Numerical simulation of solidification.

Abstract

Solidification is a common phenomenon in nature and in engineering. In particular, solidification is important in materials processing for obtaining desired material properties. During solidification, there exists a morphological instability at the solid-liquid interface. This creates wavy forms of unstable interface, leading to columnar growth or dendritic growth. The present study consists of four inter-dependent topics. (1) By asymptotic analysis of the non-dimensionalized growth rate equation in conjunction with realistic material properties and common solidification parameters, a simplified relationship for the critical wavelength is derived with less restrictive assumptions than existing theories. The relation between the wavelength at maximum growth rate and the critical wavelength is obtained. In addition, a dimensionless correlation of dendrite spacing versus solidification velocity is suggested and tested for several materials. (2) A front tracking method using a fully-implicit finite difference method for phase change has been developed and tested. The front tracking technique employs a discrete phase change front with a second order scheme for the flux jump conditions, although the present implementation included a first order interpolation, thus achieved less than full second order accuracy. Singular behavior of the finite-difference method near a discontinuity is avoided by deriving new, singularity-tolerant difference formulas. (3) Full numerical simulations of solidification for pure and alloy materials under near-critical and supercritical conditions have been performed. The low level of numerical diffusion in the present method was first demonstrated by the good agreement between the numerical simulation of marginal stability and theoretical predictions. In addition, successful simulation of dendritic solidification without the intentional injection of random noise provided evidence that the present method has less numerical diffusion than many existing front tracking methods. (4) Full Direct Numerical Simulation of the mushy zone has been undertaken to investigate how the macroscopic properties of the mushy zone depend on the primary microscopic structure. Mean temperature, solid fraction and solution composition are obtained for a number of conditions, and compared with known theories.