An Enthalpy Model for Simulation of Dendritic Growth

Abstract

In this article we present an enthalpy-based simulation for the evolution of equiaxial dendrites, growing in an undercooled melt of a pure substance. The enthalpy formulation, which is used extensively for macroscale modeling of solidification, is modified appropriately by combining relevant macroscale and microscale features. An implicit finite-volume method is employed for the numerical solution of continuum equations (mass, momentum, and energy conservation equations). Microscale effects such as anisotropy, surface tension, and noise are incorporated through empirical rules, as implemented in existing cellular automaton models in the literature. In two dimensions, two problems are studied separately: The first is a diffusion-dominated case of dendrite growth, while the second consists of combined convection-diffusion effects. In order to illustrate the model capabilities, simulation results for dendritic growth under various conditions are presented. The results are compared with those employing other models found in the literature, and good qualitative agreement is observed.