Front tracking in the numerical simulation of binary alloy solidification

James Edward Simpson, Purdue University

Abstract

A model for directional solidification in dilute binary alloys is presented. The energy equation is solved for the temperature field, while the species equation is solved for the solute distribution. Either the vorticity-vector potential formulation or the pressure-velocity formulation is used to solve the governing equations for the velocity field. The constitutive equations are solved using a fully transient scheme. A variety of fast numerical schemes for solving sparse systems are used in the solution procedure. A single domain approach is used for the solution scheme for the energy and concentration equations. The effects of phase-change (energy equation) and solute rejection at the advancing solid/liquid interface (concentration equation) are handled via the introduction of appropriate source terms. The numerical approach was validated by comparing numerical results to data from a series of experiments of the Bridgman growth of pure succinonitrile. These experiments were performed as part of this work and are explained in detail. The numerical results agree well with the experimental data in terms of interface shape, temperature and velocity data. The key contribution of this work is the investigation of the Bridgman crystal growth of bismuth-tin in support of NASA's MEPHISTO project. The simulations reported in this work are among the first fully transient simulations of the process; no simplifying steady state approximations were used. Results are obtained for Bi-Sn alloys at a variety of initial concentrations and gravity levels. For most of the work, the solid/liquid interface temperature is assumed to be constant. For the richer alloy (Bi-1.0 at.% Sn) the results indicate that a secondary convective cell, driven by solutal gradients, forms near the interface. The magnitude of the velocities in this cell increases with time, causing increasing solute segregation at the solid/liquid interface. At lower gravity levels, convection-induced segregation is minimal and the process is diffusion-dominated. With increasing residual gravity the process departs from the conditions associated with diffusion, and convective action becomes the dominating effect even at a gravity level of only 50 μg. The trend predicted by the numerical results for solid solute concentrations agrees with that from Space flight data.

Degree

Ph.D.

Advisors

Garimella, Purdue University.

Subject Area

Mechanical engineering|Materials science

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