Desarrollo de un método numérico para predecir el crecimiento dendrítico y efecto de la convección durante la solidificación de metales.

Abstract

: In the present study, a numerical method is proposed to predict two-dimensional dendritic growth and the effect of convection in the solidification of metals and/or alloys. For this purpose, the phase field method (PFM) is used together with the lattice Boltzmann method (LBM). The phase field method is used to capture the phase transformation during the solidification of the metal, while the lattice Boltzmann method is used to resolve the effect of the flow of the liquid part of the melt, which in this case of study is a forced convection process. The no-slip boundary condition at the solid-liquid interface is imposed by adding a dissipative force in LBM formulation. This method is called phase field-lattice Boltzmann method (PF-LBM). Two-dimensional calculations of the solidification of an Al-Cu alloy are carried out to analyze the effect of the fluid flow of the liquid part of the melt on the dendritic growth. Compared to previous studies, the real physical viscosity of the alloy is used in this study to define the dimensionless values of the viscosity, time and space increments that allow obtaining stable computations. The simulations with different values of melt flow velocity and initial concentrations of the alloy successfully reproduce the patterns of dendritic growth during solidification. Additionally, the variation of the relaxation time in LBM is an effective way to optimize the numerical computations. To simulate the dendritic growth of an Al-Cu alloy, dimensionless values of viscosity, velocity and time are obtained to satisfy. The results obtained can be compared with other results.