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By Ch. -A. Gandin, M. Rappaz

"The grain selection mechanism which occurs during the growth of columnar dendritic structures is routinely used in the investment casting industry to produce directionally solidified (DS) and single crystal turbine blades. However, the evolution of the grain density with increasing distance from the chill has rarely been correlated with the evolution of the grain texture. This contribution presents a three-dimensional (3-D) stochastic modeling approach which permits the computation of grain maps, pole figures and grain density evolutions in DS superalloys. These predictions are compared with measurements resulting from an automatic indexing technique of Electron Back-Scattered diffraction Patterns. This 3-D stochastic model, which applies to uniform temperature situations, has to be extended to the dendritic growth in a thermal gradient. As a preliminary step, a 2-D Cellular Automaton (CA) has been coupled recently to Finite Element (FE) heat flow computations in order to predict the grain structures in complex shape investment cast part. The application of this CAFE model to the investment casting of a turbine blade is presented. Considering these results, the extension of the CAFE algorithm to three dimensions is discussed.INTRODUCTIONThe selection of columnar grains during the directional solidification of alloys plays a key role during the investment casting of directionally solidified (DS) and single crystal (SC) components for aerospace applications [I]. This selection mechanism, leading to a competition of the dendritic network propagation at grain boundaries, has been the subject of many investigations. In particular, the study of Walton and Chalmers [2] is remarkable since it provides a link between the evolutions of the density and of the texture of columnar grains with increasing distance from the mold wall. Since this original work of Walton and Chalmers, two new tools have become available, which enable one to revisit the problem of grain selection in much greater depth. The first one is a fully automatic indexing technique of Electron Back-Scattered diffraction Patterns (EBSPs) [3-6] which directly gives the crystallographic orientation of the solid at any location of the specimen. Pole figures, orientation distributions, misorientations between grains can be visualized very easily with this technique. This information can be directly compared with the results of a second tool: a three-dimensional (3-D) stochastic model (SM) describing the nucleation and growth of grains in a uniform temperature field [6-9]. In order to extend this model to non-uniform temperature situations, a preliminary 2-D model has been developed [10]. It is based on a Cellular Automaton (CA) algorithm coupled with Finite Element (FE) heat flow computations. Since the details of both the automatic indexing technique of EBSPs and the simulation tools have already been published [3-10], only a brief summary is given here."

Jan 1, 1994

By Fuming Wang, Lifu Hu, Changrong Li, Ruipeng Pang

The solidification structure of 430 ferritic stainless steel has been calculated in the solidification process by using 3D-CAFE model under the condition of water cooling. The calculated results consistent with those obtained from experiment. Under watercooling condition, the solidification structure consists of chilled layer, columnar grain zone, transition zone and equiaxed grain zone

Jan 1, 2015

By Tatsuo Inoue, Marnoru Mizuno, Toru Matsuoka, Kenichiro Abe

"The distribution of particle reinforcements and the residual stresses in metal matrix composite are simulated by considering the motion of particles and the solidification of matrix associated with temperature variation in the course of centrifugal casting process. In the analysis, a heat conduction equation including heat generation due to latent heat and also mechanical work as well as heat input from successively accumulated element on the air/metal boundary is solved by the finite element technique. After the movement of particles subjected to the centrifugal force and drag are analyzed, the residual stresses are elucidated by using a unified constitutive equation which can describe the behavior both in liquid and solid states. Results of the simulation are compared with the experimental data, and the validity and utility of the procedure is confirmed.IntroductionProcess simulation of metal matrix composite (MMC) is required to determine the mechanical properties of the materials and the efficient process and conditions of the fabrication. Properties of bonding matrix with reinforcements in the course of the processing, for example, affects the strength of the composite, while the final costs of the productions depends on the efficiency of fabrication. Therefore, the simulation of processing of MMC is prerequisite in order to clarify the mechanism to fabricate the material which has been expected to maintain high mechanical properties and the cost performance.Some techniques of processing MMC[l] have been developed so far. Among them, the centrifugal casting technique [2-5] has many attractive characteristics as processing of the MMC: The centrifugal casting technique makes the reinforcements such as particles or short fibers to be distributed in the radial direction by the centrifugal force acting on reinforcements due to the difference in density between reinforcements and matrix. Since the distribution of reinforcements affect the mechanical properties of MMC, the composite with functionally gradient mechanical properties can be provided by the centrifugal casting technique."

Jan 1, 1994

By Wilhelm Brandstätter, Johannes Steiner, Alois Triessnig, Christian Redl

"The results of numerical simulations of bubble detachment from an orifice in a horizontal plate submerged in liquid are presented. The bubbles are created by forcing gas through this orifice into stagnant liquid. The simulations are performed with a two-dimensional incompressible Lattice Boltzmann (LB) scheme. In previous works the same problem was investigated by two-phase simulations in which surface tension effects were considered by an interaction potential formulation between the phases. In contrast, in the present work a volume of fluid (VOF) model consisting of a carrier fluid and a passively advected scalar function for the calculation of gravitational and surface tension forces, respectively, is used. The aims of this study are to examine the applicability of the one-phase LB method to the numerical analysis of bubble formation and to verify the theoretical and experimental predictions of the dependencies of the departure diameter on gravitational forces, surface forces and wettability effects. To this purpose the simulations were performed at different values of gravitational acceleration g, surface tension coefficient s and contact angle ß. Nonlinear fits to the data yield functional dependencies which are in good agreement with the predictions. IntroductionBubble formation behavior is an extensively studied subject, especially in chemical engineering, power industries and metallurgical processing. Knowledge of the underlying physics of bubble motion is, for example, required for the design of chemical reaction towers and agitation tanks. Another important application is the argon gas injection through the wall of the tundish nozzle into liquid steel stream to deter clogging with solid inclusions. Argon bubble motion and its effect on flow depends greatly on different parameters, e.g. gas flow rate and size of the bubbles. Thus, if these bubbles are not managed properly, they can become encapsulated upon solidification and result in undesirable impurities in the material [1, 2]."

Jan 1, 2004

"In this paper, a mobile heat treatment furnace from Akkermans Gloeitechniek, a Dutch company, was simulated with Computational Fluid Dynamics (CFD). The furnace is cylindrical with four oil burners, and large metal products such as dredging pumps and impellers can be flexibly heat treated to obtain required microstructure and mechanical properties through stress relief, annealing, hardening and tempering. The furnaces are exposed to the open air, and thus the heat loss becomes significant and varies from day to day and from season to season. Since the temperature of the metal products to be heat treated can only be measured on the surface, the temperature evolution inside the metal could not be tracked in practice. CFD simulation provides a useful tool to predict the temperature evolution within the metal pieces and within the combustion space of the furnace. Energy distribution and heat loss can be subsequently estimated. An overall energy balance through temperature measurement indicted relatively low energy efficiency. Especially during the soaking period, the high energy supplied is barely used to compensate the heat loss of the furnace to maintain a constant temperature of the metal piece. The current CFD modeling aims to give advice on how to modify the design and optimize the operation to reach higher energy efficiency and low heat loss. The CFD model consists of turbulent combustion model, radiation model in participating media, and conjugate heat transfer between the combustion space and solid metal. Temperature measurement was carried out to provide thermal boundary conditions and overall energy balance of the operation. After the model validation with temperature measurement within the combustion space and metal surfaces, furnace optimization will be conducted.IntroductionHeat treatment is a common practice in metal production and manufacturing industries. Through heat treatment at certain temperatures with special patterns, unique mechanical properties of the metals and the metallic products could be obtained. ""Akkermans Gloeitechniek"" is a company situated in K.inderdijk, at location of LHC-Holland (www.ihccaland.com), the Netherlands. Heat treatment of metals is its core business. Various type of heat treatment are applied, such as stress relieving, soft annealing and hardening (quenching), tempering, transformation and precipitation. At the company 6 furnaces are in operation and the 7th is being built"

Jan 1, 2004

By Vladimir Mindin

Simulation of complex equilibria is usually done in the P-T-X coordinates, where "Xu is the amount of individual chemical components in the system. This approach is not productive in some very important cases: (i) investigation of "open" systems, (ii) determination of coordinates (trajectories) of mono-variant points, among others. To solve these and some other problems, we use the idea of chemical potentials of elements (CPE) of the system. A system of different coordinates axes (CPE-axes ) leads to a new strategy of simulation, observing the results of the simulation, and to efficient technology of compressing and storage the data of the simulation.

Jan 1, 1994

By J. P. Gu, C. Beckermann

"Melt convection and macrosegregation in casting of a large steel ingot is numerically simulated. The simulation is based on a previously developed model for multicomponent steel solidification with melt convection, and involves the solution of fully coupled conservation equations for the transport phenomena in the liquid, mush, and solid. Heat transfer in the mold and insulation materials, as well as the formation of a shrinkage cavity at the top are taken into account. The numerical results show the evolution of the temperature, melt velocity, and species concentration fields during solidification. The predicted variation of the macrosegregation of carbon and sulfur along the vertical centerline is compared with measurements from an industrial steel ingot that was sectioned and analyzed. Although generally good agreement is obtained, the neglect of sedimentation of free equiaxed grains prevents the prediction of the zone of negative macrosegregation observed in the lower part of the ingot. It is also shown that the inclusion of the shrinkage cavity at the top is important in obtaining good agreement between the predictions and measurements.IntroductionMacrosegregation in large steel ingots is one of the most well-known and now classical problems in the field of solidification and casting [1]. Commonly found macrosegregation patterns in steel ingots are a positively segregated zone at the top, negative segregation near the bottom in the equiaxed zone, inverse segregation near the ingot surface, V-segregates along the centerline, and A-segregates in the columnar zone [2, 3]. It is well established that the macroscopic transport of species leading to macrosegregation can occur by a variety of mechanisms, including thermally and solutally driven natural convection of the melt in the mushy zone, flow due to solidification contraction, and the sedimentation of free equiaxed crystals. Fredriksson and coworkers [ 4,5] provide recent overviews of the solidification transport phenomena and macrosegregation in ingot casting."

Jan 1, 1999

By S. Malinov, J. J. McKeown, W. Sha, S. McShane

"A model is developed for prediction of fatigue stress life S-N diagrams for Ti-6Al-4V alloy at different conditions, using Artificial Neural Network (ANN). Different factors which have influence on the S-N diagram are involved as input parameters of the NN, namely microstructure, environment, texture, test/work temperature, surface treatment and stress amplitude. As the output the S-N fatigue diagram is simulated and plotted.The model is based on standard multilayer feedforward neural network. The NN is trained with a comprehensive data set collected from the literature, using Levenberg-Marquardt training algorithm in combination with Bayesian regularisation. A very good performance of the trained Neural Network is achieved. Good correspondence between ANN"" prediction and experimental S-N diagrams is observed. Using the model S-N diagrams for different conditions are predicted and analysed. Graphical User Interface is developed for use of the model. We believe that the model will be important for practical applications in solving various problems on fatigue behaviour of the titanium alloy.IntroductionTitanium and its alloys have an increasing range of applications due to their very good combination of mechanical properties, corrosion and erosion resistance. They are currently finding widespread applications in many industries due to their desirable and versatile properties. Most important among the alloys is Ti-6AI-4Y. Jet aircraft manufacturers are the principal 'consumers of Ti-6Al-4V and it is often specified for critical parts, the failure of which could result in the loss of an entire system. A generic class of Ti-6AI-4V has been developed over the past years and it has become the best understood of all the titanium alloys. The advantages of titanium alloys include: (i) low densities, giving very attractive strength to weight ratios allowing lighter and stronger structures; (ii) superior corrosion and erosion resistance in many environments; (iii) high temperature capability. Although the titanium materials are still considered as expensive materials, for many applications the cost of titanium alloys can be justified on the basis of their desirable properties."

Jan 1, 2001

By Alan P. Prosser

The heap leaching of gold ores by cyanide solution was simulated by computer program. The program uses only basic m1neralogical and chemical data; no process testwork data, such as column leach results, are required. The simulation can be used to forecast the consequences of various changes before and during the testwork, design and operation stages of a particular ore-process system. Also, data about the state of different parts of the heap at various times help create an understanding of what is happening. The effects of mineralogical and process variables on the overall performance of the ?heap leaching process are illustrated. Comparisons are made to column leach tests and production data. The potential of the simulation strategy is discussed for making better use of operating experience and for suggesting specific research objectives. It has become clear that more attention should be paid to other metals that dissolve in the solution.

Jan 1, 1989

By Kenji Matsuzaki

A mathematical simulation model of the Imperial Smelting Furnace operation has been developed for purpose of improving the furnace operation. The model consists of top, shaft and bottom regions, Analysis in the shaft region is based on differential heat and materials balances taking account of reaction kinetics and heat transfer rates, and those in the top and the bottom regions are based on heat and materials balances under a steady-state condition, Longitudinal distributions of process variables such as temperatures of gas, sinter and coke, gas composition and fractional conversion under a practical operating condition were calculated, With this model, the furnace performance under various operating conditions also can be shown reasonably predicted,

Jan 1, 2003

By Malsuzaki. Kenji

A mathematical simulation model of the Imperial Smelting Furnace operation has been developed for purpose of improving the furnace operation. The model consists of top, shaft and bottom regions. Analysis in the shaft region is based on differential heat and materials balances taking account of reaction kinetics and heat transfer rates, and those in the top and the bottom regions are based on heat and materials balances under a steady-state condition. Longitudinal distributions of process variables such as temperatures of gas, sinter and coke, gas composition and fractional conversion under a practical operating condition were calculated. With this model, the furnace performance under various operating conditions also can be shown reasonably predicted.

Jan 1, 2003

By M Phil Schwarz

"A CFD model for the gas-side of an impinging jet iron bath reactor has been developed to assist in the interpretation and design of oxidizing gas-melt reaction rate experiments. Heat transfer and reaction at the surface have been included. A free surface model, which solves for the liquid motion within the bath as well as the gas motion above the bath, has also been developed. This model also predicts extent and shape of the dimple formed on the liquid surface by the impinging jet. Both models have been run for conditions typical of jet impingement experiments using CO2 , H2O and O2• The main conclusions are• Results from the model for gas-side mass transport are in good agreement with the empirical correlation of Belton and Belton (1980)• Experimentally determined rates of decarburization by CO2 should be corrected for mass transfer because the experiments are often carried out under mixed rate control, eg for gas flow rate 10 L/min when the sulphur concentration is lower than 0.045• If the rate constant for oxygen reaction is greater than about 5 mol/m2.s.atm, it cannot be determined using a gas flow rate of 10 L/min or lower because of mass transfer control.• A cavity of depth 4.5 mm is predicted for a gas flow rate of 10 L/min and this substantially changes the flow field (and hence reaction rate) compared with a simulation in which the surface is assumed to be flat."

Jan 1, 1999

By John ?gren, Martin Schwind, Henrik Larsson

"A new model for internal oxidation, as well as similar processes, has been implemented on computer. It is based upon a combination of random walk and cellular automata and is capable of treating 3-dimensional cases. To model diffusion, it utilises quantised units of matter. All steps of the process are included: nucleation, growth and coarsening. The effect of grain boundaries on diffusion as well as nucleation is taken into account. Further possible development is briefly discussed; especially the treatment of nucleation needs further consideration. IntroductionComplex diffusion-controlled processes may now be simulated on a routine basis when concentration varies along one co-ordinate only. One-dimensional simulations capture much of the information of interest but not all. For the case at hand, especially the spatial and the size distribution of precipitates, as well as the impact of grain boundaries, would be interesting information not accessible from 1-D simulationsSolving the full Fick-Onsager law in three dimensions does not seem feasible with the computers of today. In the model described in this article, random walk by quantised units of matter are considered. The model should be useful for a number of cases involving dispersed systems. With further development, it would indeed seem possible to simulate most types of phase transformations.Previous workWe have previously published two articles [1,2] on the new approach discussed in this work. In those articles we described the basic idea and showed, among other things, that very good agreement with an experimental concentration profile can be obtained, in a single-phase system, using independently assessed thermodynamic and kinetic data. Also, Schwind used the same random walk based concept to model coarsening [3]."

Jan 1, 2001

By Baicheng Liu, Houfa Shen, Wensheng Li

"In order to understand the formation of macrosegregation in steel ingots, a mixture model has been developed which accounts for coupled mass, momentum, species, and energy transport to describe the sedimentation of free equiaxed grains during solidification. In this model, the mushy zone is divided into the slurry and porous regimes according to a solid packing fraction. Settling velocity of equiaxed grains in the slurry regime is given by an explicit expression. The solidification of a binary steel ingot (Fe-0.36wt.%C) with a two-dimensional geometry is numerically simulated. It is demonstrated that the predicted macrosegregation patterns agree to some extent with classical experimental results. Further refinement of this model is still necessary for realistically simulating steel ingot solidification.IntroductionModeling macrosegregation in steel ingots is still a challenging study, mainly due to the length scale of the products and the complexity of global multiphase transport phenomena coupled with microscopic solidification kinetics [l]. The thermal-solutal convection and the motion of equiaxed grains are the two main mechanisms responsible for macrosegregation. But there are few models that deal with the motion of equiaxed grains, which is confirmed as the main phenomenon that explains the negative macrosegregation along the centerline of large steel ingots [2]. A model which takes into account melt convection and grain sedimentation was first proposed by Beckermann and co-workers ([3], and references therein). More recently, similar multiphase solidification models with advanced nature have been presented by Wu and Ludwig [1,4] and Combeau and co-workers [5,6]. It is known that the application of these sophisticated models to steel ingot casting is at its beginning.In this paper, a solidification model based on continuum mixture approach, using much less sophisticated relations to obtain the settling velocity of free equiaxed grains, has been proposed in order to predict the macrosegregation in steel ingots. The model is applied to simulate the solidification of a binary steel ingot with a two-dimensional geometry, and preliminary modeling results are presented."

Jan 1, 2011

By Jie Ma, Shun-Li Zhao, Jian Zhao, Jie-Yu Zhang

"Microstructural morphology evolution of Ni-45wt.%Mo droplets during rapid solidification process was investigated using an advanced modified 3D cellular automaton-finite element(CAFE) model by CALCOSOFT software. The model was modified by User-defined functions (UDFs) and validated with experimental solidification microstructural morphology of Ni-45wt.%Mo droplets available in the literature. Then, the influences of convection heat transfer coefficient, superheat of the alloy droplets and droplets size were investigated during the rapid solidification process. The predictions show that microstructural morphology is obviously sensitive to convection heat transfer coefficient and droplet size. With the decrease of convection heat transfer coefficient, the grain density decreases. In addition, the decrease of the droplet size could obtain refined microstructure. However, decrease the superheat ofNi-45wt.%Mo droplets has little effect on microstructural morphology.IntroductionFor several decades, much attention has been paid to undercooled alloy droplets of rapid solidification process for which can obtain refined microstructure, decreased microsegregation and extended solubility of alloying elements [1-3]. Extensive prior work shows that solidification of droplets plays an essential role in advanced material properties [ 4]. Consequently, it is very important to investigate the microstructural morphology evolution, especially for dendrite growth during non-equilibrium solidification process, for dendrite growth reflected the kinetics of the crystal growth process."

Jan 1, 2013

By Hebi Yin

A coupled cellular automaton (CA) - finite element (FE) model was developed to calculate the growth of dendrites during the solidification of cubic and hexagonal metals. The model solves the conservation equations of mass, energy and solutes in order to calculate the temperature field, solute concentration and the growth morphology of dendrites, including the grain structure and the dendritic microstructure. Validation of the model was performed by comparing the simulation results with calculation results from previously published works, showing qualitatively good agreement in the dendritic morphology. Application to magnesium alloy AZ91 illustrates the difficulty of modeling dendrite growth in hexagonal systems, observed as deviations in growth direction caused by mesh-induced anisotropy. The model was applied to the simulation of small specimens with single- and multiple- equiaxed grain growths and columnar grain growth in directional solidification. The influence of cooling rate and some kinetics parameters on the grain morphology are also discussed.

Jan 1, 2009

By I. Ohnaka

Although many works have been reported on the semisolid casting, the mold filling behavior of semi-solid alloys has not been so well understood. This paper compares the physical and numerical simulation results on the mold filling behavior. Physical simulation was performed by using solid-water mixture. The numerical simulation was made under the assumption of one phase flow with an effective viscosity. It was found that the solid particles stabilize the flow greatly if the kaction solid exceeds about 0.4, because viscosity increases greatly. The overall flow behavior can be estimated by the numerical simulation. Interesting flow behavior was also found which can not be observed in the case of one phase flow and which is difficult to simulate by the one phase flow assumption.

Jan 1, 1997

By Luiz R. P. De Andrade Lima

This paper presents a mathematical model for the oxide copper ore heap leaching process. The data used in the model include physical-chemical, .geometrical and operational data, as: leachable metals ore contents, .flow rate and acid concentration, parameters of passivity, ore size distribution, the average residence time of the solution in the heap, height, irrigated area and weight of ore in the heap. In this model the heap is divided into horizontal and plane layers of constant area. The flow of the liquid in the heap is considered unidirectional and the solid-fluid reaction model is considered under diffusive control. The average residence time of the solution into the heap and the apparent effective diffusivity of the acid through the ore particles have .a significant influence on the rate of the copper extraction and its concentration in the pregnant solution; therefore these parameters are used in the model calibration. When this algorithm was applied to a laboratory test, the results showed that the model is adequate to predict the process performance.

Jan 1, 1999

By J. Rajek

The novel multi-component, multi-particle, multi-phase precipitation model developed recently is used to predict the precipitation kinetics in complex 9-12% Cr steels investigated within the European COST 522 project. These steels are used for tubes, pipes, casings and rotors in USC (ultra super critical) steam power plants for the 21st century. In the computer simulations, the evolution of the precipitate microstructure is monitored over the entire production heat treatment starting with the casting process, including austenizing, several annealing treatments and in-service conditions. The main interest lies on the concurrent growth and coarsening interaction of different types of precipitates. Keywords: Precipitation kinetics, heat treatment, power plant steels, simulation

Jan 1, 2003

By Paul W. Cleary

Keywords: Reactive pellets, CFD, Lagrangian SPH, Pyrometallurgy In several pyrometallurgical processes, reactive pellets are added to a melt. Heat is transferred to the pellets and reaction products such as gases, metal and slag are formed. For many pyrometallurgical processes traditional grid based CFD methods, such as using the Finite Element Method (FEM) and Finite Volume (or Control Volume methods), produce suitable predictions. However, the inclusion of solids in the bath represents significant challenges for these methods. Smoothed Particle Hydrodynamics (SPH), a Lagrangian simulation method, is able to simulate both the fluid component of the bath and any immersed solid materials, tracking the motion of these solids, and their interaction with the fluid, including gas generation. In this paper, we will summarize the key aspects of the SPH method and will show a series of structured examples illustrating the behavior of the different physics sub-systems that are used in the model of the overall system.

Jan 1, 2005