A numerical study of the turbulent flow of molten steel in a domain with a phase-change boundary

A numerical algorithm, based on the Galerkin finite element method and the enthalpy formulation, is developed for solving the coupled turbulent fluid flow and heat transfer problem in a domain with a moving phase-change boundary. The governing equations consist of the continuity equation, the Navier–Stokes equations, the energy equation and the modified K–ε equations. The formulation of the method is cast into the framework of the Bubnov–Galerkin finite element method. A numerical study shows that the developed numerical algorithm is stable and capable of capturing the rapid change of temperature and velocity near the phase-change boundary.