Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth

TL;DR

This paper develops and tests new phase field models for dendritic crystal growth, focusing on the latent heat release distribution, and demonstrates their effectiveness through numerical simulations aligned with experimental data.

Contribution

It introduces simplified, robust variants of the reaction term in the Allen-Cahn equation for better modeling of dendritic growth under high supercooling.

Findings

Models show good agreement with experimental data

New variants are mathematically and numerically robust

Simulations are mesh-independent despite large interface thickness

Abstract

We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. The central object of interest is the reaction term in the Allen-Cahn equation, which is responsible for spatial distribution of latent heat release during solidification. In this context, several existing forms of the reaction term are analyzed. Inspired by the known conclusions of matched asymptotic analysis, we propose new variants that are simple enough to allow mathematical and numerical analysis and robust enough to be applicable to solidification under very large supercooling. The resulting models are tested in a number of numerical simulations focusing on mesh-dependence and model parameter settings. Despite the phase interface thickness being relatively large to make numerical computations feasible, the obtained results exhibit a good quantitative agreement with experimental data from rapid solidification of nickel melts.