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The deflection of columnar grains grown under melt flow is characteristic of the alloy solidification structure and strongly influences the performance of products. Here, a model of grain growth in melt flow was established with the cellular automaton (CA) method. After validation by comparison to an analytical model, the model was used to investigate the deflection of columnar grains in high-carbon steel. The deflection angle of columnar grains increases with the flow velocity and decreases with the melt undercooling. At the flow velocity of 0.10 m s–1 and the melt undercooling of 2°C, a maximum deflection angle of 18.2° is achieved. The deflection angles predicted by the model agree well with the empirical values. The melt flow was found to promote the grains with a preferred growth orientation towards the upstream direction over others. This flow-influenced selection mechanism is a key reason for the deflection of columnar grains. [ABSTRACT FROM AUTHOR] more...

Recalescence and segregation are two characteristic phenomena for the equiaxed dendritic solidification of alloys. The present work developed a two-dimensional dendritic model with cellular automaton (CA) method to investigate influence mechanisms of thermal conditions on recalescence and segregation behaviors of Fe-0.82wt pct C alloy. The released latent heat reduces the undercooling around the equiaxed dendrite, and thus eases its growth velocity. The predicted steady growth velocity agrees well with the analytical results as the melt undercooling is 9 K. Additionally, the present CA model can ensure the growth consistence of equiaxed dendrites in the undercooled melt. With improving the convective heat transfer coefficients applied around the domain boundaries, the temperature recalescence in the domain center becomes more significant, and the corresponding solid fractions enhance. It is because that the stronger cooling promotes the solidification, resulting in more latent heat released. Accordingly, the heat dissipation can be neutralized. Moreover, a deeper undercooling for the temperature recalescence is needed under a stronger cooling condition. With the increase of both the cooling rate and the convection coefficient, secondary arms of the equiaxed dendrite become more developed. At the lower cooling rate range, the segregation ratio in the domain enlarges with the improvement of the cooling rate. However, it gets weaker under the condition with super cooling intensity due to the expansion of the low concentration region. As the convection coefficient is enhanced, the solute segregation in the domain gets less pronounced. [ABSTRACT FROM AUTHOR] more...

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] more...

Embedded the thermal and solutal buoyancy into the momentum conservation equation as an additional force term using the Boussinesq approximation, a 2D CA-FVM model is extended to simulate the dendritic growth with thermosolutal convection. The model is firstly validated by comparison of numerical predictions with the benchmark test of Rayleigh – Bénard convection and the analytical solutions of the stagnant film model for the free dendritic growth with thermosolutal convection, and good agreements between the numerical results with analytical solutions are obtained. Later, numerical simulations for both the equiaxed and columnar dendritic growth of Fe-0.82wt%C binary alloy with thermosolutal convection are performed. The results show that, for the equiaxed dendritic growth in an undercooled melt, the dendrite tip growth rapidly decreases from the high velocity to a relative low steady-state value. With the further growth of dendrite, the thermosolutal convection induced by the solute rejection and latent heat release is enhanced and four vortexes are developed between the dendrite arms. Thus, the asymmetries of the dendrite morphology, temperature and solute profiles are intensified. For the columnar dendritic growth with thermosolutal convection under the unidirectional solidification process, the thermosolutal convection transports the rejected solute downward and makes the solute enrich at the interdendritic region. The thermosolutal convection facilitates the upstream dendritic growth, but inhibits the downstream dendritic growth. Moreover, with the increase of deflection angle of gravity, the advection on the top region and the clock-wise vortex flow at the interdendritic region intensified, and finally the columnar dendrite morphology becomes more asymmetrical. [ABSTRACT FROM AUTHOR] more...

A 3D parallel cellular automaton-finite volume method (CA-FVM) model was used to simulate the equiaxed dendritic growth of an Fe-0.82 wt pct C alloy with xy- in- out and xyz- in- out type forced flows and the columnar dendritic growth with y- in- out type forced flow. In addition, the similarities and differences between the results of the 3D and 2D models are discussed and summarized in detail. The capabilities of the 3D and 2D CA-FVM models to predict the dendritic growth of the alloy with forced flow are validated through comparison with the boundary layer correction and Oseen-Ivanstov models, respectively. Because the forced flow can pass around perpendicular arms of the dendrites, the secondary arms at the sides upstream from the perpendicular arms are more developed than those on the upstream side of the upstream arms, especially at higher inlet velocities. In addition, compared to the xy- in- out case, the growth of the downstream arms is less inhibited and the secondary arms are more developed in the xyz- in- out case because of the greater lateral flow around their tips. Compared to the 3D case, the 2D equiaxed dendrites are more asymmetrical and lack secondary arms because of the thicker solute envelope. In the 3D case, the columnar dendrites on the upstream side (left one) are promoted, while the middle and downstream dendrites are inhibited in sequence. However, the sequential inhibition starts on the upstream side in the 2D case. This is mainly because the melt can pass around the upstream branch in 3D space. However, it can only climb over the upstream tip in 2D space. Additionally, the secondary arms show upstream development, which is more significant with increasing inlet velocity. The level of development of the secondary arms is also affected by the decay of the forced flow in the flow direction. [ABSTRACT FROM AUTHOR] more...

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] more...

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] more...

Abstract: A two-dimensional cellular automaton model was developed for simulating the diffusion-controlled dendritic growth in the low Péclet regime. The growth velocity of the solid/liquid interface was determined by the local solute diffusion, and the modified decentered square growth was improved to capture the first eight neighboring cells of the interface cell. In order to quantitatively validate the developed model, the free dendritic growth from an undercooled melt was simulated and compared with the classic Lipton–Glicksman–Kurz (LGK) analytical model. The results show that the predicted steady state tip velocity is in a reasonable agreement with the analytical value, and the dendritic growth can be quantitatively determined by the present model. Meanwhile, the simulation of the dendritic growth with random crystallographic orientation shows that the effects of the mesh dependency of the model on the growth kinetics and crystallographic orientation can be reduced to an accepted level. Moreover, the single dendritic growth and the multi-dendritic growth from an undercooled melt and the competitive dendritic growth in a unidirectional solidification were simulated and the dendritic growth features, such as crystallographic orientation, dendrite arm growing and coarsening, side branching, and arms fusion were graphically revealed. [Copyright &y& Elsevier] more...

• The process and type of CET for Fe-C alloy are described at the microscopic scale. • The columnar and equiaxed mixed structure is found in the inner domain. • Sizes of the inner dendrites are quantitatively measured with CAD. • Influences of thermal conditions and initial carbon contents are investigated. The columnar to equiaxed transition (CET) is crucial to the solidification quality and the mechanical property of steels. With the cellular automaton approach, the present work developed a solidification model that consists of dendritic growth and heterogeneous nucleation to investigate the CET behaviors of Fe-C alloys at the microscopic scale, as well as the influencing mechanisms of thermal conditions (thermal gradient and cooling rate) and the initial carbon contents on the CET location, CET type and quantitative characteristics of the inner structure. The results show that the predicted CET map that illustrates whether the CET occurs or not at given thermal gradients and cooling rates for the Fe-0.82C alloy in weight percentage agrees with the analytical result calculated with the Hunt model. Two CET types are observed in the simulation. The columnar-tip type prefers conditions with low thermal gradients and high initial carbon contents, while it is the opposite for the interbranch type. The difference in conditions is an interaction effect of the distributions of the melt undercooling and the solute segregation. The CET is promoted by decreasing the thermal gradient and by increasing the cooling rate and the initial carbon content. Meanwhile, the inner dendritic structure gradually changes from the columnar-equiaxed mixed type to the equiaxed type. The CET location and the average and the mean square deviation of the inner dendritic diameter change sharply within the high thermal gradient, weak cooling rate and low initial carbon content range and become gentler with the decrease in the thermal gradient and the increase in the cooling rate and the initial carbon content. Therefore, the inner dendrites become finer and more uniform. Thermal conditions directly influence the undercooling distribution, whereas the initial carbon content works through the dendritic growth velocity and the solidification time. [ABSTRACT FROM AUTHOR] more...