Simulation of convection and macrosegregation in a large steel ingot

Melt convection and macrosegregation in casting of a large steel ingot are 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, is 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 and the variation of the final solidification temperature due to macrosegregation is important in obtaining good agreement between the predictions and measurements.     

Numerical simulation of a solidifying Pb-Sn alloy: The effects of cooling rate on thermosolutal convection and macrosegregation

Numerical simulations of a binary metal alloy (Pb-Sn) undergoing solidification phase change are performed using a continuum model for conservation of total mass, momentum, energy, and species. The system is contained in an axisymmetric, annular mold which is cooled along its outer vertical wall. Results show that thermosolutal convection in the melt and mushy zones is strongly coupled and that macrosegregation is reduced with increased cooling rate. For low cooling rates, solutally induced convection in the mushy zone favors the development of channels, which subsequently spawn macrosegregation in the form of A-segregates. With increasing solidification rate, however, thermosolutal interactions in the melt contribute to reducing the formation of channels and A-segregates.     

Macrosegregation Formation in an Al–Si Casting Sample with Cross-sectional Change During Directional Solidification

A unidirectional solidification experiment of hypoeutectic Al-7.0 wt% Si alloy against gravity direction in a cylindrical mold with cross-sectional change was made, and the macrosegregation in different parts of the as-solidified sample was investigated (Ghods et al. in J Cryst Growth 441:107–116, 2016; J Cryst Growth 449:134–147, 2016). The current study is to use a two-phase columnar solidification model to analyze the segregation mechanisms as used in this experiment. Following flow phenomena and their contributions to the formation of macrosegregation are simulated and compared: (1) solidification shrinkage-induced feeding flow; (2) thermo-solutal convection; and (3) combined thermo-solutal convection and shrinkage-induced feeding flow. The shrinkage-induced feeding flow leads to an inverse (positive) segregation in the bottom part, and a severe negative segregation in the part below cross-sectional change. Thermo-solutal buoyancy leads to a so-called steepling convection in the main part of the sample (away from the bottom and cross-sectional change), and this kind of flow leads to a positive macrosegregation near the sample surface. The calculations have successfully explained the experimental result of macrosegregation.     

Modeling freckle formation in three dimensions during solidification of multicomponent alloys

The formation of macrosegregation defects known as “freckles” was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-W alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.     

Grain Floatation During Equiaxed Solidification of an Al-Cu Alloy in a Side-Cooled Cavity: Part II—Numerical Studies

In this article, a single-phase, one-domain macroscopic model is developed for studying binary alloy solidification with moving equiaxed solid phase, along with the associated transport phenomena. In this model, issues such as thermosolutal convection, motion of solid phase relative to liquid and viscosity variations of the solid–liquid mixture with solid fraction in the mobile zone are taken into account. Using the model, the associated transport phenomena during solidification of Al-Cu alloys in a rectangular cavity are predicted. The results for temperature variation, segregation patterns, and eutectic fraction distribution are compared with data from in-house experiments. The model predictions compare well with the experimental results. To highlight the influence of solid phase movement on convection and final macrosegregation, the results of the current model are also compared with those obtained from the conventional solidification model with stationary solid phase. By including the independent movement of the solid phase into the fluid transport model, better predictions of macrosegregation, microstructure, and even shrinkage locations were obtained. Mechanical property prediction models based on microstructure will benefit from the improved accuracy of this model.     

Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys

A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.     

The Use of Steady Electromagnetic Fields to Control the Columnar Solidification of Binary-Metal Alloys

This article considers the nondirectional solidification of a binary-metal alloy in a cylindrical cavity, which is cooled along its outer vertical wall and the bottom. To study the influence of convection within the liquid phase on the final segregation, three cases are examined: the purely buoyancy-driven convection (case 0), the impact of an external steady axial magnetic field on the melt flow during solidification (case 1), and the effect of the combination of an external magnetic field with a steady electrical current (DC) applied directly to the melt (case 2). The results show that convection in the form of multivortices caused by the thermosolutal buoyancy leads to macrosegregations in the form of V-channels. The application of an external axial magnetic field alone suppresses the multivortex structure and, thus, the macrosegregation. By contrast, the parallel use of an additional voltage of 10⁻³ V leads to an increase in final macrosegregation. This article is based on a presentation given at the International Symposium on Liquid Metal Processing and Casting (LMPC 2007), which occurred in September 2007 in Nancy, France.     

A model for macrosegregation and its application to Al-Cu castings

A macrosegregation model has been developed to evaluate solute redistribution during solidification of casting alloys. The continuum formulations were used to describe the macroscopic transports of mass, energy, and momentum, associated with the microscopic transport phenomena, for two-phase systems. It was assumed that liquid flow is driven by thermal and solutal buoyancy, as well as by solidification contraction. The movement of free surface was also considered to ensure volume con-servation. In numerical calculations, the solidification event was divided into two stages. In the first stage, the liquid containing freely moving equiaxed grains was described through the relative vis-cosity concept. In the second stage, when a fixed dendritic network formed after dendrite coherency, the mushy zone was treated as a porous medium. After validation of the proposed model for the case of segregation in a bottom-chilled unidirectionally solidified casting of Al-Cu alloys, the nu-merical model was applied to the study of three different castings with simple geometry. It was found that solutal convection tends to decrease the macrosegregation generated by thermal convec-tion. When shrinkage-driven convection was also considered, segregation was again increased, with highly segregated areas forming away from the riser and next to the mold wall. It was demonstrated that solidification contraction has a stronger effect on the liquid flow in the mushy region than buoyancy. The model also was applied to assess the probability of pore formation based on the pressure drop concept. While in the absence of experimental data for the critical pressure drop it was not possible to uniquely predict the formation of porosity, it was possible to indicate the regions where porosity may form preferentially.     

Modeling of macrosegregation caused by volumetric deformation in a coherent mushy zone

A two-phase volume-averaged continuum model is presented that quantifies macrosegregation formation during solidification of metallic alloys caused by deformation of the dendritic network and associated melt flow in the coherent part of the mushy zone. Also, the macrosegregation formation associated with the solidification shrinkage (inverse segregation) is taken into account. Based on experimental evidence established elsewhere, volumetric viscoplastic deformation (densification/dilatation) of the coherent dendritic network is included in the model. While the thermomechanical model previously outlined (M. M’Hamdi, A. Mo, and C.L. Martin: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2081–93) has been used to calculate the temperature and velocity fields associated with the thermally induced deformations and shrinkage driven melt flow, the solute conservation equation including both the liquid and a solid volume-averaged velocity is solved in the present study. In modeling examples, the macrosegregation formation caused by mechanically imposed as well as by thermally induced deformations has been calculated. The modeling results for an Al-4 wt pct Cu alloy indicate that even quite small volumetric strains (≈2 pct), which can be associated with thermally induced deformations, can lead to a macroscopic composition variation in the final casting comparable to that resulting from the solidification shrinkage induced melt flow. These results can be explained by the relatively large volumetric viscoplastic deformation in the coherent mush resulting from the applied constitutive model, as well as the relatively large difference in composition for the studied Al-Cu alloy in the solid and liquid phases at high solid fractions at which the deformation takes place.     

Study on the Macrosegregation Behavior for the Bloom Continuous Casting: Model Development and Validation

With the aid of a coupling electromagnetic-thermal-solute transportation model validated by the industrial investigation, a three-dimensional (3-D) plus two-dimensional (2-D) hybrid modeling method has been presented for the exploration of the macrosegregation and macroscale transport phenomena in the bloom continuous casting (CC) processes of high-carbon GCr15-bearing steel. The evolution and characteristics of solute distribution and its influence on the porosity formation in the strand during CC process have been revealed. Solute segregation degree changes from a positive to a negative value with distance from strand surface in the region of initial solidification shell within thickness of 25 mm, which can be attributed to the circulation flow ahead the solidification front and the floatation of solute-rich molten steel at the upper part of the mold. The discontinuous, nonfrozen band induced by the zigzag solute distribution is proven to be the main reason that leads to the porosity formation in the final solidification stage of the CC strand. As the solidification proceeds, the segregation degree of C at the strand center is increased from 1.0 to 1.2, while the melt liquidus temperature is reduced from 1726 K (1453 °C) to 1706.91 K (1433.91 °C) during the CC process. Moreover, with the action of gravity and thermosolutal convection, a negative segregation region in the concave shape and an irregular positive segregation zone are produced in the fixed and loosened side of shell, respectively.     

Thermosolutal convection and macrosegregation during solidification of hypereutectic and hypoeutectic binary alloys in statically cast trapezoidal ingots

Thermosolutal convection patterns and evolution of macrosegregation during solidification of hypereutectic and hypoeutectic NH₄CL-H₂O binary systems in trapezoidal side-chilled ingots with negative and positive slopes have been numerically investigated. The results have been compared with the base case of solidification in a rectangular ingot. During solidification of NH₄CL-70 pct H₂O hypereutectic alloy, channels and “A segregates” develop early in the solidification process. When the slope is positive, channels penetrate to a larger distance inside the ingot. Whereas, for negative slope, they are shifted outward toward the chilled wall and are vertically oriented. During solidification of NH₄CL10 pct-H₂O hypoeutectic alloy, circulation cells which emerge in the narrow melt at later stages of the process are shown to be responsible for the development of V-shaped segregates in the final casting. The final degree of macrosegregation is higher for both positive and negative slopes of the ingot chilled wall compared to the rectangular ingot. deceased.     

Formation and control of macrosegregation for round bloom continuous casting

Based on the developed coupled model of electromagnetism, heat and solute transportation, the macrosegregation formation and effect of secondary cooling water ratio on macrosegregation degree in strand during round bloom continuous casting process have been investigated. The solute segregation degree fluctuates from a positive to a negative value with distance from strand surface in the initial solidified shell region within thickness of 20?mm. A negative segregation region in concave shape and an irregular positive segregation zone are presented in the fixed and loosened side of strand respectively due to the gravity and thermosolutal convection. As the secondary cooling water ratio decreases from 0.25 to 0.15?L?kg^??1, the solidification ratio at final electromagnetic stirring (F-EMS) centre increases from 73.14 to 77.83%. For the steel grade of 50Mn casted by round bloom casting within diameter of 0.35?m, the optimal solidification ratio at F-EMS centre is 75.05%, where the radial centre crack and shrinkage cavity at strand cross-section are removed.     

Mathematical modeling of macrosegregation of iron carbon binary alloy: Role of double diffusive convection

During alloy solidification, macrosegregation results from long range transport of solute under the influence of convective flow and leads to nonuniform quality of a solidified material. The present study is an attempt to understand the role of double diffusive convection resulting from the solutal rejection in the evolution of macrosegregation in an iron carbon system. The solifification process of an alloy is governed by conservation of heat, mass, momentum, and species and is accompanied by the evolution of latent heat and the rejection or incorporation of solute at the solid liquid interface. Using a continuum formulation, the goverming equations were solved using the finite volume method. The numerical model was validated by simulating experiments on an ammonium chloride water system reported in the literature. The model was further used to study the role of double diffusive convection in the evolution of macrosegregation during solidification of Fe 1 wt pct C alloy in a rectangular cavity. Simulation of this transient process was carried out until complete solidification, and the results, depicting the influence of flow field on thermal and solutal field andvice versa, are shown at various stages of solidification. Under the given set of parameters, it was found that the thermal buoyancy affects the macrosegregation field globally, whereas the solutal buoyancy has a localized effect.     

Convection and channel formation in solidifying Pb-Sn alloys

A suite of experiments on the dendritic solidification of Pb-Sn melts has been carried out. The first goal has been to quantify the longitudinal macrosegregation, and hence the convective vigor through the dendritic (“mushy”) zone during solidification, as a function of the mushy zone Rayleigh number. The mushy zone Rayleigh number Ra _m is a ratio of the driving compositional buoyancy force to the retarding Darcy frictional force. The second goal has been to characterize the formation of convection channels as a function of Ra _m . In a fixed furnace, the melts were program cooled and solidified from beneath, at various cooling rates. Two different temperature gradients were examined. Each pairing of cooling rate and temperature gradient results in a different Ra _m . As expected, the measured longitudinal macrosegregation increased with Ra _m . The vestiges of convection channels on a solidified ingot surface (which we call “freckle trails”) were observed for all conditions except for the most rapid cooling rate with the smaller temperature gradient (i.e., the smallest Ra _m ) and for the slowest cooling rate with the larger temperature gradient (i.e., the largest Ra _m ). Under the latter solidification conditions, the vestiges of convection channels in an ingot interior (which we call “chimneys”) were observed. Chimneys were not observed in other ingots. When present, the number of freckle trails decreased and the width of the trails increased with increasing Ra _m . The trails became more diffuse as well. It appears that Ra _m may control channel characteristics as well as convection and the resulting macrosegregation. There appear to be two critical values, a lower one for surface freckle trails and a higher one for interior chimneys. Conditions at the Earth’s inner-outer core boundary (ICB) may be those exhibiting high Ra _m convection, so that convection channels, if they exist, could be as large as several hundred meters in width.     

Macrosegregation and sedimentation in liquid-phase sintering

Macrosegregation has been observed in a series of Pb-Sn alloys isothermally treated in an α + L (or β + L) two-phase region. Depending on the alloy composition, the Pb-rich α (or the Sn-rich β) solid phase quickly settles (or floats) to the bottom (or top) of the crucible as the alloy is heated into the solid-plus-liquid two-phase region. This settling or floating persists until such time as a skeletal solid structure is formed at the crucible bottom or top. The skeleton (the “mushy” zone) resembles liquid-phase-sintered structures; that is, it consists of interconnected solid and liquid phases. The initial settling can give rise to macrosegregation. Elimination of macrosegregation requires substantial time and is accompanied by a reduction in length of the mushy zone, giving rise to apparent sedimentation of this zone. We argue that this sedimentation results from the compositional readjustments accompanying macrosegregation elimination. On this basis, it appears that many observations of sedimentation in liquid-phase-sintered structures are due to these readjustments.     

Macrosegregation during dendritic arrayed growth of hypoeutectic pb- sn alloys: Influence of primary arm spacing and mushy zone length

Thermosolutal convection in the dendritic mushy zone occurs during directional solidification of hypoeutectic lead tin alloys in a positive thermal gradient, with the melt on the top and the solid below. This results in macrosegregation along the length of the solidified samples. The extent of macrosegregation increases with increasing primary dendrite spacings for constant mushy zone length. For constant primary spacings, the macrosegregation increases with decreasing mushy zone length. Presence of convection reduces the primary dendrite spacings. However, convection in the interdendritic melt has significantly more influence on the spacings as compared with that in the overlying melt, which is caused by the solutal buildup at the dendrite tips. Formerly Graduate Student, Chemical Engineering Department, Cleveland State University     

Macrosegregation of Impurities in Directionally Solidified Silicon

Directional solidification of molten metallurgical-grade Si was carried out in a vertical Bridgman furnace. The effects of changing the mold velocity from 5 to 110 μm seconds^–1 on the macrosegregation of impurities during solidification were investigated. The macrostructures of the cylindrical Si ingots obtained in the experiments consist mostly of columnar grains parallel to the ingot axis. Because neither cells nor dendrites can be observed on ingot samples, the absence of precipitated particles and the fulfillment of the constitutional supercooling criterion suggest a planar solid–liquid interface for mold velocities ≤10 μm seconds^–1. Concentration profiles of several impurities were measured along the ingots, showing that their bottom and middle are purer than the metallurgical Si from which they solidified. At the ingot top, however, impurities accumulated, indicating the typical normal macrosegregation. When the mold velocity decreases, the macrosegregation and ingot purity increase, changing abruptly for a velocity variation from 20 to 10 μm seconds^–1. A mathematical model of solute transport during solidification shows that, for mold velocities ≥20 μm seconds^–1, macrosegregation is caused mainly by diffusion in a stagnant liquid layer assumed at the solid–liquid interface, whereas for lower velocities, macrosegregation increases as a result of more intense convective solute transport.     

A thermodynamic prediction for microporosity formation in aluminum-rich Al-Cu alloys

A computer model is used to predict the formation and the amount of microporosity in directionally solidified Al-4.5 wt pct Cu alloy. The model considers the interplay between so-called “solidification shrinkage” and “gas porosity” that are often thought to be two contributing and different causes of interdendritic porosity. There is an accounting of the alloy element, Cu, and of dissolved hydrogen in the solid- and liquid-phase during solidification. Consistent with thermodynamics, therefore, a prediction of forming the gas-phase in the interdendritic liquid is made. The local pressure within the interdendritic liquid is calculated by macrosegregation theory that considers the convection of the interdendritic liquid, which is driven by density variations within the mushy zone. Process variables that have been investigated include the effects of thermal gradients and solidification rate, and the effect of the concentration of hydrogen on the formation and the amount of interdendritic porosity. These calculations show that for an initial hydrogen content less than approximately 0.03 ppm, no interdendritic porosity results. For initial hydrogen contents in the range of 0.03 to 1 ppm, there is interdendritic porosity. The amount is sensitive to the thermal gradient and solidification rate; an increase in either or both of these variables decreases the amount of interdendritic porosity.     

Experimental Investigation of Macrosegregation During Vertical Solidification of Lead–Tin Alloys

Thermosolutal convection during solidification of alloys is one of the major causes of macrosegregation. An experimental investigation was carried out on lead–tin alloys to study the evolution of macrosegregation during vertical solidification in laboratory. The emphasis was on accurate measurements of temperatures during solidification as well as segregation measurements and microstructural examination of solidified samples. The nominal compositions of ingots were Pb–35% Sn, Pb–19 wt% Sn and Sn–15 wt% Pb. Experiments were carried out at two superheats and different cooling rates. With decreasing cooling rate, increase in axial macrosegregation was observed in lead rich alloys. No macrosegregation was observed in tin rich alloys. Convection of interdendritic liquid was found to be responsible for macrosegregation. Also, from experimental data, heat flux to cooling water, local solidification times in the melt as well as dendritic arm spacings were determined.