Fixed-Grid Sharp-Interface Numerical Solutions to the Three-Phase Spherical Stefan Problem

Many metal manufacturing processes involve phase change phenomena, which include melting, boiling, and vaporization. These phenomena often occur concurrently. A prototypical 1D model for understanding the phase change phenomena is the Stefan problem. In our recent work, we provide analytical and numerical solutions to the three-phase Stefan problem with simultaneous occurrences of melting, solidification, boiling, and condensation in Cartesian coordinates. The problem was set in a semi-infinite domain with two moving interfaces—melt and boiling fronts. Our current work builds on our previous work to solve a more challenging problem: the three-phase Stefan problem in spherical coordinates for finite-sized particles. There are three moving interfaces in this system: the melt front, the boiling front, and the outer boundary which is in contact with the atmosphere. Although an analytical solution could not be found for this problem, we solved the governing equations using a fixed-grid sharp-interface method with second-order spatio-temporal accuracy. Using a small-time analytical solution, we predict a reasonably accurate estimate of temperature (in the three phases) and interface positions and velocities at the start of the simulation. Our numerical method is validated by reproducing the two-phase nanoparticle melting results of Font et al. Lastly, we solve the three-phase Stefan problems numerically to demonstrate the importance of kinetic energy terms during phase change of smaller (nano) particles. In contrast, these effects diminish for large particles (microns and larger).