Numerical simulation for dendrite growth in directional solidification using LBM-CA (cellular automata) coupled method

Abstract

To predict the dendrite morphology and microstructure evolution in the solidification of molten metal, numerically, lattice Boltzmann method (LBM) - cellular automata (CA) model has been developed by integrating the LBM to solve the mass transport by diffusion and convection during solidification and the CA to determine the phase transformation with respect to the solid fraction based on the local equilibrium theory. It is successfully validated with analytic solutions such as Lipton-Glicksman-Kurz (LGK) model in static melt, and Oseen-Ivantsov solution under the fluid flow conditions in terms of tip radius and velocity of the dendrite growth. The proposed LBM-CA model does not only describe different types of dendrite formations with respect to various solidification conditions such as temperature gradient and growth rate, but also predict the primary dendrite arm spacing (PDAS) and the secondary dendrite arm spacing (SDAS), quantitatively, in directional solidification (DS) experiment with Ni-based superalloy. (C) 2020 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.