Abstract
In this paper, a new method is proposed to solve the solute field of moving grains, and a Cellular automaton (CA)-Lattice Boltzmann method (LBM)-Semi rebound format(Ladd) coupling model which can accurately simulate the motion behavior of multiple dendrites is established. The growth process of microstructure in the solidification process of Al-4.7% Cu alloy ingot was calculated by Cellular automaton (CA) method, the momentum, heat, and mass transfer processes were calculated by Lattice Boltzmann method (LBM), and the melt-dendrite sharp interface interaction was treated by Ladd method. The reliability of the model is verified, and then the growth and movement of single dendrite and multiple dendrites under the action of gravity field are simulated. The simulation results show that the growth and movement mode of multiple dendrites are quite different from that of single dendrite, which is shown in two aspects: (1) the original motion state of dendrites is changed by the combination of flow field, which slows down the falling speed of dendrites to a certain extent; (2) the fusion of solute field between dendrites changed the original growth mode of boundary dendrites and increased their rotation speed.
Highlights
During the solidification process of the alloy, the fine grains formed on the surface of the mold will fall off, and the solidified dendrite arms will be remelted and fractured, resulting in a large number of free equiaxed dendrites in the liquid phase area, which will move under the action of natural convection and gravity [1]
The movement and falling process of a large number of group grains has an important influence on the formation of positive segregation at the top of ingot, A-type and V-type segregation [2], and is the main reason for the formation of triangular cone-shaped negative segregation at the bottom of large ingot [3,4].it is of great significance to add the calculation of grain movement process into the numerical model of ingot macrosegregation to improve the prediction accuracy
The simulation results show that the multi dendrite growth pattern is significantly different from that of the single dendrite
Summary
During the solidification process of the alloy, the fine grains formed on the surface of the mold will fall off, and the solidified dendrite arms will be remelted and fractured, resulting in a large number of free equiaxed dendrites in the liquid phase area, which will move under the action of natural convection and gravity [1]. The phase field method is mostly used to simulate grain movement in the world. In 2008, Do-Quang M et al [5] used the phase field-virtual domain method to simulate the growth and movement of single dendrite under the action of gravity. Phase Field-Lattice Boltzmann method (LBM) coupling model to calculate the dendrite growth and Crystals 2020, 10, 70; doi:10.3390/cryst10020070 www.mdpi.com/journal/crystals. In 2015, Rojas and Takaki [8] used a PF-LBM model to simulate the growth and movement of dendrites under shear flow, and analyzed the effect of solution flow on the growth and movement of dendrites. This paper presents a method to deal with the solute field of multi grain movement, which realizes the calculation of solute field in the real sense of dendrite movement
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