Year of Publication


Document Type





Mechanical Engineering

First Advisor

James M. McDonough

Second Advisor

Kaveh A. Tagavi


Numerous efforts have contributed to the study of phase-change problems for over a century|both analytical and numerical. Among those numerical approximations applied to solve phase-transition problems, phase-field models attract more and more attention because they not only capture two important effects, surface tension and supercooling, but also enable explicitly labeling the solid and liquid phases and the position of the interface. In the research of this dissertation, a phase-field model has been employed to simulate 2-D dendrite growth of pure nickel without a flow, and 2-D ice crystal growth in a high-Reynolds-number lid-driven-cavity flow. In order to obtain the details of ice crystal structures as well as the flow field behavior during freezing for the latter simulation, it is necessary to solve the phase-field model without convection and the equations of motion on two different scales. To accomplish this, a heterogeneous multiscale method is implemented for the phase-field model with convection such that the phase-field model is simulated on a microscopic scale and the equations of motion are solved on a macroscopic scale. Simulations of 2-D dendrite growth of pure nickel provide the validation of the phase-field model and the study of dendrite growth under different conditions, e.g., degree of supercooling, interface thickness, kinetic coefficient, and shape of the initial seed. In addition, simulations of freezing in a lid-driven-cavity flow indicate that the flow field has great effect on the small-scale dendrite structure and the flow eld behavior on the large scale is altered by freezing inside it.