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The Electroslag Remelting (ESR) is an advanced technology for the production of high quality materials, for example, hot work tool steels or nickel base alloys. In the past years, several models are developed aiming to predict the way in which the operational parameters affect the structure and chemical composition of the final ESR ingot. Proper modeling of this process depends on the ability of the model to predict the Multiphysics resulting from the complex coupling between many physical phenomena. This review includes the main findings starting from the 1970's, with a special focus on the results obtained in the period of 1999–2017. The difficulties related to the poorly known physical properties of ESR slags are discussed. Then, the main achievements in the field of electromagnetism, fluid flow, heat transfer, and solidification are also summarized. The review finishes by presenting the special topics representing the actual scientific frontiers, such as the physics of mold current, the importance of multiphase phenomena, and the difficulties in predicting the electrode melting rate. [ABSTRACT FROM AUTHOR]

Some of the most recent examples of simulations of as‐cast steel ingots are presented in this paper, focusing on discussions concerning available simulation/modeling tools and their capacities and limitations. Although, there has been some success from implementing criterion functions into commercial codes to predict shrinkage porosity and hot tearing, large‐scale ingot sectioning experiments, similar to what is done a century ago, are still needed to investigate other issues, such as macrosegregation, since models are currently unable to predict such issues well. Models with more sophisticated features for macrosegregation prediction that incorporate multiphase transport phenomena are already under development. A limiting factor in application of these models for simulating steel ingots is the demand on large computation resources. Following the recent development trend and the projection of Moore's law (computer hardware), in the foreseeable future, it is predicted that multiphase models will to a great extent reduce the need for the experimental pouring‐sectioning trials. [ABSTRACT FROM AUTHOR]

Macrosegregation originates from the solute partitioning at the liquid-solid interface and the relative motion between liquid and solid phases during solidification of metal alloys. A suitable macrosegregation model should incorporate solidification thermodynamics, crystal growth kinetics, multiphase computational fluid dynamics, and even thermal-structural mechanics. No current model includes all those phenomena, hence leading to assumptions having to be made. This paper discusses some modeling assumptions regarding the treatment of (1) diffusion kinetics of crystal growth, (2) crystal dendritic morphology and (3) solidification shrinkage. Theoretical analyses based on test calculations were made. We find that some previous models, which oversimplified some of the aspects mentioned above for the purpose of computational efficiency, can only be applied to study macrosegregation qualitatively. They lead to significant error estimations of macrosegregation. When the quantitative accuracy for macrosegregation is of primary importance, the multiphase-based models with an appropriate treatment of these aspects, despite the sophisticated computational requirements, are recommended. [ABSTRACT FROM AUTHOR]

A full 3D simulation of an industrial scale electroslag remelting (ESR) process ( ϕ 750 mm ingot) is performed, and results are verified by experiment. A typical non-axis symmetry flow pattern and temperature field in the slag region is demonstrated. A statistical analysis of the turbulent flow in the slag and melt pool is performed to quantitatively characterize the transient behavior of the flow. By comparing the 3D calculation with a 2D axis-symmetrical calculation, we find that the predicted shape of melt pool (profile of the solidifying mushy zone of the ingot) are quite similar, leading to the conclusion that a 2D calculation is sufficient to solve the melt pool profile of the ingot. [ABSTRACT FROM AUTHOR]

Positive centerline macrosegregation is an undesired casting defect that frequently occurs in the continuous casting process of steel strands. Mechanical softreduction (MSR) is a generally applied technology to avoid this casting defect in steel production. In the current paper, the mechanism of MSR is numerically examined. Therefore, two 25-m long horizontal continuous casting strand geometries of industrial scale are modeled. Both of these strand geometries have periodically bulged surfaces, but only one of them considers the cross-section reduction due to a certain MSR configuration. The macrosegregation formation inside of these strands with and without MSR is studied for a binary Fe-C-alloy based on an Eulerian multiphase model. Comparing the macrosegregation patterns obtained for different casting speed definitions allows investigating the fundamental influence of feeding, bulging and MSR mechanisms on the formation of centerline macrosegregation. [ABSTRACT FROM AUTHOR]

• The hydrodynamic influence on faceted crystal growth was clearly observed and evidence was presented in this paper. • An asymmetry of the crystal facets growth was introduced by the melt flow magnitude and direction. • The flow hydrodynamics is able to induce a similar effect to that caused by natural anisotropy in a faceted crystal growth. In this paper we show that the presence of liquid flow around a crystal growing from melt can induce dissymmetry in growth similar to that described by anisotropic interfacial kinetic coefficients. A front tracking interface model based on a cellular automaton approach was applied to the growth of a Fe 2 Al 5 crystal (also known as top dross particle) in a saturated Zn melt at constant temperature. The growth rate was found to be influenced by the intensity of the melt flow and by the direction of the flow with respect to the crystal orientation. The magnitude and the direction of flow modify the diffusion boundary layer, changing the conditions (temperature and concentration) at the facet interface, therefore the mass transfer. We have shown that despite the isotropy of interfacial kinetics, hydrodynamics was able to introduce an anisotropy in the crystal growth similar to the natural anisotropy in interfacial kinetics of the facets. The facets grow rate was found to be strongly dependant on the Reynolds number as well as on the orientation of the crystalline orientation with respect to the flow direction. [ABSTRACT FROM AUTHOR]

Slag fuming (SF) is a metallurgical process designed to recycle Zn‐containing slags derived from various industrial residues. To protect the reactor from corrosive molten slag, a deliberate as‐solidified slag layer, known as a freeze lining (FL), is formed on the reactor walls using intense water‐cooled jackets. In this article, a computational‐fluid‐dynamics‐based model capable of simulating FL formation in a SF furnace is presented. To capture the complex multiphase flow dynamics, heat transfer, and FL formation during SF, a volume‐of‐fluid model is coupled with a mixture continuum solidification model. Three phases are considered: gas, liquid bulk slag, and solid slag (FL). Moreover, two types of FL are distinguished: one that solidifies on the reactor wall in the bulk slag region and another that solidifies on the reactor wall in the freeboard region owing to slag splashing. Comparisons between calculated FL thickness and heat fluxes and corresponding industrial data demonstrate satisfactory agreement. In this outcome, the robustness of the model is underscored and confidence in its accuracy is instilled. In the simulation results, valuable insights are provided into the evolution of the fuming process, particularly regarding the slag bath temperature, slag splashing dynamics, FL formation, local heat fluxes through the reactor wall, and global net energy balance. [ABSTRACT FROM AUTHOR]

Ammonium chloride (NH4Cl) has been extensively studied as a transparent analogue for investigating the solidification of metals due to its distinctive properties and the simplicity of the experimentation. Furthermore, NH4Cl exhibits a striking resemblance in solidification behavior to the majority of binary eutectic alloy systems, rendering it a valuable model for studying phase transition phenomena. Experiments conducted on ammonium chloride are frequently employed to validate numerical models for predicting grain structures, macrosegregation, and the columnar-to-equiaxed transition (CET). This latter phenomenon arises due to differences in the velocities of columnar dendrite tips and the liquidus isosurface. However, the kinetics of dendrite tip growth, as a function of supersaturation, remains poorly understood for this commonly used alloy. The objective of this study was to utilize the available experimental data in conjunction with Ivantsov correlations to shed light on the ambiguous kinetics. The results indicate that when considering the crystal–melt density ratio, the Ivantsov solution offers a good correlation. Furthermore, incorporating a moderate interfacial kinetic coefficient enhances the correlations further. This correlation can be implemented in numerical models, which will aid in the determination of the columnar front, the columnar-to-equiaxed transition, and the equiaxed growth velocities. [ABSTRACT FROM AUTHOR]

• When a strand is subjected to rolling and pressing during MR, deformation-induced strand deflection can occur. • A novel modeling strategy is proposed to dynamically capture this contraction/dilatation effect in a fixed geometry. • The strategy is based on the deformation behavior of the viscoplastic network during rolling and pressing of the strand. • The strand deflection magnitude has been found to depend on solidification evolution and pressing intensity. • This work can be extended to industrial applications where deformation-induced strand deflection are critical to outcome. When a strand is subjected to rolling and pressing during mechanical reduction (MR), deformation-induced strand contraction or dilatation can occur. A novel modeling strategy has been designed to account for this mechanism in a two-phase Eulerian–Eulerian volume-average model with a fixed geometry. The strategy is based on the following ideas: (1) during MR, the pressing force from the rolls to the solidifying strand leads to the compression of the viscoplastic network that causes melt to be squeezed out of that region; (2) if the pressing is strong enough to cause the melt to penetrate the surrounding solid shell, the strand deflects outwards (the dilatation state); (3) as the melt flow weakens and the following pair of rolls approaches, the "expanded" strand structure is forced to go back to its original form (the contraction state). Numerically, special Robin type boundary conditions have been imposed on the strand surface to comply with the above description while maintaining a fixed domain. Strand deflection has been estimated and correlates well with the mush deformation intensity and solidification evolution during the casting process. Macrosegregation is also discussed based on the strand deflection and deformation parameters. [ABSTRACT FROM AUTHOR]

In the present study, we investigate arc plasma expansion in an industrial vacuum arc remelting (VAR) process using experimental and numerical tools. Stainless steel is the alloy of interest for the electrode (cathode) and ingot (anode). During the operation of the VAR process, behaviors of cathode spots and plasma arc were captured using the high-speed camera (Phantom v2512). We found that spots prefer to onset and remain within the partially melted surface at the center of the electrode tip. Existing spots outside the melting zone accelerate toward the edge of the electrode to extinguish. We observed a fairly symmetrical and centric plasma column during the operation. For further investigation of the observed arc column in our experiment, we used the two-fluid magnetohydrodynamics (MHD) model of plasma proposed by Braginskii. Thus, we modeled the arc column as a mixture of two continuous interpenetrating compressible fluids involving ions and electrons. Through numerical simulations, we calculated plasma parameters such as number density of ions/electrons, electric current density, flow of ions/electrons, temperature of ions/electrons, and light intensity for the observed arc column in our experiment. The calculated light intensity of plasma was compared with images captured by the camera to verify the model. The distribution of electric current density along the surface of the anode, namely ingot, is a decisive parameter that impacts the quality of the final product (ingot) in VAR process. Herein, we confirm that the traditionally used Gaussian distribution of electric current density along the surface of the ingot is viable. [ABSTRACT FROM AUTHOR]

• Importance of crystal remelting during alloy solidification. • Role of TMF in promoting the equiaxed grain formation through crystal fragmentation. • Formation mechanism for the as-cast structure and macrosegregation under the effect of TMF. • A refined three-phase mixed columnar-equiaxed solidification model considering TMF. A series of solidification benchmark experiments based on Sn-10wt.% Pb alloy were performed at the SIMAP Laboratory in Grenoble, France (Hachani et al., 2015) to study the effect of different types of forced convection on the as-cast structure and macrosegregation. Forced convection was achieved by using a traveling magnetic field (TMF). Four cases were investigated: without TMF; TMF in the same direction as natural convection; TMF in the opposite direction as natural convection; and TMF periodically reversed with respect to natural convection. In the current study, a three-phase mixed columnar-equiaxed solidification model was used to "reproduce" the above experiments to understand the flow effect on the as-cast structure formation. The dendrite fragmentation is regarded as the only source of equiaxed grains. Remelting/destruction of equiaxed grains in the superheated melt is considered. The continuous growth of the surviving equiaxed grains and further competition with the as-developed columnar dendrites, leading to columnar-to-equiaxed transition (CET), are included. Except for Case III (i.e., a TMF in the opposite direction as natural convection), satisfactory simulation-experiment agreements in terms of the temperature field, as-cast structure and macrosegregation are obtained for the remaining three cases. Based on the simulation results, it is found that 1) TMF plays an important role in homogenizing the temperature field and promoting the formation of equiaxed grains via fragmentation, consequently facilitating the appearance of CET; 2) TMF tends to generally intensify macrosegregation and increase the number of channel segregations; and 3) the simultaneous solidification/remelting process represents a significant species/energy transport mechanism. Ignoring the remelting of equiaxed grains would lead to an overestimate of the local temperature in the remelting zone. The reason for the mismatch between the simulation and experimental results obtained for Case III is discussed. [ABSTRACT FROM AUTHOR]

Single-crystal superalloy turbine blades (TBs) fabricated using directional solidification are key components of aeroengines and gas turbines. Owing to thermal–solutal convection during solidification, such components are susceptible to flow-induced defects such as freckles and/or eutectic accumulation. The formation mechanisms of the above defects are well understood, but reliable theories or empirical laws are unavailable to guide the engineering production process as the thermal–solutal convection is sensitive to the alloy, Bridgeman furnace design, shape and internal structure of the TB, withdrawal parameters, etc. This study proposes a novel method to 'digitally twin' the directional solidification of the TB, i.e. to utilise a physically based numerical model to quantitatively simulate the solidification process, including freckle formation and eutectic accumulation. It includes two simulations: one for the global thermal field in the Bridgeman furnace, including the casting system, and the other for the flow and solidification within the casting component. The former is modelled using ProCAST, the latter is modelled using a volume-average-based multiphase solidification model, and both are coupled. To verify the digital twin concept, an actual industrial TB with slight geometrical modification (removal of the fins while maintaining the inner surface profile) was cast in a Bridgman furnace, and the as-solidified TB was inspected for freckles. An excellent agreement between the simulation and experimental results was obtained. Typically, an actual TB features a complex inner structure (fins) that connects the front and back blades with an average wall thickness of 1.5 mm. A fresh simulation was performed for the TB with inner fins. It was observed that the inner fins of the TB along with other process conditions, such as the shadowing effect of the furnace, play an important role in freckle formation. This study demonstrates the necessity of the digital twin in future TB production. [Display omitted] [ABSTRACT FROM AUTHOR]

Forced convection and its effect on the microstructure evolution of an Al-7wt.%Si alloy during unidirectional solidification were studied experimentally. Under natural convection (gravity), columnar structures develop. However, under forced convection by activating a rotating magnetic field (RMF: 10 mT, 50 Hz), many equiaxed grains form in the half-radius region of the cylindrical sample, and a severe macrosegregation channel forms at the centre of the sample. Crystal fragmentation is regarded as the main source of equiaxed grains, but their formation mechanism and the fragment transport phenomenon are not fully understood. A mixed columnar-equiaxed solidification model with extension to consider two dendrite fragmentation mechanisms (capillary-driven and flow-driven), was used to reproduce the experiment with the objective to investigate the formation process of the microstructure and macrosegregation. Under the effect of the RMF-induced primary/secondary flow, the capillary-driven fragmentation mechanism, which is associated with dendrite coarsening, operates mainly in the peripheral region of the sample at a certain depth of the mushy zone. These fragments are difficult to be transported out of the (columnar dendritic) mushy zone. The flow-driven fragmentation mechanism associated with the interdendritic flow-induced re-melting of dendrites, operates mostly near the front of the mushy zone and/or around the central segregation channel. Some of these fragments can be transported out of the columnar tip region. In this case, a thin undercooled layer exists. Therefore, fragments can grow and become equiaxed grains. Some fragments are transported distally from the mushy zone into the bulk superheated region and are re-melted/destroyed there. The fragments, which continue to grow in the deep mushy zone or in the thin undercooled layer, are easily trapped by columnar dendrites, thereby competing with the growth of columnar dendrites to form a mixed columnar-equiaxed structure or even leading to a columnar-to-equiaxed transition. [Display omitted] [ABSTRACT FROM AUTHOR]

Mold electromagnetic stirring (M-EMS) has been introduced into the continuous casting of steel billets to promote the formation of a central equiaxed zone; however, the formation mechanism of the equiaxed crystals and the effect of M-EMS on crystal transport are not fully understood. Currently, a three-phase volume average model was used to study the solidification in a billet continuous casting (195 mm × 195 mm). The modeling results showed that the main function of M-EMS in this type of billet casting is to promote superheat dissipation in the mold region, leaving the liquid core out of the mold region undercooled. Although both, heterogeneous nucleation and crystal fragmentation, are considered to be the origins of equiaxed crystals, M-EMS appeared to impact crystal fragmentation more effectively. A small portion of equiaxed crystals could be brought by the M-EMS induced swirling flow into the superheated zone (upper mold region) and remelted; most equiaxed crystals settled in the lower undercooled zone, where they continued to grow and form a central equiaxed zone. These simultaneous phenomena represent an important species/energy transport mechanism, influencing the as-cast structure and macrosegregation. Negative segregation occurred in the central equiaxed zone, positive segregation occurred at the border of the columnar zone, and a trail of negative segregation occurred in the subsurface region of the billet. Finally, parameter studies were performed, and it was found that the shielding effect of the copper mold, electrical isolation at the strand-mold interface, and relatively high electrical conductivity of the strand shell affect the M-EMS efficiency. [ABSTRACT FROM AUTHOR]

Segregation channels with misoriented spurious grains, known as freckles, are an unacceptable casting defect in superalloy turbine blades. A digital-twin method to predict segregation channels was proposed in our previous studies; however, the formation of spurious grains was ignored. Here, we extend the digital twin methodology by incorporating dendrite fragmentation, which is recognized as the predominant mechanism in the formation of spurious grains. The flow-induced fragmentation process has been refined to account for the timing of dendrite pinch-off. A three-phase mixed columnar-equiaxed solidification model was used to track the motion of the crystal fragments. Directional solidification experiments for superalloy casting were conducted in an industrial-scale Bridgman furnace, and the distribution of spurious grains in the freckles was metallographically analysed. Excellent simulation-experiment-agreement was achieved. Based on this study, the formation of spurious grains within the segregation channels is mainly caused by the flow-driven fragmentation mechanism. Experimentally measured freckles can be reproduced only if the timing of the dendrite pinch-off is considered., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2024.)