Stability of two-dimensional low Prandtl number natural convection with phase change in a square enclosure

A numerical simulation of the two-dimensional low Prandtl number natural convection with phase change in a square enclosure is conducted. The problem is mathematically modeled by the continuity, momentum and energy conservation partial differential equations. The energy equation is used with the enthalpy as the dependent variable allowing an easy treatment of the phase change. A finite volume method is used to descretize the model equations and a sequential iterative time marching algorithm is used to solve the discretisation algebraic equations. A continuous increase of the Grashof number (Gr) leads to many bifurcations. The solution evolves from a steady equilibrium of the solid phase and a single rotating cell liquid phase to a steady equilibrium of the solid phase and a two rotating cells liquid phase. An oscillatory solution with a single dominating frequency is obtained for a critical Grashof number (Gr(c) = 9.375 x 10(6)). A further increase of the Gr leads to the appearance of subharmonic frequencies which are characteristics of a supercritical state.