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A numerical model is built for the solidification of a binary alloy with thermosolutal convection under centrifugal condition. The model is based on the macroscopic transport equations derived using the volume-averaging method. New formulations are derived for a non-linear phase diagram and temperature-dependent thermophysical properties. Simulations are performed to substantiate experiments with TiAl alloys carried out on ESA’s Large Diameter Centrifuge (LDC) using different angular velocities, ω. These experiments comprise a region of transient columnar growth of β-Ti dendrites under decreasing temperature gradient and increasing growth velocity followed by the columnar-to-equiaxed transition (CET). The simulation results show that CET is triggered by a sudden drop of the temperature gradient ahead of the advancing solidification front being a consequence of a sudden change of the flow pattern. We show that the flow pattern driven by density inversion changes abruptly once the permeability of the columnar structure increases above some critical value. This promotes the Rayleigh–Benard instability and the development of local convection cells along with an extended region of very low temperature gradient. The intensity and asymmetry of the flow in the local convection cells increase with increasing ω. The results show that a mushy zone developing in transient conditions and with gradually increasing permeability can significantly alter the flow pattern even in centrifugal conditions with a dominant contribution from Coriolis forces.

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.

Modeling the formation of macroscopic segregation channels during directional solidification processes has important applications in the casting industry. Computations that consider thermosolutal convection involve different length scales ranging from the small solute boundary layer at the dendrite tips to the characteristic size of the casting. In general, numerical models of solidification in the presence of a developing mushy zone are computationally inefficient because of nonlinear transport in an anisotropic porous medium. In the current work, mesh adaptation with triangular finite elements is used in conjunction with an efficient fractional-step solver of the momentum equations to predict the occurrence of channel-type segregation defects or freckles. The triangulations are created dynamically using an unstructured grid generator and a refinement criterion that tracks the position of the channel segregates. The efficiency of mesh adaptation is illustrated with simulations showing channel formation and macrosegregation in directional solidification of a Pb–Sn alloy.

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.

Experimental studies were performed to investigate the role and influence of grain movement on macrosegregation and microstructure evolution during equiaxed solidification. Casting experiments were performed with a grain-refined Al-Cu alloy in a rectangular sand mold. For the aluminum alloy studied, the equiaxed grains are lighter than the bulk melt and thus float up. Experiments were designed to investigate floatation phenomena of equiaxed grains in the presence of thermosolutal convection. Cooling curves were recorded at key locations in both the casting and the chill. Quantitative image analysis and spatial chemical analysis were performed on the solidified casting to observe the chemical and microstructural inhomogeneity created by the melt convection and solid floatation. Several notable features that can be attributed to grain movement were observed in temperature histories, macrosegregation patterns, and microstructures. In our experiments, the floatation of grains influences the thermal conditions and the overall flow direction in the casting cavity. In some cases, the induced flow resulting from the grain movement caused a flow reversal. This in turn influences the solidification direction, microstructure evolution, and the overall macrosegregation behavior.

A promising approach is proposed for controlling the channel formation during solidification, which is characterized as inserting alloy inserts into the cavity before pouring the melt. A mathematical model, which couples melting with solidification, is developed for simulating the channel formation during solidification of the Sn-10 wt pct Bi alloy in the cavity with alloy inserts. The validity of the model is tested by real-time X-ray observation and experimental measurement. With different superheats, the effects of insert parameters, such as the amount (0.0 pct and 1.2 pct), shape (rod and particle), and initial position, on the melting process of the insert itself, thermosolutal convection, and channel formation are investigated numerically. Calculated results reveal that at a higher superheat, the extent of channel segregation is reduced with the addition of alloy inserts. Because inserts dissolve quickly, only a slight difference in channel formation is noted when the shape and initial position of inserts are changed. At a lower superheat, no channel is formed by adding the alloy inserts. Results are better with the addition of alloy balls. The local positive segregations around the unmelted inserts, which occur when alloy rods are added, are avoided.

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.