Russian Federation, State Rsrch.Inst. of Non-ferrous Metals “Gintsvetmet”, 13, Acad.Korolyov St., 129515 Moscow, Russia A mathematical model of the low-temperature (soft) nickeloxide reduction (SNOR) in a tubular kiln has been devel-oped including an equation describing changes in the nickeloxide content of the solid material along the length of thekiln; an equation describing the changes in the content ofreagents ensuring nickel reduction (i.e., hydrogen and car-bon monoxide) in the gas phase along the kiln length; aswell as the temperature along the kiln length. The kineticrelationships used for the development of the model hadbeen determined based on experiments conducted speciallyfor this purpose. Model investigations were conducted todetermine the distribution of such parameters along thelength of the kiln as the contents of metals oxides in thesolids, partial pressure of hydrogen and carbon monoxide,variations of the temperature depending on the SNOR pro-cess conditions, including the kiln rotation speed. Basedon the data obtained, a simplified regression model of thereducing roasting process was developed.

4:40 PMIntegrating Computational Mechanics and NumericalOptimization for the Design of Material Properties in Elec-tronic Packages: Stoyan Stoyanov1; C. Bailey1; M. Cross1;1University of Greenwich, Sch. of Compg. & Mathl. Sci., 30Park Row, Greenwich, London SE10 9LS UK Silicon components containing transistor circuitry are atthe heart of electronic products such as computers, mobilephones, etc. These components are connected to printedcircuit boards (PCB’s) using solder material that acts as theconductor for both electricity and heat. During the lifetimeof a product it will undergo many thermal cycles where thechip becomes hot during product operation and then coolswhen the product is switched off. At the product designstage engineers undertake thermo-mechanical simulationsto predict the thermal stress in the solder joints due to thisthermal cycle and to ensure that the stress magnitude willnot result in early fatigue-type failure. The design engineer’saim is to identify component parameters which ensure thatthe solder will survive beyond a certain number of thermalcycles. The aim of integrating computational mechanicsand optimization tools together is to speed up dramati-cally the design process. From viewpoint of a design engi-neer in the electronics manufacturing sector, these toolscan be used to quickly estimate key design parameters (i.e.material properties, product dimensions, etc.) that will guar-antee the required product performance. In this paper amodeling approach coupling computational mechanicstechniques with numerical optimization is presented anddemonstrated. The integrated modeling framework is ob-tained by coupling the multi-physics framework–PHYSICA–with the design optimisation tool–VisualDOC.Thermo-mechanical simulations are presented that predictthe creep strains in solder material. Different numericaloptimization procedures: Direct and Response Surfacebased optimization plus Design of Experiments, are testedas a part of this modeling framework.

5:05 PMComputer-Aided Modeling and Control of AutogenousCopper Smelting Process: A. V. Tarasov1; V. M. Paretsky1;1State Research Center of Russian Federation, State Rsrch.Inst. of Non-ferrous Metals “Gintsvetmet”, 13, Acad.Korolyov St., 129515 Moscow, Russia Based on theoretical and experimental studies into thespecific features of the mechanism, kinetics, aerodynamicsand heat transfer parameters of the flame-type oxidation ofmetal sulfides in a stream of technical-grade oxygen, a three-dimensional deterministic mathematical model of an oxy-gen-flame smelting furnace has been developed on the ba-sis of the zonal method for computation of heat exchange.The model is presented in the form of equations taking intoconsideration the radiation component of the selective ra-diation, the convection component of mass transfer betweenthe space and surface zones, heating of charge particlesdue to heat conductivity, accretions formation on a multi-layer refractory lining with inserted cooling elements. Theadaptation of the model for a full-scale furnace has demon-strated the possibility for its use for computation of mainsmelting process parameters. Multifactor model investiga-tions were conducted and the results obtained were ap-plied using statistical methods for development of a sim-plified computational regression model describing the in-terrelation of the main output parameters: temperatures offlame, lining, slag and off-gas; heat fluxes to the lining;thickness of accretions; heat removed by cooling elements;copper content of matte. On the basis of this model, a blockdiagram of the algorithm was developed for control of thethermal conditions of the furnace, as well as the controlalgorithm itself.

Track B - Melting & Solidification - I

Monday PM Room: Portofino/MarseillesSeptember 24, 2001 Location: Hilton San Diego Resort

Session Chairs: Vaughan Voller, University of Minnesota, SaintAnthony Falls Lab., Minneapolis, MN 55414-2196 USA; Matt Krane,Purdue University, Dept. of Matls. Eng., West Lafayette, IN 47907 USA

2:45 PMA Marker Chain Front Tracking Method for ModellingMeniscus Dynamics in the Al Ingot Casting Process: FionnIversen1; Jon Arne Bakken1; Stein Tore Johansen1; 1Norwe-gian Institute of Science and Technology (NTNU), Matls.Tech. & Electrochem., A. Getz vei 2B, Trondheim N-7491Norway In conventional direct chill (DC) hot-top casting of alu-minium extrusion ingot using ‘gas-slip’, poor surface qual-ity of the cast ingot may appear. It is believed that thesedefects are related to instabilities such as periodic oscilla-tions or folding of the meniscus (the interface between liq-uid metal and gas in the mould). The object of this work isto develop a stable and reliable model for simulation of themeniscus dynamics. A new 2D cylinder symmetric fronttracking model has been developed for the meniscus propa-gation, and is implemented in a general Navier Stokes

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solver. The model is based on a finite volume cubic splinemarker chain technique. The advantages of the model is itsapplicability to cases with large density ratios and its abil-ity to calculate independent velocity fields for phases onseparate sides of an interface, thereby making it possible tomodel the dynamics of thin films with a thickness scalesmaller than the typical grid size. Effects of surface tensionand wetting are also easily applied in the marker chainmodel. The model is applied to the DC casting process.Results are compared with data from plant test runs andsuggestions are made on how to improve the casting pro-cess.

3:10 PMComputational Modeling of Heat Mass and Solute Trans-port in Directional Solidification Processes: MohammedEl Ganaoui1; Patrick Bontoux2; 1Université de Limoges,Phys./Numcl. Mod., 123 Albert Thomas, Limoges 87000France; 2CNRS, Numcl. Mod., IRPHE, Marseille, 13451France During directional solidification, absorption or rejectionof latent heat or solute by the solidification front induceconvective flows in the liquid phase. These convectivemotions affect heat and mass transfer in the vicinity of thesolidification interface and is subject to many studies. Inthis work a numerical approach is presented. To avoidremeshing needed by front tracking methods a time-depen-dent homogeneous formulation is considered to verify im-plicitly thermal and solutal Stefan conditions at the inter-face. The numerical solution is based on finite volume ap-proximation. The previous work show that the presentmethod describe accurately the hydrodynamic transitionand the interaction with the solid liquid interface in thecase of pure material. This study focuses on the occurrenceof solutal convection in gradient freezing applications. Ina first step only the fluid phase is investigated and theresults are validated with respect to spectral ones. In a sec-ond step the full solid/liquid model is investigated. A lin-ear approximation of the equilibrium phase diagram isconsidered for establishing relations between mass frac-tion and temperature fields to close the set of conservationequations. The present work shows that the method is ableto describe with accuracy close to spectral one complexphenomena occurring in reduced configuration to fluidphase. The global model with solid phase account correctlythe interface displacement and its interaction with solutalfield.

3:35 PM Break

3:50 PMComputational Modelling of Freeze Layers in SmeltingProcesses: Andrew P. Campbell1; Koulis A. Pericleous1;Mark Cross1; 1University of Greenwich, Ctr. for Numl.Modlg. & Proc. Analy., 30 Park Row, Greenwich, LondonSE10 9LS UK The use of computational modelling in examining pro-cess engineering issues is very powerful. It has been usedin the development of the HIsmelt® process from its con-cept. It is desirable to further water-cool the HIsmelt® ves-sel to reduce downtime for replacing refractory. Water-cooled elements close to a metal bath run the risk of failure.This generally occurs when a process perturbation causesthe freeze and refractory layers to come away from the wa-

ter-cooled element, which is then exposed to liquid metal.The element fails as they are unable to remove all the heat.Modelling of the water-cooled element involves modellingthe heat transfer, fluid flow, stress and solidification for alocalised section of the reaction vessel. The complex inter-action between the liquid slag and the refractory applied tothe outside of the water-cooled element is also being exam-ined to model the wear of this layer. The model is beingconstructed in Physica, a CFD code developed at the Uni-versity of Greenwich. Modelling of this system has com-menced with modelling solidification test cases. These testcases have been used to validate the CFD code’s capabilityto model the solidification in this system. A model to trackthe penetration of slag into refractory has also been devel-oped and tested.

4:15 PMMathematical Modeling of Heat Transfer andMicroporosity Formation in Die Cast A356 Wheels: P. Vo1;D. Maijer1; S. L. Cockcroft1; M. A. Wells1; C. Hermesmann2;1University of British Columbia, Dept. of Metals & Matls.Eng., Vancouver, British Columbia V6T 1Z4, Canada; 2Ca-nadian Autoparts Toyota, Inc., 7233 Progress Way, Delta,British Columbia V4G 1E7, Canada Die cast aluminum wheels are one of the most difficultautomotive castings to produce because of stringent castsurface and internal quality requirements. A mathematicalmodel has been developed to predict heat transport andporosity formation in die cast A356 wheels as part of acollaborative research agreement between researchers atthe University of British Columbia and Canadian AutoParts Toyota Incorporated. The heat transfer model, em-ploying the commercial finite element code ABAQUS, is athree-dimensional, 30° slice of the wheel and die that de-scribes forced air cooling, natural convection of the die tothe surrounding environment, and interfacial heat trans-port between the wheel and die sections. Extensive tem-perature measurements in the die and in the wheel takenover several cycles in the casting process were used to finetune and validate the model. Preliminary work on predict-ing porosity formation focused on using the Niyama pa-rameter as a measure of the probability of porosity. Thelatest version of the model incorporates a new more funda-mentally based porosity criterion, which takes into accountthe effect of hydrogen and inclusion content. The develop-ment of this model together with some early results will bepresented.

4:40 PMModelling Filters in Metal Casting Processes: Mark R.Jolly1; Jean-Christophe Gebelin1; 1The University of Bir-mingham, IRC in Matls., Edgbaston, Birmingham, W. Mid-lands B15 2TT UK A number of different types of so-called filters are usedon the metal casting industries to impart some cleaningeffect and flow control on the liquid metal as it passesthrough them. The filters range from simple planar meshesthrough extruded channels to reticulated foam structures.It is most common that software packages used in the in-dustry model the filters by a simple pressure drop associ-ated with some area fraction and permeability parameters.Recent experimental work at the IRC in Birmingham hasshown that filters of the same type can behave very differ-

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ently depending upon the casting process in which theyare employed. Modelling filter geometries for a range ofdifferent casting processes has indicated that the flow ofmetal and heat losses through the filters are rather com-plex and should be considered when using filters in thecasting processes. This paper will present a number of casesof different types of filters modeled and different processesand indicate some of the sensitivities of the processes toboundary conditions imposed by the process.

5:05 PMComputer Heat Transfer Model for Directionally Solidi-fied Castings: Deming Wang1; R. A. Overfelt1; 1AuburnUniversity, Mechl. Eng. Dept., 201 Ross Hall, Auburn Uni-versity, AL 36849 USA Thermal transfer control is very important indirectionally solidified (DS) castings. This paper presentsa simple and efficient computer-aided heat transfer simu-lation method to predict the thermal characteristics of analloy sample in a special furnace for directional solidifica-tion. A two-dimensional transient heat transfer by radia-tion combined with conduction is developed to calculatethe energy exchange between the symmetric furnace andthe sample. A control volume technique is used to obtain aset of highly efficient finite difference equations for heatconduction and heat radiation with changeable view fac-tors. The model well simulates the transient process of DScastings. The simulation results are verified by a few mea-surable experimental results. Using the two-dimensionalcomputer simulation model, many thermal properties ofthe samples can be obtained, such as temperature distribu-tion, solidification velocity, the shapes and positions of theliquid/solid interface and thermal gradient at the inter-faces. These are very important to analyze microstructureof DS casting alloy, avoid casting defects and control thequality of DS castings.

Tuesday AM Plenary Session9:00 AM–9:45 AM

Tuesday AM Room: St. Tropez/Monte CarloSeptember 25, 2001 Location: Hilton San Diego Resort

Session Chair: James W. Evans, University of California, Dept. ofMatls. Sci. & Min. Eng., 585 Evans Hall, Berkeley, CA 94720-1760USA

KeynotePhase Field Methods for Modeling Microstructure: JamesA. Warren1; 1National Institute of Standards and Technol-ogy, Metall. Div. & Ctr. for Theoretl. & Computl. Matl. Sci.,Gaithersburg, MD 20899 USA The phase field method has been successfully employedas both a tool to model heterogeneous materials and asnumerical method for calculating the motion of interfacesand phase boundaries without explicitly tracking thoseinterfaces. The method has been used to model a diversesuite of problems describing the microstructural evolutionin materials. These models are derived from thermodynamicarguments and symmetry principles, and usually guaran-

tee positive local entropy production for systems out ofequilibrium. Descriptions of how phase field methods canbe applied to the problems of solidification, grain growth,and electroplating will be presented.

Track A - Structure

Tuesday AM Room: St. TropezSeptember 25, 2001 Location: Hilton San Diego Resort

Session Chair: Jim Warren, NIST, CTCMS & Metall. Div.,Gaithersburg, MD 20899-8554 USA

9:45 AMMicroporosity Evolution and Interdendritic Fluid Flowsduring Solidification: Adrian S. Sabau1; SrinathViswanathan1; 1Oak Ridge National Laboratory, Matls. &Cer. Div., Bldg. 4508, MS 6083, Oak Ridge, TN 37831 USA The occurrence of microporosity during metal casting isdue to the combined effects of solidification shrinkage andgas precipitation. The governing equations for fluid flowand hydrogen evolution indicate that porosity formationand fluid flow are strongly coupled. However, in most stud-ies on microporosity, it is considered that the porosity for-mation does not influence the fluid flow in the mushy zone.In this study, a computational methodology is presentedfor the numerical simulation of microporosity evolutionand interdendritic fluid flow. The solution algorithm pre-sented includes a fully coupled, implicit treatment ofmicroporosity and local pressure in the mushy zone. It isshown that neglecting the effect of porosity formation onthe pressure in the mushy zone yields higher pressure dropsand an over-prediction of final porosity. By its growth,microporosity compensates partially for the solidificationshrinkage, reducing the feeding demand. Therefore, in or-der to accurately describe casting defects, comprehensivemodels of fluid flow, heat transfer, solidification, must in-clude the effect of microporosity as well.

10:10 AMCellular Automata Computer Model of PolycrystallinePlastic Deformation: Alexander V. Spuskanyuk1; Yakiv E.Beygelzimer1; Victor M. Varyukhin1; 1Donetsk Physical &Technical Institute of the NAS of Ukraine, High Press. Phys.& Adv. Tech. Dept., 72 R. Luxembourg St., Donetsk 83114Ukraine Effects stipulated by interdependence of microlevel andmacrolevel of plastic deformation processes were analyzed.Using computing mechanics instead of constitutive rela-tionships the adequate computer models were used, whichwas opened by cellular automata approach. By means ofnumerical experiments, the cellular automata allowed tostudy the macrobehavior of the ensemble of cells at themacrolevel depending on the local microscopic laws thatdefine evolution of each cell and its interaction with theclosest environment. A cellular model of the plastic defor-mation of polycrystalline aggregate was proposed and com-prehensively described. Representative volume of the de-formed solid body deformed was described as a popula-tion of interconnected units which, in turn, consisted of

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lower scale level units. Sliding along the various allowedsliding systems deforms simple units, which do not havean internal structure. For consideration of stress distribu-tion within the limits of components, the approach of self-consistent field was used. Rotation of units and momentstresses connected with it were taken into account. Resultsof computer experiments are analyzed, software is de-scribed.

10:35 AM Break

10:50 AMSimulations of Microstructural Evolution: Martin E.Glicksman1; Kegang Wang1; P. Crawford1; 1Rensselaer Poly-technic Institute (CII-9111), Matls. Sci. & Eng., 110 8th St.,Troy, NY 12180-3590 USA Predicting microstructure evolution in alloys remains akeystone of materials science. The mean-field theory ofphase coarsening, in the (impractical) limit of zero volumefraction, was first formulated by Lifshitz and Slyozov, andby Wagner (LSW). Numerous attempts have been made toextend LSW theory toward microstructures with nonzerovolume fractions. The successes achieved with analyticaltheories, however, have been limited, due primarily to thedifficulties of characterizing interactions among particlesand the matrix, and accounting for stochastic variations inthe microstructural locale surrounding each particle. Suchtheories predict unrealistic particle size distributions(PSDs) when compared with experimental observations.The importance of large-scale simulation of microstructureswas realized with concurrently increasing capability ofcomputer hardware and software. Since the 1980s we for-mulated and solved multiparticle diffusion equations tosimulate the dynamics of phase coarsening. These simula-tions provide insight into the nature of diffusion interac-tions and multiparticle stochastics. The rate constants,PSDs, and higher-order correlations can all be extracted bysimulation. “Snap shot” simulation techniques, developedrecently permit study of microstructure size at various vol-ume fractions. Gradually, a bridge has been built connect-ing fundamental theory and experiment through computersimulations. Some recent examples of progress in simulat-ing microstructure evolution will be discussed.

11:15 AMAb Initio Calculations of Theoretical Tensile Strength inMetals and Intermetallics: Mojmir Sob1; Ligen Wang1; Mar-tin Friak1; Vaclav Vitek2; 1Institute of Physics of Materials,Zizkova 22, Brno 616 62 Czech Republic; 2University ofPennsylvania, Dept. of MSE, 3231 Walnut St., Philadelphia,PA 19104-6272 USA Fully self-consistent ab initio electronic structure calcu-lations of the theoretical tensile strength in metals and in-termetallics loaded uniaxially along several crystallo-graphic directions are performed using the full-potentialLAPW method. It turns out that the theoretical tensilestrength and elastic anisotropy at higher strains are closelyconnected with the presence or absence of higher-symme-try structures along corresponding deformation paths. To-tal energy calculations show that all higher-energy cubicstructures studied are locally unstable with respect to tet-ragonal and/or trigonal deformation modes. In interme-tallics, there may or may not be symmetry-dictated energyextrema corresponding to cubic lattices depending on the

atomic ordering. However, other energy extrema along thedeformation paths besides those required by symmetry oc-cur. Configurations corresponding to energy minima onthe deformation paths may represent metastable structuresthat can play an important role in interfaces and other ex-tended defects. As a specific example, tensile strength ofsingle-crystalline tungsten loaded uniaxially along the[001] and [111] directions is analyzed. Although tungstenis elastically nearly isotropic for small deformations theo-retical tensile strength exhibits a marked anisotropy. Thisanisotropy is explained in terms of structural energydiferences between bcc, fcc and simple cubic structureswhich occur on the calculated deformation paths. Theo-retical results compare favorably with available experimen-tal value obtained for tungsten whiskers grown along the[110] direction. Further examples include computer simu-lations of a tensile test for single-crystalline NiAl, wherethe theoretical tensile strength for the “hard” orientation[001] differs very significantly from that for the [111] orien-tation. Again, this anisotropy may be understood in termsof higher-symmetry structures present or absent along thedeformation paths.

11:40 AMModeling of Interdendritic Strain and Interden-driticCracking Phenomena during Dendritic Solidification Pro-cesses: Mostafa El-Bealy1; 1Material Processing Interna-tional, 100 Trade Centre Dr., #103, Champaign, IL 61820USA A one-dimensional mathematical model to calculate theinterdendritic cracking tendencies for low alloyed carbonsteel casting processes is described. The model combinesan interdendritic strain model with concept of the effect ofalloying element on the solidification behaviour, segrega-tion of carbon, and therefore, critical elementaryinterdendritic area EIA. A susceptibility of cracking of dif-ferent steels is modelled by using El-Bealy approach. Modelpredictions were performed to explain the effects of vari-ous alloying elements on the solidification and crackingphenomena. Some typical cases in conventional castingprocesses related to increase cracking susceptibility arediscussed. It is shown that there is a satisfactory degree ofcorrelation between prediction a practical casting knowl-edge. Possible solutions to these problems based on theadjustment of chemical composition are proposed.

Track B - Melting & Solidification -II

Tuesday AM Room: Portofino/MarseillesSeptember 25, 2001 Location: Hilton San Diego Resort

Session Chairs: Dan Cook, Virginia Commonwealth University, Mechl.Eng. Dept., 601 W. Main St., Rm. 312, Box 843015, Richmond, VA23284-3015 USA; Mark Jolly, University of Birmingham, Birmingham,Great Britain B15 2TT UK

9:45 AMWax Injection in the Investment Casting Industry: Jean-Christophe Gebelin1; Alexander Cendrowicz1; Mark R.

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Jolly1; 1The University of Birmingham, IRC in Matls.,Edgbaston, Birmingham, W. Midlands B15 2TT UK Injection of wax patterns is the first stage of the multi-stage process of investment casting. The quality of the finalcasting and its dimensional accuracy is highly dependenton this stage of the process. Pattern waxes used in the in-dustry behave in a complex visco-elastic-plastic manner.The modelling of such material behaviour is therefore notsimple. In this paper a number of configurations of die willbe shown in which the injection of the wax has been car-ried out for a range of processing conditions. Some of thedies are transparent and the movements of wax front ob-served can be compared with those predicted by simula-tion. Surface defects in final components will also be shownand compared with the location predicted by simulationsoftware. Some discussion will be presented on the limita-tions of the software used and the time-scales achieved forpractical use as a design tool within the foundry environ-ment.

10:10 AMMicro/Macro Modeling of Ingot Cooling Processes for Ni-Cu-S Alloys: Apostle Mouchmov1; Mark Cross1; KoulisPericleous1; 1University of Greenwich, Sch. of Compg. &Mathl. Sci., 30 Park Row, Greenwich, London SE10 9LS UK Copper–nickel–sulphide alloys are typically cooled andsolidified in 4, 8 and 16 tonne ingots. These ingots exhibita variation of grain size distribution and macro segrega-tion of the prime alloy components throughout. The formeris assumed to be primarily due to the dominant relationbetween grain growth rate and the cooling profile, whilstthe latter is heavily influenced by buoyancy driven residualconvection. The objective of this research program is to ex-amine the extent to which it is possible to develop a ‘broadbrush’ computational model of this ingot cooling process,that can predict some ‘integral’ measure of the grain size(e.g. average diameter) and the macro-segregation as a func-tion of operating conditions. A computational modelingsoftware framework, PHYSICA+ is used to simulate thecomplex process of ingot casting, which involves couplingbetween different physical phenomena. The entire modelinvolves: (i) a ‘broad brush’ grain growth model that couldbe used in the prediction of micro/macro-structure of alloyingot cooling processes, (ii) a heat transfer and solidifica-tion model which takes into account a second phase trans-formation of Ni3S2 to heazle-woodite, and (iii) NS fluidflow simulation which provides a good basis for furthermicro/macro segregation modeling. At this stage some re-sults of the 3D convection driven thermal cooling and so-lidification profiles will be shown, together with the ‘inte-gral’ model for the grain size prediction.

10:35 AM Break

10:50 AMComparison of Numerical Models of Solidification Be-havior in Direct Chill Casting with Experiments: Christo-pher J. Vreeman2; David Schloz3; Matthew John M. Krane1;1Purdue University, Sch. of Matls. Eng., W. Lafayette, IN47907 USA; 2Boeing North American, Rocketdyne Div., 6633Canoga Ave., Canoga Park, CA 91309 USA; 3Wagstaff, Inc.,3910 N. Flora Rd., Spokane, WA 99216 USA Numerical results from a continuum mixture model ofthe Direct Chill casting process is compared to experimen-

tal results from industrial scale aluminum billets. Themodel, which includes the transport of free-floating solidparticles, is used to simulate the effect of a grain refiner onmacroseg-regation and fluid flow. It is applied to an Al-6wt%Cu alloy and the effect of casting speed, grain refiner,and assumed mushy zone permeability on predictedmacrosegregation, sump profile, and temperature fields arepresented. Three 45 cm diameter billets were cast underproduction conditions with and without grain refiner andat two casting speeds. Temperature and composition mea-surements and sump profiles are compared to the numeri-cal results. The comparison shows qualitative agreementand limitations of application of the model to industrialprocesses are discussed.

11:15 AMTwo-Phase Predictive Finite-Element Flow Model forSemi-Solid Slurries: Frédéric Pineau1; 1National ResearchCouncil Canada, Indl. Matls. Inst., Proc. Modlg. & Instrm.,75 de Mortagne Blvd., Boucherville, Québec J4B 6Y4 Canada Semisolid metal alloys have a special microstructure ofglobular grains suspended in a liquid metal matrix. Thisparticular physical state of the matter can be exploited toproduce near-net-shape parts with improved mechanicalproperties. However, the behavior of the slurry is stronglyinfluenced by the local solid fraction and state of agglom-eration. Different flow instabilities associated with the com-bined flow and solidification process result, which makedifficult the application of semisolid processing in the cast-ing industry. Moreover, the rheology of semisolid materialsis not well understood. Most of the theory has been derivedfrom experimental data, which are somewhat difficult tomeasure. A model that accounts for the multiphase natureof the slurry is required to get more insight into such com-plex flows. This paper thus describes a mixture model forsemisolid slurries. It assumes that the mixture of liquid-solid components behaves as a single fluid as far as overallmass and momentum balances are concerned. The cou-pling force between the phases is derived on the assump-tion that the slurry is a fluid saturated isotropic media. Theproposed methodology is implemented in a finite elementcode. The filling of an industrial-scale capillary flow vis-cometer is investigated numerically. Segregation patternsare obtained and discussed.

11:40 AMCFD Simulation of Continuous Charging and Melting ofSmall Metallic Particles in a Melting Reactor: StefanPirker1; Oszkar Biro3; Philipp Gittler1; Peter Mittag2; Ber-nard Aigner2; 1Johannes Kepler University, Altenbergerstr.69, Linz A-4040 Austria; 2VOEST ALPINEIndustrieanlagenbau GmbH, Postfach 3, Linz A-4031 Aus-tria; 3Technical University Graz, Kopernikusgasse 24, 8010Graz, Austria This paper considers CFD modelling of processing andmelting of small metallic particles by means of electricalheating. The particles fall continuously onto a liquid metalbath which is heated by an electric arc. After melting of theparticles liquid metal is tapped. The charging behavior ofthe particles in the supply unit as well as in the reactorfreeboard is studied by means of Euler-Euler granular simu-lations. The flow situation in the metal bath due to gasinjection and magnetic fields is calculated by combining

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Navier-Stokes and Maxwell solvers. The macroscopic melt-ing process occurring during the continuous charging ofthe particles is studied by kinetic laws for melting reac-tions. The temperature field is evaluated by balancing heatsources due to Joule’s heating and heat losses due to latentheat of melting as well as convection and radiation. As aresult of these simulations the fully three-dimensional flowfields of particles and gas in the atmosphere is obtained.Furthermore the flow field as well as the magnetic field inthe metal bath can be studied. As a main result the three-dimensional concentration field of the still unsolved par-ticles in the liquid metal can be evaluated.

12:05 PMNumerical Simulation of Wax Pattern Dimensions in In-vestment Casting: Adrian S. Sabau1; Srinath Viswanathan1;1Oak Ridge National Laboratory, Matls. & Cer. Div., Bldg.4508, MS 6083, Oak Ridge, TN 37831 USA Dimensional Changes between a pattern die and its cor-responding investment cast part occur as a result of com-plex phenomena such as thermal expansion/contractionand hot deformation (elastic, plastic, and creep) during theprocessing of the pattern material (wax), mold material(shell), and solidifying alloy. Determining the pattern tool-ing dimensions is crucial to the dimensional control of theinvestment casting process. To date, there are no computa-tional methodologies available for predicting dimensionalchanges during investment casting. This paper deals withthe evaluation of wax pattern dimensions, which is oneimportant factor in determining the pattern tooling dimen-sions in investment casting. Cerita 29-51, an industrial waxis considered in this study. The wax pattern dimensionsare affected by its thermophysical and thermomechanicalproperties, restraint of geometrical features by the metaldie, and process parameters such as dwell time, platen tem-perature, injection pressure and injection temperature. Nu-merical simulation results for the wax pattern dimensionsare compared with experimental measurements. Criticalvariables that determine dimensional changes associatedwith the wax system are identified.

Tuesday PM Plenary Session2:00 PM–2:45 PM

Tuesday PM Room: St. Tropez/Monte CarloSeptember 25, 2001 Location: Hilton San Diego Resort

Session Chair: Koulis Pericleous, University of Greenwich, GreenwichMaritime Campus, Greenwich, London SE10 9LS UK

KeynoteComputational Modelling of Metals Reduction Processes:Phil Schwarz1; 1CSIRO Minerals, Box 312, Clayton S.,Victoria 3163 Australia This paper reviews the status of computational model-ling of a variety of common metals reduction processes,namely the blast furnace, rotary kiln and fluidised bed,and one new process not yet commercialised, namely smelt-ing-reduction as in the HIsmelt® Process. In each case, thelast decade has seen the emergence of the capability to simu-

late the processes using multi-phase reacting computationalfluid dynamics techniques. In some cases this capability isstill in the process of being developed, and the next fewyears will see the maturing of the modelling techniques. Asthey become established, it will be possible to apply themto further refine the older technologies such as blast fur-naces and rotary kilns, and assist in the optimisation,commercialisation and acceptance of the newer technolo-gies such as fluidised bed and molten bath reduction. Thedevelopment of a computational fluid dynamic model ofbath smelting-reduction is described in some detail to il-lustrate how a large number of complex and interactingphenomena can be successfully simulated within a CFDframework.

Track A - CFD Modelling - II

Tuesday PM Room: St. TropezSeptember 25, 2001 Location: Hilton San Diego Resort

Session Chairs: Phil Schwarz, CSIRO Minerals, Box 312, Clayton S.,Victoria 3163 Australia; Pascal Gardin, IRSID, Maizieres-les-MetzFrance

2:45 PMModelling of Raceway Hysteresis: Govind S. Gupta1; S.Sarkar1; M. G. Basavaraj1; P. D. Patil2; 1Indian Institute ofScience, Dept. of Metall., Bangalore 560 012 India; 2IndianInstitute of Science, Dept. of Cheml. Eng., Bangalore 560012 India Previous experimental study on raceway size hysteresison two-dimensional cold model showed that the interpar-ticle and wall-particle friction had a very large effect on theraceway size. Existing literature correlations for racewaysize ignore the frictional effects. It has also been shown inthe present study that their applicability to the ironmakingblast furnace is questionable. To take into account the effectof friction on the raceway size a stress analysis has beendone for the raceway region. The partial differential equa-tions for the stresses have been developed and solvedcomputationally. The frictional forces were obtained interms of stresses. To predict the raceway size a force bal-ance was done for the raceway zone considering the pres-sure force, the frictional force and the bed weight. The re-sulting equations from the force balance are able to de-scribe the raceway hysteresis phenomena correctly alongwith the raceway size. A two dimensional experimental setup has been fabricated in order to validate the computerpredictions. Predicted values agree well with the experi-mental values. A correlation has been developed to predictthe raceway size.

3:10 PMLifetime Prediction of Pneumatic Conveyor Bends withthe Aid of Computational Models: Mayur K. Patel1; RobertHanson1; 1University of Greenwich, Ctr. for Numl. Modlg.& Proc. Analy., 30 Park Row, Greenwich SE10 9LS UK The puncture of pneumatic conveyor bends in industrycauses several problems. Two important factors are: (1)Escape of the conveyed product causing health and dust

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hazard and (2) Repairing and cleaning up after puncturesnecessitates shutting down conveyors, which will affectthe operation of the plant, thus reducing profitability. Bendsin pneumatic conveying systems tend to wear out and punc-ture first since particles generally strike the bend walls withlarger intensity than straight pipe sections. Current mod-els for bend lifetime prediction are inaccurate as they fail toaccount for key parameters that are of fundamental impor-tance to the progression of the wear. The provision of anaccurate predictive method would lead to improvementsin the structure of the planned maintenance programmes,thus reducing unplanned shutdowns. The paper reportsthe first phase of a study undertaken to develop and imple-ment a CFD based engineering tool to predict the lifetime ofconveyor bends for two- and three-dimensional test cases.The model used is based on Eulerian and Lagrangian meth-ods. It is unique in that the erosion due to the particle im-pacts is accounted for within a CFD framework, thus tak-ing into account angle of attack and impact velocity, ensur-ing more realistic predictions of the wear profile and theirgrid dependency and sensitivity to the inlet particle distri-butions.

3:35 PM Break

3:50 PMA Parametric Study of Oxy-Fuel Burners in SecondaryAluminum Melting: Madhu Huggahalli1; Neeraj Saxena1;Ken Grieshaber2; Jerry Bernardski2; David Stoffel2; 1BOCGases, Tech., 100 Mountain Ave., Murray Hill, NJ 07974USA; 2BOC Gases, 575 Mountain Ave., Murray Hill, NJ07974 USA The use of oxy-fuel burners in secondary aluminum melt-ing applications offers several advantages including re-duced fuel consumption, faster charge to tap times andlower NOx emissions. Their successful, safe and economi-cal use in a furnace depends on several factors and consid-erations such as burner and flue placement, metal circula-tion, charge practices and the type of refractory used in thefurnace. These factors required in the successful conver-sion of furnaces from air-fuel to oxy-fuel based burners arediscussed in detail in this paper. Critical parameters areidentified and examined using computational fluid dynam-ics (CFD) simulations. Parameters are estimated via labo-ratory testing and validated through trials performed atcommercial installations. Guidelines and a simplified ap-proach to estimate à priori the economic impact of convert-ing from air-fuel to oxy-fuel are presented. The final prod-ucts of this research are simplified and validated tools formodeling aluminum furnaces. These include improved heatand energy balance models and parameterized CFD solu-tions which allow rapid customization to individual fur-nace configurations. These tools provide field engineerswith immediate and accurate predictions of performance,allowing for repeated precise scenario analyses.

4:15 PMComputational Modelling of Vortex Formation in the LeadRefining Kettle: Suman Kumar1; Chris Bailey1; MayurPatel1; A. W. Piper2; M. Cowling2; R. A. Forsdick2; 1Univer-sity of Greenwich, 30 Park Row, Greenwich, SE10 9LS UK;2Britannia Refined Metals, Ltd., Northfleet, UK The refining of lead bullion takes place in hemisphericalvessels (known as kettles) of various sizes. It is normal

practice to remove impurity elements (i.e. copper, silver,bismuth, antimony, etc.) sequentially, by the addition ofreagents. This process has been in operation for many yearsin refineries all over the world. Unfortunately very little isunderstood about the actual mixing and refining processtaking place in these kettles. This paper will present a de-tailed modelling analysis of this process, where computa-tional and physical modelling techniques have been used.The computational fluid dynamics (CFD) techniques usedto model fluid mixing by impellers will be discussed andresults will be presented comparing CFD data with plantdata. Also discussed will be the modelling techniques usedto simulate the reactions taking place in the vessel duringimpurity removal.

4:40 PMCFD Modeling of Solids Suspensions in Stirred Tanks:Lanre Oshinowo1; André Bakker2; 1Hatch, 2800 SpeakmanDr., Mississauga, Ontario L5K 2R7 Canada; 2Fluent, Inc.,10 Cavendish Ct., Lebanon, NH 03766 USA Mechanical agitation is widely used in process industryoperations involving solid-liquid flows. The typical pro-cess requirement is for the solid phase to be suspended forthe purpose of dissolution, reaction, or to provide feed uni-formity. If these vessels are not functioning properly, byinadequately maintaining suspension, the quality of theproducts being generated can suffer. Associated with theoperation of these units is a need to maintain the suspen-sion at the lowest possible cost. The challenge is in under-standing the fluid dynamics in the vessel and relating thisknowledge to design. CFD modeling can provide insight toboth the multiphase transport and the design parameters.An understanding of the parameters that govern the just-suspended impeller speed, Njs, and the distribution of sol-ids, is critical. Recent advances in computational fluid dy-namics allow for the modeling of multiphase systems, suchas the liquid-solid mixtures discussed here. Of particularinterest is the Eulerian multiphase model, which uses sepa-rate sets of Navier-Stokes equations for the liquid and sol-ids (or granular) phases. Incorporating moving impellermodeling techniques, such as, the sliding mesh method,provides a rigorous estimate of the solids suspension be-havior. This paper will assess the current design param-eter Njs in the context of scale-up and compare it to thequality of solids dispersion as a means of assessing correctscale-up in suspension tank design. The work presentedincludes a study of a 45° pitched-blade turbine and a hy-drofoil impeller. Both single and dual impeller operationhave been evaluated. For a given impeller style in a fixedvessel, D/T and C/T are varied to explore suspension flowpatterns at Njs. The settled solids fraction for speeds belowNjs, and the cloud height for impeller speeds above Njswere studied. The CFD results correspond well with ex-perimental literature data on velocity distribution and cloudheight.

5:05 PMWater Model and Numerical Study on the Spout Heightin a Gas Stirred Vessel: Diancai Guo1; G. A. Irons1;1McMaster University, Steel Rsrch. Ctr., 1280 Main St.,Hamilton, Ontario L8S 4L7 Canada The average spout height and width produced by bot-tom gas injection in a water model of a steel ladle were

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measured with an image processing technique. It was re-vealed that the spout height could be described by aGaussian curve. A combined SIMPLE-VOF model was de-veloped to simulate the liquid surface and flow. The resultsshowed that, though the model produced reasonable ve-locity distributions and free surface positions, the spoutheight due to the dynamic head of the rising liquid wassubstantially lower than observed, indicating that thebubble dynamics at the bath surface play an important rolein spout height.

Track B - Thermo-MechanicalModelling - I

Tuesday PM Room: Portofino/MarseillesSeptember 25, 2001 Location: Hilton San Diego Resort

Session Chairs: Brian G. Thomas, University of Illinois–Urbana, Dept.of Mechl. & Indl. Eng., Urbana, IL 61801 USA; Danny Wheeler, NIST,Gaithersburg, MD 20899-8555 USA

2:45 PMThick Yield Surface: An Approach to the Processing ofComputer Experiments on Polycrystalline Deformation:Yan E. Beygelzimer1; Alexander V. Spuskanyuk1; VictorVaryukhin1; 1Donetsk Physical & Technical Institute of theNAS of Ukraine, High Press. Phys. & Adv. Tech. Dept., 72R. Luxembourg St., Donetsk 83114 Ukraine The main idea of the report is that the yield surface canbe presented as thick, “foamed surface” with dimensional-ity exceeding two. By other words, perhaps, the yield sur-face is fractal, i.e. it belongs to the geometric objects withfractional dimensionality. Apparently, fractal structure ofthe yield surface is determined by the fractal structure ofnatural materials. Besides, the “cloud of internal stresses”term is introduced to describe the stress distribution in RVE.Its plastic flow is determined by the interaction of this cloudwith the thick yield surface. Thick yield surface and inter-nal stress cloud concepts allow to determine the additionalcorrelation between micromechanical models of polycrys-tals and phenomenological theory of plasticity.

3:10 PMModel for Stress, Temperature and Phase Transforma-tion Behaviour of Steels on Run-Out Table in Hot StripMill: Heung Nam Han1; Jae Kon Lee1; Hong Jun Kim1;Young-Sool Jin1; 1Pohang Iron & Steel Co., Ltd. (POSCO),Sheet Prod. & Rsrch. Grp., Techl. Rsrch. Labs., Pohang POBox 36, 1 Koedong-dong, Nam-ku, Pohang-shi, Kyungbuk790-785 Korea A mathematical model was developed considering non-symmetric cooling and stress distribution in both thick-ness and width direction of strip on a run-out table of hotstrip mill. In order to solve a transient heat transfer equa-tion including the heat evolved from phase transforma-tion, a finite difference method coupled with thermody-namic and kinetic analyses was applied. The heat capac-ity of each phase and heat evolution due to phase transfor-mation were obtained from the thermodynamic analysis ofthe Fe-C-Mn-Si system based on a sublattice model. The

phase transformation kinetics of the steels was derived byusing continuous cooling experiments and the thermody-namic analysis. Heat transfer coefficients of strips on therun-out table were, by applying an inverse method, deter-mined from actual mill data under various cooling condi-tions. As for the stress analysis, the density change of stripdue to cooling and phase transformation and the transfor-mation induced plasticity were considered. A constitutiveequation for the transformation induced plasticity, whichis related to the phase transformation kinetics and the ap-plied stress, was newly suggested. A finite element methodwas adopted to calculate the deformation behaviour of stripon run-out table.

3:35 PM Break

3:50 PMThermo-Mechanical Coupling Finite Element Analysisof Sheet Metal Extrusion Process: Zhanghua Chen1; C. Y.Tang1; T. C. Lee1; 1The Hong Kong Polytechnic University,Dept. of Mfg. Eng., Hung Hom, Hong Kong, China In sheet metal forming process, the forming limit andstrain distribution are governed by plastic instability andfracture following strain localization. It has been provedthat the temperature gradient caused by plastic deforma-tion, heat transfer, and friction between sheet and tools isone of crucial factors to induce the strain localization inhigh speed metal forming processes. In this paper, a nu-merical simulation of the sheet metal extrusion process hasbeen conducted by using thermal-mechanical coupling fi-nite element method. In the investigation, the sheet metalextrusion is assumed to be a non-isothermal and elasto-plastic process. The material of workpiece is SS400 steelwhich is the same as that used in experiment. The bound-ary energy dissipation due to heat convection has beentaken into account. Bishop’s step-wise decoupled strategyis adopted to handle coupling between mechanical defor-mation and the temperature variation. This technique hasbeen proven to be robust and efficient for large thermal-plastic deformation computation. By adopting this ap-proach only the pure mechanical parts of the weak formshave to be consistently linearized since the coupling termsare held constant during the iteration. In order to avoidlocking deficiency that frequently exhibited in classicaldisplace-based finite element method, an improved largedeformation mixed finite element method has been used tosolve this near-incompressible metal forming problem. Thestandard Newton-Raphson iteration method together withthe corresponding consistent tangent operator has beenadopted to solve nonlinear algorithmic equations. In ther-mal phase, the transient heat transfer finite element methodtogether with the Crank-Nicholson algorithm has beenemployed to determine the temperature field. The total timefor extrusion process is specified to be 0.4 second. Usi