Modeling motion and growth of multiple dendrites during solidification based on vector-valued phase field and two-phase flow models

Abstract

Movement and growth of dendrites are common phenomena during solidification. To numerically investigate these phenomena, two-phase flow model is employed to formulate the FSI (fluid-structure interaction) problem during dendritic solidification. In this model, solid is assumed to have huge viscosity to maintain its own shape and an exponential expression is constructed to describe variable viscosity across s-l (solid-liquid) interface. With an effective preconditioner for saddle point structure, we build a N-S (Navier-Stokes) solver robust to tremendous viscosity ratio (as large as 1010) between solid and liquid. Polycrystalline solidification is computed by vector-valued phase field model, which is computationally convenient to handle contact between dendrites. Locations of dendrites are updated by solving advection equations. Orientation change due to dendrite’s rotation has been considered as well. Calculation is accelerated by two-level time stepping scheme, adaptive mesh refinement, and parallel computation. Settlement and growth of a single dendrite and multiple dendrites in Al-Cu alloy were simulated, showing the availability of the provided model to handle anisotropic growth, motion and impingement of dendrites. This study lays foundation to simulate solidification coupled with deformation in the future.