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For decades, the fixed-grid method (FGM) has undergone extensive development and widespread application in addressing phase change problems. Nonetheless, comparative studies on various FGMs in convective regime are considerably scarce. Moreover, it has been proven that two-dimensional (2D) numerical simulations can cause large deviations from experimental observations. Therefore, this study, based on a reference experiment involving gallium melting, seeks to comprehensively and quantitatively compare three prevalent FGMs: enthalpy method (EM), total enthalpy method (TEM), and heat source method (HSM). The TEM validates overestimation of temperature at low Péclet numbers, as the heat dissipation induced by non-uniform thermal properties in solid and liquid phases is not accounted for. To address this issue, a revised TEM has been introduced. The three FGMs were implemented within the OpenFOAM software, with over 150 simulations conducted on 3D meshes. The comparison focused on evaluating the numerical robustness, accuracy and stability of these FGMs, along with exploring their similarities and differences in flow patterns and velocities. Results obtained reveal that EM offers accuracy but lacks robustness, TEM manifests relatively large errors and instability due to oscillation with variations in grid size and time step, while HSM excels in robustness, accuracy, and stability. Under an identical discretization scheme, all FGMs predict similar melt front shapes, vortex structures, and velocity magnitudes. However, with the upwind scheme, the velocity magnitude of the secondary flow is approximately 50 pct of that with high-order schemes, yet it tends to overestimate the melting rate. The reason lies in the limited capacity of the slow secondary flow to effectively disrupt the stable and persistent vortex in the primary flow direction, consequently enhancing heat transfer efficiency in this direction. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Considering the influence of the latent heat released during the solidification of high carbon liquid steel, a cellular automaton (CA) model coupled with the heat transfer was developed to investigate the growth of equiaxed dendrites which is controlled by the solute diffusion during the continuous casting process. Additionally, the growth of columnar dendrites and primary dendrite arm spacings were predicted and measured. The results show that the CA model is able to describe the growth behavior of equiaxed dendrites, especially at 5 K to 7 K melt undercoolings, and the approach adjusting the cooling medium temperature is reliable to keep the undercooling condition stable for equiaxed dendrites although its hysteresis is reinforced as the pre-set undercooling increases. With the increase of the melt undercooling, the growth of equiaxed dendrites becomes faster, and the thickness of dendritic arms increases slightly, however, the thickness of the diffusion layer in front of dendritic tips keeps constant. The growth of thin and tiny columnar dendrites will be confined due to the competition and absorbed by neighboring strong columnar dendrites, giving rise to the coarsening of columnar dendrites, which is observed both from the experimental observation and the numerical simulation. With the decrease of the cooling intensity, columnar dendrites get sparser, primary dendrite arm spacings increase, and secondary dendritic arms become undeveloped. [ABSTRACT FROM AUTHOR]

A cellular automaton (CA) model coupled with momentum, mass and heat transport models was developed to investigate equiaxed and columnar dendritic growth of Fe–0.82 wt%C alloy under four elaborately designed forced flows. During the iterative solution, the evolution of solidification interface and the solute diffusion in solid phase were explicitly tracked and solved, while other transport equations were implicitly solved in staggered grids with the block-corrected TDMA approach. The self-developed codes show a good performance in predicting dendritic growth and melt flow and temperature fields according to the comparisons with LGK analytical model and commercial software. The growth behavior of dendrites under melt flow is determined by the competition between bringing in solute enriched melt from upstream side and carrying away solute rejected at interfaces. The growth of equiaxed dendrites is promoted at the upstream side and inhibited at the downstream side, which becomes more significant with the increase of inlet velocity and the decrease of melt undercooling. Meanwhile, the oblique flow plays an important role in the growth of arms at the downstream side and alleviates the inhibited growth at the lower melt undercooling. Columnar dendrites are under inhibited growth in sequence along the flow direction, except that those near the outlet are promoted under weaker melt flow. Secondary dendrite arms firstly well formed at left sides of columnar dendrites become fatter and better developed compared with those without flow, although those near the upstream side are difficult to be developed. Under the circular flow condition, columnar dendrites at the bottom wall of the modeling domain firstly grow faster than those symmetrically in the right wall, and then become slower as the solidification proceeds under stronger melt flow. Moreover, the effect of melt flow on dendritic growth becomes more significant under the lower melt undercooling condition for equiaxed dendrites and the weaker cooling condition for columnar dendrites. In addition, compared with the effect on the temperature distribution, the effect of the melt flow on the solute distribution around columnar dendrites governs their growth. [ABSTRACT FROM AUTHOR]

Based on the assumption that the transverse cross-section of dendrites is a regular hexagon, a coupled macro-heat transfer and solute diffusion model was developed to describe micro-segregation behavior of solute elements in the mushy zone during wide-thick slab continuous casting. The heat transfer model and the micro-segregation model were validated by the industrial tests and the experiment measurements in literatures, respectively. The results show that the cooling rate decreases from 51.1°C s−1 at the surface to 0.13°C s−1 at the center of the wide-thick slab of peritectic steel continuous casting. The effective cooling rate equaling to 1.78°C s−1 mainly depends on mold cooling and varies little with casting speed. The micro-segregation behavior of solute elements in the mushy zone depends on back diffusion ability and local equilibrium at interfaces. Compared with other elements in the steel, phosphorus, and sulfur elements exhibit a much higher segregation ratio at the end of the solidification and are more significantly affected by the initial carbon content. [ABSTRACT FROM AUTHOR]

Electromagnetic stirring in mold (M-EMS) has been widely used in continuous casting process to improve the solidification quality of the steel strand. In the present study, a 3D multi-physical-field mathematical model was developed to predict the macro transport phenomena in continuous casting mold with M-EMS using ANSYS commercial software, and was adopted to investigate the effect of current intensity (0, 150, 200, and 240 A) on the heat, momentum, and species transports in the billet continuous casting mold with a size of 160 mm × 160 mm. The results show that when the M-EMS is on, the horizontal swirling flow appears and shifts the high-temperature zone upward. With the increase of current intensity, two swirling flows form on the longitudinal section of continuous casting mold and become more intensive, and the flow velocity of the molten steel at the solidification front increases. Thus, the wash effects of the fluid flow on the initial solidified shell become intensive, resulting in a thinner shell thickness at the mold exit and a significant negative segregation of carbon at the billet subsurface. [ABSTRACT FROM AUTHOR]