A numerical study of solidification in the presence of a free surface under microgravity conditions

A numerical study of the relative importance of Marangoni effects under microgravity conditions is presented. The mathematical formulation adopted is based on the enthalpy porosity method. One of the advantages of the fixed grid method is that a unique set of equations and boundary conditions is used for the whole domain, including both solid and liquid phases. The governing equations written in a vorticity–velocity formulation are discretized using a finite volume technique on a staggered grid. A fully implicit method has been adopted for the mass and momentum equations, while the temperature field is solved separately in order to evaluate the variation in the local liquid mass fraction. The resulting algebraic system of equations is solved using a preconditioned BI-CGStab method. Numerical results modelling the free surface, including the effects on it of Marangoni convection, are presented. The influence of the presence of argon in the gap above the free surface is investigated. During the numerical simulations presented in this paper 161X41 and 641X161 uniform meshes on the whole computational domain for values of Marangoni number (Ma) up to 16,120 and Rayleigh number (Ra) of 5 have been used.