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.

Volume-Averaged Modeling of Multiphase Flow Phenomena during Alloy Solidification

The flow, temperature, solidification, and solute concentration field in a continuous casting bloom mold were solved simultaneously by a multiphysics numerical model by considering the effect of in-mold electromagnetic stirring (M-EMS). The mold metallurgical differences between cases with and without EMS are discussed first, and then the solute transport model verified. Moreover, the effects of EMS current intensity on the metallurgical behavior in the bloom mold were also investigated. The simulated solute distributions were basically consistent with the test results. The simulations showed that M-EMS can apparently homogenize the initial solidified shell, liquid steel temperature, and solute element in the EMS effective zone. Meanwhile, the impingement effect of jet flow and molten steel superheat can be reduced, and the degree of negative segregation in the solidified shell at the mold corner alleviated from 0.74 to 0.78. However, the level fluctuation and segregation degree in the shell around the center of the wide and narrow sides were aggravated from 4.5 mm to 6.2 mm and from 0.84 to 0.738, respectively. With the rise of current intensity the bloom surface temperature, level fluctuation, stirring intensity, uniformity of molten steel temperature, and solute distribution also increased, while the growth velocity of the solidifying shell in the EMS effective zone declined and the solute mass fraction at the center of the computational outlet (z = 1.5 m) decreased. M-EMS with a current intensity of 600 A is more suitable for big bloom castings.

https://www.mdpi.com/2075-4701/7/3/72/pdf

Effects of EMS Induced Flow on Solidification and Solute Transport in Bloom Mold

Numerical modelling of fluid flow and macrosegregation in a continuous casting slab with asymmetrical bulging and mechanical reduction

With a multiphase solidification model built, the effect of F-EMS parameters on center segregation was investigated in 160 mm × 160 mm billet continuous casting process. In the model, the initial growth of equiaxed grains which could move freely with liquid was treated as slurry, while the coherent equiaxed zone was regarded as porous media. The results show that the stirring velocity is not the main factor influencing center segregation improvement, which is more affected by current intensity and stirring pool width. Because solute transport is controlled by solidification rate as stirring pool width is 73 mm, center segregation declines continuously with current intensity increasing. As liquid pool width decreases to 61 mm and less latent heat needs to dissipate in the later solidification, the center segregation could be improved more obviously by F-EMS. Due to center liquid solute enrichment and liquid phase accumulation in the stirring zone, center segregation turns to rise reversely with higher current intensity and becomes more serious with stirring pool width further decreasing to 43 mm. As the stirring pool width is 25 mm, the positive segregation has already formed and solute could still concentrate with weak stirring, leading to center segregation deterioration. With the optimized current intensity (400 A) and stirring pool width (61 mm) set for continuous mode, center segregation improvement is better than that of alternative mode.

Center Segregation with Final Electromagnetic Stirring in Billet Continuous Casting Process

In order to predict the dendritic evolution during the continuous steel casting process, a simple mechanism to connect the heat transfer at the macroscopic scale and the dendritic growth at the microscopic scale was proposed in the present work. As the core of the across-scale simulation, a two-dimensional cell automaton (CA) model with a decentered square algorithm was developed and parallelized. Apart from nucleation undercooling and probability, a temperature gradient was introduced to deal with the columnar-to-equiaxed transition (CET) by considering its variation during continuous casting. Based on the thermal history, the dendritic evolution in a 4 mm × 40 mm region near the centerline of a SWRH82B steel billet was predicted. The influences of the secondary cooling intensity, superheat, and casting speed on the dendritic structure of the billet were investigated in detail. The results show that the predicted equiaxed dendritic solidification of Fe-5.3Si alloy and columnar dendritic solidification of Fe-0.45C alloy are consistent with in situ experimental results [Yasuda et al. Int J Cast Metals Res 22:15–21 (2009); Yasuda et al. ISIJ Int 51:402–408 (2011)]. Moreover, the predicted dendritic arm spacing and CET location agree well with the actual results in the billet. The primary dendrite arm spacing of columnar dendrites decreases with increasing secondary cooling intensity, or decreasing superheat and casting speed. Meanwhile, the CET is promoted as the secondary cooling intensity and superheat decrease. However, the CET is not influenced by the casting speed, owing to the adjusting of the flow rate of secondary spray water. Compared with the superheat and casting speed, the secondary cooling intensity can influence the cooling rate and temperature gradient in deeper locations, and accordingly exerts a more significant influence on the equiaxed dendritic structure.

Modeling of Dendritic Evolution of Continuously Cast Steel Billet with Cellular Automaton

Coupling macroscale heat transfer and fluid flow with microscale grain nucleation and crystal growth, a mixed columnar–equiaxed solidification model was established to study the SWRT82B steel solidification structure and macrosegregation in 160 mm × 160 mm billet continuous casting with dual electromagnetic stirrings in mold and final stage of solidification (M-EMS and F-EMS). In the model, the phases of liquid, columnar, and equiaxed were treated separately and the initial growing equiaxed phase, which could move freely with liquid, was regarded as slurry. To obtain the equiaxed grains nucleation and columnar front evolution, the unit tracking method and the columnar front tracking model were built. The model was validated by magnetic induction intensity of stirrer, billet surface temperature, and carbon segregation. The equiaxed phase evolution and the solute transport with effect of fluid flow and grains transport were described in this article. The results show that the equiaxed phase ratio will not increase obviously with higher current intensity of M-EMS, while the negative segregation near the strand surface becomes more serious. The negative segregation zone near the billet center and the center positive segregation come into being with the effect of equiaxed grains sedimentation and liquid thermosolutal flow. It is also found that the liquid solute transport in the F-EMS zone becomes the main factor with higher current intensity rather than the solidification rate, and therefore, the final billet center segregation decreases first and then turns to rise with the current intensity. The optimal current intensities of M-EMS and F-EMS proposed for SWRT82B billet continuous casting are 200 and 400 A, respectively.

Solidification Structure and Macrosegregation of Billet Continuous Casting Process with Dual Electromagnetic Stirrings in Mold and Final Stage of Solidification: A Numerical Study

Numerical simulation of slab centerline segregation with mechanical reduction during continuous casting process

Solidified shell bulging is supposed to be the main reason for slab center segregation, while the influence of thermal shrinkage rarely has been considered. In this article, a thermal shrinkage model coupled with the multiphase solidification model is developed to investigate the effect of the thermal shrinkage, solidification shrinkage, grain sedimentation, and thermal flow on solute transport in the continuous casting slab. In this model, the initial equiaxed grains contract freely with the temperature decrease, while the coherent equiaxed grains and columnar phase move directionally toward the slab surface. The results demonstrate that the center positive segregation accompanied by negative segregation in the periphery zone is mainly caused by thermal shrinkage. During the solidification process, liquid phase first transports toward the slab surface to compensate for thermal shrinkage, which is similar to the case considering solidification shrinkage, and then it moves opposite to the slab center near the solidification end. It is attributed to the sharp decrease of center temperature and the intensive contract of solid phase, which cause the enriched liquid to be squeezed out. With the effect of grain sedimentation and thermal flow, the negative segregation at the external arc side (zone A1) and the positive segregation near the columnar-to-equiaxed transition at the inner arc side (position B1) come into being. Besides, it is found that the grain sedimentation and thermal flow only influence solute transport before equiaxed grains impinge with each other, while the solidification and thermal shrinkage still affect solute redistribution in the later stage.

Mechanism of Macrosegregation Formation in Continuous Casting Slab: A Numerical Simulation Study

A numerical model of heat transfer was developed to investigate the heat transfer of continuously cast billet with the aid of surface temperature tests by ThermaCAM™ researcher and nail shooting experiments. The effects of secondary cooling practice and casting speed on the solidification process and central segregation of carbon were investigated as well with the actual central segregation tests. The results show that the surface center and billet center temperatures exhibit a different pattern during solidification, and the solidified shell thickness is presented as an “S” type. With the increase of secondary cooling intensity and the decrease of casting speed, the end points of the solidus line and the liquidus line move forward, and the central segregation level of carbon decreases. The optimal casting condition is suggested for continuously cast high carbon billet with F-EMS (final electromagnetic stirring).

Dongbin Jiang

Papers

Solidification Structure and Macrosegregation of Billet Continuous Casting Process with Dual Electromagnetic Stirrings in Mold and Final Stage of Solidification: A Numerical Study

Center Segregation with Final Electromagnetic Stirring in Billet Continuous Casting Process

Numerical simulation of slab centerline segregation with mechanical reduction during continuous casting process

Mechanism of Macrosegregation Formation in Continuous Casting Slab: A Numerical Simulation Study

Heat Transfer and Central Segregation of Continuously Cast High Carbon Steel Billet