On the Origin of Grid Anisotropy in the Simulation of Dendrite Growth by a VFT Model
- PDF / 3,423,230 Bytes
- 14 Pages / 593.972 x 792 pts Page_size
- 80 Downloads / 240 Views
ODUCTION
IN the last two decades, numerical simulation has been significantly enhanced by the availability of techniques employing quantitatively precise computer processing, opening the way for a full analysis of microstructural changes during solidification of metal alloys. Several kinds of numerical methods and a large variety of concepts are investigated to characterize the dendrite growth especially in binary alloys. In such studies, attention is given to thermal and solute diffusion fields. In the simulations, analytical models, Lipton, Glickman and Kurz model (LGK model),[1] or Lipton, Kurz and Trivedi model (LKT model),[2] have been widely used for the validation of the numerical models. Among all known models, the most popular are those based on the Phase field (PF) method[3–7] and Cellular Automaton (CA) method: front tracking (FT) method.[8–14] These models allow significant advances in the fundamental understanding of how solute gradients affect the shape of a solid growth front, how growth velocity of a dendrite tip is related to the constitutional undercooling and of the detailed microstructure evolution. The widely recognized interest of the phase field method is the introduction of the phase variable that changes continuously from 0 to 1, over a certain
AFAF DJARAOUI, Postdoctoral Student, is with the De´partement de LMD ST, Faculte´ des sciences de l’inge´nieur, Universite´ de Batna, 05000 Batna, Algerie. Contact e-mail: [email protected] SAMIA NEBTI, Doctor and Supervisor, is with the De´partement de Physique, Faculte´ des Sciences Exactes, Universite´ Constantine 1, 25000 Constantine, Algerie. Manuscript submitted March 17, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS A
thickness, across the solid–liquid interface considering the diffuse nature of this region. This method has been rooted in continuum models of phase transformations, sometimes also called ‘‘diffuse interface models,’’ and much of the numerical simulations were originally focused on the dendritic solidification of pure melts. The first phase field model developed for alloys was the WBM model,[3] and others followed almost all recover Kobayashi’s model.[4] This method has emerged rapidly as a method of choice for simulating the liquid solid interface development during solidification in both pure metals and binary or ternary alloys.[15] The phase field method is reported to be the most appropriate for the capture of all physical phenomena associated with dendrite formation. The other emerging numerical approach is the CA method. It consists of a set of algorithms used to describe the evolution of discrete systems in time and space. Generally, the computational domain is divided into a uniform orthogonal arrangement of cells, square cells or cubic cells, respectively, in two or three-dimensional coordinates. Simulation by this method requires following the solid–liquid interface (front tracking), and a concept of a solidified fraction is introduced: it is equal to unity in the solid, zero in the liquid, and intermediate in the interface. Althou
Data Loading...
