Feasibility Study of Different Pseudopotential Multiphase Lattice Boltzmann Methods for Dendritic Solidification

The formation of porosity and bubbles during solidification in manufacturing processes like casting or welding of metals has a negative effect on the mechanical properties of the manufactured components. Numerical simulation of this problem is important since the direct observation of the interaction of bubbles with dendrites is limited by the opacity of metals. Therefore, developing a reliable numerical model is essential to predict the mechanical properties of materials after solidification. The pseudopotential multiphase model is a popular method for simulating multiphase flow using the lattice Boltzmann method. This model and its variations have been used to simulate a variety of problems successfully. However, the original pseudopotential model has some deficiencies, including large spurious current and restriction to model low density and viscosity ratios. Several schemes have been proposed to improve the pseudopotential multiphase model and overcome the limitations, including using a realistic equation of state, introducing a force with higher order of isotropy, introducing a middle-range repulsion force, and implementing the force similarly to the Exact Difference Method (EDM). The aim of this article is to investigate these various enhancements available for the pseudopotential multiphase model in order to come up with a reliable scheme to simulate motion and interaction of bubbles during dendritic solidification in binary alloys. The proposed model is validated against published literature.