Abstract
In order to match the growth of the decentered square and the evolution of the interface cell in a two-dimensional cellular automaton-finite volume method (CA-FVM) model with decentered square algorithm, the present work first alters the determination of the half length of the square diagonal according to the preferential growth orientation, and then modifies the interface evolution considering the contribution of neighboring solid cells. Accordingly, the sharp interface (physical basis of the model), the growth orientation, and the growth consistence are reasonably guaranteed. The CA-FVM model presents some capabilities in predicting the free growth of equiaxed dendrites. With the increase of the cooling rate, the solidification structure gradually changes from cell to dendrite, and the solute segregation becomes more severe. Meanwhile, the predicted solute segregation under the intensive cooling condition is consistent with the calculation by Ueshima model at the initial solidification stage. The predicted competition behavior of columnar dendrites is qualitatively consistent with the observation in the continuously cast steel billet. The predicted dendrite arm spacings are close to the measurements.
Highlights
The solidification structure of continuously cast steel strands typically consists of surface fine equiaxed dendrite, intermediate columnar dendrite, and interior equiaxed dendrite
Different from the use of additional governing equations to characterize the interface evolution in phase field (PF) and level set (LS) models, the cellular automaton (CA) approach depends on the designed neighboring configuration and capture rules [6]
Inspired by the successful application of decentered square algorithm (DCSA) in grain structure, Wang et al [19] connected the growth of the decentered square with the evolution of the CA cell according to the solid fraction to develop a CA-FDM model known as μMatIC, simulating the multi-oriented dendritic growth of Ni-based alloys in two-dimensional (2D) and three-dimensional (3D) spaces
Summary
The solidification structure of continuously cast steel strands typically consists of surface fine equiaxed dendrite, intermediate columnar dendrite, and interior equiaxed dendrite. Inspired by the successful application of DCSA in grain structure, Wang et al [19] connected the growth of the decentered square with the evolution of the CA cell according to the solid fraction to develop a CA-FDM (finite difference method) model known as μMatIC, simulating the multi-oriented dendritic growth of Ni-based alloys in two-dimensional (2D) and three-dimensional (3D) spaces. If squares grow too fast, for example, as the maximum half length of the diagonal is 2 times the mesh size [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33], they will capture multi-layers of interface cells around the solid dendrite, which goes against with the physical basis of the CA model—namely, the sharp interface—especially as the growth velocity is determined by the solute balance at the interface. The CA-FVM model is employed to predict the multi-oriented dendritic solidification of Fe–0.82C alloy
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