GROWTH OF SOLUTAL DENDRITES - A QUANTITATIVE FRONT TRACKING MODEL

摘要

Capitalizing on previous efforts (Beltran-Sanchez/Stefanescu, BSS, and Zhu/Hong, ZH models) the authors have developed a computationally efficient quantitative model for the two-dimensional simulation of dendritic growth in the low Peclet number regime. The model relaxes the assumption of solute conservation at the moving solid/liquid (SL) interface used in most cellular automaton (CA) based diffusion controlled growth models. Instead, the evolution of the SL interface is driven by the difference between the local equilibrium composition and the local actual liquid composition. The local equilibrium composition is calculated from the local temperature and curvature, including the anisotropy of surface tension. The local actual liquid composition is determined by solving the solutal transport equation in the whole domain. Using this approach, the dynamics of dendrite growth from the initial unstable stage to the steady-state stage can be accurately described. Side branching developed without the need to introduce local noise. The model adopts the solutions previously proposed by BSS for the evaluation of curvature and interface capturing rules with a virtual interface tracking scheme, which make the model virtually mesh-independent. However, because in the proposed model dendrite growth is calculated directly from the change in the fraction of solid, without the need to first calculate growth velocity, the computational time is decreased dramatically.rnThe analysis of the proposed model included demonstration of mesh independence and comparison with calculations performed with the BSS model. Subsequently, extensive model validation was carried out. The simulated steady state tip velocity and radius as a function of initial solute composition of succinonitrile-acetone (SCN-Ace) alloys were very close to the predictions of the Lipton-Glicksman-Kurz (LGK) analytical model and to available experimental data. The simulated secondary dendrite arm spacing compared well with literature values for an Al-4.5wt% Cu alloy. Finally, the simulated solute concentration profile in the dendrites as a function of solid fraction in multi-grain equiaxed dendrite solidification for an Al-4.5wt% Cu alloy was compared with the prediction of the Scheil model. The simulated data with limited liquid diffusivity and zero solid diffusivity increasingly approached the Scheil profile as the cooling rate decreased. The extensive analytical and experimental validation of the proposed model demonstrates its quantitative capabilities for the predictions of both single free dendrite growth and multi dendrite solidification of alloys.