A cellular automaton technique for modelling of a binary dendritic growth with convection

@article{citeulike:2599502, abstract = {A two-dimensional model for the simulation of a binary dendritic growth with convection has been developed in order to investigate the effects of convection on dendritic morphologies. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (s/l) interface. The dynamics of the interface controlled by temperature, solute diffusion and Gibbs-Thomson effects, is coupled with the continuum model for energy, solute and momentum transfer with liquid convection. The solid fraction is calculated by a governing equation, instead of some approximate methods such as lever rule method [A. Jacot, M. Rappaz, Acta Mater. 50 (2002) 1909-1926.] or interface velocity method [L. Nastac, Acta Mater. 47 (1999) 4253; L. Beltran-Sanchez, D.M. Stefanescu, Mat. and Mat. Trans. A 26 (2003) 367.]. For the dendritic growth without convection, mesh independency of simulation results is achieved. The simulated steady-state tip velocity are compared with the predicted values of LGK theory [Lipton, M.E. Glicksmanm, W. Kurz, Metall. Trans. 18(A) (1987) 341.] as a function of melt undercooling, which shows good agreement. The growth of dendrite arms in a forced convection has been investigated. It was found that the dendritic growth in the upstream direction was amplified, due to larger solute gradient in the liquid ahead of the s/l interface caused by melt convection. In the isothermal environment, the calculated results under very fine mesh are in good agreement with the Oseen-Ivanstov solution for the concentration-driven growth in a forced flow.}, author = {Li, Daming and Li, Ruo and Zhang, Pingwen }, citeulike-article-id = {2599502}, doi = {10.1016/j.apm.2006.04.004}, journal = {Applied Mathematical Modelling}, keywords = {ca, convection, dendritic\_growth}, month = {June}, number = {6}, pages = {971--982}, posted-at = {2008-03-26 18:55:52}, priority = {2}, title = {A cellular automaton technique for modelling of a binary dendritic growth with convection}, url = {http://dx.doi.org/10.1016/j.apm.2006.04.004}, volume = {31}, year = {2007} }

TY - JOUR ID - citeulike:2599502 L3 - citeulike-article-id:2599502 TI - A cellular automaton technique for modelling of a binary dendritic growth with convection JF - Applied Mathematical Modelling VL - 31 IS - 6 SP - 971 EP - 982 N2 - A two-dimensional model for the simulation of a binary dendritic growth with convection has been developed in order to investigate the effects of convection on dendritic morphologies. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (s/l) interface. The dynamics of the interface controlled by temperature, solute diffusion and Gibbs-Thomson effects, is coupled with the continuum model for energy, solute and momentum transfer with liquid convection. The solid fraction is calculated by a governing equation, instead of some approximate methods such as lever rule method [A. Jacot, M. Rappaz, Acta Mater. 50 (2002) 1909-1926.] or interface velocity method [L. Nastac, Acta Mater. 47 (1999) 4253; L. Beltran-Sanchez, D.M. Stefanescu, Mat. and Mat. Trans. A 26 (2003) 367.]. For the dendritic growth without convection, mesh independency of simulation results is achieved. The simulated steady-state tip velocity are compared with the predicted values of LGK theory [Lipton, M.E. Glicksmanm, W. Kurz, Metall. Trans. 18(A) (1987) 341.] as a function of melt undercooling, which shows good agreement. The growth of dendrite arms in a forced convection has been investigated. It was found that the dendritic growth in the upstream direction was amplified, due to larger solute gradient in the liquid ahead of the s/l interface caused by melt convection. In the isothermal environment, the calculated results under very fine mesh are in good agreement with the Oseen-Ivanstov solution for the concentration-driven growth in a forced flow. KW - ca KW - convection KW - dendritic_growth AU - Li, Daming AU - Li, Ruo AU - Zhang, Pingwen PY - 2007/06// UR - http://dx.doi.org/10.1016/j.apm.2006.04.004 ER -