Project A1

1
Level set method for modeling solidification
processes
Cornell University
College of Engineering
Sibley school of Mechanical and Aerospace
Engineering
PI Prof. Nicholas Zabaras
Participating students L.Tan,
B.Ganapathysubramanian Materials Process
Design and Control Laboratory
Objective To accurately and efficiently compute
the micro-structure evolution in alloy
solidification given the processing parameters
for purpose of design and control.
Extended finite element method (X-FEM)
approximation
Level set method is a mathematical tool to
compute interface motion on a fixed grid.
Level set variable signed distance from
interface
Thermodynamic database
Phase diagram
The Standard FE Approximation
The X-FEM Approximation
Phase change
Governing equation
Solute redistribute
Heat transfer
Normal and curvature
Fluid flow
Dendritic solidification of Pb-2.2Sb alloy
Convection effects on microstructure evolution
Solidification of ternary alloy Ni-5.8Al-15.2Ta
Segregation of Ta
Planar/Cellular/Dendritic transition of Ni-0.4Cu
alloy
Planar growth at low or high solidification speed
Cellular growth inside the MS loop
Without convection
With convection
Multi-scale modeling
Flow passes between the growing arms of the
crystal. The colder fluid that flows between the
arms of the dendrites leads to the formation of
the small globules
Alloy solidification with multiple solid phases
Peritectic growth of Fe-0.3C
Stable/unstable Eutectic growth
Dendritic growth with high copper concentration
(1.6,4.1)
Selected Publications N. Zabaras, B.
Ganapathysubramanian and L. Tan, "Modeling
dendritic solidification with melt convection
using the extended finite element method (XFEM)
and level set methods", Journal of Computational
Physics, submitted for publication Lijian Tan and
N. Zabaras, "A level set simulation of dendritic
solidification with combined features of front
tracking and fixed domain methods", Journal of
Computational Physics, Vol. 211, pp. 36-63, 2006