A cellular automaton-lattice Boltzmann method for modeling growth and settlement of the dendrites for Al-4.7%Cu solidification

A coupled model of CA-LBM for simulating the simultaneous growth and motion of equiaxed dendrites in solidifying melt is presented. The model uses the CA method for the growth of the dendrite, the LBM for the momentum, mass, and heat transfer of the domain, the Ladd method for handling the rigid solid-liquid interfaces and the equations of motion for tracking the translational and rotational motion of the solid phase. The simulation of a circular particle between two infinite and parallel walls proved the accuracy of boundary treatment. Two-dimensional computations of dendritic translation and rotation show that the shape preservation conditions are satisfied in this method. Then, the present method is used to calculate the growth behavior of a binary alloy dendrite in the process of its dropping motion in the melt. Initially, the dendrite is standard and only translation happened, but later the dendrite is inclined and simultaneous translational and rotational motion happened. The simulation result shows that during its falling process the dendrite settles and grows in a specific morphology, which differs from that of a dendrite dropping vertically without rotation.