Mixed Columnar-equiaxed Solidification Research Articles

Solidification Principle in Large Vertical Steel Casting Under the EMS Effect

The surging demand for large high-quality rotor shafts or similar steel components in heavy industries (energy sector) poses new challenges to steelmakers. Based on the experience of conventional ingot and continuous casting, several new process concepts have been proposed, e.g., vertical continuous casting (VCC), semi-continuous casting (SCC), and segment casting (SC), but none of them are optimally put in operation. The main problems include the control of the as-cast structure and macrosegregation. Electromagnetic stirring (EMS) is necessary to obtain the center equiaxed zone, but EMS-induced multiphase flow can cause severe macrosegregation and uneven distribution of the as-cast structure between equiaxed and columnar. In this study, an advanced mixed columnar-equiaxed solidification model was used to investigate the formation of the as-cast structure and macrosegregation in an example of SCC with a large format (diameter 1 m). The main role of EMS is to create crystal fragments by fragmentation, which is regarded in this work as the only origin of equiaxed grains. The created equiaxed grains are brought by the EMS-induced (primary and secondary) flow and gravity-induced sedimentation to the central/lower part of the casting. The main goal of this study was to understand the solidification principle of SCC. In addition, a numerical parameter study by varying the EMS parameters was also performed to demonstrate the model capability towards the process optimization of SCC.

Flow-enhanced remelting of settling/floating globular crystals during mixed columnar-equiaxed solidification

Previously, the authors have used a mixed columnar-equiaxed solidification model, successfully ‘reproduced’ the solidification benchmark experiments on the Sn-10wt.%Pb alloy under natural/forced convections (travelling magnetic stirring) as performed at SIMAP laboratory [Int. J. Heat Mass Transf. 85 (2015) 438-54]. The current contribution is to address the flow-effect on the remelting of settling/floating crystals during the mixed columnar-equiaxed solidification. The re-melting or growth is controlled by diffusion of solute in the liquid boundary layer. The diffusion length due to the flow-effect is modelled as a function of Schmidt and Reynolds numbers. The modelling results show that remelting rate of the floating/settling crystals, which originate from fragmentation and then brought to the superheated region by the forced flow, can be enhanced by the flow. In turn the released latent heat can reduce the temperature locally (even globally), hence to speed up the solidification of the columnar structure. Additionally, the solidification-migration-remelting of equiaxed grains present an important macrosegregation mechanism. By solidification of a crystal in the cold region it rejects solute, while by remelting of the crystal it dilutes the surrounding melt. These phenomena are found critical in many engineering castings with mixed columnar-equiaxed solidification.

Effect of forced convection on the formation of the as-cast structure and macrosegregation of Sn-10wt.% Pb alloy: A numerical study

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.

Dendrite fragmentation mechanism under forced convection condition by rotating magnetic field during unidirectional solidification of AlSi7 alloy

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.

Validation of a capillary-driven fragmentation model during mixed columnar-equiaxed solidification with melt convection and grain transport

A mixed columnar-equiaxed solidification model was recently extended to capture the capillary-driven fragmentation phenomenon, which was considered the only mechanism for the formation of equiaxed crystals. The purpose of the present study was to validate the model by replicating a laboratory experiment on the solidification of an aqueous ammonium chloride solution (Gao and Wang, 1999). The experiment was performed by cooling the solution in a vertical test cell from the top surface to allow columnar dendrites to grow. Owing to the fragmentation of the downward-growing columnar dendrites, equiaxed fragments appeared, sedimented, and created a bed of crystals at the bottom of the cell. This pile-up of crystals ultimately met the columnar-tip front coming from the top, thereby leading to a structural transition (columnar-to-equiaxed transition). This experiment was successfully reproduced numerically for the first time, which involved coupling between the following phenomena: fragmentation, melt convection, grain transport, a pile-up of equiaxed crystals, and the potential growth of columnar dendrites from a bed of equiaxed crystals (equiaxed-to-columnar transition). A satisfactory agreement was achieved between the simulation and experimental results. Knowledge about capillary-driven fragmentation was strengthened by analyzing the microstructural evolution. Alloy-dependent parameters Ss0, K0, and a that govern dendrite coarsening and fragmentation were proposed for an aqueous ammonium chloride solution. Finally, the limitations of the current version of the fragmentation model were discussed.

Validation of a Capillary-Driven Fragmentation Model During Mixed Columnar-Equiaxed Solidification with Melt Convection and Grain Transport

Validation of a Capillary-Driven Fragmentation Model During Mixed Columnar-Equiaxed Solidification with Melt Convection and Grain Transport

Validation of a Capillary-Driven Fragmentation Model During Mixed Columnar-Equiaxed Solidification with Melt Convection and Grain Transport

Validation of a Capillary-Driven Fragmentation Model During Mixed Columnar-Equiaxed Solidification with Melt Convection and Grain Transport

Bridging Capillary-Driven Fragmentation and Grain Transport with Mixed Columnar-Equiaxed Solidification

In this study, a first attempt is made to bridge capillary-driven fragmentation and grain transport using a mixed columnar-equiaxed solidification model. Grain transport is an intrinsic feature of the employed solidification model which has been extensively investigated over the years. Regarding the capillary-driven fragmentation event, a new correlation between the number of fragments and interfacial area density of the columnar structure was recently established by Cool and Voorhees (2017) based on experimental research under isothermal conditions. Here, we propose to modify Cool and Voorhees’ equation to extend its range of applicability to the solidification-dominant stage without destroying the agreement with the reported measurements in the coarsening-dominant stage. With this improvement in the mixed columnar-equiaxed solidification model, capillary effects can be isolated from the motion of the phases during fragmentation events, which facilitates understanding of the results. Under pure diffusive solidification conditions (no flow or crystal sedimentation), the simulation results were validated against phase-field simulations. In more realistic scenarios where liquid flow and fragment sedimentation are both considered, the simulations indicate very reasonable results for the detection of columnar-to-equiaxed transition, which suggests that the newly proposed model can be an important tool for industrial casting applications. Moreover, flow direction and intensity were shown to affect the potential for local fragmentation.Graphic

Physical and numerical simulation of mixed columnar-equiaxed solidification during cold strip feeding in continuous casting

Feeding a steel strip into a continuous casting (CC) mold is an effective method for improving the internal quality of CC slabs. An alloy experiment and three-phase mixed columnar-equiaxed solidification modeling were used to investigate the solidification structure evolution during the cold strip feeding process. The Euler method was adopted to treat the liquid phase, columnar grain phase, and equiaxed grain phase as continuous phases, and the mass, momentum, energy, and species transport equations of each phase, as well as the equiaxed grain density equation, were solved simultaneously. A comparison of the simulation and experimental results shows that the model can be used for calculating phase transitions, thermal-solute convection, grain deposition, macro-segregation, and the transformation of columnar grains into equiaxed grains in the solidification-melting system, which reveals the inherent relationship between the cold strip parameter and equiaxed grain percentage that is unquantifiable in the experiments. The results show that cold strip feeding improves the solidification structure quality by accelerating nucleation, strengthening convection, and promoting the columnar-equiaxed grain transition (CET). The subcooling nucleation rate around the cold strip first increases to a maximum and then decreases over time. A mathematical relationship between the equiaxed grain percentage and the initial temperature and size of the cold strip was established.

Modeling mixed columnar-equiaxed solidification of Sn-10wt%Pb alloy under forced convection driven by travelling magnetic stirring

A mixed columnar-equiaxed solidification model was used to investigate the solidification benchmark experiments, as performed at SIMAP Laboratory. The first experiment case of the benchmark made under natural convection condition was successfully simulated previously. The current work is to simulate the second experiment case, i.e. the casting under travelling magnetic stirring (TMS) which is applied in the direction of natural convection to enhance the natural convection. Crystal fragmentation of columnar dendrites is assumed as the sole origin of equiaxed crystals. Through the analysis of the simulation results, deep understanding to the experimentally reported phenomena was achieved. In comparison to the first experiment case of pure natural convection condition, the TMS-enhanced convection provides a favorable condition for columnar-to-equiaxed transition (CET) by homogenizing the temperature distribution in the bulk liquid region, enhancing the fragmentation of the columnar secondary arms and the transport of the fragments to bulk liquid region. Contradicting with the previous knowledge, the TMS-enhanced convection in this experiment case does not enhance the global macrosegregation significantly. However, it strengthens the channel segregates.

Numerical investigation of an in-situ observed flow regimes during solidification of an NH4Cl – 70 wt%H2O solution

A volume-average mixed columnar-equiaxed solidification model, where the dendritic morphology of crystals is described with the dendrite envelope, was developed by the current authors. As an evaluation effort, this model is used to simulate a solidification experiment of ammonium chloride water (NH4Cl – 70 wt%H2O) solution. The solution was cooled in a water cooled copper mould (10×8×1 cm3), and the solidification process and the flow dynamics during solidification were in-situ observed/recorded with a Particle Imagine Velocimetry technique. The striking features of solidification in this experiment are that the crystal morphology is dominant in columnar structure, and typical 4 flow regimes in the bulk solution during solidification appear: pure thermal convection (TH), unstable (turbulent) flow caused by double diffusive convection (TU), turbulent-stratified flow (TU-ST), meandering flow (MF). These flow regimes correspond to different cooling/solidification stages, and reflect their interactions with the developing mushy zone. The calculated solidification sequence and the flow dynamics (4 flow regimes) agree with the experimental ones. The experimentally observed phenomena were successfully explained by the simulation.

Influence of crystal fragmentation on the formation of microstructure and macrosegregation during directional solidification under forced convection condition

Directional solidification experiment under forced convection condition was conducted. The AlSi7 alloy was solidified in an alumina cylindrical crucible (ø8 mm) in a Bridgeman furnace; and forced convection was induced by applying rotating magnetic field (RMF). The RMF induced flow in the sample during solidification leads to the formation of equiaxed crystals by the mechanism of crystal fragmentation (assumption). The current study is to use a mixed columnar-equiaxed solidification model to simulate this experiment by considering the crystal fragmentation as sole origin of equiaxed crystals. An inward flow (Ekman effect) forms in the front of the (columnar) mushy zone under the RMF. Solute-driven remelting, as enhanced by the interdendritic flow, leads to fragmentation near the columnar tip front. Some fragments are transported by the forced convection to the sample centre and remelted there, while many of them are captured by the columnar structure near the sample centre. The modelling result on the mixed columnar-equiaxed structure agrees with the post-mortem analysis of as-solidified sample. As conclusion following impacts of the crystal fragmentation on solidification are suggested: (1) it widens the central segregation channel and promotes the formation of side-arms; (2) it leads to the formation of relatively high volume fraction of equiaxed crystals near the sample centre.

Volume-Averaged Modeling of Multiphase Flow Phenomena during Alloy Solidification

The most recent developments and applications in volume-averaged modeling of solidification processes have been reviewed. Since the last reviews of this topic by Beckermann and co-workers [Applied Mech. Rev. 1993, p. 1; Annual Rev. Heat Transfer 1995, p. 115], major progress in this area has included (i) the development of a mixed columnar-equiaxed solidification model; (ii) further consideration of moving crystals and crystal dendritic morphology; and (iii) the model applications to analyze the formation mechanisms of macrosegregation, as-cast structure, shrinkage cavity and porosity in different casting processes. The capacity of computer hardware is still a limiting factor. However, many calculation examples, as verified by the laboratory casting experiments, or even by the casting processes at a small industrial scale, show great application potential. Following the trend of developments in computer hardware (projection according to Moore’s law), a full 3D calculation of casting at the industry scale with the multiphase volume-averaged solidification models will become practically feasible in the foreseeable future.

Premature melt solidification during mold filling and its influence on the as-cast structure

Premature melt solidification is the solidification of a melt during mold filling. In this study, a numerical model is used to analyze the influence of the pouring process on the premature solidification. The numerical model considers three phases, namely, air, melt, and equiaxed crystals. The crystals are assumed to have originated from the heterogeneous nucleation in the undercooled melt resulting from the first contact of the melt with the cold mold during pouring. The transport of the crystals by the melt flow, in accordance with the socalled “big bang” theory, is considered. The crystals are assumed globular in morphology and capable of growing according to the local constitutional undercooling. These crystals can also be remelted by mixing with the superheated melt. As the modeling results, the evolutionary trends of the number density of the crystals and the volume fraction of the solid crystals in the melt during pouring are presented. The calculated number density of the crystals and the volume fraction of the solid crystals in the melt at the end of pouring are used as the initial conditions for the subsequent solidification simulation of the evolution of the as-cast structure. A five-phase volume-average model for mixed columnar-equiaxed solidification is used for the solidification simulation. An improved agreement between the simulation and experimental results is achieved by considering the effect of premature melt solidification during mold filling. Finally, the influences of pouring parameters, namely, pouring temperature, initial mold temperature, and pouring rate, on the premature melt solidification are discussed.

Use of a mixed columnar-equiaxed solidification model to analyse the formation of as-cast structure and macrosegregation in a Sn-10 wt% Pb benchmark experiment

A solidification benchmark experiment based on a Sn-10 wt% Pb alloy was performed at the SIMAP Laboratory in Grenoble, France, to investigate the formation of as-cast structure and macro- and mesosegregation (Wang et al., 2009; Hachani et al., 2015). The current study simulated this benchmark using a mixed columnar-equiaxed solidification model. This model was developed by the current authors (Wu et al., 2006), and recently extended to consider the crystal fragmentation of columnar dendrites as the source of equiaxed grains. A satisfactory experiment-simulation agreement in the temperature evolution, the as-cast structure, and the distribution of macro- and mesosegregation, was obtained. By analysis of the modelling results, new knowledge regarding the formation of the as-cast structure (mixed columnar-equiaxed) was obtained: The fragmentation-induced equiaxed crystals are transported away from the front region of the columnar zone by the melt flow; those crystals continue to grow or re-melt depending on the condition of local constitutional undercooling or supersaturation; the density of the melt varies with the Pb enrichment in the melt, and the equiaxed crystals can settle down or float up through the balance of the flow-induced drag force and the gravity-driven sedimentation; it is the motion of equiaxed crystals that determines the final distribution of the equiaxed zone in this benchmark experiment; the interdendritic flow and its interaction with the solidification in the front region of the columnar zone lead to the formation of segregation channels.

Incorporation of fragmentation into a volume average solidification model

In this study, a volume average solidification model was extended to consider fragmentation as a source of equiaxed crystals during mixed columnar-equiaxed solidification. The formulation suggested for fragmentation is based on two hypotheses: the solute-driven remelting is the dominant mechanism; and the transport of solute-enriched melt through an interdendritic flow in the columnar growth direction is favorable for solute-driven remelting and is the necessary condition for fragment transportation. Furthermore, a test case with Sn-10 wt%Pb melt solidifying vertically downward in a 2D domain (50 × 60 mm2) was calculated to demonstrate the model’s features. Solidification started from the top boundary, and a columnar structure developed initially with its tip growing downward. Furthermore, thermo-solutal convection led to fragmentation in the mushy zone near the columnar tip front. The fragments transported out of the columnar region continued to grow and sink, and finally settled down and piled up in the bottom domain. The growing columnar structure from the top and pile-up of equiaxed crystals from the bottom finally led to a mixed columnar-equiaxed structure, in turn leading to a columnar-to-equiaxed transition (CET). A special macrosegregation pattern was also predicted, in which negative segregation occurred in both columnar and equiaxed regions and a relatively strong positive segregation occurred in the middle domain near the CET line. A parameter study was performed to verify the model capability, and the uncertainty of the model assumption and parameter was discussed.

Role of fragmentation in as-cast structure: numerical study and experimental validation

A volume average solidification model is extended to incorporate fragmentation as the source of equiaxed crystals during mixed columnar-equiaxed solidification. This study is to use this model to analyze the role of fragmentation in the formation of as-cast structure. Test simulations are made for the solidification of a model alloy (Sn-10wt.%Pb) with two different geometries. The first one is a 2D rectangular domain (50 × 60 mm2) as cooled from the top boundary. Solidification starts unidirectionally as columnar structure from the top. The solute (Pb) enriched interdendritic melt is heavier than the bulk melt, and sinks downwards, hence leads to solutal convection. Fragmentation phenomenon occurs near the columnar tip front. The fragments are transported out of the columnar region, and they continue to grow and sink, and finally settle down and pile up at the bottom. The growing columnar structure from the top and pile-up of equiaxed crystals from the bottom finally lead to a mixed columnar-equiaxed structure, in turn leading to a columnar-to-equiaxed transition (CET). The second geometry is a 3D plate, 100 × 60 ×10 mm3, as cooled laterally from one side. It was cast experimentally and analyzed for the as-cast structure. The equiaxed fragments are produced in the solidification front and transported into the bulk melt, leading to a special pattern of as-cast structure: columnar structure in the cool wall side and equiaxed structure in the upper left corner near the hot wall side, extending downwards to the middle bottom region. Numerically calculated as-cast structures agree with the experiment results.

Numerical analysis of macrosegregation in vertically solidified Pb-Sn test castings – Part II: Equiaxed solidification

In order to get basic understandings of the macrosegregation mechanisms, 8 test cases of a 2D casting (50×60mm2) with unidirectional cooling from either top or bottom were simulated. Part I of this two-part study has presented 4 cases of pure columnar solidification. Part II will present the other 4 cases of equiaxed solidification. Two alloys were considered: Sn–10wt%Pb with solute element Pb heavier than the solvent Sn; Pb–18wt%Sn with solute element Sn lighter than the solvent Pb. The solidified equiaxed crystal is considered always heavier than the melt. With such simple configurations, it is believed that the macrosegregation tendency during equiaxed solidification can be estimated. However, the modeling results show that complicated macrosegregation patterns can develop due to the complexity of the event of equiaxed-to-columnar transition (ECT). Analysis of the segregation mechanisms for each case is made. The three-phase mixed columnar-equiaxed solidification model (Wu and Ludwig, MMTA, 2006, p. 1613) is modified and used for this study. One modification is to consider the heterogeneous nucleation of equiaxed crystals and transport of inoculants (embryos). The inoculants serve as heterogeneous nucleation sites for the equiaxed crystals, which can be transported as well. Another modification is to include the ECT. When all inoculants are consumed and the equiaxed crystals settle down in the bottom region, the remaining melt in the upper part can only solidify as columnar structure. Those columnar structures develop/grow from the packed equiaxed crystals by triggering the event of ECT.

Simulation of macrosegregation in a large vertical continuous casting of steel

A three-phase mixed columnar-equiaxed solidification model considering fluid flow, heat and solute transport is applied to simulate the solidification in a vertical continuous casting. The key features of solidification phenomena in this process, such as evolution of columnar phase, evolution and floatation/sedimentation of equi- axed crystals, thermal solutal convection of the melt and the flow caused by crystal sedimentation, development of as-cast structure, the columnar-to-equiaxed transition (CET), and formation of macrosegregation, are simulated. It is predicted that there is an equiaxed zone in the central part of the strand, and the rest section is filled with columnar phase (or dominant with columnar phase). A relatively strong negative segregation in the equiaxed zone and a mostly neutral concentration in the columnar region are found. Near the CET, there is a so-called middle radius positive segregation band. Formation mechanisms of this segregation pattern are discussed.

Using four-phase Eulerian volume averaging approach to model macrosegregation and shrinkage cavity

This work is to extend a previous 3-phase mixed columnar-equiaxed solidification model to treat the formation of shrinkage cavity by including an additional phase. In the previous model the mixed columnar and equiaxed solidification with consideration of multiphase transport phenomena (mass, momentum, species and enthalpy) is proposed to calculate the as- cast structure including columnar-to-equiaxed transition (CET) and formation of macrosegregation. In order to incorporate the formation of shrinkage cavity, an additional phase, i.e. gas phase or covering liquid slag phase, must be considered in addition to the previously introduced 3 phases (parent melt, solidifying columnar dendrite trunks and equiaxed grains). No mass and species transfer between the new and other 3 phases is necessary, but the treatment of the momentum and energy exchanges between them is crucially important for the formation of free surface and shrinkage cavity, which in turn influences the flow field and formation of segregation. A steel ingot is preliminarily calculated to exam the functionalities of the model.