A robust numerical framework for modeling non-isothermal phase changing multiphase flows

The enthalpy technique is a widely used method for modeling phase change in engineering processes, such as welding, casting, and metal additive manufacturing. These manufacturing applications are inherently multiphysics problems and involve widely varying thermo-physical properties (density, viscosity, thermal conductivity) among different phases. Nevertheless, most enthalpy formulations assume the constant density of the phase change material (PCM) and ignore its volume change effect. To model phase change problems with arbitrary large volume/density changes, we present a robust and efficient computational framework. In this framework, the level set method is combined with the enthalpy technique to simulate phase-changing solid-liquid-gas flows. A novel low Mach equation captures the volume change effect. We derive an analytical solution to the Stefan one-dimensional problem with volume change and convective effects. It's the first time this has been done. The analytical solution validates our computational model for PCMs that change density during melting/solidification. A metal casting problem exhibiting a pipe shrinkage defect is simulated to demonstrate the practical utility of our formulation.